Paula Beceiro (corresponding author) Maria do Céu Almeida Hydraulic and Environment Department (DHA), National Laboratory for Civil Engineering, Avenida do Brasil 101, 1700-066 Lisbon, Portugal E-mail: pbeceiro@lnec.pt Jorge Matos Department of Civil Engineering, Arquitecture and Geosources, Technical University of Lisbon (IST), Avenida Rovisco Pais 1, 1049-001 Lisbon, Portugal
ABSTRACT
물 흐름에 용존 산소(DO)의 존재는 해로운 영향의 발생을 방지하는 데 유익한 것으로 인식되는 호기성 조건을 보장하는 중요한 요소입니다.
하수도 시스템에서 흐르는 폐수에 DO를 통합하는 것은 공기-액체 경계면 또는 방울이나 접합부와 같은 특이점의 존재로 인해 혼입된 공기를 통한 연속 재방출의 영향을 정량화하기 위해 광범위하게 조사된 프로세스입니다. 공기 혼입 및 후속 환기를 향상시키기 위한 하수구 드롭의 위치는 하수구의 호기성 조건을 촉진하는 효과적인 방법입니다.
본 논문에서는 수직 낙하, 배경 및 계단식 낙하를 CFD(전산유체역학) 코드 FLOW-3D®를 사용하여 모델링하여 이러한 유형의 구조물의 존재로 인해 발생하는 난류로 인한 공기-물 흐름을 평가했습니다. 이용 가능한 실험적 연구에 기초한 수력학적 변수의 평가와 공기 혼입의 분석이 수행되었습니다.
이러한 구조물에 대한 CFD 모델의 결과는 Soares(2003), Afonso(2004) 및 Azevedo(2006)가 개발한 해당 물리적 모델에서 얻은 방류, 압력 헤드 및 수심의 측정을 사용하여 검증되었습니다.
유압 거동에 대해 매우 잘 맞았습니다. 수치 모델을 검증한 후 공기 연행 분석을 수행했습니다.
The presence of dissolved oxygen (DO) in water flows is an important factor to ensure the aerobic conditions recognised as beneficial to prevent the occurrence of detrimental effects. The incorporation of DO in wastewater flowing in sewer systems is a process widely investigated in order to quantify the effect of continuous reaeration through the air-liquid interface or air entrained due the presence of singularities such as drops or junctions. The location of sewer drops to enhance air entrainment and subsequently reaeration is an effective practice to promote aerobic conditions in sewers. In the present paper, vertical drops, backdrops and stepped drop was modelled using the computational fluid dynamics (CFD) code FLOW-3D® to evaluate the air-water flows due to the turbulence induced by the presence of this type of structures. The assessment of the hydraulic variables and an analysis of the air entrainment based in the available experimental studies were carried out. The results of the CFD models for these structures were validated using measurements of discharge, pressure head and water depth obtained in the corresponding physical models developed by Soares (2003), Afonso (2004) and Azevedo (2006). A very good fit was obtained for the hydraulic behaviour. After validation of numerical models, analysis of the air entrainment was carried out.
Key words | air entrainment, computational fluid dynamics (CFD), sewer drops
Figure 1.| Physical models of the vertical drop, backdrop and stepped drop developed in the Technical University of Lisbon.Figure 3. Comparison between the experimental and numerical pressure head along of the invert of the outlet pipe.Figure 4. Average void fraction along the longitudinal axis of the outlet pipe for the lower discharges in the vertical drop and backdrop.
REFERENCES
Afonso, J. Dissipação de energia e rearejamento em quedas em colectores. M.Sc. Thesis, UTL/IST, Lisboa, Portugal. Almeida, M. C., Butler, D. & Matos, J. S. Reaeration by sewer drops. In: 8th Int. Conf. on Urban Storm Drainage, Sydney, Australia. Azevedo, R. I. Transferência de oxigénio em quedas guiadas em colectores. M.Sc. Thesis, IST, Lisboa, Portugal. Beceiro, P., Almeida, M. C. & Matos, J. Numerical Modelling of air-water flows in a vertical drop and a backdrop. In: 3rd IAHR Europe Congress, Porto, Portugal. Bombardelli, F. A., Meireles, I. & Matos, J. S. Laboratory measurements and multi-block numerical simulations of the mean flow and turbulence in the non-aerated skimming flow region of step stepped spillways. Environ. Fluid Mech. 11 (3), 263–288. Brethour, J. M. & Hirt, C. W. Drift Model for TwoComponent Flows. Flow Science, Inc., Los Alamos, NM, USA. Chamani, M. R. Jet Flow on Stepped Spillways and Drops. M.Sc. Thesis, University of Alberta, Alberta, Canada. Chanson, H. Air Bubble Entrainment in Free-Surface Turbulent Shear Flow. Academic Press Inc., California, USA. Chanson, H. Air bubble entrainment in open channels: flow structure and bubble size distribution. Int. J. Multiphase 23 (1), 193–203. Chanson, H. Hydraulics of aerated flows: qui pro quo? Journal of Hydraulic Research 51 (3), 223–243. Dufresne, M., Vazques, J., Terfous, A., Ghenaim, A. & Poulet, J. Experimental investigation and CFD modelling of flow, sedimentation, and solids separation in a combined sewer detention tank. Computer and Fluids 38, 1042–1049. Durve, A. P. & Patwardhan, A. W. Numerical and experimental investigation of onset of gas entrainment phenomenon. Chemical Engineering Science 73, 140–150. Felder, S. & Chanson, H. Air–water flows and free-surface profiles on a non-uniform stepped chute. Journal of Hydraulic Research 52 (2), 253–263. Flow Science FLOW-3D User’s Manuals Version 10.0. Vol.1/2. Flow Science Inc., Los Alamos, NM, USA. Granata, F., Marinis, G., Gargano, R. & Hager, W. H. Energy loss in circular drop manholes. In: 33rd IAHR Congress: Water Engineering for Sustainable Environment, British Columbia, Vancouver, Canada. Hirt, C. W. Modeling Turbulent Entrainment of air at A Free Surface. Flow Science Inc., Los Alamos, NM, USA. Hirt, C. W. & Nichols, B. D. Volume of fluid (VOF) method for the dynamics of free boundaries. Journal of Computational Physics 39, 201–225. Hirt, C. W. & Sicilian, J. M. A porosity technique for the definition of obstacles in rectangular cell meshes. In: Proc. 4th Int, Conf. Ship Hydro., National Academy of Science, Washington, DC, USA. Isfahani, A. H. G. & Brethour, J. On the Implementation of Two-Equation Turbulence Models in FLOW-3D. Flow Science Inc., Los Alamos, NM, USA. Kouyi, G. L., Bret, P., Didier, J. M., Chocat, B. & Billat, C. The use of CFD modelling to optimise measurement of overflow rates in a downstream-controlled dual-overflow structure. Water Science and Technology 64 (2), 521–527. Lopes, P., Leandro, J., Carvalho, R. F., Páscoa, P. & Martins, R. Numerical and experimental investigation of a gully under surcharge conditions. Urban Water Journal 12 (6), 468–476. Martins, R., Leandro, J. & Carvalho, R. F. Characterization of the hydraulic performance of a gully under drainage conditions. Water Science and Technology 69 (12), 2423–2430. Matias, N., Nielsel, A. H., Vollertsen, J., Ferreira, F. & Matos, J. S. Reaeration and hydrogen sulfide release at drop structures. In: 8th International Conference on Sewer Processes and Networks (SPN8), Rotterdam, Netherlands. Matos, J. S. & Sousa, E. R. Prediction of dissolved oxygen concentration along sanitary sewers. Water Science and Technology 34 (5–6), 525–532. Mignot, E., Bonakdari, H., Knothe, P., Lipeme Kouyi, G., Bessette, A., Rivière, N. & Bertrand-Krajewski, J. L. Experiments and 3D simulations of flow structures in junctions and of their influence on location of flowmeters. In: 12th International Conference on Urban Drainage, Porto Alegre, Brazil. Ozmen-Cagatay, H. & Kocaman, S. Dam-break flow in the presence of obstacle: experiment and CFD Simulation. Engineering Applications of Computational Fluid Mechanics 5 (4), 541–552. Shojaee Fard, M. H. & Boyaghchi, F. A. Studies of the influence of various blade outlet angles in a centrifugal pump when handling viscous fluids. American Journal of Applied Sciences 4 (9), 718–724. Soares, A. Rearejamento em Quedas em Colectores de Águas Residuais. M.Sc. Thesis, FCTUC, Coimbra, Portugal. Sousa, C. M. & Lopes, R. R. Hidráulica e rearejamento em quedas verticais em colectores. Estudo Experimental. Research Report, UTL/IST, Lisboa, Portugal. Sousa, V., Meireles, I., Matos, J. & Almeida, M. C. Numerical modelling of air-water flow in a vertical drop manhole. In: 7th International Conference on Sewer Processes and Networks (SPN7), Shefield, UK. Stovin, V., Guymer, I. & Lau, S. D. Approaches to validating a 3D CFD manhole model. In: 11th International Conference on Urban Drainage, Edinburgh, Scotland, UK. Tota, P. V. Turbulent Flow Over A Backward-Facing Step Using the RNG Model. Flow Science Inc., Los Alamos, NM, USA. Valero, D. & García-Bartual, R. Calibration of an air entrainment model for CFD spillway applications. In: Advances in Hydroinformatics. Springer, Singapore, pp. 571–582. Versteeg, H. K. & Malalasekera, W. An Introduction to Computational Fluid Dynamics. The Finite Volume Method. Longman Group limited, England. Yang, Y., Yang, J., Zuo, J., Li, Y., He, S., Yang, X. & Zhang, K. Study on two operating conditions of a full-scale oxidation ditch for optimization of energy consumption and effluent quality by using CFD model. Water Research 45 (11), 3439–3452. Zhai, A. J., Zhang, Z., Zhang, W. & Chen, Q. Y. Evaluation of various turbulence models in predicting airflow and turbulence in enclosed environments by CFD: part 1— summary of prevalent Turbulence models. HVAC&R Research 13 (6), 853–870. Zhao, C., Zhu, D. Z. & Rajaratnam, N. Computational and experimental study of surcharged flow at a 90W combining sewer junction. Journal of Hydraulic Engineering 134 (6), 688–700.
The elimination of internal macro-defects is a key issue in Ti–6Al–4V alloys fabricated via powder bed fusion using electron beams (PBF-EB), wherein internal macro-defects mainly originate from the virgin powder and inappropriate printing parameters. This study compares different types powders by combining support vector machine techniques to determine the most suitable powder for PBF-EB and to predict the processing window for the printing parameters without internal macro-defects. The results show that powders fabricated via plasma rotating electrode process have the best sphericity, flowability, and minimal porosity and are most suitable for printing. Surface roughness criterion was also applied to determine the quality of the even surfaces, and support vector machine was used to construct processing maps capable of predicting a wide range of four-dimensional printing parameters to obtain macro-defect-free samples, offering the possibility of subsequent development of Ti–6Al–4V alloys with excellent properties. The macro-defect-free samples exhibited good elongation, with the best overall mechanical properties being the ultimate tensile strength and elongation of 934.7 MPa and 24.3%, respectively. The elongation of the three macro-defect-free samples was much higher than that previously reported for additively manufactured Ti–6Al–4V alloys. The high elongation of the samples in this work is mainly attributed to the elimination of internal macro-defects.
Introduction
Additive manufacturing (AM) technologies can rapidly manufacture complex or custom parts, reducing process steps and saving manufacturing time [[1], [2], [3], [4]], and are widely used in the aerospace, automotive, and other precision industries [5,6]. Powder bed fusion using an electron beam (PBF-EB) is an additive manufacturing method that uses a high-energy electron beam to melt metal powders layer by layer to produce parts. In contrast to selective laser melting, PBF-EB involves the preparation of samples in a high vacuum environment, which effectively prevents the introduction of impurities such as O and N. It also involves a preheating process for the print substrate and powder, which reduces residual thermal stress on the sample and subsequent heat treatment processes [[2], [3], [4],7]. Due to these features and advantages, PBF-EB technology is a very important AM technology with great potential in metallic materials. Moreover, PBF-EB is the ideal AM technology for the manufacture of complex components made of many alloys, such as titanium alloys, nickel-based superalloys, aluminum alloys and stainless steels [[2], [3], [4],8].
Ti–6Al–4V alloy is one of the prevalent commercial titanium alloys possessing high specific strength, excellent mechanical properties, excellent corrosion resistance, and good biocompatibility [9,10]. It is widely used in applications requiring low density and excellent corrosion resistance, such as the aerospace industry and biomechanical applications [11,12]. The mechanical properties of PBF-EB-processed Ti–6Al–4V alloys are superior to those fabricated by casting or forging, because the rapid cooling rate in PBF-EB results in finer grains [[12], [13], [14], [15], [16], [17], [18]]. However, the PBF-EB-fabricated parts often include internal macro-defects, which compromises their mechanical properties [[19], [20], [21], [22]]. This study focused on the elimination of macro-defects, such as porosity, lack of fusion, incomplete penetration and unmelted powders, which distinguishes them from micro-defects such as vacancies, dislocations, grain boundaries and secondary phases, etc. Large-sized fusion defects cause a severe reduction in mechanical strength. Smaller defects, such as pores and cracks, lead to the initiation of fatigue cracking and rapidly accelerate the cracking process [23]. The issue of internal macro-defects must be addressed to expand the application of the PBF-EB technology. The main studies for controlling internal macro-defects are online monitoring of defects, remelting and hot isostatic pressing (HIP). The literatures [24,25] report the use of infrared imaging or other imaging techniques to identify defects, but the monitoring of smaller sized defects is still not adequate. And in some cases remelting does not reduce the internal macro-defects of the part, but instead causes coarsening of the macrostructure and volatilization of some metal elements [23]. The HIP treatment does not completely eliminate the internal macro-defects, the original defect location may still act as a point of origin of the crack, and the subsequent treatment will consume more time and economic costs [23]. Therefore, optimizing suitable printing parameters to avoid internal macro-defects in printed parts at source is of great industrial value and research significance, and is an urgent issue in PBF-EB related technology.
There are two causes of internal macro-defects in the AM process: gas pores trapped in the virgin powder and the inappropriate printing parameters [7,23]. Gui et al. [26] classify internal macro-defects during PBF-EB process according to their shape, such as spherical defects, elongated shape defects, flat shape defects and other irregular shape defects. Of these, spherical defects mainly originate from raw material powders. Other shape defects mainly originate from lack of fusion or unmelted powders caused by unsuitable printing parameters, etc. The PBF-EB process requires powders with good flowability, and spherical powders are typically chosen as raw materials. The prevalent techniques for the fabrication of pre-alloyed powders are gas atomization (GA), plasma atomization (PA), and the plasma rotating electrode process (PREP) [27,28]. These methods yield powders with different characteristics that affect the subsequent fabrication. The selection of a suitable powder for PBF-EB is particularly important to produce Ti–6Al–4V alloys without internal macro-defects. The need to optimize several printing parameters such as beam current, scan speed, line offset, and focus offset make it difficult to eliminate internal macro-defects that occur during printing [23]. Most of the studies [11,12,22,[29], [30], [31], [32], [33]] on the optimization of AM processes for Ti–6Al–4V alloys have focused on samples with a limited set of parameters (e.g., power–scan speed) and do not allow for the guidance and development of unknown process windows for macro-defect-free samples. In addition, process optimization remains a time-consuming problem, with the traditional ‘trial and error’ method demanding considerable time and economic costs. The development of a simple and efficient method to predict the processing window for alloys without internal macro-defects is a key issue. In recent years, machine learning techniques have increasingly been used in the field of additive manufacturing and materials development [[34], [35], [36], [37]]. Aoyagi et al. [38] recently proposed a novel and efficient method based on a support vector machine (SVM) to optimize the two-dimensional process parameters (current and scan speed) and obtain PBF-EB-processed CoCr alloys without internal macro-defects. The method is one of the potential approaches toward effective optimization of more than two process parameters and makes it possible for the machine learning techniques to accelerate the development of alloys without internal macro-defects.
Herein, we focus on the elimination of internal macro-defects, such as pores, lack of fusion, etc., caused by raw powders and printing parameters. The Ti–6Al–4V powders produced by three different methods were compared, and the powder with the best sphericity, flowability, and minimal porosity was selected as the feedstock for subsequent printing. The relationship between the surface roughness and internal macro-defects in the Ti–6Al–4V components was also investigated. The combination of SVM and surface roughness indices (Sdr) predicted a wider four-dimensional processing window for obtaining Ti–6Al–4V alloys without internal macro-defects. Finally, we investigated the tensile properties of Ti–6Al–4V alloys at room temperature with different printing parameters, as well as the corresponding microstructures and fracture types.
Section snippets
Starting materials
Three types of Ti–6Al–4V alloy powders, produced by GA, PA, and PREP, were compared. The particle size distribution of the powders was determined using a laser particle size analyzer (LS230, Beckman Coulter, USA), and the flowability was measured using a Hall flowmeter (JIS-Z2502, Tsutsui Scientific Instruments Co., Ltd., Japan), according to the ASTM B213 standard. The powder morphology and internal macro-defects were determined using scanning electron microscopy (SEM, JEOL JCM-6000) and X-ray
Comparison of the characteristics of GA, PA, and PREP Ti–6Al–4V powders
The particle size distributions (PSDs) and flowability of the three types of Ti–6Al–4V alloy powders produced by GA, PA, and PREP are shown in Fig. 2. Although the average particle sizes are similar (89.4 μm for GA, 82.5 μm for PA, and 86.1μm for PREP), the particle size range is different for the three types of powder (6.2–174.8 μm for GA, 27.3–139.2 μm for PA, and 39.4–133.9 μm for PREP). The flowability of the GA, PA, and PREP powders was 30.25 ± 0.98, 26.54 ± 0.37, and 25.03 ± 0.22 (s/50
Conclusions
The characteristics of the three types of Ti–6Al–4V alloy powders produced via GA, PA, and PREP were compared. The PREP powder with the best sphericity, flowability, and low porosity was found to be the most favorable powder for subsequent printing of Ti–6Al–4V alloys without internal macro-defects. The quantitative criterion of Sdr <0.015 for even surfaces was also found to be applicable to Ti–6Al–4V alloys. The process maps of Ti–6Al–4V alloys include two regions, high beam current/scan speed
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgments
This study was based on the results obtained from project JPNP19007, commissioned by the New Energy and Industrial Technology Development Organization (NEDO). This work was also supported by JSPS KAKENHI (Proposal No. 21K03801) and the Inter-University Cooperative Research Program (Proposal nos. 18G0418, 19G0411, and 20G0418) of the Cooperative Research and Development Center for Advanced Materials, Institute for Materials Research, Tohoku University. It was also supported by the Council for
Pages 541-551 | Received 03 Mar 2020, Accepted 07 May 2020, Published online: 21 May 2020
ABSTRACT
Dams fall in ‘installations containing dangerous forces’ because of their massive impact on the environment and civilian life and property as per International humanitarian law. As such, it becomes vital for hydraulic engineers to refurbish various solutions for dam rehabilitation. This paper presents a review of a new type of weir installation called Piano Key Weir (PKW), which is becoming popular around the world for its higher spillway capacity both for existing and new dam spillway installations. This paper reviews the geometry along with structural integrity, discharging capacity, economic aspects, aeration requirements, sediment transport and erosion aspects of Piano Key Weir (PKW) as compared with other traditional spillway structures and alternatives from literature. The comparison with other alternatives shows PKW to be an excellent alternative for dam risk mitigation owing to its high spillway capabilities and economy, along with its use in both existing and new hydraulic structures.
댐은 국제 인도법에 따라 환경과 민간인 생활 및 재산에 막대한 영향을 미치기 때문에 ‘위험한 힘을 포함하는 시설물’에 속합니다. 따라서 유압 엔지니어는 댐 복구를 위한 다양한 솔루션을 재정비해야 합니다.
이 백서에서는 PKW(Piano Key Weir)라는 새로운 유형의 둑 설치에 대한 검토를 제공합니다. PKW는 기존 및 신규 댐 방수로 설치 모두에서 더 높은 방수로 용량으로 전 세계적으로 인기를 얻고 있습니다.
이 백서에서는 구조적 무결성, 배출 용량, 경제적 측면, 폭기 요구 사항, 퇴적물 운반 및 PKW(Piano Key Weir)의 침식 측면과 함께 다른 전통적인 여수로 구조 및 문헌의 대안과 비교하여 기하학을 검토합니다.
다른 대안과의 비교는 PKW가 높은 여수로 기능과 경제성으로 인해 댐 위험 완화를 위한 탁월한 대안이며 기존 및 새로운 수력 구조물 모두에 사용됨을 보여줍니다.
Anderson, R., and Tullis, B. (2011). Influence of Piano Key Weir geometry on discharge. Proc. Int. Conf. Labyrinth and Piano Key Weirs Liège B. Liège, Belgium. [Crossref], [Google Scholar]
Anderson, R.M. 2011. Piano key weir head discharge relationships, M.S. Thesis, Utah State University, Logan, Utah. [Google Scholar]
Bashiri, H., Dewals, B., Pirotton, M., Archambeau, P., and Erpicum, S. (2016). “Towards a new design equation for piano key weirs discharge capacity.” Proc. of the 6th International Symposium on Hydraulic Structures. Portland, USA. [Google Scholar]
Bianucci, S.P., Sordo Ward, Á.F., Pérez Díaz, J.I., García-Palacios, J.H., Mediero Orduña, L.J., and Garrote de Marcos, L. (2013). “Risk-based methodology for parameter calibration of a reservoir flood control model”. Natl. Hazard Earth Syst. Sci., 13(4), 965–981. doi:https://doi.org/10.5194/nhess-13-965-2013[Crossref], [Web of Science ®], [Google Scholar]
Blancher, B., Montarros, F., and Laugier, F. (2011). Hydraulic comparison between Piano Key Weirs and labyrinth spillways. Proc. Int. Conf. Labyrinth and Piano Key Weirs Liège B. Liège, Belgium. [Crossref], [Google Scholar]
Botha, A., Fitz, I., Moore, A., Mulder, F., and Van Deventer, N. 2013. “Application of the Piano Key Weir spillway in the Republic of South Africa”. Labyrinth and Piano Key Weirs II, Proceedings of the Second International Workshop on Labyrinth and Piano key weirs, Chatou, Paris, France, 20–22, 185. [Crossref], [Google Scholar]
Chi Hien, T., Thanh Son, H., and Ho Ta Khanh, M. (2006). Results of some ‘piano keys’ weir hydraulic model tests in Vietnam. Proc., 22nd Int. Congress of Large Dams, Question 87, Response 39, International Commission on Large Dams (ICOLD). Barcelona, Spain. [Google Scholar]
Cicero, G., Barcouda, M., Luck, M., and Vettori, E. (2011). Study of a piano key morning glory to increase the spillway capacity of the Bage dam. Proc. Int. Conf. Labyrinth Piano Key Weirs-PKW2011, Taylor & Francis, London. [Crossref], [Google Scholar]
Cicero, G., De Miranda, D., and Luck, M. (2012). “Assessment of the code Wolf 1D PKW for predicting the hydraulic behaviour of PK-Weirs.” Congrès SHF-33èmes journées de l’hydraulique “Grands aménagements hydrauliques 2012”, Paris, France. [Google Scholar]
Cicero, G., and Delisle, J. (2013). “Discharge characteristics of Piano Key weirs under submerged flow”. Labyrinth and Piano Key Weirs II–PKW 2013, 101–109. [Crossref], [Google Scholar]
Cicero, G., Delisle, J., Lefebvre, V., and Vermeulen, J. (2013). “Experimental and numerical study of the hydraulic performance of a trapezoidal Piano Key weir.” Labyrinth and Piano Key Weirs II: Proceedings of the Second International Workshop on Labyrinth and Piano key weirs, Chatou, Paris, France, 20–22, 265. [Crossref], [Google Scholar]
Cicéro, G., Guene, C., Luck, M., Pinchard, T., Lochu, A., and Brousse, P. (2010). “Experimental optimization of a Piano Key Weir to increase the spillway capacity of the Malarce dam.” 1st IAHR European Congress, Edinbourgh, Mai 4–6, 2010. [Google Scholar]
Das Singhal, G., and Sharma, N. 2011. “Rehabilitation of Sawara Kuddu Hydroelectric Project–Model studies of Piano Key Weir in India”. Proc. Int. Workshop on Labyrinths and Piano Key Weirs PKW 2011. Taylor & Francis, London. [Crossref], [Google Scholar]
Denys, F., Basson, G., and Strasheim, J. (2017). Fluid Structure Interaction of Piano Key Weirs. Labyrinth and Piano Key Weirs III: Proceedings of the 3rd International Workshop on Labyrinth and Piano Key Weirs (PKW 2017), Feb 22–24, 2017, CRC Press, Qui Nhon, Vietnam. [Crossref], [Google Scholar]
Eichenberger, P. (2013). “The first commercial piano key weir in Switzerland.” Labyrinth and Piano Key Weirs II, Proceedings of the Second International Workshop on Labyrinth and Piano key weirs 2013, Chatou, Paris, France, 20–22, 227. [Crossref], [Google Scholar]
Erpicum, S., Laugier, F., Pfister, M., Pirotton, M., Cicero, G.-M., and Schleiss, A.J. 2013. Labyrinth and Piano Key Weirs II, Proceedings of the Second International Workshop on Labyrinth and Piano key weirs 2013, Chatou, Paris, France, 20–22, CRC Press. [Crossref], [Google Scholar]
Erpicum, S., Machiels, O., Dewals, B., Pirotton, M., and Archambeau, P. (2012). “Numerical and physical hydraulic modelling of Piano Key Weirs.” Proceedings of the 4th Int. Conf. on Water Resources and Renewable Energy Development in Asia. Chiang Mai, Thailande. [Google Scholar]
Erpicum, S., Nagel, V., and Laugier, F. (2011). “Piano Key Weir design study at Raviege dam”. Labyrinth and Piano Key Weirs–PKW 2011, 43–50. [Crossref], [Google Scholar]
Ervine, D., and Elsawy, E. (1975). “The effect of a falling nappe on river aeration.” Proc. 16th IAHR Congress, Sao Paulo, Brazil. [Google Scholar]
Falvey, H.T. 1980. “Air-water flow in hydraulic structures”. NASA STI/Recon Technical Report N, 81. [Google Scholar]
Javaheri, A., and Kabiri-Samani, A. (2012). “Threshold submergence of flow over PK weirs”. Int. J. Civil Geol. Eng., 6, 46–49. [Google Scholar]
Jayatillake, H., and Perera, K. (2013). “Design of a Piano-Key Weir for Giritale Dam spillway in Sri Lanka.” Labyrinth and Piano Key Weirs II, Proceedings of the Second International Workshop on Labyrinth and Piano key weirs 2013, Chatou, Paris, France, 20–22, 151. [Crossref], [Google Scholar]
Jayatillake, H., and Perera, K. (2017). “Adoption of a type D Piano Key Weir spillway with tapered noses at Rambawa Tank, Sri Lanka.” Labyrinth and Piano Key Weirs III: Proceedings of the 3rd International Workshop on Labyrinth and Piano Key Weirs (PKW 2017), Feb 22–24, 2017, CRC Press, Qui Nhon, Vietnam. [Crossref], [Google Scholar]
Karimi, M., Attari, J., Saneie, M., and Jalili-Ghazizadeh, M. (2017). “Experimental study of discharge coefficient of a piano key side weir.” Labyrinth and Piano Key Weirs III: Proceedings of the 3rd International Workshop on Labyrinth and Piano Key Weirs (PKW 2017). Proceedings of the Third International Workshop on Labyrinth and Piano key weirs 2017, Qui Nhon, Vietnam, 22–24. [Crossref], [Google Scholar]
Khanh, M.H.T. (2013). “The Piano Key Weirs: 15 years of Research & Development–Prospect.” Labyrinth and piano key weirs II, Proceedings of the Second International Workshop on Labyrinth and Piano key weirs 2013, Chatou, Paris, France, 20–22, 3. [Crossref], [Google Scholar]
Khanh, M.H.T. (2017). “History and development of Piano Key Weirs in Vietnam from 2004 to 2016.” Labyrinth and Piano Key Weirs III: Proceedings of the 3rd International Workshop on Labyrinth and Piano Key Weirs (PKW 2017), Feb 22–24, 2017, CRC Press, Qui Nhon, Vietnam. [Google Scholar]
Khanh, M.H.T., Hien, T.C., and Hai, N.T. (2011). “Main results of the PK weir model tests in Vietnam (2004 to 2010).” Labyrinth and Piano Key Weirs, 191. Liège, Belgium. [Crossref], [Google Scholar]
Khassaf, S.I., Aziz, L.J., and Elkatib, Z.A. (2016). “Hydraulic behavior of piano key weir type B under free flow conditions”. Int. J. Sci. Technol. Res., 5(3), 158–163. [Google Scholar]
Khassaf, S.I., and Al-Baghdadi, M.B. (2015). “Experimental study of non-rectangular piano key weir discharge coefficient”. J. Homepage, 6(5), 425–436. [Google Scholar]
Khassaf, S.I., and Al-Baghdadi, M.B.N. (2018). “Experimental investigation of submerged flow over piano key weir”. Int. J. Energy Environ., 9(3), 249–260. [Google Scholar]
Laugier, F. (2007). “Design and construction of the first Piano Key Weir spillway at Goulours dam”. Int. J. Hydropower Dams, 14(5), 94. [Google Scholar]
Laugier, F., Lochu, A., Gille, C., Leite Ribeiro, M., and Boillat, J.-L. (2009). “Design and construction of a labyrinth PKW spillway at Saint-Marc dam, France”. Hydropower Dams, 16(LCH–ARTICLE–2009–023), 100–107. [Google Scholar]
Laugier, F., Pralong, J., and Blancher, B. (2011). “Influence of structural thickness of sidewalls on PKW spillway discharge capacity.” Proc. Intl Workshop on Labyrinths and Piano Key Weirs PKW 2011. Liège, Belgium. [Crossref], [Google Scholar]
Le Blanc, M., Spinazzola, U., and Kocahan, H. (2011). “Labyrinth fusegate applications on free overflow spillways–Overview of recent projects.” Labyrinth and Piano Key Weirs, 261, Liège, Belgium. [Crossref], [Google Scholar]
Leite Ribeiro, M., Bieri, M., Boillat, J.-L., Schleiss, A., Delorme, F., and Laugier, F. (2009). “Hydraulic capacity improvement of existing spillways–design of a piano key weirs.” Proc. (on CD) of the 23rd Congress of the Int. Commission on Large Dams CIGB-ICOLD. Brasilia, Brazil. [Google Scholar]
Lempérière, F., and Ouamane, A. (2003). “The Piano Keys weir: a new cost-effective solution for spillways”. Int. J. Hydropower Dams, 10(5), 144–149. [Google Scholar]
Lempérière, F., and Vigny, J. (2011). “General comments on labyrinth and Piano Keys Weirs–The future”. Labyrinth and Piano Key weirs–PKW 2011, 289–294. [Crossref], [Google Scholar]
Lempérière, F., Vigny, J., and Ouamane, A. (2011). General comments on Labyrinth and Piano Key Weirs: The past and present. Proc. Intl. Conf. Labyrinth and Piano Key Weirs, Liège B. Liège, Belgium. [Crossref], [Google Scholar]
Lewin, J., Ballard, G., and Bowles, D.S. (2003). “Spillway gate reliability in the context of overall dam failure risk.” USSD Annual Lecture, Charleston, South Carolina. [Google Scholar]
Lodomez, M., Pirotton, M., Dewals, B., Archambeau, P., and Erpicum, S. (2017). “Could piano key weirs be subject to nappe oscillations?” Labyrinth and Piano Key Weirs III: Proceedings of the 3rd International Workshop on Labyrinth and Piano Key Weirs (PKW 2017), Feb 22–24, 2017, CRC Press, Qui Nhon, Vietnam [Crossref], [Google Scholar]
Machiels, O., Erpicum, S., Archambeau, P., Dewals, B., and Pirotton, M. (2009). “Large scale experimental study of piano key weirs.” Proc. 33rd IAHR Congress: Water Engineering for a Sustainable Environment, IAHR. Vancouver, Canada [Google Scholar]
Machiels, O., Erpicum, S., Archambeau, P., Dewals, B., and Pirotton, M. (2011a). “Piano Key Weir preliminary design method–Application to a new dam project.” Proc. Int. Conf. Labyrinth and Piano Key Weirs Liège B. Liège, Belgium. [Crossref], [Google Scholar]
Machiels, O., Erpicum, S., Dewals, B., Archambeau, P., and Pirotton, M. (2010). “Piano Key Weirs: The experimental study of an efficient solution for rehabilitation”. WIT Trans. Ecol., 133, 95–106. [Crossref], [Google Scholar]
Oertel, M. (2015). “Discharge coefficients of piano key weirs from experimental and numerical modelS.” E= proceedings of the 36th IAHR world congress. 28 June – 3 July, The Hague, The Netherlands. [Google Scholar]
Ouamane, A. (2011). Nine years of study of the Piano Key Weir in the university laboratory of Biskra “lessons and reflections”. Proc. Int. Conf. Labyrinth Piano Key Weirs-PKW2011, Taylor & Francis, London. [Crossref], [Google Scholar]
Ouamane, A., Debabeche, M., Lempérière, F., and Vigny, J. (2017). Twenty years of research in Biskra University for Labyrinths and Piano Key Weirs and associated fuse plugs. Labyrinth and Piano Key Weirs III: Proceedings of the 3rd International Workshop on Labyrinth and Piano Key Weirs (PKW 2017), Feb 22–24, 2017, CRC Press, Qui Nhon, Vietnam. [Crossref], [Google Scholar]
Ouamane, A., and Lempérière, F. (2006). Design of a new economic shape of weir. Proc. Int. Symp. on Dams in the Societies of the 21st Century. Barcelona, Spain. [Crossref], [Google Scholar]
Paxson, G., Tullis, B., and Hertel, D. 2013. “Comparison of Piano Key Weirs with labyrinth and gated spillways: Hydraulics, cost, constructability and operations”. Labyrinth and Piano Key Weirs II, Proceedings of the Second International Workshop on Labyrinth and Piano key weirs 2013, Chatou, Paris, France, 20–22, 123–130. [Crossref], [Google Scholar]
Phillips, M., and Lesleighter, E. 2013. “Piano Key Weir spillway: Upgrade option for a major dam”. Labyrinth and Piano Key Weirs II, Proceedings of the Second International Workshop on Labyrinth and Piano key weirs 2013, Chatou, Paris, France, 20–22, 159–168. [Crossref], [Google Scholar]
Pinchard, T., Boutet, J., and Cicero, G. (2011). “Spillway capacity upgrade at Malarce dam: design of an additional Piano Key Weir spillway.” Proc. Int. Workshop on Labyrinths and Piano Key Weirs PKW. Liège, Belgium. [Crossref], [Google Scholar]
Pralong, J., J. Vermeulen, B. Blancher, F. Laugier, S. Erpicum, O. Machiels, M. Pirotton, J.-L. Boillat, M. Leite Ribeiro and A. Schleiss (2011). “A naming convention for the piano key weirs geometrical parameters.” Labyrinth and piano key weirs, 271–278. [Crossref], [Google Scholar]
Ribeiro, M.L., Boillat, J.-L., Schleiss, A., Laugier, F., and Albalat, C. (2007). “Rehabilitation of St-Marc dam.” Experimental optimization of a piano key weir. Proc. of 32nd Congress of IAHR, Vince, Italy. [Google Scholar]
Ribeiro, M.L., Pfister, M., and Schleiss, A.J. (2013). “Overview of Piano Key weir prototypes and scientific model investigations”. Labyrinth and Piano Key Weirs II, Proceedings of the Second International Workshop on Labyrinth and Piano key weirs 2013, Chatou, Paris, France, 20–22, 273. [Crossref], [Google Scholar]
Ribi, J., Spahni, B., Dorthe, D., and Pfister, M. (2017). Piano Key Weir as overflow on sedimentation basin of wastewater treatment plant. Labyrinth and Piano Key Weirs III: Proceedings of the 3rd International Workshop on Labyrinth and Piano Key Weirs (PKW 2017), Feb 22–24, 2017, CRC Press, Qui Nhon, Vietnam [Crossref], [Google Scholar]
Schleiss, A. (2011). “From labyrinth to piano key weirs: a historical review.” Proc. Int. Conf. Labyrinth and Piano Key Weirs Liège B. Liège, Belgium. [Crossref], [Google Scholar]
Sharma, N., and Tiwari, H. (2013). “Experimental study on vertical velocity and submergence depth near Piano Key Weir.” Labyrinth and Piano Key Weirs II-PKW, Proceedings of the Second International Workshop on Labyrinth and Piano key weirs 2013, Chatou, Paris, France, 20–22, 93–100. [Crossref], [Google Scholar]
Tiwari, H. (2016). Experimental Study of Turbulence Characteristics Near Piano Key Weir. PhD, Indian Institute of Technology Roorkee. [Google Scholar]
Valley, P., and Blancher, B. (2017). Construction and testing of two Piano Key Weirs at Charmines dam. Labyrinth and Piano Key Weirs III: Proceedings of the 3rd International Workshop on Labyrinth and Piano Key Weirs (PKW 2017), Feb 22–24, 2017, CRC Press, Qui Nhon, Vietnam. [Crossref], [Google Scholar]
Vermeulen, J., Lassus, C., and Pinchard, T. (2017). Design of a Piano Key Weir aeration network. Labyrinth and Piano Key Weirs III: Proceedings of the 3rd International Workshop on Labyrinth and Piano Key Weirs (PKW 2017), February 22- 24,2017, Qui Nhon, Vietnam, CRC Press. [Crossref], [Google Scholar]
Vermeulen, J., Laugier, F., Faramond, L., and Gille, C. (2011). “Lessons learnt from design and construction of EDF first Piano Key Weirs”. Labyrinth and Piano Key weirs-PKW 2011, 215–224. [Crossref], [Google Scholar]
Publication: Canadian Journal of Civil Engineering
3 December 2008
Abstract
Throughout the design and planning period for future hydroelectric generating stations, hydraulic engineers are increasingly integrating computational fluid dynamics (CFD) into the process. As a result, hydraulic engineers are interested in the reliability of CFD software to provide accurate flow data for a wide range of structures, including a variety of different spillways. In the literature, CFD results have generally been in agreement with physical model experimental data. Despite past success, there has not been a comprehensive assessment that looks at the ability of CFD to model a range of different spillway configurations, including flows with various gate openings. In this article, Flow-3D is used to model the discharge over ogee-crested spillways. The numerical model results are compared with physical model studies for three case study evaluations. The comparison indicates that the accuracy of Flow-3D is related to the parameter P/Hd.
미래의 수력 발전소를 위한 설계 및 계획 기간 동안 유압 엔지니어는 전산유체역학(CFD)을 프로세스에 점점 더 많이 통합하고 있습니다. 결과적으로 유압 엔지니어는 다양한 여수로를 포함하여 광범위한 구조에 대한 정확한 흐름 데이터를 제공하는 CFD 소프트웨어의 신뢰성에 관심을 갖고 있습니다. 문헌에서 CFD 결과는 일반적으로 물리적 모델 실험 데이터와 일치했습니다. 과거의 성공에도 불구하고 다양한 게이트 개구부가 있는 흐름을 포함하여 다양한 여수로 구성을 모델링하는 CFD의 기능을 살펴보는 포괄적인 평가는 없었습니다. 이 기사에서는 Flow-3D를 사용하여 ogee-crested 방수로의 배출을 모델링합니다. 세 가지 사례 연구 평가를 위해 수치 모델 결과를 물리적 모델 연구와 비교합니다. 비교는 Flow-3D의 정확도가 매개변수 P/Hd와 관련되어 있음을 나타냅니다.
Résumé
Les ingénieurs en hydraulique intègrent de plus en plus la dynamique des fluides numérique (« CFD ») dans le processus de conception et de planification des futures centrales. Ainsi, les ingénieurs en hydraulique s’intéressent à la fiabilité du logiciel de « CFD » afin de fournir des données précises sur le débit pour une large gamme de structures, incluant différents types d’évacuateurs. Les résultats de « CFD » dans la littérature ont été globalement sont généralement en accord avec les données expérimentales des essais physiques. Malgré les succès antérieurs, il n’y avait aucune évaluation complète de la capacité des « CFD » à modéliser une plage de configuration des évacuateurs, incluant les débits à diverses ouvertures de vannes. Dans le présent article, le logiciel Flow-3D est utilisé pour modéliser le débit par des évacuateurs en doucine. Les résultats du modèle de calcul sont comparés à ceux des essais physiques pour trois études de cas. La comparaison montre que la précision du logiciel Flow-3D est associée au paramètre P/Hd.
Fig. 1. Averaged error trend.
Get full access to this article
View all available purchase options and get full access to this article.
Chanel, P.G., and Doering, J.C. 2007. An evaluation of computational fluid dynamics for spillway modelling. In Proceedings of the 16th Australasian Fluid Mechanics Conference (AFMC), Gold Coast, Queensland, Australia, 3–7 December 2007. pp. 1201–1206.
Gessler, D. 2005. CFD modeling of spillway performance, EWRI 2005: Impacts of global climate change. In Proceedings of the World Water and Environmental Resources Congress, Anchorage, Alaska, 15–19 May 2005. Edited by R. Walton. American Society of Civil Engineers, Reston, Va.
Hirt, C.W., and Nichols, B.D. 1981. Volume of fluid (VOF) method for the dynamics of free boundaries. Journal of Computational Physics, 39(1): 201–225.
Hirt, C.W., and Sicilian, J.M. 1985. A porosity technique for the definition of obstacles in rectangular cell meshes. In Proceedings of the 4th International Conference on Ship Hydro-dynamics, Washington, D.C., 24–27 September 1985. National Academy of Sciences, Washington, D.C.
Ho, D., Cooper, B., Riddette, K., and Donohoo, S. 2006. Application of numerical modelling to spillways in Australia. In Dams and Reservoirs, Societies and Environment in the 21st Century. Edited by Berga et al. Taylor and Francis Group, London.
Lemke, D.E. 1989. A comparison of the hydraulic performance of an orifice and an overflow spillway in a northern application using physical modeling. M.Sc. thesis, University of Manitoba, Winnipeg, Man.
Savage, B.M., and Johnson, M.C. 2001. Flow over ogee spillway: Physical and numerical model case study. Journal of Hydraulic Engineering, 127(8): 640–649.
Teklemariam, E., Korbaylo, B., Groeneveld, J., Sydor, K., and Fuchs, D. 2001. Optimization of hydraulic design using computational fluid dynamics. In Proceedings of Waterpower XII, Salt Lake City, Utah, 9–11 July 2001.
Teklemariam, E., Korbaylo, B., Groeneveld, J., and Fuchs, D. 2002. Computational fluid dynamics: Diverse applications in hydropower project’s design and analysis. In Proceedings of the CWRA 55th Annual Conference, Winnipeg, Man., 11–14 June 2002. Canadian Water Resources Association, Cambridge, Ontario.
Western Canadian Hydraulic Laboratories Inc. 1980. Hydraulics model studies limestone generating station spillway/diversion structure flume study. Final report. Western Canadian Hydraulic Laboratories Inc., Port Coquitlam, B.C.
Analysis of behavior and hydraulic characteristics of flow over the dam spillway is a complicated task that takes lots of money and time in water engineering projects planning. To model those hydraulic characteristics, several methods such as physical and numerical methods can be used. Nowadays, by utilizing new methods in computational fluid dynamics (CFD) and by the development of fast computers, the numerical methods have become accessible for use in the analysis of such sophisticated flows. The CFD softwares have the capability to analyze two- and three-dimensional flow fields. In this paper, the flow pattern at the guide wall of the Kamal-Saleh dam was modeled by Flow 3D. The results show that the current geometry of the left wall causes instability in the flow pattern and making secondary and vortex flow at beginning approach channel. This shape of guide wall reduced the performance of weir to remove the peak flood discharge.
댐 여수로 흐름의 거동 및 수리학적 특성 분석은 물 공학 프로젝트 계획에 많은 비용과 시간이 소요되는 복잡한 작업입니다. 이러한 수력학적 특성을 모델링하기 위해 물리적, 수치적 방법과 같은 여러 가지 방법을 사용할 수 있습니다. 요즘에는 전산유체역학(CFD)의 새로운 방법을 활용하고 빠른 컴퓨터의 개발로 이러한 정교한 흐름의 해석에 수치 방법을 사용할 수 있게 되었습니다. CFD 소프트웨어에는 2차원 및 3차원 유동장을 분석하는 기능이 있습니다. 본 논문에서는 Kamal-Saleh 댐 유도벽의 흐름 패턴을 Flow 3D로 모델링하였다. 결과는 왼쪽 벽의 현재 형상이 흐름 패턴의 불안정성을 유발하고 시작 접근 채널에서 2차 및 와류 흐름을 만드는 것을 보여줍니다. 이러한 형태의 안내벽은 첨두방류량을 제거하기 위해 둑의 성능을 저하시켰다.
Introduction
Spillways are one of the main structures used in the dam projects. Design of the spillway in all types of dams, specifically earthen dams is important because the inability of the spillway to remove probable maximum flood (PMF) discharge may cause overflow of water which ultimately leads to destruction of the dam (Das and Saikia et al. 2009; E 2013 and Novak et al. 2007). So study on the hydraulic characteristics of this structure is important. Hydraulic properties of spillway including flow pattern at the entrance of the guide walls and along the chute. Moreover, estimating the values of velocity and pressure parameters of flow along the chute is very important (Chanson 2004; Chatila and Tabbara 2004). The purpose of the study on the flow pattern is the effect of wall geometry on the creation transverse waves, flow instability, rotating and reciprocating flow through the inlet of spillway and its chute (Parsaie and Haghiabi 2015a, b; Parsaie et al. 2015; Wang and Jiang 2010). The purpose of study on the values of velocity and pressure is to calculate the potential of the structure to occurrence of phenomena such as cavitation (Fattor and Bacchiega 2009; Ma et al. 2010). Sometimes, it can be seen that the spillway design parameters of pressure and velocity are very suitable, but geometry is considered not suitable for conducting walls causing unstable flow pattern over the spillway, rotating flows at the beginning of the spillway and its design reduced the flood discharge capacity (Fattor and Bacchiega 2009). Study on spillway is usually conducted using physical models (Su et al. 2009; Suprapto 2013; Wang and Chen 2009; Wang and Jiang 2010). But recently, with advances in the field of computational fluid dynamics (CFD), study on hydraulic characterist–ics of this structure has been done with these techniques (Chatila and Tabbara 2004; Zhenwei et al. 2012). Using the CFD as a powerful technique for modeling the hydraulic structures can reduce the time and cost of experiments (Tabbara et al. 2005). In CFD field, the Navier–Stokes equation is solved by powerful numerical methods such as finite element method and finite volumes (Kim and Park 2005; Zhenwei et al. 2012). In order to obtain closed-form Navier–Stokes equations turbulence models, such k − ε and Re-Normalisation Group (RNG) models have been presented. To use the technique of computational fluid dynamics, software packages such as Fluent and Flow 3D, etc., are provided. Recently, these two software packages have been widely used in hydraulic engineering because the performance and their accuracy are very suitable (Gessler 2005; Kim 2007; Kim et al. 2012; Milési and Causse 2014; Montagna et al. 2011). In this paper, to assess the flow pattern at Kamal-Saleh guide wall, numerical method has been used. All the stages of numerical modeling were conducted in the Flow 3D software.
Materials and methods
Firstly, a three-dimensional model was constructed according to two-dimensional map that was prepared for designing the spillway. Then a small model was prepared with scale of 1:80 and entered into the Flow 3D software; all stages of the model construction was conducted in AutoCAD 3D. Flow 3D software numerically solved the Navier–Stokes equation by finite volume method. Below is a brief reference on the equations that used in the software. Figure 1 shows the 3D sketch of Kamal-Saleh spillway and Fig. 2 shows the uploading file of the Kamal-Saleh spillway in Flow 3D software.
Fig. 1Fig. 2
Review of the governing equations in software Flow 3D
Continuity equation at three-dimensional Cartesian coordinates is given as Eq (1).
where u, v, z are velocity component in the x, y, z direction; Ax, Ay, Az cross-sectional area of the flow; ρ fluid density; PSOR the source term; vf is the volume fraction of the fluid and three-dimensional momentum equations given in Eq (2).
where P is the fluid pressure; Gx, Gy, Gz the acceleration created by body fluids; fx, fy, fz viscosity acceleration in three dimensions and vf is related to the volume of fluid, defined by Eq. (3). For modeling of free surface profile the VOF technique based on the volume fraction of the computational cells has been used. Since the volume fraction F represents the amount of fluid in each cell, it takes value between 0 and 1.
Flow 3D offers five types of turbulence models: Prantl mixing length, k − ε equation, RNG models, Large eddy simulation model. Turbulence models that have been proposed recently are based on Reynolds-averaged Navier–Stokes equations. This approach involves statistical methods to extract an averaged equation related to the turbulence quantities.
Steps of solving a problem in Flow 3D software
(1) Preparing the 3D model of spillway by AutoCAD software. (2) Uploading the file of 3D model in Flow 3D software and defining the problem in the software and checking the final mesh. (3) Choosing the basic equations that should be solved. (4) Defining the characteristics of fluid. (5) Defining the boundary conditions; it is notable that this software has a wide range of boundary conditions. (6) Initializing the flow field. (7) Adjusting the output. (8) Adjusting the control parameters, choice of the calculation method and solution formula. (9) Start of calculation. Figure 1 shows the 3D model of the Kamal-Saleh spillway; in this figure, geometry of the left and right guide wall is shown.
Figure 2 shows the uploading of the 3D spillway dam in Flow 3D software. Moreover, in this figure the considered boundary condition in software is shown. At the entrance and end of spillway, the flow rate or fluid elevation and outflow was considered as BC. The bottom of spillway was considered as wall and left and right as symmetry.
Model calibration
Calibration of the Flow 3D for modeling the effect of geometry of guide wall on the flow pattern is included for comparing the results of Flow 3D with measured water surface profile. Calibration the Flow 3D software could be conducted in two ways: first, changing the value of upstream boundary conditions is continued until the results of water surface profile of the Flow 3D along the spillway successfully covered the measurement water surface profile; second is the assessment the mesh sensitivity. Analyzing the size of mesh is a trial-and-error process where the size of mesh is evaluated form the largest to the smallest. With fining the size of mesh the accuracy of model is increased; whereas, the cost of computation is increased. In this research, the value of upstream boundary condition was adjusted with measured data during the experimental studies on the scaled model and the mesh size was equal to 1 × 1 × 1 cm3.
Results and discussion
The behavior of water in spillway is strongly affected by the flow pattern at the entrance of the spillway, the flow pattern formation at the entrance is affected by the guide wall, and choice of an optimized form for the guide wall has a great effect on rising the ability of spillway for easy passing the PMF, so any nonuniformity in flow in the approach channel can cause reduction of spillway capacity, reduction in discharge coefficient of spillway, and even probability of cavitation. Optimizing the flow guiding walls (in terms of length, angle and radius) can cause the loss of turbulence and flow disturbances on spillway. For this purpose, initially geometry proposed for model for the discharge of spillway dam, Kamal-Saleh, 80, 100, and 120 (L/s) were surveyed. These discharges of flow were considered with regard to the flood return period, 5, 100 and 1000 years. Geometric properties of the conducting guidance wall are given in Table 1.Table 1 Characteristics and dimensions of the guidance walls tested
Results of the CFD simulation for passing the flow rate 80 (L/s) are shown in Fig. 3. Figure 3 shows the secondary flow and vortex at the left guide wall.
Fig. 3
For giving more information about flow pattern at the left and right guide wall, Fig. 4 shows the flow pattern at the right side guide wall and Fig. 5 shows the flow pattern at the left side guide wall.
Fig. 4Fig. 5
With regard to Figs. 4 and 5 and observing the streamlines, at discharge equal to 80 (L/s), the right wall has suitable performance but the left wall has no suitable performance and the left wall of the geometric design creates a secondary and circular flow, and vortex motion in the beginning of the entrance of spillway that creates cross waves at the beginning of spillway. By increasing the flow rate (Q = 100 L/s), at the inlet spillway secondary flows and vortex were removed, but the streamline is severely distorted. Results of the guide wall performances at the Q = 100 (L/s) are shown in Fig. 6.
Fig. 6
Also more information about the performance of each guide wall can be derived from Figs. 7 and 8. These figures uphold that the secondary and vortex flows were removed, but the streamlines were fully diverted specifically near the left side guide wall.
Fig. 7Fig. 8
As mentioned in the past, these secondary and vortex flows and diversion in streamline cause nonuniformity and create cross wave through the spillway. Figure 9 shows the cross waves at the crest of the spillway.
Fig. 9
The performance of guide walls at the Q = 120 (L/s) also was assessed. The result of simulation is shown in Fig. 10. Figures 11 and 12 show a more clear view of the streamlines near to right and left side guide wall, respectively. As seen in Fig. 12, the left side wall still causes vortex flow and creation of and diversion in streamline.
Fig. 10Fig. 11Fig. 12
The results of the affected left side guide wall shape on the cross wave creation are shown in Fig. 13. As seen from Fig. 3, the left side guide wall also causes cross wave at the spillway crest.
Fig. 13
As can be seen clearly in Figs. 9 and 13, by moving from the left side to the right side of the spillway, the cross waves and the nonuniformity in flow is removed. By reviewing Figs. 9 and 13, it is found that the right side guide wall removes the cross waves and nonuniformity. With this point as aim, a geometry similar to the right side guide wall was considered instead of the left side guide wall. The result of simulation for Q = 120 (L/s) is shown in Fig. 14. As seen from this figure, the proposed geometry for the left side wall has suitable performance smoothly passing the flow through the approach channel and spillway.
Fig. 14
More information about the proposed shape for the left guide wall is shown in Fig. 15. As seen from this figure, this shape has suitable performance for removing the cross waves and vortex flows.
Fig. 15
Figure 16 shows the cross section of flow at the crest of spillway. As seen in this figure, the proposed shape for the left side guide wall is suitable for removing the cross waves and secondary flows.
Fig. 16
Conclusion
Analysis of behavior and hydraulic properties of flow over the spillway dam is a complicated task which is cost and time intensive. Several techniques suitable to the purposes of study have been undertaken in this research. Physical modeling, usage of expert experience, usage of mathematical models on simulation flow in one-dimensional, two-dimensional and three-dimensional techniques, are some of the techniques utilized to study this phenomenon. The results of the modeling show that the CFD technique is a suitable tool for simulating the flow pattern in the guide wall. Using this tools helps the designer for developing the optimal shape for hydraulic structure which the flow pattern through them are important.
References
Chanson H (2004) 19—Design of weirs and spillways. In: Chanson H (ed) Hydraulics of open channel flow, 2nd edn. Butterworth-Heinemann, Oxford, pp 391–430ChapterGoogle Scholar
Chatila J, Tabbara M (2004) Computational modeling of flow over an ogee spillway. Comput Struct 82:1805–1812ArticleGoogle Scholar
Das MM, Saikia MD (2009) Irrigation and water power engineering. PHI Learning, New DelhiGoogle Scholar
E, Department Of Army: U.S. Army Corps (2013) Hydraulic Design of Spillways. BiblioBazaar, CharlestonGoogle Scholar
Fattor C, Bacchiega J (2009) Design conditions for morning-glory spillways: application to potrerillos dam spillway. Adv Water Res Hydraul Eng Springer, Berlin, pp 2123–2128Google Scholar
Gessler D (2005) CFD modeling of spillway performance. Impacts Glob Clim Change. doi:10.1061/40792(173)398
Kim D-G (2007) Numerical analysis of free flow past a sluice gate. KSCE J Civ Eng 11:127–132ArticleGoogle Scholar
Kim D, Park J (2005) Analysis of flow structure over ogee-spillway in consideration of scale and roughness effects by using CFD model. KSCE J Civ Eng 9:161–169ArticleGoogle Scholar
Kim S, Yu K, Yoon B, Lim Y (2012) A numerical study on hydraulic characteristics in the ice Harbor-type fishway. KSCE J Civ Eng 16:265–272ArticleGoogle Scholar
Ma X-D, Dai G-Q, Yang Q, Li G-J, Zhao L (2010) Analysis of influence factors of cavity length in the spillway tunnel downstream of middle gate chamber outlet with sudden lateral enlargement and vertical drop aerator. J Hydrodyn Ser B 22:680–686ArticleGoogle Scholar
Milési G, Causse S (2014) 3D numerical modeling of a side-channel spillway. In: Gourbesville P, Cunge J, Caignaert G (eds) Advances in hydroinformatics. Springer, Singapore, pp 487–498ChapterGoogle Scholar
Montagna F, Bellotti G, Di Risio M (2011) 3D numerical modeling of landslide-generated tsunamis around a conical island. Nat Hazards 58:591–608ArticleGoogle Scholar
Novak P, Moffat AIB, Nalluri C, Narayanan R (2007) Hydraulic structures. Taylor & Francis, LondonGoogle Scholar
Parsaie A, Haghiabi A (2015a) Computational modeling of pollution transmission in rivers. Appl Water Sci. doi:10.1007/s13201-015-0319-6
Parsaie A, Haghiabi A (2015b) The effect of predicting discharge coefficient by neural network on increasing the numerical modeling accuracy of flow over side weir. Water Res Manag 29:973–985ArticleGoogle Scholar
Parsaie A, Yonesi H, Najafian S (2015) Predictive modeling of discharge in compound open channel by support vector machine technique. Model Earth Syst Environ 1:1–6ArticleGoogle Scholar
Su P-L, Liao H-S, Qiu Y, Li CJ (2009) Experimental study on a new type of aerator in spillway with low Froude number and mild slope flow. J Hydrodyn Ser B 21:415–422ArticleGoogle Scholar
Suprapto M (2013) Increase spillway capacity using Labyrinth Weir. Procedia Eng 54:440–446ArticleGoogle Scholar
Tabbara M, Chatila J, Awwad R (2005) Computational simulation of flow over stepped spillways. Comput Struct 83:2215–2224ArticleGoogle Scholar
Wang J, Chen H (2009) Experimental study of elimination of vortices along guide wall of bank spillway. Adv Water Res Hydraul Eng Springer, Berlin, pp 2059–2063Google Scholar
Wang Y, Jiang C (2010) Investigation of the surface vortex in a spillway tunnel intake. Tsinghua Sci Technol 15:561–565ArticleGoogle Scholar
Zhenwei MU, Zhiyan Z, Tao Z (2012) Numerical simulation of 3-D flow field of spillway based on VOF method. Procedia Eng 28:808–812ArticleGoogle Scholar
Parsaie, A., Haghiabi, A.H. & Moradinejad, A. CFD modeling of flow pattern in spillway’s approach channel. Sustain. Water Resour. Manag.1, 245–251 (2015). https://doi.org/10.1007/s40899-015-0020-9
by Faizal Yusuf, M.A.Sc., P.Eng. Specialist Engineer in the Hydrotechnical Department at BC Hydro
BC Hydro, a public electric utility in British Columbia, uses FLOW-3D to investigate complex hydraulics issues at several existing dams and to assist in the design and optimization of proposed facilities.
Faizal Yusuf, M.A.Sc., P.Eng., Specialist Engineer in the Hydrotechnical department at BC Hydro, presents three case studies that highlight the application of FLOW-3D to different types of spillways and the importance of reliable prototype or physical hydraulic model data for numerical model calibration.
W.A.C. Bennett Dam At W.A.C. Bennett Dam, differences in the spillway geometry between the physical hydraulic model from the 1960s and the prototype make it difficult to draw reliable conclusions on shock wave formation and chute capacity from physical model test results. The magnitude of shock waves in the concrete-lined spillway chute are strongly influenced by a 44% reduction in the chute width downstream of the three radial gates at the headworks, as well as the relative openings of the radial gates. The shock waves lead to locally higher water levels that have caused overtopping of the chute walls under certain historical operations.Prototype spill tests for discharges up to 2,865 m3/s were performed in 2012 to provide surveyed water surface profiles along chute walls, 3D laser scans of the water surface in the chute and video of flow patterns for FLOW-3D model calibration. Excellent agreement was obtained between the numerical model and field observations, particularly for the location and height of the first shock wave at the chute walls (Figure 1).
W.A.C에서 Bennett Dam, 1960년대의 물리적 수력학 모델과 프로토타입 사이의 여수로 형상의 차이로 인해 물리적 모델 테스트 결과에서 충격파 형성 및 슈트 용량에 대한 신뢰할 수 있는 결론을 도출하기 어렵습니다. 콘크리트 라이닝 방수로 낙하산의 충격파 크기는 방사형 게이트의 상대적인 개구부뿐만 아니라 헤드워크에 있는 3개의 방사형 게이트 하류의 슈트 폭이 44% 감소함에 따라 크게 영향을 받습니다. 충격파는 특정 역사적 작업에서 슈트 벽의 범람을 야기한 국부적으로 더 높은 수위로 이어집니다. 최대 2,865m3/s의 배출에 대한 프로토타입 유출 테스트가 2012년에 수행되어 슈트 벽을 따라 조사된 수면 프로필, 3D 레이저 스캔을 제공했습니다. FLOW-3D 모델 보정을 위한 슈트의 수면 및 흐름 패턴 비디오. 특히 슈트 벽에서 첫 번째 충격파의 위치와 높이에 대해 수치 모델과 현장 관찰 간에 탁월한 일치가 이루어졌습니다(그림 1).
Figure 1. Comparison between prototype observations and FLOW-3D for a spill discharge of 2,865 m^3/s at Bennett Dam spillway.
The calibrated FLOW-3D model confirmed that the design flood could be safely passed without overtopping the spillway chute walls as long as all three radial gates are opened as prescribed in existing operating orders with the outer gates open more than the inner gate.
The CFD model also provided insight into the concrete damage in the spillway chute. Cavitation indices computed from FLOW-3D simulation results were compared with empirical data from the USBR and found to be consistent with the historical performance of the spillway. The numerical analysis supported field inspections, which concluded that deterioration of the concrete conditions in the chute is likely not due to cavitation.
Strathcona Dam FLOW-3D was used to investigate poor approach conditions and uncertainties with the rating curves for Strathcona Dam spillway, which includes three vertical lift gates on the right abutment of the dam. The rating curves for Strathcona spillway were developed from a combination of empirical adjustments and limited physical hydraulic model testing in a flume that did not include geometry of the piers and abutments.
Numerical model testing and calibration was based on comparisons with prototype spill observations from 1982 when all three gates were fully open, resulting in a large depression in the water surface upstream of the leftmost bay (Figure 2). The approach flow to the leftmost bay is distorted by water flowing parallel to the dam axis and plunging over the concrete retaining wall adjacent to the upstream slope of the earthfill dam. The flow enters the other two bays much more smoothly. In addition to very similar flow patterns produced in the numerical model compared to the prototype, simulated water levels at the gate section matched 1982 field measurements to within 0.1 m.
보정된 FLOW-3D 모델은 외부 게이트가 내부 게이트보다 더 많이 열려 있는 기존 운영 명령에 규정된 대로 3개의 방사형 게이트가 모두 열리는 한 여수로 낙하산 벽을 넘지 않고 설계 홍수를 안전하게 통과할 수 있음을 확인했습니다.
CFD 모델은 방수로 낙하산의 콘크리트 손상에 대한 통찰력도 제공했습니다. FLOW-3D 시뮬레이션 결과에서 계산된 캐비테이션 지수는 USBR의 경험적 데이터와 비교되었으며 여수로의 역사적 성능과 일치하는 것으로 나타났습니다. 수치 분석은 현장 검사를 지원했으며, 슈트의 콘크리트 상태 악화는 캐비테이션 때문이 아닐 가능성이 높다고 결론지었습니다.
Strathcona 댐 FLOW-3D는 Strathcona Dam 여수로에 대한 등급 곡선을 사용하여 열악한 접근 조건과 불확실성을 조사하는 데 사용되었습니다. 여기에는 댐의 오른쪽 접합부에 3개의 수직 리프트 게이트가 포함되어 있습니다. Strathcona 여수로에 대한 등급 곡선은 경험적 조정과 교각 및 교대의 형상을 포함하지 않는 수로에서 제한된 물리적 수리 모델 테스트의 조합으로 개발되었습니다.
수치 모델 테스트 및 보정은 세 개의 수문이 모두 완전히 개방된 1982년의 프로토타입 유출 관측과의 비교를 기반으로 했으며, 그 결과 가장 왼쪽 만의 상류 수면에 큰 함몰이 발생했습니다(그림 2). 최좌단 만으로의 접근 흐름은 댐 축과 평행하게 흐르는 물과 흙채움댐의 상류 경사면에 인접한 콘크리트 옹벽 위로 떨어지는 물에 의해 왜곡됩니다. 흐름은 훨씬 더 원활하게 다른 두 베이로 들어갑니다. 프로토타입과 비교하여 수치 모델에서 생성된 매우 유사한 흐름 패턴 외에도 게이트 섹션에서 시뮬레이션된 수위는 1982년 현장 측정과 0.1m 이내로 일치했습니다.
Figure 2. Prototype observations and FLOW-3D results for a Strathcona Dam spill in 1982 with all three gates fully open.
The calibrated CFD model produces discharges within 5% of the spillway rating curve for the reservoir’s normal operating range with all gates fully open. However, at higher reservoir levels, which may occur during passage of large floods (as shown in Figure 3), the difference between simulated discharges and the rating curves are greater than 10% as the physical model testing with simplified geometry and empirical corrections did not adequately represent the complex approach flow patterns. The FLOW-3D model provided further insight into the accuracy of rating curves for individual bays, gated conditions and the transition between orifice and free surface flow.
보정된 CFD 모델은 모든 게이트가 완전히 열린 상태에서 저수지의 정상 작동 범위에 대한 여수로 등급 곡선의 5% 이내에서 배출을 생성합니다. 그러나 대규모 홍수가 통과하는 동안 발생할 수 있는 더 높은 저수지 수위에서는(그림 3 참조) 단순화된 기하학과 경험적 수정을 사용한 물리적 모델 테스트가 그렇지 않았기 때문에 모의 배출과 등급 곡선 간의 차이는 10% 이상입니다. 복잡한 접근 흐름 패턴을 적절하게 표현합니다. FLOW-3D 모델은 개별 베이, 게이트 조건 및 오리피스와 자유 표면 흐름 사이의 전환에 대한 등급 곡선의 정확도에 대한 추가 통찰력을 제공했습니다.
Figure 3. FLOW-3D results for Strathcona Dam spillway with all gates fully open at an elevated reservoir level during passage of a large flood. Note the effects of poor approach conditions and pier overtopping at the leftmost bay.
John Hart Dam The John Hart concrete dam will be modified to include a new free crest spillway to be situated between an existing gated spillway and a low level outlet structure that is currently under construction. Significant improvements in the design of the proposed spillway were made through a systematic optimization process using FLOW-3D.
The preliminary design of the free crest spillway was based on engineering hydraulic design guides. Concrete apron blocks are intended to protect the rock at the toe of the dam. A new right training wall will guide the flow from the new spillway towards the tailrace pool and protect the low level outlet structure from spillway discharges.
FLOW-3D model results for the initial and optimized design of the new spillway are shown in Figure 4. CFD analysis led to a 10% increase in discharge capacity, significant decrease in roadway impingement above the spillway crest and improved flow patterns including up to a 5 m reduction in water levels along the proposed right wall. Physical hydraulic model testing will be used to confirm the proposed design.
존 하트 댐 John Hart 콘크리트 댐은 현재 건설 중인 기존 배수로와 저층 배수로 사이에 위치할 새로운 자유 마루 배수로를 포함하도록 수정될 것입니다. FLOW-3D를 사용한 체계적인 최적화 프로세스를 통해 제안된 여수로 설계의 상당한 개선이 이루어졌습니다.
자유 마루 여수로의 예비 설계는 엔지니어링 수력학 설계 가이드를 기반으로 했습니다. 콘크리트 앞치마 블록은 댐 선단부의 암석을 보호하기 위한 것입니다. 새로운 오른쪽 훈련 벽은 새 여수로에서 테일레이스 풀로 흐름을 안내하고 여수로 배출로부터 낮은 수준의 배출구 구조를 보호합니다.
새 여수로의 초기 및 최적화된 설계에 대한 FLOW-3D 모델 결과는 그림 4에 나와 있습니다. CFD 분석을 통해 방류 용량이 10% 증가하고 여수로 마루 위의 도로 충돌이 크게 감소했으며 최대 제안된 오른쪽 벽을 따라 수위가 5m 감소합니다. 제안된 설계를 확인하기 위해 물리적 수압 모델 테스트가 사용됩니다.
Figure 4. FLOW-3D model results for the preliminary and optimized layout of the proposed spillway at John Hart Dam.
Conclusion
BC Hydro has been using FLOW-3D to investigate a wide range of challenging hydraulics problems for different types of spillways and water conveyance structures leading to a greatly improved understanding of flow patterns and performance. Prototype data and reliable physical hydraulic model testing are used whenever possible to improve confidence in the numerical model results.
다양한 유형의 여수로 및 물 수송 구조로 인해 흐름 패턴 및 성능에 대한 이해가 크게 향상되었습니다. 프로토타입 데이터와 신뢰할 수 있는 물리적 유압 모델 테스트는 수치 모델 결과의 신뢰도를 향상시키기 위해 가능할 때마다 사용됩니다.
About Flow Science, Inc. Based in Santa Fe, New Mexico USA, Flow Science was founded in 1980 by Dr. C. W. (Tony) Hirt, who was one of the principals in pioneering the “Volume-of-Fluid” or VOF method while working at the Los Alamos National Lab. FLOW-3D is a direct descendant of this work, and in the subsequent years, we have increased its sophistication with TruVOF, boasting pioneering improvements in the speed and accuracy of tracking distinct liquid/gas interfaces. Today, Flow Science products offer complete multiphysics simulation with diverse modeling capabilities including fluid-structure interaction, 6-DoF moving objects, and multiphase flows. From inception, our vision has been to provide our customers with excellence in flow modeling software and services.
화학적 CO 2 고정 및 이용 시스템 을 위한 수소 저장 합금을 이용한 수소 저장 시스템의 시뮬레이션 및 평가
K.NishimuraaC.InazumiaK.OgurobI.UeharacY.ItohdS.FujitanidI.YonezudaResearch Institute of Innovative Technology for the Earth, Ikeda City, Osaka 563-8577, JapanbOsaka National Research Institute, 1-8-31, Midorigaoka, Ikeda City, Osaka 563-8577, JapancToyama Industrial Technology Center, 150, Futagami-machi, Takaoka City, Toyama 933-0981, JapandSanyo Electric Co. Ltd, 1-18-13, Hashiridani, Hirakata-City, Osaka 573-8534, Japan
Two-dimensional model and simulation programs for designing a hydrogen storage vessel using hydrogen absorbing alloy with tubular heat exchanger were developed with the “Flow-3D” program in which physical properties of the hydrogen storage alloy were incorporated. The calculated results showed good agreement with experimental data obtained from 10 Nm3 scale hydrogen storage vessel with MmNi4.64Al0.36 alloy. It was concluded that this simulation program could be an adequate tool to design a practical scale hydrogen storage system for hydrogen from solid polymer electrolyte water electrolysis and to evaluate its hydrogen storage performance.
관형 열교환기를 갖는 수소흡수합금을 이용한 수소저장용기 설계를 위한 2차원 모델 및 시뮬레이션 프로그램은 수소저장합금의 물성을 반영한 “Flow-3D” 프로그램으로 개발하였다. 계산된 결과는 MmNi 4.64 Al 0.36 합금 이 있는 10 Nm 3 규모의 수소 저장 용기 에서 얻은 실험 데이터와 잘 일치하는 것으로 나타났습니다. 이 시뮬레이션 프로그램은 고체 고분자 전해질 물 전기분해에서 수소를 위한 실용적인 규모의 수소 저장 시스템을 설계하고 수소 저장 성능을 평가하는 데 적절한 도구가 될 수 있다는 결론을 내렸습니다.
Keywords
Hydrogen storage alloy, Chemical CO2 fixation and utilization systems, Simulation, Hydrogen storage vessel
Fig. 1. Schematic of the hydrogen storage vessel.Fig. 2. Cross-section of the reaction bed, tube exchangers and thermocouples (A±L).
References
[1] Masuda S. In: Book of abstracts of second international conference on carbon dioxide removal, 1994. p. 24±7. [2] Mayer U, Groll M, Supper W. J Less-Common Metals 1987;131:235±44. [3] Choi H, Mills AF. Int J Heat Mass Transfer 1990;33:1281±8. [4] Sun DW, Deng SJ. J Less-Common Metals 1989;155:271±9. [5] Sun DW, Deng SJ. Int J Hydrogen Energy 1990;15:807± 16. [6] Jemini A, Nasrallah B. Int J Hydrogen Energy 1995;20:43±52. [7] Fisher PW, Watson JS. Int J Hydrogen Energy 1983;8:109±19. [8] Suda S, Kobayashi N, Morishita E, Takemoto N. J Less-Common Metals 1983;89:325±32. [9] Fujitani S, Nakamura H, Furukawa A, Nasako K, Satoh K, Imoto T, Saito T, Yonezu I. Z Phys Chem Bd 1993;179:27. [10] Hahne E, Kallweit J. Int J Hydrogen Energy 1998;23:107±14. [11] Pons M, Dantzer P. J Less-Common Metals 1991;172(174):1147±56. [12] Pons M, Dantzer P, Guilleminot JJ. Int J Heat Mass Transfer 1993;36:2635±46. [13] Evance MJB, Everett DH. J Less-Common Metals 1976;49:13. [14] Pons M, Dantzer P. Int J Hydrogen Energy 1994;19:611±6.
이 연구에서 FLOW 3D 전산 유체 역학(CFD) 소프트웨어를 사용하여 파키스탄 Mirani 댐 방수로에 대한 에너지 소산 옵션으로 미국 매립지(USBR) 유형 II 및 USBR 유형 III 유역의 성능을 추정했습니다. 3D Reynolds 평균 Navier-Stokes 방정식이 해결되었으며, 여기에는 여수로 위의 자유 표면 흐름을 캡처하기 위해 공기 유입, 밀도 평가 및 드리프트-플럭스에 대한 하위 그리드 모델이 포함되었습니다. 본 연구에서는 5가지 모델을 고려하였다. 첫 번째 모델에는 길이가 39.5m인 USBR 유형 II 정수기가 있습니다. 두 번째 모델에는 길이가 44.2m인 USBR 유형 II 정수기가 있습니다. 3번째와 4 번째모델에는 길이가 각각 48.8m인 USBR 유형 II 정수조와 39.5m의 USBR 유형 III 정수조가 있습니다. 다섯 번째 모델은 네 번째 모델과 동일하지만 마찰 및 슈트 블록 높이가 0.3m 증가했습니다. 최상의 FLOW 3D 모델 조건을 설정하기 위해 메쉬 민감도 분석을 수행했으며 메쉬 크기 0.9m에서 최소 오차를 산출했습니다. 세 가지 경계 조건 세트가 테스트되었으며 최소 오류를 제공하는 세트가 사용되었습니다. 수치적 검증은 USBR 유형 II( L = 48.8m), USBR 유형 III( L = 35.5m) 및 USBR 유형 III 의 물리적 모델 에너지 소산을 0.3m 블록 단위로 비교하여 수행되었습니다( L= 35.5m). 통계 분석 결과 평균 오차는 2.5%, RMSE(제곱 평균 제곱근 오차) 지수는 3% 미만이었습니다. 수리학적 및 경제성 분석을 바탕으로 4 번째 모델이 최적화된 에너지 소산기로 밝혀졌습니다. 흡수된 에너지 백분율 측면에서 물리적 모델과 수치적 모델 간의 최대 차이는 5% 미만인 것으로 나타났습니다.
In this study, the FLOW 3D computational fluid dynamics (CFD) software was used to estimate the performance of the United States Bureau of Reclamation (USBR) type II and USBR type III stilling basins as energy dissipation options for the Mirani Dam spillway, Pakistan. The 3D Reynolds-averaged Navier–Stokes equations were solved, which included sub-grid models for air entrainment, density evaluation, and drift–flux, to capture free-surface flow over the spillway. Five models were considered in this research. The first model has a USBR type II stilling basin with a length of 39.5 m. The second model has a USBR type II stilling basin with a length of 44.2 m. The 3rd and 4th models have a USBR type II stilling basin with a length of 48.8 m and a 39.5 m USBR type III stilling basin, respectively. The fifth model is identical to the fourth, but the friction and chute block heights have been increased by 0.3 m. To set up the best FLOW 3D model conditions, mesh sensitivity analysis was performed, which yielded a minimum error at a mesh size of 0.9 m. Three sets of boundary conditions were tested and the set that gave the minimum error was employed. Numerical validation was done by comparing the physical model energy dissipation of USBR type II (L = 48.8 m), USBR type III (L =35.5 m), and USBR type III with 0.3-m increments in blocks (L = 35.5 m). The statistical analysis gave an average error of 2.5% and a RMSE (root mean square error) index of less than 3%. Based on hydraulics and economic analysis, the 4th model was found to be an optimized energy dissipator. The maximum difference between the physical and numerical models in terms of percentage energy absorbed was found to be less than 5%.
Abbasi S, Fatemi S, Ghaderi A, Di Francesco S (2021) The effect of geometric parameters of the antivortex on a triangular labyrinth side weir. Water (Switzerland) 13(1). https://doi.org/10.3390/w13010014
Amorim JCC, Amante RCR, Barbosa VD (2015) Experimental and numerical modeling of flow in a stilling basin. Proceedings of the 36th IAHR World Congress 28 June–3 July, the Hague, the Netherlands, 1, 1–6
Asaram D, Deepamkar G, Singh G, Vishal K, Akshay K (2016) Energy dissipation by using different slopes of ogee spillway. Int J Eng Res Gen Sci 4(3):18–22Google Scholar
Celik IB, Ghia U, Roache PJ, Freitas CJ, Coleman H, Raad PE (2008) Procedure for estimation and reporting of uncertainty due to discretization in CFD applications. J Fluids Eng Trans ASME 130(7):0780011–0780014. https://doi.org/10.1115/1.2960953ArticleGoogle Scholar
Chen Q, Dai G, Liu H (2002) Volume of fluid model for turbulence numerical simulation of stepped spillway overflow. J Hydraul Eng 128(7):683–688. 10.1061/共ASCE兲0733-9429共2002兲128:7共683兲 CE
Damiron R (2015) CFD modelling of dam spillway aerator. Lund University Sweden
Dunlop SL, Willig IA, Paul GE (2016) Cabinet Gorge Dam spillway modifications for TDG abatement – design evolution and field performance. 6th International Symposium on Hydraulic Structures: Hydraulic Structures and Water System Management, ISHS 2016, 3650628160, 460–470. 10.15142/T3650628160853
Frizell KW, Frizell KH (2015) Guidelines for hydraulic design of stepped spillways. Hydraulic Laboratory Report HL-2015-06, May
Ghaderi A, Abbasi S (2021) Experimental and numerical study of the effects of geometric appendance elements on energy dissipation over stepped spillway. Water (Switzerland) 13(7). https://doi.org/10.3390/w13070957
Ghaderi A, Dasineh M, Aristodemo F, Ghahramanzadeh A (2020) Characteristics of free and submerged hydraulic jumps over different macroroughnesses. J Hydroinform 22(6):1554–1572. https://doi.org/10.2166/HYDRO.2020.298ArticleGoogle Scholar
Nangare PB, Kote AS (2017) Experimental investigation of an ogee stepped spillway with plain and slotted roller bucket for energy dissipation. Int J Civ Eng Technol 8(8):1549–1555Google Scholar
Parsaie A, Moradinejad A, Haghiabi AH (2018) Numerical modeling of flow pattern in spillway approach channel. Jordan J Civ Eng 12(1):1–9Google Scholar
Pasbani Khiavi M, Ali Ghorbani M, Yusefi M (2021) Numerical investigation of the energy dissipation process in stepped spillways using finite volume method. J Irrig Water Eng 11(4):22–37Google Scholar
Peng Y, Zhang X, Yuan H, Li X, Xie C, Yang S, Bai Z (2019) Energy dissipation in stepped spillways with different horizontal face angles. Energies 12(23). https://doi.org/10.3390/en12234469
Raza A, Wan W, Mehmood K (2021) Stepped spillway slope effect on air entrainment and inception point location. Water (Switzerland) 13(10). https://doi.org/10.3390/w13101428
Rong Y, Zhang T, Peng L, Feng P (2019) Three-dimensional numerical simulation of dam discharge and flood routing in Wudu reservoir. Water (Switzerland) 11(10). https://doi.org/10.3390/w11102157
Saqib N, Akbar M, Pan H, Ou G, Mohsin M, Ali A, Amin A (2022) Numerical analysis of pressure profiles and energy dissipation across stepped spillways having curved risers. Appl Sci 12(448):1–18Google Scholar
Saqib N, Ansari K, Babar M (2021) Analysis of pressure profiles and energy dissipation across stepped spillways having curved treads using computational fluid dynamics. Intl Conf Adv Mech Eng :1–10
Saqib Nu, Akbar M, Huali P, Guoqiang O (2022) Numerical investigation of pressure profiles and energy dissipation across the stepped spillway having curved treads using FLOW 3D. Arab J Geosci 15(1):1363–1400. https://doi.org/10.1007/s12517-022-10505-8ArticleGoogle Scholar
Sarkardeh H, Marosi M, Roshan R (2015) Stepped spillway optimization through numerical and physical modeling. Int J Energy Environ 6(6):597–606Google Scholar
Valero D, Bung DB, Crookston BM, Matos J (2016) Numerical investigation of USBR type III stilling basin performance downstream of smooth and stepped spillways. 6th International Symposium on Hydraulic Structures: Hydraulic Structures and Water System Management, ISHS 2016, 3406281608, 635–646. https://doi.org/10.15142/T340628160853
aNational Cheng Kung University, Department of Mechanical Engineering, Tainan, Taiwan
bNational Cheng Kung University, Academy of Innovative Semiconductor and Sustainable Manufacturing, Tainan, Taiwan
cJum-bo Co., Ltd, Xinshi District, Tainan, Taiwan
Abstract
워블 전략이 포함된 펄스 레이저 용접(PLW) 방법을 사용하여 알루미늄 및 구리 이종 랩 조인트의 제조를 위한 최적의 가공 매개변수에 대해 실험 및 수치 조사가 수행됩니다. 피크 레이저 출력과 접선 용접 속도의 대표적인 조합 43개를 선택하기 위해 원형 패킹 설계 알고리즘이 먼저 사용됩니다.
선택한 매개변수는 PLW 프로세스의 전산유체역학(CFD) 모델에 제공되어 용융 풀 형상(즉, 인터페이스 폭 및 침투 깊이) 및 구리 농도를 예측합니다. 시뮬레이션 결과는 설계 공간 내에서 PLW 매개변수의 모든 조합에 대한 용융 풀 형상 및 구리 농도를 예측하기 위해 3개의 대리 모델을 교육하는 데 사용됩니다.
마지막으로, 대체 모델을 사용하여 구성된 처리 맵은 용융 영역에 균열이나 기공이 없고 향상된 기계적 및 전기적 특성이 있는 이종 조인트를 생성하는 PLW 매개변수를 결정하기 위해 세 가지 품질 기준에 따라 필터링됩니다.
제안된 최적화 접근법의 타당성은 최적의 용접 매개변수를 사용하여 생성된 실험 샘플의 전단 강도, 금속간 화합물(IMC) 형성 및 전기 접촉 저항을 평가하여 입증됩니다.
결과는 최적의 매개변수가 1209N의 높은 전단 강도와 86µΩ의 낮은 전기 접촉 저항을 생성함을 확인합니다. 또한 용융 영역에는 균열 및 기공과 같은 결함이 없습니다.
An experimental and numerical investigation is performed into the optimal processing parameters for the fabrication of aluminum and copper dissimilar lap joints using a pulsed laser welding (PLW) method with a wobble strategy. A circle packing design algorithm is first employed to select 43 representative combinations of the peak laser power and tangential welding speed. The selected parameters are then supplied to a computational fluidic dynamics (CFD) model of the PLW process to predict the melt pool geometry (i.e., interface width and penetration depth) and copper concentration. The simulation results are used to train three surrogate models to predict the melt pool geometry and copper concentration for any combination of the PLW parameters within the design space. Finally, the processing maps constructed using the surrogate models are filtered in accordance with three quality criteria to determine the PLW parameters that produce dissimilar joints with no cracks or pores in the fusion zone and enhanced mechanical and electrical properties. The validity of the proposed optimization approach is demonstrated by evaluating the shear strength, intermetallic compound (IMC) formation, and electrical contact resistance of experimental samples produced using the optimal welding parameters. The results confirm that the optimal parameters yield a high shear strength of 1209 N and a low electrical contact resistance of 86 µΩ. Moreover, the fusion zone is free of defects, such as cracks and pores.
Fig. 1. Schematic illustration of Al-Cu lap-joint arrangementFig. 2. Machine setup (MFQS-150W_1500WFig. 5. Lap-shear mechanical tests: (a) experimental setup and specimen dimensions, and (b) two different failures of lap-joint welding.
N. Thi Tien et al.
Fig. 9. Simulation and experimental results for melt pool profile. (a) Simulation results for melt pool cross-section, and (b) OM image of melt pool cross-section.
(Note that laser processing parameter of 830 W and 565 mm/s is chosen.).
CrossRefView Record in ScopusGoogle Scholar[11]S. Smith, J. Blackburn, M. Gittos, P. de Bono, and P. Hilton, “Welding of dissimilar metallic materials using a scanned laser beam,” in International Congress on Applications of Lasers & Electro-Optics, 2013, vol. 2013, no. 1: Laser Institute of America, pp. 493-502.
Welding strategies for joining copper and aluminum by fast oscillating, high quality laser beam
High-Power Laser Materials Processing: Applications, Diagnostics, and Systems IX, vol. 11273, International Society for Optics and Photonics (2020), p. 112730C
Experimental investigation on the effect of spot diameter on continuous-wave laser welding of copper and aluminum thin sheets for battery manufacturing
Systematic approach for determining optimal processing parameters to produce parts with high density in selective laser melting process
Int. J. Adv. Manuf. Technol., 105 (10) (2019), pp. 4443-4460 View PDF
CrossRefView Record in ScopusGoogle Scholar[32]A. Ascari, A. Fortunato, E. Liverani, and A. Lutey, “Application of different pulsed laser sources to dissimilar welding of Cu and Al alloys,” in Proceedings of Lasers in Manufacturing Conference (LIM), 2019.
본 연구에서는 범람으로 인한 토사댐 붕괴에 대한 테일워터 깊이의 영향을 실험적으로 조사하였다. 테일워터 깊이의 네 가지 다른 값을 검사합니다. 각 실험에 대해 댐 수심 측량 프로파일의 진화, 고장 기간, 침식 체적 및 유출 수위곡선을 관찰하고 기록합니다.
결과는 tailwater 깊이를 늘리면 고장 시간이 최대 57% 감소하고 상대적으로 침식된 마루 높이가 최대 77.6% 감소한다는 것을 보여줍니다. 또한 상대 배수 깊이가 3, 4, 5인 경우 누적 침식 체적의 감소는 각각 23, 36.5 및 75%인 반면 최대 유출량의 감소는 각각 7, 14 및 17.35%입니다.
실험 결과는 침식 과정을 복제할 때 Flow 3D 소프트웨어의 성능을 평가하는 데 활용됩니다. 수치 모델은 비응집성 흙댐의 침식 과정을 성공적으로 시뮬레이션합니다.
The influence of tailwater depth on earth dam failure due to overtopping is investigated experimentally in this work. Four different values of tailwater depths are examined. For each experiment, the evolution of the dam bathymetry profile, the duration of failure, the eroded volume, and the outflow hydrograph are observed and recorded. The results reveal that increasing the tailwater depth reduces the time of failure by up to 57% and decreases the relative eroded crest height by up to 77.6%. In addition, for relative tailwater depths equal to 3, 4, and 5, the reduction in the cumulative eroded volume is 23, 36.5, and 75%, while the reduction in peak discharge is 7, 14, and 17.35%, respectively. The experimental results are utilized to evaluate the performance of the Flow 3D software in replicating the erosion process. The numerical model successfully simulates the erosion process of non-cohesive earth dams.
Eroded height of the dam measured at distance of 0.7 m from the dam heel (cm)t
Total time of failure (sec)t1
Time of crest width erosion (sec)Zcrest
The crest height (cm)Vtotal
Total volume of the dam (m3)Veroded
Cumulative eroded volume (m3)RMSE
The statistical variable root- mean- square errord
Degree of agreement indexyu.s.
The upstream water depth (cm)yd.s
The downstream water depth (cm)H
Water surface elevation over sharp crested weir (cm)Q
Outflow discharge (liter/sec)Qpeak
Peak discharge (liter/sec)
1. Introduction
Earth dams are compacted structures composed of natural materials that are usually mined or quarried from local locations. The failures of the earth dams have proven to be deadly, destructive, and costly. According to People’s Daily, two earthen dams, Yong’an Dam and Xinfa Dam located in Hulun Buir City in North China’s Inner Mongolia failed on 2021, due to a surge in the water level of the Nuomin River caused by heavy rain. The dam breach affected 16,660 people, flooded 325,622 mu of farmland (21708.1 ha), and destroyed 22 bridges, 124 culverts, and 15.6 km of roadways. Also, the failure of south fork dam (earth and rock fill dam) near Johnstown on 1889 is considered the worst U.S dam disaster in terms of loss of life. The dam was overtopped and washed away due to unexpected heavy rains, releasing 20 million tons of water which destroyed Johnstown and resulted in 2209 deaths, [1], [2]. Piping or shear sliding, failure due to natural factors, and failure due to overtopping are all possible causes of earth dam failure. However, overtopping failure is the most frequent cause of dam failure. According to The International Committee on Large Dams (ICOLD, 1995), and [3], more than one-third of the total known dam failures were caused by dam overtopping.
Overtopping occurs as the result of insufficient flood design or freeboard in some cases. Extreme rainstorms can cause floods which can overtop the dam and cause it to fail. The size and geometry of the reservoir or the dam (side slopes, top width, height, etc.), the homogeneity of the material used in the construction of the dam, overtopping depth, and the presence or absence of tailwater are all elements that influence this type of failure which will be illustrated in the following literature. Overtopping failures of earth dams may be divided into several failure mechanisms based on the material composition and the inner structure of the dam. For cohesive earth dams because of low permeability, no seepage exists on the slopes. Erosion often begins at the earth dam toe during turbulent erosion and moves upstream, undercutting the slope, causing the removal of large chunks of materials. While for non-cohesive earth dams the downstream face of the dam flattens progressively and is often said to rotate around a point near the downstream toe [4], [5], [6] In the last few decades, the study of failures due to overtopping has gained popularity among researchers. The overtopping failure, in fact, has been widely investigated in coastal and river hydraulics and morpho dynamic. In addition, several laboratory experimental studies have been conducted in this field in order to better understand different involved factors. Also, many numerical types of research have been conducted to investigate the process of overtopping failure as well as the elements that influence this type of failure.
Tabrizi et al. [5] conducted a series of embankment overtopping tests to find the effect of compaction on the failure of a homogenous sand embankment. A plane breach process occurred across the flume width due to the narrow flume width. They measured the downstream hydrographs and embankment surface profile for every case. They concluded that the peak discharge decreased with a high compaction level, while the time to peak increased. Kansoh et al. [6] studied experimentally the failure of compacted homogeneous non-cohesive earthen embankment due to overtopping. They investigated the influence of different shape parameters including the downstream slope, the crest width, and the height of the embankment on the erosion process. The erosion process was initiated by carving a pilot channel into the embankment crest. They evaluated the time of embankment failure for different shape parameters. They concluded that the failure time increases with increasing the downstream slope and the crest width. Zhu et al. [7] investigated experimentally the breaching of five embankments, one constructed with pure sand, and four with different sand-silt–clay mixtures. The erosion pattern was similar across the flume width. They stated that for cohesive soil mixtures the head cut erosion was the most important factor that affected the breach growth, while for non-cohesive soil the breach erosion was affected by shear erosion.
Amaral et al. [8] studied experimentally the failure by overtopping for two embankments built from silt sand material. They studied the effect of the degree of compaction of the embankment and the geometry of the pilot channel carved at the centre of the dam crest. They studied two shapes of pilot channel a rectangular shape and triangular shape. They stated that the breach development is influenced by a higher degree of compaction, however, the pilot channel geometry did not influence the breach’s final form. Bereta et al. [9] studied experimentally the breach formation of five dam models, three of them were homogenous clay soil while two were sandy-clay mixtures. The erosion process was initiated by cutting a pilot channel at the centre of the dam crest. They observed the initiation of erosion, flow shear erosion, sidewall bottom erosion, and distinguished the soil mechanical slope mass failure from the head cut vertically and laterally during these tests. Verma et al. [10] investigated experimentally a two-dimensional erosion phenomenon due to overtopping by using a wooden fuse plug model and five different soils. They concluded that the erosion process was affected mostly by cohesiveness and degree of compaction. For cohesive soils, a head cut erosion was observed, while for non-cohesive soils surface erosion occurred gradually. Also, the dimensions of fuse plug, type of fill material, reservoir capacity, and inflow were found to affect the behaviour of the overall breaching process.
Wu and Qin [11] studied the effect of adding coarse grains to the downstream face of a non-cohesive dam as a result of tailings deposition. The process of overtopping during tailings dam failures is analyzed and its effect on delaying the dam-break process and disaster mitigation are investigated. They found that the tested protective measures decreased the breach area, the maximum breaching flow discharge and flow velocity, and the downstream inundated area. Khankandi et al. [12] studied experimentally the effect of reservoir geometry on dam break flow in case of dry and wet bed conditions. They considered four different reservoir shapes, a long reservoir, a wide, a trapezoidal shaped and one with a 90◦ bend all with identical water volume and horizontal bed. The dam break is simulated by the sudden gate removal using a pneumatic jack. They measured the variation of water level over time with ultrasonic sensors and flow velocity component with an acoustic Doppler velocimeter. Also, the experimental results of water level variation are compared with Ritters solution (1892) [13]. They stated that for dry bed condition the long and 90 bend reservoirs results are close to the analytical solution by ritter also in these two shapes a 1D flow is noticed. However, for wide and trapezoidal reservoirs a 2D effect is significant due to flow contraction at channel entrance.
Rifai et al. [14] conducted a series of experiments to investigate the effect of tailwater depth on the outflow discharge and breach geometry during non-cohesive homogenous fluvial dikes overtopping failure. They cut an initial notch in the crest at 0.8 m from the upstream end of the dike to initiate overtopping. They compared their results to previous experiments under different main channel inflow discharges combined with a free floodplain. They divided the dike breaching process into three stages: gradual start of overtopping flow resulting in slow initiation of dike erosion, deepening and widening breach due to large flow depth and velocity, finally the flow depth starts stabilizing at its minimal level with or without sustained breach expansion. They stated that breach discharge has lower values than in free floodplain tests. Jiang [15] studied the effect of bed slope on breach parameters and peak discharge in non-cohesive embankment failure. An initial triangular breach with a depth and width of 4 cm was pre-set on one side of the dam. He stated that peak discharge increases with the increase of bed slope and then decreases.
Ozmen-cagatay et al. [16] studied experimentally flood wave propagation resulted from a sudden dam break event. For dam-break modelling, they used a mechanism that permitted the rapid removal of a vertical plate with a thickness of 4 mm and made of rigid plastic. They conducted three tests, one with dry bed condition and two tests with tailwater depths equal 0.025 m and 0.1 m respectively. They recorded the free surface profile during initial stages of dam break by using digital image processing. Finally, they compared the experimental results with the with a commercially available VOF-based CFD program solving the Reynolds-averaged Navier –Stokes equations (RANS) with the k– Ɛ turbulence model and the shallow water equations (SWEs). They concluded that Wave breaking was delayed with increasing the tailwater depth to initial reservoir depth ratio. They also stated that the SWE approach is sufficient more to represent dam break flows for wet bed condition. Evangelista [17] investigated experimentally and numerically using a depth-integrated two-phase model, the erosion of sand dike caused by the impact of a dam break wave. The dam break is simulated by a sudden opening of an upstream reservoir gate resulting in the overtopping of a downstream trapezoidal sand dike. The evolution of the water wave caused from the gate opening and dike erosion process are recorded by using a computer-controlled camera. The experimental results demonstrated that the progression of the wave front and dike erosion have a considerable influence on each other during the process. In addition, the dike constructed from fine sands was more resistant to erosion than the one built with coarse sand. They also stated that the numerical model can is capable of accurately predicting wave front position and dike erosion. Also, Di Cristo et al. [18] studied the effect of dam break wave propagation on a sand embankment both experimentally and numerically using a two-phase shallow-water model. The evolution of free surface and of the embankment bottom are recorded and used in numerical model assessment. They stated that the model allows reasonable simulation of the experimental trends of the free surface elevation regardeless of the geofailure operator.
Lots of numerical models have been developed over the past few years to simulate the dam break flooding problem. A one-dimensional model, such as Hec-Ras, DAMBRK and MIKE 11, ect. A two-dimensional model such as iRIC Nay2DH is used in earth embankment breach simulation. Other researchers studied the failure process numerically using (3D) computational fluid dynamics (CFD) models, such as FLOW-3D, and FLUENT. Goharnejad et al. [19] determined the outflow hydrograph which results from the embankment dam break due to overtopping. Hu et al. [20] performed a comparison between Flow-3D and MIKE3 FM numerical models in simulating a dam break event under dry and wet bed conditions with different tailwater depths. Kaurav et al. [21] simulated a planar dam breach process due to overtopping. They conducted a sensitivity analysis to find the effect of dam material, dam height, downstream slope, crest width, and inlet discharge on the erosion process and peak discharge through breach. They concluded that downstream slope has a significant influence on breaching process. Yusof et al. [22] studied the effect of embankment sediment sizes and inflow rates on breaching geometric and hydrodynamic parameters. They stated that the peak outflow hydrograph increases with increasing sediment size and inflow rates while time of failure decreases.
In the present work, the effect of tailwater depth on earth dam failure during overtopping is studied experimentally. The relation between the eroded volume of the dam and the tailwater depth is presented. Also, the percentage of reduction in peak discharge due to tailwater existence is calculated. An assessment of Flow 3D software performance in simulating the erosion process during earth dam failure is introduced. The statistical variable root- mean- square error, RMSE, and the agreement degree index, d, are used in model assessment.
2. Material and methods
The tests are conducted in a straight rectangular flume in the laboratory of Irrigation Engineering and Hydraulics Department, Faculty of Engineering, Alexandria University, Egypt. The flume dimensions are 10 m long, 0.86 m wide, and 0.5 m deep. The front part of the flume is connected to a storage basin 1 m long by 0.86 m wide. The storage basin is connected to a collecting tank for water recirculation during the experiments as shown in Fig. 1, Fig. 2. A sharp-crested weir is placed at a distance of 4 m downstream the constructed dam to keep a constant tailwater depth in each experiment and to measure the outflow discharge.
To measure the eroded volume with time a rods technique is used. This technique consists of two parallel wooden plates with 10 cm distance in between and five rows of stainless-steel rods passing vertically through the wooden plates at a spacing of 20 cm distributed across flume width. Each row consists of four rods with 15 cm spacing between them. Also, a graph board is provided to measure the drop in each rod with time as shown in Fig. 3, Fig. 4. After dam construction the rods are carefully rested on the dam, with the first line of rods resting in the middle of the dam crest and then a constant distance of 15 cm between rods lines is maintained.
A soil sample is taken and tested in the laboratory of the soil mechanics to find the soil geotechnical parameters. The soil particle size distribution is also determined by sieve analysis as shown in Fig. 5. The soil mean diameter d50,equals 0.38 mm and internal friction angle equals 32.6°.
2.1. Experimental procedures
To investigate the effect of the tailwater depth (do), the tailwater depth is changed four times 5, 15, 20, and 25 cm on the sand dam model. The dam profile is 35 cm height, with crest width = 15 cm, the dam base width is 155 cm, and the upstream and downstream slopes are 2:1 as shown in Fig. 6. The dam dimensions are set as the flume permitted to allow observation of the dam erosion process under the available flume dimensions and conditions. All of the conducted experiments have the same dimensions and configurations.
The optimum water content, Wc, from the standard proctor test is found to be 8 % and the maximum dry unit weight is 19.42 kN/m3. The soil and water are mixed thoroughly to ensure consistency and then placed on three horizontal layers. Each layer is compacted according to ASTM standard with 25 blows by using a rammer (27 cm × 20.5 cm) weighing 4 kg. Special attention is paid to the compaction of the soil to guarantee the repeatability of the tests.
After placing and compacting the three layers, the dam slopes are trimmed carefully to form the trapezoidal shape of the dam. A small triangular pilot channel with 1 cm height and 1:1 side slopes is cut into the dam crest to initiate the erosion process. The position of triangular pilot channel is presented in Fig. 1. Three digital video cameras with a resolution of 1920 × 1080 pixels and a frame rate of 60 fps are placed in three different locations. One camera on one side of the flume to record the progress of the dam profile during erosion. Another to track the water level over the sharp-crested rectangular weir placed at the downstream end of the flume. And the third camera is placed above the flume at the downstream side of the dam and in front of the rods to record the drop of the tip of the rods with time as shown previously in Fig. 1.
Before starting the experiment, the water is pumped into the storage basin by using pump with capacity 360 m3/hr, and then into the upstream section of the flume. The upstream boundary is an inflow condition. The flow discharge provided to the storage basin is kept at a constant rate of 6 L/sec for all experiments, while the downstream boundary is an outflow boundary condition.
Also, the required tailwater depth for each experiment is filled to the desired depth. A dye container valve is opened to color the water upstream of the dam to make it easy to distinguish the dam profile from the water profile. A wooden board is placed just upstream of the dam to prevent water from overtopping the dam until the water level rises to a certain level above the dam crest and then the wooden board is removed slowly to start the experiment.
2.2. Repeatability
To verify the accuracy of the results, each experiment is repeated two times under the same conditions. Fig. 7 shows the relative eroded crest height, Zeroded / Zo, with time for 5 cm tailwater depth. From the Figure, it can be noticed that results for all runs are consistent, and accuracy is achieved.
3. Numerical model
The commercially available numerical model, Flow 3D is used to simulate the dam failure due to overtopping for the cases of 15 cm, 20 cm and 25 cm tailwater depths. For numerical model calibration, experimental results for dam surface evolution are used. The numerical model is calibrated for selection of the optimal turbulence model (RNG, K-e, and k-w) and sediment scour equations (Van Rin, Meyer- peter and Muller, and Nielsen) that produce the best results. In this, the flow field is solved by the RNG turbulence model, and the van Rijn equation is used for the sediment scour model. A geometry file is imported before applying the mesh.
A Mesh sensitivity is analyzed and checked for various cell sizes, and it is found that decreasing the cell size significantly increases the simulation time with insignificant differences in the result. It is noticed that the most important factor influencing cell size selection is the value of the dam’s upstream and downstream slopes. For example, the slopes in the dam model are 2:1, thus the cell size ratio in X and Z directions should be 2:1 as well. The cell size in a mesh block is set to be 0.02 m, 0.025 m, and 0.01 m in X, Y and Z directions respectively.
In the numerical computations, the boundary conditions employed are the walls for sidewalls and the channel bottom. The pressure boundary condition is applied at the top, at the air–water interface, to account for atmospheric pressure on the free surface. The upstream boundary is volume flow rate while the downstream boundary is outflow discharge.
The initial condition is a fluid region, which is used to define fluid areas both upstream and downstream of the dam. To assess the model accuracy, the statistical variable root- mean- square error, RMSE, and the agreement degree index, d, are calculated as(1)RMSE=1N∑i=1N(Pi-Mi)2(2)d=1-∑Mi-Pi2∑Mi-M¯+Pi-P¯2
where N is the number of samples, Pi and Mi are the models and experimental values, P and M are the means of the model and experimental values. The best fit between the experimental and model results would have an RMSE = 0 and degree of agreement, d = 1.
4. Results of experimental work
The results of the total time of failure, t (defined as the time from when the water begins to overtop the dam crest until the erosion reaches a steady state, when no erosion occurs), time of crest width erosion t1, cumulative eroded volume Veroded, and peak discharge Qpeak for each experiment are listed in Table 1. The case of 5 cm tailwater depth is considered as a reference case in this work.
Table 1. Results of experimental work.
Tailwater depth, do (cm)
Total time of failure, t (sec)
Time of crest width erosion, t1 (sec)
cumulative eroded volume, Veroded (m3)
Peak discharge, Qpeak (liter/sec)
5
255
22
0.21
13.12
15
165
30
0.16
12.19
20
140
34
0.13
11.29
25
110
39
0.05
10.84
5. Discussion
5.1. Side erosion
The evolution of the bathymetry of the erosion line recorded by the video camera1. The videos are split into frames (60 frames/sec) by the Free Video to JPG Converter v.5.063 build and then converted into an excel spreadsheet using MATLAB code as shown in Fig. 8.
Fig. 9 shows a sample of numerical model output. Fig. 10, Fig. 11, Fig. 12 show a dam profile development for different time steps from both experimental and numerical model, for tailwater depths equal 15 cm, 20 cm and 25 cm. Also, the values of RMSE and d for each figure are presented. The comparison shows that the Flow 3D software can simulate the erosion process of non-cohesive earth dam during overtopping with an RMSE value equals 0.023, 0.0218, and 0.0167 and degree of agreement, d, equals 0.95, 0.968, and 0.988 for relative tailwater depths, do/(do)ref, = 3, 4 and 5, respectively. The low values of RMSE and high values of d show that the Flow 3D can effectively simulate the erosion process. From Fig. 10, Fig. 11, Fig. 12, it can be noticed that the model is not capable of reproducing the head cut, while it can simulate well the degradation of the crest height with a minor difference from experimental work. The reason of this could be due to inability of simulation of all physical conditions which exists in the experimental work, such as channel friction and the grain size distribution of the dam soil which is surely has a great effect on the erosion process and breach development. In the experimental work the grain size distribution is shown in Fig. 5, while the numerical model considers that the soil is uniform and exactly 50 % of the dam particles diameter are equal to the d50 value. Another reason is that the model is not considering the increased resistance of the dam due to the apparent cohesion which happens due to dam saturation [23].
It is clear from both the experimental and numerical results that for a 5 cm tailwater depth, do/(do)ref = 1.0, erosion begins near the dam toe and continues upward on the downstream slope until it reaches the crest. After eroding the crest width, the crest is lowered, resulting in increased flow rates and the speeding up of the erosion process. While for relative tailwater depths, do/(do)ref = 3, 4, and 5 erosion starts at the point of intersection between the downstream slope and tailwater. The existence of tailwater works as an energy dissipater for the falling water which reduces the erosion process and prevents the dam from failure as shown in Fig. 13. It is found that the time of the failure decreases with increasing the tailwater depth because most of the dam height is being submerged with water which decreases the erosion process. The reduction in time of failure from the referenced case is found to be 35.3, 45, and 57 % for relative tailwater depth, do /(do)ref equals 3, 4, and 5, respectively.
The relation between the relative eroded crest height, Zeroded /Zo, with time is drawn as shown in Fig. 14. It is found that the relative eroded crest height decreases with increasing tailwater depth by 10, 41, and 77.6 % for relative tailwater depth, do /(do)ref equals 3, 4, and 5, respectively. The time required for the erosion of the crest width, t1, is calculated for each experiment. The relation between relative tailwater depth and relative time of crest width erosion is shown in Fig. 15. It is found that the time of crest width erosion increases linearly with increasing, do /Zo. The percent of increase is 36.4, 54.5 and 77.3 % for relative tailwater depth, do /(do)ref = 3, 4 and 5, respectively.
Crest height, Zcrest is calculated from the experimental results and the Flow 3D results for relative tailwater depths, do/(do)ref, = 3, 4, and 5. A relation between relative crest height, Zcrest/Zo with time from experimental and numerical results is presented in Fig. 16. From Fig. 16, it is seen that there is a good consistency between the results of numerical model and the experimental results in the case of tracking the erosion of the crest height with time.
5.2. Upstream and downstream water depths
It is noticed that at the beginning of the erosion process, both upstream and downstream water depths increase linearly with time as long as erosion of the crest height did not take place. However, when the crest height starts to lower the upstream water depth decreases with time while the downstream water depth increases. At the end of the experiment, the two depths are nearly equal. A relation between relative downstream and upstream water depths with time is drawn for each experiment as shown in Fig. 17.
5.3. Eroded volume
A MATLAB code is used to calculate the cumulative eroded volume every time interval for each experiment. The total volume of the dam, Vtotal is 0.256 m3. The cumulative eroded volume, Veroded is 0.21, 0.16, 0.13, and 0.05 m3 for tailwater depths, do = 5, 15, 20, and 25 cm, respectively. Fig. 18 presents the relation between cumulative eroded volume, Veroded and time. From Fig. 18, it is observed that the cumulative eroded volume decreases with increasing the tailwater depth. The reduction in cumulative eroded volume is 23, 36.5, and 75 % for relative tailwater depth, do /(do)ref = 3, 4, and 5, respectively. The relative remained volume of the dam equals 0.18, 0.375, 0.492, and 0.8 for tailwater depths = 5, 15, 20, and 25 cm, respectively. Fig. 19 shows a relation between relative tailwater depth and relative cumulative eroded volume from experimental results. From that figure, it is noticed that the eroded volume decreases exponentially with increasing relative tailwater depth.
5.4. The outflow discharge
The inflow discharge provided to the storage tank is maintained constant for all experiments. The water surface elevation, H, over the sharp-crested weir placed at the downstream side is recorded by the video camera 2. For each experiment, the outflow discharge is then calculated by using the sharp-crested rectangular weir equation every 10 sec.
The outflow discharge is found to increase rapidly until it reaches its peak then it decreases until it is constant. For high values of tailwater depths, the peak discharge becomes less than that in the case of small tailwater depth as shown in Fig. 20 which agrees well with the results of Rifai et al. [14] The reduction in peak discharge is 7, 14, and 17.35 % for relative tailwater depth, do /(do)ref = 3, 4, and 5, respectively.
The scenario presented in this article in which the tailwater depth rises due to unexpected heavy rainfall, is investigated to find the effect of rising tailwater depth on earth dam failure. The results revealed that rising tailwater depth positively affects the process of dam failure in terms of preventing the dam from complete failure and reducing the outflow discharge.
6. Conclusions
The effect of tailwater depth on earth dam failure due to overtopping is investigated experimentally in this work. The study focuses on the effect of tailwater depth on side erosion, upstream and downstream water depths, eroded volume, outflow hydrograph, and duration of the failure process. The Flow 3D numerical software is used to simulate the dam failure, and a comparison is made between the experimental and numerical results to find the ability of this software to simulate the erosion process. The following are the results of the investigation:
The existence of tailwater with high depths prevents the dam from completely collapsing thereby turning it into a broad crested weir. The failure time decreases with increasing the tailwater depth and the reduction from the reference case is found to be 35.3, 45, and 57 % for relative tailwater depth, do /(do)ref = 3, 4, and 5, respectively. The difference between the upstream and downstream water depths decreases with time till it became almost negligible at the end of the experiment. The reduction in cumulative eroded volume is 23, 36.5, and 75 % for relative tailwater depth, do /(do)ref = 3, 4, and 5, respectively. The peak discharge decreases by 7, 14, and 17.35 % for relative tailwater depth, do /(do)ref = 3, 4, and 5, respectively. The relative eroded crest height decreases linearly with increasing the tailwater depth by 10, 41, and 77.6 % for relative tailwater depth, do /(do)ref = 3, 4, and 5, respectively. The numerical model can reproduce the erosion process with a minor deviation from the experimental results, particularly in terms of tracking the degradation of the crest height with time.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Google Scholar[2]Rose AT. The influence of dam failures on dam safety laws in Pennsylvania. Association of State Dam Safety Officials Annual Conference 2013, Dam Safety 2013. 2013;1:738–56.
View Record in ScopusGoogle Scholar[4]Pickert, G., Jirka, G., Bieberstein, A., Brauns, J. Soil/water interaction during the breaching process of overtopped embankments. In: Greco, M., Carravetta, A., Morte, R.D. (Eds.), Proceedings of the Conference River-Flow 2004, Balkema.
YongHui Zhu, P.J. Visser, J.K. Vrijling, GuangQian Wang
Experimental investigation on breaching of embankments
Experimental investigation on breaching of embankments, 54 (1) (2011), pp. 148-155 View PDF
CrossRefView Record in ScopusGoogle Scholar[8]Amaral S, Jónatas R, Bento AM, Palma J, Viseu T, Cardoso R, et al. Failure by overtopping of earth dams. Quantification of the discharge hydrograph. Proceedings of the 3rd IAHR Europe Congress: 14-15 April 2014, Portugal. 2014;(1):182–93.
View Record in ScopusGoogle Scholar[11]Wu T, Qin J. Experimental Study of a Tailings Impoundment Dam Failure Due to Overtopping. Mine Water and the Environment [Internet]. 2018;37(2):272–80. Available from: doi: 10.1007/s10230-018-0529-x.
C. Di Cristo, S. Evangelista, M. Greco, M. Iervolino, A. Leopardi, A. Vacca
Dam-break waves over an erodible embankment: experiments and simulations
J Hydraul Res, 56 (2) (2018), pp. 196-210 View PDF
CrossRefView Record in ScopusGoogle Scholar[19]Goharnejad H, Sm M, Zn M, Sadeghi L, Abadi K. Numerical Modeling and Evaluation of Embankment Dam Break Phenomenon (Case Study : Taleghan Dam) ISSN : 2319-9873. 2016;5(3):104–11.
Google Scholar[20]Hu H, Zhang J, Li T. Dam-Break Flows : Comparison between Flow-3D , MIKE 3 FM , and Analytical Solutions with Experimental Data. 2018;1–24. doi: 10.3390/app8122456.
My name is Shaimaa Ibrahim Mohamed Aman and I am a teaching assistant in Irrigation and Hydraulics department, Faculty of Engineering, Alexandria University. I graduated from the Faculty of Engineering, Alexandria University in 2013. I had my MSc in Irrigation and Hydraulic Engineering in 2017. My research interests lie in the area of earth dam Failures.
Peer review under responsibility of Ain Shams University.
In this blog, Flow Science’s IT Manager Matthew Taylor breaks down the different hardware components and suggests some ideal configurations for getting the most out of your FLOW-3D products.
개요
본 자료는 Flow Science의 IT 매니저 Matthew Taylor가 작성한 자료를 기반으로 STI C&D에서 일부 자료를 보완한 자료입니다. 본 자료를 통해 FLOW-3D 사용자는 최상의 해석용 컴퓨터를 선택할 때 도움을 받을 수 있을 것으로 기대합니다.
수치해석을 하는 엔지니어들은 사용하는 컴퓨터의 성능에 무척 민감합니다. 그 이유는 수치해석을 하기 위해 여러 준비단계와 분석 시간들이 필요하지만 당연히 압도적으로 시간을 소모하는 것이 계산 시간이기 때문일 것입니다.
따라서 수치해석용 컴퓨터의 선정을 위해서 단위 시간당 시스템이 처리하는 작업의 수나 처리량, 응답시간, 평균 대기 시간 등의 요소를 복합적으로 검토하여 결정하게 됩니다.
또한 수치해석에 적합한 성능을 가진 컴퓨터를 선별하는 방법으로 CPU 계산 처리속도인 Flops/sec 성능도 중요하지만 수치해석을 수행할 때 방대한 계산 결과를 디스크에 저장하고, 해석결과를 분석할 때는 그래픽 성능도 크게 좌우하기 때문에 SSD 디스크와 그래픽카드에도 관심을 가져야 합니다.
FLOW SCIENCE, INC. 에서는 일반적인 FLOW-3D를 지원하는 최소 컴퓨터 사양과 O/S 플랫폼 가이드를 제시하지만, 도입 담당자의 경우, 최상의 조건에서 해석 업무를 수행해야 하기 때문에 가능하면 최고의 성능을 제공하는 해석용 장비 도입이 필요합니다. 이 자료는 2022년 현재 FLOW-3D 제품을 효과적으로 사용하기 위한 하드웨어 선택에 대해 사전에 검토되어야 할 내용들에 대해 자세히 설명합니다. 그리고 실행 중인 시뮬레이션 유형에 따라 다양한 구성에 대한 몇 가지 아이디어를 제공합니다.
CPU 최신 뉴스
2022년 11월 23일 기준 (https://www.itworld.co.kr/news/265948 기사 원문 발췌)
ⓒ Rob Schultz/IDG
현재 AMD의 라이젠 7000 시리즈와 인텔 13세대 코어 CPU는 환상적인 성능을 제공하나 앞으로는 더욱 좋은 칩이 출시될 예정이다. 물론 강력한 성능을 원한다면 고민할 필요도 없이 최대한 빠른 클럭 속도, 최대한 많은 코어 수를 찾으면 된다. 여기서 어려운 부분은 새로운 칩 라인업의 복잡하다는 것이다. 특히 최신 프로세서와 지난 세대 최상급 프로세서 중에서 고민한다면 여러 부분을 세밀하게 이해해야 한다.
모든 CFD 엔지니어의 고민은 예산이 넉넉하여 무조건 최고 사양의 제품을 구매하면 간단하지만, 현실의 예산은 그렇지 못하기 때문에 선택의 기로에서 힘들어 한다.
현재 워크스테이션에서 최고 사양은 AMD 라이젠 스레드리퍼 PRO 5995WX 샤갈 프로 거의 슈퍼컴퓨터 수준이다. 가격 조회 사이트인 다나와에서 현재 일자(2022년 12월 07일) 기준으로 검색해 보면 CPU 가격만 1000만원대인 매우 고가의 CPU인 것을 알 수 있다.
AMD와 인텔의 최신 아키텍처는 모두 성능만큼 에너지 소비량도 늘어난다. AMD의 라이젠 7950X와 인텔의 코어 i9-13900K는 DDR5 RAM을 지원한다.
다양한 가격대의 CPU가 있으므로 아래 CPU 성능 차트의 성능대비 가격을 보고 CPU를 선택하도록 한다.
인텔® 코어™ i9-13900K 프로세서(36M 캐시, 최대 5.80GHz)
완제품의 경우 그래픽 카드에 따라 가격이 심하게 차이가 나기 때문에 단순 비교가 어려우므로, 구입사양을 정하고 검색을 통해 적당한 제품을 선정하면 된다.
CPU의 선택
CPU는 전반적인 성능에 큰 영향을 미치며, 대부분의 경우 컴퓨터의 가장 중요한 구성 요소입니다. 그러나 데스크탑 프로세서를 구입할 때가 되면 Intel 과 AMD의 모델 번호와 사양을 이해하는 것이 어려워 보일 것입니다. 그리고, CPU 성능을 평가하는 방법에 의해 가장 좋은 CPU를 고른다고 해도 보드와, 메모리, 주변 Chip 등 여러가지 조건에 의해 성능이 달라질 수 있기 때문에 성능평가 결과를 기준으로 시스템을 구입할 경우, 단일 CPU나 부품으로 순위가 정해진 자료보다는 시스템 전체를 대상으로 평가한 순위표를 보고 선정하는 지혜가 필요합니다.
수치해석을 수행하는 CPU의 경우 예산에 따라 Core가 많지 않은 CPU를 구매해야 하는 경우도 있을 수 있습니다. 보통 Core가 많다고 해석 속도가 선형으로 증가하지는 않으며, 해석 케이스에 따라 적정 Core수가 있습니다. 이 경우 예산에 맞는 성능 대비 최상의 코어 수가 있을 수 있기 때문에 Single thread Performance 도 매우 중요합니다. 아래 성능 도표를 참조하여 예산에 맞는 최적 CPU를 찾는데 도움을 받을 수 있습니다.
FLOW-3D의 CFD 솔버 성능은 CPU의 부동 소수점 성능에 전적으로 좌우되기 때문에 계산 집약적인 프로그램입니다. FlowSight 또한 CPU에 크게 의존합니다. 현재 출시된 사용 가능한 모든 CPU를 벤치마킹할 수는 없지만 상대적인 성능을 합리적으로 비교할 수는 있습니다.
특히, 수치해석 분야에서 주어진 CPU에 대해 FLOW-3D 성능을 추정하거나 여러 CPU 옵션 간의 성능을 비교하기 위한 최상의 옵션은 Standard Performance Evaluation Corporation의 SPEC CPU2017 벤치마크(현재까지 개발된 가장 최신 평가기준임)이며, 특히 SPECspeed 2017 Floating Point 결과가 CFD Solver 성능을 매우 잘 예측합니다.
이는 유료 벤치마크이므로 제공된 결과는 모든 CPU 테스트 결과를 제공하지 않습니다. 보통 제조사가 ASUS, Dell, Lenovo, HP, Huawei 정도의 제품에 대해 RAM이 많은 멀티 소켓 Intel Xeon 기계와 같은 값비싼 구성으로 된 장비 결과들을 제공합니다.
CPU 비교를 위한 또 다른 옵션은 Passmark Software의 CPU 벤치마크입니다. PerformanceTest 제품군은 유료 소프트웨어이지만 무료 평가판을 사용할 수 있습니다. 대부분의 CPU는 저렴한 옵션을 포함하여 나열됩니다. 부동 소수점 성능은 전체 벤치마크의 한 측면에 불과하지만 다양한 워크로드에서 전반적인 성능을 제대로 테스트합니다.
예산을 결정하고 해당 예산에 해당하는 CPU를 선택한 후에는 벤치마크를 사용하여 가격에 가장 적합한 성능을 결정할 수 있습니다.
다른 컴퓨터 시스템에서 컴퓨팅 계산에 대한 집약적인 워크로드를 비교하는데 사용할 수 있는 성능 측정을 제공하도록 설계된 SPEC CPU 2017에는 SPECspeed 2017 정수, SPECspeed 2017 부동 소수점, SPECrate 2017 정수 및 SPECrate 2017 부동 소수점의 4 가지 제품군으로 구성된 43 개의 벤치 마크가 포함되어 있습니다. SPEC CPU 2017에는 에너지 소비 측정을 위한 선택적 메트릭도 포함되어 있습니다.
<SPEC CPU 벤치마크 보고서>
벤치마크 결과보고서는 제조사별, 모델별로 테스트한 결과를 아래 사이트에 가면 볼 수 있습니다.
Designed to provide performance measurements that can be used to compare compute-intensive workloads on different computer systems, SPEC CPU 2017 contains 43 benchmarks organized into four suites: SPECspeed 2017 Integer, SPECspeed 2017 Floating Point, SPECrate 2017 Integer, and SPECrate 2017 Floating Point. SPEC CPU 2017 also includes an optional metric for measuring energy consumption.
일반적으로 클럭 속도가 높은 칩은 CPU 코어를 더 적게 포함합니다. FLOW-3D는 병렬화가 잘되어 있지만, 디스크 쓰기와 같이 일부 작업은 기본적으로 단일 스레드 방식으로 수행됩니다. 따라서 데이터 출력이 빈번하거나 큰 시뮬레이션은 종종 더 많은 코어가 아닌, 더 높은 클럭 속도를 활용합니다. 마찬가지로 코어 및 소켓의 다중 스레딩은 오버헤드를 발생시키므로 작은 문제의 해석일 경우 사용되는 코어 수를 제한하면 성능이 향상될 수 있습니다.
CPU 아키텍처
CPU 아키텍처는 중요합니다. 최신 CPU는 일반적으로 사이클당 더 많은 기능을 제공합니다. 즉, 현재 세대의 CPU는 일반적으로 동일한 클럭 속도에서 이전 CPU보다 성능이 우수합니다. 또한 전력 효율이 높아져 와트당 성능이 향상될 수 있습니다. Flow Science에는 구형 멀티 소켓 12, 16, 24 코어 Xeon보다 성능이 뛰어난 최근 세대 10~12 Core i9 CPU 시스템을 보유하고 있습니다.
오버클럭
해석용 장비에서는 CPU를 오버클럭 하지 않는 것이 좋습니다. 하드웨어를 다년간의 투자라고 생각한다면, 오버클럭화는 발열을 증가시켜 수명을 단축시킵니다. CPU에 따라 안정성도 저하될 수 있습니다. CPU를 오버클럭 할 때는 세심한 열 관리가 권장됩니다.
하이퍼스레딩
<이미지출처:https://gameabout.com/krum3/4586040>
하이퍼스레딩은 물리적으로 1개의 CPU를 가상으로 2개의 CPU처럼 작동하게 하는 기술로 파이프라인의 단계수가 많고 각 단계의 길이가 짧을때 유리합니다. 다만 수치해석 처럼 모든 코어의 CPU를 100% 사용중인 장시간 수행 시뮬레이션은 일반적으로 Hyper Threading이 비활성화 된 상태에서 더 잘 수행됩니다. FLOW-3D는 100% CPU 사용률이 일반적이므로 새 하드웨어를 구성할 때 Hyper Threading을 비활성화하는 것이 좋습니다. 설정은 시스템의 BIOS 설정에서 수행합니다.
몇 가지 워크로드의 경우에는 Hyper Threading을 사용하여 약간 더 나은 성능을 보이는 경우가 있습니다. 따라서, 최상의 런타임을 위해서는 두 가지 구성중에서 어느 구성이 더 적합한지 시뮬레이션 유형을 테스트하는 것이 좋습니다.
스케일링
여러 코어를 사용할 때 성능은 선형적이지 않습니다. 예를 들어 12 코어 CPU에서 24 코어 CPU로 업그레이드해도 시뮬레이션 런타임이 절반으로 줄어들지 않습니다. 시뮬레이션 유형에 따라 16~32개 이상의 CPU 코어를 선택할 때는 FLOW-3D 및 FLOW-3D CAST의 HPC 버전을 사용하거나 FLOW-3D CLOUD로 이동하는 것을 고려하여야 합니다.
AMD Ryzen 또는 Epyc CPU
AMD는 일부 CPU로 벤치마크 차트를 석권하고 있으며 그 가격은 매우 경쟁력이 있습니다. FLOW SCIENCE, INC. 에서는 소수의 AMD CPU로 FLOW-3D를 테스트했습니다. 현재 Epyc CPU는 이상적이지 않고 Ryzen은 성능이 상당히 우수합니다. 발열은 여전히 신중하게 다뤄져야 할 문제입니다. 현재 32 코어 옵션에 영향을 주는 Windows 버그가 초기 버전에서 성능을 크게 저하시키는 것으로 알려져 있습니다. Bug Fix가 되었는지 업데이트 하여 확인하고, 해결되지 않은 경우 이러한 CPU에는 Linux를 권장됩니다.
FLOW-3D는 OpenGL 드라이버가 만족스럽게 수행되는 최신 그래픽 카드가 필요합니다. 최소한 OpenGL 3.0을 지원하는 것이 좋습니다. FlowSight는 DirectX 11 이상을 지원하는 그래픽 카드에서 가장 잘 작동합니다. 권장 옵션은 엔비디아의 쿼드로 K 시리즈와 AMD의 파이어 프로 W 시리즈입니다.
특히 엔비디아 쿼드로(NVIDIA Quadro)는 엔비디아가 개발한 전문가 용도(워크스테이션)의 그래픽 카드입니다. 일반적으로 지포스 그래픽 카드가 게이밍에 초점이 맞춰져 있지만, 쿼드로는 다양한 산업 분야의 전문가가 필요로 하는 영역에 광범위한 용도로 사용되고 있습니다. 주로 산업계의 그래픽 디자인 분야, 영상 콘텐츠 제작 분야, 엔지니어링 설계 분야, 과학 분야, 의료 분석 분야 등의 전문가 작업용으로 사용되고 있습니다. 따라서 일반적인 소비자를 대상으로 하는 지포스 그래픽 카드와는 다르계 산업계에 포커스 되어 있으며 가격이 매우 비싸서 도입시 예산을 고려해야 합니다.
유의할 점은 엔비디아의 GTX 게이밍 하드웨어는 볼륨 렌더링의 속도가 느리거나 오동작 등 몇 가지 제한 사항이 있습니다. 일반적으로 노트북에 내장된 통합 그래픽 카드보다는 개별 그래픽 카드를 강력하게 추천합니다. 최소한 그래픽 메모리는 512MB 이상을 권장합니다.
Flow Science는 nVidia 드라이버 버전이 341.05 이상인 nVidia Quadro K, M 또는 P 시리즈 그래픽 하드웨어를 권장합니다. 이 카드와 드라이버 조합을 사용하면 원격 데스크톱 연결이 완전한 3D 가속 기능을 갖춘 기본 하드웨어에서 자동으로 실행됩니다.
원격 데스크톱 세션에 연결할 때 nVidia Quadro 그래픽 카드가 설치되어 있지 않으면 Windows는 소프트웨어 렌더링을 사용합니다. 이는 FLOW-3D 및 FlowSight 모두 성능에 부정적인 영향을 미칩니다. FLOW-3D 가 소프트웨어 렌더링을 사용하고 있는지 확인하려면 FLOW-3D 도움말 메뉴에서 정보를 선택하십시오. GDI Generic을 소프트웨어 렌더링으로 사용하는 경우 GL_RENDERER 항목에 표시됩니다.
하드웨어 렌더링을 활성화하는 몇 가지 옵션이 있습니다. 쉬운 방법 중 하나는 실제 콘솔에서 FLOW-3D를 시작한 다음 원격 데스크톱 세션을 연결하는 것입니다. Nice Software DCV 와 같은 일부 VNC 소프트웨어는 기본적으로 하드웨어 렌더링을 사용합니다.
RAM 고려 사항
프로세서 코어당 최소 4GB의 RAM은 FLOW-3D의 좋은 출발입니다. FlowSight POST Processor를 사용하여 후처리 작업을 할 경우 상당한 양의 RAM을 사용하는 것이 좋습니다.
현재 주력제품인 DDR4보다 2배 빠른 DDR5가 곧 출시된다는 소식도 있습니다.
일반적으로 FLOW-3D를 이용하여 해석을 할 경우 격자(Mesh)수에 따라 소요되는 적정 메모리 크기는 아래와 같습니다.페이지 보기
초대형 (2억개 이상의 셀) : 최소 128GB
대형 (60 ~ 1억 5천만 셀) : 64 ~ 128GB
중간 (30-60백만 셀) : 32-64GB
작음 (3 천만 셀 이하) : 최소 32GB
HDD 고려 사항
수치해석은 해석결과 파일의 데이터 양이 매우 크기 때문에 읽고 쓰는데, 속도면에서 매우 빠른 SSD를 적용하면 성능면에서 큰 도움이 됩니다. 다만 SSD 가격이 비싸서 가성비 측면을 고려하여 적정수준에서 결정이 필요합니다.
CPU와 저장장치 간 데이터가 오고 가는 통로가 그림과 같이 3가지 방식이 있습니다. 이를 인터페이스라 부르며 SSD는 흔히 PCI-Express 와 SATA 통로를 이용합니다.
흔히 말하는 NVMe는 PCI-Express3.0 지원 SSD의 경우 SSD에 최적화된 NVMe (NonVolatile Memory Express) 전송 프로토콜을 사용합니다. 주의할 점은 MVMe중에서 SATA3 방식도 있기 때문에 잘 구별하여 구입하시기 바랍니다.
그리고 SSD를 선택할 경우에도 SSD 종류 중에서 PCI Express 타입은 매우 빠르고 가격이 고가였지만 최근에는 많이 저렴해졌습니다. 따라서 예산 범위내에서 NVMe SSD등 가장 효과적인 선택을 하는 것이 좋습니다. ( 참고 :해석용 컴퓨터 SSD 고르기 참조 )
기존의 물리적인 하드 디스크의 경우, 디스크에 기록된 데이터를 읽기 위해서는 데이터를 읽어내는 헤드(바늘)가 물리적으로 데이터가 기록된 위치까지 이동해야 하므로 이동에 일정한 시간이 소요됩니다. (이러한 시간을 지연시간, 혹은 레이턴시 등으로 부름) 따라서 하드 디스크의 경우 데이터를 읽기 위한 요청이 주어진 뒤에 데이터를 실제로 읽기까지 일정한 시간이 소요되는데, 이 시간을 일정한 한계(약 10ms)이하로 줄이는 것이 불가능에 가까우며, 데이터가 플래터에 실제 기록된 위치에 따라서 이러한 데이터에의 접근시간 역시 차이가 나게 됩니다.
하지만 HDD의 최대 강점은 가격대비 용량입니다. 현재 상용화되어 판매하는 대용량 HDD는 12TB ~ 15TB가 공급되고 있으며, 이는 데이터 저장이나 백업용으로 가장 좋은 선택이 됩니다. 결론적으로 데이터를 직접 읽고 쓰는 드라이브는 SSD를 사용하고 보관하는 용도의 드라이브는 기존의 HDD를 사용하는 방법이 효과적인 선택이 될 수 있습니다.
상기 벤치마크 테스트는 테스트 조건에 따라 그 성능 곡선이 달라질 수 있기 때문에 조건을 확인할 필요가 있습니다. 예를 들어 Windows7, windows8, windows10 모두에서 테스트한 결과를 평균한 점수와 자신이 사용할 컴퓨터 O/S에서 테스트한 결과는 다를 수 있습니다. 상기 결과에 대한 테스트 환경에 대한 내용은 아래 사이트를 참고하시기 바랍니다.
A. Safarzadeh1*, P. Mohsenzadeh2, S. Abbasi3 1 Professor of Civil Eng., Water Engineering and Mineral Waters Research Center, Univ. of Mohaghegh Ardabili,Ardabil, Iran 2 M.Sc., Graduated of Civil-Hydraulic Structures Eng., Faculty of Eng., Univ. of Mohaghegh Ardabili, Ardabil, Iran 3 M.Sc., Graduated of Civil -Hydraulic Structures Eng., Faculty of Eng., Univ. of Mohaghegh Ardabili, Ardabil, Iran Safarzadeh@uma.ac.ir
Highlights
유체 이동에 의해 생성된 RBF는 Ls-Dyna에서 Fluent, ICFD ALE 및 SPH 방법으로 시뮬레이션되었습니다. RBF의 과예측은 유체가 메인 도메인에서 고속으로 분리될 때 발생합니다. 이 과잉 예측은 요소 크기, 시간 단계 크기 및 유체 모델에 따라 다릅니다. 유체 성능을 검증하려면 최대 RBF보다 임펄스가 권장됩니다.
Abstract
Dam break is a very important problem due to its effects on economy, security, human casualties and environmental consequences. In this study, 3D flow due to dam break over the porous substrate is numerically simulated and the effect of porosity, permeability and thickness of the porous bed and the water depth in the porous substrate are investigated. Classic models of dam break over a rigid bed and water infiltration through porous media were studied and results of the numerical simulations are compared with existing laboratory data. Validation of the results is performed by comparing the water surface profiles and wave front position with dam break on rigid and porous bed. Results showed that, due to the effect of dynamic wave in the initial stage of dam break, a local peak occurs in the flood hydrograph. The presence of porous bed reduces the acceleration of the flood wave relative to the flow over the solid bed and it decreases with the increase of the permeability of the bed. By increasing the permeability of the bed, the slope of the ascending limb of the flood hydrograph and the peak discharge drops. Furthermore, if the depth and permeability of the bed is such that the intrusive flow reaches the rigid substrate under the porous bed, saturation of the porous bed, results in a sharp increase in the slope of the flood hydrograph. The maximum values of the peak discharge at the end of the channel with porous bed occurred in saturated porous bed conditions.
댐 붕괴는 경제, 보안, 인명 피해 및 환경적 영향으로 인해 매우 중요한 문제입니다. 본 연구에서는 다공성 기재에 대한 댐 파괴로 인한 3차원 유동을 수치적으로 시뮬레이션하고 다공성 기재의 다공성, 투과도 및 다공성 층의 두께 및 수심의 영향을 조사합니다. 단단한 바닥에 대한 댐 파괴 및 다공성 매체를 통한 물 침투의 고전 모델을 연구하고 수치 시뮬레이션 결과를 기존 실험실 데이터와 비교합니다. 결과 검증은 강체 및 다공성 베드에서 댐 파단과 수면 프로파일 및 파면 위치를 비교하여 수행됩니다. 그 결과 댐파괴 초기의 동적파동의 영향으로 홍수수문곡선에서 국부첨두가 발생하는 것으로 나타났다. 다공성 베드의 존재는 고체 베드 위의 유동에 대한 홍수파의 가속을 감소시키고 베드의 투과성이 증가함에 따라 감소합니다. 베드의 투수성을 증가시켜 홍수 수문곡선의 오름차순 경사와 첨두방류량이 감소한다. 더욱이, 만약 층의 깊이와 투과성이 관입 유동이 다공성 층 아래의 단단한 기질에 도달하는 정도라면, 다공성 층의 포화는 홍수 수문곡선의 기울기의 급격한 증가를 초래합니다. 다공층이 있는 채널의 끝단에서 최대 방전 피크값은 포화 다공층 조건에서 발생하였다.
Keywords
Keywords: Dams Break, 3D modeling, Porous Bed, Permeability, Flood wave
Reference
[1] D.L. Fread, In: Maidment, D.R. (Ed.), Flow Routing in Handbook of Hydrology, McGraw-Hill Inc., New York, USA, pp. 10(1) (1993) 1-36. [2] M. Morris, CADAM: Concerted Action on Dambreak Modeling – Final Report, Rep. SR 571. HR Wallingford, 2000. [3] H. Chanson, The Hydraulics of Open Channel Flows: an Introduction, ButterworthHeinemann, Oxford, 2004. [4] A. Ritter, Die Fortpflanzung der Wasserwellen (The Propagation of Water Waves), Zeitschrift Verein Deutscher Ingenieure, 36 (33) (1892) 947–954 [in German]. [5] B. Ghimire, Hydraulic Analysis of Free-Surface Flows into Highly Permeable Porous Media and its Applications, Phd. Thesis, Kyoto University, 2009. [6] R. Dressler, Hydraulic Resistance Effect Upon the Dam-Break Function, Journal of Research of the National Bureau of Standards, 49 (3) 1952. [7] G. Lauber, and W.H. Hager, Experiments to Dambreak Wave: horizontal channel, Journal of Hydraulic Research. 36 (3) (1998) 291–307. [8] L.W. Tan, and V.H. Chu, Lagrangian Block Hydrodynamics of Macro Resistance in a River-Flow Model, [9] L. Tan, V.H. Lauber and Hager’s Dam-Break Wave Data for Numerical Model Validation, Journal of Hydraulic Research, 47 (4) (2009) 524-528. [10] S. Mambretti, E.D. Larcan, and D. Wrachien, 1D Modelling of Dam-Break Surges with Floating Debris, J. of Biosystems engineering, 100 (2) (2008) 297-308. [11] M. Pilotti, M. Tomirotti, G. Valerio, and B. Bacchi, Simplified Method for the Characterization of the Hydrograph Following a Sudden Partial Dam Break, Journal of Hydraulic Engineering, 136 (10) (2010) 693-704. [12] T.J. Chang, H.M. Kao, K.H. Chang, and Mi.H. Hsu, Numerical Simulation of ShallowWater Dam Break Flows in Open Channels Using Smoothed Particle Hydrodynamics, J. Hydraul. Eng., 408 (78–90) 2011. [13] T. Tawatchai, and W. Rattanapitikon, 2-D Modelling of Dambreak Wave Propagation on Initially Dry Bed, Thammasat Int. J. Sc. 4 (3) 1999. [14] Y.F. Le, Experimental Study of landslide Dam-Break Flood over Erodible Bed in open Channels. Journal of Hydrodynamics, Ser. B, 21 (5) 2006. [15] O. Castro-Orgaz, & H. Chanson, Ritter’s Dry-Bed Dam-Break Flows: Positive and Negative Wave Dynamics, J. of Environmental Fluid Mechanics, 17 (4) (2017) 665-694. [16] A. Jozdani, A.R. Kabiri-Samani, Application of Image Processing Method to Analysis of Flood Behavior Due to Dam Break, 9th Iranian Hydraulic Conference. Univ. of Tarbiat Moddares, 2011.(in persian) [17] A. Safarzadeh, Three Dimensional Hydrodynamics of Sudden Dam Break in Curved Channels, Journal of Modares Civil Engineering, 17(3) (2017) 77-86. (in persian) [18] P. C. Carman, Fluid Flow Through Granular Beds, Transactions, Institution of Chem. Eng. Res. Des. 75 (Dec): S32–S48, London, 15, (1937) 150-166. [19] P. Forchheimer, Wasserbewegung Durch Boden. Z. Ver. Deutsch. Ing. 45 (1901) 1782– 1788. [20] S. Ergun, Fluid Flow through Packed Columns. Chemical Engineering Progress, 48(2) (1952) 89-93. [21] A. Parsaei, S. Dehdar-Behbahani, Numerical Modeling of Cavitation on Spillway’s Flip Bucket, Frontiers of Structural and Civil Engineering, 10 (4) (2016) 438-444. [22] S. Dehdar-Behbahani, A. Parsaei, Numerical Modeling of Flow Pattern in Dam Spillway’s Guide Wall. Case study: Balaroud dam, Iran, Alexandria Engineering Journal, 55(1) (2016) 467-473. [23] A. Parsaei, AH. Haghiabi, A. Moradnejad, CFD Modeling of Flow Pattern in Spillway’s ACCEPTED MANUSCRIPT 19 Approach Channel, Sustainable Water Resources Management, 1(3) (2015) 245-251. [24] SH. Najafian, H. Yonesi, A. Parsaei, PH. Torabi, Physical and Numerical Modeling of Flow in Heterogeneous Roughness Non-Prismatic Compound Open Channel, Irrigation and Drainage Structures Engineering Research, 17(66) (2016) 87-104. [25] SH. Najafian, H. Yonesi, A. Parsaei, PH. Torabi, Physical and Numerical Modeling of Flow Properties in Prismatic Compound Open Channel with Heterogeneous Roughness, Irrigation and Drainage Structures Engineering Research, 18(68) (2017) 1-16. [26] A. Safarzadeh, S.H. Mohajeri, Hydrodynamics of Rectangular Broad-Crested Porous Weirs, Journal of Irrig. & Drain. Eng., 144(10) (2018) 1-12. [27] M. Fathi-moghaddam, M.T. Sadrabadi, M, Rahamnshahi, Numerical Simulation of the Hydraulic Performance of Triangular and Trapezoidal Gabion Weirs in Free Flow Condition, Journal of Flow Measurement & Instrumentation, 62 (2018) 93-104. [28] A. Parsaei, A. Moradnejad, Numerical Modeling of Flow Pattern in Spillway Approach Channel, Jordan Journal of Civil Engineering, 12(1) (2018) 1-9.
천해 방정식을 기반으로 하는 2차원 흐름 모델은 댐 붕괴 흐름을 모델링하기 위해 개발되었습니다. 공간 이산화는 유한 체적 셀 중심 유형 방법에 의해 얻어집니다.
수치 시스템은 명시적인 방식으로 해결됩니다. 플럭스 모델링은 시간과 공간 모두에서 2차 정확도로 TVD WAF 방식으로 배포되었습니다. 로컬 리만 문제는 셀 인터페이스에서 HLLC 방법으로 해결됩니다. 수치 모델은 모델 결과와 해석 솔루션을 비교하여 검증합니다.
그런 다음 수치 모델의 결과는 90° 및 180° 편차 각도를 갖는 수로 및 삼각형 바텀 씰 위의 직선 수로에서 사용 가능한 실험 데이터와 비교됩니다. 결과는 댐 파괴파를 예측하는 현재 모델의 합리적인 성능을 확인합니다.
A two-dimensional flow model based on shallow water equations is developed for modeling dam-break flows. The spatial discretization is obtained by the finite volume cell centered type method. The numerical system is solved in explicit way. The flux modeling has been deployed by TVD WAF scheme with a second-order accuracy in both time and space. The local Riemann problem is solved by the HLLC method in the interface of the cells. The numerical model is verified by comparison of model results and analytical solutions. Then the results of numerical model are compared with available experimental data of dam-break waves in a channel with 90° and 180° deviation angle and in a straight channel over a triangular bottom sill. The results confirm the reasonable performance of the present model in predicting dam-break waves.
Fig. 2 Generic control volume and notationsFig. 1 The generated grid for a channel with a 180° bendFig. 4 a Water surface profle and b velocity profle of dam-break
problem with left dry bedFig. 5 a Water surface profle and b velocity profle of appearance
dry regionFig. 6 Comparison of the
present model results and exact
solution for transcritical fow
over a bump with a shockFig. 7 Geometry of the reservoir and L-shaped channel: plan
view (Soares-Frazao et al. 2019)Fig. 9 Test facility a plan view, b the bottom elevation of the reservoir to the channel (Bell et al. 1992)
References
Ata R, Pavan S, Khelladi S, Toro EF (2013) A Weighted Average Flux (WAF) scheme applied to shallow water equations for real-life applications. Adv Water Resour 62:155–172ArticleGoogle Scholar
Aureli F, Maranzoni A, Mignosa P, Ziveri C (2008) A weighted surface-depth gradient method for the numerical integration of the 2D shallow water equations with topography. Adv Water Resour 31(7):962–974ArticleGoogle Scholar
Bell SW, Elliot RC, Hanif Chaudhry M (1992) Experimental results of two-dimensional dam-break flows. J Hydraul Res 30(2):225–252ArticleGoogle Scholar
Benkhaldoun F, Sari S, Seaid M (2015) Projection finite volume method for shallow water flows. Math Comput Simul 118:87–101MathSciNetArticleGoogle Scholar
Chung TJ (2010) Computational fluid dynamics. Cambridge University PressBookGoogle Scholar
Einfeldt B, Munz CD, Roe PL, Sjögreen B (1991) On Godunov-type methods near low densities. J Comput Phys 92(2):273–295MathSciNetArticleGoogle Scholar
Erduran KS, Kutija V, Hewett CJM (2002) Performance of finite volume solutions to the shallow water equations with shock-capturing schemes. Int J Numer Meth Fluids 40(10):1237–1273MathSciNetArticleGoogle Scholar
Gallardo JM, Schneider KA, Castro MJ (2019) On a class of two-dimensional incomplete Riemann solvers. J Comput Phys 386:541–567MathSciNetArticleGoogle Scholar
Fraccarollo L, Toro EF (1995) Experimental and numerical assessment of the shallow water model for two-dimensional dam-break type problems. J Hydraul Res 33(6):843–864ArticleGoogle Scholar
Gupta SC (2019) Numerical grid generation and parallel computations. J Aerosp Eng Technol 5(1):11–22Google Scholar
Hosseinzadeh-Tabrizi A, Ghaeini-Hessaroeyeh M (2015) Coupled dam-break flow and bed load modelling using HLLC-WAF scheme. Water Sci Technol 72(7):1155–1167ArticleGoogle Scholar
Kocaman S, Ozmen-Cagatay H (2015) Investigation of dam-break induced shock waves impact on a vertical wall. J Hydrol 525:1–12ArticleGoogle Scholar
Liang Q, Borthwick AGL, Stelling G (2004) Simulation of dam-and dyke-break hydrodynamics on dynamically adaptive quadtree grids. Int J Numer Meth Fluids 46(2):127–162ArticleGoogle Scholar
Liang D, Lin B, Falconer RA (2007) Simulation of rapidly varying flow using an efficient TVD–MacCormack scheme. Int J Numer Meth Fluids 53(5):811–826ArticleGoogle Scholar
Munoz DH, Constantinescu G (2020) 3-D dam break flow simulations in simplified and complex domains. Adv Water Resour 103510
Muscat L, Puigt G, Montagnac M, Brenner P (2019) A coupled implicit-explicit time integration method for compressible unsteady flows. J Comput Phys 398:183MathSciNetArticleGoogle Scholar
Ozmen-Cagatay H, Kocaman S (2010) Dam-break flows during initial stage using SWE and RANS approaches. J Hydraul Res 48(5):603–611ArticleGoogle Scholar
Ozmen-Cagatay H, Kocaman S, Guzel H (2014) Investigation of dam-break flood waves in a dry channel with a hump. J Hydro Environ Res 8(3):304–315ArticleGoogle Scholar
Pongsanguansin T, Maleewong M, Mekchay K (2015) Consistent weighted average flux of well-balanced TVD-RK discontinuous galerkin method for shallow water flows. Modelling and simulation in Engineering, pp. 591282
Pongsanguansin T, Maleewong M, Mekchay K (2016) Shallow-water simulations by a well-balanced WAF finite volume method: a case study to the great flood in 2011. Thailand Comput Geosci 20(6):1269–1285MathSciNetArticleGoogle Scholar
Soares-Frazão S (2007) Experiments of dam-break wave over a triangular bottom sill. J Hydraul Res 45(sup1):19–26MathSciNetArticleGoogle Scholar
Soares Frazao S, Abbeels S, Messens M (2019) Dam-break flow in a channel with a 90° bend and mobile bed: experimental and numerical simulations. In: 38th IAHR world congress
Toro EF (1992) Riemann problems and the WAF method for solving the two-dimensional shallow water equations. Philos Trans Roy Soc Lond Ser A Phys Eng Sci 338(1649):43–68MathSciNetMATHGoogle Scholar
Toro EF, Spruce M, Speares W (1994) Restoration of the contact surface in the HLL-Riemann solver. Shock Waves 4(1):25–34ArticleGoogle Scholar
Toro EF (2001) Shock-capturing methods for free-surface shallow flows, vol 868. Wiley, New YorkMATHGoogle Scholar
Toro EF, Garcia-Navarro P (2007) Godunov-type methods for free-surface shallow flows: a review. J Hydraul Res 45(6):736–751ArticleGoogle Scholar
Toro, E.F., 2013. Riemann solvers and numerical methods for fluid dynamics: a practical introduction. Springer Science & Business Media.
Valiani A, Caleffi V, Zanni A (2002) Case study: Malpasset dam-break simulation using a two-dimensional finite volume method. J Hydraul Eng 128(5):460–472ArticleGoogle Scholar
Xia J, Lin B, Falconer RA, Wang G (2010) Modelling dam-break flows over mobile beds using a 2-D coupled approach. Adv Water Resour 33(2):171–183ArticleGoogle Scholar
Zia A, Banihashemi MA (2008) Simple efficient algorithm (SEA) for shallow flows with shock wave on dry and irregular beds. Int J Numer Meth Fluids 56(11):2021–2043MathSciNetArticleGoogle Scholar
Zoppou C, Roberts S (2003) Explicit schemes for dam-break simulations. J Hydraul Eng 129(1):11–34ArticleGoogle Scholar
Zhou JG, Causon DM, Ingram DM, Mingham CG (2002) Numerical solutions of the shallow water equations with discontinuous bed topography. Int J Numer Meth Fluids 38(8):769–788ArticleGoogle Scholar
N.M.T De Silva University of Colombo School of Computing 2018
Abstract
산사태가 발생하기 쉬운 구릉 지역 근처에서 발생하는 최근 인구 증가 및 개발은 취약성을 증가시킵니다. 기후 변화의 영향은 산사태 위험의 가능성을 더욱 높입니다. 따라서 인명 및 재산 피해를 방지하기 위해서는 불안정한 경사면 거동에 대한 적절한 관찰과 분석이 중요합니다.
산사태 흐름 경로 예측은 산사태 흐름 경로를 결정하는 데 중요하며 위험 매핑의 필수 요소입니다. 그러나 현상의 복잡한 특성과 관련 매개변수의 불확실성으로 인해 흐름 경로 예측은 어려운 작업입니다. 이 작업에서는 Kegalle 지역의 Aranayaka 지역의 주요 산사태 사고를 흐름 경로를 모델링하기 위한 사례 연구로 사용합니다.
위치에서 디지털 고도 모델을 기반으로 잠재적 소스 영역이 식별되었습니다. 확산 영역 평가는 D8 및 다중 방향 흐름 알고리즘이라는 두 가지 흐름 방향 알고리즘을 기반으로 했습니다. 이 프로토타입 모델을 사용하여 사용자는 슬라이드의 최대 너비, 런아웃 거리 및 슬립 표면적과 같은 산사태 관련 통계를 대화식으로 얻을 수 있습니다.
모델에서 얻은 결과는 실제 Aranayaka 산사태 데이터 세트와 해당 지역의 산사태 위험 지도와 비교되었습니다. D8 알고리즘을 사용하여 구현된 도구에서 생성된 산사태 흐름 경로는 65% 이상의 일치를 나타내고 다중 방향 흐름 알고리즘은 실제 흐름 경로 및 기타 관련 통계와 69% 이상의 일치를 나타냅니다.
또한, 생성된 유동 경로 방향과 예상되는 산사태 시작 지점이 실제 산사태 경계 내부에 잘 일치합니다.
Recent population growth and developments taking place close to landslides prone hilly areas increase their vulnerability. Climate change impacts further raise the potential of landslide hazard. Therefore, to prevent loss of lives and damage to property, proper observation and analysis of unstable slope behavior is crucial. Landslide flow path forecasting is important for determining a landslide flow route and it is an essential element in hazard mapping. However, due to the complex nature of the phenomenon and the uncertainties of associated parameters flow path prediction is a challenging task. In this work, the major landslide incident at Aranayaka area in Kegalle district is taken as the case study to model the flow path. At the location, potential source areas were identified on the basis of the Digital Elevation Model. Spreading area assessment was based on two flow directional algorithms namely D8 and Multiple Direction Flow Algorithm. Using this prototype model, a user can interactively get landslide specific statistics such as the maximum width of the slide, runout distance, and slip surface area. Results obtained by the model were compared with the actual Aranayaka landslide data set the landslide hazard map of the area. Landslide flow paths generated from the implemented tool using D8 algorithm shows more than 65% agreement and Multiple Direction Flow Algorithm shows more than 69% agreement with the actual flow paths and other related statistics. Also, the generated flow path directions and predicted possible landslide initiation points fit inside the actual landslide boundary with good agreement.
Figure 2.1: Types of Landslides[2]Figure 2.2: Landslide Glossary [2]
References
[1] na, “Landslides 101,” [Online]. Available: https://landslides.usgs.gov/learn/ls101.php. [Accessed 20 01 2017]. [2] U.S. Department of the Interior, “Landslide Types and Processes,” July 2004. [Online]. Available: https://pubs.usgs.gov/fs/2004/3072/fs-2004-3072.html. [Accessed 20 July 2017]. [3] “Department of conservation,” 2016. [Online]. Available: http://www.conservation.ca.gov/cgs/geologic_hazards/landslides/Pages/LandslideTypes.aspx. [Accessed 20 July 2017]. [4] 22nd May 2016, Aerial Survey report on inundation damages and sediment disasters, 2016. [5] Peter V. Gorsevski, Paul Gessler and Randy B. Foltz, “Spatial Prediction of Landslide Hazard Using Discriminant Analysis and GIS,” in GIS in the Rockies 2000 Conference and Workshop Applications for the 21st Century, Denver, Colorado. , 2000. [6] M. Casadei, W. E. Dietrich and N. L. Miller, “Testing A Model For Predicting The Timing And Location Of Shallow Landslide Initiation In Soil-Mantled Landscapes,” Earth Surface Processes and Landforms, vol. 28, p. 925–950, 2003. [7] Roberto Arnaldo Trancoso Gomes, Renato Fontes, Osmar Abílio de Carvalho Júnior, Nelson Ferreira and Eurípedes Vargas do Amaral, “Combining Spatial Models for Shallow Landslides and Debris-Flows Prediction,” Remote Sensing, no. 5, pp. 2219-2237, 2013. [8] P. Bertolo and G. F. Wieczorek, “Calibration of numerical models for small debris flow in Yosemite Valley, California, USA,” Documentation and monitoring of landslides and debris flows for mathematical modelling and design of mitigation measures, 13 December 2005. [9] T. A. Gebreslassie, “Dynamic simulations of landslide runout in cohesive Soils,” Oslo, 2015. [10] P. Tarolli and D. G. Tarboton, “A new method for determination of most likely landslide initiation points and the evaluation of digital terrain model scale in terrain stability mapping,” Hydrology and Earth System Sciences, no. 10, p. 663–677, 2006. [11] G.-B. Kim, “Numerical Simulation Of Three-Dimensional Tsunami Generation By Subaerial Landslides,” 2013.
[12] Giuseppe Formetta, Giovanna Capparelli, and Pasqua, “Evaluating performance of simplified physically based models for shallow landslide susceptibility,” Hydrol. Earth System, no. 20, p. 4585–4603, 2016. [13] F. Dai and C. Lee, “Landslide characteristics and slope instability modeling using GIS, Lantau Island, Hong Kong,” 2001. [14] S. McDougall, “Landslide runout analysis — current practice and challenges,” Canadian Geotechnical Colloquium, vol. 57, pp. 605-620, 2017. [15] P. Quinn, K. Beven, P. Chevallier And O. Planchon, “The Prediction Of Hillslope Flow Paths For Distributed Hydrological Modelling Using Digital Terrain Models,” Hydrological Processes, Vol. Vol. 5, Pp. 59-79, 1991. [16] V. B., “Comparison of Single and Multiple Flow Direction Algorithm for Computing Topographic Parameters in Topmodel,” 2000. [17] J.-f. G. P. T. K. T. Guang-ju ZHAO, “Comparison of two different methods for determining flow direction in catchment hydrological modeling,” Water Science and Engineering, vol. 2, no. 4, pp. 1-15, 2009. [18] D. G. Tarboton, “A New Method For The Determination Of Flow Directions And Upslope Areas In Grid Digital Elevation Models,” Water Resources Research, Vol. 33, No. 2, P. 33, 309-319. [19] V. Baumann, “Debris flow susceptibility mapping at a regional scale along the National Road N7, Argentina,” in CGS Geotechnical Conference, Argentina, 2011. [20] Q. Z. Petter Pilesjö, “Theoretical Estimation Of Flow Accumulation From A Grid-Based Digital Elevation Model,” In Proceedings Of Gis Am/Fm Asia’97 And Geoinformatics’97 Conference, Taipei, 1997. [21] G. A. D. Y. a. C. S. L. John P. WILSON, “Water in the Landscape: A Review of Contemporary Flow Routing Algorithms,” pp. 213-236. [22] “MathWorks,” The MathWorks, Inc., [Online]. Available: https://in.mathworks.com/. [Accessed 1 10 2017]. [23] “What is GIS?,” Esri, [Online]. Available: http://www.esri.com/what-is-gis. [Accessed 12 11 2017]. [24] P. Barrett, “Paul Barrett,” Wikimedia Foundation, Inc, [Online]. Available: http://www.pbarrett.net/techpapers/euclid.pdf. [Accessed 05 01 2018].
[25] S. S. Gruber, Land-surface parameters and objects in hydrology., Elsevier, 2009. [26] “Landscape Evolution Modeling with CHILD,” Community Surface Dynamics Modeling System, [Online]. Available: http://csdms.colorado.edu/wiki/Labs_Landscape_Evolution_Modeling_With_Child_Part_2. [Accessed 13 01 2018]. [27] M. Cooper, “Depth Recovery through Linear Algebra,” in Line Drawing Interpretation, Springer Science & Business Media., p. 118. [28] A. P. Nicholas, “Cellular modelling in fluvial geomorphology,” in Earth Surface Processes and Landforms, 2005, p. 645–649. [29] “Making Successful Maps,” DroneDeploy, [Online]. Available: https://support.dronedeploy.com/v1.0/docs/making-successful-maps. [Accessed 15 10 2017]. [30] “M_Map:A mapping package for Matlab,” rich@eos.ubc.ca, [Online]. Available: https://www.eoas.ubc.ca/~rich/map.html. [Accessed 15 01 2018]. [31] P. Dulanjalee, “Landslide Flow Path Assessment for Susceptibility Mapping at a Regional Scale,” in ‘Investing in Disaster Risk Reduction for Resilience’’- NBRO holds 8th Annual Symposium, Colombo, 2017. [32] L. K. a. D. M. E. Boyagoda, ” Subsurface Geotechnical Characterization,” in International Symposium, NBRO, Colombo, Sri Lanka, 2016. [33] E. E. Duncan and A. A. Rahman, “An Amalgamation Of 3d Spatial Data Model For Surface And Subsurface Spatial Objects.,” in Knowing To Manage The Territory, Protect The Environment, Evaluate The Cultural Heritage, Rome, Italy, 2012.
In this study a gating system including sprue, runner and overflows for semi-solid rheocasting of aluminum alloy was designed by means of numerical simulations with a commercial software. The effects of pouring temperature, mold temperature and injection speed on the filling process performance of semi-solid die casting were studied. Based on orthogonal test analysis, the optimal die casting process parameters were selected, which were metal pouring temperature 590 °C, mold temperature 260 °C and injection velocity 0.5 m/s. Semi-solid slurry preparation process of Swirled Enthalpy Equilibration Device (SEED) was used for die casting production experiment. Aluminum alloy semi-solid bracket components were successfully produced with the key die casting process parameters selected, which was consistent with the simulation result. The design of semi-solid gating system was further verified by observing and analyzing the microstructure of different zones of the casting. The characteristic parameters, particle size and shape factor of microstructure of the produced semi-solid casting showed that the semi-solid aluminum alloy components are of good quality.
이 연구에서 알루미늄 합금의 반고체 레오캐스팅을 위한 스프루, 러너 및 오버플로를 포함하는 게이팅 시스템은 상용 소프트웨어를 사용한 수치 시뮬레이션을 통해 설계되었습니다. 주입 온도, 금형 온도 및 사출 속도가 반고체 다이캐스팅의 충전 공정 성능에 미치는 영향을 연구했습니다. 직교 테스트 분석을 기반으로 금속 주입 온도 590°C, 금형 온도 260°C 및 사출 속도 0.5m/s인 최적의 다이 캐스팅 공정 매개변수가 선택되었습니다. Swirled Enthalpy Equilibration Device(SEED)의 반고체 슬러리 제조 공정을 다이캐스팅 생산 실험에 사용하였다. 알루미늄 합금 반고체 브래킷 구성 요소는 시뮬레이션 결과와 일치하는 주요 다이 캐스팅 공정 매개변수를 선택하여 성공적으로 생산되었습니다. 반고체 게이팅 시스템의 설계는 주조의 다른 영역의 미세 구조를 관찰하고 분석하여 추가로 검증되었습니다. 생산된 반고체 주조물의 특성 매개변수, 입자 크기 및 미세 구조의 형상 계수는 반고체 알루미늄 합금 부품의 품질이 양호함을 보여주었습니다.
Gating System Design Based on Numerical Simulation and Production Experiment Verification of Aluminum Alloy Bracket Fabricated by Semi-solid Rheo-Die Casting Process
References
G. Li, H. Lu, X. Hu et al., Current progress in rheoforming of wrought aluminum alloys: a review. Met. Open Access Metall. J. 10(2), 238 (2020)CASGoogle Scholar
C. Xghab, D. Qza, E. Spma et al., Blistering in semi-solid die casting of aluminium alloys and its avoidance. Acta Mater. 124, 446–455 (2017)ArticleGoogle Scholar
M. Modigell, J. Koke, Rheological modelling on semi-solid metal alloys and simulation of thixocasting processes. J. Mater. Process. Technol. 111(1–3), 53–58 (2001)CASArticleGoogle Scholar
A. Pola, M. Tocci, P. Kapranos, Microstructure and properties of semi-solid aluminum alloys: a literature review. Met. Open Access Metall. J. 8(3), 181 (2018)Google Scholar
Q. Zhu, Semi-solid moulding: competition to cast and machine from forging in making automotive complex components. Trans. Nonferrous Met. Soc. China 20, 1042–1047 (2010)ArticleGoogle Scholar
B. Zhou, S. Lu, K. Xu et al., Microstructure and simulation of semisolid aluminum alloy castings in the process of stirring integrated transfer-heat (SIT) with water cooling. Int. J. Metalcast. 14(2), 396–408 (2019). https://doi.org/10.1007/s40962-019-00357-6CASArticleGoogle Scholar
S. Ji, Z. Fan, Solidification behavior of Sn–15 wt Pct Pb alloy under a high shear rate and high intensity of turbulence during semisolid processing. Metall. Mater. Trans. A. 33(11), 3511–3520 (2002). https://doi.org/10.1007/s11661-002-0338-4ArticleGoogle Scholar
H.V. Atkinson, Alloys for semi-solid processing. Solid State Phenom. 192–193, 16–27 (2013)Google Scholar
L. Rogal, Critical assessment: opportunities in developing semi-solid processing: aluminium, magnesium, and high-temperature alloys. Mater. Sci. Technol. Mst A Publ. Inst. Met. 33, 759–764 (2017)CASArticleGoogle Scholar
H. Guo, Rheo-diecasting process for semi-solid aluminum alloys. J. Wuhan Univ. Technol. Mater. Sci. Ed. 22(004), 590–595 (2007)CASArticleGoogle Scholar
T. Chucheep, J. Wannasin, R. Canyook, T. Rattanochaikul, S. Janudom, S. Wisutmethangoon, M.C. Flemings, Characterization of flow behavior of semi-solid slurries with low solid fractions. Metall. Mater. Trans. A 44(10), 4754–4763 (2013)CASArticleGoogle Scholar
M. Li, Y.D. Li, W.L. Yang et al., Effects of forming processes on microstructures and mechanical properties of A356 aluminum alloy prepared by self-inoculation method. Mater. Res. 22(3) (2019)
P. Côté, M.E. Larouche, X.G. Chen et al., New developments with the SEED technology. Solid State Phenom. 192(3), 373–378 (2012)ArticleGoogle Scholar
I. Dumanić, S. Jozić, D. Bajić et al., Optimization of semi-solid high-pressure die casting process by computer simulation, Taguchi method and grey relational analysis. Inter Metalcast. 15, 108–118 (2021). https://doi.org/10.1007/s40962-020-00422-5ArticleGoogle Scholar
A. Guo, J. Zhao, C. Xu et al., Effects of pouring temperature and electromagnetic stirring on porosity and mechanical properties of A357 aluminum alloy rheo-diecasting. J. Mater. Eng. Perform. (2018). https://doi.org/10.1007/s11665-018-3310-1ArticleGoogle Scholar
C.G. Kang, S.M. Lee, B.M. Kim, A study of die design of semi-solid die casting according to gate shape and solid fraction. J. Mater. Process. Technol. 204(1–3), 8–21 (2008)CASArticleGoogle Scholar
Z.Y. Liu, W.M. Mao, W.P. Wang et al., Investigation of rheo-diecasting mold filling of semi-solid A380 aluminum alloy slurry. Int. J. Miner. Metall. Mater. 24(006), 691–700 (2017)CASArticleGoogle Scholar
M. Arif, M.Z. Omar, N. Muhamad et al., Microstructural evolution of solid-solution-treated Zn–22Al in the semisolid state. J. Mater. Sci. Technol. 29(008), 765–774 (2013)CASArticleGoogle Scholar
Jongchan Yi 1, Jonghun Lee 1, Mohd Amiruddin Fikri 2,3, Byoung-In Sang 4 and Hyunook Kim 1,*
Abstract
염소화는 상대적인 효율성과 저렴한 비용으로 인해 발전소 냉각 시스템에서 생물학적 오염을 제어하는데 선호되는 방법입니다. 해안 지역에 발전소가 있는 경우 바닷물을 사용하여 현장에서 염소를 전기화학적으로 생성할 수 있습니다. 이를 현장 전기염소화라고 합니다. 이 접근 방식은 유해한 염소화 부산물이 적고 염소를 저장할 필요가 없다는 점을 포함하여 몇 가지 장점이 있습니다. 그럼에도 불구하고, 이 전기화학적 공정은 실제로는 아직 초기 단계에 있습니다. 이 연구에서는 파일럿 규모 냉각 시스템에서 염소 붕괴를 시뮬레이션하기 위해 병렬 1차 동역학을 적용했습니다. 붕괴가 취수관을 따라 발생하기 때문에 동역학은 전산유체역학(CFD) 코드에 통합되었으며, 이후에 파이프의 염소 거동을 시뮬레이션하는데 적용되었습니다. 실험과 시뮬레이션 데이터는 강한 난류가 형성되는 조건하에서도 파이프 벽을 따라 염소 농도가 점진적인 것으로 나타났습니다. 염소가 중간보다 파이프 표면을 따라 훨씬 더 집중적으로 남아 있다는 사실은 전기 염소화를 기반으로 하는 시스템의 전체 염소 요구량을 감소시킬 수 있었습니다. 현장 전기 염소화 방식의 냉각 시스템은 직접 주입 방식에 필요한 염소 사용량의 1/3만 소비했습니다. 따라서 현장 전기염소화는 해안 지역의 발전소에서 바이오파울링 제어를 위한 비용 효율적이고 환경 친화적인 접근 방식으로 사용될 수 있다고 결론지었습니다.
Chlorination is the preferred method to control biofouling in a power plant cooling system due to its comparative effectiveness and low cost. If a power plant is located in a coastal area, chlorine can be electrochemically generated in-situ using seawater, which is called in-situ electrochlorination; this approach has several advantages including fewer harmful chlorination byproducts and no need for chlorine storage. Nonetheless, this electrochemical process is still in its infancy in practice. In this study, a parallel first-order kinetics was applied to simulate chlorine decay in a pilot-scale cooling system. Since the decay occurs along the water-intake pipe, the kinetics was incorporated into computational fluid dynamics (CFD) codes, which were subsequently applied to simulate chlorine behavior in the pipe. The experiment and the simulation data indicated that chlorine concentrations along the pipe wall were incremental, even under the condition where a strong turbulent flow was formed. The fact that chlorine remained much more concentrated along the pipe surface than in the middle allowed for the reduction of the overall chlorine demand of the system based on the electro-chlorination. The cooling system, with an in-situ electro-chlorination, consumed only 1/3 of the chlorine dose demanded by the direct injection method. Therefore, it was concluded that in-situ electro-chlorination could serve as a cost-effective and environmentally friendly approach for biofouling control at power plants on coastal areas.
Keywords
computational fluid dynamics; power plant; cooling system; electro-chlorination; insitu chlorination
Figure 1. Electrodes and batch experiment set-up. (a) Two cylindrical electrodes used in this study.
(b) Batch experiment set-up for kinetic tests. Figure 2. Schematic diagram for pilot-scale cooling-water circulation system (a) along with a real
picture of the system (b).Figure 3. Free chlorine decay curves in seawater with different TOC and initial chlorine concentration.
Each line represents the predicted concentration of chlorine under a given condition. (a) Artificial
seawater solution with 1 mg L−1 of TOC; (b) artificial seawater solution with 2 mg L−1 of TOC; (c)
artificial seawater solution with 3 mg L−1 of TOC; (d) West Sea water (1.3 mg L−1 of TOC). Figure 4. Correlation between model and experimental data in the chlorine kinetics using seawater.Figure 5. Free chlorine concentrations in West Sea water under different current conditions in an insitu electro-chlorination system. Figure 6. Free chlorine distribution along the sampling ports under different flow rates. Each dot
represents experimental data, and each point on the black line is the expected chlorine concentration
obtained from computational fluid dynamics (CFD) simulation with a parallel first-order decay
model. The red-dotted line is the desirable concentration at the given flow rate: (a) 600 L min−1 of flow
rate, (b) 700 L min−1 of flow rate, (c) 800 L min−1 of flow rate, (d) 900 L min−1 of flow rate.Figure 7. Fluid contour images from CFD simulation of the electro-chlorination experiment. Inlet flow
rate is 800 L min−1. Outlet pressure was set to 10.8 kPa. (a) Chlorine concentration; (b) expanded view
of electrode side in image (a); (c) velocity magnitude; (d) pressure. Figure 8. Chlorine concentration contour in the simulation of full-scale in-situ electro-chlorination
with different cathode positions. The pipe diameter is 2 m and the flow rate is 14 m3 s−1. The figure
shows 10 m of the pipeline. (a) The simulation result when the cathode is placed on the surface of the
pipe wall. (b) The simulation result when the cathode is placed on the inside of the pipe with 100 mm
of distance from the pipe wall.Figure 9. Comparison of in-situ electro-chlorination and direct chlorine injection in full-scale
applications. (a) Estimated chlorine concentrations along the pipe surface. (b) Relative chlorine
demands.
References
Macknick, J.; Newmark, R.; Heath, G.; Hallett, K.C. Operational water consumption and withdrawal factors for electricity generating technologies: A review of existing literature. Environ. Res. Lett. 2012, 7, 045802.
Pan, S.-Y.; Snyder, S.W.; Packman, A.I.; Lin, Y.J.; Chiang, P.-C. Cooling water use in thermoelectric power generation and its associated challenges for addressing water-energy nexus. Water-Energy Nexus 2018, 1, 26–41.
Feeley, T.J., III; Skone, T.J.; Stiegel, G.J., Jr.; McNemar, A.; Nemeth, M.; Schimmoller, B.; Murphy, J.T.; Manfredo, L. Water: A critical resource in the thermoelectric power industry. Energy 2008, 33, 1–11.
World Nuclear Association. World Nuclear Performance Report 2016; World Nuclear Association: London, UK, 2016.
Pugh, S.; Hewitt, G.; Müller-Steinhagen, H. Fouling during the use of seawater as coolant—The development of a user guide. Heat Transf. Eng. 2005, 26, 35–43.
Satpathy, K.K.; Mohanty, A.K.; Sahu, G.; Biswas, S.; Prasad, M.; Slvanayagam, M. Biofouling and its control in seawater cooled power plant cooling water system—A review. Nucl. Power 2010, 17, 191–242.
Cristiani, P.; Perboni, G. Antifouling strategies and corrosion control in cooling circuits. Bioelectrochemistry 2014, 97, 120–126.
Walker, M.E.; Safari, I.; Theregowda, R.B.; Hsieh, M.-K.; Abbasian, J.; Arastoopour, H.; Dzombak, D.A.; Miller, D.C. Economic impact of condenser fouling in existing thermoelectric power plants. Energy 2012,44, 429–437.
Yi, J.; Ahn, Y.; Hong, M.; Kim, G.-H.; Shabnam, N.; Jeon, B.; Sang, B.-I.; Kim, H. Comparison between OCl−-Injection and In Situ Electrochlorination in the Formation of Chlorate and Perchlorate in Seawater. Appl.Sci. 2019, 9, 229.
Xue, Y.; Zhao, J.; Qiu, R.; Zheng, J.; Lin, C.; Ma, B.; Wang, P. In Situ glass antifouling using Pt nanoparticle coating for periodic electrolysis of seawater. Appl. Surf. Sci. 2015, 357, 60–68.
Mahfouz, A.B.; Atilhan, S.; Batchelor, B.; Linke, P.; Abdel-Wahab, A.; El-Halwagi, M.M. Optimal scheduling of biocide dosing for seawater-cooled power and desalination plants. Clean Technol. Environ. Policy 2011, 13, 783–796.
Rubio, D.; López-Galindo, C.; Casanueva, J.F.; Nebot, E. Monitoring and assessment of an industrial antifouling treatment. Seasonal effects and influence of water velocity in an open once-through seawater cooling system. Appl. Therm. Eng. 2014, 67, 378–387.
European Integrated Pollution Prevention and Control (IPPC) Bureau, European Commission. Reference Document on the Application of Best Available Techniques to Industrial Cooling Systems December 2001; European Commission, Tech. Rep: Brussels, Belgium, 2001.
Venkatesan R.; Murthy P. S. Macrofouling Control in Power Plants. In Springer Series on Biofilms; Springer: Berlin/Heidelberg, Germany, 2008.
Kastl, G.; Fisher, I.; Jegatheesan, V. Evaluation of chlorine decay kinetics expressions for drinking water distribution systems modelling. J. Water Supply Res. Technol. AQUA 1999, 48, 219–226.
Fisher, I.; Kastl, G.; Sathasivan, A.; Cook, D.; Seneverathne, L. General model of chlorine decay in blends of surface waters, desalinated water, and groundwaters. J. Environ. Eng. 2015, 141, 04015039.
Fisher, I.; Kastl, G.; Sathasivan, A.; Jegatheesan, V. Suitability of chlorine bulk decay models for planning and management of water distribution systems. Crit. Rev. Environ. Sci. Technol. 2011, 41, 1843–1882.
Fisher, I.; Kastl, G.; Sathasivan, A. Evaluation of suitable chlorine bulk-decay models for water distribution systems. Water Res. 2011, 45, 4896–4908.
Haas, C.N.; Karra, S. Kinetics of wastewater chlorine demand exertion. J. (Water Pollut. Control Fed.) 1984, 56, 170–173.
Zeng, J.; Jiang, Z.; Chen, Q.; Zheng, P.; Huang, Y. The decay kinetics of residual chlorine in cooling seawater simulation experiments. Acta Oceanol. Sin. 2009, 28, 54–59.
Saeed, S.; Prakash, S.; Deb, N.; Campbell, R.; Kolluru, V.; Febbo, E.; Dupont, J. Development of a sitespecific kinetic model for chlorine decay and the formation of chlorination by-products in seawater. J. Mar. Sci. Eng. 2015, 3, 772–792.
Al Heboos, S.; Licskó, I. Application and comparison of two chlorine decay models for predicting bulk chlorine residuals. Period. Polytech. Civ. Eng. 2017, 61, 7–13.
Shadloo, M.S.; Oger, G.; Le Touzé, D. Smoothed particle hydrodynamics method for fluid flows, towards industrial applications: Motivations, current state, and challenges. Comput. Fluids 2016, 136, 11–34.
Wols, B.; Hofman, J.; Uijttewaal, W.; Rietveld, L.; Van Dijk, J. Evaluation of different disinfection calculation methods using CFD. Environ. Model. Softw. 2010, 25, 573–582.
Angeloudis, A.; Stoesser, T.; Falconer, R.A. Predicting the disinfection efficiency range in chlorine contact tanks through a CFD-based approach. Water Res. 2014, 60, 118–129.
Zhang, J.; Tejada-Martínez, A.E.; Zhang, Q. Developments in computational fluid dynamics-based modeling for disinfection technologies over the last two decades: A review. Environ. Model. Softw. 2014, 58,71–85.
Lim, Y.H.; Deering, D.D. In Modeling Chlorine Residual in a Ground Water Supply Tank for a Small Community in Cold Conditions, World Environmental and Water Resources Congress 2017; American Society of Civil Engineers: Reston, Virginia, USA, 2017; pp. 124–138.
Hernández-Cervantes, D.; Delgado-Galván, X.; Nava, J.L.; López-Jiménez, P.A.; Rosales, M.; Mora Rodríguez, J. Validation of a computational fluid dynamics model for a novel residence time distribution analysis in mixing at cross-junctions. Water 2018, 10, 733.
Hua, F.; West, J.; Barker, R.; Forster, C. Modelling of chlorine decay in municipal water supplies. Water Res. 1999, 33, 2735–2746.
Nejjari, F.; Puig, V.; Pérez, R.; Quevedo, J.; Cugueró, M.; Sanz, G.; Mirats, J. Chlorine decay model calibration and comparison: Application to a real water network. Procedia Eng. 2014, 70, 1221–1230.
Kohpaei, A.J.; Sathasivan, A.; Aboutalebi, H. Effectiveness of parallel second order model over second and first order models. Desalin. Water Treat. 2011, 32, 107–114.
Powell, J.C.; Hallam, N.B.; West, J.R.; Forster, C.F.; Simms, J. Factors which control bulk chlorine decay rates. Water Res. 2000, 34, 117–126.
Clark, R.M.; Sivaganesan, M. Predicting chlorine residuals in drinking water: Second order model. J. Water Resour. Plan. Manag. 2002, 128, 152–161.
Li, X.; Li, C.; Bayier, M.; Zhao, T.; Zhang, T.; Chen, X.; Mao, X. Desalinated seawater into pilot-scale drinking water distribution system: Chlorine decay and trihalomethanes formation. Desalin. Water Treat. 2016, 57,19149–19159.
United States Environmental Protection Agency (EPA). Chlorine, Total Residual (Spectrophotometric, DPD); EPA-NERL: 330.5; EPA: Cincinnati, OH, USA, 1978.
Polman, H.; Verhaart, F.; Bruijs, M. Impact of biofouling in intake pipes on the hydraulics and efficiency of pumping capacity. Desalin. Water Treat. 2013, 51, 997–1003.
Rajagopal, S.; Van der Velde, G.; Van der Gaag, M.; Jenner, H.A. How effective is intermittent chlorination to control adult mussel fouling in cooling water systems? Water Res. 2003, 37, 329–338.
Bruijs, M.C.; Venhuis, L.P.; Daal, L. Global Experiences in Optimizing Biofouling Control through PulseChlorination®. 2017. Available online: https://www.researchgate.net/publication/318561645_Global_Experiences_in_Optimizing_Biofouling_Co ntrol_through_Pulse-ChlorinationR (accessed on 1 May 2020).
Kim, H.; Hao, O.J.; McAvoy, T.J. Comparison between model-and pH/ORP-based process control for an AAA system. Tamkang J. Sci. Eng. 2000, 3, 165–172.
Brdys, M.; Chang, T.; Duzinkiewicz, K. Intelligent Model Predictive Control of Chlorine Residuals in Water Distribution Systems, Bridging the Gap: Meeting the World’s Water and Environmental Resources Challenges. In Proceedings of the ASCE Water Resource Engineering and Water Resources Planning and Management, July 30–August 2, 2000; pp. 1–11
1Tecnológico Nacional de México/ITS de Los Reyes. Carretera Los Reyes-Jacona, Col. Libertad. 60300. Los Reyes de Salgado, Michoacán. México.
ernesto.ar@losreyes.tecnm.mx – 3541013901 (*Autor de correspondencia)
2Instituto de Ciencias Aplicadas y Tecnología, UNAM. Cto. Exterior S/N, C.U., Coyoacán, 04510, Ciudad de México. México. 3Riego y Drenaje. Instituto Mexicano de Tecnología del Agua. Paseo Cuauhnáhuac 8532, Progreso, Jiutepec, Morelos, C.P. 62550. México.
Abstract
공학에서 유체의 거동은 설명하기에 광범위하고 복잡한 과정이며, 유체역학은 유체의 거동을 지배하는 방정식을 통해 유체 역학 현상을 분석할 수 있는 과학 분야이지만 이러한 방정식에는 전체 솔루션이 없습니다. . 전산유체역학(Computational Fluid Dynamics, 이하 CFD)은 수치적 기법을 통해 방정식의 해에 접근할 수 있는 도구로, 신뢰할 수 있는 계산 모델을 얻기 위해서는 물리적 모델의 실험 데이터로 평가해야 합니다. 수력구조물에서 선형 및 미로형 여수로에서 시뮬레이션을 수행하고 배출 시트의 거동과 현재의 폭기 조건을 분석했습니다. 침강기에서 유체의 특성화를 수행하고 필요한 특성에 따라 사체적, 피스톤 또는 혼합의 분수를 수정하는 것이 가능합니다. 농업에서는 온실 환경을 특성화하고 환경에 대한 재료의 디자인, 방향 및 유형 간의 관계를 찾는 데 사용할 수 있습니다. 발견된 가장 중요한 결과 중 온실의 길이와 설계가 환기율에 미칠 수 있는 영향으로 온실의 길이는 높이의 6배 미만인 것이 권장됩니다.
키워드: Computational Fluid Dynamics, 온실,
Spillway, Settler 기사: COMEII-21048 소개
CFD는 유체 운동 문제에 대한 수치적 솔루션을 얻어 수리학적 현상을 더 잘 이해할 수 있게 함으로써 공간 시각화를 가능하게 하는 수치 도구입니다. 예를 들어, 수력 공학에서 벤츄리(Xu, Gao, Zhao, & Wang, 2014) 워터 펌핑(ȘCHEAUA, 2016) 또는 개방 채널 적용( Wu et 알., 2000).
문헌 검토는 실험 연구에서 검증된 배수로의 흐름 거동에 대한 수리학적 분석을 위한 CFD 도구의 효율성을 보여줍니다. 이 검토는 둑의 흐름 거동에 대한 수리학적 분석을 위한 CFD의 효율성을 보여줍니다. Crookston et al. (2012)는 미로 여수로에 대해 Flow 3D로 테스트를 수행했으며, 배출 계수의 결과는 3%에서 7%까지 다양한 오류로 실험적으로 얻은 결과로 허용 가능했으며 연구 결과 측면에 저압 영역이 있음을 발견했습니다. 익사 방식으로 작업할 때 위어의 벽. Zuhair(2013)는 수치 모델링 결과를 Mandali weir 원형의 실험 데이터와 비교했습니다.
최근 연구에서는 다양한 난류 모델을 사용하여 CFD를 적용할 가능성이 있음을 보여주었습니다. 그리고 일부만이 음용수 처리를 위한 침적자의 사례 연구를 제시했으며, 다른 설계 변수 중에서 기하학적인 대안, 수온 변화 등을 제안했습니다. 따라서 기술 개발로 인해 설계 엔지니어가 유체 거동을 분석하는 데 CFD 도구를 점점 더 많이 사용하게 되었습니다.
보호 농업에서 CFD는 온실 환경을 모델링하고 보조 냉방 또는 난방 시스템을 통해 온실의 미기후 관리를 위한 전략을 제안하는 데 사용되는 기술이었습니다(Aguilar Rodríguez et al., 2020).
2D 및 3D CFD 모델을 사용한 본격적인 온실 시뮬레이션은 태양 복사 모델과 현열 및 잠열 교환 하위 모델의 통합을 통해 온실의 미기후 분포를 연구하는 데 사용되었습니다(Majdoubi, Boulard, Fatnassi, & Bouirden, 2009). 마찬가지로 이 모델을 사용하여 온실 설계(Sethi, 2009), 덮개 재료(Baxevanou, Fidaros, Bartzanas, & Kittas, 2018), 시간, 연중 계절( Tong, Christopher, Li, & Wang, 2013), 환기 유형 및 구성(Bartzanas, Boulard, & Kittas, 2004).
CFD 거래 프로그램은 사용자 친화적인 플랫폼으로 설계되어 결과를 쉽게 관리하고 이해할 수 있습니다.
…
Figura 1. Distribución de presiones y velocidades en un vertedor de pared delgada.Figura 2. Perfiles de velocidad y presión en la cresta vertedora.Figura 3. Condiciones de aireación en vertedor tipo laberinto. (A)lámina adherida a la pared del vertedor, (B) aireado, (C) parcialmente aireado, (D) ahogado.Figura 4. Realización de prueba de riego.Figura 5. Efecto de la posición y dirección de los calefactores en un invernadero a 2 m del suelo.Figura 6. Indicadores ambientales para medir el confort ambiental de los cultivos.Figura 7. Líneas de corriente dentro del sedimentador experimental en estado estacionario
(Ramirez-Ruiz, 2019).
Referencias Bibliográficas
Aguilar-Rodriguez, C.; Flores-Velazquez, J.; Ojeda-Bustamante, W.; Rojano, F.; Iñiguez- Covarrubias, M. 2020. Valuation of the energyperformance of a greenhouse with
an electric heater using numerical simulations. Processes, 8, 600.
Aguilar-Rodriguez, C.; Flores-Velazquez, J.; Rojano, F.; Ojeda-Bustamante, W.; Iñiguez- Covarrubias, M. 2020. Estimación del ciclo de cultivo de tomate (Solanum
lycopersicum L.) en invernadero, con base en grados días calor (GDC) simulados con CFD. Tecnología y ciencias del agua, ISSN 2007-2422, 11(4), 27-57. Al-Sammarraee, M., y Chan, A. (2009). Large-eddy simulations of particle sedimentation in a longitudinal sedimentation basin of a water treatment plant. Part 2: The effects of baffles. Chemical Engineering Journal, 152(2-3), 315-321. doi:https://doi.org/10.1016/j.cej.2009.01.052. Bartzanas, T.; Boulard, T.; Kittas, C. 2004. Effect of vent arrangement on windward ventilation of a tunnel greenhouse. Biosystems Engineering, 88(4). Baxevanou, C.; Fidaros, D.; Bartzanas, T.; Kittas, C. 2018. Yearly numerical evaluation of greenhouse cover materials. Computers and Electronics in Agriculture, 149, 54–
DOI: https://doi.org/10.1016/j.compag.2017.12.006. Crookston, B. M., & Tullis, B. P. 2012. Labyrinth weirs: Nappe interference and local submergence. Journal of Irrigation and Drainage Engineering, 138(8), 757-765. Fernández, J. M. 2012. Técnicas numéricas en Ingeniería de Fluidos: Introducción a la Dinámica de Fluidos Computacional (CFD) por el Método de Volumen Finito; Reverté, Barcelona, pp. 98-294. Goula, A., Kostoglou, M., Karapantsios, T., y Zouboulis, A. (2008). The effect of influent temperature variations in a sedimentation tank for potable water treatment— A computational fluid dynamics study. Water Research, 42(13), 3405-3414. doi://doi.org/10.1016/j.watres.2008.05.002. Majdoubi, H.; Boulard, T.; Fatnassi, H.; Bouirden, L. 2009. Airflow and microclimate patterns in a one-hectare Canary type greenhouse: an experimental and CFD assisted study. Agricultural and Forest Meteorology, 149(6-7), 1050-1062. Ramirez-Ruiz Candido (2019). Estudio hidrodinámico de sedimentadores de alta tasa en plantas potabilizadoras utilizando dinámica de fluidos computacional (CFD). Universidad Nacional Autónoma de México. Tesis de maestría. Sánchez, J. M. C., & Elsitdié, L. G. C. 2011. Consideraciones del mallado aplicadas al cálculo de flujos bifásicos con las técnicas de dinámica de fluidos computacional. J. Introd. Inv. UPCT., 4, 33-35. Sethi, V.P. 2009. On the selection of shape and orientation of a greenhouse: Thermal modeling and experimental validation, Sol. Energy, 83, 21–38. ȘCHEAUA, F. 2016. AGRICULTURAL FIELD IRRIGATION SOLUTION BASED ON VENTURI NOZZLE γ 2 g γ 2 g. JOURNAL OF INDUSTRIAL DESIGN AND ENGINEERING GRAPHICS, 2(1), 31–35.
Tong, G.; Christopher, D.; Li, T.; Wang, T. 2013. Passive solar energy utilization: a review of cross-section building parameter selection for Chinese solar greenhouses. Renewable and Sustainable Energy Reviews, 26, 540-548.
Xu, Y., Gao, L., Zhao, Y., & Wang, H. 2014. Wet gas overreading characteristics of a long- throat Venturi at high pressure based on CFD. Flow Measurement and
Instrumentation, 40, 247–255. https://doi.org/10.1016/j.flowmeasinst.2014.09.004 Wu, W., Rodi, W y Wenka, T. 2000. 3D numerical modeling of flow and sediment transport in open channels. ASCE Journal of Hydraulic Engineering. Vol 126 Num 1. Zuhair al zubaidy, Riyadh. 2013. Numerical Simulation of Two-Phase Flow. En:International Journal of Structural and Civil Engineering Research. Vol 2, No 3; 13p
aUniversity of Padova, Department of Management and Engineering, Vicenza, Italy bUniversity of Bayburt, Mechanical Engineering, Bayburt, Turkey cAtilim University, Metallurgical and Materials Engineering, Ankara, Turkey dIstanbul Technical University, Metallurgical and Materials Engineering, Istanbul, Turkey eCenter for Critical and Functional Materials, ITU, Istanbul, Turkey
ABSTRACT
The demand for lighter weight decreased thickness and higher strength has become the focal point in the automotive industry. In order to meet such requirements, the addition of several alloying elements has been started to be investigated. In this work, the additions of V, B, and Sr on feedability and tensile properties of A360 has been studied. A mold design that consisted of test bars has been produced. Initially, a simulation was carried out to optimize the runners, filling, and solidification parameters. Following the tests, it was found that V addition revealed the highest UTS but low elongation at fracture, while B addition exhibited visa verse. On the other hand, impact energy was higher with B additions.
더 가벼운 무게의 감소된 두께와 더 높은 강도에 대한 요구는 자동차 산업의 초점이 되었습니다. 이러한 요구 사항을 충족하기 위해 여러 합금 원소의 추가가 조사되기 시작했습니다. 이 연구에서는 A360의 이송성 및 인장 특성에 대한 V, B 및 Sr의 첨가가 연구되었습니다. 시험봉으로 구성된 금형 설계가 제작되었습니다. 처음에는 러너, 충전 및 응고 매개변수를 최적화하기 위해 시뮬레이션이 수행되었습니다. 시험 결과, V 첨가는 UTS가 가장 높지만 파단 연신율은 낮았고, B 첨가는 visa verse를 나타냈다. 반면에 충격 에너지는 B 첨가에서 더 높았다.
Fig. 1. Modified Timelli mold design.Fig. 2. Microstructural images (a) unmodified alloy, (b) Sr modified, (c) V added, (d) B added. Fig. 3. Effect of Sr and V addition on the tensile properties of A360Fig. 4. Effect of Sr and B addition on the tensile properties of A360.Fig. 5. Bubbles chart of tensile properties values obtained from Weibull statistics. Fig. 6. Effect of Sr, V and B addition on the impact properties of A360.Fig. 7. SEM images on the fracture surfaces (a) V added, (b) B added.
References
[1] A. Johanson, Effect of Vanadium on Grain Refinement of Aluminium, Institutt for materialteknologi, 2013. [2] D.G. McCartney, Grain refining of aluminium and its alloys using inoculants, Int. Mater. Rev. 34 (1) (1989) 247–260. [3] M.T. Di Giovanni, The Influence of Ni and V Trace Elements on the High Temperature Tensile Properties of A356 Aluminium Foundry Alloy, Institutt for materialteknologi, 2014. [4] D. Casari, T.H. Ludwig, M. Merlin, L. Arnberg, G.L. Garagnani, The effect of Ni and V trace elements on the mechanical properties of A356 aluminium foundry alloy in as-cast and T6 heat treated conditions, Mater. Sci. Eng., A 610 (2014) 414–426. [5] D. Casari, T.H. Ludwig, M. Merlin, L. Arnberg, G.L. Garagnani, Impact behavior of A356 foundry alloys in the presence of trace elements Ni and V, J. Mater. Eng. Perform. 24 (2) (2015) 894–908. [6] T.H. Ludwig, P.L. Schaffer, L. Arnberg, Influence of some trace elements on solidification path and microstructure of Al-Si foundry alloys, Metall. Mater. Trans. 44 (8) (2013) 3783–3796. [7] H.A. Elhadari, H.A. Patel, D.L. Chen, W. Kasprzak, Tensile and fatigue properties of a cast aluminum alloy with Ti, Zr and V additions, Mater. Sci. Eng., A 528 (28) (2011) 8128–8138. [8] Y. Wu, H. Liao, K. Zhou, “Effect of minor addition of vanadium on mechanical properties and microstructures of as-extruded near eutectic Al–Si–Mg alloy, Mater. Sci. Eng., A 602 (2014) 41–48. [9] E.S. Dæhlen, The Effect of Vanadium on AlFeSi-Intermetallic Phases in a Hypoeutectic Al-Si Foundry Alloy, Institutt for materialteknologi, 2013. [10] B. Lin, H. Li, R. Xu, H. Xiao, W. Zhang, S. Li, Effects of vanadium on modification of iron-rich intermetallics and mechanical properties in A356 cast alloys with 1.5 wt. % Fe, J. Mater. Eng. Perform. 28 (1) (2019) 475–484. [11] P.A. Tøndel, G. Halvorsen, L. Arnberg, Grain refinement of hypoeutectic Al-Si foundry alloys by addition of boron containing silicon metal, Light Met. (1993) 783. [12] Z. Chen, et al., Grain refinement of hypoeutectic Al-Si alloys with B, Acta Mater. 120 (2016) 168–178. [13] T. Wang, Z. Chen, H. Fu, J. Xu, Y. Fu, T. Li, “Grain refining potency of Al–B master alloy on pure aluminum, Scripta Mater. 64 (12) (2011) 1121–1124. [14] M. Gorny, ´ G. Sikora, M. Kawalec, Effect of titanium and boron on the stability of grain refinement of Al-Cu alloy, Arch. Foundry Eng. 16 (2016). [15] O. ¨ Gürsoy, E. Erzi, D. Dıs¸pınar, Ti grain refinement myth and cleanliness of A356 melt, in: Shape Casting, Springer, 2019, pp. 125–130. [16] D. Dispinar, A. Nordmark, J. Voje, L. Arnberg, Influence of hydrogen content and bi-film index on feeding behaviour of Al-7Si, in: 138th TMS Annual Meeting, Shape Casting, 3rd International Symposium, San Francisco, California, USA, 2009, pp. 63–70. February 2009. [17] M. Uludag, ˘ R. Çetin, D. Dıs¸pınar, Observation of hot tearing in Sr-B modified A356 alloy, Arch. Foundry Eng. 17 (2017). [18] X.L. Cui, Y.Y. Wu, T. Gao, X.F. Liu, “Preparation of a novel Al–3B–5Sr master alloy and its modification and refinement performance on A356 alloy, J. Alloys Compd. 615 (2014) 906–911. [19] F. Wang, Z. Liu, D. Qiu, J.A. Taylor, M.A. Easton, M.-X. Zhang, Revisiting the role of peritectics in grain refinement of Al alloys, Acta Mater. 61 (1) (2013) 360–370. [20] M. Akhtar, A. Khajuria, Effects of prior austenite grain size on impression creep and microstructure in simulated heat affected zones of boron modified P91 steels, Mater. Chem. Phys. 249 (2020) 122847. [21] M. Akhtar, A. Khajuria, Probing true creep-hardening interaction in weld simulated heat affected zone of P91 steels, J. Manuf. Process. 46 (2019) 345–356. [22] E.M. Schulson, T.P. Weihs, I. Baker, H.J. Frost, J.A. Horton, Grain boundary accommodation of slip in Ni3Al containing boron, Acta Metall. 34 (7) (1986) 1395–1399. [23] I. Baker, E.M. Schulson, J.R. Michael, The effect of boron on the chemistry of grain boundaries in stoichiometric Ni3Al, Philos. Mag. A B 57 (3) (Mar. 1988) 379–385. [24] S. Zhu, et al., Influences of nickel and vanadium impurities on microstructure of aluminum alloys, JOM (J. Occup. Med.) 65 (5) (2013) 584–592. [25] D.J. Beerntsen, Effect of vanadium and zirconium on the formation of CrAI 7 primary crystals in 7075 aluminum alloy, Metall. Mater. Trans. B 8 (3) (1977) 687–688. [26] G. Timelli, A. Fabrizi, S. Capuzzi, F. Bonollo, S. Ferraro, The role of Cr additions and Fe-rich compounds on microstructural features and impact toughness of AlSi9Cu3 (Fe) diecasting alloys, Mater. Sci. Eng., A 603 (2014) 58–68. [27] S. Kirtay, D. Dispinar, Effect of ranking selection on the Weibull modulus estimation, Gazi Univ. J. Sci. 25 (1) (2012) 175–187. [28] J. Rakhmonov, G. Timelli, F. Bonollo, “The effect of transition elements on hightemperature mechanical properties of Al–Si foundry alloys–A review, Adv. Eng. Mater. 18 (7) (2016) 1096–1105.
Liril D.SilviaDinesh K.ChandrakercSumanaGhoshaArup KDasb aDepartment of Chemical Engineering, Indian Institute of Technology, Roorkee, India bDepartment of Mechanical Engineering, Indian Institute of Technology, Roorkee, India cReactor Engineering Division, Bhabha Atomic Research Centre, Mumbai, India
Abstract
Present work reports numerical understanding of interfacial dynamics during co-flow of vapor and liquid phases of water inside a typical Boiling Water Reactor (BWR), consisting of a nuclear fuel rod bundle assembly of 7 pins in a circular array. Two representative spacings between rods in a circular array are used to carry out the simulation. In literature, flow boiling in a nuclear reactor is dealt with mechanistic models or averaged equations. Hence, in the present study using the Volume of Fluid (VOF) based multiphase model, a detailed numerical understanding of breaking and making in interfaces during flow boiling in BWR is targeted. Our work will portray near realistic vapor bubble and liquid flow dynamics in rod bundle scenario. Constant wall heat flux for fuel rod and uniform velocity of the liquid at the inlet patch is applied as a boundary condition. The saturation properties of water are taken at 30 bar pressure. Flow boiling stages involving bubble nucleation, growth, merging, local dry-out, rewetting with liquid patches, and complete dry-out are illustrated. The dry-out phenomenon with no liquid presence is numerically observed with phase fraction contours at various axial cut-sections. The quantification of the liquid phase fraction at different axial planes is plotted over time, emphasizing the progressive dry-out mechanism. A comparison of liquid-vapor distribution for inner and outer rods reveals that the inner rod’s dry-out occurs sooner than that of the outer rod. The heat transfer coefficient to identify the heat dissipation capacity of each case is also reported.
현재 작업은 원형 배열에 있는 7개의 핀으로 구성된 핵연료봉 다발 어셈블리로 구성된 일반적인 끓는 물 원자로(BWR) 내부의 물의 증기 및 액체상의 동시 흐름 동안 계면 역학에 대한 수치적 이해를 보고합니다.
원형 배열의 막대 사이에 두 개의 대표적인 간격이 시뮬레이션을 수행하는 데 사용됩니다. 문헌에서 원자로의 유동 비등은 기계론적 모델 또는 평균 방정식으로 처리됩니다.
따라서 VOF(Volume of Fluid) 기반 다상 모델을 사용하는 본 연구에서는 BWR에서 유동 비등 동안 계면의 파괴 및 생성에 대한 자세한 수치적 이해를 목표로 합니다.
우리의 작업은 막대 번들 시나리오에서 거의 사실적인 증기 기포 및 액체 흐름 역학을 묘사합니다. 연료봉에 대한 일정한 벽 열유속과 입구 패치에서 액체의 균일한 속도가 경계 조건으로 적용됩니다. 물의 포화 특성은 30bar 압력에서 취합니다.
기포 핵 생성, 성장, 병합, 국소 건조, 액체 패치로 재습윤 및 완전한 건조를 포함하는 유동 비등 단계가 설명됩니다. 액체가 존재하지 않는 건조 현상은 다양한 축 단면에서 위상 분율 윤곽으로 수치적으로 관찰됩니다.
다른 축 평면에서 액상 분율의 정량화는 점진적인 건조 메커니즘을 강조하면서 시간이 지남에 따라 표시됩니다. 내부 막대와 외부 막대의 액-증기 분포를 비교하면 내부 막대의 건조가 외부 막대보다 더 빨리 발생함을 알 수 있습니다. 각 경우의 방열 용량을 식별하기 위한 열 전달 계수도 보고됩니다.
Fig. 1. A typical Boiling Water Reactor (BWR) and selected segment of study for simulationFig. 2. (a-c) dimensions and mesh configuration for G = 6 mm; (d-f) dimensions and mesh configuration for G = 0.6 mm
Fig. 3. Simulating the effect of spacer (a) Spacer configuration around rod bundle (b) Mesh structure in spacer zone (c) Distribution of vapor bubbles in a rod bundle with
spacer (d) Liquid phase fraction comparison for geometry with and without spacer (e,f,g) Wall temperature comparison for geometry with and without spacer; WS: With
Spacer, WOS: Without Spacer; Temperature in the y-axis is in (f) and (g) is same as (e).Fig. 4. Validation of the present numerical model with crossflow boiling over a heated cylindrical rod [40]
Fig. 5. Grid-Independent study in terms of vapor volume in 1/4th of computational domainFig. 6. Interface contour for G = 6 mm; ul = 1.2 m/s; q˙ w = 396 kW/m2; they are showing nucleation, growth, merging, and pseudo-steady-state condition.Fig. 7. Interface contours for G = 0.6 mm; ul = 1.2 m/s; q˙ w = 396 kW/m2; It shows dry-out at pseudo-steady-state near the exit Fig. 8. Vapor-liquid distribution across various distant cross-sections (Black color indicates liquid; Gray color indicates vapor); Magnification factor: 1 × (for a and b),
1.5 × (for c and d)
Fig. 21. Two-phase flow mixture velocity (u¯z); for G = 6 mm, r = 5 means location at inner heated wall and r = 25 means location at outer adiabatic wall; for G = 0.66
mm, r = 5 means location at inner heated wall and r = 16.6 mm means location at outer adiabatic wall.
References
[1] J. Würtz, An Experimental and Theoretical Investigation of Annular Steam-Water Flow in Tubes and Annuli at 30 to 90 Bar, Risø National Laboratory, Roskilde, 1978. [2] W. Tian, A. Myint, Z. Li, S. Qiu, G.H. Su, D. Jia, Experimental study on dryout point in vertical narrow annulus under low flow conditions, in: International Conference on Nuclear Engineering, 4689, 2004, pp. 643–648. Jan 1Vol. [3] K.M. Becker, C.H. Ling, S. Hedberg, G. Strand, An experimental investigation of post dryout heat transfer, R. Inst. Technol. (1983). [4] K.M. Becker, A Burnout Correlation for Flow of Boiling Water in Vertical Rod Bundles, AB Atomenergi, 1967. [5] Jr J.R. Barbosa, G.F. Hewitt, S.M. Richardson, High-speed visualisation of nucleate boiling in vertical annular flow, Int. J. Heat Mass Transf. 46 (26) (2003) 5153–5160 1, doi:10.1016/S0017-9310(03)00255-2. [6] Y. Mizutani, A. Tomiyama, S. Hosokawa, A. Sou, Y. Kudo, K. Mishima, Twophase flow patterns in a four by four rod bundle, J. Nucl. Sci. Technol. 44 (6) (2007) 894–901 1, doi:10.1080/18811248.2007.9711327. [7] S.S. Paranjape, Two-Phase Flow Interfacial Structures in a Rod Bundle Geometry, Purdue University, 2009. [8] D. Lavicka, J. Polansky, Model of the cooling of a nuclear reactor fuel rod, Multiph. Sci. Technol. 25 (2-4) (2013), doi:10.1615/MultScienTechn.v25.i2-4.90. [9] M. Thurgood, J. Kelly, T. Guidotti, R. Kohrt, K. Crowell, Tech. rep., Pacific Northwest National Laboratory, 1983. [10] S. Sugawara, Droplet deposition and entrainment modeling based on the three-fluid model, Nucl. Eng. Des. 122 (1-3) (1990) 67–84, doi:10.1016/ 0029-5493(90)90197-6. [11] C. Adamsson, J.M. Le Corre, Modeling and validation of a mechanistic tool (MEFISTO) for the prediction of critical power in BWR fuel assemblies, Nucl. Eng. Des. 241 (8) (2011) 2843–2858, doi:10.1016/j.nucengdes.2011.01.033. [12] S. Talebi, H. Kazeminejad, A mathematical approach to predict dryout in a rod bundle, Nucl. Eng. Des. 249 (2012) 348–356, doi:10.1016/j.nucengdes.2012.04. 016. [13] H. Anglart, O. Nylund, N. Kurul, M.Z. Podowski, CFD prediction of flow and phase distribution in fuel assemblies with spacers, Nucl. Eng. Des. 177 (1-3) (1997) 215–228, doi:10.1016/S0029-5493(97)00195-7. [14] H. Li, H. Anglart, CFD model of diabatic annular two-phase flow using the Eulerian–Lagrangian approach, Ann. Nucl. Energy 77 (2015) 415–424, doi:10. 1016/j.anucene.2014.12.002. [15] G. Sorokin, A. Sorokin, Experimental and numerical investigation of liquid metal boiling in fuel subassemblies under natural circulation conditions, Prog. Nucl. Energy 47 (1-4) (2005) 656–663, doi:10.1016/j.pnucene.2005. 05.069. [16] W.D. Pointer, A. Tentner, T. Sofu, D. Weber, S. Lo, A. Splawski, Eulerian two-phase computational fluid dynamics for boiling water reactor core analysis, Joint International Topical Meeting on Mathematics and Computation and Supercomputing in Nuclear Applications (M and C± SNA), 2007. [17] K. Podila, Y. Rao, CFD modelling of supercritical water flow and heat transfer in a 2 × 2 fuel rod bundle, Nucl. Eng. Des. 301 (2016) 279–289, doi:10.1016/j. nucengdes.2016.03.019. [18] H. Pothukuchi, S. Kelm, B.S. Patnaik, B.V. Prasad, H.J. Allelein, Numerical investigation of subcooled flow boiling in an annulus under the influence of eccentricity, Appl. Therm. Eng. 129 (2018) 1604–1617, doi:10.1016/j.applthermaleng. 2017.10.105. [19] H. Pothukuchi, S. Kelm, B.S. Patnaik, B.V. Prasad, H.J. Allelein, CFD modeling of critical heat flux in flow boiling: validation and assessment of closure models, Appl. Therm. Eng. 150 (2019) 651–665, doi:10.1016/j.applthermaleng.2019.01. 030. [20] W. Fan, H. Li, H. Anglart, A study of rewetting and conjugate heat transfer influence on dryout and post-dryout phenomena with a multi-domain coupled CFD approach, Int. J. Heat Mass Transf. 163 (2020) 120503, doi:10.1016/j. ijheatmasstransfer.2020.120503. [21] R. Zhang, T. Cong, G. Su, J. Wang, S. Qiu, Investigation on the critical heat flux in typical 5 by 5 rod bundle at conditions prototypical of PWR based on CFD methodology, Appl. Therm. Eng. 179 (2020) 115582, doi:10.1016/j. applthermaleng.2020.115582.
[22] L.D. Silvi, A. Saha, D.K. Chandraker, S. Ghosh, A.K. Das, Numerical analysis of pre-dryout sequences through the route of interfacial evolution in annular gasliquid two-phase flow with phase change, Chem. Eng. Sci. 212 (2020) 115356, doi:10.1016/j.ces.2019.115356. [23] L.D. Silvi, D.K. Chandraker, S. Ghosh, A.K. Das, On-route to dryout through sequential interfacial dynamics in annular flow boiling around temperature and heat flux controlled heater rod, Chem. Eng. Sci. 229 (2021) 116014, doi:10.1016/ j.ces.2020.116014. [24] J.U. Brackbill, D.B. Kothe, C. Zemach, A continuum method for modeling surface tension, J. Comput. Phys. 100 (2) (1992) 335–354, doi:10.1016/0021-9991(92) 90240-Y. [25] B. Lafaurie, C. Nardone, R. Scardovelli, S. Zaleski, G. Zanetti, Modelling merging and fragmentation in multiphase flows with SURFER, J. Comput. Phys. 113 (1) (1994) 134–147, doi:10.1006/jcph.1994.1123. [26] I. Tanasawa, Advances in condensation heat transfer, Ad. Heat Transf. 21 (1991) 55–139 Vol, doi:10.1016/S0065-2717(08)70334-4. [27] V.H. Del Valle, D.B. Kenning, Subcooled flow boiling at high heat flux, Int. J. Heat Mass Transf. 28 (10) (1985) 1907–1920, doi:10.1016/0017-9310(85) 90213-3. [28] B. Matzner, G.M. Latter, Reduced pressure drop space for boiling water reactor fuel bundles, US Patent US5375154A, (1993) [29] C. Unal, O. Badr, K. Tuzla, J.C. Chen, S. Neti, Pressure drop at rod-bundle spacers in the post-CHF dispersed flow regime, Int. J. Multiphase Flow 20 (3) (1994) 515–522, doi:10.1016/0301-9322(94)90025-6. [30] D.K. Chandraker, A.K. Nayak, V.P. Krishnan, Effect of spacer on the dryout of BWR fuel rod assemblies, Nucl. Eng. Des. 294 (2015), doi:10.1016/j.nucengdes. 2015.09.004. [31] S.K Verma, S.L. Sinha, D.K. Chandraker, A comprehensive review of the spacer effect on performance of nuclear fuel bundle using computational fluid dynamics methodology, Mater. Today: Proc. 4 (2017) 100030–110034, doi:10. 1016/j.matpr.2017.06.315. [32] S.K Verma, S.L. Sinha, D.K. Chandraker, Experimental investigation on the effect of space on the turbulent mixing in vertical pressure tube-type boiling water reactor, Nucl. Sci. Eng. 190 (2) (2018), doi:10.1080/00295639.2017.1413874. [33] T. Zhang, Y. Liu, Numerical investigation of flow and heat transfer characteristics of subcooled boiling in a single rod channel with/without spacer grid, Case Stud. Therm. Eng. 20 (2020) 100644, doi:10.1016/j.csite.2020.100644. [34] K.M. Becker, G. Hernborg, M. Bode, O. Eriksson, Burnout data for flow of boiling water in vertical round ducts, annuli and rod clusters, AB Atomenergi (1965). [35] A. Saha, A.K. Das, Numerical study of boiling around wires and influence of active or passive neighbours on vapour film dynamics, Int. J. Heat Mass Transf. 130 (2019) 440–454, doi:10.1016/j.ijheatmasstransfer.2018.10.117. [36] M. Reimann, U. Grigull, Heat transfer with free convection and film boiling in the critical area of water and carbon dioxide, Heat Mass Transf. 8 (1975) 229– 239, doi:10.1007/BF01002151. [37] M.S. Plesset, S.A. Zwick, The growth of vapor bubbles in superheated liquids, J. Appl. Phys. 25 (4) (1954) 493–500, doi:10.1063/1.1721668. [38] N. Samkhaniani, M.R. Ansari, Numerical simulation of superheated vapor bubble rising in stagnant liquid, Heat Mass Transf. 53 (9) (2017) 2885–2899, doi:10.1007/S00231-017-2031-6. [39] N. Samkhaniani, M.R. Ansari, The evaluation of the diffuse interface method for phase change simulations using OpenFOAM, Heat Transf. Asian Res. 46 (8) (2017) 1173–1203, doi:10.1002/htj.21268. [40] P. Goel, A.K. Nayak, M.K. Das, J.B. Joshi, Bubble departure characteristics in a horizontal tube bundle under cross flow conditions, Int. J. Multiph. Flow 100 (2018) 143–154, doi:10.1016/j.ijmultiphaseflow.2017.12.013. [41] K.M. Becker, J. Engstorm, B.Scholin Nylund, B. Sodequist, Analysis of the dryout incident in the Oskarshamn 2 boiling water reactor, Int. J. Multiph. Flow 16 (6) (1990) 959–974, doi:10.1016/0301-9322(90)90101-N. [42] H.G. Weller, A New Approach to VOF-Based Interface Capturing Methods for Incompressible and Compressible Flow, A New Approach to VOF-Based Interface Capturing Methods for Incompressible and Compressible Flow, 4, OpenCFD Ltd., 2008 Report TR/HGW. [43] G. Boeing, Visual analysis of nonlinear dynamical systems: chaos, fractals, selfsimilarity and the limits of prediction, Systems 4 (4) (2016) 37, doi:10.3390/ systems4040037.
Investigating the breach outflow hydrograph is an essential task to conduct mitigation plans and flood warnings. In the present study, the spatial dam breach is simulated by using a three-dimensional computational fluid dynamics model, FLOW-3D. The model parameters were adjusted by making a comparison with a previous experimental model. The different parameters (initial breach shape, dimensions, location, and dam slopes) are studied to investigate their effects on dam breaching. The results indicate that these parameters have a significant impact. The maximum erosion rate and peak outflow for the rectangular shape are higher than those for the V-notch by 8.85% and 5%, respectively. Increasing breach width or decreasing depth by 5% leads to increasing maximum erosion rate by 11% and 15%, respectively. Increasing the downstream slope angle by 4° leads to an increase in both peak outflow and maximum erosion rate by 2.0% and 6.0%, respectively.
유출 유출 수문곡선을 조사하는 것은 완화 계획 및 홍수 경보를 수행하는 데 필수적인 작업입니다. 본 연구에서는 3차원 전산유체역학 모델인 FLOW-3D를 사용하여 공간 댐 붕괴를 시뮬레이션합니다. 이전 실험 모델과 비교하여 모델 매개변수를 조정했습니다.
다양한 매개변수(초기 붕괴 형태, 치수, 위치 및 댐 경사)가 댐 붕괴에 미치는 영향을 조사하기 위해 연구됩니다. 결과는 이러한 매개변수가 상당한 영향을 미친다는 것을 나타냅니다. 직사각형 형태의 최대 침식율과 최대 유출량은 V-notch보다 각각 8.85%, 5% 높게 나타났습니다.
위반 폭을 늘리거나 깊이를 5% 줄이면 최대 침식률이 각각 11% 및 15% 증가합니다. 하류 경사각을 4° 증가시키면 최대 유출량과 최대 침식률이 각각 2.0% 및 6.0% 증가합니다.
Keywords
Spatial dam breach; FLOW-3D; Overtopping erosion; Computational fluid dynamics (CFD)
1. Introduction
There are many purposes for dam construction, such as protection from flood disasters, water storage, and power generation. Embankment failures may have a catastrophic impact on lives and infrastructure in the downstream regions. One of the most common causes of embankment dam failure is overtopping. Once the overtopping of the dam begins, the breach formation will start in the dam body then end with the dam failure. This failure occurs within a very short time, which threatens to be very dangerous. Therefore, understanding and modeling the embankment breaching processes is essential for conducting mitigation plans, flood warnings, and forecasting flood damage.
The analysis of the dam breaching process is implemented by different techniques: comparative methods, empirical models with dimensional and dimensionless solutions, physical-based models, and parametric models. These models were described in detail [1]. Parametric modeling is commonly used to simulate breach growth as a time-dependent linear process and calculate outflow discharge from the breach using hydraulics principles [2]. Alhasan et al. [3] presented a simple one-dimensional mathematical model and a computer code to simulate the dam breaching process. These models were validated by small dams breaching during the floods in 2002 in the Czech Republic. Fread [4] developed an erosion model (BREACH) based on hydraulics principles, sediment transport, and soil mechanics to estimate breach size, time of formation, and outflow discharge. Říha et al. [5] investigated the dam break process for a cascade of small dams using a simple parametric model for piping and overtopping erosion, as well as a 2D shallow-water flow model for the flood in downstream areas. Goodarzi et al. [6] implemented mathematical and statistical methods to assess the effect of inflows and wind speeds on the dam’s overtopping failure.
Dam breaching studies can be divided into two main modes of erosion. The first mode is called “planar dam breach” where the flow overtops the whole dam width. While the second mode is called “spatial dam breach” where the flow overtops through the initial pilot channel (i.e., a channel created in the dam body). Therefore, the erosion will be in both vertical and horizontal directions [7].
The erosion process through the embankment dams occurs due to the shear stress applied by water flows. The dam breaching evolution can be divided into three stages [8], [9], but Y. Yang et al. [10] divided the breach development into five stages: Stage I, the seepage erosion; Stage II, the initial breach formation; Stage III, the head erosion; Stage IV, the breach expansion; and Stage V, the re-equilibrium of the river channel through the breach. Many experimental tests have been carried out on non-cohesive embankment dams with an initial breach to examine the effect of upstream inflow discharges on the longitudinal profile evolution and the time to inflection point[11].
Zhang et al. [12] studied the effect of changing downstream slope angle, sediment grain size, and dam crest length on erosion rates. They noticed that increasing dam crest length and decreasing downstream slope angle lead to decreasing sediment transport rate. While the increase in sediment grain size leads to an increased sediment transport rate at the initial stages. Höeg et al. [13] presented a series of field tests to investigate the stability of embankment dams made of various materials. Overtopping and piping were among the failure tests carried out for the dams composed of homogeneous rock-fill, clay, or gravel with a height of up to 6.0 m. Hakimzadeh et al. [14] constructed 40 homogeneous cohesive and non-cohesive embankment dams to study the effect of changing sediment diameter and dam height on the breaching process. They also used genetic programming (GP) to estimate the breach outflow. Refaiy et al. [15] studied different scenarios for the downstream drain geometry, such as length, height, and angle, to minimize the effect of piping phenomena and therefore increase dam safety.
Zhu et al. [16] examined the effect of headcut erosion on dam breach growth, especially in the case of cohesive dams. They found that the breach growth in non-cohesive embankments is slower than cohesive embankments due to the little effect of headcut. Schmocker and Hager [7] proposed a relationship for estimating peak outflow from the dam breach process.(1)QpQin-1=1.7exp-20hc23d5013H0
where: Qp = peak outflow discharge.
Qin = inflow discharge.
hc = critical flow depth.
d50 = mean sediment diameter.
Ho = initial dam height.
Yu et al. [17] carried out an experimental study for homogeneous non-cohesive embankment dams in a 180° bending rectangular flume to determine the effect of overtopping flows on breaching formation. They found that the main factors influencing breach formation are water level, river discharge, and embankment material diameter.
Wu et al. [18] carried out a series of experiments to investigate the effect of breaching geometry on both non-cohesive and cohesive embankment dams in a U-bend flume due to overtopping flows. In the case of non-cohesive embankments, the non-symmetrical lateral expansion was noticed during the breach formation. This expansion was described by a coefficient ranging from 2.7 to 3.3.
The numerical models of the dam breach can be categorized according to different parameters, such as flow dimensions (1D, 2D, or 3D), flow governing equations, and solution methods. The 1D models are mainly used to predict the outflow hydrograph from the dam breach. Saberi et al. [19] applied the 1D Saint-Venant equation, which is solved by the finite difference method to investigate the outflow hydrograph during dam overtopping failure. Because of the ability to study dam profile evolution and breach formation, 2D models are more applicable than 1D models. Guan et al. [20] and Wu et al. [21] employed both 2D shallow water equations (SWEs) and sediment erosion equations, which are solved by the finite volume method to study the effect of the dam’s geometry parameters on outflow hydrograph and dam profile evolution. Wang et al. [22] also proposed a second-order hybrid-type of total variation diminishing (TVD) finite-difference to estimate the breach outflow by solving the 2D (SWEs). The accuracy of (SWEs) for both vertical flow contraction and surface roughness has been assessed [23]. They noted that the accuracy of (SWEs) is acceptable for milder slopes, but in the case of steeper slopes, modelers should be more careful. Generally, the accuracy of 2D models is still low, especially with velocity distribution over the flow depth, lateral momentum exchange, density-driven flows, and bottom friction[24]. Therefore, 3D models are preferred. Larocque et al. [25] and Yang et al. [26] started to use three-dimensional (3D) models that depend on the Reynolds-averaged Navier-Stokes (RANS) equations.
Previous experimental studies concluded that there is no clear relationship between the peak outflow from the dam breach and the initial breach characteristics. Some of these studies depend on the sharp-crested weir fixed at the end of the flume to determine the peak outflow from the breach, which leads to a decrease in the accuracy of outflow calculations at the microscale. The main goals of this study are to carry out a numerical simulation for a spatial dam breach due to overtopping flows by using (FLOW-3D) software to find an empirical equation for the peak outflow discharge from the breach and determine the worst-case that leads to accelerating the dam breaching process.
2. Numerical simulation
The current study for spatial dam breach is simulated by using (FLOW-3D) software [27], which is a powerful computational fluid dynamics (CFD) program.
2.1. Geometric presentations
A stereolithographic (STL) file is prepared for each change in the initial breach geometry and dimensions. The CAD program is useful for creating solid objects and converting them to STL format, as shown in Fig. 1.
2.2. Governing equations
The governing equations for water flow are three-dimensional Reynolds Averaged Navier-Stokes equations (RANS).
The momentum equation:(3)∂ui∂t+1VFuj∂ui∂xj=1ρ∂∂xj-pδij+ν∂ui∂xj+∂uj∂xi-ρu`iu`j¯
where u is time-averaged velocity,ν is kinematic viscosity, VF is fractional volume open to flow, p is averaged pressure and -u`iu`j¯ are components of Reynold’s stress. The Volume of Fluid (VOF) technique is used to simulate the free surface profile. Hirt et al. [28] presented the VOF algorithm, which employs the function (F) to express the occupancy of each grid cell with fluid. The value of (F) varies from zero to unity. Zero value refers to no fluid in the grid cell, while the unity value refers to the grid cell being fully occupied with fluid. The free surface is formed in the grid cells having (F) values between zero and unity.(4)∂F∂t+1VF∂∂xFAxu+∂∂yFAyv+∂∂zFAzw=0
where (u, v, w) are the velocity components in (x, y, z) coordinates, respectively, and (Ax, Ay, Az) are the area fractions.
2.3. Boundary and initial conditions
To improve the accuracy of the results, the boundary conditions should be carefully determined. In this study, two mesh blocks are used to minimize the time consumed in the simulation. The boundary conditions for mesh block 1 are as follows: The inlet and sides boundaries are defined as a wall boundary condition (wall boundary condition is usually used for bound fluid by solid regions. In the case of viscous flows, no-slip means that the tangential velocity is equal to the wall velocity and the normal velocity is zero), the outlet is defined as a symmetry boundary condition (symmetry boundary condition is usually used to reduce computational effort during CFD simulation. This condition allows the flow to be transferred from one mesh block to another. No inputs are required for this boundary condition except that its location should be defined accurately), the bottom boundary is defined as a uniform flow rate boundary condition, and the top boundary is defined as a specific pressure boundary condition with assigned atmospheric pressure. The boundary conditions for mesh block 2 are as follows: The inlet is defined as a symmetry boundary condition, the outlet is defined as a free flow boundary condition, the bottom and sides boundaries are defined as a wall boundary condition, and the top boundary is defined as a specific pressure boundary condition with assigned atmospheric pressure as shown in Fig. 2. The initial conditions required to be set for the fluid (i.e., water) inside of the domain include configuration, temperature, velocities, and pressure distribution. The configuration of water depends on the dimensions and shape of the dam reservoir. While the other conditions have been assigned as follows: temperature is normal water temperature (25 °c) and pressure distribution is hydrostatic with no initial velocity.
2.4. Numerical method
FLOW-3D uses the finite volume method (FVM) to solve the governing equation (Reynolds-averaged Navier-Stokes) over the computational domain. A finite-volume method is an Eulerian approach for representing and evaluating partial differential equations in algebraic equations form [29]. At discrete points on the mesh geometry, values are determined. Finite volume expresses a small volume surrounding each node point on a mesh. In this method, the divergence theorem is used to convert volume integrals with a divergence term to surface integrals. After that, these terms are evaluated as fluxes at each finite volume’s surfaces.
2.5. Turbulent models
Turbulence is the chaotic, unstable motion of fluids that occurs when there are insufficient stabilizing viscous forces. In FLOW-3D, there are six turbulence models available: the Prandtl mixing length model, the one-equation turbulent energy model, the two-equation (k – ε) model, the Renormalization-Group (RNG) model, the two-equation (k – ω) models, and a large eddy simulation (LES) model. For simulating flow motion, the RNG model is adopted to simulate the motion behavior better than the k – ε and k – ω.
models [30]. The RNG model consists of two main equations for the turbulent kinetic energy KT and its dissipation.εT(5)∂kT∂t+1VFuAx∂kT∂x+vAy∂kT∂y+wAz∂kT∂z=PT+GT+DiffKT-εT(6)∂εT∂t+1VFuAx∂εT∂x+vAy∂εT∂y+wAz∂εT∂z=C1.εTKTPT+c3.GT+Diffε-c2εT2kT
where KT is the turbulent kinetic energy, PT is the turbulent kinetic energy production, GT is the buoyancy turbulence energy, εT is the turbulent energy dissipation rate, DiffKT and Diffε are terms of diffusion, c1, c2 and c3 are dimensionless parameters, in which c1 and c3 have a constant value of 1.42 and 0.2, respectively, c2 is computed from the turbulent kinetic energy (KT) and turbulent production (PT) terms.
2.6. Sediment scour model
The sediment scour model available in FLOW-3D can calculate all the sediment transport processes including Entrainment transport, Bedload transport, Suspended transport, and Deposition. The erosion process starts once the water flows remove the grains from the packed bed and carry them into suspension. It happens when the applied shear stress by water flows exceeds critical shear stress. This process is represented by entrainment transport in the numerical model. After entrained, the grains carried by water flow are represented by suspended load transport. After that, some suspended grains resort to settling because of the combined effect of gravity, buoyancy, and friction. This process is described through a deposition. Finally, the grains sliding motions are represented by bedload transport in the model. For the entrainment process, the shear stress applied by the fluid motion on the packed bed surface is calculated using the standard wall function as shown in Eq.7.(7)ks,i=Cs,i∗d50
where ks,i is the Nikuradse roughness and Cs,i is a user-defined coefficient. The critical bed shear stress is defined by a dimensionless parameter called the critical shields number as expressed in Eq.8.(8)θcr,i=τcr,i‖g‖diρi-ρf
where θcr,i is the critical shields number, τcr,i is the critical bed shear stress, g is the absolute value of gravity acceleration, di is the diameter of the sediment grain, ρi is the density of the sediment species (i) and ρf is the density of the fluid. The value of the critical shields number is determined according to the Soulsby-Whitehouse equation.(9)θcr,i=0.31+1.2d∗,i+0.0551-exp-0.02d∗,i
where d∗,i is the dimensionless diameter of the sediment, given by Eq.10.(10)d∗,i=diρfρi-ρf‖g‖μf213
where μf is the fluid dynamic viscosity. For the sloping bed interface, the value of the critical shields number is modified according to Eq.11.(11)θ`cr,i=θcr,icosψsinβ+cos2βtan2φi-sin2ψsin2βtanφi
where θ`cr,i is the modified critical shields number, φi is the angle of repose for the sediment, β is the angle of bed slope and ψ is the angle between the flow and the upslope direction. The effects of the rolling, hopping, and sliding motions of grains along the packed bed surface are taken by the bedload transport process. The volumetric bedload transport rate (qb,i) per width of the bed is expressed in Eq.12.(12)qb,i=Φi‖g‖ρi-ρfρfdi312
where Φi is the dimensionless bedload transport rate is calculated by using Meyer Peter and Müller equation.(13)Φi=βMPM,iθi-θ`cr,i1.5cb,i
where βMPM,i is the Meyer Peter and Müller user-defined coefficient and cb,i is the volume fraction of species i in the bed material. The suspended load transport is calculated as shown in Eq.14.(14)∂Cs,i∂t+∇∙Cs,ius,i=∇∙∇DCs,i
where Cs,i is the suspended sediment mass concentration, D is the diffusivity, and us,i is the grain velocity of species i. Entrainment and deposition are two opposing processes that take place at the same time. The lifting and settling velocities for both entrainment and deposition processes are calculated according to Eq.15 and Eq.16, respectively.(15)ulifting,i=αid∗,i0.3θi-θ`cr,igdiρiρf-1(16)usettling,i=υfdi10.362+1.049d∗,i3-10.36
where αi is the entrainment coefficient of species i and υf is the kinematic viscosity of the fluid.
2.7. Grid type
Using simple rectangular orthogonal elements in planes and hexahedral in volumes in the (FLOW-3D) program makes the mesh generation process easier, decreases the required memory, and improves numerical accuracy. Two mesh blocks were used in a joined form with a size ratio of 2:1. The first mesh block is coarser, which contains the reservoir water, and the second mesh block is finer, which contains the dam. For achieving accuracy and efficiency in results, the mesh size is determined by using a grid convergence test. The optimum uniform cell size for the first mesh block is 0.012 m and for the second mesh block is 0.006 m.
2.8. Time step
The maximum time step size is determined by using a Courant number, which controls the distance that the flow will travel during the simulation time step. In this study, the Courant number was taken equal to 0.25 to prevent the flow from traveling through more than one cell in the time step. Based on the Courant number, a maximum time step value of 0.00075 s was determined.
2.9. Numerical model validation
The numerical model accuracy was achieved by comparing the numerical model results with previous experimental results. The experimental study of Schmocker and Hager [7] was based on 31 tests with changes in six parameters (d50, Ho, Bo, Lk, XD, and Qin). All experimental tests were conducted in a straight open glass-sided flume. The horizontal flume has a rectangular cross-section with a width of 0.4 m and a height of 0.7 m. The flume was provided with a flow straightener and an intake with a length of 0.66 m. All tested dams were inserted at various distances (XD) from the intake. Test No.1 from this experimental program was chosen to validate the numerical model. The different parameters used in test No.1 are as follows:
(1) uniform sediment with a mean diameter (d50 = 0.31 mm), (2) Ho = 0.2 m, (3) Bo = 0.2 m, (4) Lk = 0.1 m,
(5) XD = 1.0 m, (6) Qin = 6.0 lit/s, (7) Su and Sd = 2:1, (8) mass density (ρs = 2650 kg/m3) (9) Homogenous and non-cohesive embankment dam. As shown in Fig. 2, the simulation is contained within a rectangular grid with dimensions: 3.56 m in the x-direction (where 0.66 m is used as inlet, 0.9 m as dam base width, and 1.0 m as outlet), in y-direction 0.2 m (dam length), and in the z-direction 0.3 m, which represents the dam height (0.2 m) with a free distance (0.1 m) above the dam. There are two main reasons that this experimental program is preferred for the validation process. The first reason is that this program deals with homogenous, non-cohesive soil, which is available in FLOW-3D. The second reason is that this program deals with small-scale models which saves time for numerical simulation. Finally, some important assumptions were considered during the validation process. The flow is assumed to be incompressible, viscous, turbulent, and three-dimensional.
By comparing dam profiles at different time instants for the experimental test with the current numerical model, it appears that the numerical model gives good agreement as shown in Fig. 3 and Fig. 4, with an average error percentage of 9% between the experimental results and the numerical model.
3. Analysis and discussions
The current model is used to study the effects of different parameters such as (initial breach shapes, dimensions, locations, upstream and downstream dam slopes) on the peak outflow discharge, QP, time of peak outflow, tP, and rate of erosion, E.
This study consists of a group of scenarios. The first scenario is changing the shapes of the initial breach according to Singh [1], the most predicted shapes are rectangular and V-notch as shown in Fig. 5. The second scenario is changing the initial breach dimensions (i.e., width and depth). While the third scenario is changing the location of the initial breach. Eventually, the last scenario is changing the upstream and downstream dam slopes.
All scenarios of this study were carried out under the same conditions such as inflow discharge value (Qin=1.0lit/s), dimensions of the tested dam, where dam height (Ho=0.20m), crest width.
(Lk=0.1m), dam length (Bo=0.20m), and homogenous & non-cohesive soil with a mean diameter (d50=0.31mm).
3.1. Dam breaching process evolution
The dam breaching process is a very complex process due to the quick changes in hydrodynamic conditions during dam failure. The dam breaching process starts once water flows reach the downstream face of the dam. During the initial stage of dam breaching, the erosion process is relatively quiet due to low velocities of flow. As water flows continuously, erosion rates increase, especially in two main zones: the crest and the downstream face. As soon as the dam crest is totally eroded, the water levels in the dam reservoir decrease rapidly, accompanied by excessive erosion in the dam body. The erosion process continues until the water levels in the dam reservoir equal the remaining height of the dam.
According to Zhou et al. [11], the breaching process consists of three main stages. The first stage starts with beginning overtopping flow, then ends when the erosion point directed upstream and reached the inflection point at the inflection time (ti). The second stage starts from the end of the stage1 until the occurrence of peak outflow discharge at the peak outflow time (tP). The third stage starts from the end of the stage2 until the value of outflow discharge becomes the same as the value of inflow discharge at the final time (tf). The outflow discharge from the dam breach increases rapidly during stage1 and stage2 because of the large dam storage capacity (i.e., the dam reservoir is totally full of water) and excessive erosion. While at stage3, the outflow values start to decrease slowly because most of the dam’s storage capacity was run out. The end of stage3 indicates that the dam storage capacity was totally run out, so the outflow equalized with the inflow discharge as shown in Fig. 6 and Fig. 7.
3.2. The effect of initial breach shape
To identify the effect of the initial breach shape on the evolution of the dam breaching process. Three tests were carried out with different cross-section areas for each shape. The initial breach is created at the center of the dam crest. Each test had an ID to make the process of arranging data easier. The rectangular shape had an ID (Rec5h & 5b), which means that its depth and width are equal to 5% of the dam height, and the V-notch shape had an ID (V-noch5h & 1:1) which means that its depth is equal to 5% of the dam height and its side slope is equal to 1:1. The comparison between rectangular and V-notch shapes is done by calculating the ratio between maximum dam height at different times (ZMax) to the initial dam height (Ho), rate of erosion, and hydrograph of outflow discharge for each test. The rectangular shape achieves maximum erosion rate and minimum inflection time, in addition to a rapid decrease in the dam reservoir levels. Therefore, the dam breaching is faster in the case of a rectangular shape than in a V-notch shape, which has the same cross-section area as shown in Fig. 8.
Also, by comparing the hydrograph for each test, the peak outflow discharge value in the case of a rectangular shape is higher than the V-notch shape by 5% and the time of peak outflow for the rectangular shape is shorter than the V-notch shape by 9% as shown in Fig. 9.
3.3. The effect of initial breach dimensions
The results of the comparison between the different initial breach shapes indicate that the worst initial breach shape is rectangular, so the second scenario from this study concentrated on studying the effect of a change in the initial rectangular breach dimensions. Groups of tests were carried out with different depths and widths for the rectangular initial breach. The first group had a depth of 5% from the dam height and with three different widths of 5,10, and 15% from the dam height, the second group had a depth of 10% with three different widths of 5,10, and 15%, the third group had a depth of 15% with three different widths of 5,10, and 15% and the final group had a width of 15% with three different heights of 5, 10, and 15% for a rectangular breach shape. The comparison was made as in the previous section to determine the worst case that leads to the quick dam failure as shown in Fig. 10.
The results show that the (Rec 5 h&15b) test achieves a maximum erosion rate for a shorter period of time and a minimum ratio for (Zmax / Ho) as shown in Fig. 10, which leads to accelerating the dam failure process. The dam breaching process is faster with the minimum initial breach depth and maximum initial breach width. In the case of a minimum initial breach depth, the retained head of water in the dam reservoir is high and the crest width at the bottom of the initial breach (L`K) is small, so the erosion point reaches the inflection point rapidly. While in the case of the maximum initial breach width, the erosion perimeter is large.
3.4. The effect of initial breach location
The results of the comparison between the different initial rectangular breach dimensions indicate that the worst initial breach dimension is (Rec 5 h&15b), so the third scenario from this study concentrated on studying the effect of a change in the initial breach location. Three locations were checked to determine the worst case for the dam failure process. The first location is at the center of the dam crest, which was named “Center”, the second location is at mid-distance between the dam center and dam edge, which was named “Mid”, and the third location is at the dam edge, which was named “Edge” as shown in Fig. 11. According to this scenario, the results indicate that the time of peak outflow discharge (tP) is the same in the three cases, but the maximum value of the peak outflow discharge occurs at the center location. The difference in the peak outflow values between the three cases is relatively small as shown in Fig. 12.
The rates of erosion were also studied for the three cases. The results show that the maximum erosion rate occurs at the center location as shown in Fig. 13. By making a comparison between the three cases for the dam storage volume. The results show that the center location had the minimum values for the dam storage volume, which means that a large amount of water has passed to the downstream area as shown in Fig. 14. According to these results, the center location leads to increased erosion rate and accelerated dam failure process compared with the two other cases. Because the erosion occurs on both sides, but in the case of edge location, the erosion occurs on one side.
3.5. The effect of upstream and downstream dam slopes
The results of the comparison between the different initial rectangular breach locations indicate that the worst initial breach location is the center location, so the fourth scenario from this study concentrated on studying the effect of a change in the upstream (Su) and downstream (Sd) dam slopes. Three slopes were checked individually for both upstream and downstream slopes to determine the worst case for the dam failure process. The first slope value is (2H:1V), the second slope value is (2.5H:1V), and the third slope value is (3H:1V). According to this scenario, the results show that the decreasing downstream slope angle leads to increasing time of peak outflow discharge (tP) and decreasing value of peak outflow discharge. The difference in the peak outflow values between the three cases for the downstream slope is 2%, as shown in Fig. 15, but changing the upstream slope has a negligible impact on the peak outflow discharge and its time as shown in Fig. 16.
The rates of erosion were also studied in the three cases for both upstream and downstream slopes. The results show that the maximum erosion rate increases by 6.0% with an increasing downstream slope angle by 4°, as shown in Fig. 17. The results also indicate that the erosion rates aren’t affected by increasing or decreasing the upstream slope angle, as shown in Fig. 18. According to these results, increasing the downstream slope angle leads to increased erosion rate and accelerated dam failure process compared with the upstream slope angle. Because of increasing shear stress applied by water flows in case of increasing downstream slope.
According to all previous scenarios, the dimensionless peak outflow discharge QPQin is presented for a fixed dam height (Ho) and inflow discharge (Qin). Fig. 19 illustrates the relationship between QP∗=QPQin and.
Lr=ho2/3∗bo2/3Ho. The deduced relationship achieves R2=0.96.(17)QP∗=2.2807exp-2.804∗Lr
4. Conclusions
A spatial dam breaching process was simulated by using FLOW-3D Software. The validation process was performed by making a comparison between the simulated results of dam profiles and the dam profiles obtained by Schmocker and Hager [7] in their experimental study. And also, the peak outflow value recorded an error percentage of 12% between the numerical model and the experimental study. This model was used to study the effect of initial breach shape, dimensions, location, and dam slopes on peak outflow discharge, time of peak outflow, and the erosion process. By using the parameters obtained from the validation process, the results of this study can be summarized in eight points as follows.1.
The rectangular initial breach shape leads to an accelerating dam failure process compared with the V-notch.2.
The value of peak outflow discharge in the case of a rectangular initial breach is higher than the V-notch shape by 5%.3.
The time of peak outflow discharge for a rectangular initial breach is shorter than the V-notch shape by 9%.4.
The minimum depth and maximum width for the initial breach achieve maximum erosion rates (increasing breach width, b0, or decreasing breach depth, h0, by 5% from the dam height leads to an increase in the maximum rate of erosion by 11% and 15%, respectively), so the dam failure is rapid.5.
The center location of the initial breach leads to an accelerating dam failure compared with the edge location.6.
The initial breach location has a negligible effect on the peak outflow discharge value and its time.7.
Increasing the downstream slope angle by 4° leads to an increase in both peak outflow discharge and maximum rate of erosion by 2.0% and 6.0%, respectively.8.
The upstream slope has a negligible effect on the dam breaching process.
References
[1]V. SinghDam breach modeling technologySpringer Science & Business Media (1996)Google Scholar[2]Wahl TL. Prediction of embankment dam breach parameters: a literature review and needs assessment. 1998.Google Scholar[3]Z. Alhasan, J. Jandora, J. ŘíhaStudy of dam-break due to overtopping of four small dams in the Czech RepublicActa Universitatis Agriculturae et Silviculturae Mendelianae Brunensis, 63 (3) (2015), pp. 717-729 View PDFCrossRefView Record in ScopusGoogle Scholar[4]D. FreadBREACH, an erosion model for earthen dam failures: Hydrologic Research LaboratoryNOAA, National Weather Service (1988)Google Scholar[5]J. Říha, S. Kotaška, L. PetrulaDam Break Modeling in a Cascade of Small Earthen Dams: Case Study of the Čižina River in the Czech RepublicWater, 12 (8) (2020), p. 2309, 10.3390/w12082309 View PDFView Record in ScopusGoogle Scholar[6]E. Goodarzi, L. Teang Shui, M. ZiaeiDam overtopping risk using probabilistic concepts–Case study: The Meijaran DamIran Ain Shams Eng J, 4 (2) (2013), pp. 185-197ArticleDownload PDFView Record in ScopusGoogle Scholar[7]L. Schmocker, W.H. HagerPlane dike-breach due to overtopping: effects of sediment, dike height and dischargeJ Hydraul Res, 50 (6) (2012), pp. 576-586 View PDFCrossRefView Record in ScopusGoogle Scholar[8]J.S. Walder, R.M. Iverson, J.W. Godt, M. Logan, S.A. SolovitzControls on the breach geometry and flood hydrograph during overtopping of noncohesive earthen damsWater Resour Res, 51 (8) (2015), pp. 6701-6724View Record in ScopusGoogle Scholar[9]H. Wei, M. Yu, D. Wang, Y. LiOvertopping breaching of river levees constructed with cohesive sedimentsNat Hazards Earth Syst Sci, 16 (7) (2016), pp. 1541-1551 View PDFCrossRefView Record in ScopusGoogle Scholar[10]Y. Yang, S.-Y. Cao, K.-J. Yang, W.-P. LiYang K-j, Li W-p. Experimental study of breach process of landslide dams by overtopping and its initiation mechanismsJ Hydrodynamics, 27 (6) (2015), pp. 872-883ArticleDownload PDFCrossRefView Record in ScopusGoogle Scholar[11]G.G.D. Zhou, M. Zhou, M.S. Shrestha, D. Song, C.E. Choi, K.F.E. Cui, et al.Experimental investigation on the longitudinal evolution of landslide dam breaching and outburst floodsGeomorphology, 334 (2019), pp. 29-43ArticleDownload PDFView Record in ScopusGoogle Scholar[12]J. Zhang, Z.-x. Guo, S.-y. CaoYang F-g. Experimental study on scour and erosion of blocked damWater Sci Eng, 5 (2012), pp. 219-229ArticleDownload PDFView Record in ScopusGoogle Scholar[13]K. Höeg, A. Løvoll, K. VaskinnStability and breaching of embankment dams: Field tests on 6 m high damsInt J Hydropower Dams, 11 (2004), pp. 88-92View Record in ScopusGoogle Scholar[14]H. Hakimzadeh, V. Nourani, A.B. AminiGenetic programming simulation of dam breach hydrograph and peak outflow dischargeJ Hydrol Eng, 19 (4) (2014), pp. 757-768View Record in ScopusGoogle Scholar[15]A.R. Refaiy, N.M. AboulAtta, N.Y. Saad, D.A. El-MollaModeling the effect of downstream drain geometry on seepage through earth damsAin Shams Eng J, 12 (3) (2021), pp. 2511-2531ArticleDownload PDFView Record in ScopusGoogle Scholar[16]Y. Zhu, P.J. Visser, J.K. Vrijling, G. WangExperimental investigation on breaching of embankmentsScience China Technological Sci, 54 (1) (2011), pp. 148-155 View PDFCrossRefView Record in ScopusGoogle Scholar[17]M.-H. Yu, H.-Y. Wei, Y.-J. Liang, Y. ZhaoInvestigation of non-cohesive levee breach by overtopping flowJ Hydrodyn, 25 (4) (2013), pp. 572-579ArticleDownload PDFCrossRefView Record in ScopusGoogle Scholar[18]S. Wu, M. Yu, H. Wei, Y. Liang, J. ZengNon-symmetrical levee breaching processes in a channel bend due to overtoppingInt J Sedim Res, 33 (2) (2018), pp. 208-215ArticleDownload PDFView Record in ScopusGoogle Scholar[19]O. Saberi, G. ZenzNumerical investigation on 1D and 2D embankment dams failure due to overtopping flowInt J Hydraulic Engineering, 5 (2016), pp. 9-18View Record in ScopusGoogle Scholar[20]M. Guan, N.G. Wright, P.A. Sleigh2D Process-Based Morphodynamic Model for Flooding by Noncohesive Dyke BreachJ Hydraul Eng, 140 (7) (2014), p. 04014022, 10.1061/(ASCE)HY.1943-7900.0000861 View PDFView Record in ScopusGoogle Scholar[21]W. Wu, R. Marsooli, Z. HeDepth-Averaged Two-Dimensional Model of Unsteady Flow and Sediment Transport due to Noncohesive Embankment Break/BreachingJ Hydraul Eng, 138 (6) (2012), pp. 503-516View Record in ScopusGoogle Scholar[22]Z. Wang, D.S. BowlesThree-dimensional non-cohesive earthen dam breach model. Part 1: Theory and methodologyAdv Water Resour, 29 (10) (2006), pp. 1528-1545ArticleDownload PDFView Record in ScopusGoogle Scholar[23]Říha J, Duchan D, Zachoval Z, Erpicum S, Archambeau P, Pirotton M, et al. Performance of a shallow-water model for simulating flow over trapezoidal broad-crested weirs. J Hydrology Hydromechanics. 2019;67:322-8.Google Scholar[24]C.B. VreugdenhilNumerical methods for shallow-water flowSpringer Science & Business Media (1994)Google Scholar[25]L.A. Larocque, J. Imran, M.H. Chaudhry3D numerical simulation of partial breach dam-break flow using the LES and k–∊ turbulence modelsJ Hydraul Res, 51 (2) (2013), pp. 145-157 View PDFCrossRefView Record in ScopusGoogle Scholar[26]C. Yang, B. Lin, C. Jiang, Y. LiuPredicting near-field dam-break flow and impact force using a 3D modelJ Hydraul Res, 48 (6) (2010), pp. 784-792 View PDFCrossRefView Record in ScopusGoogle Scholar[27]FLOW-3D. Version 11.1.1 Flow Science, Inc., Santa Fe, NM. https://wwwflow3dcom.Google Scholar[28]C.W. Hirt, B.D. NicholsVolume of fluid (VOF) method for the dynamics of free boundariesJ Comput Phys, 39 (1) (1981), pp. 201-225ArticleDownload PDFGoogle Scholar[29]S.V. PatankarNumerical heat transfer and fluid flow, Hemisphere PublCorp, New York, 58 (1980), p. 288View Record in ScopusGoogle Scholar[30]M. Alemi, R. MaiaNumerical simulation of the flow and local scour process around single and complex bridge piersInt J Civil Eng, 16 (5) (2018), pp. 475-487 View PDFCrossRefView Record in ScopusGoogle Scholar
1 Civil Enigneering Department, Lahijan Branch.Islamic Azad University.Lahijan.Iran
2 Department of Civil Engnieering, University of Qom,Qom,Iran
3 Civil Engineering Department, Lahijan Branch,Islamic Azad Univeristy,Lahijan,Iran
Abstract
홍수와 그 위험을 통제해야 할 필요성은 누구에게도 숨겨져 있지 않습니다. 또한 이 현상으로 인해 다양한 경제, 사회 및 환경 문제가 영향을 받습니다. 홍수 제어 방법의 설계 및 최적 관리의 첫 번째 단계는 홍수 중 하천 거동을 올바르게 식별하는 것입니다.
홍수 경로 지정, 하상 및 하천 면적 결정 등과 같은 대부분의 하천 엔지니어링 프로젝트에서 하천 단면의 수리학적 매개변수의 평균값을 계산하는 것으로 충분합니다. 오늘날 유체 환경 연구에서 수치 및 분석 방법의 사용이 성장하고 발전했습니다.
신뢰할 수 있는 결과 생성으로 인해 물리적 모델에 대한 좋은 대안이 될 수 있었습니다. 오늘날 수치 모델의 급속한 발전과 컴퓨터 계산 속도의 증가로 인해 3D 수치 모델의 사용이 선호되며 또한 강의 속도 분포 및 전단 응력을 측정하는 데 시간이 많이 걸리고 비용이 많이 들기 때문에 결과 3D 수치 모델의 가치가 있을 것입니다.
한편, 본 연구에서는 복합단면에 대해 FLOW-3D 모델을 이용한 종합적인 수치연구가 이루어지지 않았음을 보여주고 있어 적절한 연구기반을 제공하고 있습니다.
따라서 본 연구의 혁신은 발산 및 수렴 범람원을 동반하는 비 각형 복합 단면에서 흐름의 상태 및 수리 성능에 대한 거칠기와 같은 매개 변수의 영향에 대한 수치 연구입니다.
수치해석 결과를 검증하기 위해 Younesi(2013) 연구를 이용하였습니다. 이 실험에서는 먼저 고정층이 있는 복합 프리즘 및 비 프리즘 단면의 수리 흐름을 조사한 다음 조건을 유지하면서 프리즘 및 비 프리즘 모드에서 퇴적물 이동 실험을 수행했습니다.
실험은 15미터 길이의 연구 채널에서 수행되었습니다. 이 운하는 초당 250리터의 시스템에서 재순환을 위해 제공될 수 있는 유속과 0.0088 000의 종경사를 가진 폭 400mm의 두 개의 대칭 범람원이 있는 합성 운하입니다. 범람원의 가장자리는 0.18미터와 같고 주요 운하의 너비는 0.4미터와 같습니다(그림 1).
본수로의 바닥과 벽을 거칠게 하기 위해 평균직경 0.65mm의 퇴적물을 사용하였으며, 각 단계에서 범람원의 벽과 바닥은 평균직경 0.65, 1.3, 1.78의 퇴적물로 거칠게 하였습다. (mm). 삼각형 오버플로는 운하 상류에서 운하로의 유입량을 측정하는 데 사용됩니다.
상대깊이 0.15와 0.25, 직경 14mm의 마이크로몰리나 실험과 상대깊이 0.35의 실험에서는 유속을 측정하기 위해 3차원 속도계(ADV)를 사용하였습니다. 수위는 0.1mm의 정확도로 깊이 게이지로 측정 되었습니다.
본 연구에서는 수면 프로파일의 수치적 모델을 검증하기 위해 실험 0.25-2에서 발산대의 시작, 중간 및 끝에서 세 단면의 평균 깊이 속도 분포 및 경계 전단 응력) -11.3-NP 및 0.25-2-5.7-NP 및 또한 각형 복합 단면의 0.25-2-2 P 테스트가 평가되었습니다.
각형 합성 단면의 P.20-2-2-P 테스트와 관련된 RMSE 및 NRMSE 지수 값 및 표 (2) 실험 11.3에서 RMSE 및 NRMSE 지수 값 -2-0.25-NP 및 -0.25. 2-5.7-NP가 제공됩니다. 실험 0.25-2-5.7-NP-11.3-2-0.25, NP 및 P.2.0-2-2-P의 평균 깊이 속도의 검증과 관련된 결과가 표시됩니다. 0.25-2-5.7-NP 실험에서 초, 중, 기말 NRMSE의 양은 각각 5.7, 11.8, 10.3%로 계산되었으며, 이는 초급이 우수, 중급이 양호, 최종 성적. 배치. 보시다시피, RMSE 값은 각각 0.026, 0.037 및 0.026으로 계산됩니다.
실험 11.3-2-0.25, NP에서 초급, 중급 및 최종 수준의 NRMSE 값은 각각 7, 11.2 및 15.4%로 계산되었으며, 이는 초급에서 우수 범주 및 우수 범주에서 중간 및 최종 수준. 가져 가다. 보시다시피, RMSE 값은 각각 0.032, 0.038, 0.04로 계산됩니다. 0.25-2-P 실험에서 NRMSE 값은 1.7%로 계산되어 우수 범주에 속한다. 보시다시피 RMSE 값도 0.004로 계산됩니다. 중간 깊이의 속도 분포와 관련하여 수치 모델은 실험실 결과에 적합하며 접합 영역에 작은 오류만 입력되었다고 말할 수 있습니다. 이는 2차 전지의 이동 결과로 간주될 수 있습니다. 모서리를 향해. 결론: 본 연구에서는 3차원 유동 해석이 가능한 Flow 3D 소프트웨어를 사용하여 각형 및 비각형 단면이 복합된 수로의 유동 패턴을 조사했습니다. 3개의 다른 상대 거칠기(1, 2 및 2.74)와 3개의 상대 깊이(0.15, 0.25 및 0.35) 및 5.7 및 11.3도의 발산 각도에 대해 속도의 세로 성분 변화, 평균 깊이 속도 분포, 경계 범람원에 의해 전달되는 유속뿐만 아니라 전단 응력 분포를 조사했습니다.
결과는 수로를 따라 범람원의 폭이 증가함에 따라 유속량이 감소함을 보여주었다. 또한 조도가 유동패턴에 미치는 영향에 대한 연구는 일반적으로 벽의 거칠기에 따라 모든 구간에서 유속량이 감소하는 것으로 나타났으며, 또한 본관과 범람원의 교차점에서의 유동패턴은 벽의 거칠기 영향을 더 많이 받는 것으로 나타났습니다. 결과는 또한 상대 깊이가 증가하거나 상대 거칠기가 감소함에 따라 주 수로와 범람원 사이의 속도 구배가 감소함을 보여주었습니다.
Intrpduction: The need to control floods and their dangers is not hidden from anyone. In addition, a wide range of economic, social and environmental issues are affected by this phenomenon. The first step in the design and optimal management of flood control methods is the correct identification of river behavior during floods. In most river engineering projects such as flood routing, determining the bed and river area, etc., calculating the average values of hydraulic parameters of the river section is sufficient. Today, the use of numerical and analytical methods in the study of fluid environment have grown and developed. Due to the production of reliable results, they have been able to be a good alternative to physical models. Today, with the rapid development of numerical models and increasing the speed of computer calculations, the use of 3D numerical models is preferred and also due to the fact that measuring the velocity distribution and shear stress in rivers is very time consuming and expensive, the results of 3D numerical models It will be valuable. On the other hand, the present studies show that comprehensive numerical research using FLOW-3D model has not been performed on composite sections, so a suitable ground for research is provided. Therefore, the innovation of the present study is the numerical study of the effects of parameters such as roughness on the status and hydraulic performance of the flow in non-prismatic composite sections, which are accompanied by divergent and convergent floodplains, which have received less attention numerically.
Methodology: Younesi (2013) research has been used to validate the results of numerical simulation. In these experiments, first the hydraulic flow in composite prismatic and non-prismatic sections with fixed bed was examined and then, while maintaining the conditions, sediment transfer experiments were performed in prismatic and non-prismatic mode. The experiments were performed in a research channel 15 meters long. This canal is a composite canal with two symmetrical floodplains with a width of 400 mm with a flow rate that can be provided for recirculation in the system of 250 liters per second and a longitudinal slope of 0.0088 000. The depth of the main canal to the edge of the floodplain is equal to 0.18 meters and the width of the main canal is equal to 0.4 meters (Figure 1). In order to roughen the bed and walls of the main canal, sediments with an average diameter of 0.65 mm have been used and at each stage, the walls and bed of floodplains have been roughened by sediments with an average diameter of 0.65, 1.3 and 1.78 (mm). A triangular overflow is used to measure the inflow to the canal, upstream of the canal. In order to measure the flow velocity in experiments with relative depth of 0.15 and 0.25, a micromolina with a diameter of 14 mm and in experiments with relative depth of 0.35, a three-dimensional speedometer (ADV) was used. The water level was also taken by depth gauges with an accuracy of 0.1 mm. Result and Diccussion: In the present study, in order to validate the numerical model of water surface profile, average depth velocity distribution and boundary shear stress in the three sections at the beginning, middle and end of the divergence zone) in experiments 0.25-2-11.3-NP and 0.25-2-5.7-NP and Also, the 0.25-2-2 P test of the prismatic composite section has been evaluated. In Table (1) the values of RMSE and NRMSE indices related to the P.20-2-2-P test of the prismatic composite section, and also in Table (2) the values of the RMSE and NRMSE indices in the experiments 11.3-2-0.25-NP and -0.25. 2-5.7-NP is provided. The results related to the validation of the average depth velocity of the experiments 0.25-2-5.7- NP-11.3-2-0.25, NP and P.2.0-2-2-P are shown. In 0.25-2-5.7-NP experiment, the amount of NRMSE in elementary, middle and final grades was calculated to be 5.7, 11.8 and 10.3%, respectively, which is in the excellent grade in the elementary grade and good in the middle and final grades. Placed. As can be seen, the RMSE values are calculated as 0.026, 0.037 and 0.026, respectively. In the experiment 11.3-2-0.25, NP, the NRMSE values in the primary, middle and final levels were calculated as 7, 11.2 and 15.4%, respectively, which are in the excellent category in the primary level and in the good category in the middle and final levels. Take. As can be seen, the RMSE values are calculated as 0.032, 0.038 and 0.04, respectively. In the 0.25-2-P experiment, the NRMSE value was calculated to be 1.7%, which is in the excellent category. As can be seen, the RMSE value is also calculated to be 0.004. Regarding the medium-depth velocity distribution, it can be said that the numerical model has an acceptable compliance with the laboratory results and only a small error has been entered in the junction area, which can be considered as a result of the movement of secondary cells towards the corners. Conclusion: in this research The flow pattern in waterways with composite prismatic and non-prismatic sections was investigated using Flow 3D software that is capable of three-dimensional flow analysis. For three different relative roughnesses (1, 2 and 2.74) as well as three relative depths (0.15, 0.25 and 0.35) and divergence angles of 5.7 and 11.3 degrees, changes in the longitudinal component of velocity, The average depth velocity distribution, the boundary shear stress distribution as well as the flow rate transmitted by the floodplains were investigated. The results showed that with increasing the width of floodplains along the canal, the amount of velocity decreases. Also, the study of the effect of roughness on the flow pattern showed that in general, with wall roughness, the amount of velocity has decreased in all sections and also the flow pattern at the junction of the main canal and floodplain is more affected by wall roughness. The results also showed that with increasing relative depth or decreasing relative roughness, the velocity gradient between the main channel and floodplains decreases
하천횡단구조물이 하천설계기준(2009)대로 설계되었음에도 불구하고, 하류부에서 물받이공 및 바닥보호공의 피해가 발생하여, 구조물 본체에 대한 안전성이 현저하 게 낮아지고 있는 실정이다. 하천설계기준이 상류부의 수리특성을 반영하였다고 하나 하류부의 수리특성인 유속의 변동 성분 또는 압력의 변동성분까지 고려하고 있지는 않다. 현재 많은 선행연구에서 이러한 난류적 특성이 구조물에 미치는 영 향에 대해 제시하고 있는 실정이며, 국내 하천에서의 피해 또한 이와 관련이 있다 고 판단된다. 이에 본 연구에서는 난류성분 특히 압력의 변동성분이 물받이공과 바닥보호공에 미치는 영향을 정량적으로 분석하여, 하천 횡단구조물의 치수 안전 성 증대에 기여하고자 한다. 물받이공과 바닥보호공에 미치는 압력의 변동성분 (pressure fluctuation) 영향을 분석하기 위해 크게 3가지로 연구내용을 분류하였 다. 첫 번째는 압력의 변동으로 순간적인 음압구배(adversed pressure gradient) 가 발생할 경우 바닥보호공의 사석 및 블록이 이탈하는 것이다. 이를 확인하기 위 해 정밀한 압력 측정장치를 통해 압력변이를 측정하여, 사석의 이탈 가능성을 검 토할 것이며, 최종적으로 이탈에 대한 한계조건을 도출할 것이다. 두 번째는 압력 의 변동이 물받이공의 진동을 유발시켜 이를 지지하고 있는 지반에 다짐효과를 가 져와 물받이공과 지반사이에 공극이 발생하는 경우이다. 이러한 공극으로 물받이 공은 자중 및 물의 압력을 받게 되어, 결국 휨에 의한 파괴가 발생할 가능성이 있 게 된다. 본 연구에서는 실험을 통하여 압력의 변동과 물받이공의 진동을 동시에 측정하여, 진동이 발생하지 않을 최소 두께를 제시할 것이다. 세 번째는 압력변이 로 인한 물받이공의 진동이 피로파괴로 연결되는 경우이다. 이 현상 또한 수리실 험을 통해 압력변이-피로파괴의 관계를 정량적으로 분석하여, 한계 조건을 제시할 것이다. 본 연구는 국내 보 및 낙차공에서 발생하는 다양한 Jet의 특성을 수리실 험으로 재현해야 하며, 이를 위해 평면 Jet 분사기(plane Jet injector)를 고안/ 제작하여, 효율적인 수리실험을 수행할 것이다. 또한 3차원 수치해석을 통해 실제 스케일에 적용함으로써 연구결과의 활용도 및 적용성을 높이고자 한다.
Keywords
압력변이, 물받이공, 바닥보호공, 난류, 진동
그림 1 하천횡단구조물 하류부 횡단구조물 파괴그림 2. 시간에 따른 압력의 변동 양상 및 정의
그림 3. 하천횡단구조물 하류부 도수현상시 발생하는 압력변이 분포도, Fr=8.0
상태이며, 바닥(slab)에 양압과 음압이 지속적으로 작용한다. (Fiorotto &
Rinaldo, 2010)
그림 4. 파괴 개념그림 6. PIV 측정 원리(www.photonics.com)그림 7. LED회로판 및 BIV기법 기본개념그림 8. BIV측정기법을 적용한 순간이미지 (Lin et al., 2012)그림 9. 감세공의 분류그림 17 수리실헐 수로시설: (a) 전체수로전경, (b) Weir 보를 포함한 측면도, (c) 도수조건
실험전경 그림 18 수리실험 개요도그림 127 난류모형별 압력 Data (측정위치는 그림 125 참조)그림 128 RNG 모형을 이용한 수치모의 결과그림 129 LES 모형을 이용한 수치모의 결과그림 130 압력 Data의 필터링그림 134 Case 1의 흐름특성 분포도 및 그래프
한국건설기술연구원 (2014) 입자영상유속계(PIV)를 이용한 하천구조물 주변 유동해석 기법 개발
한국건설기술연구원 (2017) 보와 하상유지공의 안전성 확보를 위한 물받이와 바닥보호공의 성능평가 기법에 대한 원천기술개발
국토기술연구센터 (1998) 하상유지공의 구조설계 지침.
감사원 (2013) 감사원 결과보고서- 4대강살리기 사업 주요시설물 품질 밑 수질관리 실태. 국토해양부 (2009) 전국 하천횡단 구조물 설치현황 및 어도 실태조사 보고서.
국토해양부 (2012) 보도자료-준공대비 점검결과, 4대강 보 안전 재확인. 국토해양부 (2012) 국가 및 지방하천 종합정비 마스터플랜.
국토교통성 (2008) 하천사방기술기준.
농림부 (1996). 농업생산기반정비사업계획 설계기
류권규(역자) (2009). 난류의 수치모의(원저자 : 梶島岳夫, 1999). 류권규, 마리안 머스테, 로버트 에테마, 윤병만 (2006). “난류 중 부유사의 속도 지체 측정.” 한국수자원학회논문집, 제39권, 제2호, pp.99-108. 배재현, 이경훈, 신종근, 양용수, 이주희 (2011). “입자영상유속계를 이용한 은어의 유영능력 측정.” 제47권, 제4호, pp.411-418. 우효섭 (2001). 하천수리학. 청문각. 한국수자원학회 (2009). 하천설계기준해설. 한국건설기술연구원 (2014) 입자영상유속계(PIV)를 이용한 하천구조물 주변 유동해석 기법 개발 한국건설기술연구원 (2017) 보와 하상유지공의 안전성 확보를 위한 물받이와 바닥보호공의 성능평가 기법에 대한 원천기술개발
Adrian, R. J., Meinhart, C. D., & Tomkins, C. D. (2000). Vortex organization in the outer region of the turbulent boundary layer. Journal of Fluid Mechanics, 422, 1-54. Anderson, T. W., & Darling, D. A. (1954). A test of goodness of fit. Journal of the American statistical association, 49(268), 765-769. Altman, E. I. (1968). Financial ratios, discriminant analysis and the prediction of corporate bankruptcy. The journal of finance, 23(4), 589-609. Barjastehmaleki, S., Fiorotto, V., & Caroni, E. (2016). Spillway stilling basins lining design via Taylor hypothesis. Journal of Hydraulic Engineering, 142(6), 04016010. Beheshti, M. R., Khosrojerdi, A., & Borghei, S. M. (2013). Experimental study of air-water turbulent flow structures on stepped spillways. International Journal of Physical Sciences, 8(25), 1362-1370. Bligh, W. G. (1910). Dams, barrages and weirs on porous foundations. Engineering News, 64(26), 708-710. Bowers, C. E., &Tsai, F. Y. (1969). Fluctuating pressure in spillway stilling basins. Journal of the Hydraulics Division, 95(6), 2071-2080. Brater, E. F., King, H. W., Lindell, J. E., & Wei, C. Y. (1976). Handbook of hydraulics for the solution of hydraulic engineering problems (Vol. 7). New York: McGraw-Hill. Castillo, L. G., Carrillo, J. M., & Sordo-Ward, Á. (2014). Simulation of overflow nappe impingement jets. Journal of Hydroinformatics, 16(4), 922-940
Lin, C., Hsieh, S. C., Lin, I. J., Chang, K. A., & Raikar, R. V. (2012). Flow property and self-similarity in steady hydraulic jumps. Experiments in Fluids, 53(5), 1591-1616
Chanson, H. (1999). The Hydraulics of Open Channel Flow: An Introduction. Physical Modelling of Hydraulics. Chow, V. T. (1959). Open-Channel Hydraulics, McGraw Hill Book Company, Inc., New York. Christensen, B. A. (1984). “Analysis of Partially Filled Circular Storm Sewers.” J. of Hydraulic Engineering, ASCE, Vol. 110, No. 8. El-Ragaby, A., El-Salakawy, E., and Benmokrane, B., “Fatigue Life Evaluation of Concrete Bridge Deck Slabs Reinforced with Glass FRP Composite Bars,” Journal of Composites for Construction, ASCE, Vol. 11, No. 3, 2007, pp. 258-268. (doi: http://dx.doi.org/10.1061/(ASCE) 1090-0268(2007)11:3(258), Fiorotto, V., & Rinaldo, A. (1992). Turbulent pressure fluctuations under hydraulic jumps. Journal of Hydraulic Research, 30(4), 499-520. Flow Science (2015). FLOW-3D User Manual(Release 11.1.0), Los Alamos, New Mexico. González-Betancourt, M. (2016). Uplift force and momenta on a slab subjected to hydraulic jump. Dyna, 83(199), 124-133. Grinstein, L., & Lipsey, S. I. (2001). Encyclopedia of mathematics education. Routledge. Grubbs, F. E., & Beck, G. (1972). Extension of sample sizes and percentage points for significance tests of outlying observations. Technometrics, 14(4), 847-854. Gylltoft K. (1983): Fracture mechanics models for fatigue in concrete structures. Doctoral thesis / Tekniska högskolan i Luleå, 25D, Luleå, 210 pp. Herlina, H. and Jirka, G. H. (2008). “Experiments on gas transfer near the air-water interface in a grid-stirred tank.” Journal of Fluid Mechanics, 594, pp.183-208. IACWD (Interagency Advisory Committee on Water Data). (1982). Guidelines for determining flood flow frequency. Bulletin 17B. JIRKA, G. H. (2008). Experiments on gas transfer at the air–water interface induced by oscillating grid turbulence. Journal of Fluid Mechanics, 594, 183-208. Kadota, A., Suzuki, K., Rummel, A. C., Weitbrecht, V., & Jirka, G. H. (2007). Shallow flow visualization around a single groyne. In Proc. of 7th International Symposium of Particle Image Velocimetry (CD-ROM). Kazemi, F., Khodashenas, S. R., & Sarkardeh, H. (2016). Experimental study of pressure fluctuation in stilling basins. International Journal of Civil Engineering, 14(1), 13-21. Klowak, C., Memon, A., and Mufti, A., “Static and fatigue investigation of second generation steel-free bridge decks,” Cement & Concrete Composites, ScienceDirect, Elsevier, Vol. 28, No.
10, 2006, pp. 890-897. (doi: http://dx.doi.org/10.1016/j.cemconcomp.2006.07.019), Koca, K., Noss, C., Anlanger, C., Brand, A., & Lorke, A. (2017). Performance of the Vectrino Profiler at the sediment–water interface. Journal of Hydraulic Research, 55(4), 573-581. Kolmogorov, A. (1933). Sulla determinazione empirica di una lgge di distribuzione. Inst. Ital. Attuari, Giorn., 4, 83-91. Leon, A., & Alnahit, A. (2016). A Remotely Controlled Siphon System for Dynamic Water Storage Management. Lin, C., Hsieh, S., Chang, K. and Raikar, R. (2012). “Flow property and self-similarity in steady hydraulic jumps.” Experiments in Fluid, 53, pp. 1591-1616. Lopardo, R., Fattor, C. A., Casado, J. M. and Lopardo, M. C. (2004). “Aspects of vibration and fatigue of materials related to coherent structures of macroturbulent flows” International Conference on Hydraulic of Dams and River Structures. Lopardo, R. A., & Romagnoli, M. (2009). Pressure and velocity fluctuations in stilling basins. In Advances in Water Resources and Hydraulic Engineering (pp. 2093-2098). Springer, Berlin, Heidelberg. Sanchez, P. A., Ramirez, G. E., Vergara, R., & Minguillo, F. (1973). Performance of Sulfur-Coated Urea Under Intermittently Flooded Rice Culture in Peru 1. Soil Science Society of America Journal, 37(5), 789-792. Matsui, S., Tokai, D., Higashiyama, H., and Mizukoshi, M., “Fatigue Durability of Fiber Reinforced Concrete Decks Under Running Wheel Load,” Proceedings 3rd International Conference on Concrete Under Severe Conditions, Ed. N. Banthia, Vancouver, Canada, 2001, pp. 982-991., Mohammadi, S. F., Galgoul, N. S., Starossek, U., & Videiro, P. M. (2016). An efficient time domain fatigue analysis and its comparison to spectral fatigue assessment for an offshore jacket structure. Marine Structures, 49, 97-115. Pothof, I. (2011). Co-current air-water flow in downward sloping pipes. Stichting Deltares Pothof, I. W. M., & Clemens, F. H. L. R. (2011). Experimental study of air–water flow in downward sloping pipes. International journal of multiphase flow, 37(3), 278-292. Ryu, Y., Chang, K. A., & Lim, H. J. (2005). Use of bubble image velocimetry for measurement of plunging wave impinging on structure and associated greenwater. Measurement Science and Technology, 16(10), 1945. Sanjou, M., & Nezu, I. (2009). Turbulence structure and coherent motion in meandering compound open-channel flows. Journal of Hydraulic Research, 47(5), 598-610. Sargison, J. E., & Percy, A. (2009). Hydraulics of broad-crested weirs with varying side slopes. Journal of irrigation and drainage engineering, 135(1), 115-118.
Sobani, A. (2014). Pressure fluctuations on the slabs of stilling basins under hydraulic jump. Song, Y., Chang, K, Ryu, Y. and Kwon, S. (2013). “ Experimental study on flow kinematics and impact pressure in liquid sloshing.”, Experiments in Fluid, 54, pp. 1592. Stagonas, D., Lara, J. L., Losada, I. J., Higuera, P., Jaime, F. F., & Muller, G. (2014). Large scale measurements of wave loads and mapping of impact pressure distribution at the underside of wave recurves. In Proceedings of the HYDRALAB IV Joint User Meeting. Toso, J. W., & Bowers, C. E. (1988). Extreme pressures in hydraulic-jump stilling basins. Journal of Hydraulic Engineering, 114(8), 829-843. Youn, S. G. and Chang, S. P., “Behavior of Composite Bridge Decks Subjected to Static and Fatigue Loading,” Structural Journal, ACI Technical paper, Title No. 95-S23, 1998, pp. 249-258. (doi: http://dx.doi.org/10.14359/543),
Parshall Flumes의 효율성 향상을 위한 수치 및 실험 모델링의 적용: 최신 기술 검토
Mehdi Heyrani 1,* , Abdolmajid Mohammadian 1, Ioan Nistor 1 and Omerul Faruk Dursun 2
Abstract
열린 채널에서 흐름을 관리하는 기본 단계 중 하나는 속성을 결정하는 것입니다. 개방 수로의 흐름에 관한 추가 정보를 제공하기 위해 경험적 방정식이 개발되었습니다. 이러한 실험 방정식을 얻는 것은 비용과 시간이 많이 소요됩니다. 따라서 대체 솔루션이 모색되었습니다.
지난 세기 동안 움직이는 부분이 없는 정적 측정 장치인 Parshall 수로가 개방 수로의 흐름을 측정하는 데 중요한 역할을 했습니다. 많은 연구자들이 관개 및 폐수 관리와 같은 다양한 분야에서 Parshall 수로의 적용을 연구하는 데 관심을 집중해 왔습니다.
여러 학자들이 실험 결과를 사용하여 Parshall 수로의 등급 방정식을 향상시켰지만 다른 학자들은 수치 시뮬레이션을 사용하여 높이-방전 관계 방정식을 재보정하기 위해 대체 데이터 소스를 사용했습니다. 컴퓨팅 하드웨어가 지난 수십 년 동안 크게 발전하여 과거에 경험했던 제한된 해상도를 뛰어넘는 것이 가능해짐에 따라 CFD(Computational Fluid Dynamic) 소프트웨어가 오늘날 대중화되고 있습니다.
여러 CFD 모델은 가용성에 따라 오픈 소스 또는 상업적으로 허가되어 수위 결과를 생성하기 위해 다양한 구성의 수로, 특히 Parshall 수로에 대한 수치 시뮬레이션을 수행하는 데 사용되었습니다.
FLOW-3D, Ansys Fluent, OpenFOAM 등 지금까지 사용되어 온 다양한 CFD 도구에 대해 실험 데이터로 정밀 교정한 결과, 출력이 안정적이고 실제 시나리오에 구현할 수 있음이 확인되었습니다.
결과를 생성하기 위해 이 기술을 사용하는 이점은 필요한 경우 유속 또는 구조적 형상과 같은 초기 조건을 조정하는 CFD 접근 방식의 능력입니다. 수로 크기와 수로가 위치한 부지의 조건과 관련하여 상황에 적합한 특정 Parshall 수로로 선택이 좁혀집니다.
표준 Parshall 수로를 선택하는 것이 항상 가능한 것은 아닙니다. 따라서 엔지니어는 가장 가까운 수로 크기에 약간의 수정을 제공하고 정확한 유량을 생성하기 위해 새로운 등급 곡선을 제공합니다.
이 검토는 기존 등급 방정식을 향상시키거나 구조의 기하학에 대한 추가 수정을 제안하기 위해 Parshall 수로에서 수치 시뮬레이션 및 물리적 실험 데이터의 적용을 목표로 하는 여러 학자의 작업에 대해 수행되었습니다.
One of the primary steps in managing the flow in an open channel is determining its properties. Empirical equations are developed to provide further information regarding the flow in open channels. Obtaining such experimental equations is expensive and time consuming; therefore, alternative solutions have been sought. Over the last century, the Parshall flume, a static measuring device with no moving parts, has played a significant role in measuring the flow in open channels. Many researchers have focused their interest on studying the application of Parshall flumes in various fields like irrigation and wastewater management. Although various scholars used experimental results to enhance the rating equation of the Parshall flume, others used an alternative source of data to recalibrate the height–discharge relation equation using numerical simulation. Computational Fluid Dynamic (CFD) software is becoming popular nowadays as computing hardware has advanced significantly within the last few decades, making it possible to go beyond the limited resolution that was experienced in the past. Multiple CFD models, depending on their availability, either open-source or commercially licensed, have been used to perform numerical simulations on different configurations of flumes, especially Parshall flumes, to produce water level results. Regarding various CFD tools that have been used, i.e., FLOW-3D, Ansys Fluent, or OpenFOAM, after precise calibration with experimental data, it has been determined that the output is reliable and can be implemented to the actual scenarios. The benefit of using this technique to produce results is the ability of the CFD approach to adjust the initial conditions, like flow velocity or structural geometry, where necessary. With respect to channel size and the condition of the site where the flume is located, the choices are narrowed to the specific Parshall flume suitable to the situation. It is not always possible to select the standard Parshall flume; therefore, engineers provide some modification to the closest flume size and provide a new rating curve to produce accurate flowrates. This review has been performed on the works of a number of scholars who targeted the application of numerical simulation and physical experimental data in Parshall flumes to either enhance the existing rating equation or propose further modification to the structure’s geometry.
Keywords
Parshall flume; CFD; OpenFOAM; FLOW-3D; numerical simulation; turbulence model
Figure 1. Parshall flume measuring structure, installed [2].Figure 2. Parshall flume measuring structure, uninstalled [3]Figure 4. Mesh sensitivity analysis: top view and side view of the Parshall flume: (a) contains 27,000 cells;
(b) 52,000 cells; (c) 75,000 cells; (d) 270,000 cells. The C setup was used in their simulation [7].Figure 7. The simulated velocity (a) and simulated pressure pattern (b) across the Parshall flume.
The patterns match the physical behavior of actual Parshall flumes [7]. Figure 8. Computational grid system in the Side A flume. (a) contains a triangular grid system (b)
demonstrates the rectangular grid system. (c) and (d) are three-dimensional schematics showing the
superimposed grid system. (e) magnifies the dashed section in (b). (Reprinted with permission from
Ref. [11]. 2020 ELSEVIER). ). Figure 10. The results of flow patterns in different flumes; (a) Cutthroat flume, (b) airfoil-shaped
flume, (c) airfoil pillar-shaped flume, (d) optimized airfoil-shaped flume [23]Figure 11. Experimental setup: contraction ratio used on each flume [23].Figure 12. Entire flume geometry [25]
References
Cone, V.M. The Venturi Flume; U.S. Government Printing Office: Washington, DC, USA, 1917.
20-Foot Concrete Parshall Flume with Radius Wing Walls. Available online: https://www.openchannelflow.com/assets/uploads/ media/_large/20-foot-parshall-flume-curved-wing-walls.jpg (accessed on 12 January 2021).
Fiberglass 6-Inch Parshall Flume with Gauge. Available online: https://www.openchannelflow.com/assets/uploads/media/ _large/flume-parshall-6-inch-fiberglass.png (accessed on 12 January 2021).
Parshall, R.L. The Parshall Measuring Flume; Colorado State College, Colorado Experiment Station: Fort Collins, CO, USA, 1936.
Selecting Between a Weir and a Flume. 2022. Available online: https://www.openchannelflow.com/blog/selecting-a-primarydevice-part-1-choosing-between-a-weir-and-a-flume (accessed on 29 December 2021).
Heyrani, M.; Mohammadian, A.; Nistor, I. Numerical Simulation of Flow in Parshall Flume Using Selected Nonlinear Turbulence Models. Hydrology 2021, 8, 151. [CrossRef]
Heyrani, M.; Mohammadian, A.; Nistor, I.; Dursun, O.F. Numerical Modeling of Venturi Flume. Hydrology 2021, 8, 27. [CrossRef]
Alfonsi, G. Reynolds-Averaged Navier–Stokes Equations for Turbulence Modeling. Appl. Mech. Rev. 2009, 62, 040802. [CrossRef]
Imanian, H.; Mohammadian, A. Numerical Simulation of Flow over Ogee Crested Spillways under High Hydraulic Head Ratio. Eng. Appl. Comput. Fluid Mech. 2019, 13, 983–1000. [CrossRef]
Khosronejad, A.; Herb, W.; Sotiropoulos, F.; Kang, S.; Yang, X. Assessment of Parshall Flumes for Discharge Measurement of Open-Channel Flows: A Comparative Numerical and Field Case Study. Measurement 2020, 167, 108292. [CrossRef]
Dursun, O.F. An Experimental Investigation of the Aeration Performance of Parshall Flume and Venturi Flumes. KSCE J. Civ. Eng. 2016, 20, 943–950. [CrossRef]
Shih, T.-H.; Liu, N.-S.; Chen, K.-H. A Non-Linear k-Epsilon Model for Turbulent Shear Flows. In Proceedings of the 34th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, Cleveland, OH, USA, 13 July 1998; p. 3983.
Lien, F.S. Low-Reynolds-Number Eddy-Viscosity Modelling Based on Non-Linear Stress-Strain/Vorticity Relations. In Proceedings of the 3rd Symposium on Engineering Turbulence Modelling and Measurement, Heraklion, Greece, 27 May 1996.
Davis, R.W.; Deutsch, S. A Numerical-Experimental Study of Parhall Flumes. J. Hydraul. Res. 1980, 18, 135–152. [CrossRef]
Xiao, Y.; Wang, W.; Hu, X.; Zhou, Y. Experimental and Numerical Research on Portable Short-Throat Flume in the Field. Flow Meas. Instrum. 2016, 47, 54–61. [CrossRef]
Wright, S.J.; Tullis, B.P.; Long, T.M. Recalibration of Parshall Flumes at Low Discharges. J. Irrig. Drain. Eng. 1994, 120, 348–362. [CrossRef]
Savage, B.M.; Heiner, B.; Barfuss, S. Parshall Flume Discharge Correction Coefficients through Modelling. Proc. ICE Water Manag. 2013, 167, 279–287. [CrossRef]
Zerihun, Y.T. A Numerical Study on Curvilinear Free Surface Flows in Venturi Flumes. Fluids 2016, 1, 21. [CrossRef]
Sun, B.; Zhu, S.; Yang, L.; Liu, Q.; Zhang, C.; Zhang, J. ping Experimental and Numerical Investigation of Flow Measurement Mechanism and Hydraulic Performance on Curved Flume in Rectangular Channel. Arab. J. Sci. Eng. 2020. [CrossRef]
Hu, H.; Huang, J.; Qian, Z.; Huai, W.; Yu, G. Hydraulic Analysis of Parabolic Flume for Flow Measurement. Flow Meas. Instrum. 2014, 37, 54–64. [CrossRef]
Sun, B.; Yang, L.; Zhu, S.; Liu, Q.; Wang, C.; Zhang, C. Study on the Applicability of Four Flumes in Small Rectangular Channels. Flow Meas. Instrum. 2021, 80, 101967. [CrossRef]
Willeitner, R.P.; Barfuss, S.L.; Johnson, M.C. Using Numerical Modeling to Correct Flow Rates for Submerged Montana Flumes. J. Irrig. Drain. Eng. 2013, 139, 586–592. [CrossRef]
Ran, D.; Wang, W.; Hu, X. Three-Dimensional Numerical Simulation of Flow in Trapezoidal Cutthroat Flumes Based on FLOW-3D. Front. Agric. Sci. Eng. 2018, 5, 168–176. [CrossRef]
Kim, S.-Y.; Lee, J.-H.; Hong, N.-K.; Lee, S.-O. Numerical Simulation for Determining Scale of Parshall Flume. Proc. Korea Water Resour. Assoc. Conf. 2010, 719–723.
Tekade, S.A.; Vasudeo, A.D.; Ghare, A.D.; Ingle, R.N. Measurement of Flow in Supercritical Flow Regime Using Cutthroat Flumes. Sadhana 2016, 41, 265–272. [CrossRef]
Wahl, T.L.; Replogle, J.A.; Wahlin, B.T.; Higgs, J.A. New Developments in Design and Application of Long-Throated Flumes. In Proceedings of the Joint Conference on Water Resource Engineering and Water Resources Planning and Management, Minneapolis, MN, USA, 30 July–2 August 2000.
Howes, D.J.; Burt, C.M.; Sanders, B.F. Subcritical Contraction for Improved Open-Channel Flow Measurement Accuracy with an Upward-Looking ADVM. J. Irrig. Drain. Eng. 2010, 136, 617–626. [CrossRef]
Tiwari, N.K.; Sihag, P. Prediction of Oxygen Transfer at Modified Parshall Flumes Using Regression Models. ISH J. Hydraul. Eng. 2020, 26, 209–220. [CrossRef]
Thornton, C.I.; Smith, B.A.; Abt, S.R.; Robeson, M.D. Supercritical Flow Measurement Using a Small Parshall Flume. J. Irrig. Drain. Eng. 2009, 135, 683–692. [CrossRef]
Cox, A.L.; Thornton, C.I.; Abt, S.R. Supercritical Flow Measurement Using a Large Parshall Flume. J. Irrig. Drain. Eng. 2013, 139, 655–662. [CrossRef]
Ribeiro, Á.S.; Sousa, J.A.; Simões, C.; Martins, L.L.; Dias, L.; Mendes, R.; Martins, C. Parshall Flumes Flow Rate Uncertainty Including Contributions of the Model Parameters and Correlation Effects. Meas. Sens. 2021, 18, 100108. [CrossRef]
Singh, J.; Mittal, S.K.; Tiwari, H.L. Discharge Relation for Small Parshall Flume in Free Flow Condition. Int. J. Res. Eng. Technol. 2014, 3, 317–321.
Kim, S.-D.; Lee, H.-J.; Oh, B.-D. Investigation on Application of Parshall Flume for Flow Measurement of Low-Flow Season in Korea. Meas. Sci. Rev. 2010, 10, 111. [CrossRef]
The effect of triangular prismatic elements on the hydraulic performance of stepped spillways in the skimming flow regime: an experimental study and numerical modeling
계단식 여수로는 댐의 여수로 위로 흐르는 큰 물의 에너지를 분산시키는 비용 효율적인 유압 구조입니다. 이 연구에서는 삼각주형 요소(TPE)가 계단식 배수로의 수력 성능에 미치는 영향에 초점을 맞췄습니다. 9개의 계단식 배수로 모델이 TPE의 다양한 모양과 레이아웃으로 실험 및 수치적으로 조사되었습니다. 적절한 난류 모델을 채택하려면 RNG k – ε 및 표준 k – ε모델을 활용했습니다. 계산 모델 결과는 계단 표면의 속도 분포 및 압력 프로파일을 포함하여 실험 사례의 계단 여수로에 대한 복잡한 흐름을 만족스럽게 시뮬레이션했습니다. 결과는 계단식 여수로에 TPE를 설치하는 것이 캐비테이션 효과를 줄이는 효과적인 방법이 될 수 있음을 나타냅니다. 계단식 여수로에 TPE를 설치하면 에너지 소실률이 최대 54% 증가했습니다. 계단식 배수로의 성능은 TPE가 더 가깝게 배치되었을 때 개선되었습니다. 또한, 실험 데이터를 이용하여 거칠기 계수( f )와 임계 깊이 대 단차 거칠기( yc / k )의 비율 사이의 관계를 높은 정확도로 얻었다.
Figure 1 | General schematics of laboratory flume facilities.Figure 2 | Different layouts of the selected TPE in the experimental study (y1 and y2 are initial, and sequent depths of hydraulic jump).Figure 3 | Geometry and alignment of TPE in the numerical study.Figure 5 | Comparison of turbulence models in Flow-3D.Figure 6 | Sequent water depths versus unit flow rate in standard stepped spillways and stepped spillways with triangular TPEs of types A
and B.Figure 7 | Energy dissipation for the standard stepped spillway and the stepped spillway with TPEs.Figure 8 | Positions of measurement points to investigate the pressure and velocity distributions on the stepped spillwayFigure 9 | Velocity distributions on the vertical surface of step number 4.Figure 10 | Contour lines of the static pressure (Pa) for the standard form of the stepped spillway with discharge of 60 liters/second.Figure 11 | Pressure distribution on the vertical surface of the fourth step.
Figure 12 | Horizontal profile of the pressure distribution on the floor of step 4.Figure 13 | Roughness coefficient changes with various unit discharges for stepped spillways.Figure 14 | Variations of sequent depth of downstream with various unit discharges for stepped spillways.Figure 15 | Energy dissipation rate changes with various unit discharges for different stepped spillways.Figure 16 | Roughness coefficients (f ) versus the critical depth to the step roughness ratio (yc/K).
REFERENCES
Abbasi, S. & Kamanbedast, A. A. 2012 Investigation of effect of changes in dimension and hydraulic of stepped spillways for maximization energy dissipation. World Applied Sciences Journal 18 (2), 261–267. Arjenaki, M. O. & Sanayei, H. R. Z. 2020 Numerical investigation of energy dissipation rate in stepped spillways with lateral slopes using experimental model development approach. Modeling Earth Systems and Environment 1–12. Attarian, A., Hosseini, K., Abdi, H. & Hosseini, M. 2014 The effect of the step height on energy dissipation in stepped spillways using numerical simulation. Arabian Journal for Science and Engineering 39 (4), 2587–2594. Azhdary Moghaddam, M. 1997 The Hydraulics of Flow on Stepped Ogee-Profile Spillways. Doctoral Dissertation, University of Ottawa, Canada. Bakhtyar, R. & Barry, D. A. 2009 Optimization of cascade stilling basins using GA and PSO approaches. Journal of Hydroinformatics 11 (2), 119–132. Barani, G. A., Rahnama, M. B. & Sohrabipoor, N. 2005 Investigation of flow energy dissipation over different stepped spillways. American Journal of Applied Sciences 2 (6), 1101–1105. Boes, R. M. & Hager, W. H. 2003 Hydraulic design of stepped spillways. Journal of Hydraulic Engineering 129 (9), 671–679. Chamani, M. R. & Rajaratnam, N. 1994 Jet flow on stepped spillways. Journal of Hydraulic Engineering 120 (2), 254–259. Chanson, H. 1994 Comparison of energy dissipation between nappe and skimming flow regimes on stepped chutes. Journal of Hydraulic Research 32 (2), 213–218. Felder, S., Guenther, P. & Chanson, H. 2012 Air-Water Flow Properties and Energy Dissipation on Stepped Spillways: A Physical Study of Several Pooled Stepped Configurations. No. CH87/12. School of Civil Engineering, The University of Queensland. Harlow, F. H. & Nakayama, P. I. 1968 Transport of Turbulence Energy Decay Rate. No. LA-3854. Los Alamos Scientific Lab, N. Mex. Hekmatzadeh, A. A., Papari, S. & Amiri, S. M. 2018 Investigation of energy dissipation on various configurations of stepped spillways considering several RANS turbulence models. Iranian Journal of Science and Technology, Transactions of Civil Engineering 42 (2), 97–109. Henderson, F. M. 1966 Open Channel Flow. MacMillan Company, New York. Kavian Pour, M. R. & Masoumi, H. R. 2008 New approach for estimating of energy dissipation over stepped spillways. International Journal of Civil Engineering 6 (3), 230–237. Li, S., Li, Q. & Yang, J. 2019 CFD modelling of a stepped spillway with various step layouts. Mathematical Problems in Engineering. Li, S., Yang, J. & Li, Q. 2020 Numerical modelling of air-water flows over a stepped spillway with chamfers and cavity blockages. KSCE Journal of Civil Engineering 24 (1), 99–109. Moghadam, M. K., Amini, A. & Moghadam, E. K. 2020 Numerical study of energy dissipation and block barriers in stepped spillways. Journal of Hydroinformatics. Morovati, K., Eghbalzadeh, A. & Javan, M. 2016 Numerical investigation of the configuration of the pools on the flow pattern passing over pooled stepped spillway in skimming flow regime. Acta Mechanic Journal 227, 353–366. Parsaie, A. & Haghiabi, A. H. 2019 The hydraulic investigation of circular crested stepped spillway. Flow Measurement and Instrumentation 70, 101624. Peng, Y., Zhang, X., Yuan, H., Li, X., Xie, C., Yang, S. & Bai, Z. 2019 Energy dissipation in stepped spillways with different horizontal face angles. Energies 12 (23), 4469. Roushangar, K., Foroudi, A. & Saneie, M. 2019 Influential parameters on submerged discharge capacity of converging ogee spillways based on experimental study and machine learning-based modeling. Journal of Hydroinformatics 21 (3), 474–492. Sarkardeh, H., Marosi, M. & Roshan, R. 2015 Stepped spillway optimization through numerical and physical modeling. International Journal of Energy and Environment 6 (6), 597. Shahheydari, H., Nodoshan, E. J., Barati, R. & Moghadam, M. A. 2015 Discharge coefficient and energy dissipation over stepped spillway under skimming flow regime. KSCE Journal of Civil Engineering 19 (4), 1174–1182. Tabari, M. M. R. & Tavakoli, S. 2016 Effects of stepped spillway geometry on flow pattern and energy dissipation. Arabian Journal for Science and Engineering 41 (4), 1215–1224. Toombes, L. & Chanson, H. 2000 Air-water flow and gas transfer at aeration cascades: a comparative study of smooth and stepped chutes. In Proceedings of the International Workshop on Hydraulics of Stepped Spillways, Zurich, Switzerland, pp. 22–24. Torabi, H., Parsaie, A., Yonesi, H. & Mozafari, E. 2018 Energy dissipation on rough stepped spillways. Iranian Journal of Science and Technology, Transactions of Civil Engineering 42 (3), 325–330. Wüthrich, D. & Chanson, H. 2014 Hydraulics, air entrainment, and energy dissipation on a Gabion stepped weir. Journal of Hydraulic Engineering 140 (9), 04014046. Yakhot, V. & Orszag, S. A. 1986 Renormalization group analysis of turbulence. I. Basic theory. Journal of Scientific Computing 1 (1), 3–51. Yakhot, V. & Smith, L. M. 1992 The renormalization group, the ɛ-expansion and derivation of turbulence models. Journal of Scientific Computing 7 (1), 35–61.
본 연구에서는 LW(Labyrinth Weir)와 PKW(Piano Key Weir)가 결합된 T자형 웨어(TSW)라는 새로운 비선형 웨어를 도입하여 수압 성능을 비교하였다.
PKW. 입구 키, 출구 키 또는 두 키 모두에서 수직 벽의 존재에 따라 TSW 위어는 각각 A, B 또는 C 유형 웨어로 분류되었습니다. 다른 TSW 사례의 흐름 패턴을 분석하고 배출 계수 곡선을 제공했습니다. 또한 테스트된 둑의 유체역학을 정확하게 연구하기 위해 FLOW-3D 소프트웨어를 사용하여 3D 수치 시뮬레이션을 수행했습니다.
결과는 출구 키(C-TSW 유형)의 상류에 수직 벽을 삽입하는 것이 PKW의 유압 성능에 미미한 영향을 미치는 것으로 나타났습니다. B-TSW의 토출계수는 PKW 대비 최대 16% 증가하였으며, Ht/p 0.45까지 수직벽의 성능향상 효과 증가 B-TSW는 유지되었습니다.
실험적 및 수치적 실험을 통해 가장 높은 방전 용량을 갖는 B-TSW에서 수직벽의 최적 높이비(Pd/P)는 0.4로 결정되었다.
In the present study, a new nonlinear weir called the T-shaped weir (TSW), which is a combination of the labyrinth weir (LW) and the piano key weir (PKW), was introduced, and its hydraulic performance was compared with the PKW. Based on the presence of the vertical walls at the inlet key, outlet key, or both keys, the TSW weirs were classified as type A, B, or C weirs, respectively. The flow pattern of different TSW cases was analyzed, and the discharge coefficient curves were provided. Furthermore, to accurately study the hydrodynamics of the tested weirs, 3D numerical simulations were performed using the FLOW-3D software. The results showed that inserting a vertical wall at the upstream of the outlet keys (C-TSW type) has a negligible effect on the hydraulic performance of the PKW. A maximum increase of 16% occurred in the discharge coefficient of the B-TSW in comparison to the PKW, and up to a head to height ratio (Ht/p) of 0.45, the effect of the vertical wall on increasing the performance of the B-TSW was maintained. Based on the experimental and numerical tests, the optimal height ratio of the vertical wall (Pd/P) in B-TSW with highest discharge capacity was determined to be equal to 0.4.
Figure 2 Idea and details of T-shaped weir.Figure 19. Water surface profile at the middle part of the inlet key for H/P = 0.4.Figure 21 Transverse water surface profile in the outlet key of tested weirs for H/P = 0.4.
REFERENCES
Anderson R. M. & Tullis B. P. 2011 Influence of Piano Key Weirs Geometry on Discharge. In Labyrinth and Piano Key Weirs – PKW 2011. CRC Press, Leiden, pp. 75–80.
Bremer F. L. & Oertel M. 2017 Numerical investigation of wall thickness influence on Piano key Weir discharge coefficients: A preliminary study. In Labyrinth and Piano Key Weirs III – PKW 2017. CRC Press, London, UK, pp. 101–108.
Cicero G. M., Delisle J. R., Lefebvre V. & Vermeulen J. 2013 Experimental and Numerical Study of the Hydraulic Performance of A Trapezoidal PKW. In Labyrinths and Piano Key Weirs PKW 2013. CRC Press, Boca Raton, FL, pp. 265–272.
Crookston B., Anderson R. M. & Tullis B. P. 2017 Free-flow discharge estimation method for piano key weir geometries. Journal of Hydro-Environment Research 19, 60–167.
Lefebvre V., Vermeulen J. & Blancher B. 2013 Influence of Geometrical Parameters on PK-Weirs Discharge with 3D Numerical Analysis. In: Labyrinth and Piano key Weirs II – PKW 2013. CRC Press, London, pp. 49–56.
Lempérière F. & Ouamane A. 2003 The piano keys weir: a new cost-effective solution for spillways. International Journal on Hydropower & Dams 10 (5), 144–149.
Machiels O., Erpicum S., Archambeau P., Dewals B. J. & Pirotton M. 2011 Influence of piano key weir height on its discharge capacity. In Proc. Int. Conf. Labyrinth and Piano Key Weirs Liège B, pp. 59–66.
Paxson G. & Savage B. 2006 Labyrinth spillways: comparison of two popular USA design methods and consideration of non-standard approach conditions and geometries. Division of Civil Engineering, p.37.
Pralong J., Vermeulen J., Blancher B., Laugier F., Erpicum S., Machiels O., Pirotton M., Boillat J.-L., Leite Ribeiro M. & Schleiss A. 2011a A naming convention for the Piano Key Weirs geometrical parameters. In Labyrinth and Piano key Weirs – PKW 2011. CRC Press, London, pp. 271–278.
Pralong J., Montarros F., Blancher B. & Laugier F. 2011b A sensitivity analysis of Piano Key Weirs geometrical parameters based on 3D numerical modelling. In Labyrinth and Piano key Weirs – PKW 2011. CRC Press, London, pp. 133–139.
Ribeiro M. L., Bieri M., Boillat J. L., Schleiss A., Delorme F. & Laugier F. 2009 Hydraulic capacity improvement of existing spillways–design of a piano key weir. In Proceedings (on CD) of the 23rd Congress of the Int. Commission on Large Dams CIGB-ICOLD, Brasilia, Vol. 2, No. CONF, pp. 100–118.
이중 여수로 간섭은 여수로가 서로 가깝게 배치될 때 수압 성능의 손실을 나타냅니다. 배수로 간섭은 물리적 실험과 수치 시뮬레이션을 모두 사용하여 조사됩니다.
이중 여수로 구성의 4개 물리적 모델의 단계 및 배출 측정값을 한국의 4개 댐 부지에서 Flow-3D 계산 결과와 비교합니다.
두 개의 배수로를 함께 사용하는 것을 각 배수로의 단일 작동과 비교합니다. 두 여수로를 동시에 운영할 경우 두 여수로를 통한 총 유량은 최대 7.6%까지 감소합니다.
간섭 계수는 단계 He가 설계 단계 Hd를 초과하고 두 배수로를 분리하는 거리 D가 배수로 너비 W에 비해 짧을 때 가장 중요합니다. 매개변수 DHd/WHe는 계산 및 측정된 간섭 계수와 매우 잘 관련됩니다.
안동댐 설계방류에 대한 홍수경로 예시는 간섭계수를 적용한 경우와 적용하지 않은 경우 저수지 수위의 차이가 42cm임을 보여줍니다. 결과적으로 댐 안전을 위해 추가 여수로의 너비(간섭 계수 포함)를 늘려야 합니다.
Dual spillway interference refers to the loss of hydraulic performance of spillways when they are placed close together. Spillway interference is examined using both physical experiments and numerical simulations. Stage and discharge measurements from four physical models with dual spillways configurations are compared to the Flow-3D computational results at four dam sites in South Korea. The conjunctive use of two spillways is compared with the singular operation of each spillway. When both spillways are operated at the same time, the total flow rate through the two spillways is reduced by up to 7.6%. Interference coefficients are most significant when the stage Heexceeds the design stage Hd and when the distance D separating two spillways is short compared to the spillway width W. The parameter DHd/WHecorrelates very well with the calculated and measured interference coefficients. A flood routing example for the design discharge at Andong dam shows a 42 cm difference in reservoir water level with and without application of the interference coefficient. Consequently, the width of additional spillways (including the interference coefficient) should be increased for dam safety.
Fig. 1. Definition sketch for dual spillwaysFig. 2. Stage-discharge rating curves for dual spillway operations.Fig. 3. Physical modeling of dual spillways: (a) Andong-1; (b) Andong-2; (c) Imha-1; and (d) Juam-1Fig. 4. Numerical modeling of dual spillways: (a) Andong-1; (b) Andong-2; (c) Imha-1; (d) Juam-1; (e) Andong-3; (f) Imha-2; (g) Imha-3; and
(h) Juam-3.Fig. 4. (Continued.)Fig. 5. Meshes and calculation domain for numerical modeling of
Andong dam.Fig. 6. Stage-discharge rating curve for existing and additional spillways (Andong-1): (a) existing spillway; (b) additional spillway; and (c) dual
spillway simulations.Fig. 7. Discharge comparison of physical experiments and numerical
simulations. The upper panel is the comparative result for the existing
spillway (ES) and the lower panel is for the additional spillway (AS) at
four dams.Fig. 8. Interference coefficients for dual spillways simulations with
various scenarios.Fig. 9. Regression model for the distance-width ratio (D=W) and head
ratio (Hd=He) by dual spillway simulationsFig. 10. Physical and numerical model validation: (a) numerical modeling; (b) solids of overflow weir of the spillway; and (c) physical models of
reservoir and spillwayFig. 11. Interference coefficients for dual spillways operations with
various scenarios. The dashed lines indicate the results of the validation
model with dual conditions of 1 þ 2, 1 þ 4, 1 þ 6, 3 þ 4, and 4 þ 5.Fig. 12. Results of reservoir operations under the PMF at Andong dam.
References
Cassidy, J. J. 1965. “Irrotational flow over spillways of finite height.” J. Eng. Mech. Div. 91 (6): 155–173. Chanel, P., and J. Doering. 2008. “Assessment of spillway modeling using computational fluid dynamics.” Can. J. Civ. Eng. 35 (12): 1481–1485. https://doi.org/10.1139/L08-094. Chow, V. T. 1959. Open-channel hydraulics, 365–380. New York: McGraw-Hill. Ho, D., B. Cooper, K. Riddette, and S. Donohoo. 2006. “Application of numerical modelling to spillways in Australia.” In Proc., Int. Symp. on Dams in the Societies of the 21st Century, 22nd Int. Congress on Large Dams (ICOLD), edited by L. Berga, et al. London: Taylor & Francis. Huff, F. A. 1967. “Time distribution of rainfall in heavy storms.” Water Resour. Res. 3 (4): 1007–1019. https://doi.org/10.1029/WR003i004 p01007. Kim, D. G., and J. H. Park. 2005. “Analysis of flow structure over ogeespillway in consideration of scale and roughness effects by using CFD model.” KSCE J. Civ. Eng. 9 (2): 161–169. https://doi.org/10.1007 /BF02829067. Koutsunis, N. A. 2015. “Impact of climatic changes on downstream hydraulic geometry and its influence on flood hydrograph routing—Applied to the bluestone dam watershed.” M.S. degree, Dept. of Civil and Environmental Engineering, Colorado State Univ. Lee, J. H., and P. Y. Julien. 2016a. “ENSO impacts on temperature over South Korea.” Int. J. Climatol. 36 (11): 3651. https://doi.org/10.1002 /joc.4581. Lee, J. H., and P. Y. Julien. 2016b. “Teleconnections of the ENSO and South Korean precipitation patterns.” J. Hydrol. 534: 237–250. https://doi.org/10.1016/j.jhydrol.2016.01.011. Lee, J. H., and P. Y. Julien. 2017. “Influence of the El Nino/southern ˜ oscillation on South Korean streamflow variability.” Hydrol. Processes 31 (12): 2162–2178. https://doi.org/10.1002/hyp.11168. Li, S., S. Cain, N. Wosnik, C. Miller, H. Kocahan, and R. Wyckoff. 2011. “Numerical modeling of probable maximum flood flowing through a system of spillways.” J. Hydraul. Eng. 137 (1): 66–74. https://doi.org /10.1061/(ASCE)HY.1943-7900.0000279. MOCT (Ministry of Construction and Transportation). 2003. Hydraulic model study of Soyanggang multipurpose dam auxiliary spillway. [In Korean.] Governing City, South Korea: MOCT. Olsen, N. R., and H. M. Kjellesvig. 1998. “Three-dimensional numerical flow modeling for estimation of spillway capacity.” J. Hydraul. Res. 36 (5): 775–784. https://doi.org/10.1080/00221689809498602. Savage, B. M., and M. C. Johnson. 2001. “Flow over ogee spillway: Physical and numerical model case study.” J. Hydraul. Eng. 127 (8): 640–649. https://doi.org/10.1061/(ASCE)0733-9429(2001)127:8(640). USACE (US Army Corps of Engineers). 2008. Hydrologic modeling system HEC-HMS, user’s manual version 3.2. Davis, CA: USACE. USBR (US Bureau of Reclamation). 1980. Hydraulic laboratory techniques: A water resources technical publication. Denver: US Dept. of the Interior, Bureau of Reclamation. Yakhot, V., and S. A. Orszag. 1986. “Renormalization group analysis of turbulence. I: Basic theory.” J. Sci. Comput. 1 (1): 3–51. https://doi .org/10.1007/BF01061452. Yakhot, V., and L. M. Smith. 1992. “The renormalization group, the e-expansion and derivation of turbulence models.” J. Sci. Comput. 7 (1): 35–61. https://doi.org/10.1007/BF01060210. Zeng, J., L. Zhang, M. Ansar, E. Damisse, and J. A. Gonzalez-Castro. 2017. “Applications of computational fluid dynamics to flow ratings at prototype spillways and weirs. I: Data generation and validation.” J. Irrig. Drain. Eng. 143 (1): 04016072. https://doi.org/10.1061/(ASCE)IR .1943-4774.0001112.
Optimization of Solar CCHP Systems with Collector Enhanced by Porous Media and Nanofluid
Navid Tonekaboni,1Mahdi Feizbahr,2 Nima Tonekaboni,1Guang-Jun Jiang,3,4 and Hong-Xia Chen3,4
Abstract
태양열 집열기의 낮은 효율은 CCHP(Solar Combined Cooling, Heating, and Power) 사이클의 문제점 중 하나로 언급될 수 있습니다. 태양계를 개선하기 위해 나노유체와 다공성 매체가 태양열 집열기에 사용됩니다.
다공성 매질과 나노입자를 사용하는 장점 중 하나는 동일한 조건에서 더 많은 에너지를 흡수할 수 있다는 것입니다. 이 연구에서는 평균 일사량이 1b인 따뜻하고 건조한 지역의 600 m2 건물의 전기, 냉방 및 난방을 생성하기 위해 다공성 매질과 나노유체를 사용하여 태양열 냉난방 복합 발전(SCCHP) 시스템을 최적화했습니다.
본 논문에서는 침전물이 형성되지 않는 lb = 820 w/m2(이란) 정도까지 다공성 물질에서 나노유체의 최적량을 계산하였다. 이 연구에서 태양열 집열기는 구리 다공성 매체(95% 다공성)와 CuO 및 Al2O3 나노 유체로 향상되었습니다.
나노유체의 0.1%-0.6%가 작동 유체로 물에 추가되었습니다. 나노유체의 0.5%가 태양열 집열기 및 SCCHP 시스템에서 가장 높은 에너지 및 엑서지 효율 향상으로 이어지는 것으로 밝혀졌습니다.
본 연구에서 포물선형 집열기(PTC)의 최대 에너지 및 엑서지 효율은 각각 74.19% 및 32.6%입니다. 그림 1은 태양 CCHP의 주기를 정확하게 설명하기 위한 그래픽 초록으로 언급될 수 있습니다.
The low efficiency of solar collectors can be mentioned as one of the problems in solar combined cooling, heating, and power (CCHP) cycles. For improving solar systems, nanofluid and porous media are used in solar collectors. One of the advantages of using porous media and nanoparticles is to absorb more energy under the same conditions. In this research, a solar combined cooling, heating, and power (SCCHP) system has been optimized by porous media and nanofluid for generating electricity, cooling, and heating of a 600 m2 building in a warm and dry region with average solar radiation of Ib = 820 w/m2 in Iran. In this paper, the optimal amount of nanofluid in porous materials has been calculated to the extent that no sediment is formed. In this study, solar collectors were enhanced with copper porous media (95% porosity) and CuO and Al2O3 nanofluids. 0.1%–0.6% of the nanofluids were added to water as working fluids; it is found that 0.5% of the nanofluids lead to the highest energy and exergy efficiency enhancement in solar collectors and SCCHP systems. Maximum energy and exergy efficiency of parabolic thermal collector (PTC) riches in this study are 74.19% and 32.6%, respectively. Figure 1 can be mentioned as a graphical abstract for accurately describing the cycle of solar CCHP.
1. Introduction
Due to the increase in energy consumption, the use of clean energy is one of the important goals of human societies. In the last four decades, the use of cogeneration cycles has increased significantly due to high efficiency. Among clean energy, the use of solar energy has become more popular due to its greater availability [1]. Low efficiency of energy production, transmission, and distribution system makes a new system to generate simultaneously electricity, heating, and cooling as an essential solution to be widely used. The low efficiency of the electricity generation, transmission, and distribution system makes the CCHP system a basic solution to eliminate waste of energy. CCHP system consists of a prime mover (PM), a power generator, a heat recovery system (produce extra heating/cooling/power), and thermal energy storage (TES) [2]. Solar combined cooling, heating, and power (SCCHP) has been started three decades ago. SCCHP is a system that receives its propulsive force from solar energy; in this cycle, solar collectors play the role of propulsive for generating power in this system [3].
Increasing the rate of energy consumption in the whole world because of the low efficiency of energy production, transmission, and distribution system causes a new cogeneration system to generate electricity, heating, and cooling energy as an essential solution to be widely used. Building energy utilization fundamentally includes power required for lighting, home electrical appliances, warming and cooling of building inside, and boiling water. Domestic usage contributes to an average of 35% of the world’s total energy consumption [4].
Due to the availability of solar energy in all areas, solar collectors can be used to obtain the propulsive power required for the CCHP cycle. Solar energy is the main source of energy in renewable applications. For selecting a suitable area to use solar collectors, annual sunshine hours, the number of sunny days, minus temperature and frosty days, and the windy status of the region are essentially considered [5]. Iran, with an average of more than 300 sunny days, is one of the suitable countries to use solar energy. Due to the fact that most of the solar radiation is in the southern regions of Iran, also the concentration of cities is low in these areas, and transmission lines are far apart, one of the best options is to use CCHP cycles based on solar collectors [6]. One of the major problems of solar collectors is their low efficiency [7]. Low efficiency increases the area of collectors, which increases the initial cost of solar systems and of course increases the initial payback period. To increase the efficiency of solar collectors and improve their performance, porous materials and nanofluids are used to increase their workability.
There are two ways to increase the efficiency of solar collectors and mechanical and fluid improvement. In the first method, using porous materials or helical filaments inside the collector pipes causes turbulence of the flow and increases heat transfer. In the second method, using nanofluids or salt and other materials increases the heat transfer of water. The use of porous materials has grown up immensely over the past twenty years. Porous materials, especially copper porous foam, are widely used in solar collectors. Due to the high contact surface area, porous media are appropriate candidates for solar collectors [8]. A number of researchers investigated Solar System performance in accordance with energy and exergy analyses. Zhai et al. [9] reviewed the performance of a small solar-powered system in which the energy efficiency was 44.7% and the electrical efficiency was 16.9%.
Abbasi et al. [10] proposed an innovative multiobjective optimization to optimize the design of a cogeneration system. Results showed the CCHP system based on an internal diesel combustion engine was the applicable alternative at all regions with different climates. The diesel engine can supply the electrical requirement of 31.0% and heating demand of 3.8% for building.
Jiang et al. [11] combined the experiment and simulation together to analyze the performance of a cogeneration system. Moreover, some research focused on CCHP systems using solar energy. It integrated sustainable and renewable technologies in the CCHP, like PV, Stirling engine, and parabolic trough collector (PTC) [2, 12–15].
Wang et al. [16] optimized a cogeneration solar cooling system with a Rankine cycle and ejector to reach the maximum total system efficiency of 55.9%. Jing et al. analyzed a big-scale building with the SCCHP system and auxiliary heaters to produced electrical, cooling, and heating power. The maximum energy efficiency reported in their work is 46.6% [17]. Various optimization methods have been used to improve the cogeneration system, minimum system size, and performance, such as genetic algorithm [18, 19].
Hirasawa et al. [20] investigated the effect of using porous media to reduce thermal waste in solar systems. They used the high-porosity metal foam on top of the flat plate solar collector and observed that thermal waste decreased by 7% due to natural heat transfer. Many researchers study the efficiency improvement of the solar collector by changing the collector’s shapes or working fluids. However, the most effective method is the use of nanofluids in the solar collector as working fluid [21]. In the experimental study done by Jouybari et al. [22], the efficiency enhancement up to 8.1% was achieved by adding nanofluid in a flat plate collector. In this research, by adding porous materials to the solar collector, collector efficiency increased up to 92% in a low flow regime. Subramani et al. [23] analyzed the thermal performance of the parabolic solar collector with Al2O3 nanofluid. They conducted their experiments with Reynolds number range 2401 to 7202 and mass flow rate 0.0083 to 0.05 kg/s. The maximum efficiency improvement in this experiment was 56% at 0.05 kg/s mass flow rate.
Shojaeizadeh et al. [24] investigated the analysis of the second law of thermodynamic on the flat plate solar collector using Al2O3/water nanofluid. Their research showed that energy efficiency rose up to 1.9% and the exergy efficiency increased by a maximum of 0.72% compared to pure water. Tiwari et al. [25] researched on the thermal performance of solar flat plate collectors for working fluid water with different nanofluids. The result showed that using 1.5% (optimum) particle volume fraction of Al2O3 nanofluid as an absorbing medium causes the thermal efficiency to enhance up to 31.64%.
The effect of porous media and nanofluids on solar collectors has already been investigated in the literature but the SCCHP system with a collector embedded by both porous media and nanofluid for enhancing the ratio of nanoparticle in nanofluid for preventing sedimentation was not discussed. In this research, the amount of energy and exergy of the solar CCHP cycles with parabolic solar collectors in both base and improved modes with a porous material (copper foam with 95% porosity) and nanofluid with different ratios of nanoparticles was calculated. In the first step, it is planned to design a CCHP system based on the required load, and, in the next step, it will analyze the energy and exergy of the system in a basic and optimize mode. In the optimize mode, enhanced solar collectors with porous material and nanofluid in different ratios (0.1%–0.7%) were used to optimize the ratio of nanofluids to prevent sedimentation.
2. Cycle Description
CCHP is one of the methods to enhance energy efficiency and reduce energy loss and costs. The SCCHP system used a solar collector as a prime mover of the cogeneration system and assisted the boiler to generate vapor for the turbine. Hot water flows from the expander to the absorption chiller in summer or to the radiator or fan coil in winter. Finally, before the hot water wants to flow back to the storage tank, it flows inside a heat exchanger for generating domestic hot water [26].
For designing of solar cogeneration system and its analysis, it is necessary to calculate the electrical, heating (heating load is the load required for the production of warm water and space heating), and cooling load required for the case study considered in a residential building with an area of 600 m2 in the warm region of Iran (Zahedan). In Table 1, the average of the required loads is shown for the different months of a year (average of electrical, heating, and cooling load calculated with CARRIER software).Table 1The average amount of electric charges, heating load, and cooling load used in the different months of the year in the city of Zahedan for a residential building with 600 m2.
According to Table 1, the maximum magnitude of heating, cooling, and electrical loads is used to calculate the cogeneration system. The maximum electric load is 96 kW, the maximum amount of heating load is 62 kW, and the maximum cooling load is 118 kW. Since the calculated loads are average, all loads increased up to 10% for the confidence coefficient. With the obtained values, the solar collector area and other cogeneration system components are calculated. The cogeneration cycle is capable of producing 105 kW electric power, 140 kW cooling capacity, and 100 kW heating power.
2.1. System Analysis Equations
An analysis is done by considering the following assumptions:(1)The system operates under steady-state conditions(2)The system is designed for the warm region of Iran (Zahedan) with average solar radiation Ib = 820 w/m2(3)The pressure drops in heat exchangers, separators, storage tanks, and pipes are ignored(4)The pressure drop is negligible in all processes and no expectable chemical reactions occurred in the processes(5)Potential, kinetic, and chemical exergy are not considered due to their insignificance(6)Pumps have been discontinued due to insignificance throughout the process(7)All components are assumed adiabatic
Schematic shape of the cogeneration cycle is shown in Figure 1 and all data are given in Table 2.
Figure 1Schematic shape of the cogeneration cycle.Table 2Temperature and humidity of different points of system.
Based on the first law of thermodynamic, energy analysis is based on the following steps.
First of all, the estimated solar radiation energy on collector has been calculated:where α is the heat transfer enhancement coefficient based on porous materials added to the collector’s pipes. The coefficient α is increased by the porosity percentage, the type of porous material (in this case, copper with a porosity percentage of 95), and the flow of fluid to the collector equation.
Collector efficiency is going to be calculated by the following equation [9]:
Total energy received by the collector is given by [9]
In the last step based on thermodynamic second law, exergy efficiency has been calculated from the following equation and the above-mentioned calculated loads [9]:
3. Porous Media
The porous medium that filled the test section is copper foam with a porosity of 95%. The foams are determined in Figure 2 and also detailed thermophysical parameters and dimensions are shown in Table 3.
Figure 2Copper foam with a porosity of 95%.Table 3Thermophysical parameters and dimensions of copper foam.
In solar collectors, copper porous materials are suitable for use at low temperatures and have an easier and faster manufacturing process than ceramic porous materials. Due to the high coefficient conductivity of copper, the use of copper metallic foam to increase heat transfer is certainly more efficient in solar collectors.
Porous media and nanofluid in solar collector’s pipes were simulated in FLOW-3D software using the finite-difference method [27]. Nanoparticles Al2O3 and CUO are mostly used in solar collector enhancement. In this research, different concentrations of nanofluid are added to the parabolic solar collectors with porous materials (copper foam with porosity of 95%) to achieve maximum heat transfer in the porous materials before sedimentation. After analyzing PTC pipes with the nanofluid flow in FLOW-3D software, for energy and exergy efficiency analysis, Carrier software results were used as EES software input. Simulation PTC with porous media inside collector pipe and nanofluids sedimentation is shown in Figure 3.
Figure 3Simulation PTC pipes enhanced with copper foam and nanoparticles in FLOW-3D software.
3.1. Nano Fluid
In this research, copper and silver nanofluids (Al2O3, CuO) have been added with percentages of 0.1%–0.7% as the working fluids. The nanoparticle properties are given in Table 4. Also, system constant parameters are presented in Table 4, which are available as default input in the EES software.Table 4Properties of the nanoparticles [9].
System constant parameters for input in the software are shown in Table 5.Table 5System constant parameters.
The thermal properties of the nanofluid can be obtained from equations (18)–(21). The basic fluid properties are indicated by the index (bf) and the properties of the nanoparticle silver with the index (np).
The density of the mixture is shown in the following equation [28]:where ρ is density and ϕ is the nanoparticles volume fraction.
The specific heat capacity is calculated from the following equation [29]:
The thermal conductivity of the nanofluid is calculated from the following equation [29]:
The parameter β is the ratio of the nanolayer thickness to the original particle radius and, usually, this parameter is taken equal to 0.1 for the calculated thermal conductivity of the nanofluids.
The mixture viscosity is calculated as follows [30]:
In all equations, instead of water properties, working fluids with nanofluid are used. All of the above equations and parameters are entered in the EES software for calculating the energy and exergy of solar collectors and the SCCHP cycle. All calculation repeats for both nanofluids with different concentrations of nanofluid in the solar collector’s pipe.
4. Results and Discussion
In the present study, relations were written according to Wang et al. [16] and the system analysis was performed to ensure the correctness of the code. The energy and exergy charts are plotted based on the main values of the paper and are shown in Figures 4 and 5. The error rate in this simulation is 1.07%.
Figure 4Verification charts of energy analysis results.
Figure 5Verification charts of exergy analysis results.
We may also investigate the application of machine learning paradigms [31–41] and various hybrid, advanced optimization approaches that are enhanced in terms of exploration and intensification [42–55], and intelligent model studies [56–61] as well, for example, methods such as particle swarm optimizer (PSO) [60, 62], differential search (DS) [63], ant colony optimizer (ACO) [61, 64, 65], Harris hawks optimizer (HHO) [66], grey wolf optimizer (GWO) [53, 67], differential evolution (DE) [68, 69], and other fusion and boosted systems [41, 46, 48, 50, 54, 55, 70, 71].
At the first step, the collector is modified with porous copper foam material. 14 cases have been considered for the analysis of the SCCHP system (Table 6). It should be noted that the adding of porous media causes an additional pressure drop inside the collector [9, 22–26, 30, 72]. All fourteen cases use copper foam with a porosity of 95 percent. To simulate the effect of porous materials and nanofluids, the first solar PTC pipes have been simulated in the FLOW-3D software and then porous media (copper foam with porosity of 95%) and fluid flow with nanoparticles (AL2O3 and CUO) are generated in the software. After analyzing PTC pipes in FLOW-3D software, for analyzing energy and exergy efficiency, software outputs were used as EES software input for optimization ratio of sedimentation and calculating energy and exergy analyses.Table 6Collectors with different percentages of nanofluids and porous media.
In this research, an enhanced solar collector with both porous media and Nanofluid is investigated. In the present study, 0.1–0.5% CuO and Al2O3 concentration were added to the collector fully filled by porous media to achieve maximum energy and exergy efficiencies of solar CCHP systems. All steps of the investigation are shown in Table 6.
Energy and exergy analyses of parabolic solar collectors and SCCHP systems are shown in Figures 6 and 7.
Figure 6Energy and exergy efficiencies of the PTC with porous media and nanofluid.
Figure 7Energy and exergy efficiency of the SCCHP.
Results show that the highest energy and exergy efficiencies are 74.19% and 32.6%, respectively, that is achieved in Step 12 (parabolic collectors with filled porous media and 0.5% Al2O3). In the second step, the maximum energy efficiency of SCCHP systems with fourteen steps of simulation are shown in Figure 7.
In the second step, where 0.1, −0.6% of the nanofluids were added, it is found that 0.5% leads to the highest energy and exergy efficiency enhancement in solar collectors and SCCHP systems. Using concentrations more than 0.5% leads to sediment in the solar collector’s pipe and a decrease of porosity in the pipe [73]. According to Figure 7, maximum energy and exergy efficiencies of SCCHP are achieved in Step 12. In this step energy efficiency is 54.49% and exergy efficiency is 18.29%. In steps 13 and 14, with increasing concentration of CUO and Al2O3 nanofluid solution in porous materials, decreasing of energy and exergy efficiency of PTC and SCCHP system at the same time happened. This decrease in efficiency is due to the formation of sediment in the porous material. Calculations and simulations have shown that porous materials more than 0.5% nanofluids inside the collector pipe cause sediment and disturb the porosity of porous materials and pressure drop and reduce the coefficient of performance of the cogeneration system. Most experience showed that CUO and AL2O3 nanofluids with less than 0.6% percent solution are used in the investigation on the solar collectors at low temperatures and discharges [74]. One of the important points of this research is that the best ratio of nanofluids in the solar collector with a low temperature is 0.5% (AL2O3 and CUO); with this replacement, the cost of solar collectors and SCCHP cycle is reduced.
5. Conclusion and Future Directions
In the present study, ways for increasing the efficiency of solar collectors in order to enhance the efficiency of the SCCHP cycle are examined. The research is aimed at adding both porous materials and nanofluids for estimating the best ratio of nanofluid for enhanced solar collector and protecting sedimentation in porous media. By adding porous materials (copper foam with porosity of 95%) and 0.5% nanofluids together, high efficiency in solar parabolic collectors can be achieved. The novelty in this research is the addition of both nanofluids and porous materials and calculating the best ratio for preventing sedimentation and pressure drop in solar collector’s pipe. In this study, it was observed that, by adding 0.5% of AL2O3 nanofluid in working fluids, the energy efficiency of PTC rises to 74.19% and exergy efficiency is grown up to 32.6%. In SCCHP cycle, energy efficiency is 54.49% and exergy efficiency is 18.29%.
In this research, parabolic solar collectors fully filled by porous media (copper foam with a porosity of 95) are investigated. In the next step, parabolic solar collectors in the SCCHP cycle were simultaneously filled by porous media and different percentages of Al2O3 and CuO nanofluid. At this step, values of 0.1% to 0.6% of each nanofluid were added to the working fluid, and the efficiency of the energy and exergy of the collectors and the SCCHP cycle were determined. In this case, nanofluid and the porous media were used together in the solar collector and maximum efficiency achieved. 0.5% of both nanofluids were used to achieve the biggest efficiency enhancement.
In the present study, as expected, the highest efficiency is for the parabolic solar collector fully filled by porous material (copper foam with a porosity of 95%) and 0.5% Al2O3. Results of the present study are as follows:(1)The average enhancement of collectors’ efficiency using porous media and nanofluids is 28%.(2)Solutions with 0.1 to 0.5% of nanofluids (CuO and Al2O3) are used to prevent collectors from sediment occurrence in porous media.(3)Collector of solar cogeneration cycles that is enhanced by both porous media and nanofluid has higher efficiency, and the stability of output temperature is more as well.(4)By using 0.6% of the nanofluids in the enhanced parabolic solar collectors with copper porous materials, sedimentation occurs and makes a high-pressure drop in the solar collector’s pipe which causes decrease in energy efficiency.(5)Average enhancement of SCCHP cycle efficiency is enhanced by both porous media and nanofluid 13%.
Nomenclature
:
Solar radiation
a:
Heat transfer augmentation coefficient
A:
Solar collector area
Bf:
Basic fluid
:
Specific heat capacity of the nanofluid
F:
Constant of air dilution
:
Thermal conductivity of the nanofluid
:
Thermal conductivity of the basic fluid
:
Viscosity of the nanofluid
:
Viscosity of the basic fluid
:
Collector efficiency
:
Collector energy receives
:
Auxiliary boiler heat
:
Expander energy
:
Gas energy
:
Screw expander work
:
Cooling load, in kilowatts
:
Heating load, in kilowatts
:
Solar radiation energy on collector, in Joule
:
Sanitary hot water load
Np:
Nanoparticle
:
Energy efficiency
:
Heat exchanger efficiency
:
Sun exergy
:
Collector exergy
:
Natural gas exergy
:
Expander exergy
:
Cooling exergy
:
Heating exergy
:
Exergy efficiency
:
Steam mass flow rate
:
Hot water mass flow rate
:
Specific heat capacity of water
:
Power output form by the screw expander
Tam:
Average ambient temperature
:
Density of the mixture.
Greek symbols
ρ:
Density
ϕ:
Nanoparticles volume fraction
β:
Ratio of the nanolayer thickness.
Abbreviations
CCHP:
Combined cooling, heating, and power
EES:
Engineering equation solver.
Data Availability
For this study, data were generated by CARRIER software for the average electrical, heating, and cooling load of a residential building with 600 m2 in the city of Zahedan, Iran.
Conflicts of Interest
The authors declare that they have no conflicts of interest.
Acknowledgments
This work was partially supported by the National Natural Science Foundation of China under Contract no. 71761030 and Natural Science Foundation of Inner Mongolia under Contract no. 2019LH07003.
References
A. Fudholi and K. Sopian, “Review on solar collector for agricultural produce,” International Journal of Power Electronics and Drive Systems (IJPEDS), vol. 9, no. 1, p. 414, 2018.View at: Publisher Site | Google Scholar
G. Yang and X. Zhai, “Optimization and performance analysis of solar hybrid CCHP systems under different operation strategies,” Applied Thermal Engineering, vol. 133, pp. 327–340, 2018.View at: Publisher Site | Google Scholar
J. Wang, Z. Han, and Z. Guan, “Hybrid solar-assisted combined cooling, heating, and power systems: a review,” Renewable and Sustainable Energy Reviews, vol. 133, p. 110256, 2020.View at: Publisher Site | Google Scholar
Y. Tian and C. Y. Zhao, “A review of solar collectors and thermal energy storage in solar thermal applications,” Applied Energy, vol. 104, pp. 538–553, 2013.View at: Publisher Site | Google Scholar
J. M. Hassan, Q. J. Abdul-Ghafour, and M. F. Mohammed, “CFD simulation of enhancement techniques in flat plate solar water collectors,” Al-Nahrain Journal for Engineering Sciences, vol. 20, no. 3, pp. 751–761, 2017.View at: Google Scholar
M. Jahangiri, O. Nematollahi, A. Haghani, H. A. Raiesi, and A. Alidadi Shamsabadi, “An optimization of energy cost of clean hybrid solar-wind power plants in Iran,” International Journal of Green Energy, vol. 16, no. 15, pp. 1422–1435, 2019.View at: Publisher Site | Google Scholar
I. H. Yılmaz and A. Mwesigye, “Modeling, simulation and performance analysis of parabolic trough solar collectors: a comprehensive review,” Applied Energy, vol. 225, pp. 135–174, 2018.View at: Google Scholar
F. Wang, J. Tan, and Z. Wang, “Heat transfer analysis of porous media receiver with different transport and thermophysical models using mixture as feeding gas,” Energy Conversion and Management, vol. 83, pp. 159–166, 2014.View at: Publisher Site | Google Scholar
H. Zhai, Y. J. Dai, J. Y. Wu, and R. Z. Wang, “Energy and exergy analyses on a novel hybrid solar heating, cooling and power generation system for remote areas,” Applied Energy, vol. 86, no. 9, pp. 1395–1404, 2009.View at: Publisher Site | Google Scholar
M. H. Abbasi, H. Sayyaadi, and M. Tahmasbzadebaie, “A methodology to obtain the foremost type and optimal size of the prime mover of a CCHP system for a large-scale residential application,” Applied Thermal Engineering, vol. 135, pp. 389–405, 2018.View at: Google Scholar
R. Jiang, F. G. F. Qin, X. Yang, S. Huang, and B. Chen, “Performance analysis of a liquid absorption dehumidifier driven by jacket-cooling water of a diesel engine in a CCHP system,” Energy and Buildings, vol. 163, pp. 70–78, 2018.View at: Publisher Site | Google Scholar
F. A. Boyaghchi and M. Chavoshi, “Monthly assessments of exergetic, economic and environmental criteria and optimization of a solar micro-CCHP based on DORC,” Solar Energy, vol. 166, pp. 351–370, 2018.View at: Publisher Site | Google Scholar
F. A. Boyaghchi and M. Chavoshi, “Multi-criteria optimization of a micro solar-geothermal CCHP system applying water/CuO nanofluid based on exergy, exergoeconomic and exergoenvironmental concepts,” Applied Thermal Engineering, vol. 112, pp. 660–675, 2017.View at: Publisher Site | Google Scholar
B. Su, W. Han, Y. Chen, Z. Wang, W. Qu, and H. Jin, “Performance optimization of a solar assisted CCHP based on biogas reforming,” Energy Conversion and Management, vol. 171, pp. 604–617, 2018.View at: Publisher Site | Google Scholar
F. A. Al-Sulaiman, F. Hamdullahpur, and I. Dincer, “Performance assessment of a novel system using parabolic trough solar collectors for combined cooling, heating, and power production,” Renewable Energy, vol. 48, pp. 161–172, 2012.View at: Publisher Site | Google Scholar
J. Wang, Y. Dai, L. Gao, and S. Ma, “A new combined cooling, heating and power system driven by solar energy,” Renewable Energy, vol. 34, no. 12, pp. 2780–2788, 2009.View at: Publisher Site | Google Scholar
Y.-Y. Jing, H. Bai, J.-J. Wang, and L. Liu, “Life cycle assessment of a solar combined cooling heating and power system in different operation strategies,” Applied Energy, vol. 92, pp. 843–853, 2012.View at: Publisher Site | Google Scholar
J.-J. Wang, Y.-Y. Jing, and C.-F. Zhang, “Optimization of capacity and operation for CCHP system by genetic algorithm,” Applied Energy, vol. 87, no. 4, pp. 1325–1335, 2010.View at: Publisher Site | Google Scholar
L. Ali, “LDA–GA–SVM: improved hepatocellular carcinoma prediction through dimensionality reduction and genetically optimized support vector machine,” Neural Computing and Applications, vol. 87, pp. 1–10, 2020.View at: Google Scholar
S. Hirasawa, R. Tsubota, T. Kawanami, and K. Shirai, “Reduction of heat loss from solar thermal collector by diminishing natural convection with high-porosity porous medium,” Solar Energy, vol. 97, pp. 305–313, 2013.View at: Publisher Site | Google Scholar
E. Bellos, C. Tzivanidis, and Z. Said, “A systematic parametric thermal analysis of nanofluid-based parabolic trough solar collectors,” Sustainable Energy Technologies and Assessments, vol. 39, p. 100714, 2020.View at: Publisher Site | Google Scholar
H. J. Jouybari, S. Saedodin, A. Zamzamian, M. E. Nimvari, and S. Wongwises, “Effects of porous material and nanoparticles on the thermal performance of a flat plate solar collector: an experimental study,” Renewable Energy, vol. 114, pp. 1407–1418, 2017.View at: Publisher Site | Google Scholar
J. Subramani, P. K. Nagarajan, S. Wongwises, S. A. El-Agouz, and R. Sathyamurthy, “Experimental study on the thermal performance and heat transfer characteristics of solar parabolic trough collector using Al2O3 nanofluids,” Environmental Progress & Sustainable Energy, vol. 37, no. 3, pp. 1149–1159, 2018.View at: Publisher Site | Google Scholar
E. Shojaeizadeh, F. Veysi, and A. Kamandi, “Exergy efficiency investigation and optimization of an Al2O3-water nanofluid based Flat-plate solar collector,” Energy and Buildings, vol. 101, pp. 12–23, 2015.View at: Publisher Site | Google Scholar
A. K. Tiwari, P. Ghosh, and J. Sarkar, “Solar water heating using nanofluids–a comprehensive overview and environmental impact analysis,” International Journal of Emerging Technology and Advanced Engineering, vol. 3, no. 3, pp. 221–224, 2013.View at: Google Scholar
D. R. Rajendran, E. Ganapathy Sundaram, P. Jawahar, V. Sivakumar, O. Mahian, and E. Bellos, “Review on influencing parameters in the performance of concentrated solar power collector based on materials, heat transfer fluids and design,” Journal of Thermal Analysis and Calorimetry, vol. 140, no. 1, pp. 33–51, 2020.View at: Publisher Site | Google Scholar
M. Feizbahr, C. Kok Keong, F. Rostami, and M. Shahrokhi, “Wave energy dissipation using perforated and non perforated piles,” International Journal of Engineering, vol. 31, no. 2, pp. 212–219, 2018.View at: Google Scholar
K. Khanafer and K. Vafai, “A critical synthesis of thermophysical characteristics of nanofluids,” International Journal of Heat and Mass Transfer, vol. 54, no. 19-20, pp. 4410–4428, 2011.View at: Publisher Site | Google Scholar
K. Farhana, K. Kadirgama, M. M. Rahman et al., “Improvement in the performance of solar collectors with nanofluids – a state-of-the-art review,” Nano-Structures & Nano-Objects, vol. 18, p. 100276, 2019.View at: Publisher Site | Google Scholar
M. Turkyilmazoglu, “Condensation of laminar film over curved vertical walls using single and two-phase nanofluid models,” European Journal of Mechanics-B/Fluids, vol. 65, pp. 184–191, 2017.View at: Publisher Site | Google Scholar
X. Zhang, J. Wang, T. Wang, R. Jiang, J. Xu, and L. Zhao, “Robust feature learning for adversarial defense via hierarchical feature alignment,” Information Sciences, vol. 2020, 2020.View at: Google Scholar
X. Zhang, T. Wang, W. Luo, and P. Huang, “Multi-level fusion and attention-guided CNN for image dehazing,” IEEE Transactions on Circuits and Systems for Video Technology, vol. 1, 2020.View at: Publisher Site | Google Scholar
X. Zhang, M. Fan, D. Wang, P. Zhou, and D. Tao, “Top-k feature selection framework using robust 0-1 integer programming,” IEEE Transactions on Neural Networks and Learning Systems, vol. 1, pp. 1–15, 2020.View at: Publisher Site | Google Scholar
X. Zhang, D. Wang, Z. Zhou, and Y. Ma, “Robust low-rank tensor recovery with rectification and alignment,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 43, no. 1, pp. 238–255, 2019.View at: Google Scholar
X. Zhang, R. Jiang, T. Wang, and J. Wang, “Recursive neural network for video deblurring,” IEEE Transactions on Circuits and Systems for Video Technology, vol. 1, 2020.View at: Publisher Site | Google Scholar
X. Zhang, T. Wang, J. Wang, G. Tang, and L. Zhao, “Pyramid channel-based feature attention network for image dehazing,” Computer Vision and Image Understanding, vol. 1, 2020.View at: Google Scholar
M. Mirmozaffari, “Machine learning algorithms based on an optimization model,” 2020.View at: Google Scholar
M. Mirmozaffari, M. Yazdani, A. Boskabadi, H. Ahady Dolatsara, K. Kabirifar, and N. Amiri Golilarz, “A novel machine learning approach combined with optimization models for eco-efficiency evaluation,” Applied Sciences, vol. 10, no. 15, p. 5210, 2020.View at: Publisher Site | Google Scholar
M. Vosoogha and A. Addeh, “An intelligent power prediction method for wind energy generation based on optimized fuzzy system,” Computational Research Progress in Applied Science & Engineering (CRPASE), vol. 5, pp. 34–43, 2019.View at: Google Scholar
A. Javadi, N. Mikaeilvand, and H. Hosseinzdeh, “Presenting a new method to solve partial differential equations using a group search optimizer method (GSO),” Computational Research Progress in Applied Science and Engineering, vol. 4, no. 1, pp. 22–26, 2018.View at: Google Scholar
F. J. Golrokh, Gohar Azeem, and A. Hasan, “Eco-efficiency evaluation in cement industries: DEA malmquist productivity index using optimization models,” ENG Transactions, vol. 1, pp. 1–8, 2020.View at: Google Scholar
H. Yu, “Dynamic Gaussian bare-bones fruit fly optimizers with abandonment mechanism: method and analysis,” Engineering with Computers, vol. 1, pp. 1–29, 2020.View at: Google Scholar
C. Yu, “SGOA: annealing-behaved grasshopper optimizer for global tasks,” Engineering with Computers, vol. 1, pp. 1–28, 2021.View at: Google Scholar
W. Shan, Z. Qiao, A. A. Heidari, H. Chen, H. Turabieh, and Y. Teng, “Double adaptive weights for stabilization of moth flame optimizer: balance analysis, engineering cases, and medical diagnosis,” Knowledge-Based Systems, vol. 1, p. 106728, 2020.View at: Google Scholar
J. Tu, H. Chen, J. Liu et al., “Evolutionary biogeography-based whale optimization methods with communication structure: towards measuring the balance,” Knowledge-Based Systems, vol. 212, p. 106642, 2021.View at: Publisher Site | Google Scholar
Y. Zhang, “Towards augmented kernel extreme learning models for bankruptcy prediction: algorithmic behavior and comprehensive analysis,” Neurocomputing, vol. 1, 2020.View at: Google Scholar
Y. Zhang, R. Liu, X. Wang, H. Chen, and C. Li, “Boosted binary Harris hawks optimizer and feature selection,” Engineering with Computers, vol. 1, pp. 1–30, 2020.View at: Google Scholar
H.-L. Chen, G. Wang, C. Ma, Z.-N. Cai, W.-B. Liu, and S.-J. Wang, “An efficient hybrid kernel extreme learning machine approach for early diagnosis of Parkinson’s disease,” Neurocomputing, vol. 184, pp. 131–144, 2016.View at: Publisher Site | Google Scholar
L. Hu, G. Hong, J. Ma, X. Wang, and H. Chen, “An efficient machine learning approach for diagnosis of paraquat-poisoned patients,” Computers in Biology and Medicine, vol. 59, pp. 116–124, 2015.View at: Publisher Site | Google Scholar
L. Shen, H. Chen, Z. Yu et al., “Evolving support vector machines using fruit fly optimization for medical data classification,” Knowledge-Based Systems, vol. 96, pp. 61–75, 2016.View at: Publisher Site | Google Scholar
J. Xia, H. Chen, Q. Li et al., “Ultrasound-based differentiation of malignant and benign thyroid Nodules: an extreme learning machine approach,” Computer Methods and Programs in Biomedicine, vol. 147, pp. 37–49, 2017.View at: Publisher Site | Google Scholar
C. Li, L. Hou, B. Y. Sharma et al., “Developing a new intelligent system for the diagnosis of tuberculous pleural effusion,” Computer Methods and Programs in Biomedicine, vol. 153, pp. 211–225, 2018.View at: Publisher Site | Google Scholar
X. Zhao, X. Zhang, Z. Cai et al., “Chaos enhanced grey wolf optimization wrapped ELM for diagnosis of paraquat-poisoned patients,” Computational Biology and Chemistry, vol. 78, pp. 481–490, 2019.View at: Publisher Site | Google Scholar
M. Wang and H. Chen, “Chaotic multi-swarm whale optimizer boosted support vector machine for medical diagnosis,” Applied Soft Computing Journal, vol. 88, 2020.View at: Publisher Site | Google Scholar
X. Xu and H.-L. Chen, “Adaptive computational chemotaxis based on field in bacterial foraging optimization,” Soft Computing, vol. 18, no. 4, pp. 797–807, 2014.View at: Publisher Site | Google Scholar
R. U. Khan, X. Zhang, R. Kumar, A. Sharif, N. A. Golilarz, and M. Alazab, “An adaptive multi-layer botnet detection technique using machine learning classifiers,” Applied Sciences, vol. 9, no. 11, p. 2375, 2019.View at: Publisher Site | Google Scholar
A. Addeh, A. Khormali, and N. A. Golilarz, “Control chart pattern recognition using RBF neural network with new training algorithm and practical features,” ISA Transactions, vol. 79, pp. 202–216, 2018.View at: Publisher Site | Google Scholar
N. Amiri Golilarz, H. Gao, R. Kumar, L. Ali, Y. Fu, and C. Li, “Adaptive wavelet based MRI brain image de-noising,” Frontiers in Neuroscience, vol. 14, p. 728, 2020.View at: Publisher Site | Google Scholar
N. A. Golilarz, H. Gao, and H. Demirel, “Satellite image de-noising with Harris hawks meta heuristic optimization algorithm and improved adaptive generalized Gaussian distribution threshold function,” IEEE Access, vol. 7, pp. 57459–57468, 2019.View at: Publisher Site | Google Scholar
M. Eisazadeh and J. Rezapour, “Multi-objective optimization of the composite sheets using PSO algorithm,” 2017.View at: Google Scholar
I. Bargegol, M. Nikookar, R. V. Nezafat, E. J. Lashkami, and A. M. Roshandeh, “Timing optimization of signalized intersections using shockwave theory by genetic algorithm,” Computational Research Progress in Applied Science & Engineering, vol. 1, pp. 160–167, 2015.View at: Google Scholar
B. Bai, Z. Guo, C. Zhou, W. Zhang, and J. Zhang, “Application of adaptive reliability importance sampling-based extended domain PSO on single mode failure in reliability engineering,” Information Sciences, vol. 546, pp. 42–59, 2021.View at: Publisher Site | Google Scholar
J. Liu, C. Wu, G. Wu, and X. Wang, “A novel differential search algorithm and applications for structure design,” Applied Mathematics and Computation, vol. 268, pp. 246–269, 2015.View at: Publisher Site | Google Scholar
X. Zhao, D. Li, B. Yang, C. Ma, Y. Zhu, and H. Chen, “Feature selection based on improved ant colony optimization for online detection of foreign fiber in cotton,” Applied Soft Computing, vol. 24, pp. 585–596, 2014.View at: Publisher Site | Google Scholar
D. Zhao, “Chaotic random spare ant colony optimization for multi-threshold image segmentation of 2D Kapur entropy,” Knowledge-Based Systems, vol. 24, p. 106510, 2020.View at: Google Scholar
H. Chen, A. A. Heidari, H. Chen, M. Wang, Z. Pan, and A. H. Gandomi, “Multi-population differential evolution-assisted Harris hawks optimization: framework and case studies,” Future Generation Computer Systems, vol. 111, pp. 175–198, 2020.View at: Publisher Site | Google Scholar
J. Hu, H. Chen, A. A. Heidari et al., “Orthogonal learning covariance matrix for defects of grey wolf optimizer: insights, balance, diversity, and feature selection,” Knowledge-Based Systems, vol. 213, p. 106684, 2021.View at: Publisher Site | Google Scholar
G. Sun, B. Yang, Z. Yang, and G. Xu, “An adaptive differential evolution with combined strategy for global numerical optimization,” Soft Computing, vol. 24, pp. 1–20, 2019.View at: Google Scholar
G. Sun, C. Li, and L. Deng, “An adaptive regeneration framework based on search space adjustment for differential evolution,” Neural Computing and Applications, vol. 24, pp. 1–17, 2021.View at: Google Scholar
A. Addeh and M. Iri, “Brain tumor type classification using deep features of MRI images and optimized RBFNN,” ENG Transactions, vol. 2, pp. 1–7, 2021.View at: Google Scholar
F. J. Golrokh and A. Hasan, “A comparison of machine learning clustering algorithms based on the DEA optimization approach for pharmaceutical companies in developing countries,” Soft Computing, vol. 1, pp. 1–8, 2020.View at: Google Scholar
H. Tyagi, P. Phelan, and R. Prasher, “Predicted efficiency of a low-temperature nanofluid-based direct absorption solar collector,” Journal of Solar Energy Engineering, vol. 131, no. 4, 2009.View at: Publisher Site | Google Scholar
S. Rashidi, M. Bovand, and J. A. Esfahani, “Heat transfer enhancement and pressure drop penalty in porous solar heat exchangers: a sensitivity analysis,” Energy Conversion and Management, vol. 103, pp. 726–738, 2015.View at: Publisher Site | Google Scholar
N. Akram, R. Sadri, S. N. Kazi et al., “A comprehensive review on nanofluid operated solar flat plate collectors,” Journal of Thermal Analysis and Calorimetry, vol. 139, no. 2, pp. 1309–1343, 2020.View at: Publisher Site | Google Scholar
The low efficiency of Collectors that absorb energy can be mentioned as one of the drawbacks in solar cogeneration cycles. In the present study, solar systems have been improved by adding porous media and Nanofluid to collectors. One advantage of using porous media and nanomaterials is to absorb more energy while the surface area is reduced. In this study, first, solar collectors are enhanced using 90% porosity copper in solar combined cooling, heating and power systems (SCCHP). Second, different percentages of CuO and Al2O3 nano-fluids are added to a flat plate and parabolic collectors to enhance thermal properties. Simulations are performed in different modes (simple parabolic collectors, simple flat plate collectors, improved flat plate collectors, parabolic collectors with porous media, and flat plate and parabolic collectors with different density of CuO and Al2O3 nanofluids). A case study is investigated for warm and dry regions with mean solar radiation Ib = 820 w / m2 in Iran. The maximum energy and exergy efficiencies are 60.12% and 18.84%, respectively, that is related to enhanced parabolic solar collectors with porous media and nanofluids. Adding porous media and nano-fluids increases an average 14.4% collector energy efficiency and 8.08% collector exergy efficiency.
[1] Center TU. Annual report on China building energy efficiency. China Construction Industry Press (In Chinese). 2016.
[2] Tonekaboni N, Salarian H, Fatahian E, Fatahian H. Energy and exergy economic analysis of cogeneration cycle of homemade CCHP with PVT collector. Canadian Journal of Basic and Applied Sciences 2015;3:224-233.
[3] Hassan JM, Abdul-Ghafour QJ, Mohammed MF. CFD simulation of enhancement techniques in flat plate solar water collectors. Al-Nahrain Journal for Engineering Sciences 2017;20:751-761.
[4] Sopian K, Daud WR, Othman MY, Yatim B. Thermal performance of the double-pass solar collector with and without porous media. Renewable Energy 1999;18:557-564. https://doi.org/10.1016/S0960-1481(99)00007-5
[5] Feizbahr M, Kok Keong C, Rostami F, Shahrokhi M. Wave energy dissipation using perforated and non perforated piles. International Journal of Engineering 2018;31:212-219. https://doi.org/10.5829/ije.2018.31.02b.04
[6] Tian Y, Zhao CY. A review of solar collectors and thermal energy storage in solar thermal applications. Applied Energy 2013;104:538-553. https://doi.org/10.1016/j.apenergy.2012.11.051
[7] Wang F, Tan J, Wang Z. Heat transfer analysis of porous media receiver with different transport and thermophysical models using mixture as feeding gas. Energy Conversion and Management 2014;83:159-166. https://doi.org/10.1016/j.enconman.2014.03.068
[8] Korti AI. Numerical 3-D heat flow simulations on double-pass solar collector with and without porous media. Journal of Thermal Engineering 2015;1:10-23. https://doi.org/10.18186/jte.86295
[9] Sharma N, Diaz G. Performance model of a novel evacuated-tube solar collector based on minichannels. Solar Energy 2011;85:881-890. https://doi.org/10.1016/j.solener.2011.02.001
[10] Tyagi VV, Kaushik SC, Tyagi SK. Advancement in solar photovoltaic/thermal (PV/T) hybrid collector technology. Renewable and Sustainable Energy Reviews 2012;16:1383-1398. https://doi.org/10.1016/j.rser.2011.12.013
[11] Zhai H, Dai YJ, Wu JY, Wang RZ. Energy and exergy analyses on a novel hybrid solar heating, cooling and power generation system for remote areas. Applied Energy 2009;86:1395-1404. https://doi.org/10.1016/j.apenergy.2008.11.020
[12] Wang J, Dai Y, Gao L, Ma S. A new combined cooling, heating and power system driven by solar energy. Renewable Energy 2009;34:2780-2788. https://doi.org/10.1016/j.renene.2009.06.010
[13] Jing YY, Bai H, Wang JJ, Liu L. Life cycle assessment of a solar combined cooling heating and power system in different operation strategies. Applied Energy 2012;92:843-853. https://doi.org/10.1016/j.apenergy.2011.08.046
[14] Temir G, Bilge D. Thermoeconomic analysis of a trigeneration system. applied thermal engineering. Applied Thermal Engineering 2004;24:2689-2699. https://doi.org/10.1016/j.applthermaleng.2004.03.014
[15] Wang JJ, Jing YY, Zhang CF. Optimization of capacity and operation for CCHP system by genetic algorithm. Applied Energy 2010;87:1325-1335. https://doi.org/10.1016/j.apenergy.2009.08.005
[16] Kleinstreuer C, Chiang H. Analysis of a porous-medium solar collector. Heat Transfer Engineering 1990;11:45-55. https://doi.org/10.1080/01457639008939728
[17] Mbaye M, Bilgen E. Natural convection and conduction in porous wall, solar collector systems without vents. Jornal of Solar Energy Engineering 1992;114:40-46. https://doi.org/10.1115/1.2929980
[18] Hirasawa S, Tsubota R, Kawanami T, Shirai K. Reduction of heat loss from solar thermal collector by diminishing natural convection with high-porosity porous medium. Solar Energy 2013;97:305-313. https://doi.org/10.1016/j.solener.2013.08.035
[19] Jouybari HJ, Saedodin S, Zamzamian A, Nimvari ME, Wongwises S. Effects of porous material and nanoparticles on the thermal performance of a flat plate solar collector: an experimental study. Renewable Energy 2017;114:1407-1418. https://doi.org/10.1016/j.renene.2017.07.008
[20] Subramani J, Nagarajan PK, Wongwises S, El‐Agouz SA, Sathyamurthy R. Experimental study on the thermal performance and heat transfer characteristics of solar parabolic trough collector using Al2O3 nanofluids. Environmental Progress & Sustainable Energy 2018;37:1149-1159. https://doi.org/10.1002/ep.12767
[21] Yousefi T, Veysi F, Shojaeizadeh E, Zinadini S. An experimental investigation on the effect of Al2O3–H2O nanofluid on the efficiency of flat-plate solar collectors. Renewable Energy 2012;39:293-298. https://doi.org/10.1016/j.renene.2011.08.056
[22] Tyagi H, Phelan P, Prasher R. Predicted efficiency of a low-temperature nanofluid-based direct absorption solar collector. Journal of Solar Energy Engineering 2009;131:041004. https://doi.org/10.1115/1.3197562
[23] Shojaeizadeh E, Veysi F, Kamandi A. Exergy efficiency investigation and optimization of an Al2O3–water nanofluid based Flat-plate solar collector. Energy and Buildings 2015;101:12-23. https://doi.org/10.1016/j.enbuild.2015.04.048
[24] Tiwari AK, Ghosh P, Sarkar J. Solar water heating using nanofluids–a comprehensive overview and environmental impact analysis. International Journal of Emerging Technology and Advanced Engineering 2013;3:221-224. [25] Akram N, Sadri R, Kazi SN, Zubir MN, Ridha M, Ahmed W, et al. A comprehensive review on nanofluid operated solar flat plate collectors. Journal of Thermal Analysis and Calorimetry 2020;139:1309-1343. https://doi.org/10.1007/s10973-019-08514-z
[26] Lemington N. Study of solar driven adsorption cooling potential in Indonesia. Journal of Thermal Engineering 2017;3:1044-1051. https://doi.org/10.18186/thermal.290257
[27] Tong Y, Lee H, Kang W, Cho H. Energy and exergy comparison of a flat-plate solar collector using water, Al2O3 nanofluid, and CuO nanofluid. Applied Thermal Engineering 2019;159:113959. https://doi.org/10.1016/j.applthermaleng.2019.113959
[28] Khanafer K, Vafai K. A critical synthesis of thermophysical characteristics of nanofluids. International Journal of Heat And Mass Transfer 2011;54:4410-4428. https://doi.org/10.1016/j.ijheatmasstransfer.2011.04.048
[29] Farhana K, Kadirgama K, Rahman MM, Ramasamy D, Noor MM, Najafi G, et al. Improvement in the performance of solar collectors with nanofluids—A state-of-the-art review. Nano-Structures & Nano-Objects 2019;18:100276. https://doi.org/10.1016/j.nanoso.2019.100276
[30] Turkyilmazoglu M. Condensation of laminar film over curved vertical walls using single and two-phase nanofluid models. European Journal of Mechanics-B/Fluids 2017;65:184-91. https://doi.org/10.1016/j.euromechflu.2017.04.007
[31] Chen CC, Huang PC. Numerical study of heat transfer enhancement for a novel flat-plate solar water collector using metal-foam blocks. International Journal of Heat And Mass Transfer 2012;55:6734-6756. https://doi.org/10.1016/j.ijheatmasstransfer.2012.06.082
[32] Huang PC, Chen CC, Hwang HY. Thermal enhancement in a flat-plate solar water collector by flow pulsation and metal-foam blocks. International Journal of Heat and Mass Transfer 2013;61:696-720. https://doi.org/10.1016/j.ijheatmasstransfer.2013.02.037
[33] Hajipour M, Dehkordi AM. Mixed-convection flow of Al2O3–H O nanofluid in a channel partially filled with porous metal foam: experimental and numerical study. Experimental Thermal and Fluid Science 2014;53:49-56. https://doi.org/10.1016/j.expthermflusci.2013.11.002
[34] Rashidi S, Bovand M, Esfahani JA. Heat transfer enhancement and pressure drop penalty in porous solar heat exchangers: a sensitivity analysis. Energy Conversion and Management 2015;103:726-738. https://doi.org/10.1016/j.enconman.2015.07.019
[35] Manikandan GK, Iniyan S, Goic R. Enhancing the optical and thermal efficiency of a parabolic trough collector–A review. Applied Energy 2019;235:1524-1540. https://doi.org/10.1016/j.apenergy.2018.11.048
실제 작동 조건에서 석탄 연소 회전 시멘트 가마의 클링커 형성은 방사선에 대한 Monte Carlo 방법, 가마 벽의 에너지 방정식에 대한 유한 체적 코드 및 클링커에 대한 화학 반응을 포함한 에너지 보존 방정식 및 종에 대한 새로운 코드. 기상의 온도 장, 벽으로의 복사 열유속, 가마 및 클링커 온도에 대한 예측 간의 반복적인 절차는 내부 벽 온도의 분포를 명시적으로 예측하는 데 사용됩니다. 여기에는 열 흐름 계산이 포함됩니다. 수갑. 가스와 가마 벽 사이의 주요 열 전달 모드는 복사에 의한 것이며 내화물을 통해 환경으로 손실되는 열은 입력 열의 약 10%이고 추가로 40%는 장입 가열 및 클링커 형성. 예측은 실제 규모의 시멘트 가마에서 경험과 제한된 측정을 기반으로 한 경향과 일치합니다.
키워드
산업용 CFD, 로타리 가마, 클링커 형성, 복사 열전달, Industrial CFD, Rotary kilns, Clinker formation, Radiative heat transfer
1 . 소개
시멘트 산업은 에너지의 주요 소비자이며, 미국에서 산업 사용자의 총 화석 연료 소비량의 약 1.4%를 차지하며 [1] 일반적인 비에너지 사용량은 제조된 클링커 1kg당 약 3.2MJ [2] 입니다. CaCO 3 → CaO + CO 2 반응이 일어나기 때문입니다., 클링커 형성의 첫 번째 단계는 높은 흡열성입니다. 시멘트 가마에서 에너지를 절약하기 위한 현재의 경향은 일반적으로 길이가 약 100m이고 직경이 약 5m인 회전 실린더인 가마를 떠나는 배기 가스로부터 에너지를 보다 효율적으로 회수하는 것과 저열량 연료의 사용에 중점을 둡니다. 값. 2-5초 정도의 화염 체류 시간을 허용하고 2200K의 높은 온도에 도달하는 회전 가마의 특성은 또한 시멘트 가마를 유기 폐기물 및 용제에 대한 상업용 소각로에 대한 경쟁력 있는 대안으로 만듭니다 [3]. 클링커의 형성이 이러한 2차 액체 연료의 사용으로 인한 화염의 변화로부터 어떤 식으로든 영향을 받지 않도록 하고, 대기 중으로 방출되는 오염 물질의 양에 대한 현재 및 미래 제한을 준수할 수 있도록, 화염 구조의 세부 사항과 화염에서 고체 충전물로의 열 전달을 더 잘 이해할 필요가 있습니다.
최근 시멘트 가마 4 , 5 , 6 , 7 에서 유동장 및 석탄 연소의 이론적 모델링복사 열 전달을 포함한 전산 유체 역학(CFD) 코드를 사용하여 달성되었습니다. 이러한 결과는 시멘트 가마에 대한 최초의 결과였으며 화염 길이, 산소 소비 등과 관련하여 실험적으로 관찰된 경향을 재현했기 때문에 그러한 코드가 수용 가능한 정확도로 대규모 산업용 용광로에 사용될 수 있음을 보여주었습니다. 킬른과 클링커는 포함하지 않았고, 벽온도의 경계조건은 가스온도와 용액영역의 열유속에 영향을 미치므로 계산에 필요한 경계조건은 예측하지 않고 실험적 측정에 기초하였다. 기상에 대한 CFD 솔루션은 앞으로의 주요 단계이지만 회전 가마를 포괄적으로 모델링하는 데만으로는 충분하지 않습니다.
내화물의 열 전달과 전하에 대한 세부 사항은 다양한 저자 8 , 9 , 10 , 11에 의해 조사되었습니다 . 충전물(보통 잘 혼합된 것으로 가정)은 노출된 표면에 직접 복사되는 열 외에도 전도에 의해 가마 벽에서 가열됩니다. 가장 완전한 이론적 노력에서, 가마 벽 (내화물)에 대한 3 차원 열전도 방정식을 해결하고, 두 개 또는 세 개의 인접하는 영역으로 한정 한 좌표 축 방향에서 어느 방사선 방사선 열전달 영역 모델과 결합 [ 10] 또는 자세히 해결 [11]. 그러나 클링커 형성 중에 일어나는 화학 반응은 고려되지 않았고 기체 상이 균일한 온도로 고정되어 필요한 수준의 정확도로 처리되지 않았습니다.
최종적으로 연소에 의해 방출되는 에너지(일부)를 받는 고체 전하가 화학 반응을 거쳐 최종 제품인 클링커를 형성합니다. 이것들은 [12]에 설명된 주요 특징에 대한 단순화된 모델과 함께 시멘트 화학 문헌에서 광범위한 조사의 주제였습니다 . 그 작업에서, 고체 온도 및 조성의 축 방향 전개를 설명하는 odes가 공식화되고 해결되었지만, 전하에 대한 열유속 및 따라서 클링커 형성 속도를 결정하는 가스 및 벽 온도는 1차원으로 근사되었습니다. 자세한 화염 계산이 없는 모델.
화염, 벽 및 장입물에 대한 위의 이론적 모델 중 어느 것도 회전식 가마 작동을 위한 진정한 예측 도구로 충분하지 않다는 것이 분명합니다. 국부 가스 온도(CFD 계산 결과 중 하나)는 벽 온도에 크게 의존합니다. 클링커 형성은 에너지를 흡수하므로 지역 가스 및 벽 온도에 따라 달라지며 둘 다 화염에 의존합니다. 벽은 화염에서 클링커로의 순 열 전달에서 “중개자” 역할을 하며, 내화재 두께에 따라 환경으로 피할 수 없는 열 손실이 발생합니다. 이러한 상호 의존성은 가마의 거동에 중요하며 개별 프로세스를 개별적으로 계산하는 데 중점을 두었기 때문에 문헌에서 발견된 수학적 모델로는 다루기 어렵습니다.
본 논문에서 우리는 위에 설명된 유형의 세 가지 개별 모델을 결합하여 수행되는 회전식 시멘트 가마에서 발생하는 대부분의 공정에 대한 포괄적인 모듈식 모델을 제시합니다. 우리 작업은 4 , 5 , 6 , 7 에서와 같이 석탄 연소를 위한 다차원 CFD 코드로 기체 상태를 처리합니다 . 10 , 11 에서와 같이 가마 벽의 3차원 열전도 방정식을 풉니다 . 9 , 12 와 유사한 모델로 잘 혼합된 전하 온도 및 조성을 해결합니다.. 3개의 모듈(화염, 벽, 전하)은 내화물에 입사하는 열유속의 축 분포에 대해 수렴이 달성될 때까지 반복적으로 계산됩니다. 충전 온도 및 구성. 따라서 이전 작업에 비해 현재의 주요 이점은 완전성에 있습니다. 이는 가스-킬른-클링커 시스템의 다양한 부분에서 에너지 흐름의 정량화를 통해 킬른 작동에 대한 더 나은 이해를 가능하게 하고 여기에서 사용된 방법을 건조 및 소각과 같은 다른 회전 킬른 응용 분야에 적용할 수 있게 합니다.
이 문서의 특정 목적은 회전식 시멘트 가마에 대한 포괄적인 모델을 제시하고 화염에서 클링커로의 에너지 플럭스와 가마에서 열 손실을 정량화하는 것입니다. 이 문서의 나머지 부분은 다음과 같이 구성됩니다. 2장 에서는 다양한 모델과 해법을 제시하고 3장 에서는 그 결과를 제시하고 논의한다 . 여기에는 본격적인 회전식 시멘트 가마의 제한된 측정값과의 비교가 포함됩니다. 이 논문은 가장 중요한 결론의 요약으로 끝납니다.
2 . 모델 공식화
2.1 . 개요
Fig. 1 은 시멘트 로터리 킬른의 단면을 보여준다. 가마의 회전은 전하의 움직임을 유도하여 후자를 대략적으로 잘 혼합되도록 합니다 [10] , 여기에서 채택할 가정입니다. 우리는 이 코팅을 클링커와 유사한 물리적 특성의 고체 재료로 모델링하여 가마 내화물에 부착된 클링커의 존재를 허용할 것입니다. 우리는 이 층의 두께가 가마를 따라 균일하다고 가정합니다. 이것은 아마도 지나치게 단순화한 것일 수 있지만 관련 데이터를 사용할 수 없습니다. 모델 설명을 진행하기 전에 그림 2 에 개략적으로 표시된 회전식 가마의 다양한 에너지 흐름을 이해하는 것이 중요합니다 .
석탄 연소에 의해 방출되는 에너지(단위 시간당)( Q 석탄 )는 배기 가스(Δ H 가스 )와 함께 가마 밖으로 흘러 가마 벽에 직접 복사( Q rad ) 및 대류( Q conv )됩니다. 공급 및 배기 덕트( Q rad,1 + Q rad,2 ) 에 대한 축 방향의 복사에 의해 작은 부분이 손실됩니다 . 전하 가마 시스템은 복사( Q rad ) 및 대류( Q conv )에 의해 가스로부터 에너지(Δ H cl )를 흡수 하고 주변으로 열을 잃습니다( Q손실 ). 전체 에너지 균형에서 개별 항의 계산, 즉(1a)큐석탄=ΔH가스-Q라드-Q전환-Q일, 1-Q일, 2,(1b)큐라드+Q전환=ΔH클+Q손실여기에서 다음 섹션에 설명된 대로 가스, 가마 및 클링커에 대한 이산화 에너지를 국부적으로 해결함으로써 수행됩니다.
2.2 . CFD 코드
가스 운동량, 종 농도 및 에너지의 Favre 평균 방정식은 표준 k – ε 모델을 사용하여 방사 모듈(RAD-3D)과 함께 상업적으로 이용 가능한 축대칭 CFD 코드(FLOW-3D)에 의해 해결됩니다. [13] . 기하학이 실제로 3차원이고 벽 온도의 각도 분포가 존재하지만 합리적인 시간과 현재 워크스테이션에서 완전한 3으로 솔루션을 얻을 수 있도록 기체상을 축대칭으로 취급합니다. -D를 요구하는 해상도로 계산하려면 슈퍼컴퓨터에 의존해야 합니다. FLOW-3D에서 사용되는 다양한 하위 모델의 일부 기능과 벽 경계 조건에 대한 특수 처리는 다음과 같습니다.
2.2.1 . 석탄 연소
Rossin-Rammler 크기 분포(45μm 평균 직경, 1.3 지수 [6] )를 따르는 석탄 입자 는 CPU 시간을 줄이기 위해 솔루션 영역(즉, 확률적 구성 요소 없이)에서 결정론적으로 추적되었지만 분산을 과소 평가하는 단점이 있습니다 . 14] . 입자는 2-반응 모델에 따라 휘발되도록 허용되었고 휘발성 연소는 무한히 빠른 것으로 간주되었습니다. 석탄 연소에 대한 설명의 세부 사항은 FLOW-3D에서 석탄 휘발 및 열분해의 “표준” 상수 집합이 합리적인 결과를 제공하고 Ref. [5] .
2.2.2 . 복사와 대류
가스의 복사 강도는 RAD-3D 모듈을 사용하여 80,000개의 입자로 Monte-Carlo 방법으로 계산되었습니다. 가마는 반경 방향으로 7개, 축 방향으로 19개(크기가 0.1 × 1.0 m와 0.2 × 5.0 m 사이)로 불균일한 구역으로 나뉘었으며 각 구역 에서 방사선 강도가 균일하다고 가정했습니다. 방사선 모듈의 출력은 내부적으로 FLOW-3D에 대한 유체 계산에 인터페이스되고 외부적으로 벽 및 클링커에 대한 코드에 인터페이스되었습니다( 섹션 2.3 섹션 2.4 참조). 방사선 패키지의 이산화된 구역은 CFD 그리드의 셀보다 훨씬 커야 하므로 구역에 온도 평균이 형성될 수 있는 많은 셀이 포함될 수 있다는 점을 이해하는 것이 중요합니다. 상대적으로 조잡한 복사 구역의 분해능과 Monte-Carlo 방법의 통계적 특성은 구역의 복사 열유속이 더 미세한 구역화 및 더 많은 입자로 몇 번의 실행에 의해 결정된 바와 같이 최대 약 10%까지 부정확할 수 있음을 의미합니다. 또한 경계면에 입사하는 열유속은 영역 크기보다 미세한 분해능으로 결정할 수 없으므로 복사 열유속은 벽에 인접한 19개 영역 각각의 중심에서만 계산됩니다. 0.15m -1 의 흡수 계수는 Ref.[11] . 엄밀히 말하면, 흡수 계수는 국부적 가스 조성과 온도의 함수이므로 균일하지 않아야 합니다. 그러나 가스 조성은 가마의 일부만 차지하는 화염 내에서만 변 하므로( 3절 참조 ) 균일한 흡수 계수를 가정하는 것이 합리적입니다. 또한, 현재 버전의 소프트웨어는 FLOW-3D의 반복 프로세스 동안 이 요소의 자동 재조정을 허용하지 않습니다. 여기서 로컬 가스 특성이 계산되므로 일정하고 균일한 흡수 계수가 필요합니다.
최종적으로, 벽에서 대류 열전달이 플로우 3D 패키지에서 표준 출력 표준 “벽 기능”제형에 혼입 난류 경계층에 대한 식에 기초하고,의 속도 경계 조건과 유사한 K – ε 모델. FLOW-3D 및 RAD-3D에서 입력으로 사용하고 출력으로 계산된 다양한 양은 그림 3에 개략적으로 표시 됩니다.
2.2.3 . 그리드
반경 방향 47개, 축 방향 155개 노드를 갖는 불균일한 격자를 사용하였으며 격자 독립성 연구를 수행한 결과 충분하다고 판단하였다. 유사한 크기의 그리드도 Refs에서 적절한 것으로 밝혀졌습니다. 4 , 5 , 6 , 7 . 매우 높은 축 방향 및 소용돌이 속도로 인해 석탄 버너 유정에 가까운 지역을 해결하기 위해 특별한 주의를 기울였습니다. HP 715/100MHz 워크스테이션에서 이 그리드의 일반적인 CPU 시간은 10시간이었습니다.
2.2.4 . 경계 조건
벽 온도에 대한 경계 조건은 기체상 및 복사 솔버 모두에 필요하다는 것을 인식하는 것이 중요합니다. 아래에서는 4 , 5 , 6 , 7 을 규정하기 보다는 축대칭 그리드에 대한 이 온도 분포를 예측하는 대략적인 방법을 설명합니다 .
내벽 온도 T w ( R in , x , ϕ ) 의 각도 분포 가 알려져 있다고 가정합니다 . 그런 다음 전체 3차원 문제를 “동등한” 축대칭 문제로 줄이기 위해 가상의 내벽 온도 T RAD ( x )는(2)2πε에티4라드(x) = ε클∫0ㄷ티4클(엑스)디ϕ + ε에∫ㄷ2π티4에(아르 자형~에, x, ϕ)디ϕ”효과적인” 경계 조건으로 사용할 수 있습니다. T RAD ( x )는 방위각으로 평균화된 “복사 가중” 온도입니다. 필요한 경계 조건으로 이 온도를 사용하는 것은 복사가 열 전달을 지배한다는 기대에 의해 동기가 부여됩니다(후반부 확인, 섹션 3.4 ). 따라서 전체 3차원 문제와 이 “유효한” 축대칭 문제에서 가스에서 가마로의 전체 에너지 흐름은 거의 동일할 것으로 예상됩니다. 식 의 사용 (2) 축대칭 코드로 기체상 및 복사장을 계산할 수 있으므로 엔지니어링 워크스테이션을 사용하여 문제를 다루기 쉽습니다.
고려되는 가마의 규모와 온도에서 가스는 광학적으로 두꺼운 것으로 간주될 수 있습니다. 솔루션(나중에 제시됨)은 평균 경로 길이(즉, “광자”의 모든 에너지가 흡수되기 전의 평균 길이)가 약 3.2m임을 보여주며, 이는 가마 내경 4.1m보다 작습니다. 이것은 내벽에 입사하는 복사 플럭스가 국부적 벽과 가스 온도에 강하게 의존하고 더 먼 축 또는 방위각 위치에서 벽의 온도에 약하게만 의존함을 의미합니다. 이것은 기체상에 사용된 축대칭 근사에 대한 신뢰를 줍니다. 그것은 또한 Refs의 “구역 방법”을 의미합니다. 8 , 9 , 10표면에 입사하는 방사선이 1-2 구역 길이보다 더 먼 축 위치와 무관한 것으로 간주되는 경우에는 충분했을 것입니다.
2.3 . 가마 온도
내부 소성로 표면 온도 T w ( R in , x , ϕ )는 Eq. 에서 필요합니다 . (2) 및 가마 벽 에너지 방정식의 솔루션 결과의 일부입니다. 각속도 ω로 회전하는 좌표계 에서 후자는 [10] 이 됩니다 .(3)ω∂(ϱ에씨피티에)∂ϕ=1아르 자형∂∂아르 자형에게에아르 자형∂티에∂아르 자형+1아르 자형2∂∂ϕ에게에∂티에∂ϕ+∂∂엑스에게에∂티에∂엑스경계 조건에 따라(3a)r=R~에,Θ<ϕ⩽2π:에게∂티에∂아르 자형=q라드(x)+q전환(엑스),(3b)r=R~에, 0 <ϕ⩽Θ:에게∂티에∂아르 자형=qw–cl(x, ϕ) = hw–cl티클(x)-T에(아르 자형~에, x, ϕ),(3c)r=R밖, 0 <ϕ⩽2π:.케이∂티에∂아르 자형=h쉿티쉿-T∞+ ε쉿티4쉿-T4∞.
전도도, 밀도 및 비열용량에 대한 값은 실제 가마에 사용되는 내화물 재료에 대한 제조업체 정보에서 가져옵니다 [15] . 외부 쉘 온도 T sh = T w ( R out , x , ϕ )는 x 및 ϕ 에 따라 달라질 수 있습니다 .
위 방정식에 대한 몇 가지 의견이 있습니다. 에서는 식. (3a) 에서 열유속의 방위각 의존성이 제거되었습니다. 이전에 언급했듯이 흐름은 광학적으로 두꺼운 것으로 간주됩니다. 즉, 화염이 너무 방사되고 너무 넓기 때문에 벽면 요소가 화염을 가로질러 반대쪽 벽을 “보지” 않습니다. 따라서 q rad ( x , ϕ ) 의 계산은 다른 각도 위치로부터의 복사를 포함할 필요 없이 T 가스 ( r , x ) 및 로컬 T w ( R in , x , ϕ )를 기반으로 할 수 있습니다. 여기부터 qrad ( x )는 Eq. 의 방위각 평균 온도를 기반으로 하는 축대칭 RAD-3D 솔루션에서 가져옵니다 . (2) , 결과적인 q rad ( x )는 어떤 의미에서 방위각으로 평균된 열유속입니다. 식 따라서 (3a) 는 우리가 이 열유속을 모든 ϕ 에 등분포한다는 것을 의미합니다 . Eq 에서 q rad 의 각도 변화를 무시한다는 점에 유의하십시오 . (3a) 는 Refs. [10] 또는 [11] 이 우선되어야 합니다.
소성로와 장입물 사이의 열전달 계수 h w-cl 은 소성로의 에너지 흐름과 온도를 정확하게 예측하는 데 중요하지만 잘 알려져 있지 않습니다. 500 W / m의 전형적인 값 이 K는 여기에 제시된 결과 사용되고있다 [8] . 계산된 T w ( r , x , ϕ ) 및 T RAD ( x) 이 계수의 선택에 따라 달라지지만 예측은 질적으로 변하지 않습니다. 껍질에서 대기로의 열 전달은 복사와 별도로 강제 및 자연 대류를 통해 발생합니다. 자연 대류에 대한 열전달 계수는 Ref. [11] , 현재 조건에서 약 5 W/m 2 K의 일반적인 값 을 사용합니다. 그러나 쉘에 불어오는 외부 팬은 과열을 피하기 위해 산업에서 종종 사용되며 이러한 효과는 총 h sh =30 W/m 2 K 를 사용하여 여기에서 모델링 되었습니다. 방사율에는 다음 값이 사용되었습니다. ε w = ε cl = 0.9 및 ε sh = 0.8.
식 (3) 은 가마의 방사형 기울기가 훨씬 더 가파르기 때문에 방위각 및 축 전도를 무시한 후 명시적 유한 체적 방법으로 해결되었습니다. 방사형으로 50개 노드와 축 방향으로 19개 노드가 있는 균일하지 않은 그리드가 사용되었으며 회전으로 인한 화염에 주기적으로 노출되는 표면으로 인해 발생하는 빠른 온도 변화를 따르기 위해 내부 표면에서 적절한 방사형 분해능이 사용되었습니다. 동일한 이유로 사용 된 작은 단계(Δ ϕ = π /100)는 가마의 큰 열 관성과 함께 가마 벽 온도가 수렴되도록 하기 위해 2시간 정도의 CPU 시간이 필요했습니다.
2.4 . 수갑
가마에 대한 모델의 마지막 부분은 클링커 온도 및 조성 보존 방정식에 관한 것으로, 축 방향 기울기만 고려하고 전도는 무시합니다.(4)씨피V클디(ϱ클티클)디엑스=−엘wclㄷㅏ클∫0ㄷ큐w–cl(x, ϕ)디ϕ +엘gclㅏ클큐라드(x)+q전환(엑스)−∑나Nsp아르 자형나시간0, 나는에프+씨피티,(5)V클디(ϱ클와이나)디엑스=r나,(6)V클디ϱ클디엑스=−r무엇2,여기서 A cl 은 속도 V cl 로 흐르는 전하가 덮는 단면적 이며 둘 다 일정하다고 가정하고 L gcl =2 R in sin( Θ /2) 전하로 덮인 섹터의 현( 그림 1 ) , L WCL = Θ R 에서는 , N SP 화학 종의 수와 r에 난을 (kg / m의 형성 속도 순 3 종의) I를 . 전하의 밀도는 Eq를 감소시킵니다 . (6) CO 2 에 대한 질량 손실로 인한하소하는 동안 초기 값은 총 질량 유량이 ϱ cl V cl A cl 과 같도록 선택되었습니다 . 참고 ρ (CL)이 있다 하지 전하 느슨하게 포장 된 입자로 이루어지는 것으로 생각 될 수있는 바와 같이, 충전 재료 밀도하지만 벌크 밀도. 우리는 또한 전하의 실제 입상 흐름 패턴을 조사하는 것보다 적은 것은 모델의 신뢰성에 크게 추가되지 않는 임시 설명 [10] 이라고 믿기 때문에 전하의 전도를 무시 합니다. 전하는 CaCO 3 , CaO, SiO 2 , Al 2 O 3 , Fe 로 구성된 것으로 가정합니다.2 O 3 , C2S, C3S, C3A 및 C4AF로, 마지막 4종은 클링커화 중에 형성된 복합 염에 대해 시멘트 화학자가 사용하는 특수 표기법으로 표시됩니다. 다음과 같은 화학 반응을 가정합니다 [12] .
(나)
CaCO3→높은+무엇2
k = 108특급(−175728/RT)
(Ⅱ)
높은+2SiO2→C2S
k = 107특급(−240000/RT)
(Ⅲ)
높은+C2S→C3S
k = 109특급(−420000/RT)
(IV)
3높은+로2그만큼3→C3A
k = 108특급(−310000/RT)
(V)
4높은+로2그만큼3+철2그만큼3→Q4AF
k = 108특급(−330000/RT)
상기 시행 착오에 의해 선택되는 아 레니 우스 식에 사용되는 사전 지수 인자 및 활성화 온도는 카코에 대한 활성화 에너지를 제외하고, 가마의 출구에서의 전하의 예상 조성물을 얻었다 (3) 에서 촬영 한 분해 참조 [16] . 우리는 이러한 반응이 임시 모델임을 강조합니다. 실제로 고체상의 화학반응은 다양한 종의 결정들 사이의 계면에서 일어나며 확산이 제한적 이지만 [17] , 클링커 화학에 대한 상세한 처리는 본 연구의 범위를 벗어난다.
클링커 형성의 마지막 단계로 간주되는 반응 (III)은 고온에서 액상이 존재할 때만 발생합니다. 클링커의 용융은 액체 분획 Y fus 에 대해서도 해결함으로써 모델링되었습니다 .(7)엘소란V클디(ϱ클와이소란)디엑스=RHS의식(4)만약 T의 CL이 융해 온도와 같거나보다 커진다 T의 FUS 와 T의 FUS 의 = 1560 K. 상한 Y의 FUS = 0.3 수행 하였다 [17] 상기 식을. (7) 무시되었다.
상미분 방정식, , , , , Gear 방식과 통합되었습니다. 가마 온도에 대한 유한 체적 코드( 2.3절 )와 클링커에 대한 코드는 반복적으로 해결되었으며( 그림 4 ), 이는 벽 클링커 열유속 q w–cl ( x , ϕ ).
2.5 . 최종 커플링
전체 문제(가스, 가마, 장입)는 반복 방식으로 해결되었습니다. T RAD 의 균일한 분포에서 시작 하여 기체상은 q rad ( x ) 및 q conv ( x ) 의 축 분포를 제공하도록 해결되었습니다 . 이것들은 다음에서 사용되었습니다., , , , , 그 솔루션의 새로운 추정 결과 T RAD ( X 통해) 식. (2) . 그런 다음 FLOW3D-RAD3D 실행이 6차 다항식 피팅의 계수 형태로 프로그램에 도입된 새로운 경계 조건으로 반복되었습니다. 의 연속 추정치 사이에 0.5 미만의 밑에 이완 인자 T RAD ( X)는 벽 온도에 대한 복사 열유속의 민감도가 크기 때문에 필요한 것으로 밝혀졌습니다. 일반적으로 HP 715 워크스테이션에서 10일 정도의 총 CPU 시간에 해당하는 내벽 온도(연속 반복이 40K 이상 변하지 않을 때 정의됨)의 수렴을 달성하기 위해 이러한 단계 사이에 약 10번의 반복이 필요했습니다. . 그림 5 는 균일한 값(1600K)에서 시작하여 최종 프로파일까지 T RAD ( x ) 의 수렴 이력을 보여줍니다 .
2.6 . 가마 조건
사용된 일부 매개변수에 대한 작동 조건 및 값은 표 1 표 2 표 3에 나와 있습니다. 이 값은 시멘트 회전 가마의 전형입니다.
표 1 . 공기 및 석탄 입자 입구 조건
축
수송
소용돌이
중고등 학년
석탄
m (kg/s)
2.253
1.759
2.910
45.930
4.0
유 (m/s)
77.1
36.5
76.1
12.73
36.5
V (m/s)
−20.7
0
63.9
0
0
W (m/s)
0
0
112.8
0
0
티 (케이)
318
383
318
1273
383
표 2 . 클링커 조성(질량 분율)
밀가루
가마 입구
가마 출구
m (kg/s)
50.374
39.815
32.775
티 (케이)
−
1100
1785
CACO 3
0.7947
0.40218
0
높은
0
0.33801
0.0229
그런가 2
0.1434
0.18143
0
알 2 O 3
0.0349
0.0442
0
철 2 O 3
0.0270
0.03416
0
C2S
0
0
0.1808
C3S
0
0
0.5981
C3A
0
0
0.0731
Q4AF
0
0
0.1242
소성 인자
0
0.6
1.0
소성 계수 카코의 비율을 3 의 CaO로 변환 된 FARINE있다.
표 3 . 재료 속성 및 기타 매개변수
ω (래드/초)
0.5
V의 CL (m / s)
0.035
T ∞ (K)
300
h sh (W/m 2 K)
30
h w–cl (W/m 2 K)
500
ε w , ε cl
0.9
ε 쉬
0.8
C의 P (클링커) (킬로 / kg K)
1.5
ϱ cl (kg/m 3 )
1200
L fus (kJ/kg)
418.4
c p (벽) (kJ/kg K)
1.5
ϱ w (kg/m 3 )
1600–3000
k는 w (W / m K)
0.6–3.0
석탄 열 방출(kJ/kg)
25475
3 . 결과 및 토론
이 섹션에서는 먼저 화염 구조에 대한 정보와 함께 예측된 공기역학적 패턴의 세부사항을 제시합니다. 소성로 내화물의 온도 분포와 클링커 조성의 변화를 설명합니다. 이 섹션은 가마의 전체 에너지 균형과 가능한 모델 개선에 대한 논의로 끝납니다.
3.1 . 화염 구조
그림 6 은 명확성을 위해 방사상 좌표가 과장된 온도의 등고선 플롯을 보여줍니다. 석탄은 주입 지점에서 약 1m 지점에서 약간 축에서 벗어나 점화되며 최대 화염 온도(약 2400K)는 경험에 따라 약 40m 하류에서 도달합니다 [15] . 완전한 입자 소진에 대한 가장 긴 시간은 버너에서 45m에 해당하는 약 1.4초였습니다. 방사형 온도 프로파일( 그림 7 ) 은 온도의 상당한 불균일성이 있음을 보여주지만 출구 프로파일이 본질적으로 평평해짐에 따라 하류에서 감소합니다. 또한 벽에 인접한 가스가 더 차가운 열 경계층이 존재한다는 것이 분명합니다.석탄 노즐에서 최대 30m까지 벽보다 이것은 이 영역에서 대류에 의한 열 전달이 음(즉, 기체 쪽으로)임을 의미하며, 3.4절 에서 더 자세히 논의된 지점 입니다.
버너 출구 바로 하류에 길이가 약 1 버너 직경인 재순환 구역이 있는데( 그림 8 ), 여기에서 화염이 더 하류에서 발화하기 때문에 소용돌이 안정화 화염 [7] 에서와 같이 화염 안정화에 기여하지 않습니다 . 그러나 액체 연료를 사용할 때는 중요할 수 있으므로 버너에 가까운 그리드의 세부 사항을 강조해야 합니다. 버너에서 처음 몇 미터는 매우 높은 전단력과 높은 난류 에너지 생산을 포함하며 이것이 그리드 미세 조정을 강조하는 또 다른 이유입니다. 휘발성 물질 연소 영역( x =10m, r =1m) 에서 k 및 ε 의 일반적인 예측 값 은 24.3 및 142m 2 /s입니다.3 , 각각. 대규모 난류 시간은 171ms이고 Kolmogorov 시간 규모는 1.1ms입니다. 휘발성 물질의 연소는 0.1ms(일반적인 탄화수소 연료) 정도의 시간 규모에서 발생하며, 이는 가마의 소규모 난류 시간보다 10배 더 짧습니다. 따라서 이 흐름에서 연소에 대한 유한 속도 동역학을 포함할 필요는 없으며 “혼합 연소” 근사가 합리적입니다.
3.2 . 가마 온도 분포
중심선에서 계산된 가스 온도, 온도 T RAD ( x ) 및 클링커 온도는 그림 9 에서 비교됩니다 . 최고 가스 온도는 25~40m 사이에 위치하며 내화 내부 표면 온도도 최고점입니다. 클링커는 놀랍게도 가마에서 나오기 전 마지막 몇 미터 동안 벽보다 뜨겁 습니다. 복사에 의해 내화물에 입사하는 열유속은 대류에 의한 것보다 1-2 배 더 높으며( 그림 10 ) 가마의 처음 10m에 대한 총 열 전달 은 가스를 향 합니다. 이 관찰의 중요성은 나중에 논의됩니다.
대류로 인한 에너지 플럭스는 화염에서 가마까지의 전체 에너지 플럭스의 매우 작은 부분인 것으로 밝혀졌습니다( 그림 10 ). 여기서 예측된 대류의 작은 기여는 Ref. [11] . 그 작업에서 대류 열 전달 계산에 사용된 가스 온도는 가마 단면의 평균이었고 따라서 축 근처에 있는 화염의 기여로 인해 벽 부근의 온도보다 훨씬 높았습니다. . 여기에서 우리는 온도와 가스 속도 및 난류 운동 에너지의 국부적 값을 기반으로 하는 보다 정확한 열전달 계수를 사용했기 때문에 보다 정확한 결과를 기대합니다.
예측된 벽 온도는 모든 방향에서 불균일합니다. Fig. 11 은 가마가 회전함에 따라 화염에 노출되었을 때 벽이 가스에 의해 연속적으로 가열되고 클링커에 열을 공급하여 냉각되는 것을 보여준다. 이것은 약 100K의 일반적인 각도 온도 변화를 갖는 대부분의 가마 길이에 해당됩니다. 대조적으로 버너에 가까우면 벽 은 (0 < ϕ < π /2) 동안 클링커에서 열을 얻고 다음으로 열을 잃 습니다. 노출될 때의 가스( π /2 < ϕ < 2 π ). 벽과 클링커 온도가 같으면서 방위각 변화가 없는 경우가 발생할 수 있습니다( 그림 11 , x = 17.5m). 이 온도 변화가 작은 것으로 간주될 수 있지만 벽에서 클링커까지의 열유속을 계산하는 위치에 있으려면 전체 3차원 내벽 온도 분포를 계산해야 합니다(0 < ϕ 범위에서 발생 < π /2).
그림 12 는 ϕ에 독립적인 외부(쉘) 온도와 함께 고체의 큰 비열로 인해 각도 방향의 변화 영역이 벽으로 약 1cm만 확장됨을 보여줍니다( 그림 12b) .. 벽 온도 방사 분포는 가스 온도, 입사 방사선 및 내화 재료의 특성이 변하기 때문에 축 방향 거리에 따라 달라집니다. 정확한 예측을 위해서는 내화물에 부착된 클링커 코팅의 두께에 대한 정확한 지식이 필요합니다. 여기에서 우리는 이 코팅을 클링커와 유사한 물성을 가진 균일한 두께의 재료로 취급했습니다. 그러나 이 코팅층의 실제 물리적 특성과 두께 분포에 관한 실험 데이터를 사용하여 예측의 신뢰성이 향상될 것입니다.
마지막으로, 그림 13 은 외부 쉘 온도가 화염 영역에서 최고조에 달하고 대략적으로 실험 경향을 따른다는 것을 보여줍니다 [15] . 외부 가마 외피는 다양한 강철 두께, 방사율(외피 착색으로 인한) 및 열 전달 계수(송풍기 간격으로 인한)를 갖고 가마는 가변 내화 두께(에 의한 침식으로 인해)를 갖기 때문에 정확한 비교는 의미가 없습니다. 클링커), 여기에 사용된 가정과 반대입니다. 전체 규모 가마는 또한 차등 코팅 및 내화 침식으로 인한 최대 ±100K의 쉘 온도 각도 변동을 보여줍니다 [15] . 따라서 우리는 그림 13 의 일치 가 실제 가마의 복잡성을 고려할 때 예상할 수 있는 만큼 우수 하다고 믿습니다 .
이 섹션에 제시된 예측은 가마 내부의 열 전달 경로에 대한 다음 그림을 뒷받침합니다. 대부분의 가마 길이에서 장입물은 화염으로부터의 복사와 벽으로부터의 열 전도에 의해 가열되고 있습니다. 장입물이 내화물보다 더 차갑기 때문입니다. 가마가 회전함에 따라 내화물은 화염에 노출될 때 열을 얻고 이를 클링커에 공급합니다( 그림 11 ). 벽의 이 “재생” 작용은 Refs. 9 , 10 및 현재 결과에서 재현되었습니다. 그러나 버너 근처에서 반대 에너지 흐름이 발생합니다( 그림 11 , 작은 x). 여기의 가스는 아직 충분히 뜨겁지 않아 내화물이나 장입물에 에너지를 공급하지 않습니다. 이 영역에서 벽은 다가오는 전하에 의해 열을 얻으므로 고체가 없을 때보다 더 뜨겁게 유지됩니다. 벽과 전하가 대류와 복사에 의해 가스에 열을 공급합니다. 우리는 이것을 “음의 재생” 작용으로 식별할 수 있으며 가마의 더 높은 온도 영역( x > 15m) 에서 클링커에 의해 흡수된 에너지에 의해 유지됩니다 . 전반적으로 클링커는 x > 15 m 에서 열을 흡수 하고 0 < x < 15 m 에서 일부를 가스로 되돌려 줍니다.
이 상호 작용은 간단하지 않으며 쉽게 예상할 수 없습니다. 이는 예를 들어 고체를 액체 연료로 대체하여 화염을 수정하면 열유속 분포를 변경하여 최종 클링커 온도에 중대한 영향을 미칠 수 있음을 의미합니다. 현재의 포괄적인 모델이 제공하는 세부 사항은 가마에서 이러한 변화를 평가하는 데 도움이 될 것입니다.
3.3 . 클링커 온도 및 조성
클링커 온도( 그림 9 )는 가장 높은 화염 온도에 도달하는 축 방향 위치에서 거의 최고조에 달하며 클링커는 약 1780K에서 킬른에 존재하며 이는 시멘트 킬른에서 실험 측정값에 가까운 값입니다 [15] . 초기 및 최종 클링커 조성은 표 2 에 나와 있으며 실제 가마에서 작동 값에 가깝습니다 [15] . 다양한 클링커 성분의 축방향 분포( 그림 14 )는 완전한 하소를 위해 고체 유입구에서 약 25m, C2S, C3A 및 C4AF 생성을 위해 추가로 10m가 소요됨을 보여줍니다. 첫 번째 액체상은 x 에서 발견됩니다.=50m이고 액화는 경험과 일치하는 예측인 매우 직후에 완료됩니다 [17] . 클링커화 반응(R-III)은 모델에서 액체가 나타날 때 시작되는 것으로 가정되었으며, 그림 14 에서 클링커화에는 나머지 길이의 거의 전체가 완료되어야 한다는 것이 분명 합니다. 예측은 전체적으로 시멘트 가마 운영의 경험과 일치하며 여기에 사용된 화학적 및 물리적 매개변수가 현실적인 값을 가지고 있음을 의미합니다.
3.4 . 글로벌 에너지 균형
전지구적 에너지 균형은 기체상(FLOW-3D 및 RAD-3D에 의한)과 소성로 장입 시스템에 대한 솔루션에서 쉽게 계산할 수 있으며 표 4 에 나와 있습니다. CFD 코드는 방사 모듈과 함께 에너지를 약 2%까지 절약합니다. 작은 것으로 간주되는 이 오류는 주로 RAD-3D의 영역 이산화와 Monte-Carlo 계산의 유한한 입자 수로 인해 발생하는 오류에 기인하며 CPU 시간을 희생하여 개선할 수 있습니다. 소성로-클링커 계산의 정확도는 더 나쁩니다. 소성로-클링커 시스템에 입력되는 에너지의 약 10% 오류( Q rad + Q conv )입니다. 이는 수렴된 솔루션이 식 (3) , 그리고 보다 정확한 암시적 솔버에 의해 개선될 수 있습니다.
시멘트 회전식 가마의 에너지 사용에 관한 몇 가지 흥미로운 결론은 표 4 의 결과를 통해 얻을 수 있습니다 . 연소에 의해 방출되는 에너지의 약 40%는 전하 가열 및 클링커 형성에 필요하고 약 10%는 내화물을 통해 대기로 손실됩니다. 나머지의 대부분은 본질적으로 배기 가스와 함께 소성로 밖으로 흐릅니다. 이 중 일부는 소성로 외부의 예비 하소기 및 사이클론에서 회수됩니다. 내부 가마 벽과 장입 온도를 자세히 다루는 여기에 제시된 포괄적인 모델에 의존하지 않고는 국지적 가스 온도를 정확하게 예측하고 이에 따라 향후 연구에서 오염 물질 형성을 예측하는 것이 불가능하다는 것이 분명합니다.
3.5 . 논의
여기에 제시된 회전식 시멘트 가마 작동에 대한 포괄적인 모델의 결과는 합리적이며 실험적으로 관찰된 경향을 재현합니다. 이전 모델링 작업에 비해 이 작업의 주요 이점은 가마에서 발생하는 대부분의 물리적 프로세스를 포함한다는 점입니다. 특히, 가스 온도와 클링커로의 열유속 및 이에 따른 클링커 형성을 결정하는 데 가장 중요한 양인 내벽 온도는 실험 데이터를 사용하여 규정된 것이 아니라 예측되었습니다. 이 특정 기능은 현재 모델을 진정한 예측형으로 만듭니다.
우리는 전체 3차원 문제를 공기역학에 대한 “동등한” 축대칭 문제로 줄이는 방법을 포함했습니다( 식 (2) ). 이를 통해 현재 워크스테이션에서 솔루션을 얻을 수 있습니다. 모델의 모듈식 특성, 즉 공기역학, 복사, 가마 및 장입에 대한 별도의 코드는 해당 모듈만 수정하면 다른 회전 가마 응용 프로그램(예: 소각 및 건조)에도 사용할 수 있음을 의미합니다. 예를 들어, 고형 폐기물의 소각은 현재 코드로 모델링할 수 있지만 적절한 화학, .
실험 데이터와의 상세한 비교는 이용 가능한 측정이 거의 없고 현지 시멘트 회사에서 제공한 경험적 데이터로 제한되어 매우 어렵습니다 [15] . 비교는 앞서 지적한 바와 같이 출구 클링커 조성과 온도가 산업적 경험( 표 2 ) 이내 이고, 배기 가스 조성은 공장 굴뚝에서 측정된 값에 가깝고(“가짜 공기” 희석을 허용한 후), 가마 외피 온도는 측정 범위 내에 있습니다( 그림 13 ). 이 동의는 모델이 프로세스의 정확한 표현임을 시사합니다.
더 높은 정확도의 예측을 달성하려면 모델의 다양한 부분에서 개선이 필요합니다. 내화물의 정확한 두께(즉, 내화물과 부착된 클링커)를 설정해야 합니다. 이는 가마 벽을 통해 주변으로 열 손실이 발생하여 외부 쉘 온도에 영향을 미치기 때문입니다. 새 내화물이 있는 가마에서 쉘 온도 측정과 자세한 비교가 이루어져야 합니다(불균일한 코팅 두께가 방지되도록). 벽 재료의 물리적 특성(열용량, 밀도, 전도도)의 적절한 값을 사용해야 합니다. 가장 큰 불확실성은 클링커 코팅의 가정된 특성에 관한 것입니다. 내벽 표면의 방사율과 가스의 흡수 계수를 더 자세히 조사해야 합니다. 가마에 입사하는 복사 열유속에 영향을 미치므로 벽 온도에 영향을 줄 수 있습니다. 클링커의 온도는 사용된 비열 용량에 따라 달라지므로 정확한 평가에 각별한 주의가 필요합니다. 화염의 국지적 온도와 종 구성에 대한 지식은 CFD 코드를 검증하는 데 매우 유용할 것이지만 그러한 적대적인 환경에서 측정은 분명히 달성하기 매우 어렵습니다. 마지막으로 클링커 화학 및 전하 이동은 개선할 수 있는 영역입니다. 그러한 적대적인 환경에서의 측정은 분명히 달성하기 매우 어렵습니다. 마지막으로 클링커 화학 및 전하 이동은 개선할 수 있는 영역입니다. 그러한 적대적인 환경에서의 측정은 분명히 달성하기 매우 어렵습니다. 마지막으로 클링커 화학 및 전하 이동은 개선할 수 있는 영역입니다.
이러한 모든 잠재적 개선과 모델과 관련된 불확실성에도 불구하고 가마의 모든 에너지 경로가 적절한 세부 사항으로 모델링되었기 때문에 전체 동작은 최소한 질적으로 정확합니다. 클링커 출구 구성, 쉘 온도 및 배기 가스 구성과 같은 중요한 양은 허용 가능한 정확도로 예측됩니다. 이 모델은 버너, 연료 유형, 품질 및 수량, 예비 하소 수준( 표 2 ) 또는 고형물 유량 등의 변경과 같은 많은 상황에서 산업계에 매우 유용할 것으로 예상됩니다 . 소성로 운영자는 최종 클링커 구성이 여전히 허용 가능하고 현재의 포괄적인 모델이 이 방향에 도움이 될 수 있는지 확인해야 합니다.
4 . 결론
실제 작동 조건에서 석탄 연소 회전 시멘트 가마의 클링커 형성은 석탄 화염과 가마 사이의 열 교환, 가마와 역류 고체 사이의 열 교환, 고형물을 최종 제품(클링커)으로 변환합니다. 방사선에 대한 Monte-Carlo 방법을 포함하는 축대칭 CFD 코드(상용 패키지 FLOW-3D)가 기상에 사용되었습니다. 가마 벽의 온도는 유한 체적 열전도 코드로 계산되었으며 클링커에 대한 종 및 에너지 보존 방정식도 공식화 및 해결되었습니다. 기체 온도 필드에 대한 예측 사이의 반복적인 절차, 벽에 대한 복사 열 유속, 가마 및 클링커 온도는 실험에서 이러한 정보를 사용한 이전 모델링 노력과 달리 내벽 온도 분포를 명시적으로 계산하는 데 사용되었습니다. 접선 좌표에 대한 통합은 CFD 코드에 필요한 경계 조건으로 사용되는 “유효” 내벽 온도의 축 분포를 초래했습니다. 이 절차를 통해 클링커로의 열 흐름 계산이 가능하고 축대칭 CFD 코드로 3차원 문제를 대략적으로 처리할 수 있습니다. CFD 코드에 필요한 경계 조건으로 사용됩니다. 이 절차를 통해 클링커로의 열 흐름 계산이 가능하고 축대칭 CFD 코드로 3차원 문제를 대략적으로 처리할 수 있습니다. CFD 코드에 필요한 경계 조건으로 사용됩니다. 이 절차를 통해 클링커로의 열 흐름 계산이 가능하고 축대칭 CFD 코드로 3차원 문제를 대략적으로 처리할 수 있습니다.
결과는 복사가 가스와 가마 벽 사이의 대부분의 열 전달을 설명하는 반면 내화물을 통한 환경으로의 열 손실은 입력 열의 약 10%를 설명한다는 것을 보여줍니다. 화학 반응과 충전물의 가열은 연소 에너지의 약 40%를 흡수합니다. 따라서 이러한 사항을 반드시 고려해야 합니다. 예측은 실제 규모의 시멘트 가마에서 얻은 경험과 측정값을 기반으로 한 경향과 일치합니다.
감사의 말
이 작업은 과학 및 기술을 위한 그리스 사무국 프로젝트 EPET-II/649의 자금 지원을 받았습니다. Mr.P에게 진심으로 감사드립니다. 시멘트 가마에 관한 지침 및 데이터는 그리스 TITAN SA의 Panagiotopoulos에게 문의하십시오.
References 1 S.R. Turns, An Introduction to Combustion, Concepts and Applications, McGraw-Hill, New York, 1996 Google Scholar 2 V. Johansen, T.V. Kouznetsova, Clinker formation and new processes, Presented at the Ninth International Congress on the Chemistry of Cement, India, 1992; also RAMBOLL Bulletin No. 42, 1993 Google Scholar 3 Basel Convention, UNEP Document No. 93-7758, 1993 Google Scholar 4 N.C Markatos Mathematical modelling of single and two-phase flow problems in the process industries Revue de l’Institut Français du Pétrole, 48 (1993), p. 631 View PDFCrossRefView Record in ScopusGoogle Scholar 5 T. Avgeropoulos, J.P. Glekas, C. Papadopoulos, Numerical simulation of the combustion aerodynamics inside a rotary cement kiln, in: Pilavachi (Ed.), Energy Efficiency in Process Technology, Elsevier, London, 1993, p. 767 Google Scholar 6 F.C. Lockwood, B. Shen, T. Lowes, Numerical study of petroleum coke fired cement kiln flames, Presented at the Third International Conference on Combustion Technologies for a Clean Environment, Lisbon, 1995 Google Scholar 7 F.C. Lockwood, B. Shen, Performance predictions of pulverised-coal flames of power station furnace and cement kiln types, Twenty-Fifth Symposium International on Combustion, The Combustion Institute, 1994 p. 503 Google Scholar 8 P.V Barr, J.K Brimacombe, A.P Watkinson A heat-transfer model for the rotary kiln: Part II, development of the cross-section model Metallurgical Transactions B, 20B (1989), p. 403 View Record in ScopusGoogle Scholar 9 V Frisch, R Jeschar Possibilities for optimizing the burning process in rotary cement kilns Zement-Kalk-Gips, 36 (1983), p. 549 View Record in ScopusGoogle Scholar 10 A.A Boateng, P.V Barr A thermal model for the rotary kiln including heat transfer within the bed Int. J. Heat Mass Transfer, 39 (1996), p. 2131 ArticleDownload PDFView Record in ScopusGoogle Scholar 11 M.G. Carvahlo, T. Farias, A. Martius, A three-dimensional modelling of the radiative heat transfer in a cement kiln, in: Carvahlo et al. (Eds.), Combustion Technologies for a Clean Environment, Gordon and Breach, London, 1995, p. 146 Google Scholar 12 H.A Spang A dynamic model of a cement kiln Automatica, 8 (1972), p. 309 ArticleDownload PDFView Record in ScopusGoogle Scholar 13 CFDS, FLOW-3D Users Manual, AEA Harwell, UK Google Scholar 14 E Mastorakos, J.J McGuirk, A.M.K.P Taylor The origin of turbulence acquired by heavy particles in a round, turbulent jet Part. Part. Syst. Charact., 7 (1990), p. 203 View PDFCrossRefView Record in ScopusGoogle Scholar 15 P. Panagiotopoulos, TITAN S.A. Cement Company, Personal communication, 1996 Google Scholar 16 M.S Murthy, B.R Harish, K.S Rajanandam, K.Y Ajoy Pavan Kumar Investigation on the kinetics of thermal decomposition of calcium carbonate Chem. Eng. Sci., 49 (1996), p. 2198 Google Scholar 17 V. Johansen, Cement production and chemistry, Presented at the Symposium on Cement Manufacturing and Chemistry, Anaheim, November 1989; also RAMBOLL Bulletin No. 41, 1993 Google Scholar 1 Also at Department of Mechanical Engineering, University of Patras, Greece.
2 Also at Department of Chemical Engineering, University of Patras, Greece.
두 개의 부유체 사이에 간격이 있는 경사진 부유식 방파제(FB)에 대한 새로운 연구가 제안되었습니다. 구조물의 기울기는 파동 에너지 소산을 유발할 수 있습니다. 경사진 구조물의 문제는 파도가 넘친다는 것입니다. 이 문제를 해결하기 위해 두 플로터 사이의 간격을 고려합니다.
오버 토핑이 발생하면 마루를 통과하는 물이 두 플로터 사이의 틈으로 쏟아지며 결과적으로 파도 에너지가 감쇠됩니다. 체인 네트가 모델에 추가되고 전송 계수에 대한 영향이 연구됩니다. 또한, 구조물의 유체역학적 성능에 대한 자유도의 영향을 조사하기 위해 말뚝으로 고정된(1 자유도) 계류 라인으로 고정된(3도의 자유도) 두 가지 고정 시스템에서 자유 모델을 연구했습니다.
게다가, 실험은 5개의 다른 파도 주기와 4개의 다른 파도 높이를 가진 규칙파에서 수행됩니다. 실험 결과, 경사형 부유식 방파제가 직사각형 상자형보다 최대 15% 성능이 우수한 것으로 나타났다. 말뚝에 의해 고정된 FB에 대한 투과계수는 단파에서 케이블에 의해 고정된 FB보다 최대값으로 약 14% 낮고 장파에서 약 4-10% 더 높다. 흘수가 증가함에 따라 전송 계수는 감소하지만 건현은 허용 비율의 초과를 제한하기 위한 최소 요구 사항을 충족해야 합니다.
체인 그물이 있는 모델은 없는 모델에 비해 전달 계수가 최대 14% 감소하여 더 나은 성능을 나타냅니다. 실험 결과, 경사형 부유식 방파제가 직사각형 상자형보다 최대 15% 성능이 우수한 것으로 나타났다. 말뚝에 의해 고정된 FB에 대한 투과계수는 단파에서 케이블에 의해 고정된 FB보다 최대값으로 약 14% 낮고 장파에서 약 4-10% 더 높다. 흘수가 증가함에 따라 전송 계수는 감소하지만 건현은 허용 비율의 초과를 제한하기 위한 최소 요구 사항을 충족해야 합니다.
체인 그물이 있는 모델은 없는 모델에 비해 전달 계수가 최대 14% 감소하여 더 나은 성능을 나타냅니다. 실험 결과, 경사형 부유식 방파제가 직사각형 상자형보다 최대 15% 성능이 우수한 것으로 나타났다. 말뚝에 의해 고정된 FB에 대한 투과계수는 단파에서 케이블에 의해 고정된 FB보다 최대값으로 약 14% 낮고 장파에서 약 4-10% 더 높다. 흘수가 증가함에 따라 전송 계수는 감소하지만 건현은 허용 비율의 초과를 제한하기 위한 최소 요구 사항을 충족해야 합니다.
체인 그물이 있는 모델은 없는 모델에 비해 전달 계수가 최대 14% 감소하여 더 나은 성능을 나타냅니다. 말뚝에 의해 고정된 FB에 대한 투과계수는 단파에서 케이블에 의해 고정된 FB보다 최대값으로 약 14% 낮고 장파에서 약 4-10% 더 높다. 흘수가 증가함에 따라 전송 계수는 감소하지만 건현은 허용 비율의 초과를 제한하기 위한 최소 요구 사항을 충족해야 합니다.
체인 그물이 있는 모델은 없는 모델에 비해 전달 계수가 최대 14% 감소하여 더 나은 성능을 나타냅니다. 말뚝에 의해 고정된 FB에 대한 투과계수는 단파에서 케이블에 의해 고정된 FB보다 최대값으로 약 14% 낮고 장파에서 약 4-10% 더 높다.
흘수가 증가함에 따라 전송 계수는 감소하지만 건현은 허용 비율의 초과를 제한하기 위한 최소 요구 사항을 충족해야 합니다. 체인 그물이 있는 모델은 없는 모델에 비해 전달 계수가 최대 14% 감소하여 더 나은 성능을 나타냅니다.
A novel study of sloping floating breakwater (FB) that has a gap between two floaters is proposed. The slope of a structure can cause wave energy dissipation. A problem with sloping structures is wave overtopping. To solve this problem, a gap is considered between the two floaters. If overtopping occurs, water passing the crest will pour into the gap between the two floaters, as a result wave energy will be attenuated. A chain net is added to the model and its effect on the transmission coefficient is studied. Furthermore, in order to investigate the effects of the degree of freedom on the hydrodynamic performance of the structure, the model is studied in the two anchorage systems which are anchored by pile (1 degree of freedom) and anchored by mooring lines (3 degree of freedom). Moreover, the experiments are performed under regular waves with five different wave periods and four different wave heights. The results of the experiments show a sloping floating breakwater that has a better performance than that of rectangular box type by 15% as maximum value. The transmission coefficients for the FB anchored by pile are lower about 14% as maximum value than that of the FB anchored by cable in shorter waves and are higher about 4–10% in longer waves. With increasing the draft, the transmission coefficient decreases but the freeboard should meet the minimum requirements to restrict overtopping in the allowable rate. The model with a chain net exhibits a better performance as compared with the model without it by a maximum 14% reduction in the transmission coefficients.
Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23
Fig.24
Fig. 25
Fig. 26
Fig. 27
References
Abul-Azm AG, Gesraha MR (2000) Approximation to the hydrodynamics of floating pontoons under oblique waves. Ocean Eng 27:365–384ArticleGoogle Scholar
Biesheuvel AC (2013) Effectiveness of floating breakwaters. Delf University of Technology, DissertaionGoogle Scholar
Chen Zh, Wang Y, Dong H, Zheng B (2012) Time-domain hydrodynamic analysis of pontoon-plate floating breakwater. J Water Sci Eng 5(3):291–303Google Scholar
Daneshfaraz R, Kaya B (2008) solution of the propagation of the waves in open channels by the transfer matrix method. J Ocean Eng 35:1075–1079ArticleGoogle Scholar
Daneshfaraz R, Sadeghfam S, Tahni A (2020) exprimental investigation of screen as energy dissipators in the movable-Bed channel. Iran J Sci Technol Trans Civil Eng 44:1237–1246ArticleGoogle Scholar
Deng Zh, Wang L, Zhao X, Huang Zh (2019) Hydrodynamic performance of a T-shaped floating breakwater. J Appl Ocean Res 82:325–336ArticleGoogle Scholar
Dong GH, Zheng YN, Li YC, Teng B, Guan CT, Lin DF (2008) Experiments on wave transmission coefficients of floating breakwaters. Ocean Eng 35:931–938ArticleGoogle Scholar
Duan WY, Xu SP, Xu QL et al (2017) Performance of an F-type floating break water: a numerical and experimental study. Proc I MechE Part M 231(2):583–599Google Scholar
Gesraha MR (2006) Analysis of π shaped floating breakwater in oblique waves: I. Impervious rigid wave boards. Appl Ocean Res 28:327–338ArticleGoogle Scholar
He F, Huang Zh, Wing-Keung Law A (2013) An experimental study of a floating breakwater with asymmetric pneumatic chambers for wave energy extraction. J Appl Energy 106:222–231ArticleGoogle Scholar
Ikeno M, Shimoda N, Iwata K (1988) A new type of breakwater utilizing air compressibility. In: Proceedings of the 21st Coastal Engineering Conference, ASCE. pp 2426–2339
Ji Ch, Cheng Y, Cui J, Yuan Zh, Gaidai O (2018) Hydrodynamic performance of floating breakwaters in long wave regime: an experimental study. J Ocean Eng 152:154–166ArticleGoogle Scholar
Koutandos E, Prinos P, Gironella X (2005) Floating breakwaters under regular and irregular wave forcing: reflection and transmission characteristics. J Hydraul Res 43(2):174–188ArticleGoogle Scholar
Liu Zh, Wang Y, Wang W, Hua X (2019) Numerical modeling and optimization of a winged box-type floating breakwater by Smoothed Particle Hydrodynamics. J Ocean Eng 188:106246ArticleGoogle Scholar
LotfollahiYaghin MA, Mojtahedi A, Aminfar MH (2012) Physical model studies and system identification of hydrodynamics around a vertical square-section cylinder in irregular sea waves. J Ocean Eng 55:10–22ArticleGoogle Scholar
Mansard E, Funke E (1980) The measurement of the incident and reflected spectra using the least squares method. In: Proceedings of the 17th Coastal Engineering Conference ASCE, Sydney. pp 154–172
Mojtahedi A, ShokatianBeiragh M, Farajpour I, Mohammadian M (2020) Investigation on hydrodynamic performance of an enviromentally friendly pile breakwater. J Ocean Eng 217:107942ArticleGoogle Scholar
Pena E, Ferreras J, Sanchez-Tembleque F (2011) Experimental study on wave transmission coefficient, mooring lines and module connector forces with different designs of floating breakwaters. J Ocean Eng 38:1150–1160ArticleGoogle Scholar
Safarzadeh A, Zaji AH, Bonakdari H (2017) Comparative Assessment of the Hybrid Genetic Algorithm-Artificial neural network and genetic programming methods for the predicition of longitudinal velocity field around a single straight groyne. Appl Soft Comput 60:213–228ArticleGoogle Scholar
Tang HJ, Huang CC, Chen WM (2011) Dynamics of dual pontoon floating structure for cage aquaculture in a two-dimensional numerical wave tank. J Fluid Struct 27:918–936ArticleGoogle Scholar
U.S. Army coastal engineering research center (1984) Shore protection manual. U.S. Government Printing Office, WashingtonGoogle Scholar
Williams AN, Lee HS, Huang Z (2000) Floating pontoon breakwaters. Ocean Eng 27:221–240ArticleGoogle Scholar
Yang Zh, Xie M, Gao Zh, Xu T, Guo W, Ji X, Yuan Ch (2018) Experimental investigation on hydrodynamic effectiveness of a water ballast type floating breakwater. J Ocean Eng 167:77–94ArticleGoogle Scholar
Zhang X, Ma Sh, Duan W (2018) A new L type floating breakwater derived from vortex dissipation simulation. J Ocean Eng 164:455–464ArticleGoogle Scholar
Comparative study of experimental and CFD analysis for predicting discharge coefficient of compound broad crested weir
ABSTRACT
Present study highlights the behavior of weir crest head and width parameter on the discharge coefficient of compound broad crested (CBC) weir. Computational fluid dynamics model (CFD) is validated with laboratory experimental investigations.
In the discharge analysis through broad crested weirs, the upstream head over the weir crest (h) is crucial, where the result is mainly dependent upon the weir crest length (L) in transverse direction to flow, water depth from channel bed. Currently, minimal investigations are known for CFD validations on compound broad crested weirs.
The hydraulic research for measuring discharge numerically is carried out using FLOW 3D software. The model applies renormalized group (RNG) using volume of fluid (VOF) method for improved accuracy in free surface simulations. Structured hexagonal meshes of cubic elements define discretized meshing.
The comparative analysis of the numerical simulations and experimental observations confirm the performance of CBC weir for precise measurement of a wide range of discharges. Series of CFD model studies and experimental validation have led to constant range of discharg coefficients for various head over weir crest. The correlation coefficient of discharge predictions is 0.999 with mean error of 0.28%.
현재 연구에서는 CBC(compound broad crested) 위어의 배출 계수에 대한 위어 볏 머리 및 너비 매개변수의 거동을 강조합니다. 전산 유체 역학 모델(CFD)은 실험실 실험 조사를 통해 검증되었습니다.
넓은 볏이 있는 둑을 통한 유출 분석에서 둑 마루의 상류 수두(h)가 중요합니다. 여기서 결과는 주로 흐름에 대한 횡 방향의 둑 마루 길이(L), 수로 바닥에서 수심에 따라 달라집니다. . 현재 복합 넓은 볏 둑에 대한 CFD 검증에 대해 최소한의 조사가 알려져 있습니다.
수압 연구는 FLOW 3D 소프트웨어를 사용하여 수치적으로 측정합니다. 이 모델은 자유 표면 시뮬레이션의 정확도 향상을 위해 VOF(유체 체적) 방법을 사용하여 RNG(재정규화 그룹)를 적용합니다. 정육면체 요소의 구조화된 육각형 메쉬는 이산화된 메쉬를 정의합니다.
수치 시뮬레이션과 실험적 관찰의 비교 분석을 통해 광범위한 배출의 정확한 측정을 위한 CBC 둑의 성능을 확인했습니다. 일련의 CFD 모델 연구와 실험적 검증을 통해 다양한 head over weir crest에 대한 일정한 범위의 방전 계수가 나타났습니다. 방전 예측의 상관 계수는 0.999이고 평균 오차는 0.28%입니다.
Figure 1 | Original Compound Broad Crested Weir Model (PVC cast).Figure 4 | CFD Simulation for max discharge (y2 ¼ 13.557 cm, Qmax ¼ 10 lps) and min discharge (y2 ¼ 6.56 cm, Qmin ¼ 2 lps).Figure 5 | (a, b) Velocity profiles corresponding to max discharge (10 lps) and min discharge (2 lps).Table 8 | Range of Froude number, Reynold number and Weber number
Key words
compound weir, flow 3D, flow measurement, numerical technique, open channel
HIGHLIGHTS
• The Head-Discharge relation is established for discharge measurement using compound broad crested weir, experimentally and numerically. • Assessment of head over weir crest for different step widths of proposed weir on discharge coefficient is executed. • Experimental and CFD results of weir performance demonstrate good agreement between the theoretical discharges by traditional rectangular weir formulae keeping Cd constant.
CONCLUSION
The head discharge relationship established for compound rectangular broad crested weir for various discharge ranges was validated by CFD technique. A three dimensional simulation software FLOW 3D was used for this purpose.
Original theoretical compound weir model depicts the relative average error between discharge predictions with Flow 3D simulation as 4.96% which is found less than the predictions made by graphical interpolation technique which is 5.33%.
The standard deviation in Cd parameter for CFD simulation model is less i.e. 0.0146 as compared to experimental output of 0.0502.
The correlation coefficient for physical and CFD studies for modified compound weir model is high, around 0.999 with error in discharge predictions being 0.28% as compared to the accuracy limits of about +3–5% stated in literature so far.
Discharge coefficient by experimental and CFD approach is maintained constant and equal to design input value of 0.6. Thus, the proposed CBC weir can be operated for various discharge ranges by maintaining constant discharge coefficients. Good agreement between the theoretical, experimental and CFD simulation results for obtaining discharge through compound broad crested weir ascertains the fact that CFD model can be used as an effective tool towards modeling flow through compound broad crested weir.
REFERENCES
Abd El-Hady Rady, R. M. 2011 2D 3D modeling of flow over sharp crested weirs. Journal of Applied Sciences Research 7 (12), 2495–2505. ISSN 1819-544X. Ackers, P., White, W. R. & Harrison, A. J. M. 1978 Weirs and Flumes for Flow Measurement. Wiley, New York. Aydin, M. C. 2016 Investigation of a sill effect on rectangular side-weir flow by using CFD. Journal of Irrigation and Drainage Engineering 142 (2), 04015043. Azimi, A. H. & Rajaratnam, N. 2009 Discharge characteristics of weirs of finite crest length. Journal of Hydraulic Engineering 135 (12), 1081–1085. Bijankhan, M., Di Stefano, C., Ferro, V. & Kouchakzadeh, S. 2014 New stage discharge relationship for weirs of finite crest length. Journal of Irrigation and Drainage Engineering 140 (3), 06013006. Boiten, W. & Pitlo, H. R. 1982 The V- shaped broad-crested weir. Journal of Irrigation and Drainage Engineering 108 (2), 142–160. Bos, M. G. 1989 Discharge Measurement Structures, 3rd edn. International Institute for Land Reclamation and Improvement, Publication 20, Wageningen, The Netherlands. Gogus, M., Defne, Z. & Ozkandemir, V. 2006 Broad-crested weirs with rectangular compound cross sections. Journal of Irrigation and Drainage Engineering 132 (3), 272–280.
Gogus, M., Al-Khatib, I. A., Atalay, A. E. & Khatib, J. I. 2016 Discharge prediction in flow measurement flumes with different downstream transition slopes. Flow Measurement and Instrumentation 47, 28–34. Hager, W. H. & Schwalt, M. 1994 Broad – crested weir. Journal of Irrigation and Drainage Engineering 120 (1), 13–25. Harrison, A. J. M. 1967 The streamlined broad-crested weir. Proceedings of the Institution of Civil Engineers 38, 657–678. Hinge, G. A., Balkrishna, S. & Khare, K. C. 2010 Improved design of stilling basin for deficient tail water. Journal of Basic and Applied Scientific Research 1 (1), 31–40. Hinge, G. A., Balkrishna, S. & Khare, K. C. 2011 Experimental and numerical study of compound broad crested weir. International Journal of Fluids Engineering 3 (2), 197–202. Horton, R. E. 1907 Weir Experiments, Coefficients, and Formulas. Dept. of the Interior, U.S. Geological Survey, Water-Supply and Irrigation Paper 200. Government Printing Office, Washington, DC. Khan, L. A., Wicklein, E. A. & Teixeira, E. C. 2006 Validation of a three-dimensional computational fluid dynamics model of a contact tank. Journal of Hydraulic Engineering 132 (7), 741–746. Kindsvater, C. E. & Carter, R. W. 1959 Discharge characteristics of rectangular thin-plate weirs. Paper No. 3001, Transactions, American Society of Civil Engineers 124. Kulin, G. & Compton, P. R. 1975 A Guide to Methods and Standards for the Measurement of Water Flow. Special Publication 421, National Bureau of Standards. Kulkarni, K. H. & Hinge, G. A. 2017 Compound broad crested weir for measurement of discharge – a novel approach. In: Proceedings International Conference Organized by Indian Society of Hydraulics – ISH HYDRO, 21–23 Dec 2017, India, pp. 678–687. Kulkarni, K. H. & Hinge, G. A. 2020 Experimental study for measuring discharge through compound broad crested weir. Flow Measurement Instrumentation 75, 101803. ISSN 0955-5986. Man, C., Zhang, G., Hong, V., Zhou, S. & Feng, Y. 2019 Assessment of turbulence models on bridge-pier scour using flow-3D. World Journal of Engineering and Technology 7, 241–255. ISSN Online: 2331-4249. Omer, B., Cihan, A. M., Emin, E. M. & Miller, C. J. 2018 Experimental and CFD analysis of circular labyrinth weirs. Journal of Irrigation and Drainage Engineering 144 (6), 04018007. RangaRaju, K. G. 1981 Flow Through Open Channels. McGraw-Hill, New York. Roushangar, K., Nouri, A., Shahnazi, S. & Azamathulla, H. M. 2021 Towards design of compound channels with minimum overall cost through grey wolf optimization algorithm. IWA – Journal of Hydroinformatics (In – press). Safarzadeh, A. & Mohajeri, S. H. 2018 Hydrodynamics of rectangular broad-crested porous weir. Journal of Irrigation and Drainage Engineering 144 (10), 04018028. Salmasi, F., Poorescandar, S., Dalir, A. H. & Zadeh, D. F. 2012 Discharge relations for rectangular broad crested weirs. Journal of Agricultural Sciences 17, 324–336. Samadi, A. & Arvanaghi, H. 2014 CFD simulation of flow over contracted compound arched rectangular sharp crested weirs. International Journal of Optimization in Civil Engineering 4 (4), 549–560. Savage, B. M. & Johnson, M. C. 2001 Flow over ogee spillway: physical and numerical model case study. Journal of Hydraulic Engineering 127 (8), 640–649. Swamee, P. K. 1988 Generalized rectangular weir equations. Journal of Hydraulic Engineering 945–952. doi:10.1061/(ASCE),0733-9429 114:8(945). The United States Bureau of Reclamation (USBR) 2001 Water Measurement Manual, Chapter 7 – Weirs. U.S. Government Printing Office, Washington, DC, p. 20402. Available from: http://www/usbr.gov/pmts/hydraulics_lab/pubs/wmm. Zahiri, A. & Azamathulla, H. M. 2014 Comparison between linear genetic programming and M5 tree models to predict flow discharge in compound channels. Neural Computing and Application 24, 413–420.
Numerical Modeling of Failure Mechanisms in Articulated Concrete Block Mattress as a Sustainable Coastal Protection Structure
Author
Ramin Safari Ghaleh(Department of Civil Engineering, K. N. Toosi University of Technology, Tehran 19967-15433, Iran)
Omid Aminoroayaie Yamini(Department of Civil Engineering, K. N. Toosi University of Technology, Tehran 19967-15433, Iran)
S. Hooman Mousavi(Department of Civil Engineering, K. N. Toosi University of Technology, Tehran 19967-15433, Iran)
Mohammad Reza Kavianpour(Department of Civil Engineering, K. N. Toosi University of Technology, Tehran 19967-15433, Iran)
Abstract
해안선 보호는 전 세계적인 우선 순위로 남아 있습니다. 일반적으로 해안 지역은 석회암과 같은 단단하고 비자연적이며 지속 불가능한 재료로 보호됩니다. 시공 속도와 환경 친화성을 높이고 개별 콘크리트 블록 및 보강재의 중량을 줄이기 위해 콘크리트 블록을 ACB 매트(Articulated Concrete Block Mattress)로 설계 및 구현할 수 있습니다. 이 구조물은 필수적인 부분으로 작용하며 방파제 또는 해안선 보호의 둑으로 사용할 수 있습니다. 물리적 모델은 해안 구조물의 현상을 추정하고 조사하는 핵심 도구 중 하나입니다. 그러나 한계와 장애물이 있습니다. 결과적으로, 본 연구에서는 이러한 구조물에 대한 파도의 수치 모델링을 활용하여 방파제에서의 파도 전파를 시뮬레이션하고, VOF가 있는 Flow-3D 소프트웨어를 통해 ACB Mat의 불안정성에 영향을 미치는 요인으로는 파괴파동, 옹벽의 흔들림, 파손으로 인한 인양력으로 인한 장갑의 변위 등이 있다. 본 연구의 가장 중요한 목적은 수치 Flow-3D 모델이 연안 호안의 유체역학적 매개변수를 모사하는 능력을 조사하는 것입니다. 콘크리트 블록 장갑에 대한 파동의 상승 값은 파단 매개변수( 0.5 < ξ m – 1 , 0 < 3.3 )가 증가할 때까지(R u 2 % H m 0 = 1.6) ) 최대값에 도달합니다. 따라서 차단파라미터를 증가시키고 파괴파(ξ m − 1 , 0 > 3.3 ) 유형을 붕괴파/해일파로 변경함으로써 콘크리트 블록 호안의 상대파 상승 변화 경향이 점차 증가합니다. 파동(0.5 < ξ m − 1 , 0 < 3.3 )의 경우 차단기 지수(표면 유사성 매개변수)를 높이면 상대파 런다운의 낮은 값이 크게 감소합니다. 또한, 천이영역에서는 파단파동이 쇄도파에서 붕괴/서징으로의 변화( 3.3 < ξ m – 1 , 0 < 5.0 )에서 상대적 런다운 과정이 더 적은 강도로 발생합니다.
Shoreline protection remains a global priority. Typically, coastal areas are protected by armoring them with hard, non-native, and non-sustainable materials such as limestone. To increase the execution speed and environmental friendliness and reduce the weight of individual concrete blocks and reinforcements, concrete blocks can be designed and implemented as Articulated Concrete Block Mattress (ACB Mat). These structures act as an integral part and can be used as a revetment on the breakwater body or shoreline protection. Physical models are one of the key tools for estimating and investigating the phenomena in coastal structures. However, it does have limitations and obstacles; consequently, in this study, numerical modeling of waves on these structures has been utilized to simulate wave propagation on the breakwater, via Flow-3D software with VOF. Among the factors affecting the instability of ACB Mat are breaking waves as well as the shaking of the revetment and the displacement of the armor due to the uplift force resulting from the failure. The most important purpose of the present study is to investigate the ability of numerical Flow-3D model to simulate hydrodynamic parameters in coastal revetment. The run-up values of the waves on the concrete block armoring will multiply with increasing break parameter ( 0.5 < ξ m − 1 , 0 < 3.3 ) due to the existence of plunging waves until it ( R u 2 % H m 0 = 1.6 ) reaches maximum. Hence, by increasing the breaker parameter and changing breaking waves ( ξ m − 1 , 0 > 3.3 ) type to collapsing waves/surging waves, the trend of relative wave run-up changes on concrete block revetment increases gradually. By increasing the breaker index (surf similarity parameter) in the case of plunging waves ( 0.5 < ξ m − 1 , 0 < 3.3 ), the low values on the relative wave run-down are greatly reduced. Additionally, in the transition region, the change of breaking waves from plunging waves to collapsing/surging ( 3.3 < ξ m − 1 , 0 < 5.0 ), the relative run-down process occurs with less intensity.
Figure 1. Armor geometric characteristics and drawing three-dimensional geometry of a breakwater section in SolidWorks software.Figure 5. Wave overtopping on concrete block mattress in (a) laboratory and (b) numerical model.
![Figure 2.1: Types of Landslides[2]](https://www.flow3d.co.kr/wp-content/uploads/Figure-2.1-Types-of-Landslides2.png)
![Figure 2.1: Types of Landslides[2]](https://flow3d.co.kr/wp-content/uploads/Figure-2.1-Types-of-Landslides2.png)
![Figure 2.2: Landslide Glossary [2]](https://flow3d.co.kr/wp-content/uploads/Figure-2.2-Landslide-Glossary-2.png)
Spillway, Settler 기사: COMEII-21048 소개 
![Fig. 4. Validation of the present numerical model with crossflow boiling over a heated cylindrical rod [40]](https://flow3d.co.kr/wp-content/uploads/Fig.-4.-Validation-of-the-present-numerical-model-with-crossflow-boiling-over-a-heated-cylindrical-rod-40.png)
![Figure 7. The simulated velocity (a) and simulated pressure pattern (b) across the Parshall flume. The patterns match the physical behavior of actual Parshall flumes [7].](https://www.flow3d.co.kr/wp-content/uploads/Figure-7.-The-simulated-velocity-a-and-simulated-pressure-pattern-b-across-the-Parshall-flume.-The-patterns-match-the-physical-behavior-of-actual-Parshall-flumes-7.-.png)
![Figure 1. Parshall flume measuring structure, installed [2].](https://flow3d.co.kr/wp-content/uploads/Figure-1.-Parshall-flume-measuring-structure-installed-2..png)
![Figure 2. Parshall flume measuring structure, uninstalled [3]](https://flow3d.co.kr/wp-content/uploads/Figure-2.-Parshall-flume-measuring-structure-uninstalled-3.png)
![Figure 4. Mesh sensitivity analysis: top view and side view of the Parshall flume: (a) contains 27,000 cells; (b) 52,000 cells; (c) 75,000 cells; (d) 270,000 cells. The C setup was used in their simulation [7].](https://flow3d.co.kr/wp-content/uploads/Figure-4.-Mesh-sensitivity-analysis-top-view-and-side-view-of-the-Parshall-flume-a-contains-27000-cells-b-52000-cells-c-75000-cells-d-270000-cells.-The-C-setup-was-used-in-their-simulation-7..png)
![Figure 7. The simulated velocity (a) and simulated pressure pattern (b) across the Parshall flume. The patterns match the physical behavior of actual Parshall flumes [7].](https://flow3d.co.kr/wp-content/uploads/Figure-7.-The-simulated-velocity-a-and-simulated-pressure-pattern-b-across-the-Parshall-flume.-The-patterns-match-the-physical-behavior-of-actual-Parshall-flumes-7.-.png)
![Figure 8. Computational grid system in the Side A flume. (a) contains a triangular grid system (b) demonstrates the rectangular grid system. (c) and (d) are three-dimensional schematics showing the superimposed grid system. (e) magnifies the dashed section in (b). (Reprinted with permission from Ref. [11]. 2020 ELSEVIER). ).](https://flow3d.co.kr/wp-content/uploads/Figure-8.-Computational-grid-system-in-the-Side-A-flume..png)
![Figure 10. The results of flow patterns in different flumes; (a) Cutthroat flume, (b) airfoil-shaped flume, (c) airfoil pillar-shaped flume, (d) optimized airfoil-shaped flume [23]](https://flow3d.co.kr/wp-content/uploads/Figure-10.-The-results-of-flow-patterns-in-different-flumes-a-Cutthroat-flume-b-airfoil-shaped-flume-c-airfoil-pillar-shaped-flume-d-optimized-airfoil-shaped-flume-23.png)
![Figure 11. Experimental setup: contraction ratio used on each flume [23].](https://flow3d.co.kr/wp-content/uploads/Figure-11.-Experimental-setup-contraction-ratio-used-on-each-flume-23..png)
![Figure 12. Entire flume geometry [25]](https://flow3d.co.kr/wp-content/uploads/Figure-12.-Entire-flume-geometry-25.png)
