Figure 3 Simulation PTC pipes enhanced with copper foam and nanoparticles in FLOW-3D software.

다공성 미디어 및 나노유체에 의해 강화된 수집기로 태양광 CCHP 시스템의 최적화

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) [21215].

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 [1819].

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 1 The 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 1 Schematic shape of the cogeneration cycle.Table 2 Temperature 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]

Also, the auxiliary boiler heat load is [2]

Energy consumed from vapor to expander is calculated by [2]

The power output form by the screw expander [9]:

The efficiency of the expander is 80% in this case [11].

In this step, cooling and heating loads were calculated and then, the required heating load to reach sanitary hot water will be calculated as follows:

First step: calculating the cooling load with the following equation [9]:

Second step: calculating heating loads [9]:

Then, calculating the required loud for sanitary hot water will be [9]

According to the above-mentioned equations, efficiency is [9]

In the third step, calculated exergy analysis as follows.

First, the received exergy collector from the sun is calculated [9]:

In the previous equation, f is the constant of air dilution.

The received exergy from the collector is [9]

In the case of using natural gas in an auxiliary heater, the gas exergy is calculated from the following equation [12]:

Delivering exergy from vapor to expander is calculated with the following equation [9]:

In the fourth step, the exergy in cooling and heating is calculated by the following equation:

Cooling exergy in summer is calculated [9]:

Heating exergy in winter is calculated [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 2 Copper foam with a porosity of 95%.Table 3 Thermophysical 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 3 Simulation 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 4 Properties of the nanoparticles [9].

System constant parameters for input in the software are shown in Table 5.Table 5 System 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 4 Verification charts of energy analysis results.

Figure 5 Verification charts of exergy analysis results.

We may also investigate the application of machine learning paradigms [3141] and various hybrid, advanced optimization approaches that are enhanced in terms of exploration and intensification [4255], and intelligent model studies [5661] as well, for example, methods such as particle swarm optimizer (PSO) [6062], differential search (DS) [63], ant colony optimizer (ACO) [616465], Harris hawks optimizer (HHO) [66], grey wolf optimizer (GWO) [5367], differential evolution (DE) [6869], and other fusion and boosted systems [4146485054557071].

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 [922263072]. 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 6 Collectors 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 6 Energy and exergy efficiencies of the PTC with porous media and nanofluid.

Figure 7 Energy 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.

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Energy and exergy analysis of an enhanced solar CCHP system with a collector embedded by porous media and nano fluid

Energy and exergy analysis of an enhanced solar CCHP system with a collector embedded by porous media and nano fluid

Year 2021, Volume 7, Issue 6, 1489 – 1505, 02.09.2021

N. TONEKABONI  H. SALARIAN  M. Eshagh NIMVARI  J. KHALEGHINIA https://doi.org/10.18186/thermal.990897

Abstract

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.

Keywords

Exergy analysisSolar cogeneration systemPorous mediaNanofluid

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Details

Primary LanguageEnglish
SubjectsEngineering
Journal SectionArticles
AuthorsN. TONEKABONI  This is me
Islamic Azad University Nour Branch
0000-0002-1563-4407
IranH. SALARIAN  This is me (Primary Author)
Islamic Azad University Nour Branch
0000-0002-2161-0276
IranM. Eshagh NIMVARI  This is me
Amol University of Special Modern Technologies
0000-0002-7401-315X
IranJ. KHALEGHINIA  This is me
Islamic Azad University Nour Branch
0000-0001-5357-193X
Iran
Publication DateSeptember 2, 2021
Application DateDecember 28, 2020
Acceptance DateMay 9, 2020
Published in IssueYear 2021, Volume 7, Issue 6
Fig. 2 Schematic diagram of the experimental Rijke tube

RIJKE 튜브 내부의 열음향 장에 대한 새로운 조사

A novel investigation of the thermoacoustic field inside a Rijke tube

B. EntezamW. Van Moorhem and J. MajdalaniPublished Online:22 Aug 2012 https://doi.org/10.2514/6.1998-2582

Abstract

이 논문에서는 Rijke 튜브 내부의 시간 종속 유동장의 실험 연구 및 계산 시뮬레이션에서 진행한 결과를 제시하고 해석합니다. 기존의 추측과 스케일링 분석을 기반으로 한 이론적 논의가 진행됩니다. 주요 결과에는 열 구동 진동에서 중요한 역할을 하는 것으로 보이는 유사성 매개변수가 포함됩니다. 이 매개변수는 열 섭동을 속도, 압력 및 특성 길이의 제곱과 관련시킵니다. 열 진동을 압력 및 속도 진동의 결합된 효과에 기인하는 간단한 이론은 계산, 실험 및 스케일링 고려 사항을 통해 논의됩니다. 이전의 분석 이론은 열 진동을 속도 또는 압력 진동에 연결했기 때문에 현재 분석 모델은 기존 추측에 동의하고 조정합니다. Rayleigh 기준에 따라 열원은 Rijke-tube 하단에서 1/4의 임계 거리에 위치해야 공명이 발생합니다. 이 관찰은 결합이 최대화되는 임계점이 음향 속도와 압력의 곱인 음향 강도가 가장 큰 공간 위치에 해당하기 때문에 제안된 해석을 확인합니다. 수치 시뮬레이션은 Rijke 튜브 내부의 압력 진동이 열 입력이 증가함에 따라 기하급수적으로 증가한다는 것을 보여줍니다. 충분히 작은 열 입력으로 음향 싱크가 소스를 초과하고 음향 감쇠가 발생합니다. 열 입력이 임계 임계값 이상으로 증가하면 음향 싱크가 불충분해져서 ​​내부 에너지 축적으로 인해 빠른 음향 증폭이 발생합니다.

In this paper, results proceeding from experimental studies and computational simulations of the time-dependent flowfield inside a Rijke tube are presented and interpreted. A theoretical discussion based on existing speculations and scaling analyses is carried out. The main results include a similarity parameter that appears to play an important role in the heat driven oscillations. This parameter relates heat perturbations to velocity, pressure, and the square of a characteristic length. A simple theory that attributes heat oscillations to the combined effects of pressure and velocity oscillations is discussed via computational, experimental, and scaling considerations. Since previous analytical theories link heat oscillations to either velocity or pressure oscillations, the current analytical model agrees with and reconciles between existing speculations. In compliance with the Rayleigh criterion, it is found that the heat source must be positioned at a critical distance of 1/4 from the Rijke-tube lower end for resonance to occur. This observation confirms our proposed interpretation since the critical point where coupling is maximized corresponds to a spatial location where the acoustic intensity, product of both acoustic velocities and pressures, is largest. Numerical simulations show that pressure oscillations inside the Rijke tube grow exponentially with increasing heat input With a sufficiently small heat input, the acoustic sinks exceed the sources and acoustic damping takes place. When the heat input is augmented beyond a critical threshold, acoustic sinks become insufficient causing rapid acoustic amplification by virtue of internal energy accumulation.

Fig. 2 Schematic diagram of the experimental Rijke tube
Fig. 2 Schematic diagram of the experimental Rijke tube
A novel investigation of the thermoacoustic field inside a Rijke tube
A novel investigation of the thermoacoustic field inside a Rijke tube

References

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Fig. 2. Schematic indication of the separate parts comprising the rotary kiln model, together with the energy fluxes from Eq. (1).

화염 모델링, 열 전달 및 클링커 화학을 포함한 시멘트 가마에 대한 CFD 예측

E Mastorakos Massias 1C.D Tsakiroglou D.A Goussis V.N Burganos A.C Payatakes 2

Abstract

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)( 석탄 )는 배기 가스(Δ 가스 )와 함께 가마 밖으로 흘러 가마 벽에 직접 복사( rad ) 및 대류( conv )됩니다. 공급 및 배기 덕트( rad,1  + rad,2 ) 에 대한 축 방향의 복사에 의해 작은 부분이 손실됩니다 . 전하 가마 시스템은 복사( rad ) 및 대류( conv )에 의해 가스로부터 에너지(Δ cl )를 흡수 하고 주변으로 열을 잃습니다( Q 손실 ). 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 w ( in , x , ϕ ) 의 각도 분포 가 알려져 있다고 가정합니다 . 그런 다음 전체 3차원 문제를 “동등한” 축대칭 문제로 줄이기 위해 가상의 내벽 온도 RAD ( x )는(2)2πε에티4라드(x) = ε클∫0ㄷ티4클(엑스)디ϕ + ε에∫ㄷ2π티4에(아르 자형~에, x, ϕ)디ϕ”효과적인” 경계 조건으로 사용할 수 있습니다. 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.  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 w ( 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 sh = w ( 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 rad ( x , ϕ ) 의 계산은 다른 각도 위치로부터의 복사를 포함할 필요 없이 가스 ( r , x ) 및 로컬 w ( 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 rad ( x )는 어떤 의미에서 방위각으로 평균된 열유속입니다. 식 따라서 (3a) 는 우리가 이 열유속을 모든 ϕ 에 등분포한다는 것을 의미합니다 . Eq 에서 rad 의 각도 변화를 무시한다는 점에 유의하십시오 . (3a) 는 Refs. [10] 또는 [11] 이 우선되어야 합니다.

소성로와 장입물 사이의 열전달 계수 w-cl 은 소성로의 에너지 흐름과 온도를 정확하게 예측하는 데 중요하지만 잘 알려져 있지 않습니다. 500 W / m의 전형적인 값  K는 여기에 제시된 결과 사용되고있다 [8] . 계산된 w ( r , x , ϕ ) 및 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 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 cl 은 속도 cl 로 흐르는 전하가 덮는 단면적 이며 둘 다 일정하다고 가정하고 gcl =2 in sin( Θ /2) 전하로 덮인 섹터의 현( 그림 1 ) , WCL = Θ 에서는 , 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 cl 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+무엇2k = 108특급(−175728/RT)
(Ⅱ)높은+2SiO2→C2Sk = 107특급(−240000/RT)
(Ⅲ)높은+C2S→C3Sk = 109특급(−420000/RT)
(IV)3높은+로2그만큼3→C3Ak = 108특급(−310000/RT)
(V)4높은+로2그만큼3+철2그만큼3→Q4AFk = 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 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 w–cl ( x , ϕ ).

2.5 . 최종 커플링

전체 문제(가스, 가마, 장입)는 반복 방식으로 해결되었습니다. RAD 의 균일한 분포에서 시작 하여 기체상은 rad ( x ) 및 conv ( x ) 의 축 분포를 제공하도록 해결되었습니다 . 이것들은 다음에서 사용되었습니다., 그 솔루션의 새로운 추정 결과 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 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 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

수송소용돌이중고등 학년석탄
m (kg/s)2.2531.7592.91045.9304.0
 (m/s)77.136.576.112.7336.5
V (m/s)−20.7063.900
W (m/s)00112.800
 (케이)3183833181273383

표 2 . 클링커 조성(질량 분율)

밀가루가마 입구가마 출구
m (kg/s)50.37439.81532.775
 (케이)11001785
CACO 30.79470.402180
높은00.338010.0229
그런가 20.14340.181430
알 2 O 30.03490.04420
철 2 O 30.02700.034160
C2S000.1808
C3S000.5981
C3A000.0731
Q4AF000.1242
소성 인자00.61.0

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
 (K)300
sh (W/m 2 K)30
w–cl (W/m 2 K)500
ε w , ε cl0.9
ε 0.8
C의 P (클링커) (킬로 / kg K)1.5
ϱ cl (kg/m 3 )1200
fus (kJ/kg)418.4
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 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  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  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( rad  + conv )입니다. 이는 수렴된 솔루션이 식 (3) , 그리고 보다 정확한 암시적 솔버에 의해 개선될 수 있습니다.

표 4 . CFD 그리드 및 가마-클링커 조합에 대한 글로벌 에너지 균형

가스(MW)
라드 , 1−2.47
라드 , 2−2.72
큐 라드−57.12
전환0.04
석탄101.2
Δ 가스41.25
균형2.32
가마 클링커
큐 라드57.12
전환−0.04
손실−10.45
Δ H의 CL40.99
균형5.64

에너지 흐름의 정의는 그림 2 를 참조하십시오 .

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
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1 Also at Department of Mechanical Engineering, University of Patras, Greece.

2 Also at Department of Chemical Engineering, University of Patras, Greece.

Figure 2. (a) Scanning electron microscopy images of Ti6Al4V powder particles and (b) simulated powder bed using discrete element modelling

Laser Powder Bed에서 Laser Drilling에 의한 Keyhole 형성 Ti6Al4V 생체 의학 합금의 융합: 메조스코픽 전산유체역학 시뮬레이션 대 경험적 검증을 사용한 수학적 모델링

Keyhole Formation by Laser Drilling in Laser Powder Bed Fusion of Ti6Al4V Biomedical Alloy: Mesoscopic Computational Fluid Dynamics Simulation versus Mathematical Modelling Using Empirical Validation

Asif Ur Rehman 1,2,3,*
,† , Muhammad Arif Mahmood 4,*
,† , Fatih Pitir 1
, Metin Uymaz Salamci 2,3
,
Andrei C. Popescu 4 and Ion N. Mihailescu 4

Abstract

LPBF(Laser Powder Bed fusion) 공정에서 작동 조건은 열 분포를 기반으로 레이저 유도 키홀 영역을 결정하는 데 필수적입니다. 얕은 구멍과 깊은 구멍으로 분류되는 이러한 영역은 LPBF 프로세스에서 확률과 결함 형성 강도를 제어합니다.

LPBF 프로세스의 핵심 구멍을 연구하고 제어하기 위해 수학적 및 CFD(전산 유체 역학) 모델이 제공됩니다. CFD의 경우 이산 요소 모델링 기법을 사용한 유체 체적 방법이 사용되었으며, 분말 베드 보이드 및 표면에 의한 레이저 빔 흡수를 포함하여 수학적 모델이 개발되었습니다.

동적 용융 풀 거동을 자세히 살펴봅니다. 실험적, CFD 시뮬레이션 및 분석적 컴퓨팅 결과 간에 정량적 비교가 수행되어 좋은 일치를 얻습니다.

LPBF에서 레이저 조사 영역 주변의 온도는 높은 내열성과 분말 입자 사이의 공기로 인해 분말층 주변에 비해 급격히 상승하여 레이저 횡방향 열파의 이동이 느려집니다. LPBF에서 키홀은 에너지 밀도에 의해 제어되는 얕고 깊은 키홀 모드로 분류될 수 있습니다. 에너지 밀도를 높이면 얕은 키홀 구멍 모드가 깊은 키홀 구멍 모드로 바뀝니다.

깊은 키홀 구멍의 에너지 밀도는 다중 반사와 키홀 구멍 내의 2차 반사 빔의 집중으로 인해 더 높아져 재료가 빠르게 기화됩니다.

깊은 키홀 구멍 모드에서는 온도 분포가 높기 때문에 액체 재료가 기화 온도에 가까우므로 얕은 키홀 구멍보다 구멍이 형성될 확률이 훨씬 높습니다. 온도가 급격히 상승하면 재료 밀도가 급격히 떨어지므로 비열과 융해 잠열로 인해 유체 부피가 증가합니다.

그 대가로 표면 장력을 낮추고 용융 풀 균일성에 영향을 미칩니다.

In the laser powder bed fusion (LPBF) process, the operating conditions are essential in determining laser-induced keyhole regimes based on the thermal distribution. These regimes, classified into shallow and deep keyholes, control the probability and defects formation intensity in the LPBF process. To study and control the keyhole in the LPBF process, mathematical and computational fluid dynamics (CFD) models are presented. For CFD, the volume of fluid method with the discrete element modeling technique was used, while a mathematical model was developed by including the laser beam absorption by the powder bed voids and surface. The dynamic melt pool behavior is explored in detail. Quantitative comparisons are made among experimental, CFD simulation and analytical computing results leading to a good correspondence. In LPBF, the temperature around the laser irradiation zone rises rapidly compared to the surroundings in the powder layer due to the high thermal resistance and the air between the powder particles, resulting in a slow travel of laser transverse heat waves. In LPBF, the keyhole can be classified into shallow and deep keyhole mode, controlled by the energy density. Increasing the energy density, the shallow keyhole mode transforms into the deep keyhole mode. The energy density in a deep keyhole is higher due to the multiple reflections and concentrations of secondary reflected beams within the keyhole, causing the material to vaporize quickly. Due to an elevated temperature distribution in deep keyhole mode, the probability of pores forming is much higher than in a shallow keyhole as the liquid material is close to the vaporization temperature. When the temperature increases rapidly, the material density drops quickly, thus, raising the fluid volume due to the specific heat and fusion latent heat. In return, this lowers the surface tension and affects the melt pool uniformity.

Keywords: laser powder bed fusion; computational fluid dynamics; analytical modelling; shallow
and deep keyhole modes; experimental correlation

Figure 1. Powder bed schematic with voids.
Figure 1. Powder bed schematic with voids.
Figure 2. (a) Scanning electron microscopy images of Ti6Al4V powder particles and (b) simulated powder bed using discrete element modelling
Figure 2. (a) Scanning electron microscopy images of Ti6Al4V powder particles and (b) simulated powder bed using discrete element modelling
Figure 3. Temperature field contour formation at various time intervals (a) 0.695 ms, (b) 0.795 ms, (c) 0.995 ms and (d) 1.3 ms.
Figure 3. Temperature field contour formation at various time intervals (a) 0.695 ms, (b) 0.795 ms, (c) 0.995 ms and (d) 1.3 ms.
Figure 4. Detailed view of shallow depth melt mode with temperature field at 0.695 ms
Figure 4. Detailed view of shallow depth melt mode with temperature field at 0.695 ms
Figure 5. Melt flow stream traces formation at various time intervals (a) 0.695 ms, (b) 0.795 ms, (c) 0.995 ms and (d) 1.3 ms
Figure 5. Melt flow stream traces formation at various time intervals (a) 0.695 ms, (b) 0.795 ms, (c) 0.995 ms and (d) 1.3 ms
Figure 6. Density evolution of the melt pool at various time intervals (a) 0.695 ms, (b) 0.795 ms, (c) 0.995 ms and (d) 1.3 ms.
Figure 6. Density evolution of the melt pool at various time intervals (a) 0.695 ms, (b) 0.795 ms, (c) 0.995 ms and (d) 1.3 ms.
Figure 7. Un-melted and melted regions at different time intervals (a) 0.695 ms, (b) 0.795 ms, (c) 0.995 ms and (d) 1.3 ms
Figure 7. Un-melted and melted regions at different time intervals (a) 0.695 ms, (b) 0.795 ms, (c) 0.995 ms and (d) 1.3 ms
Figure 8. Transformation from shallow depth melt flow to deep keyhole formation when laser power increased from (a) 170 W to (b) 200 W
Figure 8. Transformation from shallow depth melt flow to deep keyhole formation when laser power increased from (a) 170 W to (b) 200 W
Figure 9. Stream traces and laser beam multiple reflections in deep keyhole melt flow mode
Figure 9. Stream traces and laser beam multiple reflections in deep keyhole melt flow mode
Figure 10. A comparison between analytical and CFD simulation results for peak thermal distribution value in the deep keyhole formation
Figure 10. A comparison between analytical and CFD simulation results for peak thermal distribution value in the deep keyhole formation
Figure 11. A comparison among experiments [49], CFD and analytical simulations for deep keyhole top width and bottom width
Figure 11. A comparison among experiments [49], CFD and analytical simulations for deep keyhole top width and bottom width

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Experimental and Numerical Investigation of Hydrodynamic Performance of a Sloping Floating Breakwater with and Without Chain-Net

Chain-Net이 있거나 없는 경사 부유식 방파제의 유체역학적 성능에 대한 실험 및 수치적 조사

Experimental and Numerical Investigation of Hydrodynamic Performance of a Sloping Floating Breakwater with and Without Chain-Net

Keywords

  • Sloping floating breakwater
  • Chain net
  • Anchorage system
  • Hydrodynamic performance

Abstract

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.

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Hydraulic Analysis of Submerged Spillway Flows and Performance Evaluation of Chute Aerator Using CFD Modeling: A Case Study of Mangla Dam Spillway

CFD 모델링을 이용한 침수 배수로 흐름의 수리학적 해석 및 슈트 폭기장치 성능 평가: Mangla Dam 배수로 사례 연구

Hydraulic Analysis of Submerged Spillway Flows and Performance Evaluation of Chute Aerator Using CFD Modeling: A Case Study of Mangla Dam Spillway

Muhammad Kaleem SarwarZohaib NisarGhulam NabiFaraz ul HaqIjaz AhmadMuhammad Masood & Noor Muhammad Khan 

Abstract

대용량 배출구가 있는 수중 여수로는 일반적으로 홍수 처리 및 침전물 세척의 이중 기능을 수행하기 위해 댐 정상 아래에 제공됩니다. 이 방수로를 통과하는 홍수 물은 난류 거동을 나타냅니다. 

게다가 이러한 난류의 수력학적 분석은 어려운 작업입니다. 

따라서 본 연구는 파키스탄 Mangla Dam에 건설된 수중 여수로의 수리학적 거동을 수치해석을 통해 조사하는 것을 목적으로 한다. 또한 다양한 작동 조건에서 화기의 유압 성능을 평가했습니다. 

Mangla Spillway의 흐름을 수치적으로 모델링하는 데 전산 유체 역학 코드 FLOW 3D가 사용되었습니다. 레이놀즈 평균 Navier-Stokes 방정식은 난류 흐름을 수치적으로 모델링하기 위해 FLOW 3D에서 사용됩니다. 

연구 결과에 따르면 개발된 모델은 최대 6%의 허용 오차로 흐름 매개변수를 계산하므로 수중 여수로 흐름을 시뮬레이션할 수 있습니다. 

또한, 여수로 슈트 베드 주변 모델에 의해 계산된 공기 농도는 폭기 장치에 램프를 설치한 후 6% 이상으로 상승한 3%로 개발된 모델도 침수형 폭기 장치의 성능을 평가할 수 있음을 보여주었습니다.

Submerged spillways with large capacity outlets are generally provided below the dam crest to perform the dual functions of flood disposal and sediment flushing. Flood water passing through these spillways exhibits turbulent behavior. Moreover; hydraulic analysis of such turbulent flows is a challenging task. Therefore, the present study aims to use numerical simulations to examine the hydraulic behavior of submerged spillways constructed at Mangla Dam, Pakistan. Besides, the hydraulic performance of aerator was also evaluated at different operating conditions. Computational fluid dynamics code FLOW 3D was used to numerically model the flows of Mangla Spillway. Reynolds-averaged Navier–Stokes equations are used in FLOW 3D to numerically model the turbulent flows. The study results indicated that the developed model can simulate the submerged spillway flows as it computed the flow parameters with an acceptable error of up to 6%. Moreover, air concentration computed by model near spillway chute bed was 3% which raised to more than 6% after the installation of ramp on aerator which showed that developed model is also capable of evaluating the performance of submerged spillway aerator.

Keywords

  • Aerator
  • CFD
  • FLOW 3D
  • Froude number
  • Submerged spillway
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Fig. 6. Configuration of Johnson (1958) hydraulic experiment.

전체 수심 범위에서 선박 파고에 대한 방정식

Equation for ship wave crests in the entire range of water depths

Byeong Wook Lee a
, Changhoon Lee b,
*a Coastal Development and Ocean Energy Research Center, Korea Institute of Ocean Science & Technology, 385 Haeyang-ro, Busan, 49111, Republic of Korea
b Department of Civil and Environmental Engineering, Sejong University, 209 Neungdong-ro, Gwangjin-gu, Seoul, 05006, Republic of Korea

ABSTRACT

An equation for ship wave crests y/x in the entire range of water depths is developed using the linear dispersion relation. In deep water, the developed equation is reduced to the equation of Kelvin (1906). The locations of ship wave crests in the x – and y -directions are obtained using a dimensionless constant C. The wave ray angle θc at the cusp locus is determined using the condition that θc is maximal at the cusp locus and the cusp locus angle is determined as αc=−tan−1(y/x)max. Numerical experiments are conducted using the FLOW-3D to simulate ship wave propagation. The cusp locus angles of the FLOW-3D are similar to both those of the present theory and Havelock (1908) theory in the entire range of the Froude number. Both the present theory and the FLOW-3D yield that, with the increase of ship speed, the Froude number increases and does the wavelength. For the Froude number equal to or greater than unity, the wavelength becomes infinitely large and the transverse waves disappear. The wavelengths of the FLOW-3D are slightly smaller than those of the present theory because the FLOW-3D considers the decrease of wavelength due to energy dissipation which happens because of viscosity of water and turbulence of high-speed particle velocities.

Fig. 6. Configuration of Johnson (1958) hydraulic experiment.
Fig. 6. Configuration of Johnson (1958) hydraulic experiment.
Fig. 8. Comparison of ship wave crest patterns: (a) Fr ¼ 0:66 (Us ¼ 6:5m=s,  kh � 0:724π), (b) Fr ¼ 0:86 (Us ¼ 8:5m=s, kh � 0:342π), (c) Fr ¼ 1:21 (Us ¼ 12:0m=s, kh � 0:003π). Line definition: red solid line ¼ present theory; yellow  dashed line ¼ Kelvin theory; white dot ¼ FLOW-3D solution. (For interpretation  of the references to colour in this figure legend, the reader is referred to the  Web version of this article.)
Fig. 8. Comparison of ship wave crest patterns: (a) Fr ¼ 0:66 (Us ¼ 6:5m=s, kh >= 0:724π), (b) Fr ¼ 0:86 (Us ¼ 8:5m=s, kh >= 0:342π), (c) Fr ¼ 1:21 (Us ¼ 12:0m=s, kh >= 0:003π). Line definition: red solid line ¼ present theory; yellow dashed line ¼ Kelvin theory; white dot ¼ FLOW-3D solution. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)

Keywords

Ship wave crests
Cusp locus angle
Entire range of water depths
Theoretical solution
Numerical experiment

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Fig. 11. Velocity vectors along x-direction through the center of the box culvert for B0, B30, B50, and B70 respectively.

Numerical investigation of scour characteristics downstream of blocked culverts

막힌 암거 하류의 세굴 특성 수치 조사

NesreenTahabMaged M.El-FekyaAtef A.El-SaiadaIsmailFathya
aDepartment of Water and Water Structures Engineering, Faculty of Engineering, Zagazig University, Zagazig 44519, Egypt
bLab Manager, Faculty of Engineering, Zagazig University, Zagazig 44519, Egypt

Abstract

횡단 구조물을 통한 막힘은 안정성을 위협하는 위험한 문제 중 하나입니다. 암거의 막힘 형상 및 하류 세굴 특성에 미치는 영향에 관한 연구는 거의 없습니다.

이 연구의 목적은 수면과 세굴 모두에서 상자 암거를 통한 막힘의 작용을 수치적으로 논의하는 것입니다. 이를 위해 FLOW 3D v11.1.0을 사용하여 퇴적물 수송 모델을 조사했습니다.

상자 암거를 통한 다양한 차단 비율이 연구되었습니다. FLOW 3D 모델은 실험 데이터로 보정되었습니다. 결과는 FLOW 3D 프로그램이 세굴 다운스트림 상자 암거를 정확하게 시뮬레이션할 수 있음을 나타냅니다.

막힌 경우에 대한 속도 분포, 최대 세굴 깊이 및 수심을 플롯하고 비차단된 사례(기본 사례)와 비교했습니다.

그 결과 암거 높이의 70% 차단율은 상류의 수심을 암거 높이의 2.3배 증가시키고 평균 유속은 기본 경우보다 3배 더 증가시키는 것으로 입증되었다. 막힘 비율의 함수로 상대 최대 세굴 깊이를 추정하는 방정식이 만들어졌습니다.

Blockage through crossing structures is one of the dangerous problems that threaten its stability. There are few researches concerned with blockage shape in culverts and its effect on characteristics of scour downstream it.

The study’s purpose is to discuss the action of blockage through box culvert on both water surface and scour numerically. A sediment transport model has been investigated for this purpose using FLOW 3D v11.1.0. Different ratios of blockage through box culvert have been studied. The FLOW 3D model was calibrated with experimental data.

The results present that the FLOW 3D program was capable to simulate accurately the scour downstream box culvert. The velocity distribution, maximum scour depth and water depths for blocked cases have been plotted and compared with the non-blocked case (base case).

The results proved that the blockage ratio 70% of culvert height makes the water depth upstream increases by 2.3 times of culvert height and mean velocity increases by 3 times more than in the base case. An equation has been created to estimate the relative maximum scour depth as a function of blockage ratio.

1. Introduction

Local scour is the removal of granular bed material by the action of hydrodynamic forces. As the depth of scour hole increases, the stability of the foundation of the structure may be endangered, with a consequent risk of damage and failure [1]. So the prediction and control of scour is considered to be very important for protecting the water structures from failure. Most previous studies were designed to study the different factors that impact on scour and their relationship with scour hole dimensions like fluid characteristics, flow conditions, bed properties, and culvert geometry. Many previous researches studied the effect of flow rate on scour hole by information Froude number or modified Froude number [2][3][4][5][6]. Cesar Mendoza [6] found a good correlation between the scour depth and the discharge Intensity (Qg−.5D−2.5). Breusers and Raudkiv [7] used shear velocity in the outlet-scour prediction procedure. Ali and Lim [8] used the densimetric Froude number in estimation of the scour depth [1][8][9][10][11][12][13][14]. “The densimetric Froude number presents the ratio of the tractive force on sediment particle to the submerged specific weight of the sediment” [15](1)Fd=uρsρ-1gD50

Ali and Lim [8] pointed to the consequence of tailwater depth on scour behavior [1][2][8][13]. Abida and Townsend [2] indicated that the maximum depth of local scour downstream culvert was varying with the tailwater depth in three ways: first, for very shallow tailwater depths, local scouring decreases with a decrease in tailwater depth; second, when the ratio of tailwater depth to culvert height ranged between 0.2 and 0.7, the scour depth increases with decreasing tailwater depth; and third for a submerged outlet condition. The tailwater depth has only a marginal effect on the maximum depth of scour [2]. Ruff et al. [16] observed that for materials having similar mean grain sizes (d50) but different standard deviations (σ). As (σ) increased, the maximum scour hole depth decreased. Abt et al. [4] mentioned to role of soil type of maximum scour depth. It was noticed that local scour was more dangerous for uniform sands than for well-graded mixtures [1][2][4][9][17][18]. Abt et al [3][19] studied the culvert shape effect on scour hole. The results evidenced that the culvert shape has a limited effect on outlet scour. Under equivalent discharge conditions, it was noted that a square culvert with height equal to the diameter of a circular culvert would reduce scour [16][20]. The scour hole dimension was also effected by the culvert slope. Abt et al. [3][21] showed that the culvert slope is a key element in estimating the culvert flow velocity, the discharge capacity, and sediment transport capability. Abt et al. [21][22] tested experimentally culvert drop height effect on maximum scour depth. It was observed that as the drop height was increasing, the depth of scour was also increasing. From the previous studies, it could have noticed that the most scour prediction formula downstream unblocked culvert was the function of densimetric Froude number, soil properties (d50, σ), tailwater depth and culvert opening size. Blockage is the phenomenon of plugging water structures due to the movement of water flow loaded with sediment and debris. Water structures blockage has a bad effect on water flow where it causes increasing of upstream water level that may cause flooding around the structure and increase of scour rate downstream structures [23][24]. The blockage phenomenon through was studied experimentally and numerical [15][25][26][27][28][29][30][31][32][33]. Jaeger and Lucke [33] studied the debris transport behavior in a natural channel in Australia. Froude number scale model of an existing culvert was used. It was noticed that through rainfall event, the mobility of debris was impressed by stream shape (depth and width). The condition of the vegetation (size and quantities) through the catchment area was the main factor in debris transport. Rigby et al. [26] reported that steep slope was increasing the ability to mobilize debris that form field data of blocked culverts and bridges during a storm in Wollongong city.

Streftaris et al. [32] studied the probability of screen blockage by debris at trash screens through a numerical model to relate between the blockage probability and nature of the area around. Recently, many commercial computational fluid programs (CFD) such as SSIIM, Fluent, and FLOW 3D are used in the analysis of the scour process. Scour and sediment transport numerical model need to validate by using experimental data or field data [34][35][36][37][38]. Epely-Chauvin et al. [36] investigated numerically the effect of a series of parallel spur diked. The experimental data were compared by SSIIM and FLOW 3D program. It was found that the accuracy of calibrated FLOW 3D model was better than SSIIM model. Nielsen et al. [35] used the physical model and FLOW 3D model to analyze the scour process around the pile. The soil around the pile was uniform coarse stones in the physical models that were simulated by regular spheres, porous media, and a mixture of them. The calibrated porous media model can be used to determine the bed shear stress. In partially blocked culverts, there aren’t many studies that explain the blockage impact on scour dimensions. Sorourian et al. [14][15] studied the effect of inlet partial blockage on scour characteristics downstream box culvert. It resulted that the partial blockage at the culvert inlet could be the main factor in estimating the depth of scour. So, this study is aiming to investigate the effects of blockage through a box culvert on flow and scour characteristics by different blockage ratios and compares the results with a non-blocked case. Create a dimensionless equation relates the blockage ratio of the culvert with scour characteristics downstream culvert.

2. Experimental data

The experimental work of the study was conducted in the Hydraulics and Water Engineering Laboratory, Faculty of Engineering, Zagazig University, Egypt. The flume had a rectangular cross-section of 66 cm width, 65.5 cm depth, and 16.2 m long. A rectangular culvert was built with 0.2 m width, 0.2 m height and 3.00 m long with θ = 25° gradually outlet and 0.8 m fixed apron. The model was located on the mid-point of the channel. The sediment part was extended for a distance 2.20 m with 0.66 m width and 0.20 m depth of coarse sand with specific weight 1.60 kg/cm3, d50 = 2.75 mm and σ (d90/d50) = 1.50. The particle size distribution was as shown in Fig. 1. The experimental model was tested for different inlet flow (Q) of 25, 30, 34, 40 l/s for different submerged ratio (S) of 1.25, 1.50, 1.75.

3. Dimensional analysis

A dimensional analysis has been used to reduce the number of variables which affecting on the scour pattern downstream partial blocked culvert. The main factors affecting the maximum scour depth are:(2)ds=f(b.h.L.hb.lb.Q.ud.hu.hd.D50.ρ.ρs.g.ls.dd.ld)

Fig. 2 shows a definition sketch of the experimental model. The maximum scour depth can be written in a dimensionless form as:(3)dsh=f(B.Fd.S)where the ds/h is the relative maximum scour depth.

4. Numerical work

The FLOW 3D is (CFD) program used by many researchers and appeared high accuracy in solving hydrodynamic and sediment transport models in the three dimensions. Numerical simulation with FLOW 3D was performed to study the impacts of blockage ratio through box culvert on shear stress, velocity distribution and the sediment transport in terms of the hydrodynamic features (water surface, velocity and shear stress) and morphological parameters (scour depth and sizes) conditions in accurately and efficiently. The renormalization group (RNG) turbulence model was selected due to its high ability to predict the velocity profiles and turbulent kinetic energy for the flow through culvert [39]. The one-fluid incompressible mode was used to simulate the water surface. Volume of fluid (VOF) method was employed in FLOW 3D to tracks a liquid interface through arbitrary deformations and apply the correct boundary conditions at the interface [40].1.

Governing equations

Three-dimensional Reynolds-averaged Navier Stokes (RANS) equation was applied for incompressible viscous fluid motion. The continuity equation is as following:(4)VF∂ρ∂t+∂∂xρuAx+∂∂yρvAy+∂∂zρwAz=RDIF(5)∂u∂t+1VFuAx∂u∂x+vAy∂u∂y+ωAz∂u∂z=-1ρ∂P∂x+Gx+fx(6)∂v∂t+1VFuAx∂v∂x+vAy∂v∂y+ωAz∂v∂z=-1ρ∂P∂y+Gy+fy(7)∂ω∂t+1VFuAx∂ω∂x+vAy∂ω∂y+ωAz∂ω∂z=-1ρ∂P∂z+Gz+fz

ρ is the fluid density,

VF is the volume fraction,

(x,y,z) is the Cartesian coordinates,

(u,v,w) are the velocity components,

(Ax,Ay,Az) are the area fractions and

RDIF is the turbulent diffusion.

P is the average hydrodynamic pressure,

(Gx, Gy, Gz) are the body accelerations and

(fx, fy, fz) are the viscous accelerations.

The motion of sediment transport (suspended, settling, entrainment, bed load) is estimated by predicting the erosion, advection and deposition process as presented in [41].

The critical shields parameter is (θcr) is defined as the critical shear stress τcr at which sediments begin to move on a flat and horizontal bed [41]:(8)θcr=τcrgd50(ρs-ρ)

The Soulsby–Whitehouse [42] is used to predict the critical shields parameter as:(9)θcr=0.31+1.2d∗+0.0551-e(-0.02d∗)(10)d∗=d50g(Gs-1ν3where:

d* is the dimensionless grain size

Gs is specific weight (Gs = ρs/ρ)

The entrainment coefficient (0.005) was used to scale the scour rates and fit the experimental data. The settling velocity controls the Soulsby deposition equation. The volumetric sediment transport rate per width of the bed is calculated using Van Rijn [43].2.

Meshing and geometry of model

After many trials, it was found that the uniform cell size with 0.03 m cell size is the closest to the experimental results and takes less time. As shown in Fig. 3. In x-direction, the total model length in this direction is 700 cm with mesh planes at −100, 0, 300, 380 and 600 cm respectively from the origin point, in y-direction, the total model length in this direction is 66 cm at distances 0, 23, 43 and 66 cm respectively from the origin point. In z-direction, the total model length in this direction is 120 cm. with mesh planes at −20, 0, 20 and 100 cm respectively.3.

Boundary condition

As shown in Fig. 4, the boundary conditions of the model have been defined to simulate the experimental flow conditions accurately. The upstream boundary was defined as the volume flow rate with a different flow rate. The downstream boundary was defined as specific pressure with different fluid elevation. Both of the right side, the left side, and the bottom boundary were defined as a wall. The top boundary defined as specified pressure with pressure value equals zero.

5. Validation of experimental results and numerical results

The experimental results investigated the flow and scour characteristics downstream culvert due to different flow conditions. The measured value of maximum scour depth is compared with the simulated depth from FLOW 3D model as shown in Fig. 5. The scour results show that the simulated results from the numerical model is quite close to the experimental results with an average error of 3.6%. The water depths in numerical model results is so close to the experimental results as shown in Fig. 6 where the experiment and numerical results are compared at different submerged ratios and flow rates. The results appear maximum error percentage in water depths upstream and downstream the culvert is about 2.37%. This indicated that the FLOW 3D is efficient for the prediction of maximum scour depth and the flow depths downstream box culvert.

6. Computation time

The run time was chosen according to reaching to the stability limit. Hydraulic stability was achieved after 50 s, where the scour development may still go on. For run 1, the numerical simulation was run for 1000 s as shown in Fig. 7 where it mostly reached to scour stability at 800 s. The simulation time was taken 500 s at about 95% of scour stability.

7. Analysis and discussions

Fig. 8 shows the study sections where sec 1 represents to upstream section, sec2 represents to inside section and sec3 represents to downstream stream section. Table 1 indicates the scour hole dimensions at different blockage case. The symbol (B) represents to blockage and the number points to blockage ratio. B0 case signifies to the non-blocked case, B30 is that blockage height is 30% to the culvert height and so on.

Table 1. The scour results of different blockage ratio.

Casehb cmB = hb/hQ lit/sSFdd50 mmds/h measuredls/hdd/hld/hds/h estimated
B000351.261.692.50.581.500.275.000.46
B3060.30351.261.682.50.481.250.274.250.40
B50100.50351.221.742.50.451.100.244.000.37
B70140.70351.231.732.50.431.500.165.500.33

7.1. Scour hole geometry

The scour hole geometry mainly depends on the properties of soil of the bed downstream the fixed apron. From Table 1, the results show that the maximum scour depth in B0 case is about 0.58 of culvert height while the maximum deposition in B0 is 0.27 culvert height. There is a symmetric scour hole as shown in Fig. 9 in B0 case. An asymmetric scour hole is created in B50 and B70 due to turbulences that causes the deviation of the jet direction from the center of the flume where appear in Fig. 11 and Fig. 19.

7.2. Flow water surface

Fig. 10 presents the relative free surface water (hw/h) along the x-direction at center of the box culvert. From the mention Figure, it is easy to release the effect of different blockage ratios. The upstream water level rises by increasing the blockage ratio. Increasing upstream water level may cause flooding over the banks of the waterway. In the 70% blockage case, the upstream water level rises to 2.3 times of culvert height more than the non-blocked case at the same discharge and submerged ratio. The water surface profile shows an increase in water level upstream the culvert due to a decrease in transverse velocity. Because of decreasing velocity downstream culvert, there is an increase in water level before it reaches its uniform depth.

7.3. Velocity vectors

Scour downstream hydraulic structures mainly affects by velocities distribution and bed shear stress. Fig. 11 shows the velocity vectors and their magnitude in xz plane at the same flow conditions. The difference in the upstream water level due to the different blockage ratios is so clear. The maximum water level is in B70 and the minimum level is in B0. The inlet mean velocity value is about 0.88 m/s in B0 increases to 2.86 m/s in B70. As the blockage ratio increases, the inlet velocity increases. The outlet velocity in B0 case makes downward jet causes scour hole just after the fixed apron in the middle of the bed while the blockage causes upward water flow that appears clearly in B70. The upward jet decreases the scour depth to 0.13 culvert height less than B0 case. After the scour hole, the velocity decreases and the flow becomes uniform.

7.4. Velocity distribution

Fig. 12 represents flow velocity (Vx) distribution along the vertical depth (z/hu) upstream the inlet for the different blockage ratios at the same flow conditions. From the Figure, the maximum velocity creates closed to bed in B0 while in blocked case, the maximum horizontal velocity creates at 0.30 of relative vertical depth (z/hu). Fig. 13 shows the (Vz) distribution along the vertical depth (z/hu) upstream culvert at sec 1. From the mentioned Figure, it is easy to note that the maximum vertical is in B70 which appears that as the blockage ratio increases the vertical ratio also increases. In the non-blocked case. The vertical velocity (Vz) is maximum at (z/hu) equals 0.64. At the end of the fixed apron (sec 3), the horizontal velocity (Vx) is slowly increasing to reach the maximum value closed to bed in B0 and B30 while the maximum horizontal velocity occurs near to the top surface in B50 and B70 as shown in Fig. 14. The vertical velocity component along the vertical depth (z/hd) is presented in Fig. 15. The vertical velocity (Vz) is maximum in B0 at vertical depth (z/hd) 0.3 with value 0.45 m/s downward. Figs. 16 and 17 observe velocity components (Vx, Vz) along the vertical depth just after the end of blockage length at the centerline of the culvert barrel. It could be noticed the uniform velocity distribution in B0 case with horizontal velocity (Vx) closed to 1.0 m/s and vertical velocity closed to zero. In the blocked case, the maximum horizontal velocity occurs in depth more than the blockage height.

7.5. Bed velocity distribution

Fig. 18 presents the x-velocity vectors at 1.5 cm above the bed for different blockage ratios from the velocity vectors distribution and magnitude, it is easy to realize the position of the scour hole and deposition region. In B0 and B30, the flow is symmetric so that the scour hole is created around the centerline of flow while in B50 and B70 cases, the flow is asymmetric and the scour hole creates in the right of flow direction in B50. The maximum scour depth is found in the left of flow direction in B70 case where the high velocity region is found.

8. Maximum scour depth prediction

Regression analysis is used to estimate maximum scour depth downstream box culvert for different ratios of blockage by correlating the maximum relative scour by other variables that affect on it in one formula. An equation is developed to predict maximum scour depth for blocked and non-blocked. As shown in the equation below, the relative maximum scour depth(ds/hd) is a function of densimetric Froude number (Fd), blockage ratio (B) and submerged ratio (S)(11)dsh=0.56Fd-0.20B+0.45S-1.05

In this equation the coefficient of correlation (R2) is 0.82 with standard error equals 0·08. The developed equation is valid for Fd = [0.9 to 2.10] and submerged ratio (S) ≥ 1.00. Fig. 19 shows the comparison between relative maximum scour depths (ds/h) measured and estimated for different blockage ratios. Fig. 20 clears the comparison between residuals and ds/h estimated for the present study. From these figures, it could be noticed that there is a good agreement between the measured and estimated relative scour depth.

9. Comparison with previous scour equations

Many previous scour formulae have been produced for calculation the maximum scour depth downstream non-blockage culvert. These equations have been included the effect of flow regime, culvert shape, soil properties and the flow rate on maximum scour depth. Two of previous experimental studies data have been chosen to be compared with the present study results in non-blocked study data. Table 2 shows comparison of culvert shape, densmetric Froude number, median particle size and scour equations for these previous studies. By applying the present study data in these studies scour formula as shown in Fig. 21, it could be noticed that there are a good agreement between present formula results and others empirical equations results. Where that Lim [44] and Abt [4] are so closed to the present study data.

Table 2. Comparison of some previous scour formula.

ResearchersFdCulvert shaped50(mm)Proposed equationSubmerged ratio
Present study0.9–2.11square2.75dsh=0.56Fd-0.20B+0.45S-1.051.25–1.75
Lim [44]1–10Circular1.65dsh=0.45Fd0.47
Abt [4]Fd ≥ 1Circular0.22–7.34-dsh=3.67Fd0.57∗D500.4∗σ-0.4

10. Conclusions

The present study has shown that the FLOW 3D model can accurately simulate water surface and the scour hole characteristics downstream the box culvert with error percentage in water depths does not exceed 2.37%. Velocities distribution through and outlets culvert barrel helped on understanding the scour hole shape.

The blockage through culvert had caused of increasing of water surface upstream structure where the upstream water level in B70 was 2.3 of culvert height more than non-blocked case at the same discharge that could be dangerous on the stability of roads above. The depth averaged velocity through culvert barrel increased by 3 times its value in non-blocked case.

On the other hand, blockage through culvert had a limited effect on the maximum scour depth. The little effect of blockage on maximum scour depth could be noticed in Fig. 11. From this Figure, it could be noted that the residual part of culvert barrel after the blockage part had made turbulences. These turbulences caused the deviation of the flow resulting in the formation of asymmetric scour hole on the side of channel. This not only but in B70 the blockage height caused upward jet which made a wide far scour hole as cleared from the results in Table 1.

An empirical equation was developed from the results to estimate the maximum scour depth relative to culvert height function of blockage ratio (B), submerged ratio (S), and densimetric Froude number (Fd). The equation results was compared with some scour formulas at the same densimetric Froude number rang where the present study results was in between the other equations results as shown in Fig. 21.

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.

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Peer review under responsibility of Faculty of Engineering, Alexandria University.

Dynamic Pressure at Flip Buckets of Chute Spillways

낙하 배수로의 플립 버킷에서의 동적 압력: 수치 해석

Dynamic Pressure at Flip Buckets of Chute Spillways: A Numerical Study

International Journal of Civil Engineering (2021)Cite this article

Abstract

이 연구는 이러한 구조물의 가장 중요한 설계 매개변수 중 하나인 슈트 여수로의 플립 버킷에서 동적 압력을 조사합니다. 첫째, 압력에 영향을 미치는 무차원 매개변수를 치수해석을 통해 결정하였다.

그 후, 플립 버킷으로 이어지는 슈트 여수로가 있는 선택된 댐의 특성에 따라 플립 버킷으로의 특정 Froude 수 간격과 슈트 경사 각도, 반경 및 플립 버킷 곡률 각도가 분석을 위해 선택되었습니다.

이러한 매개변수의 조합으로 FLOW-3D에서 총 137개 모델을 시뮬레이션하여 플립 버킷의 바닥 압력과 최대 압력 값을 얻었습니다.

다음으로 고려된 무차원 매개변수를 기반으로 다중 회귀 분석을 사용하여 슈트의 플립 버킷 다운스트림에서 바닥 압력과 최대 압력을 결정하기 위한 방정식이 제안되었습니다. 수치 모델링 실행 결과와 다중 회귀 분석을 사용하여 무차원 압력 관계의 미지의 계수를 결정하고 바닥 압력과 최대 압력에 대한 최종 방정식을 제시했습니다.

저압과 최고압을 결정하기 위해 제안된 식의 상관계수와 MAPE(Mean Absolute Percentage Error) 값은 각각 0.94와 0.96, 6.75%와 8.49%였습니다.

이 값은 제안된 방정식의 적절한 정확도를 나타냅니다. 제안된 방정식에서 Froude 수, 상대 곡률, 슈트 경사각, 이륙 각도 및 플립 버킷의 곡률 각도가 각각 저면 압력과 최대 압력에 가장 큰 영향을 미쳤습니다.

This study investigates the dynamic pressure at the flip buckets of chute spillways, which is one of the most important design parameters of these structures. First, the dimensionless parameters affecting pressure were determined by dimensional analysis. Following that, according to the characteristics of selected dams with chute spillways leading to flip buckets, certain Froude number intervals of inflow to the flip bucket, as well as the chute slope angle, radius, and flip bucket curvature angle were selected for analysis. The combination of these parameters resulted in a total of 137 models simulated in FLOW-3D to obtain bottom pressure and maximum pressure values in the flip bucket. Next, based on the dimensionless parameters considered, equations were proposed to determine the bottom pressure and maximum pressure in the flip bucket downstream of the chute, using multiple regression analysis. Using the numerical modeling run results, along with multiple regression analyses, the unknown coefficients of the dimensionless pressure relationship were determined, and final equations for the bottom pressure and maximum pressure were presented. The correlation coefficient and Mean Absolute Percentage Error (MAPE) values of the proposed equations for determining the bottom pressure and maximum pressure were 0.94 and 0.96, and, 6.75% and 8.49%, respectively. These values indicate the appropriate accuracy of the proposed equations. In the proposed equations, the Froude number, relative curvature, chute slope angle, takeoff angle, and flip bucket’s curvature angle, respectively, had the highest impacts on the bottom pressure and maximum pressure.

Keywords

  • Dam spillway
  • Flip bucket
  • Ski jump
  • Dynamic pressure
  • Numerical modeling
  • FLOW-3D
  • Fig. 1extended data figure 1
  • Fig. 2extended data figure 2
  • Fig. 3extended data figure 3
  • Fig. 4extended data figure 4
  • Fig. 5extended data figure 5
  • Fig. 6extended data figure 6
  • Fig. 7extended data figure 7
  • Fig. 8extended data figure 8
  • Fig. 9extended data figure 9
  • Fig. 10extended data figure 10

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Design of Inductive Sensor System for Wear Particles in Oil

금속재료 표면의 잔류응력 초음파 측정법

Design of Inductive Sensor System for Wear Particles in Oil

NIU Ze, LI Kai, BAI Wenbin, SUN Yuanyuan, GONG Qingqing, HAN Yan
Shanxi Provincial Key Laboratory of Information Detection and Processing, North University of China, Taiyuan 030051

Abstract

오일의 연마 입자는 엔진 및 기타 장비의 마모 상태를 반영할 수 있습니다.오일 금속 연마 입자의 온라인 모니터링을 실현하기 위해 전자기 원리에 기반한 3코일 센서의 수학적 모델이 설정되었습니다. 유도 및 센서의 최적 구조 매개변수(내경), 간격, 너비 등), 간섭성 복조 모델을 사용하여 마모 입자 신호를 추출하고 마모 입자 신호의 생성 원리를 분석합니다. 

시스템은 다층 차폐 구조를 채택하여 외부 자기장 간섭을 효과적으로 줄일 수 있으며 설계된 센서 감지 시스템은 관련 테스트를 위해 팬 기어 박스의 오일 회로에 연결됩니다. 테스트 결과 시스템은 마모 입자 신호를 효과적으로 추출할 수 있으며 마모 입자 신호는 동시에 연마 입자의 속도와 크기에 영향을 받습니다.

1-18의 유속에서 187μm 강자성을 달성할 수 있습니다 L/min 금속 연마 입자 및 578μm 비강자성 금속 연마 입자의 검출은 BP 신경망과 결합되어 오일 금속 연마 입자의 특성 매개변수를 적응적으로 구별할 수 있으며, 이는 오일 연마 입자의 개발에 대한 이론적 지원을 제공합니다.

미래의 라인 모니터링 장비 그리고 기술 지원은 기계 장비의 고장 진단을 위한 중요한 기반을 제공합니다.

Key words

oil,wear particle detection,coherent demodulation,multilayer shielding

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Fig. 5 Comparison of experimental SEM image and CtFD simulated melt pool with beam diameters of(a)700 μm,(b)1000 μm, and(c)1300 μm and an absorption rate of 0.3. Electron beam power and scan speed are 900 W and 100 mm s-1, respectively

추가 생산용 전자빔 조사에 의한 316L 스테인리스 용융 · 응고 거동

Melting and Solidification Behavior of 316L Steel Induced by Electron-Beam Irradiation for Additive Manufacturing

付加製造用電子ビーム照射による 316L ステンレス鋼の溶融・凝固挙動

奥 川 将 行*・宮 田 雄一朗*・王     雷*・能 勢 和 史*
小 泉 雄一郎*・中 野 貴 由*
Masayuki OKUGAWA, Yuichiro MIYATA, Lei WANG, Kazufumi NOSE,
Yuichiro KOIZUMI and Takayoshi NAKANO

Abstract

적층 제조(AM) 기술은 복잡한 형상의 3D 부품을 쉽게 만들고 미세 구조 제어를 통해 재료 특성을 크게 제어할 수 있기 때문에 많은 관심을 받았습니다. PBF(Powderbed fusion) 방식의 AM 공정에서는 금속 분말을 레이저나 전자빔으로 녹이고 응고시키는 과정을 반복하여 3D 부품을 제작합니다.

일반적으로 응고 미세구조는 Hunt[Mater. 과학. 영어 65, 75(1984)]. 그러나 CET 이론이 일반 316L 스테인리스강에서도 높은 G와 R로 인해 PBF형 AM 공정에 적용될 수 있을지는 불확실하다.

본 연구에서는 미세구조와 응고 조건 간의 관계를 밝히기 위해 전자빔 조사에 의해 유도된 316L 강의 응고 미세구조를 분석하고 CtFD(Computational Thermal-Fluid Dynamics) 방법을 사용하여 고체/액체 계면에서의 응고 조건을 평가했습니다.

CET 이론과 반대로 높은 G 조건에서 등축 결정립이 종종 형성되는 것으로 밝혀졌다. CtFD 시뮬레이션은 약 400 mm s-1의 속도까지 유체 흐름이 있음을 보여 주며 수상 돌기의 파편 및 이동의 영향으로 등축 결정립이 형성됨을 시사했습니다.

Additive manufacturing(AM)technologies have attracted much attention because it enables us to build 3D parts with complicated geometry easily and control material properties significantly via the control of microstructures. In the powderbed fusion(PBF)type AM process, 3D parts are fabricated by repeating a process of melting and solidifying metal powders by laser or electron beams. In general, the solidification microstructures can be predicted from solidification conditions defined by the combination of temperature gradient G and solidification rate R on the basis of columnar-equiaxed transition(CET)theory proposed by Hunt [Mater. Sci. Eng. 65, 75(1984)]. However, it is unclear whether the CET theory can be applied to the PBF type AM process because of the high G and R, even for general 316L stainless steel. In this study, to reveal relationships between microstructures and solidification conditions, we have analyzed solidification microstructures of 316L steel induced by electronbeam irradiation and evaluated solidification conditions at the solid/liquid interface using a computational thermal-fluid dynamics (CtFD)method. It was found that equiaxed grains were often formed under high G conditions contrary to the CET theory. CtFD simulation revealed that there is a fluid flow up to a velocity of about 400 mm s-1, and suggested that equiaxed grains are formed owing to the effect of fragmentations and migrations of dendrites.

Keywords

Additive Manufacturing, 316L Stainless Steel, Powder Bed Fusion, Electron Beam Melting, Computational Thermal
Fluid Dynamics Simulation

Fig. 1 Width, height, and height differences calculated from laser microscope analysis of melt tracks formed by scanning electron beam. Fig. 2(a)Scanning electron microscope(SEM)image and(b) corresponding electron back-scattering diffraction(EBSD) IPF-map taken from the electron-beam irradiated region in P900-V100 sample. Fig. 3 Average grain size and their aspect ratio calculated from EBSD IPF-map taken from the electron-beam irradiated region.
Fig. 1 Width, height, and height differences calculated from laser microscope analysis of melt tracks formed by scanning electron beam. Fig. 2(a)Scanning electron microscope(SEM)image and(b) corresponding electron back-scattering diffraction(EBSD) IPF-map taken from the electron-beam irradiated region in P900-V100 sample. Fig. 3 Average grain size and their aspect ratio calculated from EBSD IPF-map taken from the electron-beam irradiated region.
Fig. 4 Comparison of experimental SEM image and computational thermal fluid dynamics(CtFD)simulated melt pool with a beam diameter of 700 μm and absorption rates of(a)0.3,(b)0.5, and (c)0.7. Electron beam power and scan speed are 900 W and 100 mm s-1, respectively.
Fig. 4 Comparison of experimental SEM image and computational thermal fluid dynamics(CtFD)simulated melt pool with a beam diameter of 700 μm and absorption rates of(a)0.3,(b)0.5, and (c)0.7. Electron beam power and scan speed are 900 W and 100 mm s-1, respectively.
Fig. 5 Comparison of experimental SEM image and CtFD simulated melt pool with beam diameters of(a)700 μm,(b)1000 μm, and(c)1300 μm and an absorption rate of 0.3. Electron beam power and scan speed are 900 W and 100 mm s-1, respectively
Fig. 5 Comparison of experimental SEM image and CtFD simulated melt pool with beam diameters of(a)700 μm,(b)1000 μm, and(c)1300 μm and an absorption rate of 0.3. Electron beam power and scan speed are 900 W and 100 mm s-1, respectively
Fig. 6 Depth of melt tracks calculated from experimental SEM image and CtFD simulation results.
Fig. 6 Depth of melt tracks calculated from experimental SEM image and CtFD simulation results.
Fig. 7 G-R plots of 316L steel colored by(a)aspect ratio of crystalline grains and(b)fluid velocity.
Fig. 7 G-R plots of 316L steel colored by(a)aspect ratio of crystalline grains and(b)fluid velocity.
Fig. 8 Comparison of solidification microstructure(EBSD IPF-map)of melt region formed by scanning electron beam and corresponding snap shot of CtFD simulation colored by fluid velocity
Fig. 8 Comparison of solidification microstructure(EBSD IPF-map)of melt region formed by scanning electron beam and corresponding snap shot of CtFD simulation colored by fluid velocity

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Numerical study of the dam-break waves and Favre waves down sloped wet rigid-bed at laboratory scale

Numerical study of the dam-break waves and Favre waves down sloped wet rigid-bed at laboratory scale

WenjunLiua  BoWangb  YakunGuoc

a State Key Laboratory of Hydraulics and Mountain River Engineering, College of Water Resource and Hydropower, Sichuan University, Chengdu, 610065, China
State Key Laboratory of Hydraulics and Mountain River Engineering, Sichuan University, College Of Water Resource and Hydropower, Chengdu, 610065, China
faculty of Engineering & Informatics, University of Bradford, BD7 1DP, UK

Abstract

The bed slope and the tailwater depth are two important ones among the factors that affect the propagation of the dam-break flood and Favre waves. Most previous studies have only focused on the macroscopic characteristics of the dam-break flows or Favre waves under the condition of horizontal bed, rather than the internal movement characteristics in sloped channel. The present study applies two numerical models, namely, large eddy simulation (LES) and shallow water equations (SWEs) models embedded in the CFD software package FLOW-3D to analyze the internal movement characteristics of the dam-break flows and Favre waves, such as water level, the velocity distribution, the fluid particles acceleration and the bed shear stress, under the different bed slopes and water depth ratios. The results under the conditions considered in this study show that there is a flow state transition in the flow evolution for the steep bed slope even in water depth ratio α = 0.1 (α is the ratio of the tailwater depth to the reservoir water depth). The flow state transition shows that the wavefront changes from a breaking state to undular. Such flow transition is not observed for the horizontal slope and mild bed slope. The existence of the Favre waves leads to a significant increase of the vertical velocity and the vertical acceleration. In this situation, the SWEs model has poor prediction. Analysis reveals that the variation of the maximum bed shear stress is affected by both the bed slope and tailwater depth. Under the same bed slope (e.g., S0 = 0.02), the maximum bed shear stress position develops downstream of the dam when α = 0.1, while it develops towards the end of the reservoir when α = 0.7. For the same water depth ratio (e.g., α = 0.7), the maximum bed shear stress position always locates within the reservoir at S0 = 0.02, while it appears in the downstream of the dam for S0 = 0 and 0.003 after the flow evolves for a while. The comparison between the numerical simulation and experimental measurements shows that the LES model can predict the internal movement characteristics with satisfactory accuracy. This study improves the understanding of the effect of both the bed slope and the tailwater depth on the internal movement characteristics of the dam-break flows and Favre waves, which also provides a valuable reference for determining the flood embankment height and designing the channel bed anti-scouring facility.

댐붕괴 홍수와 파브르 파도의 전파에 영향을 미치는 요인 중 하상경사와 후미수심은 두 가지 중요한 요소이다. 대부분의 선행 연구들은 경사 수로에서의 내부 이동 특성보다는 수평층 조건에서 댐파괴류나 Favre파동의 거시적 특성에만 초점을 맞추었다.

본 연구에서는 CFD 소프트웨어 패키지 FLOW-3D에 내장된 LES(Large Eddy Simulation) 및 SWE(Shallow Water Equation) 모델의 두 가지 수치 모델을 적용하여 댐-파괴 흐름 및 Favre 파도의 내부 이동 특성을 분석합니다.

수위, 속도 분포, 유체 입자 가속도 및 층 전단 응력, 다양한 층 경사 및 수심 비율로. 본 연구에서 고려한 조건하의 결과는 수심비 α = 0.1(α는 저수지 수심에 대한 tailwater 깊이의 비율)에서도 급경사면에 대한 유동상태 전이가 있음을 보여준다. 유동 상태 전이는 파면이 파단 상태에서 비정형으로 변하는 것을 보여줍니다.

수평 경사와 완만한 바닥 경사에서는 이러한 흐름 전이가 관찰되지 않습니다. Favre 파의 존재는 수직 속도와 수직 가속도의 상당한 증가로 이어집니다. 이 상황에서 SWE 모델은 예측이 좋지 않습니다.

분석에 따르면 최대 바닥 전단 응력의 변화는 바닥 경사와 꼬리 수심 모두에 영향을 받습니다. 동일한 바닥 경사(예: S0 = 0.02)에서 최대 바닥 전단 응력 위치는 α = 0.1일 때 댐의 하류에서 발생하고 α = 0.7일 때 저수지의 끝쪽으로 발생합니다.

동일한 수심비(예: α = 0.7)에 대해 최대 바닥 전단 응력 위치는 항상 S0 = 0.02에서 저수지 내에 위치하는 반면, S0 = 0 및 0.003에 대해 흐름이 진화한 후 댐 하류에 나타납니다. 수치적 시뮬레이션과 실험적 측정을 비교한 결과 LES 모델이 내부 움직임 특성을 만족스러운 정확도로 예측할 수 있음을 알 수 있습니다.

본 연구는 댐 파절류 및 Favre파의 내부 이동 특성에 대한 하상 경사 및 후미 수심의 영향에 대한 이해를 향상 시키며, 이는 또한 제방 높이를 결정하고 수로 저반위 설계를 위한 귀중한 참고자료를 제공한다.

Keywords

Figure Numerical study of the dam-break waves and Favre waves down sloped wet rigid-bed at laboratory scale
Figure Numerical study of the dam-break waves and Favre waves down sloped wet rigid-bed at laboratory scale

Dam-break flow, Bed slope, Wet bed, Velocity profile, Bed shear stress, Large eddy simulation
댐파괴유동, 하상경사, 습상, 유속분포, 하상전단응력, 대와류 시뮬레이션

Laser powder bed fusion Figure

A study of transient and steady-state regions from single-track deposition in laser powder bed fusion

SubinShrestha KevinChou

J.B. Speed School of Engineering, University of Louisville, Louisville, KY 40292, United States

Abstract

The surface morphology of parts made by the laser powder bed fusion (L-PBF) process is governed by the flow of the melt pool. The nature of the molten metal flow depends on the material properties, process parameters, and powder-bed particles, etc., and may result in potentially significant variations along a laser scanning path.

This study investigates the formation of transient and steady-state zones through a single-track l-PBF experiment using Inconel 625 powder. Single tracks with lengths of 1 mm and 2 mm were fabricated using 195 W laser power and scan speeds of 400 mm/s or 800 mm/s. The surface morphology of the track was analyzed using a white light interferometer (WLI), and an individual single track can be divided into three distinct zones based on the track width and height.

The initial transient region has a wider and taller solidified track geometry, the region near the end of a scan has a tapered profile with a decreasing track width and height, while the steady-state region in the middle has a smaller variation in the width and height.

A mesoscale numerical model was further developed using FLOW-3D to examine the formation of the transient and steady-state zones. At the start of a scan, strong flow occurs outward and backward, leading to the formation of a wider track with a bump. As the scan continues, the thermal gradient stabilizes, leading to a steady state, which resulted in a very small fluctuation in the width. Furthermore, the tapered end of the scan track is due to the half-lemniscate shape of the melt pool during laser scanning.

L-PBF(Laser Powder Bed fusion) 공정으로 만든 부품의 표면 형태는 용융 풀의 흐름에 따라 결정됩니다. 용융 금속 흐름의 특성은 재료 특성, 공정 매개변수 및 분말층 입자 등에 따라 달라지며 레이저 스캐닝 경로를 따라 잠재적으로 상당한 변동이 발생할 수 있습니다.

이 연구는 Inconel 625 분말을 사용하여 단일 트랙 l-PBF 실험을 통해 과도 및 정상 상태 영역의 형성을 조사합니다. 1 mm 및 2 mm 길이의 단일 트랙은 195 W 레이저 출력과 400 mm/s 또는 800 mm/s의 스캔 속도를 사용하여 제작되었습니다. 트랙의 표면 형태는 백색광 간섭계(WLI)를 사용하여 분석되었으며 개별 단일 트랙은 트랙 너비와 높이에 따라 3개의 별개 영역으로 나눌 수 있습니다.

초기 과도 영역은 더 넓고 더 높은 응고된 트랙 형상을 가지며, 스캔 끝 근처의 영역은 트랙 너비와 높이가 감소하는 테이퍼 프로파일을 갖는 반면, 중간의 정상 상태 영역은 너비와 높이에서 더 작은 변동을 가집니다. 신장. 중간 규모 수치 모델은 과도 및 정상 상태 영역의 형성을 조사하기 위해 FLOW-3D를 사용하여 추가로 개발되었습니다.

스캔이 시작될 때 강한 흐름이 바깥쪽과 뒤쪽으로 발생하여 범프가 있는 더 넓은 트랙이 형성됩니다. 스캔이 계속됨에 따라 열 구배가 안정화되어 정상 상태로 이어지며 폭의 변동이 매우 작습니다. 또한 스캔 트랙의 끝이 가늘어지는 것은 레이저 스캔 중 용융 풀의 반-렘니케이트 모양 때문입니다.

A study of transient and steady-state regions from single-track deposition in laser powder bed fusion
A study of transient and steady-state regions from single-track deposition in laser powder bed fusion

Keywords

Additive manufacturing, Laser powder bed fusion, Numerical modelling, Transient region

Fig6. 실험실 연구에서 계단식 오버 플로우에 대한 쐐기 요소의 선택된 형상 및 배열

Numerical and Experimental Study of Wedge Elements Influence on Hydraulic Parameters and Energy Dissipation over Stepped Spillway in Skimming Flow Regime

Wedge Elements의 수치 및 실험적 연구가 스키밍 흐름 체제에서 계단식 배수로에 대한 유압 매개 변수 및 에너지 소산에 미치는 영향

Authors

  • Kiyoumars Roushangar  1 ; samira akhgar 2
  • 1 Civil Engineering Department, Tabriz University, Tabriz, Iran.
  • 2 Water Engineering Department, Faculty of Civil Engineering, Tabriz University, Tabriz, Iran

Abstract

A stepped spillway is a hydraulic and cost-effective measure to dissipate the energy of large water flow over the spillway. Due to some limitations in stepped spillways, this study has intended a plan to increase and improve the effectiveness of energy depreciation. For this purpose, the effect of the wedge-shaped elements on the velocity and pressure changes over the steps, water level, and energy dissipation downstream the stepped spillway are evaluated.In this regard, several forms of wedge elements are studied with changes in wedge arrangement and the rate of discharge by using a numerical model of Flow-3D, and the appropriate models from the aspect of the most energy depreciation are selected and studied in the laboratory.In the laboratory, 25 experiments were performed on 5 physical models. Numerical and experimental results show that the addition of wedge elements on the stepped spillway has reduced the velocity and water depth downstream of the spillway to about 80% and 30%, respectively, and the energy dissipation over the stepped spillway increased by about 2.7 times. Also, by drawing the distribution profiles of pressure on the edge and the floor of steps, it was observed that the negative pressure in the horizontal section turned into a positive one. Also, negative pressure in the vertical section decreased up to 96% and positive pressure increased about 2 times. As well as increasing the density of the elements, the results that increase the energy dissipation are going to be more remarkable.

요약계단식 배수로는 배수로를 통해 큰 물 흐름의 에너지를 분산시키는 유압적이고 비용 효율적인 조치입니다. 계단식 배수로의 일부 한계로 인해 본 연구는 에너지 감가 상각의 효과를 높이고 개선하기위한 계획을 세웠습니다. 이를 위해 계단, 수위 및 계단식 배수로 하류의 에너지 소실에 대한 속도 및 압력 변화에 대한 쐐기 모양 요소의 영향을 평가합니다. 이와 관련하여 Flow-3D의 수치 모델을 이용하여 쐐기 배열 및 배출 속도의 변화로 여러 형태의 쐐기 요소를 연구하고 가장 에너지 감가 상각 측면에서 적절한 모델을 선택하여 실험실에서 연구합니다. .실험실에서는 5 개의 물리적 모델에 대해 25 개의 실험이 수행되었습니다. 수치 및 실험 결과에 따르면 계단식 배수로에 쐐기 요소를 추가하면 배수로 하류의 속도와 수심이 각각 약 80 % 및 30 %로 감소했으며 계단식 배수로에 대한 에너지 소산은 약 2.7 배 증가했습니다. 또한 계단의 가장자리와 바닥의 압력 분포 프로파일을 그려서 수평 단면의 부압이 양압으로 변하는 것을 관찰했습니다. 또한 수직 부의 부압은 96 %까지 감소했고 양압은 약 2 배 증가했습니다. 요소의 밀도를 높이는 것 외에도 에너지 소산을 증가시키는 결과가 더욱 두드러 질 것입니다.

키워드

Stepped spillway Wedge elements Change of the velocity and pressure Energy dissipation Flow-3D, 계단식 방수로, 웨지 요소 , 속도와 압력의 변화 , 에너지 소산 


Fig. 1. Geometry and alignment of the wedges in the numerical study    Fig. 2. Secondary water depth versus unit flow rate in the simple stepped spillway and stepped spillway with wedge elements.
Fig. 1. Geometry and alignment of the wedges in the numerical study Fig. 2. Secondary water depth versus unit flow rate in the simple stepped spillway and stepped spillway with wedge elements.
Fig6. 실험실 연구에서 계단식 오버 플로우에 대한 쐐기 요소의 선택된 형상 및 배열
Fig6. 실험실 연구에서 계단식 오버 플로우에 대한 쐐기 요소의 선택된 형상 및 배열

 참고 문헌

[1] H. CHANSON. Comparison of energy dissipation between
nappe and skimming flow regimes on stepped chutes. Journal of
hydraulic research, 32.1994, 213-218.
[2] M. R. CHAMANI & N. RAJARATNAM. Jet flow on stepped
spillways. Journal of Hydraulic Engineering, 120.1994, 254-259.
[3] J.A. KELLS. Comparison of energy dissipation between nappe
and skimming flow regimes on stepped chutes discussion. IAHR
Journal of Hydraulic Research 33.1995, 128-133.
[4] M. TABBARA, J. CHATILA & R. AWWAD. Computational
simulation of flow over stepped spillways. Computers &
structures, 83.2005, 2215-2224.
[5] S. RAZI, F. SALMASI & A. H. DALIR. Laboratory Study of
the Effects of Step Number, Slope and Particle Size on Energy
Dissipation in Gabion Stepped Spillways. Amir Kabir Civil
Engineering Journal, 2018.

Fig.1 Schematic diagram of the novel cytometric device

Fabrication and Experimental Investigation of a Novel 3D Hydrodynamic Focusing Micro Cytometric Device

Yongquan Wang*a , Jingyuan Wangb, Hualing Chenc

School of Mechanical Engineering, Xi’an Jiaotong University, Xi’an, Shaanxi, 710049, P. R. China
a yqwang@mail.xjtu.edu.cn,, bwjy2006@stu.xjtu.edu.cn,, c hlchen@mail.xjtu.edu.cn,

Abstract:

This paper presents the fabrication of a novel micro-machined cytometric device, and the experimental investigations for its 3D hydrodynamic focusing performance. The proposed device is simple in structure, with the uniqueness that the depth of its microchannels is non-uniform. Using the SU-8 soft lithography containing two exposures, as well as micro-molding techniques, the PDMS device is successfully fabricated. Two kinds of experiments, i.e., the red ink fluidity observation experiments and the fluorescent optical experiments, are then performed for the device prototypes with different step heights, or channel depth differences, to explore the influence laws of the feature parameter on the devices hydrodynamic focusing behaviors. The experimental results show that the introducing of the steps can efficiently enhance the vertical focusing performance of the device. At appropriate geometry and operating conditions, good 3D hydrodynamic focusing can be obtained.

Korea Abstract

이 논문은 새로운 마이크로 머신 세포 측정 장치의 제조와 3D 유체 역학적 초점 성능에 대한 실험적 조사를 제시합니다. 제안 된 장치는 구조가 단순하며, 마이크로 채널의 깊이가 균일하지 않다는 독특함이 있습니다. 두 가지 노출이 포함 된 SU-8 소프트 리소그래피와 마이크로 몰딩 기술을 사용하여 PDMS 장치가 성공적으로 제작되었습니다. 그런 다음 두 종류의 실험, 즉 적색 잉크 유동성 관찰 실험과 형광 광학 실험을 단계 높이 또는 채널 깊이 차이가 다른 장치 프로토 타입에 대해 수행하여 장치 유체 역학적 초점에 대한 기능 매개 변수의 영향 법칙을 탐색합니다. 행동. 실험 결과는 단계의 도입이 장치의 수직 초점 성능을 효율적으로 향상시킬 수 있음을 보여줍니다. 적절한 형상과 작동 조건에서 우수한 3D 유체 역학적 초점을 얻을 수 있습니다.

Keywords

Flow cytometer, Hydrodynamic focusing, Three-dimensional (3D), Micro-machined

Fig.1 Schematic diagram of the novel cytometric device
Fig.1 Schematic diagram of the novel cytometric device
Fig.2 Overview of the cytometric device fabrication process
Fig.2 Overview of the cytometric device fabrication process
Fig.3 The fabricated micro cytometric device Fig.4 Experiment setup for focusing performance
Fig.3 The fabricated micro cytometric device Fig. 4 Experiment setup for focusing performance
Fig.5 Horizontal focusing images of two devices with and without steps
Fig.5 Horizontal focusing images of two devices with and without steps
Fig.6 Channel cross-section fluorescence images for different step heights
Fig.6 Channel cross-section fluorescence images for different step heights

References 

Fig.7 Effect of the step height on the 3D focusing at different velocity ratios
Fig.7 Effect of the step height on the 3D focusing at different velocity ratios

Conclusions

In this paper, we presented a novel micro-machined cytometric device and its fabrication process,
emphasizing on the experimental investigations for its 3D hydrodynamic focusing performance. The
proposed device is simple in structure, low cost, and easy to be batch produced. Besides this, as a
device based on standard micro-fabrication methodology, it can be conveniently integrated with other
micro-fluidic and/or micro-optical units to form a complete detection and analysis system.
The experimental tests for the prototype devices not only verified the design conception, but also
gave us a comprehensive understanding of the device hydro-focusing performance. The experimental
results show that, as the uniqueness of this design, the introducing of the feature steps can
significantly enhance the vertical focusing performance of the devices, which is crucial for the
achievement of 3D focusing. In summary, for the proposed novel device, good 3D hydrodynamic
focusing can be attained at appropriate geometry and operating conditions.
In addition, an improved design can be obtained by replacing the flat cover with an identical
device unit, in other words, the same two device units are bonded together (The channels are inward
and aligned) to form a new device. Then the sample stream can focused to the center of the assembly
outlet channel due to the hydrodynamic forces equally in both horizontal and vertical directions, and
thus avoiding the adsorption or friction issues of cells/particles to the top channel wall.

References

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Figure 1. (a) Top view of the microfluidic-magnetophoretic device, (b) Schematic representation of the channel cross-sections studied in this work, and (c) the magnet position relative to the channel location (Sepy and Sepz are the magnet separation distances in y and z, respectively).

Continuous-Flow Separation of Magnetic Particles from Biofluids: How Does the Microdevice Geometry Determine the Separation Performance?

1Department of Chemical and Biomolecular Engineering, ETSIIT, University of Cantabria, Avda. Los Castros s/n, 39005 Santander, Spain
2William G. Lowrie Department of Chemical and Biomolecular Engineering, The Ohio State University, 151 W. Woodruff Ave., Columbus, OH 43210, USA
*Author to whom correspondence should be addressed.
Sensors 202020(11), 3030; https://doi.org/10.3390/s20113030
Received: 16 April 2020 / Revised: 21 May 2020 / Accepted: 25 May 2020 / Published: 27 May 2020
(This article belongs to the Special Issue Lab-on-a-Chip and Microfluidic Sensors)

Abstract

The use of functionalized magnetic particles for the detection or separation of multiple chemicals and biomolecules from biofluids continues to attract significant attention. After their incubation with the targeted substances, the beads can be magnetically recovered to perform analysis or diagnostic tests. Particle recovery with permanent magnets in continuous-flow microdevices has gathered great attention in the last decade due to the multiple advantages of microfluidics. As such, great efforts have been made to determine the magnetic and fluidic conditions for achieving complete particle capture; however, less attention has been paid to the effect of the channel geometry on the system performance, although it is key for designing systems that simultaneously provide high particle recovery and flow rates. Herein, we address the optimization of Y-Y-shaped microchannels, where magnetic beads are separated from blood and collected into a buffer stream by applying an external magnetic field. The influence of several geometrical features (namely cross section shape, thickness, length, and volume) on both bead recovery and system throughput is studied. For that purpose, we employ an experimentally validated Computational Fluid Dynamics (CFD) numerical model that considers the dominant forces acting on the beads during separation. Our results indicate that rectangular, long devices display the best performance as they deliver high particle recovery and high throughput. Thus, this methodology could be applied to the rational design of lab-on-a-chip devices for any magnetically driven purification, enrichment or isolation.

Keywords: particle magnetophoresisCFDcross sectionchip fabrication

Korea Abstract

생체 유체에서 여러 화학 물질과 생체 분자의 검출 또는 분리를위한 기능화 된 자성 입자의 사용은 계속해서 상당한 관심을 받고 있습니다. 표적 물질과 함께 배양 한 후 비드를 자기 적으로 회수하여 분석 또는 진단 테스트를 수행 할 수 있습니다. 연속 흐름 마이크로 장치에서 영구 자석을 사용한 입자 회수는 마이크로 유체의 여러 장점으로 인해 지난 10 년 동안 큰 관심을 모았습니다. 

따라서 완전한 입자 포획을 달성하기 위한 자기 및 유체 조건을 결정하기 위해 많은 노력을 기울였습니다. 그러나 높은 입자 회수율과 유속을 동시에 제공하는 시스템을 설계하는 데있어 핵심이기는 하지만 시스템 성능에 대한 채널 형상의 영향에 대해서는 덜주의를 기울였습니다. 

여기에서 우리는 자기 비드가 혈액에서 분리되고 외부 자기장을 적용하여 버퍼 스트림으로 수집되는 YY 모양의 마이크로 채널의 최적화를 다룹니다. 비드 회수 및 시스템 처리량에 대한 여러 기하학적 특징 (즉, 단면 형상, 두께, 길이 및 부피)의 영향을 연구합니다. 

이를 위해 분리 중에 비드에 작용하는 지배적인 힘을 고려하는 실험적으로 검증 된 CFD (Computational Fluid Dynamics) 수치 모델을 사용합니다. 우리의 결과는 직사각형의 긴 장치가 높은 입자 회수율과 높은 처리량을 제공하기 때문에 최고의 성능을 보여줍니다. 

따라서 이 방법론은 자기 구동 정제, 농축 또는 분리를 위한 랩온어 칩 장치의 합리적인 설계에 적용될 수 있습니다.

Figure 1. (a) Top view of the microfluidic-magnetophoretic device, (b) Schematic representation of the channel cross-sections studied in this work, and (c) the magnet position relative to the channel location (Sepy and Sepz are the magnet separation distances in y and z, respectively).
Figure 1. (a) Top view of the microfluidic-magnetophoretic device, (b) Schematic representation of the channel cross-sections studied in this work, and (c) the magnet position relative to the channel location (Sepy and Sepz are the magnet separation distances in y and z, respectively).
Figure 2. (a) Channel-magnet configuration and (b–d) magnetic force distribution in the channel midplane for 2 mm, 5 mm and 10 mm long rectangular (left) and U-shaped (right) devices.
Figure 2. (a) Channel-magnet configuration and (b–d) magnetic force distribution in the channel midplane for 2 mm, 5 mm and 10 mm long rectangular (left) and U-shaped (right) devices.
Figure 3. (a) Velocity distribution in a section perpendicular to the flow for rectangular (left) and U-shaped (right) cross section channels, and (b) particle location in these cross sections.
Figure 3. (a) Velocity distribution in a section perpendicular to the flow for rectangular (left) and U-shaped (right) cross section channels, and (b) particle location in these cross sections.
Figure 4. Influence of fluid flow rate on particle recovery when the applied magnetic force is (a) different and (b) equal in U-shaped and rectangular cross section microdevices.
Figure 4. Influence of fluid flow rate on particle recovery when the applied magnetic force is (a) different and (b) equal in U-shaped and rectangular cross section microdevices.
Figure 5. Magnetic bead capture as a function of fluid flow rate for all of the studied geometries.
Figure 5. Magnetic bead capture as a function of fluid flow rate for all of the studied geometries.
Figure 6. Influence of (a) magnetic and fluidic forces (J parameter) and (b) channel geometry (θ parameter) on particle recovery. Note that U-2mm does not accurately fit a line.
Figure 6. Influence of (a) magnetic and fluidic forces (J parameter) and (b) channel geometry (θ parameter) on particle recovery. Note that U-2mm does not accurately fit a line.
Figure 7. Dependence of bead capture on the (a) functional channel volume and (b) particle residence time (tres). Note that in the curve fitting expressions V represents the functional channel volume and that U-2mm does not accurately fit a line.
Figure 7. Dependence of bead capture on the (a) functional channel volume and (b) particle residence time (tres). Note that in the curve fitting expressions V represents the functional channel volume and that U-2mm does not accurately fit a line.

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Fluid velocity magnitude including velocity vectors and blood volumetric fraction contours for scenario 3: (a,b) Magnet distance d = 0; (c,d) Magnet distance d = 1 mm.

Numerical Analysis of Bead Magnetophoresis from Flowing Blood in a Continuous-Flow Microchannel: Implications to the Bead-Fluid Interactions

Scientific Reports volume 9, Article number: 7265 (2019) Cite this article

Abstract

이 연구에서는 비드 운동과 유체 흐름에 미치는 영향에 대한 자세한 분석을 제공하기 위해 연속 흐름 마이크로 채널 내부의 비드 자기 영동에 대한 수치 흐름 중심 연구를 보고합니다.

수치 모델은 Lagrangian 접근 방식을 포함하며 영구 자석에 의해 생성 된 자기장의 적용에 의해 혈액에서 비드 분리 및 유동 버퍼로의 수집을 예측합니다.

다음 시나리오가 모델링됩니다. (i) 운동량이 유체에서 점 입자로 처리되는 비드로 전달되는 단방향 커플 링, (ii) 비드가 점 입자로 처리되고 운동량이 다음으로부터 전달되는 양방향 결합 비드를 유체로 또는 그 반대로, (iii) 유체 변위에서 비드 체적의 영향을 고려한 양방향 커플 링.

결과는 세 가지 시나리오에서 비드 궤적에 약간의 차이가 있지만 특히 높은 자기력이 비드에 적용될 때 유동장에 상당한 변화가 있음을 나타냅니다.

따라서 높은 자기력을 사용할 때 비드 운동과 유동장의 체적 효과를 고려한 정확한 전체 유동 중심 모델을 해결해야 합니다. 그럼에도 불구하고 비드가 중간 또는 낮은 자기력을 받을 때 계산적으로 저렴한 모델을 안전하게 사용하여 자기 영동을 모델링 할 수 있습니다.

Sketch of the magnetophoresis process in the continuous-flow microdevice.
Sketch of the magnetophoresis process in the continuous-flow microdevice.
Schematic view of the microdevice showing the working conditions set in the simulations.
Schematic view of the microdevice showing the working conditions set in the simulations.
Bead trajectories for different magnetic field conditions, magnet placed at different distances “d” from the channel: (a) d = 0; (b) d = 1 mm; (c) d = 1.5 mm; (d) d = 2 mm
Bead trajectories for different magnetic field conditions, magnet placed at different distances “d” from the channel: (a) d = 0; (b) d = 1 mm; (c) d = 1.5 mm; (d) d = 2 mm
Separation efficacy as a function of the magnet distance. Comparison between one-way and two-way coupling.
Separation efficacy as a function of the magnet distance. Comparison between one-way and two-way coupling.
(a) Fluid velocity magnitude including velocity vectors and (b) blood volumetric fraction contours with magnet distance d = 0 mm for scenario 1 (t = 0.25 s).
(a) Fluid velocity magnitude including velocity vectors and (b) blood volumetric fraction contours with magnet distance d = 0 mm for scenario 1 (t = 0.25 s).
luid velocity magnitude including velocity vectors and blood volumetric fraction contours for scenario 2: (a,b) Magnet distance d = 0 mm at t = 0.4 s; (c,d) Magnet distance d = 1 mm at t = 0.4 s.
luid velocity magnitude including velocity vectors and blood volumetric fraction contours for scenario 2: (a,b) Magnet distance d = 0 mm at t = 0.4 s; (c,d) Magnet distance d = 1 mm at t = 0.4 s.
Fluid velocity magnitude including velocity vectors and blood volumetric fraction contours for scenario 3: (a,b) Magnet distance d = 0; (c,d) Magnet distance d = 1 mm.
Fluid velocity magnitude including velocity vectors and blood volumetric fraction contours for scenario 3: (a,b) Magnet distance d = 0; (c,d) Magnet distance d = 1 mm.
Blood volumetric fraction contours. Scenario 1: (a) Magnet distance d = 0 and (b) Magnet distance d = 1 mm; Scenario 2: (c) Magnet distance d = 0 and (d) Magnet distance d = 1 mm; and Scenario 3: (e) Magnet distance d = 0 and (f) Magnet distance d = 1 mm.
Blood volumetric fraction contours. Scenario 1: (a) Magnet distance d = 0 and (b) Magnet distance d = 1 mm; Scenario 2: (c) Magnet distance d = 0 and (d) Magnet distance d = 1 mm; and Scenario 3: (e) Magnet distance d = 0 and (f) Magnet distance d = 1 mm.

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Author information

  1. Edward P. Furlani is deceased.

Affiliations

  1. Department of Chemical and Biomolecular Engineering, ETSIIT, University of Cantabria, Avda. Los Castros s/n, 39005, Santander, SpainJenifer Gómez-Pastora, Eugenio Bringas & Inmaculada Ortiz
  2. Flow Science, Inc, Santa Fe, New Mexico, 87505, USAIoannis H. Karampelas
  3. Department of Chemical and Biological Engineering, University at Buffalo (SUNY), Buffalo, New York, 14260, USAEdward P. Furlani
  4. Department of Electrical Engineering, University at Buffalo (SUNY), Buffalo, New York, 14260, USAEdward P. Furlani
Hierarchical grain refinement during the laser additive manufacturing of Ti-6Al-4V alloys by the addition of micron-sized refractory particles

Hierarchical grain refinement during the laser additive manufacturing of Ti-6Al-4V alloys by the addition of micron-sized refractory particles

Xiang Wang  Lin-Jie Zhang  Jie Ning  Sen Li  Liang-Liang Zhang  Jian Long
State Key Laboratory for Mechanical Behavior of Materials, Xi’an Jiaotong University, Xi’an 710049, China

Received 22 January 2021, Revised 6 April 2021, Accepted 6 May 2021, Available online 2 June 2021.

Abstract

Ti-6Al-4V alloys mad by additive manufacturing (AM) with slower cooling rate (e. g., direct energy deposition (DED)) generally have the problem of severe coarsening of α phase. This study presents a method to refine the microstructure of the primary β phase formed during the solid–liquid transformation, microstructures formed during the β → α + β transformation, and recrystallized microstructures formed during the repeated heating cycles encountered in AM processes. This is accomplished by the in situ precipitation of nano-sized dispersed high-melting-point yttria Y2O3 particles. The addition of micron-sized particles with high melting points can refine primary crystallized grains and transformed grains corresponding to the secondary phase in Ti-6Al-4V alloys. In addition, they can effectively inhibit the recrystallization and growth of prior-deposited metal grains. The microstructural and tensile properties of laser additive manufactured with filler wire Ti-6Al-4V components with different amounts of Y2O3 (0, 0.12, and 0.22 wt%) were investigated. The refining effect of Y2O3 was significant and the tensile strength of Ti-6Al-4V containing 0.22 wt% Y2O3 in the longitudinal and transverse directions was greater than that of Ti-6Al-4V by approximately 12% and 9%, respectively. Concurrently, there was no loss in the elongation of the material in either direction. The strategy of using micron-sized refractory particles to control phase transformation (primary crystallization, solid-state phase transformation, and recrystallization) can be applied to the AM of different metals, in which microstructures are susceptible to coarsening.

Korea Abstract

더 느린 냉각 속도 (예를 들어, 직접 에너지 증착 (DED))를 가진 적층 제조 (AM)에 의해 미친 Ti-6Al-4V 합금은 일반적으로 α상의 심한 조 대화 문제가 있습니다. 이 연구는 고체-액체 변환 중에 형성된 1 차 β상의 미세 구조, β → α + β 변환 중에 형성된 미세 구조, AM 공정에서 발생하는 반복되는 가열주기 동안 형성된 재결정 화 된 미세 구조를 정제하는 방법을 제시합니다.

이는 나노 크기의 분산 된 고 융점이 트리아 Y2O3 입자의 현장 침전에 의해 달성됩니다. 녹는 점이 높은 미크론 크기의 입자를 추가하면 Ti-6Al-4V 합금의 2 차 상에 해당하는 1 차 결정 입자 및 변형 된 입자를 정제 할 수 있습니다. 또한 사전에 증착 된 금속 입자의 재결정 화 및 성장을 효과적으로 억제 할 수 있습니다.

Y2O3 (0, 0.12, 0.22 wt %)의 양이 다른 필러 와이어 Ti-6Al-4V 성분으로 제조 된 레이저 첨가제의 미세 구조 및 인장 특성을 조사했습니다. Y2O3의 정제 효과는 유의미했으며, Y2O3 0.22 wt %를 세로 및 가로 방향으로 포함하는 Ti-6Al-4V의 인장 강도는 Ti-6Al-4V보다 각각 약 12 ​​% 및 9 % 더 컸습니다.

동시에 어느 방향으로도 재료의 연신율에 손실이 없었습니다. 미크론 크기의 내화 입자를 사용하여 상 변환 (1 차 결정화, 고체 상 변환 및 재결정 화)을 제어하는 ​​전략은 미세 구조가 거칠어지기 쉬운 다양한 금속의 AM에 적용될 수 있습니다.

Hierarchical grain refinement during the laser additive manufacturing of Ti-6Al-4V alloys by the addition of micron-sized refractory particles
Hierarchical grain refinement during the laser additive manufacturing of Ti-6Al-4V alloys by the addition of micron-sized refractory particles
Hierarchical grain refinement during the laser additive manufacturing of Ti-6Al-4V alloys by the addition of micron-sized refractory particles Fig1
Hierarchical grain refinement during the laser additive manufacturing of Ti-6Al-4V alloys by the addition of micron-sized refractory particles Fig1
Hierarchical grain refinement during the laser additive manufacturing of Ti-6Al-4V alloys by the addition of micron-sized refractory particles Fig2
Hierarchical grain refinement during the laser additive manufacturing of Ti-6Al-4V alloys by the addition of micron-sized refractory particles Fig2
Hierarchical grain refinement during the laser additive manufacturing of Ti-6Al-4V alloys by the addition of micron-sized refractory particles Fig3
Hierarchical grain refinement during the laser additive manufacturing of Ti-6Al-4V alloys by the addition of micron-sized refractory particles Fig3
Hierarchical grain refinement during the laser additive manufacturing of Ti-6Al-4V alloys by the addition of micron-sized refractory particles Fig4
Hierarchical grain refinement during the laser additive manufacturing of Ti-6Al-4V alloys by the addition of micron-sized refractory particles Fig4
Hierarchical grain refinement during the laser additive manufacturing of Ti-6Al-4V alloys by the addition of micron-sized refractory particles Fig5
Hierarchical grain refinement during the laser additive manufacturing of Ti-6Al-4V alloys by the addition of micron-sized refractory particles Fig5
Hierarchical grain refinement during the laser additive manufacturing of Ti-6Al-4V alloys by the addition of micron-sized refractory particles Fig6
Hierarchical grain refinement during the laser additive manufacturing of Ti-6Al-4V alloys by the addition of micron-sized refractory particles Fig6
Hierarchical grain refinement during the laser additive manufacturing of Ti-6Al-4V alloys by the addition of micron-sized refractory particles Fig7
Hierarchical grain refinement during the laser additive manufacturing of Ti-6Al-4V alloys by the addition of micron-sized refractory particles Fig7

Keywords

Grain hierarchical refinement, Yttria, Solidification microstructures, Solid phase transition microstructures, Recrystallization microstructures

A new dynamic masking technique for time resolved PIV analysis

A new dynamic masking technique for time resolved PIV analysis

시간 분해 PIV 분석을위한 새로운 동적 마스킹 기술

물체 가시성을 허용하기 위해 형광 코팅과 결합 된 새로운 프리웨어 레이 캐스팅 도구

Journal of Visualization ( 2021 ) 이 기사 인용

Abstract

Time resolved PIV encompassing moving and/or deformable objects interfering with the light source requires the employment of dynamic masking (DM). A few DM techniques have been recently developed, mainly in microfluidics and multiphase flows fields. Most of them require ad-hoc design of the experimental setup, and may spoil the accuracy of the resulting PIV analysis. A new DM technique is here presented which envisages, along with a dedicated masking algorithm, the employment of fluorescent coating to allow for accurate tracking of the object. We show results from measurements obtained through a validated PIV setup demonstrating the need to include a DM step even for objects featuring limited displacements. We compare the proposed algorithm with both a no-masking and a static masking solution. In the framework of developing low cost, flexible and accurate PIV setups, the proposed algorithm is made available through a freeware application able to generate masks to be used by an existing, freeware PIV analysis package.

광원을 방해하는 이동 또는 변형 가능한 물체를 포함하는 시간 해결 PIV는 동적 마스킹 (DM)을 사용해야 합니다. 주로 미세 유체 및 다상 흐름 분야에서 몇 가지 DM 기술이 최근 개발되었습니다. 대부분은 실험 설정의 임시 설계가 필요하며 결과 PIV 분석의 정확도를 떨어 뜨릴 수 있습니다. 여기에는 전용 마스킹 알고리즘과 함께 형광 코팅을 사용하여 물체를 정확하게 추적 할 수있는 새로운 DM 기술이 제시되어 있습니다. 제한된 변위를 특징으로 하는 물체에 대해서도 DM 단계를 포함해야 하는 필요성을 보여주는 검증 된 PIV 설정을 통해 얻은 측정 결과를 보여줍니다. 제안 된 알고리즘을 no-masking 및 static masking 솔루션과 비교합니다. 저비용, 유연하고 정확한 PIV 설정 개발 프레임 워크에서 제안 된 알고리즘은 기존 프리웨어 PIV 분석 패키지에서 사용할 마스크를 생성 할 수 있는 프리웨어 애플리케이션을 통해 사용할 수 있습니다.

Keywords

  • Time resolved PIV, Dynamics masking, Image processing, Vibration inducers, Fluorescent coating

그래픽 개요

소개

PIV (입자 영상 속도계)의 사용은 70 년대 후반 (Archbold 및 Ennos 1972 )이 반점 계측의 확장 (Barker and Fourney 1977 ) 으로 도입된 이래 실험 유체 역학에서 중심적인 역할을 했습니다 . PIV 기술의 기본 아이디어는 유체에 주입된 입자의 속도를 측정하여 유동장을 재구성하는 것입니다. 입자의 크기와 밀도는 확실하게 선택되고 유동을 만족스럽게 따르게 됩니다.

흐름은 레이저 / LED 소스를 통해 조명되고 입자에 의해 산란 된 빛은 추적을 허용합니다. 독자는 리뷰 작품 Grant ( 1997 ), Westerweel et al. ( 2013 년)에 대한 자세한 설명을 참조하십시오. 기본 2D 기술은 고유한 설정으로 발전했으며, 가장 진보 된 것은 단일 / 다중 평면 입체 PIV (Prasad 2000 ) 및 체적 / 단층 PIV (Scarano 2013 )입니다. 광범위한 유동장의 비 침습적 측정이 필요한 산업 및 연구 응용 분야에서 광범위하게 사용되었습니다.

조사된 유동장이 단단한 서있는 경계의 영향을 받는 경우 정적 마스킹 (SM) 접근 방식을 사용하여 PIV 분석을 수행하는 영역에서 솔리드 객체와 그림자가 차지하는 영역을 빼기 위해 주의를 기울여야 합니다. 실제로 이러한 영역에서는 파종 입자를 식별 할 수 없으므로 유속 재구성을 수행 할 수 없습니다. 제대로 처리되지 않으면 이 마스킹 단계는 잘못된 예측으로 이어질 수 있으며, 불행히도 그림자 영역 경계의 근접성에 국한되지 않습니다.

PIV 기술은 획득 프레임 속도를 관심있는 시간 척도로 조정하여 정상 상태 또는 시간 변화 흐름에 적용 할 수 있습니다. 시간의 가변성이 고체 물체의 위치 / 모양과 관련된 경우 이미지를 동적으로 마스킹하기 위해 추가 노력이 필요합니다. 고체 물체뿐만 아니라 다른 유체 단계도 가려야한다는 점에 유의해야합니다 (Foeth et al. 2006). 

이 프로세스는 고체 물체의 움직임이 선험적으로 알려진 경우 비교적 쉬우므로 SM 알고리즘에 대한 최소한의 수정이 목적에 부합 할 수 있습니다. 그러나 고체 물체의 위치 및 / 또는 모양이 알려지지 않은 방식으로 시간에 따라 변할 경우 물체를 동적으로 추적 할 수 있는 마스킹 기술이 필요합니다. PIV 분석을위한 동적 마스킹 (DM) 접근 방식은 현재 상당한 주목을 받고 있습니다 (Sanchis and Jensen 2011 , Masullo 및 Theunissen 2017 , Anders et al. 2019 ) . 시간 분해 PIV 시스템의 확산 덕분에 고속 카메라의 가용성이 높아집니다. 

DM 기술의 주요 발전은 마이크로 PIV 분야에서 비롯됩니다 (Lindken et al. 2009) 마이크로 및 나노 스위 머 (Ergin et al. 2015 ) 및 다상 흐름 (Brücker 2000 , Khalitov 및 Longmire 2002 ) 주변의 유동장을 조사 하려면 정확하고 유연한 알고리즘이 필요합니다. DM 기술은 상용 PIV 분석 소프트웨어 패키지 (TSI Instruments 2014 , DantecDynamics 2018 )에 포함되어 있습니다. 최근 개발 (Vennemann 및 Rösgen 2020 )은 신경망 자동 마스킹 기술의 적용을 예상하지만, 네트워크를 훈련하려면 합성 데이터 세트를 생성해야합니다.

많은 알고리즘은 이미지 처리 기술을 사용하여 개체를 추적하며, 대부분 사용자는 획득 한 이미지에서 추적 할 개체를 강조 표시 할 수있는 임시 실험 설정을 개발해야합니다. 따라서 실험 설정의 설계는 알고리즘의 최종 정확도에 영향을줍니다.

몇 가지 해결책을 구상 할 수 있습니다. 다음에서는 간단한 2D PIV 설정을 참조하지만 대부분의 고려 사항은 더 복잡한 설정으로 확장 할 수 있습니다. PIV 설정에서 객체를 쉽고 정확하게 추적 할 수 있도록 렌더링하는 가장 간단한 방법은 일반적으로 PIV 레이저 시트에 대략 수직 인 카메라를 향한 반사를 최대화하는 방향을 가리키는 추가 광원을 사용하여 조명하는 것입니다. 이 순진한 솔루션과 관련된 주요 문제는 PIV의 ROI (관심 영역)를 비추 지 않고는 광원을 움직이는 물체에만 겨냥하는 것이 사실상 불가능하여 시딩에 의해 산란 된 레이저 광 사이의 명암비를 감소 시킨다는 것입니다. 입자와 어두운 배경.

카메라의 프레임 속도가 높을수록 센서에 닿는 빛의 양이 적다는 사실로 인해 상황이 가혹 해집니다. 고체 물체의 움직임과 유동 입자가 모두 사용 된 설정의 획득 속도에 비해 충분히 느리다면, 가능한 해결책은 레이저 펄스 쌍 사이에 단일 확산 광 샷을 삽입하는 것입니다 (반드시 대칭 삽입은 아님). 그리고 카메라 샷을 둘 모두에 동기화합니다. 각 레이저 커플에서 물체의 위치는 확산 광에 의해 생성 된 이전 샷과 다음 샷의 두 위치를 보간하여 결정될 수 있습니다. 이 접근 방식에는 레이저, 카메라 및 빛을 제어 할 수있는 동기화 장치가 필요합니다.

이 문제에 대한 해결책이 제안되었으며 유체 인터페이스 (Foeth et al. 2006 ; Dussol et al. 2016 ) 의 밝은 반사를 활용 하여 이미지에서 많은 양의 산란 레이저 광을 획득 할 수 있습니다. 고체 표면에는 효과를 높이기 위해 반사 코팅이 제공 될 수 있습니다. 그런 다음 물체는 비정상적으로 큰 입자로 식별되고 경계를 쉽게 추적 할 수 있습니다. 이 솔루션의 단점은 물체 표면에서 산란 된 빛이 레이저 시트에 있지 않은 많은 시딩 입자를 비추어 PIV 분석의 정확도를 점진적으로 저하 시킨다는 것입니다.

위의 접근 방식의 개선은 다른 파장 의 두 번째 동일 평면 레이저 시트 (Driscoll et al. 2003 )를 사용합니다. 첫 번째 레이저 파장을 중심으로 한 좁은 반사 대역. 전체 설정은 매우 비쌀 수 있습니다. 파장 방출의 차이를 이용하여 설정을 저렴하게 만들 수 있습니다. 서로 다른 필터가 장착 된 두 대의 카메라를 적용하면 인터페이스로부터의 반사와 독립적으로 형광 시드 입자를 식별 할 수 있습니다 (Pedocchi et al. 2008 ).

객체의 변위가 작을 때 기본 솔루션은 실제 시간에 따라 변하는 음영 영역에 가장 근접한 하나의 정적 마스크를 추출하는 것입니다. 일반적인 경험 법칙은 예상되는 음영 영역보다 약간 더 크게 마스크를 그려 분석에 포함 된 조명 영역의 양을 단순화하고 최소화하는 것 사이의 최상의 균형을 찾는 것입니다.

본 논문에서는 PIV 분석을위한 DM 문제에 대한 새로운 실험적 접근법을 제안합니다. 우리의 방법은 형광 페인팅을 사용하여 물체를 쉽게 추적 할 수 있도록 하는 기술과 시변 마스크를 생성 할 수있는 특정 오픈 소스 알고리즘을 포함합니다. 이 접근법은 레이저 광에 불투명 한 물체의 큰 변위를 허용함으로써 효과적인 것으로 입증되었습니다. 

우리의 방법인 NM (no-masking)과 SM (static masking) 접근 방식을 비교합니다. 우리의 접근 방식의 타당성을 입증하는 것 외에도 이 백서는 마스킹 단계가 정확한 결과를 얻기 위해 가장 중요하다는 것을 확인합니다. 실제로 물체의 변위가 무시할 수 없는 경우 DM에 대한 리조트는 필수이며 SM 접근 방식은 음영 처리 된 영역의 주변 환경에 국한되지 않는 부정확성을 유발합니다. 

논문의 구조는 다음과 같습니다. 먼저 형광 코팅 기술과 마스킹 소프트웨어를 설명하는 제안된 접근법의 근거를 소개합니다. 그런 다음 PIV 설정에 대한 설명 후 두 벤치 마크 사례를 통해 전체 PIV 체인 분석의 신뢰성을 평가합니다. 그런 다음 제안 된 DM 방법의 결과를 NM 및 SM 솔루션과 비교합니다. 마지막으로 몇 가지 결론이 도출됩니다.

행동 양식

제안 된 DM 기술은 PIV 분석을 위해 캡처 한 동일한 이미지에서 쉽고 정확한 추적 성을 허용하기 위해 움직이는 물체 표면의 형광 코팅을 구상합니다. 물체가 가시화되면 특정 알고리즘이 물체 추적을 수행하고 레이저 위치가 알려지면 (그림 1 참조  ) 음영 영역의 마스킹을 수행합니다.

형광 코팅

코팅은 구조적 매트릭스 에 시판되는 형광 분말 (fluorescein (Taniguchi and Lindsey 2018 ; Taniguchi et al. 2018 )) 의 분산액으로 구성됩니다 . 단단한 물체의 경우 매트릭스는 폴리 에스터 / 에폭시 (대상 재료와의 화학적 호환성에 따라) 투명 수지 일 수 있습니다. 변형 가능한 물체의 경우 매트릭스는 투명한 실리콘 고무로 만들 수 있습니다. 형광 코팅 된 물체는 실행 중에 지속적으로 빛을 방출하기 위해 실험 전에 충분히 오랫동안 조명을 비춰 야합니다. 우리는 4W LED 소스 (그림 2 에서 볼 수 있음)에 20 초 긴 노출이  실험 실행 (몇 초)의 짧은 기간 동안 일관된 형광 방출을 제공하기에 충분하다는 것을 발견했습니다.

우리 실험에서 물체와 입자 크기 사이의 상당한 차이를 감안할 때 전자를 식별하는 것은 간단합니다. 그림  3 은 씨 뿌리기 입자와 물체 모양이 서로 다른 세 번에 겹쳐진 모습을 보여줍니다 (색상은 다른 순간을 나타냄).

대신, 이러한 크기 기반 분류가 가능하지 않은 경우 입자와 물체의 파장을 분리해야합니다. 이러한 분리는 시드 입자에 의해 산란 된 빛과 현저하게 다른 파장에서 방출되는 형광 코팅을 선택하여 달성 할 수 있습니다. 또는 레이저에서 멀리 떨어진 대역에서 방출되는 형광 입자를 이용하는 것 (Pedocchi et al. 2008 ). 두 경우 모두 컬러 이미지 획득의 채널 분리 또는 멀티 카메라 설정의 애드혹 필터링은 물체 식별을 크게 촉진 할 수 있습니다. 우리의 경우에는 그러한 파장 분리를 달성 할 필요가 없습니다. 실제로 형광 코팅의 방출 스펙트럼의 피크는 540nm입니다 (Taniguchi and Lindsey 2018 ; Taniguchi et al. 2018), 사용 된 레이저의 532 nm에 매우 가깝습니다.

마스킹 소프트웨어

DM 용으로 개발 된 알고리즘 은 무료 PIV 분석 패키지 PIVlab (Thielicke 2020 , Thielicke 및 Stamhuis 2014 ) 과 함께 작동하도록 고안된 오픈 소스 프리웨어 GUI 기반 도구 (Prestininzi 및 Lombardi 2021 )입니다. 이것은 세 단계의 순차적 실행으로 구성됩니다 (그림 1 에서 a–b–c라고 함 ). 첫 번째 단계 (a)는 장면에서 레이저 위치를 찾는 데 사용됩니다 (즉, 소스의 좌표를 계산합니다. 장애물에 부딪히는 빛); 두 번째 항목 (b)은 개체 위치를 추적하고 각 프레임의 음영 영역을 계산합니다. 세 번째 항목 (c)은 추적 된 개체 영역과 음영 처리 된 개체 영역을 PIV 알고리즘을위한 단일 마스크로 병합합니다.

각 단계에 대한 자세한 내용은 다음과 같습니다.

  1. (ㅏ)레이저 위치는 프레임 (즉, 획득 한 프레임의 시야 (FOV)) 내에서 가시적 일 수도 있고 아닐 수도 있습니다. 전자의 경우 사용자는 GUI에서 레이저 소스를 클릭하여 찾기 만하면됩니다. 후자의 경우, 사용자는 음영 영역의 경계에 속하는 두 개의 세그먼트 (두 쌍의 점)를 그리도록 요청받습니다. 그러면 FOV 외부에있는 레이저 위치가 두 선의 교차점으로 계산됩니다. 세그먼트로 구성됩니다. 개체 그림자는 ROI 프레임 상자에 도달하는 것으로 간주됩니다.
  2. (비)레이저 위치가 알려지면 물체 추적은 다음과 같이 수행됩니다. 각 프레임의 하나의 채널 (이 경우 RGB 색상 공간이 사용되기 때문에 녹색 채널이지만 GUI는 선호하는 채널을 지정할 수 있음)은 다음과 같습니다. 로컬 적응 임계 값을 사용하여 이진화 됨 (Bradley and Roth 2007), 후자는 이웃 주변의 로컬 평균 강도를 사용하여 각 픽셀에 대해 계산됩니다. 그런 다음 입자와 물체로 구성된 이진 이미지가 영역으로 변환됩니다. 우리 실험에 존재하는 유일한 장애물은 모든 입자에 비해 더 큰 크기를 기준으로 식별됩니다. 다른 전략은 이전에 논의되었습니다. 그런 다음 장애물 영역의 경계 다각형은 사용자 정의 포인트 밀도로 결정됩니다. 여기에서는 그림자 결정을 위해 광선 투사 (RC) 접근 방식을 채택했습니다. RC는 컴퓨터 그래픽을 기반으로하는 “경 운송 모델링”의 틀에 속합니다. 수치 적으로 정확한 그림자를 제공하기 때문에 여기에서 선택됩니다. 정확도는 떨어지지 만 주로 RC의 계산 부하를 줄이는 것을 목표로하는 몇 가지 다른 방법이 개발되었습니다.2015 ), 여기서 간략히 회상합니다. 각 프레임 (명확성을 위해 여기에 색인화되지 않음)에 대해 광선아르 자형나는 j아르 자형나는제이레이저 위치 L 에서 i 번째 정점 으로 캐스트됩니다.피나는 j피나는제이의 J 오브젝트의 경계 다각형 일; 목표는피나는 j피나는제이 하위 집합에 속 ㅏ제이ㅏ제이 레이저에 의해 직접 조명되는 경계 정점의 피나는 j피나는제이 에 추가됩니다 ㅏ제이ㅏ제이 만약 아르 자형나는 j아르 자형나는제이 적어도 한쪽을 교차 에스k j에스케이제이( j 번째 개체 경계 다각형 의 모든면에 걸쳐있는 k )피나는 j피나는제이 (그것이 교차로 큐나는 j k큐나는제이케이 레이저 위치와 정점 사이에 있지 않습니다. 피나는 j피나는제이). 두 개의 광선, 즉ρ1ρ1 과 ρ2ρ2추가면을 가로 지르지 않는는 저장됩니다.
  3. (씨)일단 정점 세트, 즉 ㅏ제이ㅏ제이 레이저에 의해 직접 비춰지고 식별되었으며 ROI 프레임 상자의 음영 부분은 후자와 교차하여 결정됩니다. ρ1ρ1 과 ρ2ρ2. 두 교차점은 다음에 추가됩니다.ㅏ제이ㅏ제이. 점으로 둘러싸인 영역ㅏ제이ㅏ제이 마침내 마스크로 변환됩니다.

레이저 소스가 여러 개인 경우 각각에 RC 알고리즘을 적용해야하며 음영 영역의 결합이 수행됩니다. 레이 캐스팅 절차의 의사 코드는 Alg에보고됩니다. 1.

그림
그림 1
그림 1

DM 검증

이 섹션에서는 제안 된 DM으로 수행 된 PIV 측정과 두 가지 다른 접근 방식, 즉 no-masking (NM)과 static masking (SM) 간의 비교를 제시합니다.

그림 2
그림 2
그림 3
그림 3

실험 설정

진동 유도기 (VI)의 성능을 분석하기 위해 PIV 설정을 설계하고 현재 DM 기술을 개발했습니다 (Curatolo et al. 2019 , 2020 ). 후자는 비 맥동 ​​유체 흐름에서 역류에 배치 된 캔틸레버의 규칙적이고 넓은 진동을 유도 할 수있는 윙렛입니다. 이러한 VI는 캔틸레버의 끝에 장착되며 (그림 2 참조   ) 진동 운동의 어느 지점에서든 캔틸레버의 중립 구성을 향해 양력을 생성 할 수있는 두 개의 오목한 날개가 있습니다.

VI는 캔틸레버 표면에 장착 된 압전 패치를 사용하여 고정 유체 흐름에서 기계적 에너지 추출을 향상시킬 수 있습니다. 그림 2 에서 강조된 날개의 전체 측면 가장자리는  Sect에 설명 된 사양에 따라 형광 페인트로 코팅되어 있습니다. 2.1 . 실험은 Roma Tre University 공학부 수력 학 실험실의 자유 표면 채널에서 수행됩니다. 10.8cm 길이의 캔틸레버는 채널의 중심선에 배치되고 상류로 향하며 수직-세로 평면에서 진동합니다. 세라믹 페 로브 스카이 트 (PZT) 압전 패치 (7××캔틸레버의 윗면에는 Physik Instrumente (PI)에서 만든 3cm)가 부착되어 있습니다. 흐름 유도 진동 하에서 변형으로 인해 AC 전압 차이를 제공합니다. VI 왼쪽 날개의 수직 중앙면에있는 2D 속도 필드는 수제 수중 PIV 장비를 통해 얻었습니다.각주1 연속파, 저비용, 저전력 (150mW), 녹색 (532nm) 레이저 빔이 2mm 두께의 부채꼴 시트에 퍼집니다.120∘120∘그림 2 와 같이 VI의 한쪽 날개를 절반으로 교차 합니다. 물은 평균 직경이 100 인 폴리 아미드 입자로 시드됩니다.μμm 및 1016 Kg / m의 밀도삼삼. 레이저 소스는 VI의 15cm 위쪽 (자유 표면 아래 약 4cm)과 VI의 하류 5cm에 경사지게 배치됩니다.5∘5∘상류. 위의 설정은 주로 날개의 후류를 조사하기 위해 고안되었습니다. 날개의 상류면과 하류 부분의 일부는 레이저 시트에 직접 맞지 않습니다. 레이저 시트에 수직으로 촬영하는 고속 상용 카메라 (Sony RX100 M5)를 사용하여 동영상을 촬영합니다. 후자는 1920의 프레임 크기로 500fps의 높은 프레임 속도 모드로 기록됩니다.×× 1080px, 나중에 더 작은 655로 잘림 ××이미지 분석 중에 분석 할 850px ROI. 시간 해결, 프리웨어, 오픈 소스, MatLab 용 PIV 분석 도구가 사용됩니다 (Thielicke and Stamhuis 2014 ). 이 도구는 질의 영역 (IA) 변형 (우리의 경우 64×× 64, 32 ×× 32 및 26 ××26). 각 패스에서 각 IA의 경계와 모서리에서 추가 변위 정보를 얻기 위해 인접한 IA 사이에 50 %의 중첩이 허용됩니다. 첫 번째 통과 후, 입자 변위 정보가 보간되어 IA의 모든 픽셀의 변위를 도출하고 그에 따라 변형됩니다.

시딩 입자 수 밀도는 첫 번째 패스에서 IA 당 약 5입니다. Keane과 Adrian ( 1992 )에 따르면 이러한 밀도 값은 95 % 유효한 탐지 확률을 보장합니다. IA는 프레임 커플 내에서 입자의 충분한 영구성을 보장하기 위해 크기가 조정됩니다. 분석 된 유동 역학은 0.4 ~ 0.7m / s 범위의 유동 속도를 특징으로합니다. 따라서 입자는 권장 최소값 인 2 프레임 (Keane and Adrian 1992 ) 보다 큰 약 3-4 프레임의 세 번째 패스 IA에 나타납니다 .

PIV 체인 분석 평가

사용 된 PIV 알고리즘의 정확성은 이전에 문헌에서 광범위하게 평가되었습니다 (예 : Guérin et al. ( 2020 ), Vennemann and Rösgen ( 2020 ), Mohammadshahi et al. ( 2020 ), Narayan et al. ( 2020 )). 그러나 PIV 측정의 물리적 일관성을 보장하기 위해 두 가지 벤치 마크 사례가 여기에 나와 있습니다.

첫 번째는 Sect에 설명 된 동일한 PIV 설정을 통해 측정 된 세로 유속의 수직 프로파일을 비교합니다. 3.1 분석 기준 용액이있는 실험 채널에서. 후자는 플로팅 트레이서로 수행되는 PTV (입자 추적 속도계) 측정을 통해 보정되었습니다. 분석 속도 프로파일은 Eq. 1 (Keulegan 1938 ).u ( z) =유∗[5.75 로그(지δ) +8.5];유(지)=유∗[5.75로그⁡(지δ)+8.5];(1)

여기서 u 는 수평 유속 성분, z 는 수직 좌표,δδ 침대 거칠기 및 V∗V∗ 균일 한 흐름 공식에 의해 주어진 것으로 가정되는 마찰 속도, 즉 유∗= U/ C유∗=유/씨; U 는 깊이 평균 유속이고 C 는 다음 과 같이 주어진 마찰 계수입니다.씨= 5.75로그( 13.3에프R / δ)씨=5.75로그⁡(13.3에프아르 자형/δ), R = 0.2아르 자형=0.2 m은 유압 반경이고 에프= 0.92에프=0.92유한 폭 채널의 형상 계수. 그림  4 는 4 초의 시간 창에 걸쳐 순간 값을 평균화하여 얻은 분석 프로필과 PIV 측정 간의 비교를 보여줍니다. 국부적 인 변동은 대략 0.5 초의 시간 척도에서 진화하는 것으로 밝혀졌습니다. PTV 결과에 가장 적합하면 다음과 같은 값이 산출됩니다.δ= 1δ=1cm, 베드 거칠기의 경우 Eq. 1 , 실험 채널 침대 표면의 실제 조건과 호환됩니다. VI의 휴지 구성 위치에서 유속의 분석 값은 그림에서 검은 색 십자가로 표시됩니다. 비교는 놀라운 일치를 보여 주므로 실험 설정과 PIV 알고리즘의 조합이 분석 된 설정에 대해 신뢰할 수있는 것으로 간주 될 수 있음을 증명합니다.

두 번째 벤치 마크는 VI 뒷면에 재 부착 된 흐름의 양을 비교합니다. 실제로 이러한 장치의 높은 캠버를 고려할 때 흐름은 하류 표면에서 분리되어 결국 다시 연결됩니다. 첨부 흐름을 나타내는 표면의 양 (Curatolo 외. 발견 2020 ) 흥미로운 압전 패치 (즉, 효율이 큰 경우에 더 빠르게 진동이 유발되는 것이다)에서 VI의 효율과 상관된다. 여기에서는 PIV 분석을 통해 측정 된 진동의 상사 점에서 재 부착 된 흐름의 길이를 CFD (전산 유체 역학) 상용 코드 FLOW-3D® (Flow Science 2019 )로 예측 한 길이와 비교하여 RANS를 해결합니다. 결합 식 (비어 스톡스 레이놀즈 평균) 케이 -ϵϵ구조화 된 그리드의 난류 폐쇄 (시뮬레이션을 위해 1mm 간격이 선택됨). 다운 스트림 측면의 흐름은 이러한 높은 캠버 VI를 위해 여러 위치에서 분리 및 재 부착됩니다. 이 벤치 마크에서 비교 된 양은 VI의 앞쪽 가장자리와 가장 가까운 흐름 재 부착 위치 사이의 호 길이입니다. 그림 5를 참조  하면 CFD 모델에 의해 예측 된 호의 길이는 측정 된 호의 길이보다 10 % 더 큽니다. 이 작업에 제시된 DM 기술을 사용하는 PIV 분석은 물리적으로 건전한 측정을 제공하는 것으로 입증됩니다. 후류의 유체 역학에 대한 자세한 분석과 VI의 전반적인 효율성과의 상관 관계는 현재 진행 중이며 향후 작업의 대상이 될 것입니다.

그림 4
그림 4
그림 5
그림 5

결과

그림 6을 참조하여  순간 유속 장의 관점에서 세 가지 접근법의 결과를 비교합니다. 선택한 순간은 진동의 상사 점에 해당합니다.

제안 된 DM (그림 6 의 패널 a  )은 부드러운 유동장을 생성하여 후류에서 일관된 소용돌이 구조를 나타냅니다.

NM 접근법 (그림 6 의 패널 b1  )도 후류의 와류 구조를 정확하게 예측하지만 음영 영역에서 대부분 부정확 한 값을 산출합니다. 또한 비교에서 합리적인 기준을 추론 할 수 없기 때문에 획득 한 유동장 의 사후 필터링이 실현 가능하지 않다는 것이 분명합니다 . 실제로 유속은 그림 6 의 패널 c1에서 볼 수 있듯이 가장 큰 오류가 생성되는 위치에서도 “합리적인”크기를 갖습니다. , DM 및 NM 접근 방식으로 얻은 속도 필드 간의 차이가 표시됩니다. 더욱이 후류에서 발생하는 매우 불안정한 소용돌이 운동이 이러한 위치에 가깝게 이동하기 때문에 그럴듯한 흐름 방향을 가정하더라도 필터링 기준을 공식화 할 수 없습니다. 모델러가 그러한 부정확성을 알고 있었다하더라도 NM 접근법은 “합리적”이지만 여전히 날개의 내부 현과 그 바로 아래에있는 유동장의 대부분은 부정확합니다. 이러한 행동은 매우 오해의 소지가 있습니다.

그림 6 의 패널 b2는  SM 접근법으로 얻은 유속 장을 보여주고 패널 c2는 SM과 DM 접근법으로 얻은 결과 간의 차이를 보여줍니다. SM 접근법은 NM 대응 물에 비해 전반적으로 더 나은 정확도를 명확하게 보여 주지만, 이는 레이저 소스의 위치가 진동 중에 음영 영역이 많이 움직이지 않기 때문입니다 (그림 3 참조). 한 번의 진동 동안 VI가 경험 한 최대 변위를 육안으로 검사합니다. 즉, 분석 된 사례의 경우 정적 마스크를 그리기위한 중립 구성을 선택하면 NM 접근 방식보다 낮은 오류를 얻을 수 있습니다. 더 큰 물체 변위를 포함하는 실험 설정은 NM이 일관되게 더 정확해질 수 있기 때문에 NM보다 SM의 우월성은 일반화 될 수 없음을 강조하고 싶습니다.

그림  6 은 분석 된 접근법에 의해 생성 된 차이를 철저히 보여 주지만 결과에 대한보다 정량적 인 평가를 제공하기 위해 오류의 빈도 분포를 계산했습니다. 그림 7 에서 이러한 분포를  살펴보면 SM 접근법이 NM보다 전체적인 예측이 더 우수하고 SM 분포가 더 정점에 있음을 확인합니다. 그럼에도 불구하고 SM은 여전히 ​​비정상적인 강도의 스파이크를 생성합니다. 분포의 꼬리로 표시되는 이러한 값은 정적 마스크 범위의 과대 평가 (왼쪽 꼬리) 및 과소 평가 (오른쪽 꼬리)에 연결됩니다. 그러나 주파수의 크기는 고려되는 경우에 SM과 NM의 적용 가능성을 배제하여 DM에 대한 리조트를 의무적으로 만듭니다.

그림 6
그림 6
그림 7
그림 7

결론

이 작업에서는 PIV 분석 도구에 DM (Dynamic Masking) 모듈을 제공하기위한 새로운 실험 기법을 제시합니다. 동적 마스킹은 유체 흐름에 잠긴 불투명 이동 / 변형 가능한 물체를 포함하는 시간 해결 PIV 설정에서 필요한 단계입니다. 마스킹 알고리즘과 함께 형광 코팅을 사용하여 물체를 정확하게 추적 할 수 있습니다. 우리는 제안 된 DM과 두 가지 다른 접근 방식, 즉 no-masking (NM)과 static masking (SM)을 비교하여 자체적으로 설계된 저비용 PIV 설정을 통해 수행 된 측정을 제시합니다. 분석 된 유동 역학은 고체 물체의 제한된 변위를 포함하지만 정량적 비교는 DM 기술을 채택해야하는 필수 필요성을 보여줍니다. 여기에서 정확성이 입증 된 현재의 실험적 접근 방식은

메모

  1. 1.실험 데이터 세트는 PIV 분석의 복제를 허용하기 위해 요청시 제공됩니다.

참고 문헌

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  1. 이탈리아 Roma, Università Roma Tre 공학과Valentina Lombardi, Michele La Rocca, Pietro Prestininzi

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Valentina Lombardi에 대한 서신 .

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Lombardi, V., Rocca, ML & Prestininzi, P. 시간 분해 PIV 분석을위한 새로운 동적 마스킹 기술. J Vis (2021). https://doi.org/10.1007/s12650-021-00756-0

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  • 시간 해결 PIV
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On the role of the powder stream on the heat and fluid flow conditions during Directed Energy Deposition of maraging steel-Fig3

On the role of the powder stream on the heat and fluid flow conditions during Directed Energy Deposition of maraging steel—Multiphysics modeling and experimental validation

MohamadBayataVenkata K.NadimpalliaFrancesco G.BiondaniaSinaJafarzadehbJesperThorborgaNiels S.TiedjeaGiulianoBissaccoaDavid B.PedersenaJesper H.Hattela
a Department of Mechanical Engineering, Technical University of Denmark, Building 425, Lyngby, Denmark
Department of Energy Conversion and Storage, Technical University of Denmark, Building 301, Lyngby, Denmark

Received 15 December 2020, Revised 12 April 2021, Accepted 19 April 2021, Available online 8 May 2021.

Abstract

The Directed Energy Deposition (DED) process of metals, has a broad range of applications in several industrial sectors. Surface modification, component repairing, production of functionally graded materials and more importantly, manufacturing of complex geometries are major DED’s applications. In this work, a multi-physics numerical model of the DED process of maraging steel is developed to study the influence of the powder stream specifications on the melt pool’s thermal and fluid dynamics conditions. The model is developed based on the Finite Volume Method (FVM) framework using the commercial software package Flow-3D. Different physical phenomena e.g. solidification, evaporation, the Marangoni effect and the recoil pressure are included in the model. As a new feature, the powder particles’ dynamics are modeled using a Lagrangian framework and their impact on the melt pool conditions is taken into account as well. In-situ and ex-situ experiments are carried out using a thermal camera and optical microscopy. The predicted track morphology is in good agreement with the experimental measurements. Besides, the predicted melt pool evolution follows the same trend as observed with the online thermal camera. Furthermore, a parametric study is carried out to investigate the effect of the powder particles incoming velocity on the track morphology. It is shown that the height-to-width ratio of tracks increases while using higher powder velocities. Moreover, it is shown that by tripling the powder particles velocity, the height-to-width ratio increases by 104% and the wettability of the track decreases by 24%.

Korea Abstract

금속의 DED (Directed Energy Deposition) 공정은 여러 산업 분야에서 광범위한 응용 분야를 가지고 있습니다. 표면 수정, 부품 수리, 기능 등급 재료의 생산 및 더 중요한 것은 복잡한 형상의 제조가 DED의 주요 응용 분야입니다.

이 작업에서는 용융 풀의 열 및 유체 역학 조건에 대한 분말 스트림 사양의 영향을 연구하기 위해 강철 마레이징 DED 공정의 다중 물리 수치 모델이 개발되었습니다. 이 모델은 상용 소프트웨어 패키지 FLOW-3D를 사용하여 FVM (Finite Volume Method) 프레임 워크를 기반으로 개발되었습니다.

다른 물리적 현상 예 : 응고, 증발, 마랑고니 효과 및 반동 압력이 모델에 포함됩니다. 새로운 기능으로 분말 입자의 역학은 Lagrangian 프레임 워크를 사용하여 모델링되며 용융 풀 조건에 미치는 영향도 고려됩니다.

현장 및 현장 실험은 열 화상 카메라와 광학 현미경을 사용하여 수행됩니다. 예측된 트랙 형태는 실험 측정과 잘 일치합니다. 게다가 예측된 용융 풀 진화는 온라인 열 화상 카메라에서 관찰된 것과 동일한 추세를 따릅니다. 또한, 분말 입자 유입 속도가 트랙 형태에 미치는 영향을 조사하기 위해 매개 변수 연구가 수행됩니다.

더 높은 분말 속도를 사용하는 동안 트랙의 높이 대 너비 비율이 증가하는 것으로 나타났습니다. 또한 분말 입자 속도를 3 배로 늘림으로써 높이 대 너비 비율이 104 % 증가하고 트랙의 젖음성은 24 % 감소하는 것으로 나타났습니다.

Keywords

Multi-physics modelDEDHeat and fluid flowFVMParticle motion

On the role of the powder stream on the heat and fluid flow conditions during Directed Energy Deposition of maraging steel-Fig
On the role of the powder stream on the heat and fluid flow conditions during Directed Energy Deposition of maraging steel-Fig
On the role of the powder stream on the heat and fluid flow conditions during Directed Energy Deposition of maraging steel-Fig2
On the role of the powder stream on the heat and fluid flow conditions during Directed Energy Deposition of maraging steel-Fig2
On the role of the powder stream on the heat and fluid flow conditions during Directed Energy Deposition of maraging steel-Fig3
On the role of the powder stream on the heat and fluid flow conditions during Directed Energy Deposition of maraging steel-Fig3
On the role of the powder stream on the heat and fluid flow conditions during Directed Energy Deposition of maraging steel-Fig4
On the role of the powder stream on the heat and fluid flow conditions during Directed Energy Deposition of maraging steel-Fig4
On the role of the powder stream on the heat and fluid flow conditions during Directed Energy Deposition of maraging steel-Fig5
On the role of the powder stream on the heat and fluid flow conditions during Directed Energy Deposition of maraging steel-Fig5
On the role of the powder stream on the heat and fluid flow conditions during Directed Energy Deposition of maraging steel-Fig6
On the role of the powder stream on the heat and fluid flow conditions during Directed Energy Deposition of maraging steel-Fig6
On the role of the powder stream on the heat and fluid flow conditions during Directed Energy Deposition of maraging steel-Fig7
On the role of the powder stream on the heat and fluid flow conditions during Directed Energy Deposition of maraging steel-Fig7
On the role of the powder stream on the heat and fluid flow conditions during Directed Energy Deposition of maraging steel-Fig8
On the role of the powder stream on the heat and fluid flow conditions during Directed Energy Deposition of maraging steel-Fig8
On the role of the powder stream on the heat and fluid flow conditions during Directed Energy Deposition of maraging steel-Fig9
On the role of the powder stream on the heat and fluid flow conditions during Directed Energy Deposition of maraging steel-Fig9
On the role of the powder stream on the heat and fluid flow conditions during Directed Energy Deposition of maraging steel-Fig10
On the role of the powder stream on the heat and fluid flow conditions during Directed Energy Deposition of maraging steel-Fig10
On the role of the powder stream on the heat and fluid flow conditions during Directed Energy Deposition of maraging steel-Fig11
On the role of the powder stream on the heat and fluid flow conditions during Directed Energy Deposition of maraging steel-Fig11
Dam-Break Flows: Comparison between Flow-3D, MIKE 3 FM, and Analytical Solutions with Experimental Data

Dam-Break Flows: Comparison between Flow-3D, MIKE 3 FM, and Analytical Solutions with Experimental Data

by Hui Hu,Jianfeng Zhang andTao Li *
State Key Laboratory Base of Eco-Hydraulic Engineering in Arid Area, School of Water Resources and Hydropower, Xi’an University of Technology, Xi’an 710048, China
*Author to whom correspondence should be addressed.
Appl. Sci.20188(12), 2456; https://doi.org/10.3390/app8122456Received: 14 October 2018 /
Revised: 20 November 2018 / Accepted: 29 November 2018 / Published: 2 December 2018

Abstract

The objective of this study was to evaluate the applicability of a flow model with different numbers of spatial dimensions in a hydraulic features solution, with parameters such a free surface profile, water depth variations, and averaged velocity evolution in a dam-break under dry and wet bed conditions with different tailwater depths. Two similar three-dimensional (3D) hydrodynamic models (Flow-3D and MIKE 3 FM) were studied in a dam-break simulation by performing a comparison with published experimental data and the one-dimensional (1D) analytical solution. The results indicate that the Flow-3D model better captures the free surface profile of wavefronts for dry and wet beds than other methods. The MIKE 3 FM model also replicated the free surface profiles well, but it underestimated them during the initial stage under wet-bed conditions. However, it provided a better approach to the measurements over time. Measured and simulated water depth variations and velocity variations demonstrate that both of the 3D models predict the dam-break flow with a reasonable estimation and a root mean square error (RMSE) lower than 0.04, while the MIKE 3 FM had a small memory footprint and the computational time of this model was 24 times faster than that of the Flow-3D. Therefore, the MIKE 3 FM model is recommended for computations involving real-life dam-break problems in large domains, leaving the Flow-3D model for fine calculations in which knowledge of the 3D flow structure is required. The 1D analytical solution was only effective for the dam-break wave propagations along the initially dry bed, and its applicability was fairly limited. 

Keywords: dam breakFlow-3DMIKE 3 FM1D Ritter’s analytical solution

이 연구의 목적은 자유 표면 프로파일, 수심 변화 및 건식 및 댐 파괴에서 평균 속도 변화와 같은 매개 변수를 사용하여 유압 기능 솔루션에서 서로 다른 수의 공간 치수를 가진 유동 모델의 적용 가능성을 평가하는 것이었습니다.

테일 워터 깊이가 다른 습식베드 조건. 2 개의 유사한 3 차원 (3D) 유체 역학 모델 (Flow-3D 및 MIKE 3 FM)이 게시된 실험 데이터와 1 차원 (1D) 분석 솔루션과의 비교를 수행하여 댐 브레이크 시뮬레이션에서 연구되었습니다.

결과는 FLOW-3D 모델이 다른 방법보다 건식 및 습식 베드에 대한 파면의 자유 표면 프로파일을 더 잘 포착함을 나타냅니다. MIKE 3 FM 모델도 자유 표면 프로파일을 잘 복제했지만, 습식 조건에서 초기 단계에서 과소 평가했습니다. 그러나 시간이 지남에 따라 측정에 더 나은 접근 방식을 제공했습니다.

측정 및 시뮬레이션 된 수심 변화와 속도 변화는 두 3D 모델 모두 합리적인 추정치와 0.04보다 낮은 RMSE (root mean square error)로 댐 브레이크 흐름을 예측하는 반면 MIKE 3 FM은 메모리 공간이 적고 이 모델의 계산 시간은 Flow-3D보다 24 배 더 빠릅니다.

따라서 MIKE 3 FM 모델은 대규모 도메인의 실제 댐 브레이크 문제와 관련된 계산에 권장되며 3D 흐름 구조에 대한 지식이 필요한 미세 계산을 위해 Flow-3D 모델을 남겨 둡니다. 1D 분석 솔루션은 초기 건조 층을 따라 전파되는 댐 파괴에만 효과적이었으며 그 적용 가능성은 상당히 제한적이었습니다.

1. Introduction

저수지에 저장된 물의 통제되지 않은 방류[1]로 인해 댐 붕괴와 그로 인해 하류에서 발생할 수 있는 잠재적 홍수로 인해 큰 자연 위험이 발생한다. 이러한 영향을 최대한 완화하기 위해서는 홍수[2]로 인한 위험을 관리하고 감소시키기 위해 홍수의 시간적 및 공간적 진화를 모두 포착하여 댐 붕괴 파동의 움직임을 예측하고 댐 붕괴 파동의 전파 과정 효과를 다운스트림[3]으로 예측하는 것이 중요하다. 

그러나 이러한 수량을 예측하는 것은 어려운 일이며, 댐 붕괴 홍수의 움직임을 정확하게 시뮬레이션하고 유동장에 대한 유용한 정보를 제공하기 위한 적절한 모델을 선택하는 것은 그러므로 필수적인 단계[4]이다.

적절한 수학적 및 수치적 모델의 선택은 댐 붕괴 홍수 분석에서 매우 중요한 것으로 나타났다.분석적 해결책에서 행해진 댐 붕괴 흐름에 대한 연구는 100여 년 전에 시작되었다. 

리터[5]는 먼저 건조한 침대 위에 1D de 생베넌트 방정식의 초기 분석 솔루션을 도출했고, 드레슬러[6,7]와 휘담[8]은 마찰저항의 영향을 받은 파동학을 연구했으며, 스토커[9]는 젖은 침대를 위한 1D 댐 붕괴 문제에 리터의 솔루션을 확장했다. 

마샬과 멩데즈[10]는 고두노프가 가스 역학의 오일러 방정식을 위해 개발한 방법론[11]을 적용하여 젖은 침대 조건에서 리만 문제를 해결하기 위한 일반적인 절차를 고안했다. Toro [12]는 습식 및 건식 침대 조건을 모두 해결하기 위해 완전한 1D 정밀 리만 용해제를 실시했다. 

Chanson [13]은 특성 방법을 사용하여 갑작스러운 댐 붕괴로 인한 홍수에 대한 간단한 분석 솔루션을 연구했다. 그러나 이러한 분석 솔루션은 특히 댐 붕괴 초기 단계에서 젖은 침대의 정확한 결과를 도출하지 못했다[14,15].과거 연구의 발전은 이른바 댐 붕괴 홍수 문제 해결을 위한 여러 수치 모델[16]을 제공했으며, 헥-라스, DAMBRK, MIK 11 등과 같은 1차원 모델을 댐 붕괴 홍수를 모델링하는 데 사용하였다.

[17 2차원(2D) 깊이 평균 방정식도 댐 붕괴 흐름 문제를 시뮬레이션하는 데 널리 사용되어 왔으며[18,19,20,21,22] 그 결과 얕은 물 방정식(SWE)이 유체 흐름을 나타내는 데 적합하다는 것을 알 수 있다. 그러나, 경우에 따라 2D 수치해결기가 제공하는 해결책이 특히 근거리 분야에서 실험과 일관되지 않을 수 있다[23,24]. 더욱이, 1차원 및 2차원 모델은 3차원 현상에 대한 일부 세부사항을 포착하는 데 한계가 있다.

[25]. RANS(Reynolds-averageed Navier-Stok크스 방정식)에 기초한 여러 3차원(3D) 모델이 얕은 물 모델의 일부 단점을 극복하기 위해 적용되었으며, 댐 붕괴 초기 단계에서의 복잡한 흐름의 실제 동작을 이해하기 위해 사용되었다 [26,27,28]장애물이나 바닥 실에 대한 파장의 충격으로 인한 튜디 댐 붕괴 흐름 [19,29] 및 근거리 영역의 난류 댐 붕괴 흐름 거동 [4] 최근 상용화된 수치 모델 중 잘 알려진 유체 방식(VOF) 기반 CFD 모델링 소프트웨어 FLOW-3D는 컴퓨터 기술의 진보에 따른 계산력 증가로 인해 불안정한 자유 표면 흐름을 분석하는 데 널리 사용되고 있다. 

이 소프트웨어는 유한 차이 근사치를 사용하여 RANS 방정식에 대한 수치 해결책을 계산하며, 자유 표면을 추적하기 위해 VOF를 사용한다 [30,31]; 댐 붕괴 흐름을 모델링하는 데 성공적으로 사용되었다 [32,33].그러나, 2D 얕은 물 모델을 사용하여 포착할 수 없는 공간과 시간에 걸친 댐 붕괴 흐름의 특정한 유압적 특성이 있다. 

실생활 현장 척도 시뮬레이션을 위한 완전한 3D Navier-Stokes 방정식의 적용은 더 높은 계산 비용[34]을 가지고 있으며, 원하는 결과는 얕은 물 모델[35]보다 더 정확한 결과를 산출하지 못할 수 있다. 따라서, 본 논문은 3D 모델의 기능과 그 계산 효율을 평가하기 위해 댐 붕괴 흐름 시뮬레이션을 위한 단순화된 3D 모델-MIKE 3 FM을 시도한다. 

MIK 3 모델은 자연 용수 분지의 여러 유체 역학 시뮬레이션 조사에 적용되었다. 보치 외 연구진이 사용해 왔다. [36], 니콜라오스 및 게오르기오스 [37], 고얄과 라토드[38] 등 현장 연구에서 유체역학 시뮬레이션을 위한 것이다. 이러한 저자들의 상당한 연구에도 불구하고, MIK 3 FM을 이용한 댐 붕괴의 모델링에 관한 연구는 거의 없었다. 

또한 댐 붕괴 홍수 전파 문제를 해결하기 위한 3D 얕은 물과 완전한 3D RANS 모델의 성능을 비교한 연구도 아직 보고되지 않았다. 이 공백을 메우기 위해 현재 연구의 주요 목표는 댐 붕괴 흐름을 시뮬레이션하기 위한 단순화된 3D SWE, 상세 RANS 모델 및 분석 솔루션을 평가하여 댐 붕괴 문제에 대한 정확도와 적용 가능성을 평가하는 것이다.실제 댐 붕괴 문제를 해결하기 위해 유체역학 시뮬레이션을 시도하기 전에 수치 모델을 검증할 필요가 있다. 

일련의 실험 벤치마크를 사용하여 수치 모델을 확인하는 것은 용인된 관행이다. 현장 데이터 확보가 어려워 최근 몇 년 동안 제한된 측정 데이터를 취득했다. 

본 논문은 Ozmen-Cagatay와 Kocaman[30] 및 Khankandi 외 연구진이 제안한 두 가지 테스트 사례에 의해 제안된 검증에서 인용한 것이다. [39] 오즈멘-카가테이와 코카만[30]이 수행한 첫 번째 실험에서, 다른 미숫물 수위에 걸쳐 초기 단계 동안 댐 붕괴 홍수파가 발생했으며, 자유 지표면 프로파일의 측정치를 제공했다. Ozmen-Cagatay와 Kocaman[30]은 초기 단계에서 Flow-3D 소프트웨어가 포함된 2D SWE와 3D RANS의 숫자 솔루션에 의해 계산된 자유 표면 프로필만 비교했다. 

Khankandi 등이 고안한 두 번째 실험 동안. [39], 이 실험의 측정은 홍수 전파를 시뮬레이션하고 측정된 데이터를 제공하는 것을 목적으로 하는 수치 모델을 검증하기 위해 사용되었으며, 말기 동안의 자유 표면 프로필, 수위의 시간 진화 및 속도 변화를 포함한다. Khankandi 등의 연구. [39] 주로 실험 조사에 초점을 맞추었으며, 초기 단계에서는 리터의 솔루션과의 수위만을 언급하고 있다.

경계 조건(상류 및 하류 모두 무한 채널 길이를 갖는 1D 분석 솔루션에서는 실험 결과를 리터와 비교하는 것이 타당하지 않기 때문이다(건조 be)d) 또는 스토커(웨트 베드) 솔루션은 벽의 반사가 깊이 프로파일에 영향을 미쳤을 때, 그리고 참조 [39]의 실험에 대한 수치 시뮬레이션과의 추가 비교가 불량할 때. 이 논문은 이러한 문제를 직접 겨냥하여 전체 댐 붕괴 과정에서의 자유 표면 프로필, 수심 변화 및 속도 변화에 대한 완전한 비교 연구를 제시한다. 

여기서 댐 붕괴파의 수치 시뮬레이션은 초기에 건조하고 습한 직사각형 채널을 가진 유한 저장소의 순간 댐 붕괴에 대해 두 개의 3D 모델을 사용하여 개발된다.본 논문은 다음과 같이 정리되어 있다. 두 모델에 대한 통치 방정식은 숫자 체계를 설명하기 전에 먼저 도입된다. 

일반적인 단순화된 시험 사례는 3D 수치 모델과 1D 분석 솔루션을 사용하여 시뮬레이션했다. 모델 결과와 이들이 실험실 실험과 비교하는 방법이 논의되고, 서로 다른 수심비에서 시간에 따른 유압 요소의 변동에 대한 시뮬레이션 결과가 결론을 도출하기 전에 제시된다.

2. Materials and Methods

2.1. Data

첫째, 수평 건조 및 습식 침상에 대한 초기 댐 붕괴 단계 동안의 자유 표면 프로필 측정은 Ozmen-Cagatay와 Kocaman에 의해 수행되었다[30]. 이 시험 동안, 매끄럽고 직사각형의 수평 채널은 그림 1에서 표시한 대로 너비 0.30m, 높이 0.30m, 길이 8.9m이었다. 

채널은 채널 입구에서 4.65m 떨어진 수직 플레이트(담) 즉, 저장소의 길이 L0=4.65mL0에 의해 분리되었다., 및 다운스트림 채널 L1=4.25 mL1. m저수지는 댐의 좌측에 위치하고 처음에는 침수된 것으로 간주되었다; 저수지의 초기 상류 수심 h0 0.25m로 일정했다.

오른쪽의 초기 수심 h1h1 건식침대의 경우 0m, 습식침대의 경우 0.025m, 0.1m이므로 수심비 α=h1/h0α으로 세 가지 상황이 있었다. 0, 0.1, 0.4의 습식침대 조건은 플룸 끝에 낮은 보를 사용함으로써 만들어졌다. 물 표면 프로필은 3개의 고속 디지털 카메라(50프레임/s)를 사용하여 초기에 관찰되었으며, 계측 측정의 정확도는 참고문헌 [30]에서 입증되었다. In the following section, the corresponding numerical results refer to positions x = −1 m (P1), −0.5 m (P2), −0.2 m (P3), +0.2 m (P4), +0.5 m (P5), +1 m (P6), +2 m (P7), and +2.85 m (P8), where the origin of the coordinate system x = 0 is at the dam site. 3수심비 ααα 0, 0.1, 0.4의 경우 x,yx의 경우 좌표는 h0.으로 정규화된다.

<중략> ……

Figure 1. Schematic view of the experimental conditions by Ozmen-Cagatay and Kocaman [30]: (a) α = 0; (b) α = 0.1; and (c) α = 0.4.
Figure 1. Schematic view of the experimental conditions by Ozmen-Cagatay and Kocaman [30]: (a) α = 0; (b) α = 0.1; and (c) α = 0.4.

Figure 2. Schematic view of the experimental conditions by Khankandi et al. [39]: (a) α = 0 and (b) α = 0.2.
Figure 2. Schematic view of the experimental conditions by Khankandi et al. [39]: (a) α = 0 and (b) α = 0.2.
Figure 3. Typical profiles of the dam-break flow regimes for Stoker’s analytical solution [9]: Wet-bed downstream
Figure 3. Typical profiles of the dam-break flow regimes for Stoker’s analytical solution [9]: Wet-bed downstream
Figure 4. Sensitivity analysis of the numerical simulation using Flow-3D for the different mesh sizes of the experiments in Reference [30].
Figure 4. Sensitivity analysis of the numerical simulation using Flow-3D for the different mesh sizes of the experiments in Reference [30].
Figure 5. Sensitivity analysis of the numerical simulation using MIKE 3 FM for the different mesh sizes of the experiments in Reference [30].
Figure 5. Sensitivity analysis of the numerical simulation using MIKE 3 FM for the different mesh sizes of the experiments in Reference [30].
Figure 6. Comparison between observed and simulated free surface profiles at dimensionless times T = t(g/h0)1/2 and for dry-bed (α=0). The experimental data are from Reference [30].
Figure 6. Comparison between observed and simulated free surface profiles at dimensionless times T = t(g/h0)1/2 and for dry-bed (α=0). The experimental data are from Reference [30].
Figure 7. Comparison between observed and simulated free surface profiles at dimensionless times T = t(g/h0)1/2 and for a wet-bed (α = 0.1). The experimental data are from Reference [30].
Figure 7. Comparison between observed and simulated free surface profiles at dimensionless times T = t(g/h0)1/2 and for a wet-bed (α = 0.1). The experimental data are from Reference [30].
Figure 8. Comparison between observed and simulated free surface profiles at dimensionless times T = t(g/h0)1/2 and for the wet-bed (α = 0.4). The experimental data are from Reference [30].
Figure 8. Comparison between observed and simulated free surface profiles at dimensionless times T = t(g/h0)1/2 and for the wet-bed (α = 0.4). The experimental data are from Reference [30].
Figure 9. Experimental and numerical comparison of free surface profiles h/h0(x/h0) during late stages at various dimensionless times T after the failure in the dry-bed by Khankandi et al. [39].
Figure 9. Experimental and numerical comparison of free surface profiles h/h0(x/h0) during late stages at various dimensionless times T after the failure in the dry-bed by Khankandi et al. [39].

Table 2. RMSE values for the free surface profiles observed by Khankandi et al. [39].

Table 2. RMSE values for the free surface profiles observed by Khankandi et al. [39].
Table 2. RMSE values for the free surface profiles observed by Khankandi et al. [39].
Figure 10. Measured and computed water level hydrograph at various positions for dry-bed by Khankandi et al. [39]: (a) G1 (−0.5 m); (b) G2 (−0.1 m); (c) G3 (0.1 m); (d) G4 (0.8 m); (e) G6 (1.2 m); (f) G8 (5.5 m).
Figure 10. Measured and computed water level hydrograph at various positions for dry-bed by Khankandi et al. [39]: (a) G1 (−0.5 m); (b) G2 (−0.1 m); (c) G3 (0.1 m); (d) G4 (0.8 m); (e) G6 (1.2 m); (f) G8 (5.5 m).
Figure 11. Measured and computed water level hydrographs at various positions for the wet-bed by Khankandi et al. [39]: (a) G1 (−0.5 m); (b) G2 (−0.1 m); (c) G4 (0.8 m); and (d) G5 (1.0 m).
Figure 11. Measured and computed water level hydrographs at various positions for the wet-bed by Khankandi et al. [39]: (a) G1 (−0.5 m); (b) G2 (−0.1 m); (c) G4 (0.8 m); and (d) G5 (1.0 m).

Table 3. RMSE values for the water depth variations observed by Khankandi et al. [39] at the late stage.

Table 3. RMSE values for the water depth variations observed by Khankandi et al. [39] at the late stage.
Table 3. RMSE values for the water depth variations observed by Khankandi et al. [39] at the late stage.
Figure 13. Comparison of simulated velocity profiles at various locations upstream and downstream of the dam at t = 0.8 s, 2 s, and 5 s for water depth ratios α = 0.1 by Ozmen-Cagatay and Kocaman [30]: (a) P1(−1 m); (b) P3 (+0.2 m); (c) P5 (+1 m); and (d) P6 (+2 m).
Figure 13. Comparison of simulated velocity profiles at various locations upstream and downstream of the dam at t = 0.8 s, 2 s, and 5 s for water depth ratios α = 0.1 by Ozmen-Cagatay and Kocaman [30]: (a) P1(−1 m); (b) P3 (+0.2 m); (c) P5 (+1 m); and (d) P6 (+2 m).
Table 5. The required computational time for the two models to address dam break flows in all cases
Table 5. The required computational time for the two models to address dam break flows in all cases

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The 3D computational domain model (50–18.6) slope change, and boundary condition for (50–30 slope change) model.

Numerical investigation of flow characteristics over stepped spillways

Güven, Aytaç
Mahmood, Ahmed Hussein
Water Supply (2021) 21 (3): 1344–1355.
https://doi.org/10.2166/ws.2020.283Article history

Abstract

Spillways are constructed to evacuate flood discharge safely so that a flood wave does not overtop the dam body. There are different types of spillways, with the ogee type being the conventional one. A stepped spillway is an example of a nonconventional spillway. The turbulent flow over a stepped spillway was studied numerically by using the Flow-3D package. Different fluid flow characteristics such as longitudinal flow velocity, temperature distribution, density and chemical concentration can be well simulated by Flow-3D. In this study, the influence of slope changes on flow characteristics such as air entrainment, velocity distribution and dynamic pressures distribution over a stepped spillway was modelled by Flow-3D. The results from the numerical model were compared with an experimental study done by others in the literature. Two models of a stepped spillway with different discharge for each model were simulated. The turbulent flow in the experimental model was simulated by the Renormalized Group (RNG) turbulence scheme in the numerical model. A good agreement was achieved between the numerical results and the observed ones, which are exhibited in terms of graphics and statistical tables.

배수로는 홍수가 댐 몸체 위로 넘치지 않도록 안전하게 홍수를 피할 수 있도록 건설되었습니다. 다른 유형의 배수로가 있으며, ogee 유형이 기존 유형입니다. 계단식 배수로는 비 전통적인 배수로의 예입니다. 계단식 배수로 위의 난류는 Flow-3D 패키지를 사용하여 수치적으로 연구되었습니다.

세로 유속, 온도 분포, 밀도 및 화학 농도와 같은 다양한 유체 흐름 특성은 Flow-3D로 잘 시뮬레이션 할 수 있습니다. 이 연구에서는 계단식 배수로에 대한 공기 혼입, 속도 분포 및 동적 압력 분포와 같은 유동 특성에 대한 경사 변화의 영향을 Flow-3D로 모델링 했습니다.

수치 모델의 결과는 문헌에서 다른 사람들이 수행한 실험 연구와 비교되었습니다. 각 모델에 대해 서로 다른 배출이 있는 계단식 배수로의 두 모델이 시뮬레이션되었습니다. 실험 모델의 난류 흐름은 수치 모델의 Renormalized Group (RNG) 난류 계획에 의해 시뮬레이션되었습니다. 수치 결과와 관찰 된 결과 사이에 좋은 일치가 이루어졌으며, 이는 그래픽 및 통계 테이블로 표시됩니다.

HIGHLIGHTS

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  • A numerical model was developed for stepped spillways.
  • The turbulent flow was simulated by the Renormalized Group (RNG) model.
  • Both numerical and experimental results showed that flow characteristics are greatly affected by abrupt slope change on the steps.

Keyword

CFDnumerical modellingslope changestepped spillwayturbulent flow

INTRODUCTION

댐 구조는 물 보호가 생활의 핵심이기 때문에 물을 저장하거나 물을 운반하는 전 세계에서 가장 중요한 프로젝트입니다. 그리고 여수로는 댐의 가장 중요한 부분 중 하나로 분류됩니다. 홍수로 인한 파괴 나 피해로부터 댐을 보호하기 위해 여수로가 건설됩니다.

수력 발전, 항해, 레크리에이션 및 어업의 중요성을 감안할 때 댐 건설 및 홍수 통제는 전 세계적으로 매우 중요한 문제로 간주 될 수 있습니다. 많은 유형의 배수로가 있지만 가장 일반적인 유형은 다음과 같습니다 : ogee 배수로, 자유 낙하 배수로, 사이펀 배수로, 슈트 배수로, 측면 채널 배수로, 터널 배수로, 샤프트 배수로 및 계단식 배수로.

그리고 모든 여수로는 입구 채널, 제어 구조, 배출 캐리어 및 출구 채널의 네 가지 필수 구성 요소로 구성됩니다. 특히 롤러 압축 콘크리트 (RCC) 댐 건설 기술과 더 쉽고 빠르며 저렴한 건설 기술로 분류 된 계단식 배수로 건설과 관련하여 최근 수십 년 동안 많은 계단식 배수로가 건설되었습니다 (Chanson 2002; Felder & Chanson 2011).

계단식 배수로 구조는 캐비테이션 위험을 감소시키는 에너지 소산 속도를 증가시킵니다 (Boes & Hager 2003b). 계단식 배수로는 다양한 조건에서 더 매력적으로 만드는 장점이 있습니다.

계단식 배수로의 흐름 거동은 일반적으로 낮잠, 천이 및 스키밍 흐름 체제의 세 가지 다른 영역으로 분류됩니다 (Chanson 2002). 유속이 낮을 때 nappe 흐름 체제가 발생하고 자유 낙하하는 낮잠의 시퀀스로 특징 지워지는 반면, 스키밍 흐름 체제에서는 물이 외부 계단 가장자리 위의 유사 바닥에서 일관된 흐름으로 계단 위로 흐릅니다.

또한 주요 흐름에서 3 차원 재순환 소용돌이가 발생한다는 것도 분명합니다 (예 : Chanson 2002; Gonzalez & Chanson 2008). 계단 가장자리 근처의 의사 바닥에서 흐름의 방향은 가상 바닥과 가상으로 정렬됩니다. Takahashi & Ohtsu (2012)에 따르면, 스키밍 흐름 체제에서 주어진 유속에 대해 흐름은 계단 가장자리 근처의 수평 계단면에 영향을 미치고 슈트 경사가 감소하면 충돌 영역의 면적이 증가합니다. 전이 흐름 체제는 나페 흐름과 스키밍 흐름 체제 사이에서 발생합니다. 계단식 배수로를 설계 할 때 스키밍 흐름 체계를 고려해야합니다 (예 : Chanson 1994, Matos 2000, Chanson 2002, Boes & Hager 2003a).

CFD (Computational Fluid Dynamics), 즉 수력 공학의 수치 모델은 일반적으로 물리적 모델에 소요되는 총 비용과 시간을 줄여줍니다. 따라서 수치 모델은 실험 모델보다 빠르고 저렴한 것으로 분류되며 동시에 하나 이상의 목적으로 사용될 수도 있습니다. 사용 가능한 많은 CFD 소프트웨어 패키지가 있지만 가장 널리 사용되는 것은 FLOW-3D입니다. 이 연구에서는 Flow 3D 소프트웨어를 사용하여 유량이 서로 다른 두 모델에 대해 계단식 배수로에서 공기 농도, 속도 분포 및 동적 압력 분포를 시뮬레이션합니다.

Roshan et al. (2010)은 서로 다른 수의 계단 및 배출을 가진 계단식 배수로의 두 가지 물리적 모델에 대한 흐름 체제 및 에너지 소산 조사를 연구했습니다. 실험 모델의 기울기는 각각 19.2 %, 12 단계와 23 단계의 수입니다. 결과는 23 단계 물리적 모델에서 관찰 된 흐름 영역이 12 단계 모델보다 더 수용 가능한 것으로 간주되었음을 보여줍니다. 그러나 12 단계 모델의 에너지 손실은 23 단계 모델보다 더 많았습니다. 그리고 실험은 스키밍 흐름 체제에서 23 단계 모델의 에너지 소산이 12 단계 모델보다 약 12 ​​% 더 적다는 것을 관찰했습니다.

Ghaderi et al. (2020a)는 계단 크기와 유속이 다른 정련 매개 변수의 영향을 조사하기 위해 계단식 배수로에 대한 실험 연구를 수행했습니다. 그 결과, 흐름 체계가 냅페 흐름 체계에서 발생하는 최소 scouring 깊이와 같은 scouring 구멍 치수에 영향을 미친다는 것을 보여주었습니다. 또한 테일 워터 깊이와 계단 크기는 최대 scouring깊이에 대한 실제 매개 변수입니다. 테일 워터의 깊이를 6.31cm에서 8.54 및 11.82cm로 늘림으로써 수세 깊이가 각각 18.56 % 및 11.42 % 증가했습니다. 또한 이 증가하는 테일 워터 깊이는 scouring 길이를 각각 31.43 % 및 16.55 % 감소 시킵니다. 또한 유속을 높이면 Froude 수가 증가하고 흐름의 운동량이 증가하면 scouring이 촉진됩니다. 또한 결과는 중간의 scouring이 횡단면의 측벽보다 적다는 것을 나타냅니다. 계단식 배수로 하류의 최대 scouring 깊이를 예측 한 후 실험 결과와 비교하기 위한 실험식이 제안 되었습니다. 그리고 비교 결과 제안 된 공식은 각각 3.86 %와 9.31 %의 상대 오차와 최대 오차 내에서 scouring 깊이를 예측할 수 있음을 보여주었습니다.

Ghaderi et al. (2020b)는 사다리꼴 미로 모양 (TLS) 단계의 수치 조사를 했습니다. 결과는 이러한 유형의 배수로가 확대 비율 LT / Wt (LT는 총 가장자리 길이, Wt는 배수로의 폭)를 증가시키기 때문에 더 나은 성능을 갖는 것으로 관찰되었습니다. 또한 사다리꼴 미로 모양의 계단식 배수로는 더 큰 마찰 계수와 더 낮은 잔류 수두를 가지고 있습니다. 마찰 계수는 다양한 배율에 대해 0.79에서 1.33까지 다르며 평평한 계단식 배수로의 경우 대략 0.66과 같습니다. 또한 TLS 계단식 배수로에서 잔류 수두의 비율 (Hres / dc)은 약 2.89이고 평평한 계단식 배수로의 경우 약 4.32와 같습니다.

Shahheydari et al. (2015)는 Flow-3D 소프트웨어, RNG k-ε 모델 및 VOF (Volume of Fluid) 방법을 사용하여 배출 계수 및 에너지 소산과 같은 자유 표면 흐름의 프로파일을 연구하여 스키밍 흐름 체제에서 계단식 배수로에 대한 흐름을 조사했습니다. 실험 결과와 비교했습니다. 결과는 에너지 소산 율과 방전 계수율의 관계가 역으로 실험 모델의 결과와 잘 일치 함을 보여 주었다.

Mohammad Rezapour Tabari & Tavakoli (2016)는 계단 높이 (h), 계단 길이 (L), 계단 수 (Ns) 및 단위 폭의 방전 (q)과 같은 다양한 매개 변수가 계단식 에너지 ​​소산에 미치는 영향을 조사했습니다. 방수로. 그들은 해석에 FLOW-3D 소프트웨어를 사용하여 계단식 배수로에서 에너지 손실과 임계 흐름 깊이 사이의 관계를 평가했습니다. 또한 유동 난류에 사용되는 방정식과 표준 k-ɛ 모델을 풀기 위해 유한 체적 방법을 적용했습니다. 결과에 따르면 스텝 수가 증가하고 유량 배출량이 증가하면 에너지 손실이 감소합니다. 얻은 결과를 다른 연구와 비교하고 경험적, 수학적 조사를 수행하여 결국 합격 가능한 결과를 얻었습니다.

METHODOLOGY

ListenReadSpeaker webReader: ListenFor all numerical models the basic principle is very similar: a set of partial differential equations (PDE) present the physical problems. The flow of fluids (gas and liquid) are governed by the conservation laws of mass, momentum and energy. For Computational Fluid Dynamics (CFD), the PDE system is substituted by a set of algebraic equations which can be worked out by using numerical methods (Versteeg & Malalasekera 2007). Flow-3D uses the finite volume approach to solve the Reynolds Averaged Navier-Stokes (RANS) equation, by applying the technique of Fractional Area/Volume Obstacle Representation (FAVOR) to define an obstacle (Flow Science Inc. 2012). Equations (1) and (2) are RANS and continuity equations with FAVOR variables that are applied for incompressible flows.

formula

(1)

formula

(2)where  is the velocity in xi direction, t is the time,  is the fractional area open to flow in the subscript directions,  is the volume fraction of fluid in each cell, p is the hydrostatic pressure,  is the density, is the gravitational force in subscript directions and  is the Reynolds stresses.

Turbulence modelling is one of three key elements in CFD (Gunal 1996). There are many types of turbulence models, but the most common are Zero-equation models, One-equation models, Two-equation models, Reynolds Stress/Flux models and Algebraic Stress/Flux models. In FLOW-3D software, five turbulence models are available. The formulation used in the FLOW-3D software differs slightly from other formulations that includes the influence of the fractional areas/volumes of the FAVORTM method and generalizes the turbulence production (or decay) associated with buoyancy forces. The latter generalization, for example, includes buoyancy effects associated with non-inertial accelerations.

The available turbulence models in Flow-3D software are the Prandtl Mixing Length Model, the One-Equation Turbulent Energy Model, the Two-Equation Standard  Model, the Two-Equation Renormalization-Group (RNG) Model and large Eddy Simulation Model (Flow Science Inc. 2012).In this research the RNG model was selected because this model is more commonly used than other models in dealing with particles; moreover, it is more accurate to work with air entrainment and other particles. In general, the RNG model is classified as a more widely-used application than the standard k-ɛ model. And in particular, the RNG model is more accurate in flows that have strong shear regions than the standard k-ɛ model and it is defined to describe low intensity turbulent flows. For the turbulent dissipation  it solves an additional transport equation:

formula

(3)where CDIS1, CDIS2, and CDIS3 are dimensionless parameters and the user can modify them. The diffusion of dissipation, Diff ɛ, is

formula

(4)where uv and w are the x, y and z coordinates of the fluid velocity; ⁠, ⁠,  and ⁠, are FLOW-3D’s FAVORTM defined terms;  and  are turbulence due to shearing and buoyancy effects, respectively. R and  are related to the cylindrical coordinate system. The default values of RMTKE, CDIS1 and CNU differ, being 1.39, 1.42 and 0.085 respectively. And CDIS2 is calculated from turbulent production (⁠⁠) and turbulent kinetic energy (⁠⁠).The kinematic turbulent viscosity is the same in all turbulence transport models and is calculated from

formula

(5)where ⁠: is the turbulent kinematic viscosity.  is defined as the numerical challenge between the RNG and the two-equation k-ɛ models, found in the equation below. To avoid an unphysically large result for  in Equation (3), since this equation could produce a value for  very close to zero and also because the physical value of  may approach to zero in such cases, the value of  is calculated from the following equation:

formula

(6)where ⁠: the turbulent length scale.

VOF and FAVOR are classifications of volume-fraction methods. In these two methods, firstly the area should be subdivided into a control volume grid or a small element. Each flow parameter like velocity, temperature and pressure values within the element are computed for each element containing liquids. Generally, these values represent the volumetric average of values in the elements.Numerous methods have been used recently to solve free infinite boundaries in the various numerical simulations. VOF is an easy and powerful method created based on the concept of a fractional intensity of fluid. A significant number of studies have confirmed that this method is more flexible and efficient than others dealing with the configurations of a complex free boundary. By using VOF technology the Flow-3D free surface was modelled and first declared in Hirt & Nichols (1981). In the VOF method there are three ingredients: a planner to define the surface, an algorithm for tracking the surface as a net mediator moving over a computational grid, and application of the boundary conditions to the surface. Configurations of the fluids are defined in terms of VOF function, F (x, y, z, t) (Hirt & Nichols 1981). And this VOF function shows the volume of flow per unit volume

formula

(7)

formula

(8)

formula

(9)where  is the density of the fluid, is a turbulent diffusion term,  is a mass source,  is the fractional volume open to flow. The components of velocity (u, v, w) are in the direction of coordinates (x, y, z) or (r, ⁠).  in the x-direction is the fractional area open to flow,  and  are identical area fractions for flow in the y and z directions. The R coefficient is based on the selection of the coordinate system.

The FAVOR method is a different method and uses another volume fraction technique, which is only used to define the geometry, such as the volume of liquid in each cell used to determine the position of fluid surfaces. Another fractional volume can be used to define the solid surface. Then, this information is used to determine the boundary conditions of the wall that the flow should be adapted for.

Case study

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In this study, the experimental results of Ostad Mirza (2016) was simulated. In a channel composed of two 4 m long modules, with a transparent sidewall of height 0.6 m and 0.5 m width. The upstream chute slope (i.e. pseudo-bottom angle) Ɵ1 = 50°, the downstream chute slope Ɵ2 = 30° or 18.6°, the step heights h = 0.06 m, the total number of steps along the 50° chute 41 steps, the total number of steps along the 30° chute 34 steps and the total number of steps along the 18.6° chute 20 steps.

The flume inflow tool contained a jetbox with a maximum opening set to 0.12 meters, designed for passing the maximum unit discharge of 0.48 m2/s. The measurements of the flow properties (i.e. air concentration and velocity) were computed perpendicular to the pseudo-bottom as shown in Figure 1 at the centre of twenty stream-wise cross-sections, along the stepped chute, (i.e. in five steps up on the slope change and fifteen steps down on the slope change, namely from step number −09 to +23 on 50°–30° slope change, or from −09 to +15 on 50°–18.6° slope change, respectively).

Sketch of the air concentration C and velocity V measured perpendicular to the pseudo-bottom used by Mirza (Ostad Mirza 2016).
Sketch of the air concentration C and velocity V measured perpendicular to the pseudo-bottom used by Mirza (Ostad Mirza 2016).

Sketch of the air concentration C and velocity V measured perpendicular to the pseudo-bottom used by Mirza (Ostad Mirza 2016).

Pressure sensors were arranged with the x/l values for different slope change as shown in Table 1, where x is the distance from the step edge, along the horizontal step face, and l is the length of the horizontal step face. The location of pressure sensors is shown in Table 1.Table 1

Location of pressure sensors on horizontal step faces

Θ(°)L(m)x/l (–)
50.0 0.050 0.35 0.64 – – – 
30.0 0.104 0.17 0.50 0.84 – – 
18.6 0.178 0.10 0.30 0.50 0.7 0.88 
Location of pressure sensors on horizontal step faces
Inlet boundary condition for Q = 0.235 m3/s and fluid elevation 4.21834 m.
Inlet boundary condition for Q = 0.235 m3/s and fluid elevation 4.21834 m.

Inlet boundary condition for Q = 0.235 m3/s and fluid elevation 4.21834 m.

Numerical model set-up

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A 3D numerical model of hydraulic phenomena was simulated based on an experimental study by Ostad Mirza (2016). The water surcharge and flow pressure over the stepped spillway was computed for two models of a stepped spillway with different discharge for each model. In this study, the package was used to simulate the flow parameters such as air entrainment, velocity distribution and dynamic pressures. The solver uses the finite volume technique to discretize the computational domain. In every test run, one incompressible fluid flow with a free surface flow selected at 20̊ was used for this simulation model. Table 2 shows the variables used in test runs.Table 2

Variables used in test runs

Test no.Θ1 (°)Θ2 (°)h(m)d0q (m3s1)dc/h (–)
50 18.6 0.06 0.045 0.1 2.6 
50 18.6 0.06 0.082 0.235 4.6 
50 30.0 0.06 0.045 0.1 2.6 
50 30.0 0.06 0.082 0.235 4.6 
Table 2 Variables used in test runs

For stepped spillway simulation, several parameters should be specified to get accurate simulations, which is the scope of this research. Viscosity and turbulent, gravity and non-inertial reference frame, air entrainment, density evaluation and drift-flux should be activated for these simulations. There are five different choices in the ‘viscosity and turbulent’ option, in the viscosity flow and Renormalized Group (RNG) model. Then a dynamical model is selected as the second option, the ‘gravity and non-inertial reference frame’. Only the z-component was inputted as a negative 9.81 m/s2 and this value represents gravitational acceleration but in the same option the x and y components will be zero. Air entrainment is selected. Finally, in the drift-flux model, the density of phase one is input as (water) 1,000 kg/m3 and the density of phase two (air) as 1.225 kg/m3. Minimum volume fraction of phase one is input equal to 0.1 and maximum volume fraction of phase two to 1 to allow air concentration to reach 90%, then the option allowing gas to escape at free surface is selected, to obtain closer simulation.

The flow domain is divided into small regions relatively by the mesh in Flow-3D numerical model. Cells are the smallest part of the mesh, in which flow characteristics such as air concentration, velocity and dynamic pressure are calculated. The accuracy of the results and simulation time depends directly on the mesh block size so the cell size is very important. Orthogonal mesh was used in cartesian coordinate systems. A smaller cell size provides more accuracy for results, so we reduced the number of cells whilst including enough accuracy. In this study, the size of cells in x, y and z directions was selected as 0.015 m after several trials.

Figure 3 shows the 3D computational domain model 50–18.6 slope change, that is 6.0 m length, 0.50 m width and 4.23 m height. The 3D model of the computational domain model 50–30 slope changes this to 6.0 m length, 0.50 m width and 5.068 m height and the size of meshes in x, y, and z directions are 0.015 m. For the 50–18.6 slope change model: both total number of active and passive cells = 4,009,952, total number of active cells = 3,352,307, include real cells (used for solving the flow equations) = 3,316,269, open real cells = 3,316,269, fully blocked real cells equal to zero, external boundary cells were 36,038, inter-block boundary cells = 0 (Flow-3D report). For 50–30 slope change model: both total number of active and passive cells = 4,760,002, total number of active cells equal to 4,272,109, including real cells (used for solving the flow equations) were 3,990,878, open real cells = 3,990,878 fully blocked real cells = zero, external boundary cells were 281,231, inter-block boundary cells = 0 (Flow-3D report).

The 3D computational domain model (50–18.6) slope change, and boundary condition for (50–30 slope change) model.
Figure3 The 3D computational domain model (50–18.6) slope change, and boundary condition for (50–30 slope change) model.

Figure 3VIEW LARGEDOWNLOAD SLIDE

The 3D computational domain model (50–18.6) slope change, and boundary condition for (50–30 slope change) model.

When solving the Navier-Stokes equation and continuous equations, boundary conditions should be applied. The most important work of boundary conditions is to create flow conditions similar to physical status. The Flow-3D software has many types of boundary condition; each type can be used for the specific condition of the models. The boundary conditions in Flow-3D are symmetry, continuative, specific pressure, grid overlay, wave, wall, periodic, specific velocity, outflow, and volume flow rate.

There are two options to input finite flow rate in the Flow-3D software either for inlet discharge of the system or for the outlet discharge of the domain: specified velocity and volume flow rate. In this research, the X-minimum boundary condition, volume flow rate, has been chosen. For X-maximum boundary condition, outflow was selected because there is nothing to be calculated at the end of the flume. The volume flow rate and the elevation of surface water was set for Q = 0.1 and 0.235 m3/s respectively (Figure 2).

The bottom (Z-min) is prepared as a wall boundary condition and the top (Z-max) is computed as a pressure boundary condition, and for both (Y-min) and (Y-max) as symmetry.

RESULTS AND DISCUSSION

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The air concentration distribution profiles in two models of stepped spillway were obtained at an acquisition time equal to 25 seconds in skimming flow for both upstream and downstream of a slope change 50°–18.6° and 50°–30° for different discharge as in Table 2, and as shown in Figure 4 for 50°–18.6° slope change and Figure 5 for 50°–30° slope change configuration for dc/h = 4.6. The simulation results of the air concentration are very close to the experimental results in all curves and fairly close to that predicted by the advection-diffusion model for the air bubbles suggested by Chanson (1997) on a constant sloping chute.

Figure 4 Experimental and simulated air concentration distribution for steps number −5, +1, +5, +8, +11 and +15 along the 50°–18.6° slope change for dc/h = 4.6. VIEW LARGEDOWNLOAD SLIDE Experimental and simulated air concentration distribution for steps number −5, +1, +5, +8, +11 and +15 along the 50°–18.6° slope change for dc/h = 4.6.
Figure 4 Experimental and simulated air concentration distribution for steps number −5, +1, +5, +8, +11 and +15 along the 50°–18.6° slope change for dc/h = 4.6. VIEW LARGEDOWNLOAD SLIDE Experimental and simulated air concentration distribution for steps number −5, +1, +5, +8, +11 and +15 along the 50°–18.6° slope change for dc/h = 4.6.

Figure 4VIEW LARGEDOWNLOAD SLIDE

Experimental and simulated air concentration distribution for steps number −5, +1, +5, +8, +11 and +15 along the 50°–18.6° slope change for dc/h = 4.6.

Figure5 Experimental and simulated air concentration distribution for steps number −5, +1, +5, +11, +19 and +22 along the 50°–30° slope change, for dc/h = 4.6.
Figure5 Experimental and simulated air concentration distribution for steps number −5, +1, +5, +11, +19 and +22 along the 50°–30° slope change, for dc/h = 4.6.

Figure 5VIEW LARGEDOWNLOAD SLIDE

Experimental and simulated air concentration distribution for steps number −5, +1, +5, +11, +19 and +22 along the 50°–30° slope change, for dc/h = 4.6.

Figure 6VIEW LARGEDOWNLOAD SLIDE

Figure 6 Experimental and simulated dimensionless velocity distribution for steps number −5, −1, +1, +5, +8, +11 and +15 along the 50°–18.6° slope change for dc/h = 2.6.
Figure 6 Experimental and simulated dimensionless velocity distribution for steps number −5, −1, +1, +5, +8, +11 and +15 along the 50°–18.6° slope change for dc/h = 2.6.

Experimental and simulated dimensionless velocity distribution for steps number −5, −1, +1, +5, +8, +11 and +15 along the 50°–18.6° slope change for dc/h = 2.6.

Figure 7 Experimental and simulated dimensionless velocity distribution for steps number −5, −1, +1, +5. +11, +15 and +22 along the 50°–30° slope change for dc/h = 2.6.
Figure 7 Experimental and simulated dimensionless velocity distribution for steps number −5, −1, +1, +5. +11, +15 and +22 along the 50°–30° slope change for dc/h = 2.6.

Figure 7VIEW LARGEDOWNLOAD SLIDE

Experimental and simulated dimensionless velocity distribution for steps number −5, −1, +1, +5. +11, +15 and +22 along the 50°–30° slope change for dc/h = 2.6.

But as is shown in all above mentioned figures it is clear that at the pseudo-bottom the CFD results of air concentration are less than experimental ones until the depth of water reaches a quarter of the total depth of water. Also the direction of the curves are parallel to each other when going up towards the surface water and are incorporated approximately near the surface water. For all curves, the cross-section is separate between upstream and downstream steps. Therefore the (-) sign for steps represents a step upstream of the slope change cross-section and the (+) sign represents a step downstream of the slope change cross-section.

The dimensionless velocity distribution (V/V90) profile was acquired at an acquisition time equal to 25 seconds in skimming flow of the upstream and downstream slope change for both 50°–18.6° and 50°–30° slope change. The simulation results are compared with the experimental ones showing that for all curves there is close similarity for each point between the observed and experimental results. The curves increase parallel to each other and they merge near at the surface water as shown in Figure 6 for slope change 50°–18.6° configuration and Figure 7 for slope change 50°–30° configuration. However, at step numbers +1 and +5 in Figure 7 there are few differences between the simulated and observed results, namely the simulation curves ascend regularly meaning the velocity increases regularly from the pseudo-bottom up to the surface water.

Figure 8 (50°–18.6° slope change) and Figure 9 (50°–30° slope change) compare the simulation results and the experimental results for the presented dimensionless dynamic pressure distribution for different points on the stepped spillway. The results show a good agreement with the experimental and numerical simulations in all curves. For some points, few discrepancies can be noted in pressure magnitudes between the simulated and the observed ones, but they are in the acceptable range. Although the experimental data do not completely agree with the simulated results, there is an overall agreement.

Figure 8 Comparison between simulated and experimental results for the dimensionless pressure for steps number  −1, −2, −3 and +1, +2 +3 and +20 on the horizontal step faces of 50°–18.6° slope change configuration, for dc/h = 4.6, x is the distance from the step edge.
Figure 8 Comparison between simulated and experimental results for the dimensionless pressure for steps number −1, −2, −3 and +1, +2 +3 and +20 on the horizontal step faces of 50°–18.6° slope change configuration, for dc/h = 4.6, x is the distance from the step edge.

Figure 8VIEW LARGEDOWNLOAD SLIDE

Comparison between simulated and experimental results for the dimensionless pressure for steps number −1, −2, −3 and +1, +2 +3 and +20 on the horizontal step faces of 50°–18.6° slope change configuration, for dc/h = 4.6, x is the distance from the step edge.

Figure 9 Comparison between simulated and experimental results for the dimensionless pressure for steps number  −1, −2, −3 and +1, +2 and +30, +31 on the horizontal step face of 50°–30° slope change configuration, for dc/h = 4.6, x is the distance from the step edge.
Figure 9 Comparison between simulated and experimental results for the dimensionless pressure for steps number −1, −2, −3 and +1, +2 and +30, +31 on the horizontal step face of 50°–30° slope change configuration, for dc/h = 4.6, x is the distance from the step edge.

Figure 9VIEW LARGEDOWNLOAD SLIDE

Comparison between simulated and experimental results for the dimensionless pressure for steps number −1, −2, −3 and +1, +2 and +30, +31 on the horizontal step face of 50°–30° slope change configuration, for dc/h = 4.6, x is the distance from the step edge.

The pressure profiles were acquired at an acquisition time equal to 70 seconds in skimming flow on 50°–18.6°, where p is the measured dynamic pressure, h is step height and ϒ is water specific weight. A negative sign for steps represents a step upstream of the slope change cross-section and a positive sign represents a step downstream of the slope change cross-section.

Figure 10 shows the experimental streamwise development of dimensionless pressure on the 50°–18.6° slope change for dc/h = 4.6, x/l = 0.35 on 50° sloping chute and x/l = 0.3 on 18.6° sloping chute compared with the numerical simulation. It is obvious from Figure 10 that the streamwise development of dimensionless pressure before slope change (steps number −1, −2 and −3) both of the experimental and simulated results are close to each other. However, it is clear that there is a little difference between the results of the streamwise development of dimensionless pressure at step numbers +1, +2 and +3. Moreover, from step number +3 to the end, the curves get close to each other.

Figure 10 Comparison between experimental and simulated results for the streamwise development of the dimensionless pressure on the 50°–18.6° slope change, for dc/h = 4.6, and x/l = 0.35 on 50° sloping chute and x/l = 0.3 on 18.6° sloping chute.
Figure 10 Comparison between experimental and simulated results for the streamwise development of the dimensionless pressure on the 50°–18.6° slope change, for dc/h = 4.6, and x/l = 0.35 on 50° sloping chute and x/l = 0.3 on 18.6° sloping chute.

Figure 10VIEW LARGEDOWNLOAD SLIDE

Comparison between experimental and simulated results for the streamwise development of the dimensionless pressure on the 50°–18.6° slope change, for dc/h = 4.6, and x/l = 0.35 on 50° sloping chute and x/l = 0.3 on 18.6° sloping chute.

Figure 11 compares the experimental and the numerical results for the streamwise development of the dimensionless pressure on the 50°–30° slope change, for dc/h = 4.6, and x/l = 0.35 on 50° sloping chute and x/l = 0.17 on 30° sloping chute. It is apparent that the outcomes of the experimental work are close to the numerical results, however, the results of the simulation are above the experimental ones before the slope change, but the results of the simulation descend below the experimental ones after the slope change till the end.

Figure 11 Comparison between experimental and simulated results for the streamwise development of the dimensionless pressure on the 50°–30° slope change, for dc/h = 4.6, and x/l = 0.35 on 50° sloping chute and x/l = 0.17 on 30° sloping chute.
Figure 11 Comparison between experimental and simulated results for the streamwise development of the dimensionless pressure on the 50°–30° slope change, for dc/h = 4.6, and x/l = 0.35 on 50° sloping chute and x/l = 0.17 on 30° sloping chute.

Figure 11VIEW LARGEDOWNLOAD SLIDE

Comparison between experimental and simulated results for the streamwise development of the dimensionless pressure on the 50°–30° slope change, for dc/h = 4.6, and x/l = 0.35 on 50° sloping chute and x/l = 0.17 on 30° sloping chute.

CONCLUSION

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In this research, numerical modelling was attempted to investigate the effect of abrupt slope change on the flow properties (air entrainment, velocity distribution and dynamic pressure) over a stepped spillway with two different models and various flow rates in a skimming flow regime by using the CFD technique. The numerical model was verified and compared with the experimental results of Ostad Mirza (2016). The same domain of the numerical model was inputted as in experimental models to reduce errors as much as possible.

Flow-3D is a well modelled tool that deals with particles. In this research, the model deals well with air entrainment particles by observing their results with experimental results. And the reason for the small difference between the numerical and the experimental results is that the program deals with particles more accurately than the laboratory. In general, both numerical and experimental results showed that near to the slope change the flow bulking, air entrainment, velocity distribution and dynamic pressure are greatly affected by abrupt slope change on the steps. Although the extent of the slope change was relatively small, the influence of the slope change was major on flow characteristics.

The Renormalized Group (RNG) model was selected as a turbulence solver. For 3D modelling, orthogonal mesh was used as a computational domain and the mesh grid size used for X, Y, and Z direction was equal to 0.015 m. In CFD modelling, air concentration and velocity distribution were recorded for a period of 25 seconds, but dynamic pressure was recorded for a period of 70 seconds. The results showed that there is a good agreement between the numerical and the physical models. So, it can be concluded that the proposed CFD model is very suitable for use in simulating and analysing the design of hydraulic structures.

이 연구에서 수치 모델링은 두 가지 다른 모델과 다양한 유속을 사용하여 스키밍 흐름 영역에서 계단식 배수로에 대한 유동 특성 (공기 혼입, 속도 분포 및 동적 압력)에 대한 급격한 경사 변화의 영향을 조사하기 위해 시도되었습니다. CFD 기술. 수치 모델을 검증하여 Ostad Mirza (2016)의 실험 결과와 비교 하였다. 오차를 최대한 줄이기 위해 실험 모형과 동일한 수치 모형을 입력 하였다.

Flow-3D는 파티클을 다루는 잘 모델링 된 도구입니다. 이 연구에서 모델은 실험 결과를 통해 결과를 관찰하여 공기 혼입 입자를 잘 처리합니다. 그리고 수치와 실험 결과의 차이가 작은 이유는 프로그램이 실험실보다 입자를 더 정확하게 다루기 때문입니다. 일반적으로 수치 및 실험 결과는 경사에 가까워지면 유동 벌킹, 공기 혼입, 속도 분포 및 동적 압력이 계단의 급격한 경사 변화에 크게 영향을받는 것으로 나타났습니다. 사면 변화의 정도는 상대적으로 작았지만 사면 변화의 영향은 유동 특성에 큰 영향을 미쳤다.

Renormalized Group (RNG) 모델이 난류 솔버로 선택되었습니다. 3D 모델링의 경우 계산 영역으로 직교 메쉬가 사용되었으며 X, Y, Z 방향에 사용 된 메쉬 그리드 크기는 0.015m입니다. CFD 모델링에서 공기 농도와 속도 분포는 25 초 동안 기록되었지만 동적 압력은 70 초 동안 기록되었습니다. 결과는 수치 모델과 물리적 모델간에 좋은 일치가 있음을 보여줍니다. 따라서 제안 된 CFD 모델은 수력 구조물의 설계 시뮬레이션 및 해석에 매우 적합하다는 결론을 내릴 수 있습니다.

DATA AVAILABILITY STATEMENT

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All relevant data are included in the paper or its Supplementary Information.

REFERENCES

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© 2021 The Authors
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Fig. 2. Semi-Lagrangian cellwise advection. (a) Forward advection scheme, (b) Backward advection scheme.

Three-dimensional cellwise conservative unsplit geometric VOF schemes

3차원 셀별 보수 미분할 기하학적 VOF 체계

Raphaël Comminal, JonSpangenberg

Abstract

This work presents two unsplit geometric VOF schemes that extend the two-dimensional cellwise conservative unsplit (CCU) scheme [Comminal et al., J. Comput. Phys. 283 (2015) 582–608] to three dimensions. The novelty of the 3D-CCU schemes lies in the representation of the streaksurfaces of donating regions by polyhedral surfaces whose vertices are calculated with the 4th order Runge-Kutta scheme. Moreover, the advected liquid volumes are computed using a truncation algorithm [López et al., J. Comput. Phys. 392 (2019) 666–693] suited for arbitrary non-convex and self-intersecting polyhedra, which removes the need for tetrahedral decomposition. The 3D-CCU advection schemes were coupled to three interface reconstruction methods (Youngs’ method, the Mixed Youngs-Centered scheme, and the Least-Square Fit algorithm). The resulting VOF methods were tested in classical benchmark advection tests, including translation, rigid-body rotation, shear and deformation flows. The proposed 3D-CCU schemes conserve the liquid volume and maintain the physical boundedness of liquid volume fractions to the machine precision. The 3D-CCU schemes perform favorably compared to other unsplit geometric VOF schemes when coupled to Youngs’ interface reconstruction method. Moreover, the 3D-CCU schemes coupled to the Least-Square Fit algorithm are more accurate than most other VOF schemes that use a second-order accurate interface reconstruction, except those where a 3D extension of the Mosso-Swartz interface reconstruction is employed. The comparison of the different VOF schemes highlights the importance of coupling accurate interface reconstruction methods with accurate unsplit advection schemes.

이 연구는 2 차원 CCU (Cellwise Conservative Unsplit) 방식을 확장하는 두 가지 분할되지 않은 기하학적 VOF 방식을 제시합니다 [Comminal et al., J. Comput. Phys. 283 (2015) 582–608]을 3 차원으로 변경했습니다. 3D-CCU 체계의 참신함은 4 차 Runge-Kutta 체계로 정점이 계산되는 다면체 표면으로 기부 지역의 줄무늬 표면을 표현하는 데 있습니다.

더욱, 가변 액체 부피는 절단 알고리즘을 사용하여 계산됩니다 [López et al., J. Comput. Phys. 392 (2019) 666–693]은 임의의 볼록하지 않고 자기 교차하는 다면체에 적합하며, 이는 사면체 분해의 필요성을 제거합니다. 3D-CCU 이류 계획은 세 가지 인터페이스 재구성 방법 (Youngs의 방법, Mixed Youngs-Centered 계획 및 Least-Square Fit 알고리즘)과 결합되었습니다. 결과 VOF 방법은 평행 이동, 강체 회전, 전단 및 변형 흐름을 포함한 고전적인 벤치 마크 이류 테스트에서 테스트되었습니다.

제안된 3D-CCU 방식은 액체 부피를 보존하고 기계 정밀도에 대한 액체 부피 분율의 물리적 경계를 유지합니다. 3D-CCU 방식은 Youngs의 인터페이스 재구성 방식과 결합 할 때 다른 분할되지 않은 기하학적 VOF 방식에 비해 우수한 성능을 발휘합니다.

또한 Least-Square Fit 알고리즘과 결합 된 3D-CCU 체계는 Mosso-Swartz 인터페이스 재구성의 3D 확장이 사용되는 경우를 제외하고 2 차 정확한 인터페이스 재구성을 사용하는 대부분의 다른 VOF 체계보다 더 정확합니다. 서로 다른 VOF 체계의 비교는 정확한 인터페이스 재구성 방법과 정확한 분할되지 않은 이류 체계를 결합하는 것의 중요성을 강조합니다.

Keywords

Volume-of-fluid methodUnsplit geometric schemeCellwise advectionSemi-Lagrangian trackingVolume conservation

Fig. 1. Eulerian fluxwise advection. (a) Positive donating region with respect to the left cell; (b) Negative donating region; (c) Intersection of a donating region with the cell's face, yielding a positive and a negative region; (d) Temporally-consistent donating regions equivalent to a cellwise advection; (e) Temporal inconsistency of adjacent donating regions.
Fig. 1. Eulerian fluxwise advection. (a) Positive donating region with respect to the left cell; (b) Negative donating region; (c) Intersection of a donating region with the cell’s face, yielding a positive and a negative region; (d) Temporally-consistent donating regions equivalent to a cellwise advection; (e) Temporal inconsistency of adjacent donating regions.
Fig. 2. Semi-Lagrangian cellwise advection. (a) Forward advection scheme, (b) Backward advection scheme.
Fig. 2. Semi-Lagrangian cellwise advection. (a) Forward advection scheme, (b) Backward advection scheme.
Fig. 3. (a) Cartesian grid cell. (b) Images of the cell's vertices with ruled surfaces. (c) Polyhedral cell's image with triangulated faces.
Fig. 3. (a) Cartesian grid cell. (b) Images of the cell’s vertices with ruled surfaces. (c) Polyhedral cell’s image with triangulated faces.
Fig. 4. Construction of donating regions. (a) Streakline of a cell's vertex P0 represented by the 2-segment polygonal line P0–P1/2–P1. (b) Triangulated streaksurface of a cell's edge P0Q0. (c) Streaktube of a cell's face P0Q0R0S0. (d) Pyramidal volume flux correction  ⁎  capping the donating region of the face P0Q0R0S0.
Fig. 4. Construction of donating regions. (a) Streakline of a cell’s vertex P0 represented by the 2-segment polygonal line P0–P1/2–P1. (b) Triangulated streaksurface of a cell’s edge P0Q0. (c) Streaktube of a cell’s face P0Q0R0S0. (d) Pyramidal volume flux correction ⁎ capping the donating region of the face P0Q0R0S0.
Fig. 5. Interface reconstruction. (a) PLIC polygon in the grid cell, (b) Non-planar image of the PLIC polygon inside the cell's image by isomorphism, (c) Planar PLIC inside the cell's image by computation of the average normal vector. (Triangulation of the cell's image faces are omitted for clarity.)
Fig. 5. Interface reconstruction. (a) PLIC polygon in the grid cell, (b) Non-planar image of the PLIC polygon inside the cell’s image by isomorphism, (c) Planar PLIC inside the cell’s image by computation of the average normal vector. (Triangulation of the cell’s image faces are omitted for clarity.)
Fig. 6. Convergence of the geometric errors in the translation tests.
Fig. 6. Convergence of the geometric errors in the translation tests.
Fig. 7. Reconstructed PLIC polygons (in light blue) superimposed to the exact sphere position (in dark blue) at the end of the rotation tests for the LSF method and CFL = 1.
Fig. 7. Reconstructed PLIC polygons (in light blue) superimposed to the exact sphere position (in dark blue) at the end of the rotation tests for the LSF method and CFL = 1.
Fig. 8. Reconstructed PLIC polygons in the shear tests, at Tf/2 (top row) and Tf (bottom row). Blue polygons are computed with the LSF procedure; green polygons with centered column differences; red polygons with Youngs' method.
Fig. 8. Reconstructed PLIC polygons in the shear tests, at Tf/2 (top row) and Tf (bottom row). Blue polygons are computed with the LSF procedure; green polygons with centered column differences; red polygons with Youngs’ method.
Fig. 9. Reconstructed PLIC polygons in the deformation tests, at Tf/2 (top row) and Tf (bottom row). Blue polygons are computed with the LSF procedure; green polygons with centered column differences; red polygons with Youngs' method.
Fig. 9. Reconstructed PLIC polygons in the deformation tests, at Tf/2 (top row) and Tf (bottom row). Blue polygons are computed with the LSF procedure; green polygons with centered column differences; red polygons with Youngs’ method.

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1
This definition of the CFL number is different from the usual definition used in multi-dimensional algebraic advection schemes. However, the component-wise definition is more meaningful in the context of geometric VOF schemes, because it determines the number of layers of cells around the interfacial cells where the liquid volume fractions need to be updated.

Effect of Y2O3 on microstructure

Hierarchical grain refinement during the laser additive manufacturing of Ti-6Al-4V alloys by the addition of micron-sized refractory particles

미크론 크기의 내화물 입자를 추가하여 Ti-6Al-4V 합금의 레이저 적층 제조중 계층적 입자 미세 조정

Xiang Wang, Lin-Jie Zhang, Jie Ning, Sen Li, Liang-Liang Zhang, Jian Long
State Key Laboratory for Mechanical Behavior of Materials, Xi’an Jiaotong University, Xi’an 710049, China

Abstract

Ti-6Al-4V alloys mad by additive manufacturing (AM) with slower cooling rate (e. g., direct energy deposition (DED)) generally have the problem of severe coarsening of α phase. This study presents a method to refine the microstructure of the primary β phase formed during the solid–liquid transformation, microstructures formed during the β → α + β transformation, and recrystallized microstructures formed during the repeated heating cycles encountered in AM processes. This is accomplished by the in situ precipitation of nano-sized dispersed high-melting-point yttria Y2O3 particles. The addition of micron-sized particles with high melting points can refine primary crystallized grains and transformed grains corresponding to the secondary phase in Ti-6Al-4V alloys. In addition, they can effectively inhibit the recrystallization and growth of prior-deposited metal grains. The microstructural and tensile properties of laser additive manufactured with filler wire Ti-6Al-4V components with different amounts of Y2O3 (0, 0.12, and 0.22 wt%) were investigated. The refining effect of Y2O3 was significant and the tensile strength of Ti-6Al-4V containing 0.22 wt% Y2O3 in the longitudinal and transverse directions was greater than that of Ti-6Al-4V by approximately 12% and 9%, respectively. Concurrently, there was no loss in the elongation of the material in either direction. The strategy of using micron-sized refractory particles to control phase transformation (primary crystallization, solid-state phase transformation, and recrystallization) can be applied to the AM of different metals, in which microstructures are susceptible to coarsening.

냉각 속도가 느린 적층 제조(AM)에 의해 제조된 Ti-6Al-4V 합금은 일반적으로 α상(예: 직접 에너지 증착(DED)의 심각한 응고 문제를 가지고 있습니다. 이 연구는 고체-액체 변환 중에 형성된 1 차 β상의 미세 구조, β → α + β 변환 중에 형성된 미세 구조, AM 공정에서 발생하는 반복되는 가열주기 동안 형성된 재 결정화된 미세 구조를 정제하는 방법을 제시합니다.

이것은 나노 크기의 분산된 고 융점이 트리아 Y2O3 입자의 현장 침전에 의해 달성됩니다. 녹는 점이 높은 미크론 크기의 입자를 추가하면 Ti-6Al-4V 합금의 2 차 상에 해당하는 1차 결정 입자 및 변형된 입자를 정제 할 수 있습니다.

또한 사전에 증착된 금속 입자의 재 결정화 및 성장을 효과적으로 억제 할 수 있습니다. Y2O3 (0, 0.12, 0.22 wt %)의 양이 다른 필러 와이어 Ti-6Al-4V 성분으로 제조 된 레이저 첨가제의 미세 구조 및 인장 특성을 조사했습니다.

Y2O3의 정제 효과는 유의미했으며, Y2O3 0.22 wt %를 세로 및 가로 방향으로 포함하는 Ti-6Al-4V의 인장 강도는 Ti-6Al-4V보다 각각 약 12 ​​% 및 9 % 더 컸습니다. 동시에 어느 방향으로도 재료의 연신율에 손실이 없었습니다.

미크론 크기의 내화 입자를 사용하여 상 변환 (1 차 결정화, 고체 상 변환 및 재결정 화)을 제어하는 ​​전략은 미세 구조가 거칠어지기 쉬운 다양한 금속의 AM에 적용될 수 있습니다.

Effect of Y2O3 on microstructure
Effect of Y2O3 on microstructure

Keywords: Grain hierarchical refinement, YttriaSolidification microstructures, Solid phase transition microstructures, Recrystallization microstructures

Numerical simulation of slag movement from Marangoni flow for GMAW with computational fluid dynamics Figures

Numerical simulation of slag movement from Marangoni flow for GMAW with computational fluid dynamics

전산 유체 역학을 사용하여 GMAW에 대한 Marangoni 흐름에서 슬래그 이동의 수치 시뮬레이션

Dae-WonChoaYeong-DoParkbMuralimohanCheepucaBusan Machinery Research Center, Korea Institute of Machinery and Materials, 48, Mieumsandan 5-ro 41beon-gil, Gangseo-gu, Busan 46744, Republic of KoreabDepartment of Advanced Materials Engineering, Dong-Eui University, Busan, Republic of KoreacSuper-TIG Welding Co., Limited, Busan, Republic of Korea

Keywords : Marangoni flowMolten slag movementMolten pool behavorSurface tension gradient

Abstract

이 연구는 전산 유체 역학을 이용하여 스프레이 모드 가스 금속 아크 용접에서 생성되는 산화물인 용융 슬래그의 거동을 분석했습니다. 주로 규산염 (SiO2)으로 구성된 용융 슬래그는 용융 풀 표면에 있습니다. 일반적으로 용융 슬래그는 아크 플라즈마 경계 주변에서 생성된다고 가정합니다.

따라서 이 연구의 수치 시뮬레이션에서 슬래그는 특정 밀도와 크기를 가진 구형 입자로 모델링됩니다. Marangoni 유동 효과를 비교하기 위해 이 연구는 표면 장력 구배가 다른 두 가지 사례 (양수 및 음수)를 조사했습니다. 수치 시뮬레이션과 실험 결과 모두 음의 표면 장력 구배가 비드 가장자리에 갇힌 슬래그를 형성하는 반면 양의 표면 장력 구배는 상단 표면의 중앙에 갇힌 슬래그를 형성하는 것으로 나타났습니다.

This study analyzed the behavior of molten slag, which is an oxide generated during spray mode gas metal arc welding, with computational fluid dynamics. The molten slag, composed mainly of silicate (SiO2), is located on the molten pool surface. It is generally assumed that the molten slag is generated around the arc plasma boundary. Therefore, in the numerical simulation in this study the slag is modeled as a spherical particle, which has a specific density and size. To compare the Marangoni flow effect, this study investigated two different cases where the surface tension gradients were different (positive and negative). In both the numerical simulation and experimental results it was found that negative surface tension gradient formed trapped slag on the bead edge while the positive surface tension gradient formed trapped slag on the center of the top surface.

Numerical simulation of slag movement from Marangoni flow for GMAW with computational fluid dynamics Figures
Numerical simulation of slag movement from Marangoni flow for GMAW with computational fluid dynamics Figures
Weld bead surface images showing the slag formation location for (a) wire 1 and (b) wire 2.

The effect of alloying elements of gas metal arc welding (GMAW) wire on weld pool flow and slag formation location in cold metal transfer (CMT)

가스 금속 아크 용접 (GMAW) 와이어의 합금 원소가 CMT (Cold Metal Transfer)에서 용접 풀 흐름 및 슬래그 형성 위치에 미치는 영향

Md. R. U. Ahsan1,3, Muralimohan. Cheepu2, Yeong-Do Park* 2,3
1Department of Mechanical Engineering, International University of Business, Agriculture and Technology,
Dhaka 1230, Bangladesh.
r.ahsan06me@gmail.com
2Department of Advanced Materials and Industrial Management Engineering, Dong-Eui University, Busan
47340, Republic of Korea.
muralicheepu@gmail.com
3Department of Advanced Materials Engineering, Dong-Eui University, B

Abstract

용접시 표면 장력 구동 흐름 또는 마랑고니 흐름은 용접 비드 모양을 제어하는데 중요한 역할을 하므로 용접 접합 품질에 영향을 미칩니다. 용해된 금속의 표면 장력은 보통 음의 온도 계수를 가지므로 용접 풀이 중심에서 토우 방향으로 흐르게 됩니다.

표면 장력의 이 온도 계수는 황(S), 산소(O), 셀레늄(Se) 및 텔루륨(Te)과 같은 표면 활성 요소가 있는 경우 양의 계수로 변경할 수 있습니다. 소모품에 존재하는 탈산화 원소의 양이 용접 금속에 존재하는 산소량을 결정합니다. 탈산화제 양이 적으면 용접 금속에 산소 농도가 높아집니다.

적절한 양의 산소가 있으면 용융지에 표면 장력 구배의 양의 온도 계수가 발생할 수 있습니다. 이 경우 용접 풀은 토우에서 중앙 방향으로 흐릅니다. 그 결과, 아크와 용융지에 있는 화농성 반응의 경우, 합금 요소의 다양한 산화물이 슬래그(slag)라고 합니다. 슬래그는 용융지 표면에 떠서 용융지 흐름 패턴에 따라 누적됩니다.

그 결과, 슬래그는 용융지 흐름 패턴에 따라 용접 비드 중심 또는 토우 중심을 따라 형성됩니다. 슬래그는 용접 비드의 외관과 도장 접착력을 저하시키므로 제거해야 합니다. 쉽게 분리할 수 있기 때문에 용접 비드 중심 부근에서 슬래그가 형성되는 것이 좋습니다.

용접 풀의 현장 고속 비디오 촬영, 용접 금속 화학 성분 분석, 소모품 합금 요소가 용접 풀 흐름 패턴 및 슬래그 형성 위치에 미치는 영향이 공개되어 CMT-GMAW의 생산성 향상을 위해 용접 소모품 선택을 용이하게 할 수 있습니다.

The surface tension driven flow or Marangoni flow in welding plays an important role in governing weld bead shape hence affecting the weld joint quality. The surface tension of molten metal usually has a negative temperature coefficient causing the weld pool to flow from the center towards the toe.

This temperature coefficient of the surface tension can be altered to be a positive one in the presence of surface-active elements like sulfur (S), oxygen (O), selenium (Se) and tellurium (Te). The amount of deoxidizing elements present in the consumables governs the amount of oxygen present in the weld metal. The presence of a lower amount of deoxidizers results in higher concentration of oxygen in the weld metal.

The presence of adequate amount of oxygen can result in a positive temperature coefficient of surface tension gradient in the weld pool. In such situation, the weld pool flows from the toe towards the direction of the center. As a result, of pyrometallurgical reactions in the arc and the weld pool various oxides of the alloying elements are former which are referred as slag.

The slags float on the weld pool surface and accumulate following the weld pool flow pattern. As a result, slags form either along the center of the weld bead or the toe depending on the weld pool flow pattern. The slags need to be removed as they degrade the weld bead appearance and paint adhesiveness.

Due to easy detachability, slag formation near the center of the weld bead is desired. From in-situ high-speed videography of weld pool, weld metal chemical composition analysis, the effect of consumables alloying elements on weld pool flow pattern and slag formation location are disclosed, which can facilitate the selection of the welding consumables for better productivity in CMT-GMAW.

Weld bead surface images showing the slag formation location for (a) wire 1 and (b) wire 2.
Weld bead surface images showing the slag formation location for (a) wire 1 and (b) wire 2.
Fig. 2: High-speed movie frames and schematic showing the weld pool flow pattern and the slag formation location for wire 1 and wire 2.
Fig. 2: High-speed movie frames and schematic showing the weld pool flow pattern and the slag formation location for wire 1 and wire 2.
Fig. 3: Quantitative analysis data on slag formation for different wire.
Fig. 3: Quantitative analysis data on slag formation for different wire.

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Fig. 9 (a) Velocity field, keyhole profile, and breakage of the keyhole to form bubble and (b) 2D temperature and velocity field along the longitudinal section

A Numerical Study on the Keyhole Formation During Laser Powder Bed Fusion Process

Keyhole에 대한 수치적 연구 : 레이저 분말 중 형성 베드 퓨전 공정

Subin Shrestha1
J.B. Speed School of Engineering,University of Louisville,Louisville, KY 40292
e-mail: subin.shrestha@louisville.edu

Y. Kevin Chou
J.B. Speed School of Engineering,University of Louisville,Louisville, KY 40292
e-mail: kevin.chou@louisville.edu

LPBF (Laser Powder Bed fusion) 공정 중 용융 풀의 동적 현상은 복잡하고 공정 매개 변수에 민감합니다. 에너지 밀도 입력이 특정 임계 값을 초과하면 키홀이라고 하는 거대한 증기 함몰이 형성 될 수 있습니다.

이 연구는 수치 분석을 통해 LPBF 과정에서 키홀 거동 및 관련 기공 형성을 이해하는 데 중점을 둡니다. 이를 위해 이산 분말 입자가 있는 열 유동 모델이 개발되었습니다.

이산 요소 방법 (DEM)에서 얻은 분말 분포는 계산 영역에 통합되어 FLOW-3D를 사용하는 3D 프로세스 물리학 모델을 개발합니다.

전도 모드 중 용융 풀 형성과 용융의 키홀 모드가 식별되고 설명되었습니다. 높은 에너지 밀도는 증기 기둥의 형성으로 이어지고 결과적으로 레이저 스캔 트랙 아래에 구멍이 생깁니다.

또한 다양한 레이저 출력과 스캔 속도로 인한 Keyhole 모양을 조사합니다. 수치 결과는 동일한 에너지 밀도에서도 레이저 출력이 증가함에 따라 Keyhole크기가 증가 함을 나타냅니다. Keyhole은 더 높은 출력에서 ​​안정되어 레이저 스캔 중 Keyhole 발생을 줄일 수 있습니다.

The dynamic phenomenon of a melt pool during the laser powder bed fusion (LPBF) process is complex and sensitive to process parameters. As the energy density input exceeds a certain threshold, a huge vapor depression may form, known as the keyhole. This study focuses on understanding the keyhole behavior and related pore formation during the LPBF process through numerical analysis. For this purpose, a thermo-fluid model with discrete powder particles is developed. The powder distribution, obtained from a discrete element method (DEM), is incorporated into the computational domain to develop a 3D process physics model using flow-3d. The melt pool formation during the conduction mode and the keyhole mode of melting has been discerned and explained. The high energy density leads to the formation of a vapor column and consequently pores under the laser scan track. Further, the keyhole shape resulted from different laser powers and scan speeds is investigated. The numerical results indicated that the keyhole size increases with the increase in the laser power even with the same energy density. The keyhole becomes stable at a higher power, which may reduce the occurrence of pores during laser scanning.

Keywords: additive manufacturing, keyhole, laser powder bed fusion, porosity

Fig. 1 (a) Powder added to the dispenser platform and (b) powder particles settled over build plate after the recoating process
Fig. 1 (a) Powder added to the dispenser platform and (b) powder particles settled over build plate after the recoating process
Fig. 2 3D computational domain used for single-track simulation
Fig. 2 3D computational domain used for single-track simulation
Fig. 3 Temperature-dependent material properties of Ti-6Al-4V
Fig. 3 Temperature-dependent material properties of Ti-6Al-4V
Fig. 4 Powder and substrate melting during laser application
Fig. 4 Powder and substrate melting during laser application
Fig. 5 Melt region formed after complete melting and solidification
Fig. 5 Melt region formed after complete melting and solidification
Fig. 6 Melt pool boundary comparison between the experiment [25] and the simulation
Fig. 6 Melt pool boundary comparison between the experiment [25] and the simulation
Fig. 7 Equilibrium points during the formation of vapor column [27]
Fig. 7 Equilibrium points during the formation of vapor column [27]
Fig. 8 Multiple reflection vectors from the keyhole wall
Fig. 8 Multiple reflection vectors from the keyhole wall
Fig. 9 (a) Velocity field, keyhole profile, and breakage of the keyhole to form bubble and (b) 2D temperature and velocity field along the longitudinal section
Fig. 9 (a) Velocity field, keyhole profile, and breakage of the keyhole to form bubble and (b) 2D temperature and velocity field along the longitudinal section
Fig. 10 Fluid flow in the transverse direction during keyhole melting
Fig. 10 Fluid flow in the transverse direction during keyhole melting
Fig. 11 Melt pool boundary compared with the experiment [21] for 195 W laser power and 400 mm/s scan speed
Fig. 11 Melt pool boundary compared with the experiment [21] for 195 W laser power and 400 mm/s scan speed
Fig. 12 Melt region formed after complete melting and solidification
Fig. 12 Melt region formed after complete melting and solidification
Fig. 13 2D images of the pores formed at the beginning of the single track and their 3D-rendered morphology
Fig. 13 2D images of the pores formed at the beginning of the single track and their 3D-rendered morphology
Fig. 14 Pore number and volume from a different level of power with LED = 0.4 J/mm [29]
Fig. 14 Pore number and volume from a different level of power with LED = 0.4 J/mm [29]
Fig. 15 Keyhole shape at different time steps from different parameters: (a) P = 100 W, v = 250 mm/s, (b) P = 200 W, v = 500 mm/s, (c) P = 300 W, v = 750 mm/s, and (d) P = 400 W, v = 1000 mm/s
Fig. 15 Keyhole shape at different time steps from different parameters: (a) P = 100 W, v = 250 mm/s, (b) P = 200 W, v = 500 mm/s, (c) P = 300 W, v = 750 mm/s, and (d) P = 400 W, v = 1000 mm/s
Fig. 16 Intensity dependence in the relationship between vapor column and evaporation pressure [27]
Fig. 16 Intensity dependence in the relationship between vapor column and evaporation pressure [27]
Fig. 17 Temperature distribution when laser has moved 0.8 mm with P = 300 W, v = 750 mm/s and P = 400 W, v = 1000 mm/s
Fig. 17 Temperature distribution when laser has moved 0.8 mm with P = 300 W, v = 750 mm/s and P = 400 W, v = 1000 mm/s
Fig. 18 Melt region with different level of power with LED of 0.4 J/mm
Fig. 18 Melt region with different level of power with LED of 0.4 J/mm

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Figure 1 (A) A schematic of ovarian cancer metastases involving tumor cells or clusters (yellow) shedding from a primary site and disseminating along ascitic currents of peritoneal fluid (green arrows) in the abdominal cavity. Ovarian cancer typically disseminates in four common abdomino-pelvic sites: (1) cul-de-sac (an extension of the peritoneal cavity between the rectum and back wall of the uterus); (2) right infracolic space (the apex formed by the termination of the small intestine of the small bowel mesentery at the ileocecal junction); (3) left infracolic space (superior site of the sigmoid colon); (4) Right paracolic gutter (communication between the upper and lower abdomen defined by the ascending colon and peritoneal wall). (B) The schematic of a perfusion model used to study the impact of sustained fluid flow on treatment resistance and molecular features of 3D ovarian cancer nodules (Top left). A side view of the perfusion model and growth of ovarian cancer nodules to a stromal bed (Top right). The photograph of a perfusion model used in the experiments (Bottom left) and depth-informed confocal imaging of ovarian cancer nodules in channels with and without carboplatin treatment (Bottom right). The perfusion model is 24 × 40 mm, with three channels that are 4 × 30 mm each and a height of 254 μm. The inlet and outlet ports of channels are 2.2 mm in diameter and positioned 5 mm from the edge of the chip. (C) A schematic of a 24-well plate model used to study the treatment resistance and molecular features of 3D ovarian cancer nodules under static conditions (without flow) (Top left). A side view of the static models and growth of ovarian cancer nodules on a stromal bed (Top right). Confocal imaging of 3D ovarian cancer nodules in a 24-well plate without and with carboplatin treatment (Bottom). Scale bars: 1 mm.

Flow-induced Shear Stress Confers Resistance to Carboplatin in an Adherent Three-Dimensional Model for Ovarian Cancer: A Role for EGFR-Targeted Photoimmunotherapy Informed by Physical Stress

난소암에 대한 일관된 3차원 모델에서 카보플라틴에 대한 유동에 의한 전단응력변화에 관한 연구

Abstract

A key reason for the persistently grim statistics associated with metastatic ovarian cancer is resistance to conventional agents, including platinum-based chemotherapies. A major source of treatment failure is the high degree of genetic and molecular heterogeneity, which results from significant underlying genomic instability, as well as stromal and physical cues in the microenvironment. Ovarian cancer commonly disseminates via transcoelomic routes to distant sites, which is associated with the frequent production of malignant ascites, as well as the poorest prognosis. In addition to providing a cell and protein-rich environment for cancer growth and progression, ascitic fluid also confers physical stress on tumors. An understudied area in ovarian cancer research is the impact of fluid shear stress on treatment failure. Here, we investigate the effect of fluid shear stress on response to platinum-based chemotherapy and the modulation of molecular pathways associated with aggressive disease in a perfusion model for adherent 3D ovarian cancer nodules. Resistance to carboplatin is observed under flow with a concomitant increase in the expression and activation of the epidermal growth factor receptor (EGFR) as well as downstream signaling members mitogen-activated protein kinase/extracellular signal-regulated kinase (MEK) and extracellular signal-regulated kinase (ERK). The uptake of platinum by the 3D ovarian cancer nodules was significantly higher in flow cultures compared to static cultures. A downregulation of phospho-focal adhesion kinase (p-FAK), vinculin, and phospho-paxillin was observed following carboplatin treatment in both flow and static cultures. Interestingly, low-dose anti-EGFR photoimmunotherapy (PIT), a targeted photochemical modality, was found to be equally effective in ovarian tumors grown under flow and static conditions. These findings highlight the need to further develop PIT-based combinations that target the EGFR, and sensitize ovarian cancers to chemotherapy in the context of flow-induced shear stress.

전이성 난소 암과 관련된 지속적으로 암울한 통계의 주요 이유는 백금 기반 화학 요법을 포함한 기존 약제에 대한 내성 때문입니다. 치료 실패의 주요 원인은 높은 수준의 유전적 및 분자적 이질성이며, 이는 중요한 기본 게놈 불안정성과 미세 환경의 기질 및 물리적 단서로 인해 발생합니다.

난소 암은 흔히 transcoelomic 경로를 통해 먼 부위로 전파되며, 이는 악성 복수의 빈번한 생산과 가장 나쁜 예후와 관련이 있습니다. 암 성장 및 진행을위한 세포 및 단백질이 풍부한 환경을 제공하는 것 외에도 복수 액은 종양에 물리적 스트레스를 부여합니다. 난소 암 연구에서 잘 연구되지 않은 분야는 유체 전단 응력이 치료 실패에 미치는 영향입니다.

여기, 우리는 백금 기반 화학 요법에 대한 반응과 부착 3D 난소 암 결절에 대한 관류 모델에서 공격적인 질병과 관련된 분자 경로의 변조에 대한 유체 전단 응력의 효과를 조사합니다.

카르보플라틴에 대한 내성은 상피 성장 인자 수용체 (EGFR)의 발현 및 활성화의 수반되는 증가 뿐만 아니라 다운 스트림 신호 구성원인 미토겐 활성화 단백질 키나제/세포 외 신호 조절 키나제 (MEK) 및 세포 외 신호 조절과 함께 관찰됩니다. 키나아제 (ERK). 3D 난소 암 결절에 의한 백금 흡수는 정적 배양에 비해 유동 배양에서 상당히 높았습니다.

포스 포-포컬 접착 키나제 (p-FAK), 빈 쿨린 및 포스 포-팍 실린의 하향 조절은 유동 및 정적 배양 모두에서 카보 플 라틴 처리 후 관찰되었습니다. 흥미롭게도, 표적 광 화학적 양식 인 저용량 항 EGFR 광 면역 요법 (PIT)은 유동 및 정적 조건에서 성장한 난소 종양에서 똑같이 효과적인 것으로 밝혀졌습니다.

이러한 발견은 EGFR을 표적으로하는 PIT 기반 조합을 추가로 개발하고 흐름 유도 전단 응력의 맥락에서 화학 요법에 난소 암을 민감하게 할 필요성을 강조합니다.

Keywords: ovarian cancer, epidermal growth factor receptor (EGFR), mitogen-activated protein kinase/extracellular signal-regulated kinase (MEK), extracellular signal-regulated kinase (ERK), chemoresistance, fluid shear stress, ascites, perfusion model, photoimmunotherapy (PIT), photodynamic therapy (PDT), carboplatin

Figure 1 (A) A schematic of ovarian cancer metastases involving tumor cells or clusters (yellow) shedding from a primary site and disseminating along ascitic currents of peritoneal fluid (green arrows) in the abdominal cavity. Ovarian cancer typically disseminates in four common abdomino-pelvic sites: (1) cul-de-sac (an extension of the peritoneal cavity between the rectum and back wall of the uterus); (2) right infracolic space (the apex formed by the termination of the small intestine of the small bowel mesentery at the ileocecal junction); (3) left infracolic space (superior site of the sigmoid colon); (4) Right paracolic gutter (communication between the upper and lower abdomen defined by the ascending colon and peritoneal wall). (B) The schematic of a perfusion model used to study the impact of sustained fluid flow on treatment resistance and molecular features of 3D ovarian cancer nodules (Top left). A side view of the perfusion model and growth of ovarian cancer nodules to a stromal bed (Top right). The photograph of a perfusion model used in the experiments (Bottom left) and depth-informed confocal imaging of ovarian cancer nodules in channels with and without carboplatin treatment (Bottom right). The perfusion model is 24 × 40 mm, with three channels that are 4 × 30 mm each and a height of 254 μm. The inlet and outlet ports of channels are 2.2 mm in diameter and positioned 5 mm from the edge of the chip. (C) A schematic of a 24-well plate model used to study the treatment resistance and molecular features of 3D ovarian cancer nodules under static conditions (without flow) (Top left). A side view of the static models and growth of ovarian cancer nodules on a stromal bed (Top right). Confocal imaging of 3D ovarian cancer nodules in a 24-well plate without and with carboplatin treatment (Bottom). Scale bars: 1 mm.
Figure 1 (A) A schematic of ovarian cancer metastases involving tumor cells or clusters (yellow) shedding from a primary site and disseminating along ascitic currents of peritoneal fluid (green arrows) in the abdominal cavity. Ovarian cancer typically disseminates in four common abdomino-pelvic sites: (1) cul-de-sac (an extension of the peritoneal cavity between the rectum and back wall of the uterus); (2) right infracolic space (the apex formed by the termination of the small intestine of the small bowel mesentery at the ileocecal junction); (3) left infracolic space (superior site of the sigmoid colon); (4) Right paracolic gutter (communication between the upper and lower abdomen defined by the ascending colon and peritoneal wall). (B) The schematic of a perfusion model used to study the impact of sustained fluid flow on treatment resistance and molecular features of 3D ovarian cancer nodules (Top left). A side view of the perfusion model and growth of ovarian cancer nodules to a stromal bed (Top right). The photograph of a perfusion model used in the experiments (Bottom left) and depth-informed confocal imaging of ovarian cancer nodules in channels with and without carboplatin treatment (Bottom right). The perfusion model is 24 × 40 mm, with three channels that are 4 × 30 mm each and a height of 254 μm. The inlet and outlet ports of channels are 2.2 mm in diameter and positioned 5 mm from the edge of the chip. (C) A schematic of a 24-well plate model used to study the treatment resistance and molecular features of 3D ovarian cancer nodules under static conditions (without flow) (Top left). A side view of the static models and growth of ovarian cancer nodules on a stromal bed (Top right). Confocal imaging of 3D ovarian cancer nodules in a 24-well plate without and with carboplatin treatment (Bottom). Scale bars: 1 mm.
Figure 2 (A) Geometry of the micronodule located at the center of the microchannel. The flow velocity is in the X-direction. The nodule is modeled as an ellipse with a semi-minor axis of 40 μm in the Z-direction. The semi-major axis varies from 40-100 μm in the X-direction. The section over which the fluid dynamics are studied is the middle part of the channel with dimensions 4 mm along the Y-axis and 250 μm along the Z-axis. The nodule is located at (0, 20 μm). The black dotted line shows the centerline of the largest nodule. (B) Shear stress distribution over the surface of the solid micro-nodule on the XZ-plane. (C) Shear stress distribution over the surface of the porous micro-nodule on the XZ-plane. (D) Flow flux distribution over the centerline of the porous micro-nodule on the XZ-plane. The flux enters the surface at the left and leaves at the right.
Figure 2 (A) Geometry of the micronodule located at the center of the microchannel. The flow velocity is in the X-direction. The nodule is modeled as an ellipse with a semi-minor axis of 40 μm in the Z-direction. The semi-major axis varies from 40-100 μm in the X-direction. The section over which the fluid dynamics are studied is the middle part of the channel with dimensions 4 mm along the Y-axis and 250 μm along the Z-axis. The nodule is located at (0, 20 μm). The black dotted line shows the centerline of the largest nodule. (B) Shear stress distribution over the surface of the solid micro-nodule on the XZ-plane. (C) Shear stress distribution over the surface of the porous micro-nodule on the XZ-plane. (D) Flow flux distribution over the centerline of the porous micro-nodule on the XZ-plane. The flux enters the surface at the left and leaves at the right.
Figure 3 Cytotoxic response in carboplatin-treated 3D OVCAR-5 cultures under static conditions. (A) Representative confocal images of 3D tumors treated with carboplatin (0-500 μM) for 96 h showing a dose-dependent reduction in viable tumor (calcein signal). (B) Image-based quantification of normalized viable tumor area in 3D OVCAR-5 cultures following treatment with increasing doses of carboplatin. A minimum nodule size cut-off of 2000 µm2 (clusters of ~15–20 cells) was applied to the fluorescence images for quantitative analysis of the normalized viable tumor area. (One-way ANOVA with Dunnett’s post hoc test; n.s., not significant; * p < 0.05; *** p < 0.001; N = 9) (C) Inductively coupled plasma mass spectrometry (ICP-MS)-based quantification of carboplatin uptake in static 3D OVCAR-5 tumors shows a dose-dependent increase in platinum levels, up to 9774 ± 3,052 ng/mg protein at an incubation concentration of 500 μM carboplatin. (One-way ANOVA with Dunn’s multiple comparisons test; n.s., not significant; * p < 0.05; ** p < 0.01; N = 3). Results are expressed as mean ± standard error of mean (SEM). Scale bars: 500 μm.
Figure 3 Cytotoxic response in carboplatin-treated 3D OVCAR-5 cultures under static conditions. (A) Representative confocal images of 3D tumors treated with carboplatin (0-500 μM) for 96 h showing a dose-dependent reduction in viable tumor (calcein signal). (B) Image-based quantification of normalized viable tumor area in 3D OVCAR-5 cultures following treatment with increasing doses of carboplatin. A minimum nodule size cut-off of 2000 µm2 (clusters of ~15–20 cells) was applied to the fluorescence images for quantitative analysis of the normalized viable tumor area. (One-way ANOVA with Dunnett’s post hoc test; n.s., not significant; * p < 0.05; *** p < 0.001; N = 9) (C) Inductively coupled plasma mass spectrometry (ICP-MS)-based quantification of carboplatin uptake in static 3D OVCAR-5 tumors shows a dose-dependent increase in platinum levels, up to 9774 ± 3,052 ng/mg protein at an incubation concentration of 500 μM carboplatin. (One-way ANOVA with Dunn’s multiple comparisons test; n.s., not significant; * p < 0.05; ** p < 0.01; N = 3). Results are expressed as mean ± standard error of mean (SEM). Scale bars: 500 μm.
Figure 4 flow-induced chemo-resistance
Figure 4 flow-induced chemo-resistance
Figure 5 The effects of flow-induced shear stress on 3D ovarian cancer biology. (A) Western blot analysis of OVCAR-5 tumors was performed 7 days after culture under static or flow conditions. A flow-induced increase in EGFR and p-ERK, compared to static cultures, was observed. Conversely, a reduction in p-FAK, p-Paxillin, and Vinculin was observed under flow, relative to static conditions. (B) Western blot analysis of 3D OVCAR-5 tumors was performed 11 days after culture under static or flow conditions, including 4 days of treatment with 500 µM carboplatin, and respective controls. In both static and flow 3D cultures, carboplatin treatment resulted in downregulation of EGFR, FAK, p-Paxillin, Paxillin, and Vinculin. Upregulation of p-ERK was observed after carboplatin treatment in both static and flow 3D cultures. (C) Baseline levels of EGFR activity and expression are maintained by a complex array of factors, including recycling and degradation of the activated receptor complex. Flow-induced shear stress has been shown to cause a posttranslational up-regulation of EGFR expression and activation, likely resulting from increased receptor recycling and decreased EGFR degradation. Activation of EGFR results in ERK phosphorylation to induce gene expression, ultimately leading to cell proliferation, survival, and chemoresistance. FAK and other tyrosine kinases are activated by the engagement of integrins with the ECM. Subsequent phosphorylation of paxillin by FAK not only influences the remodeling of the actin cytoskeleton, but also modulates vinculin activation to regulate mitogen-activated protein kinase (MAPK) cascades, thereby stimulating pro-survival gene expression.
Figure 5 The effects of flow-induced shear stress on 3D ovarian cancer biology. (A) Western blot analysis of OVCAR-5 tumors was performed 7 days after culture under static or flow conditions. A flow-induced increase in EGFR and p-ERK, compared to static cultures, was observed. Conversely, a reduction in p-FAK, p-Paxillin, and Vinculin was observed under flow, relative to static conditions. (B) Western blot analysis of 3D OVCAR-5 tumors was performed 11 days after culture under static or flow conditions, including 4 days of treatment with 500 µM carboplatin, and respective controls. In both static and flow 3D cultures, carboplatin treatment resulted in downregulation of EGFR, FAK, p-Paxillin, Paxillin, and Vinculin. Upregulation of p-ERK was observed after carboplatin treatment in both static and flow 3D cultures. (C) Baseline levels of EGFR activity and expression are maintained by a complex array of factors, including recycling and degradation of the activated receptor complex. Flow-induced shear stress has been shown to cause a posttranslational up-regulation of EGFR expression and activation, likely resulting from increased receptor recycling and decreased EGFR degradation. Activation of EGFR results in ERK phosphorylation to induce gene expression, ultimately leading to cell proliferation, survival, and chemoresistance. FAK and other tyrosine kinases are activated by the engagement of integrins with the ECM. Subsequent phosphorylation of paxillin by FAK not only influences the remodeling of the actin cytoskeleton, but also modulates vinculin activation to regulate mitogen-activated protein kinase (MAPK) cascades, thereby stimulating pro-survival gene expression.
Figure 6 PIT efficacy in 3D tumors. (A) Dose-dependent change in normalized viable tumor area in static 3D cultures treated with PIC (1 μM BPD equivalent) and increasing energy densities (10–50 J/cm2 @ 50 mW/cm2). Significant tumoricidal efficacy is observed in a light-dose-dependent manner, starting at 15 J/cm2. (One-way ANOVA with Dunnett’s post hoc test; n.s., not significant; ** p < 0.01, *** p < 0.001, N = 9) (B) Comparison of cytotoxic response in PIT-treated 3D cultures under static and flow conditions. For quantitative analysis of fluorescence images, a minimum nodule size cut-off of 2000 µm2 (clusters of ~15–20 cells) was used to establish normalized viable tumor area. PIT is equally effective in 3D tumors grown in static cultures (green) and under flow-induced shear stress (blue) (in contrast to flow-induced chemo-resistance shown in Figure 4) (Two-tailed t test; n.s., not significant; N = 9).
Figure 6 PIT efficacy in 3D tumors. (A) Dose-dependent change in normalized viable tumor area in static 3D cultures treated with PIC (1 μM BPD equivalent) and increasing energy densities (10–50 J/cm2 @ 50 mW/cm2). Significant tumoricidal efficacy is observed in a light-dose-dependent manner, starting at 15 J/cm2. (One-way ANOVA with Dunnett’s post hoc test; n.s., not significant; ** p < 0.01, *** p < 0.001, N = 9) (B) Comparison of cytotoxic response in PIT-treated 3D cultures under static and flow conditions. For quantitative analysis of fluorescence images, a minimum nodule size cut-off of 2000 µm2 (clusters of ~15–20 cells) was used to establish normalized viable tumor area. PIT is equally effective in 3D tumors grown in static cultures (green) and under flow-induced shear stress (blue) (in contrast to flow-induced chemo-resistance shown in Figure 4) (Two-tailed t test; n.s., not significant; N = 9).

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Figure 3. (a) Velocity distribution in a section perpendicular to the flow for rectangular (left) and Ushaped (right) cross section channels, and (b) particle location in these cross sections.

Continuous-Flow Separation of Magnetic Particles from Biofluids: How Does the Microdevice Geometry Determine the Separation Performance?

Cristina González Fernández,1 Jenifer Gómez Pastora,2 Arantza Basauri,1 Marcos Fallanza,1 Eugenio Bringas,1 Jeffrey J. Chalmers,2 and Inmaculada Ortiz1,*
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생체 유체에서 자성 입자의 연속 흐름 분리 : 마이크로 장치 형상이 분리 성능을 어떻게 결정합니까?

Abstract

The use of functionalized magnetic particles for the detection or separation of multiple chemicals and biomolecules from biofluids continues to attract significant attention. After their incubation with the targeted substances, the beads can be magnetically recovered to perform analysis or diagnostic tests. Particle recovery with permanent magnets in continuous-flow microdevices has gathered great attention in the last decade due to the multiple advantages of microfluidics. As such, great efforts have been made to determine the magnetic and fluidic conditions for achieving complete particle capture; however, less attention has been paid to the effect of the channel geometry on the system performance, although it is key for designing systems that simultaneously provide high particle recovery and flow rates. Herein, we address the optimization of Y-Y-shaped microchannels, where magnetic beads are separated from blood and collected into a buffer stream by applying an external magnetic field. The influence of several geometrical features (namely cross section shape, thickness, length, and volume) on both bead recovery and system throughput is studied. For that purpose, we employ an experimentally validated Computational Fluid Dynamics (CFD) numerical model that considers the dominant forces acting on the beads during separation. Our results indicate that rectangular, long devices display the best performance as they deliver high particle recovery and high throughput. Thus, this methodology could be applied to the rational design of lab-on-a-chip devices for any magnetically driven purification, enrichment or isolation.

생체 유체에서 여러 화학 물질과 생체 분자의 검출 또는 분리를 위한 기능화된 자성 입자의 사용은 계속해서 상당한 관심을 받고 있습니다. 표적 물질과 함께 배양 한 후 비드는 자기적으로 회수되어 분석 또는 진단 테스트를 수행 할 수 있습니다.

연속 흐름 마이크로 장치에서 영구 자석을 사용한 입자 회수는 마이크로 유체의 여러 장점으로 인해 지난 10 년 동안 큰 관심을 모았습니다. 따라서 완전한 입자 포획을 달성하기 위한 자기 및 유체 조건을 결정하기 위해 많은 노력을 기울였습니다.

그러나 높은 입자 회수율과 유속을 동시에 제공하는 시스템을 설계하는데 있어 핵심이기는 하지만 시스템 성능에 대한 채널 형상의 영향에 대해서는 덜 주의를 기울였습니다.

여기에서 우리는 자기 비드가 혈액에서 분리되어 외부 자기장을 적용하여 버퍼 스트림으로 수집되는 Y-Y 모양의 마이크로 채널의 최적화를 다룹니다. 비드 회수 및 시스템 처리량에 대한 여러 기하학적 특징 (즉, 단면 형상, 두께, 길이 및 부피)의 영향을 연구합니다.

이를 위해 분리 중에 비드에 작용하는 지배적인 힘을 고려하는 실험적으로 검증된 CFD (Computational Fluid Dynamics) 수치 모델을 사용합니다.

우리의 결과는 직사각형의 긴 장치가 높은 입자 회수율과 높은 처리량을 제공하기 때문에 최고의 성능을 보여줍니다. 따라서 이 방법론은 자기 구동 정제, 농축 또는 분리를 위한 랩 온어 칩 장치의 합리적인 설계에 적용될 수 있습니다.

Keywords: particle magnetophoresis, CFD, cross section, chip fabrication

Figure 1 (a) Top view of the microfluidic-magnetophoretic device, (b) Schematic representation of the channel cross-sections studied in this work, and (c) the magnet position relative to the channel location (Sepy and Sepz are the magnet separation distances in y and z, respectively).
Figure 1 (a) Top view of the microfluidic-magnetophoretic device, (b) Schematic representation of the channel cross-sections studied in this work, and (c) the magnet position relative to the channel location (Sepy and Sepz are the magnet separation distances in y and z, respectively).
Figure 2. (a) Channel-magnet configuration and (b–d) magnetic force distribution in the channel midplane for 2 mm, 5 mm and 10 mm long rectangular (left) and U-shaped (right) devices.
Figure 2. (a) Channel-magnet configuration and (b–d) magnetic force distribution in the channel midplane for 2 mm, 5 mm and 10 mm long rectangular (left) and U-shaped (right) devices.
Figure 3. (a) Velocity distribution in a section perpendicular to the flow for rectangular (left) and Ushaped (right) cross section channels, and (b) particle location in these cross sections.
Figure 3. (a) Velocity distribution in a section perpendicular to the flow for rectangular (left) and Ushaped (right) cross section channels, and (b) particle location in these cross sections.
Figure 4. Influence of fluid flow rate on particle recovery when the applied magnetic force is (a) different and (b) equal in U-shaped and rectangular cross section microdevices.
Figure 4. Influence of fluid flow rate on particle recovery when the applied magnetic force is (a) different and (b) equal in U-shaped and rectangular cross section microdevices.
Figure 5. Magnetic bead capture as a function of fluid flow rate for all of the studied geometries.
Figure 5. Magnetic bead capture as a function of fluid flow rate for all of the studied geometries.
Figure 6. Influence of (a) magnetic and fluidic forces (J parameter) and (b) channel geometry (θ parameter) on particle recovery. Note that U-2mm does not accurately fit a line.
Figure 6. Influence of (a) magnetic and fluidic forces (J parameter) and (b) channel geometry (θ parameter) on particle recovery. Note that U-2mm does not accurately fit a line.
Figure 7. Dependence of bead capture on the (a) functional channel volume, and (b) particle residence time (tres). Note that in the curve fitting expressions V represents the functional channel volume and that U-2mm does not accurately fit a line.
Figure 7. Dependence of bead capture on the (a) functional channel volume, and (b) particle residence time (tres). Note that in the curve fitting expressions V represents the functional channel volume and that U-2mm does not accurately fit a line.

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