레이저 금속 적층 제조(AM) 공정의 낮은 에너지 효율은 대규모 산업 생산에서 잠재적인 지속 가능성 문제입니다. 레이저 용융을 위한 에너지 효율의 명시적 조사는 용융 금속의 불투명한 특성으로 인해 매우 어려운 용융 풀 치수 및 증기 내림의 직접적인 특성화를 요구합니다.
여기에서 우리는 현장 고속 고에너지 x-선 이미징에 의해 Al6061의 레이저 분말 베드 융합(LPBF) 동안 증기 강하 및 용융 풀 형성에 대한 TiC 나노 입자의 효과에 대한 직접적인 관찰 및 정량화를 보고합니다. 정량 결과를 바탕으로, 우리는 Al6061의 LPBF 동안 TiC 나노 입자가 있거나 없을 때 레이저 용융 에너지 효율(여기서 재료를 용융하는 데 필요한 에너지 대 레이저 빔에 의해 전달되는 에너지의 비율로 정의)을 계산했습니다.
결과는 TiC 나노 입자를 Al6061에 추가하면 레이저 용융 에너지 효율이 크게 증가한다는 것을 보여줍니다(평균 114% 증가, 312에서 521% 증가). W 레이저 출력, 0.4m /s 스캔 속도). 체계적인 특성 측정, 시뮬레이션 및 x-선 이미징 연구를 통해 우리는 처음으로 세 가지 메커니즘이 함께 작동하여 레이저 용융 에너지 효율을 향상시킨다는 것을 확인할 수 있었습니다.
(1) TiC 나노 입자를 추가하면 흡수율이 증가합니다. (2) TiC 나노입자를 추가하면 열전도율이 감소하고, (3) TiC 나노입자를 추가하면 더 낮은 레이저 출력에서 증기 억제 및 다중 반사를 시작할 수 있습니다(즉, 키홀링에 대한 레이저 출력 임계값을 낮춤).
여기서 보고한 Al6061의 LPBF 동안 레이저 용융 에너지 효율을 증가시키기 위해 TiC 나노입자를 사용하는 방법 및 메커니즘은 보다 에너지 효율적인 레이저 금속 AM을 위한 공급원료 재료의 개발을 안내할 수 있습니다.
The low energy efficiency of the laser metal additive manufacturing (AM) process is a potential sustainability concern for large-scale industrial production. Explicit investigation of the energy efficiency for laser melting requires the direct characterization of melt pool dimension and vapor depression, which is very difficult due to the opaque nature of the molten metal. Here we report the direct observation and quantification of effects of the TiC nanoparticles on the vapor depression and melt pool formation during laser powder bed fusion (LPBF) of Al6061 by in-situ high-speed high-energy x-ray imaging. Based on the quantification results, we calculated the laser melting energy efficiency (defined here as the ratio of the energy needed to melt the material to the energy delivered by the laser beam) with and without TiC nanoparticles during LPBF of Al6061. The results show that adding TiC nanoparticles into Al6061 leads to a significant increase of laser melting energy efficiency (114% increase on average, 521% increase under 312 W laser power, 0.4 m/s scan speed). Systematic property measurement, simulation, and x-ray imaging studies enable us, for the first time, to identify that three mechanisms work together to enhance the laser melting energy efficiency: (1) adding TiC nanoparticles increases the absorptivity; (2) adding TiC nanoparticles decreases the thermal conductivity, and (3) adding TiC nanoparticles enables the initiation of vapor depression and multiple reflection at lower laser power (i.e., lowers the laser power threshold for keyholing). The method and mechanisms of using TiC nanoparticles to increase the laser melting energy efficiency during LPBF of Al6061 we reported here may guide the development of feedstock materials for more energy efficient laser metal AM.
Nanoparticle-enabled increase of energy efficiency during laser metal additive manufacturing
TianLiabJ.M.T.DaviesaXiangzhenZhuc aUniversity of Birmingham, Birmingham B15 2TT, United Kingdom bGrainger and Worrall Ltd, Bridgnorth WV15 5HP, United Kingdom cBrunel Centre for Advanced Solidification Technology, Brunel University London, Kingston Ln, London, Uxbridge UB8 3PH, United Kingdom
Abstract
An entrainment defect (also known as a double oxide film defect or bifilm) acts a void containing an entrapped gas when submerged into a light-alloy melt, thus reducing the quality and reproducibility of the final castings. Previous publications, carried out with Al-alloy castings, reported that this trapped gas could be subsequently consumed by the reaction with the surrounding melt, thus reducing the void volume and negative effect of entrainment defects. Compared with Al-alloys, the entrapped gas within Mg-alloy might be more efficiently consumed due to the relatively high reactivity of magnesium. However, research into the entrainment defects within Mg alloys has been significantly limited. In the present work, AZ91 alloy castings were produced under different carrier gas atmospheres (i.e., SF6/CO2, SF6/air). The evolution processes of the entrainment defects contained in AZ91 alloy were suggested according to the microstructure inspections and thermodynamic calculations. The defects formed in the different atmospheres have a similar sandwich-like structure, but their oxide films contained different combinations of compounds. The use of carrier gases, which were associated with different entrained-gas consumption rates, affected the reproducibility of AZ91 castings.
연행 결함(이중 산화막 결함 또는 이중막이라고도 함)은 경합금 용융물에 잠길 때 갇힌 가스를 포함하는 공극으로 작용하여 최종 주물의 품질과 재현성을 저하시킵니다. Al-합금 주물을 사용하여 수행된 이전 간행물에서는 이 갇힌 가스가 주변 용융물과의 반응에 의해 후속적으로 소모되어 공극 부피와 연행 결함의 부정적인 영향을 줄일 수 있다고 보고했습니다. Al-합금에 비해 마그네슘의 상대적으로 높은 반응성으로 인해 Mg-합금 내에 포집된 가스가 더 효율적으로 소모될 수 있습니다. 그러나 Mg 합금 내 연행 결함에 대한 연구는 상당히 제한적이었습니다. 현재 작업에서 AZ91 합금 주물은 다양한 캐리어 가스 분위기(즉, SF6/CO2, SF6/공기)에서 생산되었습니다. AZ91 합금에 포함된 연행 결함의 진화 과정은 미세 조직 검사 및 열역학 계산에 따라 제안되었습니다. 서로 다른 분위기에서 형성된 결함은 유사한 샌드위치 구조를 갖지만 산화막에는 서로 다른 화합물 조합이 포함되어 있습니다. 다른 동반 가스 소비율과 관련된 운반 가스의 사용은 AZ91 주물의 재현성에 영향을 미쳤습니다.
As the lightest structural metal available on Earth, magnesium became one of the most attractive light metals over the last few decades. The magnesium industry has consequently experienced a rapid development in the last 20 years [1,2], indicating a large growth in demand for Mg alloys all over the world. Nowadays, the use of Mg alloys can be found in the fields of automobiles, aerospace, electronics and etc.[3,4]. It has been predicted that the global consumption of Mg metals will further increase in the future, especially in the automotive industry, as the energy efficiency requirement of both traditional and electric vehicles further push manufactures lightweight their design [3,5,6].
The sustained growth in demand for Mg alloys motivated a wide interest in the improvement of the quality and mechanical properties of Mg-alloy castings. During a Mg-alloy casting process, surface turbulence of the melt can lead to the entrapment of a doubled-over surface film containing a small quantity of the surrounding atmosphere, thus forming an entrainment defect (also known as a double oxide film defect or bifilm) [7], [8], [9], [10]. The random size, quantity, orientation, and placement of entrainment defects are widely accepted to be significant factors linked to the variation of casting properties [7]. In addition, Peng et al. [11] found that entrained oxides films in AZ91 alloy melt acted as filters to Al8Mn5 particles, trapping them as they settle. Mackie et al. [12] further suggested that entrained oxide films can act to trawl the intermetallic particles, causing them to cluster and form extremely large defects. The clustering of intermetallic compounds made the entrainment defects more detrimental for the casting properties.
Most of the previous studies regarding entrainment defects were carried out on Al-alloys [7,[13], [14], [15], [16], [17], [18], and a few potential methods have been suggested for diminishing their negative effect on the quality of Al-alloy castings. Nyahumwa et al.,[16] shows that the void volume within entrainment defects could be reduced by a hot isostatic pressing (HIP) process. Campbell [7] suggested the entrained gas within the defects could be consumed due to reaction with the surrounding melt, which was further verified by Raiszedeh and Griffiths [19].The effect of the entrained gas consumption on the mechanical properties of Al-alloy castings has been investigated by [8,9], suggesting that the consumption of the entrained gas promoted the improvement of the casting reproducibility.
Compared with the investigation concerning the defects within Al-alloys, research into the entrainment defects within Mg-alloys has been significantly limited. The existence of entrainment defects has been demonstrated in Mg-alloy castings [20,21], but their behaviour, evolution, as well as entrained gas consumption are still not clear.
In a Mg-alloy casting process, the melt is usually protected by a cover gas to avoid magnesium ignition. The cavities of sand or investment moulds are accordingly required to be flushed with the cover gas prior to the melt pouring [22]. Therefore, the entrained gas within Mg-alloy castings should contain the cover gas used in the casting process, rather than air only, which may complicate the structure and evolution of the corresponding entrainment defects.
SF6 is a typical cover gas widely used for Mg-alloy casting processes [23], [24], [25]. Although this cover gas has been restricted to use in European Mg-alloy foundries, a commercial report has pointed out that this cover is still popular in global Mg-alloy industry, especially in the countries which dominated the global Mg-alloy production, such as China, Brazil, India, etc. [26]. In addition, a survey in academic publications also showed that this cover gas was widely used in recent Mg-alloy studies [27]. The protective mechanism of SF6 cover gas (i.e., the reaction between liquid Mg-alloy and SF6 cover gas) has been investigated by several previous researchers, but the formation process of the surface oxide film is still not clearly understood, and even some published results are conflicting with each other. In early 1970s, Fruehling [28] found that the surface film formed under SF6 was MgO mainly with traces of fluorides, and suggested that SF6 was absorbed in the Mg-alloy surface film. Couling [29] further noticed that the absorbed SF6 reacted with the Mg-alloy melt to form MgF2. In last 20 years, different structures of the Mg-alloy surface films have been reported, as detailed below.(1)
Single-layered film. Cashion [30,31] used X-ray Photoelectron Spectroscopy (XPS) and Auger Spectroscopy (AES) to identify the surface film as MgO and MgF2. He also found that composition of the film was constant throughout the thickness and the whole experimental holding time. The film observed by Cashion had a single-layered structure created from a holding time from 10 min to 100 min.(2)
Double-layered film. Aarstad et. al [32] reported a doubled-layered surface oxide film in 2003. They observed several well-distributed MgF2 particles attached to the preliminary MgO film and grew until they covered 25–50% of the total surface area. The inward diffusion of F through the outer MgO film was the driving force for the evolution process. This double-layered structure was also supported by Xiong’s group [25,33] and Shih et al. [34].(3)
Triple-layered film. The triple-layered film and its evolution process were reported in 2002 by Pettersen [35]. Pettersen found that the initial surface film was a MgO phase and then gradually evolved to the stable MgF2 phase by the inward diffusion of F. In the final stage, the film has a triple-layered structure with a thin O-rich interlayer between the thick top and bottom MgF2 layers.(4)
Oxide film consisted of discrete particles. Wang et al [36] stirred the Mg-alloy surface film into the melt under a SF6 cover gas, and then inspect the entrained surface film after the solidification. They found that the entrained surface films were not continues as the protective surface films reported by other researchers but composed of discrete particles. The young oxide film was composed of MgO nano-sized oxide particles, while the old oxide films consist of coarse particles (about 1 µm in average size) on one side that contained fluorides and nitrides.
The oxide films of a Mg-alloy melt surface or an entrained gas are both formed due to the reaction between liquid Mg-alloy and the cover gas, thus the above-mentioned research regarding the Mg-alloy surface film gives valuable insights into the evolution of entrainment defects. The protective mechanism of SF6 cover gas (i.e., formation of a Mg-alloy surface film) therefore indicated a potential complicated evolution process of the corresponding entrainment defects.
However, it should be noted that the formation of a surface film on a Mg-alloy melt is in a different situation to the consumption of an entrained gas that is submerged into the melt. For example, a sufficient amount of cover gas was supported during the surface film formation in the studies previously mentioned, which suppressed the depletion of the cover gas. In contrast, the amount of entrained gas within a Mg-alloy melt is finite, and the entrained gas may become fully depleted. Mirak [37] introduced 3.5%SF6/air bubbles into a pure Mg-alloy melt solidifying in a specially designed permanent mould. It was found that the gas bubbles were entirely consumed, and the corresponding oxide film was a mixture of MgO and MgF2. However, the nucleation sites (such as the MgF2 spots observed by Aarstad [32] and Xiong [25,33]) were not observed. Mirak also speculated that the MgF2 formed prior to MgO in the oxide film based on the composition analysis, which was opposite to the surface film formation process reported in previous literatures (i.e., MgO formed prior to MgF2). Mirak’s work indicated that the oxide-film formation of an entrained gas may be quite different from that of surface films, but he did not reveal the structure and evolution of the oxide films.
In addition, the use of carrier gas in the cover gases also influenced the reaction between the cover gas and the liquid Mg-alloy. SF6/air required a higher content of SF6 than did a SF6/CO2 carrier gas [38], to avoid the ignition of molten magnesium, revealing different gas-consumption rates. Liang et.al [39] suggested that carbon was formed in the surface film when CO2 was used as a carrier gas, which was different from the films formed in SF6/air. An investigation into Mg combustion [40] reported a detection of Mg2C3 in the Mg-alloy sample after burning in CO2, which not only supported Liang’s results, but also indicated a potential formation of Mg carbides in double oxide film defects.
The work reported here is an investigation into the behaviour and evolution of entrainment defects formed in AZ91 Mg-alloy castings, protected by different cover gases (i.e., SF6/air and SF6/CO2). These carrier gases have different protectability for liquid Mg alloy, which may be therefore associated with different consumption rates and evolution processes of the corresponding entrained gases. The effect of the entrained-gas consumption on the reproducibility of AZ91 castings was also studied.
2. Experiment
2.1. Melting and casting
Three kilograms AZ91 alloy was melted in a mild steel crucible at 700 ± 5 °C. The composition of the AZ91 alloy has been shown in Table 1. Prior to heating, all oxide scale on the ingot surface was removed by machining. The cover gases used were 0.5%SF6/air or 0.5%SF6/CO2 (vol.%) at a flow rate of 6 L/min for different castings. The melt was degassed by argon with a flow rate of 0.3 L/min for 15 min [41,42], and then poured into sand moulds. Prior to pouring, the sand mould cavity was flushed with the cover gas for 20 min [22]. The residual melt (around 1 kg) was solidified in the crucible.
Table 1. Composition (wt.%) of the AZ91 alloy used in this study.
Al
Zn
Mn
Si
Fe
Ni
Mg
9.4
0.61
0.15
0.02
0.005
0.0017
Residual
Fig. 1(a) shows the dimensions of the casting with runners. A top-filling system was deliberately used to generate entrainment defects in the final castings. Green and Campbell [7,43] suggested that a top-filling system caused more entrainment events (i.e., bifilms) during a casting process, compared with a bottom-filling system. A melt flow simulation (Flow-3D software) of this mould, using Reilly’s model [44] regarding the entrainment events, also predicted that a large amount of bifilms would be contained in the final casting (denoted by the black particles in Fig. 1b).
Shrinkage defects also affect the mechanical properties and reproducibility of castings. Since this study focused on the effect of bifilms on the casting quality, the mould has been deliberately designed to avoid generating shrinkage defects. A solidification simulation using ProCAST software showed that no shrinkage defect would be contained in the final casting, as shown in Fig. 1c. The casting soundness has also been confirmed using a real time X-ray prior to the test bar machining.
The sand moulds were made from resin-bonded silica sand, containing 1wt. % PEPSET 5230 resin and 1wt. % PEPSET 5112 catalyst. The sand also contained 2 wt.% Na2SiF6 to act as an inhibitor [45]. The pouring temperature was 700 ± 5 °C. After the solidification, a section of the runner bars was sent to the Sci-Lab Analytical Ltd for a H-content analysis (LECO analysis), and all the H-content measurements were carried out on the 5th day after the casting process. Each of the castings was machined into 40 test bars for a tensile strength test, using a Zwick 1484 tensile test machine with a clip extensometer. The fracture surfaces of the broken test bars were examined using Scanning Electron Microscope (SEM, Philips JEOL7000) with an accelerating voltage of 5–15 kV. The fractured test bars, residual Mg-alloy solidified in the crucible, and the casting runners were then sectioned, polished and also inspected using the same SEM. The cross-section of the oxide film found on the test-bar fracture surface was exposed by the Focused Ion Beam milling technique (FIB), using a CFEI Quanta 3D FEG FIB-SEM. The oxide film required to be analysed was coated with a platinum layer. Then, a gallium ion beam, accelerated to 30 kV, milled the material substrate surrounding the platinum coated area to expose the cross section of the oxide film. EDS analysis of the oxide film’s cross section was carried out using the FIB equipment at accelerating voltage of 30 kV.
2.2. Oxidation cell
As previously mentioned, several past researchers investigated the protective film formed on a Mg-alloy melt surface [38,39,[46], [47], [48], [49], [50], [51], [52]. During these experiments, the amount of cover gas used was sufficient, thus suppressing the depletion of fluorides in the cover gas. The experiment described in this section used a sealed oxidation cell, which limited the supply of cover gas, to study the evolution of the oxide films of entrainment defects. The cover gas contained in the oxidation cell was regarded as large-size “entrained bubble”.
As shown in Fig. 2, the main body of the oxidation cell was a closed-end mild steel tube which had an inner length of 400 mm, and an inner diameter of 32 mm. A water-cooled copper tube was wrapped around the upper section of the cell. When the tube was heated, the cooling system created a temperature difference between the upper and lower sections, causing the interior gas to convect within the tube. The temperature was monitored by a type-K thermocouple located at the top of the crucible. Nie et al. [53] suggested that the SF6 cover gas would react with the steel wall of the holding furnace when they investigated the surface film of a Mg-alloy melt. To avoid this reaction, the interior surface of the steel oxidation cell (shown in Fig. 2) and the upper half section of the thermocouple were coated with boron nitride (the Mg-alloy was not in contact with boron nitride).
During the experiment, a block of solid AZ91 alloy was placed in a magnesia crucible located at the bottom of the oxidation cell. The cell was heated to 100 °C in an electric resistance furnace under a gas flow rate of 1 L/min. The cell was held at this temperature for 20 min, to replace the original trapped atmosphere (i.e. air). Then, the oxidation cell was further heated to 700 °C, melting the AZ91 sample. The gas inlet and exit valves were then closed, creating a sealed environment for oxidation under a limited supply of cover gas. The oxidation cell was then held at 700 ± 10 °C for periods of time from 5 min to 30 min in 5-min intervals. At the end of each holding time, the cell was quenched in water. After cooling to room temperature, the oxidised sample was sectioned, polished, and subsequently examined by SEM.
3. Results
3.1. Structure and composition of the entrainment defects formed in SF6/air
The structure and composition of the entrainment defect formed in the AZ91 castings under a cover gas of 0.5%SF6/air was observed by SEM and EDS. The results indicate that there exist two types of entrainment defects which are sketched in Fig. 3: (1) Type A defect whose oxide film has a traditional single-layered structure and (2) Type B defect, whose oxide film has two layers. The details of these defects were introduced in the following. Here it should be noticed that, as the entrainment defects are also known as biofilms or double oxide film, the oxide films of Type B defect were referred to as “multi-layered oxide film” or “multi-layered structure” in the present work to avoid a confusing description such as “the double-layered oxide film of a double oxide film defect”.
Fig. 4(a-b) shows a Type A defect having a compact single-layered oxide film with about 0.4 µm thickness. Oxygen, fluorine, magnesium and aluminium were detected in this film (Fig. 4c). It is speculated that oxide film is the mixture of fluoride and oxide of magnesium and aluminium. The detection of fluorine revealed that an entrained cover gas was contained in the formation of this defect. That is to say that the pores shown in Fig. 4(a) were not shrinkage defects or hydrogen porosity, but entrainment defects. The detection of aluminium was different with Xiong and Wang’s previous study [47,48], which showed that no aluminium was contained in their surface film of an AZ91 melt protected by a SF6 cover gas. Sulphur could not be clearly recognized in the element map, but there was a S-peak in the corresponding ESD spectrum.
Fig. 5(a-b) shows a Type B entrainment defect having a multi-layered oxide film. The compact outer layers of the oxide films were enriched with fluorine and oxygen (Fig. 5c), while their relatively porous inner layers were only enriched with oxygen (i.e., poor in fluorine) and partly grew together, thus forming a sandwich-like structure. Therefore, it is speculated that the outer layer is the mixture of fluoride and oxide, while the inner layer is mainly oxide. Sulphur could only be recognized in the EDX spectrum and could not be clearly identified in the element map, which might be due to the small S-content in the cover gas (i.e., 0.5% volume content of SF6 in the cover gas). In this oxide film, aluminium was contained in the outer layer of this oxide film but could not be clearly detected in the inner layer. Moreover, the distribution of Al seems to be uneven. It can be found that, in the right side of the defect, aluminium exists in the film but its concentration can not be identified to be higher than the matrix. However, there is a small area with much higher aluminium concentration in the left side of the defect. Such an uneven distribution of aluminium was also observed in other defects (shown in the following), and it is the result of the formation of some oxide particles in or under the film.
Figs. 4 and 5 show cross sectional observations of the entrainment defects formed in the AZ91 alloy sample cast under a cover gas of SF6/air. It is not sufficient to characterize the entrainment defects only by the figures observed from the two-dimensional section. To have a further understanding, the surface of the entrainment defects (i.e. the oxide film) was further studied by observing the fracture surface of the test bars.
Fig. 6(a) shows fracture surfaces of an AZ91 alloy tensile test bar produced in SF6/air. Symmetrical dark regions can be seen on both sides of the fracture surfaces. Fig. 6(b) shows boundaries between the dark and bright regions. The bright region consisted of jagged and broken features, while the surface of the dark region was relatively smooth and flat. In addition, the EDS results (Fig. 6c-d and Table 2) show that fluorine, oxygen, sulphur, and nitrogen were only detected in the dark regions, indicating that the dark regions were surface protective films entrained into the melt. Therefore, it could be suggested that the dark regions were an entrainment defect with consideration of their symmetrical nature. Similar defects on fracture surfaces of Al-alloy castings have been previously reported [7]. Nitrides were only found in the oxide films on the test-bar fracture surfaces but never detected in the cross-sectional samples shown in Figs. 4 and 5. An underlying reason is that the nitrides contained in these samples may have hydrolysed during the sample polishing process [54].
Table 2. EDS results (wt.%) corresponding to the regions shown in Fig. 6 (cover gas: SF6/air).
In conjunction with the cross-sectional observation of the defects shown in Figs. 4 and 5, the structure of an entrainment defect contained in a tensile test bar was sketched as shown in Fig. 6(e). The defect contained an entrained gas enclosed by its oxide film, creating a void section inside the test bar. When the tensile force applied on the defect during the fracture process, the crack was initiated at the void section and propagated along the entrainment defect, since cracks would be propagated along the weakest path [55]. Therefore, when the test bar was finally fractured, the oxide films of entrainment defect appeared on both fracture surfaces of the test bar, as shown in Fig. 6(a).
3.2. Structure and composition of the entrainment defects formed in SF6/CO2
Similar to the entrainment defect formed in SF6/air, the defects formed under a cover gas of 0.5%SF6/CO2 also had two types of oxide films (i.e., single-layered and multi-layered types). Fig. 7(a) shows an example of the entrainment defects containing a multi-layered oxide film. A magnified observation to the defect (Fig. 7b) shows that the inner layers of the oxide films had grown together, presenting a sandwich-like structure, which was similar to the defects formed in an atmosphere of SF6/air (Fig. 5b). An EDS spectrum (Fig. 7c) revealed that the joint area (inner layer) of this sandwich-like structure mainly contained magnesium oxides. Peaks of fluorine, sulphur, and aluminium were recognized in this EDS spectrum, but their amount was relatively small. In contrast, the outer layers of the oxide films were compact and composed of a mixture of fluorides and oxides (Fig. 7d-e).
Fig. 8(a) shows an entrainment defect on the fracture surfaces of an AZ91 alloy tensile test bar, which was produced in an atmosphere of 0.5%SF6/CO2. The corresponding EDS results (Table 3) showed that oxide film contained fluorides and oxides. Sulphur and nitrogen were not detected. Besides, a magnified observation (Fig. 8b) indicated spots on the oxide film surface. The diameter of the spots ranged from hundreds of nanometres to a few micron meters.
To further reveal the structure and composition of the oxide film clearly, the cross-section of the oxide film on a test-bar fracture surface was onsite exposed using the FIB technique (Fig. 9). As shown in Fig. 9a, a continuous oxide film was found between the platinum coating layer and the Mg-Al alloy substrate. Fig. 9 (b-c) shows a magnified observation to oxide films, indicating a multi-layered structure (denoted by the red box in Fig. 9c). The bottom layer was enriched with fluorine and oxygen and should be the mixture of fluoride and oxide, which was similar to the “outer layer” shown in Figs. 5 and 7, while the only-oxygen-enriched top layer was similar to the “inner layer” shown in Figs. 5 and 7.
Except the continuous film, some individual particles were also observed in or below the continuous film, as shown in Fig. 9. An Al-enriched particle was detected in the left side of the oxide film shown in Fig. 9b and might be speculated to be spinel Mg2AlO4 because it also contains abundant magnesium and oxygen elements. The existing of such Mg2AlO4 particles is responsible for the high concentration of aluminium in small areas of the observed film and the uneven distribution of aluminium, as shown in Fig. 5(c). Here it should be emphasized that, although the other part of the bottom layer of the continuous oxide film contains less aluminium than this Al-enriched particle, the Fig. 9c indicated that the amount of aluminium in this bottom layer was still non-negligible, especially when comparing with the outer layer of the film. Below the right side of the oxide film shown in Fig. 9b, a particle was detected and speculated to be MgO because it is rich in Mg and O. According to Wang’s result [56], lots of discrete MgO particles can be formed on the surface of the Mg melt by the oxidation of Mg melt and Mg vapor. The MgO particles observed in our present work may be formed due to the same reasons. While, due to the differences in experimental conditions, less Mg melt can be vapored or react with O2, thus only a few of MgO particles formed in our work. An enrichment of carbon was also found in the film, revealing that CO2 was able to react with the melt, thus forming carbon or carbides. This carbon concentration was consistent with the relatively high carbon content of the oxide film shown in Table 3 (i.e., the dark region). In the area next to the oxide film.
Table 3. EDS results (wt.%) corresponding to the regions shown in Fig. 8 (cover gas: SF6/ CO2).
This cross-sectional observation of the oxide film on a test bar fracture surface (Fig. 9) further verified the schematic of the entrainment defect shown in Fig. 6(e). The entrainment defects formed in different atmospheres of SF6/CO2 and SF6/air had similar structures, but their compositions were different.
3.3. Evolution of the oxide films in the oxidation cell
The results in Section 3.1 and 3.2 have shown the structures and compositions of entrainment defects formed in AZ91 castings under cover gases of SF6/air and SF6/CO2. Different stages of the oxidation reaction may lead to the different structures and compositions of entrainment defects. Although Campbell has conjectured that an entrained gas may react with the surrounding melt, it is rarely reported that the reaction occurring between the Mg-alloy melt and entrapped cover gas. Previous researchers normally focus on the reaction between a Mg-alloy melt and the cover gas in an open environment [38,39,[46], [47], [48], [49], [50], [51], [52], which was different from the situation of a cover gas trapped into the melt. To further understand the formation of the entrainment defect in an AZ91 alloy, the evolution process of oxide films of the entrainment defect was further studied using an oxidation cell.
Fig. 10 (a and d) shows a surface film held for 5 min in the oxidation cell, protected by 0.5%SF6/air. There was only one single layer consisting of fluoride and oxide (MgF2 and MgO). In this surface film. Sulphur was detected in the EDS spectrum, but its amount was too small to be recognized in the element map. The structure and composition of this oxide film was similar to the single-layered films of entrainment defects shown in Fig. 4.
After a holding time of 10 min, a thin (O, S)-enriched top layer (around 700 nm) appeared upon the preliminary F-enriched film, forming a multi-layered structure, as shown in Fig. 10(b and e). The thickness of the (O, S)-enriched top layer increased with increased holding time. As shown in Fig. 10(c and f), the oxide film held for 30 min also had a multi-layered structure, but the thickness of its (O, S)-enriched top layer (around 2.5 µm) was higher than the that of the 10-min oxide film. The multi-layered oxide films shown in Fig. 10(b-c) presented a similar appearance to the films of the sandwich-like defect shown in Fig. 5.
The different structures of the oxide films shown in Fig. 10 indicated that fluorides in the cover gas would be preferentially consumed due to the reaction with the AZ91 alloy melt. After the depletion of fluorides, the residual cover gas reacted further with the liquid AZ91 alloy, forming the top (O, S)-enriched layer in the oxide film. Therefore, the different structures and compositions of entrainment defects shown in Figs. 4 and 5 may be due to an ongoing oxidation reaction between melt and entrapped cover gas.
This multi-layered structure has not been reported in previous publications concerning the protective surface film formed on a Mg-alloy melt [38,[46], [47], [48], [49], [50], [51]. This may be due to the fact that previous researchers carried out their experiments with an un-limited amount of cover gas, creating a situation where the fluorides in the cover gas were not able to become depleted. Therefore, the oxide film of an entrainment defect had behaviour traits similar to the oxide films shown in Fig. 10, but different from the oxide films formed on the Mg-alloy melt surface reported in [38,[46], [47], [48], [49], [50], [51].
Similar with the oxide films held in SF6/air, the oxide films formed in SF6/CO2 also had different structures with different holding times in the oxidation cell. Fig. 11(a) shows an oxide film, held on an AZ91 melt surface under a cover gas of 0.5%SF6/CO2 for 5 min. This film had a single-layered structure consisting of MgF2. The existence of MgO could not be confirmed in this film. After the holding time of 30 min, the film had a multi-layered structure; the inner layer was of a compact and uniform appearance and composed of MgF2, while the outer layer is the mixture of MgF2 and MgO. Sulphur was not detected in this film, which was different from the surface film formed in 0.5%SF6/air. Therefore, fluorides in the cover gas of 0.5%SF6/CO2 were also preferentially consumed at an early stage of the film growth process. Compared with the film formed in SF6/air, the MgO in film formed in SF6/CO2 appeared later and sulphide did not appear within 30 min. It may mean that the formation and evolution of film in SF6/air is faster than SF6/CO2. CO2 may have subsequently reacted with the melt to form MgO, while sulphur-containing compounds accumulated in the cover gas and reacted to form sulphide in very late stage (may after 30 min in oxidation cell).
4. Discussion
4.1. Evolution of entrainment defects formed in SF6/air
HSC software from Outokumpu HSC Chemistry for Windows (http://www.hsc-chemistry.net/) was used to carry out thermodynamic calculations needed to explore the reactions which might occur between the trapped gases and liquid AZ91 alloy. The solutions to the calculations suggest which products are most likely to form in the reaction process between a small amount of cover gas (i.e., the amount within a trapped bubble) and the AZ91-alloy melt.
In the trials, the pressure was set to 1 atm, and the temperature set to 700 °C. The amount of the cover gas was assumed to be 7 × 10−7 kg, with a volume of approximately 0.57 cm3 (3.14 × 10−8 kmol) for 0.5%SF6/air, and 0.35 cm3 (3.12 × 10−8 kmol) for 0.5%SF6/CO2. The amount of the AZ91 alloy melt in contact with the trapped gas was assumed to be sufficient to complete all reactions. The decomposition products of SF6 were SF5, SF4, SF3, SF2, F2, S(g), S2(g) and F(g) [57], [58], [59], [60].
Fig. 12 shows the equilibrium diagram of the thermodynamic calculation of the reaction between the AZ91 alloy and 0.5%SF6/air. In the diagram, the reactants and products with less than 10−15 kmol have not been shown, as this was 5 orders of magnitude less than the amount of SF6 present (≈ 1.57 × 10−10 kmol) and therefore would not affect the observed process in a practical way.
This reaction process could be divided into 3 stages.
Stage 1: The formation of fluorides. the AZ91 melt preferentially reacted with SF6 and its decomposition products, producing MgF2, AlF3, and ZnF2. However, the amount of ZnF2 may have been too small to be detected practically (1.25 × 10−12 kmol of ZnF2 compared with 3 × 10−10 kmol of MgF2), which may be the reason why Zn was not detected in any the oxide films shown in Sections 3.1–3.3. Meanwhile, sulphur accumulated in the residual gas as SO2.
Stage 2: The formation of oxides. After the liquid AZ91 alloy had depleted all the available fluorides in the entrapped gas, the amount of AlF3 and ZnF2 quickly reduced due to a reaction with Mg. O2(g) and SO2 reacted with the AZ91 melt, forming MgO, Al2O3, MgAl2O4, ZnO, ZnSO4 and MgSO4. However, the amount of ZnO and ZnSO4 would have been too small to be found practically by EDS (e.g. 9.5 × 10−12 kmol of ZnO,1.38 × 10−14 kmol of ZnSO4, in contrast to 4.68 × 10−10 kmol of MgF2, when the amount of AZ91 on the X-axis is 2.5 × 10−9 kmol). In the experimental cases, the concentration of F in the cover gas is very low, whole the concentration f O is much higher. Therefore, the stage 1 and 2, i.e, the formation of fluoride and oxide may happen simultaneously at the beginning of the reaction, resulting in the formation of a singer-layered mixture of fluoride and oxide, as shown in Figs. 4 and 10(a). While an inner layer consisted of oxides but fluorides could form after the complete depletion of F element in the cover gas.
Stages 1- 2 theoretically verified the formation process of the multi-layered structure shown in Fig. 10.
The amount of MgAl2O4 and Al2O3 in the oxide film was of a sufficient amount to be detected, which was consistent with the oxide films shown in Fig. 4. However, the existence of aluminium could not be recognized in the oxide films grown in the oxidation cell, as shown in Fig. 10. This absence of Al may be due to the following reactions between the surface film and AZ91 alloy melt:(1)
Mg + MgAl2O4 = MgO + Al, △G(700 °C) =-106.34 kJ/molwhich could not be simulated by the HSC software since the thermodynamic calculation was carried out under an assumption that the reactants were in full contact with each other. However, in a practical process, the AZ91 melt and the cover gas would not be able to be in contact with each other completely, due to the existence of the protective surface film.
Stage 3: The formation of Sulphide and nitride. After a holding time of 30 min, the gas-phase fluorides and oxides in the oxidation cell had become depleted, allowing the melt reaction with the residual gas, forming an additional sulphur-enriched layer upon the initial F-enriched or (F, O)-enriched surface film, thus resulting in the observed multi-layered structure shown in Fig. 10 (b and c). Besides, nitrogen reacted with the AZ91 melt until all reactions were completed. The oxide film shown in Fig. 6 may correspond to this reaction stage due to its nitride content. However, the results shows that the nitrides were not detected in the polished samples shown in Figs. 4 and 5, but only found on the test bar fracture surfaces. The nitrides may have hydrolysed during the sample preparation process, as follows [54]:(3)
Mg3N2 + 6H2O =3Mg(OH)2 + 2NH3↑(4)
AlN+ 3H2O =Al(OH)3 + NH3↑
In addition, Schmidt et al. [61] found that Mg3N2 and AlN could react to form ternary nitrides (Mg3AlnNn+2, n= 1, 2, 3…). HSC software did not contain the database of ternary nitrides, and it could not be added into the calculation. The oxide films in this stage may also contain ternary nitrides.
4.2. Evolution of entrainment defects formed in SF6/CO2
Fig. 13 shows the results of the thermodynamic calculation between AZ91 alloy and 0.5%SF6/CO2. This reaction processes can also be divided into three stages.
Stage 1: The formation of fluorides. SF6 and its decomposition products were consumed by the AZ91 melt, forming MgF2, AlF3, and ZnF2. As in the reaction of AZ91 in 0.5%SF6/air, the amount of ZnF2 was too small to be detected practically (1.51 × 10−13 kmol of ZnF2 compared with 2.67 × 10−10 kmol of MgF2). Sulphur accumulated in the residual trapped gas as S2(g) and a portion of the S2(g) reacted with CO2, to form SO2 and CO. The products in this reaction stage were consistent with the film shown in Fig. 11(a), which had a single layer structure that contained fluorides only.
Stage 2: The formation of oxides. AlF3 and ZnF2 reacted with the Mg in the AZ91 melt, forming MgF2, Al and Zn. The SO2 began to be consumed, producing oxides in the surface film and S2(g) in the cover gas. Meanwhile, the CO2 directly reacted with the AZ91 melt, forming CO, MgO, ZnO, and Al2O3. The oxide films shown in Figs. 9 and 11(b) may correspond to this reaction stage due to their oxygen-enriched layer and multi-layered structure.
The CO in the cover gas could further react with the AZ91 melt, producing C. This carbon may further react with Mg to form Mg carbides, when the temperature reduced (during solidification period) [62]. This may be the reason for the high carbon content in the oxide film shown in Figs. 8–9. Liang et al. [39] also reported carbon-detection in an AZ91 alloy surface film protected by SO2/CO2. The produced Al2O3 may be further combined with MgO, forming MgAl2O4[63]. As discussed in Section 4.1, the alumina and spinel can react with Mg, causing an absence of aluminium in the surface films, as shown in Fig. 11.
Stage 3: The formation of Sulphide. the AZ91 melt began to consume S2(g) in the residual entrapped gas, forming ZnS and MgS. These reactions did not occur until the last stage of the reaction process, which could be the reason why the S-content in the defect shown Fig. 7(c) was small.
In summary, thermodynamic calculations indicate that the AZ91 melt will react with the cover gas to form fluorides firstly, then oxides and sulphides in the last. The oxide film in the different reaction stages would have different structures and compositions.
4.3. Effect of the carrier gases on consumption of the entrained gas and the reproducibility of AZ91 castings
The evolution processes of entrainment defects, formed in SF6/air and SF6/CO2, have been suggested in Sections 4.1 and 4.2. The theoretical calculations were verified with respect to the corresponding oxide films found in practical samples. The atmosphere within an entrainment defect could be efficiently consumed due to the reaction with liquid Mg-alloy, in a scenario dissimilar to the Al-alloy system (i.e., nitrogen in an entrained air bubble would not efficiently react with Al-alloy melt [64,65], however, nitrogen would be more readily consumed in liquid Mg alloys, commonly referred to as “nitrogen burning” [66]).
The reaction between the entrained gas and the surrounding liquid Mg-alloy converted the entrained gas into solid compounds (e.g. MgO) within the oxide film, thus reducing the void volume of the entrainment defect and hence probably causing a collapse of the defect (e.g., if an entrained gas of air was depleted by the surrounding liquid Mg-alloy, under an assumption that the melt temperature is 700 °C and the depth of liquid Mg-alloy is 10 cm, the total volume of the final solid products would be 0.044% of the initial volume taken by the entrapped air).
The relationship between the void volume reduction of entrainment defects and the corresponding casting properties has been widely studied in Al-alloy castings. Nyahumwa and Campbell [16] reported that the Hot Isostatic Pressing (HIP) process caused the entrainment defects in Al-alloy castings to collapse and their oxide surfaces forced into contact. The fatigue lives of their castings were improved after HIP. Nyahumwa and Campbell [16] also suggested a potential bonding of the double oxide films that were in contact with each other, but there was no direct evidence to support this. This binding phenomenon was further investigated by Aryafar et.al.[8], who re-melted two Al-alloy bars with oxide skins in a steel tube and then carried out a tensile strength test on the solidified sample. They found that the oxide skins of the Al-alloy bars strongly bonded with each other and became even stronger with an extension of the melt holding time, indicating a potential “healing” phenomenon due to the consumption of the entrained gas within the double oxide film structure. In addition, Raidszadeh and Griffiths [9,19] successfully reduced the negative effect of entrainment defects on the reproducibility of Al-alloy castings, by extending the melt holding time before solidification, which allowed the entrained gas to have a longer time to react with the surrounding melt.
With consideration of the previous work mentioned, the consumption of the entrained gas in Mg-alloy castings may diminish the negative effect of entrainment defects in the following two ways.
(1) Bonding phenomenon of the double oxide films. The sandwich-like structure shown in Fig. 5 and 7 indicated a potential bonding of the double oxide film structure. However, more evidence is required to quantify the increase in strength due to the bonding of the oxide films.
(2) Void volume reduction of entrainment defects. The positive effect of void-volume reduction on the quality of castings has been widely demonstrated by the HIP process [67]. As the evolution processes discussed in Section 4.1–4.2, the oxide films of entrainment defects can grow together due to an ongoing reaction between the entrained gas and surrounding AZ91 alloy melt. The volume of the final solid products was significant small compared with the entrained gas (i.e., 0.044% as previously mentioned).
Therefore, the consumption rate of the entrained gas (i.e., the growth rate of oxide films) may be a critical parameter for improving the quality of AZ91 alloy castings. The oxide film growth rate in the oxidization cell was accordingly further investigated.
Fig. 14 shows a comparison of the surface film growth rates in different cover gases (i.e., 0.5%SF6/air and 0.5%SF6/CO2). 15 random points on each sample were selected for film thickness measurements. The 95% confidence interval (95%CI) was computed under an assumption that the variation of the film thickness followed a Gaussian distribution. It can be seen that all the surface films formed in 0.5%SF6/air grew faster than those formed in 0.5%SF6/CO2. The different growth rates suggested that the entrained-gas consumption rate of 0.5%SF6/air was higher than that of 0.5%SF6/CO2, which was more beneficial for the consumption of the entrained gas.
It should be noted that, in the oxidation cell, the contact area of liquid AZ91 alloy and cover gas (i.e. the size of the crucible) was relatively small with consideration of the large volume of melt and gas. Consequently, the holding time for the oxide film growth within the oxidation cell was comparatively long (i.e., 5–30 min). However, the entrainment defects contained in a real casting are comparatively very small (i.e., a few microns size as shown in Figs. 3–6, and [7]), and the entrained gas is fully enclosed by the surrounding melt, creating a relatively large contact area. Hence the reaction time for cover gas and the AZ91 alloy melt may be comparatively short. In addition, the solidification time of real Mg-alloy sand castings can be a few minutes (e.g. Guo [68] reported that a Mg-alloy sand casting with 60 mm diameter required 4 min to be solidified). Therefore, it can be expected that an entrained gas trapped during an Mg-alloy melt pouring process will be readily consumed by the surrounding melt, especially for sand castings and large-size castings, where solidification times are long.
Therefore, the different cover gases (0.5%SF6/air and 0.5%SF6/CO2) associated with different consumption rates of the entrained gases may affect the reproducibility of the final castings. To verify this assumption, the AZ91 castings produced in 0.5%SF6/air and 0.5%SF6/CO2 were machined into test bars for mechanical evaluation. A Weibull analysis was carried out using both linear least square (LLS) method and non-linear least square (non-LLS) method [69].
Fig. 15(a-b) shows a traditional 2-p linearized Weibull plot of the UTS and elongation of the AZ91 alloy castings, obtained by the LLS method. The estimator used is P= (i-0.5)/N, which was suggested to cause the lowest bias among all the popular estimators [69,70]. The casting produced in SF6/air has an UTS Weibull moduli of 16.9, and an elongation Weibull moduli of 5.0. In contrast, the UTS and elongation Weibull modulus of the casting produced in SF6/CO2 are 7.7 and 2.7 respectively, suggesting that the reproducibility of the casting protected by SF6/CO2 were much lower than that produced in SF6/air.
In addition, the author’s previous publication [69] demonstrated a shortcoming of the linearized Weibull plots, which may cause a higher bias and incorrect R2 interruption of the Weibull estimation. A Non-LLS Weibull estimation was therefore carried out, as shown in Fig. 15 (c-d). The UTS Weibull modulus of the SF6/air casting was 20.8, while the casting produced under SF6/CO2 had a lower UTS Weibull modulus of 11.4, showing a clear difference in their reproducibility. In addition, the SF6/air elongation (El%) dataset also had a Weibull modulus (shape = 5.8) higher than the elongation dataset of SF6/CO2 (shape = 3.1). Therefore, both the LLS and Non-LLS estimations suggested that the SF6/air casting has a higher reproducibility than the SF6/CO2 casting. It supports the method that the use of air instead of CO2 contributes to a quicker consumption of the entrained gas, which may reduce the void volume within the defects. Therefore, the use of 0.5%SF6/air instead of 0.5%SF6/CO2 (which increased the consumption rate of the entrained gas) improved the reproducibility of the AZ91 castings.
However, it should be noted that not all the Mg-alloy foundries followed the casting process used in present work. The Mg-alloy melt in present work was degassed, thus reducing the effect of hydrogen on the consumption of the entrained gas (i.e., hydrogen could diffuse into the entrained gas, potentially suppressing the depletion of the entrained gas [7,71,72]). In contrast, in Mg-alloy foundries, the Mg-alloy melt is not normally degassed, since it was widely believed that there is not a ‘gas problem’ when casting magnesium and hence no significant change in tensile properties[73]. Although studies have shown the negative effect of hydrogen on the mechanical properties of Mg-alloy castings [41,42,73], a degassing process is still not very popular in Mg-alloy foundries.
Moreover, in present work, the sand mould cavity was flushed with the SF6 cover gas prior to pouring [22]. However, not all the Mg-alloy foundries flushed the mould cavity in this way. For example, the Stone Foundry Ltd (UK) used sulphur powder instead of the cover-gas flushing. The entrained gas within their castings may be SO2/air, rather than the protective gas.
Therefore, although the results in present work have shown that using air instead of CO2 improved the reproducibility of the final casting, it still requires further investigations to confirm the effect of carrier gases with respect to different industrial Mg-alloy casting processes.
7. Conclusion
Entrainment defects formed in an AZ91 alloy were observed. Their oxide films had two types of structure: single-layered and multi-layered. The multi-layered oxide film can grow together forming a sandwich-like structure in the final casting.2.
Both the experimental results and the theoretical thermodynamic calculations demonstrated that fluorides in the trapped gas were depleted prior to the consumption of sulphur. A three-stage evolution process of the double oxide film defects has been suggested. The oxide films contained different combinations of compounds, depending on the evolution stage. The defects formed in SF6/air had a similar structure to those formed in SF6/CO2, but the compositions of their oxide films were different. The oxide-film formation and evolution process of the entrainment defects were different from that of the Mg-alloy surface films previous reported (i.e., MgO formed prior to MgF2).3.
The growth rate of the oxide film was demonstrated to be greater under SF6/air than SF6/CO2, contributing to a quicker consumption of the damaging entrapped gas. The reproducibility of an AZ91 alloy casting improved when using SF6/air instead of SF6/CO2.
Acknowledgements
The authors acknowledge funding from the EPSRC LiME grant EP/H026177/1, and the help from Dr W.D. Griffiths and Mr. Adrian Carden (University of Birmingham). The casting work was carried out in University of Birmingham.
WenjunLiuaBoWangaYakunGuobaState Key Laboratory of Hydraulics and Mountain River Engineering, College of Water Resource and Hydropower, Sichuan University, Chengdu 610065, ChinabFaculty of Engineering & Informatics, University of Bradford, BD7 1DP, UK
Highlights
경사진 습윤층에서 댐파괴유동과 FFavre 파를 수치적으로 조사하였다. 수직 대 수평 속도의 비율이 먼저 정량화됩니다. 유동 상태는 유상 경사가 큰 후기 단계에서 크게 변경됩니다. Favre 파도는 수직 속도와 수직 가속도에 큰 영향을 미칩니다. 베드 전단응력의 변화는 베드 기울기와 꼬리물의 영향을 받습니다.
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.
Fig. 1. Sketch of related variables involved in shallow water model. Fig. 2. Flume model in numerical simulation. Fig. 3. Grid sensitivity analysis (a) water surface profile; (b) velocity profile.Fig. 4. Sketch of experimental set-up for validating the velocity profile.Fig. 5. Sketch of experimental set-up for validating the bed shear stress.Fig. 6. Model validation results (a) variation of the velocity profile; (b) error value of the velocity profile; (c) variation of the bed shear stress; (d) error value of the
bed shear stress.
Fig. 7. Schematic diagram of regional division. Fig. 8. Variation of water surface profile (a) α = 0.1; (b) α = 0.3; (c) α = 0.5; (d) α = 0.7.
Fig. 8. (continued). Fig. 8. (continued).Fig. 8. (continued).Fig. 9. Froude number for α = 0.1 (a) variation with time; (b) variation with wavefront position. Fig. 10. Characteristics of velocity distribution (a) α = 0.1; (b) α = 0.3; (c) α = 0.5; (d) α = 0.7.Fig. 11. Average proportion of the vertical velocity (a) α = 0.1; (b) α = 0.3; (c) α = 0.5; (d) α = 0.7.Fig. 12. Bed shear stress distribution (a) α = 0.1; (b) α = 0.3; (c) α = 0.5; (d) α = 0.7.Fig. 12. (continued). Fig. 13. Variation of the maximum bed shear stress position with time (a) α = 0.1; (b) α = 0.3; (c) α = 0.5; (d) α = 0.7. Fig. 14. Time when the maximum bed shear stress appears at different positions (a) α = 0.1; (b) α = 0.3; (c) α = 0.5; (d) α = 0.7.Fig. 15. Movement characteristics of the fluid particles (a) α = 0.1; (b) α = 0.3; (c) α = 0.5; (d) α = 0.7.Fig. 15. (continued).
Keywords
Dam-break flow, Bed slope, Wet bed, Velocity profile, Bed shear stress, Large eddy simulation
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316-L 스테인리스강의 레이저 분말 베드 융합 중 콜드 스패터 형성의 충실도 높은 수치 모델링
M. BAYAT1,* , AND J. H. HATTEL1
Corresponding author 1 Technical University of Denmark (DTU), Building 425, Kgs. 2800 Lyngby, Denmark
ABSTRACT
Spatter and denudation are two very well-known phenomena occurring mainly during the laser powder bed fusion process and are defined as ejection and displacement of powder particles, respectively. The main driver of this phenomenon is the formation of a vapor plume jet that is caused by the vaporization of the melt pool which is subjected to the laser beam. In this work, a 3-dimensional transient turbulent computational fluid dynamics model coupled with a discrete element model is developed in the finite volume-based commercial software package Flow-3D AM to simulate the spatter phenomenon. The numerical results show that a localized low-pressure zone forms at the bottom side of the plume jet and this leads to a pseudo-Bernoulli effect that drags nearby powder particles into the area of influence of the vapor plume jet. As a result, the vapor plume acts like a momentum sink and therefore all nearby particles point are dragged towards this region. Furthermore, it is noted that due to the jet’s attenuation, powder particles start diverging from the central core region of the vapor plume as they move vertically upwards. It is moreover observed that only particles which are in the very central core region of the plume jet get sufficiently accelerated to depart the computational domain, while the rest of the dragged particles, especially those which undergo an early divergence from the jet axis, get stalled pretty fast as they come in contact with the resting fluid. In the last part of the work, two simulations with two different scanning speeds are carried out, where it is clearly observed that the angle between the departing powder particles and the vertical axis of the plume jet increases with increasing scanning speed.
스패터와 denudation은 주로 레이저 분말 베드 융합 과정에서 발생하는 매우 잘 알려진 두 가지 현상으로 각각 분말 입자의 배출 및 변위로 정의됩니다.
이 현상의 주요 동인은 레이저 빔을 받는 용융 풀의 기화로 인해 발생하는 증기 기둥 제트의 형성입니다. 이 작업에서 이산 요소 모델과 결합된 3차원 과도 난류 전산 유체 역학 모델은 스패터 현상을 시뮬레이션하기 위해 유한 체적 기반 상용 소프트웨어 패키지 Flow-3D AM에서 개발되었습니다.
수치적 결과는 플룸 제트의 바닥면에 국부적인 저압 영역이 형성되고, 이는 근처의 분말 입자를 증기 플룸 제트의 영향 영역으로 끌어들이는 의사-베르누이 효과로 이어진다는 것을 보여줍니다.
결과적으로 증기 기둥은 운동량 흡수원처럼 작용하므로 근처의 모든 입자 지점이 이 영역으로 끌립니다. 또한 제트의 감쇠로 인해 분말 입자가 수직으로 위쪽으로 이동할 때 증기 기둥의 중심 코어 영역에서 발산하기 시작합니다.
더욱이 플룸 제트의 가장 중심 코어 영역에 있는 입자만 계산 영역을 벗어날 만큼 충분히 가속되는 반면, 드래그된 나머지 입자, 특히 제트 축에서 초기 발산을 겪는 입자는 정체되는 것으로 관찰됩니다. 그들은 휴식 유체와 접촉하기 때문에 꽤 빠릅니다.
작업의 마지막 부분에서 두 가지 다른 스캔 속도를 가진 두 가지 시뮬레이션이 수행되었으며, 여기서 출발하는 분말 입자와 연기 제트의 수직 축 사이의 각도가 스캔 속도가 증가함에 따라 증가하는 것이 명확하게 관찰되었습니다.
Fig 1. Two different views of the computational domain for the fluid domain. The vapor plume is
simulated by a moving momentum source with a prescribed temperature of 3000 K.Fig 2. (a) and (b) are two snapshots taken at an x-y plane parallel to the powder layer plane before and
0.008 seconds after the start of the scanning process. (c) Shows a magnified view of (b) where detailed
powder particles’ movement along with their velocity magnitude and directions are shown.Fig 3. Front view of the ejected powder particles due to the plume movement. Powder particles are
colored by their respective temperature while trajectory colors show their magnitude at 0.007 seconds.
References
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•The limitation of increasing the rotational speed in decreasing powder size was clarified.
•Cooling and disturbance effects varied with the gas flowing rate.
•Inclined angle of the residual electrode end face affected powder formation.
•Additional cooling gas flowing could be applied to control powder size.
Abstract
The plasma rotating electrode process (PREP) is rapidly becoming an important powder fabrication method in additive manufacturing. However, the low production rate of fine PREP powder limits the development of PREP. Herein, we investigated different factors affecting powder formation during PREP by combining experimental methods and numerical simulations. The limitation of increasing the rotation electrode speed in decreasing powder size is attributed to the increased probability of adjacent droplets recombining and the decreased tendency of granulation. The effects of additional Ar/He gas flowing on the rotational electrode on powder formation is determined through the cooling effect, the disturbance effect, and the inclined effect of the residual electrode end face simultaneously. A smaller-sized powder was obtained in the He atmosphere owing to the larger inclined angle of the residual electrode end face compared to the Ar atmosphere. Our research highlights the route for the fabrication of smaller-sized powders using PREP.
플라즈마 회전 전극 공정(PREP)은 적층 제조 에서 중요한 분말 제조 방법으로 빠르게 자리잡고 있습니다. 그러나 미세한 PREP 분말의 낮은 생산율은 PREP의 개발을 제한합니다. 여기에서 우리는 실험 방법과 수치 시뮬레이션을 결합하여 PREP 동안 분말 형성에 영향을 미치는 다양한 요인을 조사했습니다. 분말 크기 감소에서 회전 전극 속도 증가의 한계는 인접한 액적 재결합 확률 증가 및 과립화 경향 감소에 기인합니다.. 회전 전극에 흐르는 추가 Ar/He 가스가 분말 형성에 미치는 영향은 냉각 효과, 외란 효과 및 잔류 전극 단면의 경사 효과를 통해 동시에 결정됩니다. He 분위기에서는 Ar 분위기에 비해 잔류 전극 단면의 경사각이 크기 때문에 더 작은 크기의 분말이 얻어졌다. 우리의 연구는 PREP를 사용하여 더 작은 크기의 분말을 제조하는 경로를 강조합니다.
Keywords
Plasma rotating electrode process
Ti-6Al-4 V alloy, Rotating speed, Numerical simulation, Gas flowing, Powder size
Introduction
With the development of additive manufacturing, there has been a significant increase in high-quality powder production demand [1,2]. The initial powder characteristics are closely related to the uniform powder spreading [3,4], packing density [5], and layer thickness observed during additive manufacturing [6], thus determining the mechanical properties of the additive manufactured parts [7,8]. Gas atomization (GA) [9–11], centrifugal atomization (CA) [12–15], and the plasma rotating electrode process (PREP) are three important powder fabrication methods.
Currently, GA is the dominant powder fabrication method used in additive manufacturing [16] for the fabrication of a wide range of alloys [11]. GA produces powders by impinging a liquid metal stream to droplets through a high-speed gas flow of nitrogen, argon, or helium. With relatively low energy consumption and a high fraction of fine powders, GA has become the most popular powder manufacturing technology for AM.
The entrapped gas pores are generally formed in the powder after solidification during GA, in which the molten metal is impacted by a high-speed atomization gas jet. In addition, satellites are formed in GA powder when fine particles adhere to partially molten particles.
The gas pores of GA powder result in porosity generation in the additive manufactured parts, which in turn deteriorates its mechanical properties because pores can become crack initiation sites [17]. In CA, a molten metal stream is poured directly onto an atomizer disc spinning at a high rotational speed. A thin film is formed on the surface of the disc, which breaks into small droplets due to the centrifugal force. Metal powder is obtained when these droplets solidify.
Compared with GA powder, CA powder exhibits higher sphericity, lower impurity content, fewer satellites, and narrower particle size distribution [12]. However, very high speed is required to obtain fine powder by CA. In PREP, the molten metal, melted using the plasma arc, is ejected from the rotating rod through centrifugal force. Compared with GA powder, PREP-produced powders also have higher sphericity and fewer pores and satellites [18].
For instance, PREP-fabricated Ti6Al-4 V alloy powder with a powder size below 150 μm exhibits lower porosity than gas-atomized powder [19], which decreases the porosity of additive manufactured parts. Furthermore, the process window during electron beam melting was broadened using PREP powder compared to GA powder in Inconel 718 alloy [20] owing to the higher sphericity of the PREP powder.
In summary, PREP powder exhibits many advantages and is highly recommended for powder-based additive manufacturing and direct energy deposition-type additive manufacturing. However, the low production rate of fine PREP powder limits the widespread application of PREP powder in additive manufacturing.
Although increasing the rotating speed is an effective method to decrease the powder size [21,22], the reduction in powder size becomes smaller with the increased rotating speed [23]. The occurrence of limiting effects has not been fully clarified yet.
Moreover, the powder size can be decreased by increasing the rotating electrode diameter [24]. However, these methods are quite demanding for the PREP equipment. For instance, it is costly to revise the PREP equipment to meet the demand of further increasing the rotating speed or electrode diameter.
Accordingly, more feasible methods should be developed to further decrease the PREP powder size. Another factor that influences powder formation is the melting rate [25]. It has been reported that increasing the melting rate decreases the powder size of Inconel 718 alloy [26].
In contrast, the powder size of SUS316 alloy was decreased by decreasing the plasma current within certain ranges. This was ascribed to the formation of larger-sized droplets from fluid strips with increased thickness and spatial density at higher plasma currents [27]. The powder size of NiTi alloy also decreases at lower melting rates [28]. Consequently, altering the melting rate, varied with the plasma current, is expected to regulate the PREP powder size.
Furthermore, gas flowing has a significant influence on powder formation [27,29–31]. On one hand, the disturbance effect of gas flowing promotes fluid granulation, which in turn contributes to the formation of smaller-sized powder [27]. On the other hand, the cooling effect of gas flowing facilitates the formation of large-sized powder due to increased viscosity and surface tension. However, there is a lack of systematic research on the effect of different gas flowing on powder formation during PREP.
Herein, the authors systematically studied the effects of rotating speed, electrode diameter, plasma current, and gas flowing on the formation of Ti-6Al-4 V alloy powder during PREP as additive manufactured Ti-6Al-4 V alloy exhibits great application potential [32]. Numerical simulations were conducted to explain why increasing the rotating speed is not effective in decreasing powder size when the rotation speed reaches a certain level. In addition, the different factors incited by the Ar/He gas flowing on powder formation were clarified.
Fig. 1. Schematic figure showing the PREP with additional gas flowing on the end face of electrode.
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FLOW-3D 제품의 새로운 2022R1 버전은 Flow Science가 FLOW-3D , FLOW-3DCAST 및 FLOW-3DHYDRO 에 대해 동일한 버전명을 채택 했음을 의미합니다. 2022R1은 FLOW-3D 제품을 위한 통합 코드 베이스로의 전환을 나타내며, 이를 통해 사용자는 최신 버전 개발이 준비되는 즉시 더 빠른 릴리스 버전을 만나실 수 있습니다.
2022R1 릴리스는 상세한 cutcell 표현이라고 하는 FAVOR™ 방법의 확장, 테마 솔버 기본값이 있는 시뮬레이션 템플릿 도입, 이동하는 액적/기포 소스, 새로운 축 펌프 모델, 능동 시뮬레이션 제어 기능에 대한 확장, 사용자는 두 개의 독립 변수를 기반으로 복잡한 속성 종속성을 지정하고 VOF-to-particle 개발과 같은 추가 수치 기능을 지정하여 분해되는 유체 영역의 질량 보존을 개선할 수 있습니다. 간소화된 GUI 개선 사항에는 재설계된 물리 대화 상자, 새로운 초기 조건 위젯, 더 쉽고 빠르고 오류 없는 시뮬레이션 설정을 위해 재설계된 출력 및 지오메트리 위젯이 포함됩니다.
상세한 Cutcell 표현 – FAVOR ™ 의 확장
FAVOR™ 방법은 일반 데카르트 그리드에서 면적 및 부피 분율을 사용하여 솔리드 형상을 구현하는 방법입니다. 이를 통해 FLOW-3D 는 구조화되지 않은 body-fitted mesh에 의존하지 않고 솔리드의 복잡한 형상과 주변의 유체 흐름을 효율적으로 시뮬레이션할 수 있습니다. 상당한 계산상의 이점에도 불구하고 FAVOR™ 방법의 한 가지 문제는 고체 표면을 따라 벽 전단 응력을 계산할 때는 문제가 발생할 수도 있었습니다. 그러나, 상세한 cutcell 표현이라고 하는 FAVOR™의 확장은 벽 전단 응력 계산을 크게 개선하여 솔리드 표면 근처의 유체 유동 해석에서 상당한 개선을 가져옵니다.
점도 및 표면 장력과 같은 재료 속성은 온도, 밀도, 변형률 또는 오염 물질 농도와 같은 것을 나타내는 사용자 정의 스칼라 양과 같은 흐름 조건에 따라 달라질 수 있습니다. 이러한 속성을 기능적 형태에 맞추려면 특히 속성이 둘 이상의 독립 변수에 종속되는 경우 복잡한 곡선 맞춤이 필요할 수 있습니다. FLOW-3D 의 새로운 Tabular Properties 기능은 사용자가 최대 2개의 독립 변수를 사용하여 테이블 형식으로 유체 속성을 정의할 수 있습니다. 예를 들어, 표면 장력은 오염 물질 농도 및 온도에 대한 복잡한 비선형 종속성을 설명하기 위해 실험 데이터에서 표로 만들 수 있으며, 점도는 변형률 속도 및 온도에 대한 종속성을 나타내기 위해 실험 데이터에서 표로 만들 수 있습니다. 사용자는 표 속성 대화 상자에서 단일 변수 또는 두 개의 변수 종속성을 입력할 수 있습니다.
점도는 고체 함량(밀도)과 변형률의 함수로 정의됩니다. 이 예에서 조밀한 유체 영역은 시간이 0일 때 조밀한 침전된 유체 영역과 위쪽에 맑은 물이 있는 정지된 풀로 미끄러져 내려갑니다.
이 대화 상자는 표 속성 기능을 사용하여 변형률 및 온도의 함수로 점도를 정의하는 방법을 보여줍니다. 세 가지 다른 온도에 대한 변형률의 함수로서의 점도에 대한 값이 대화 상자의 오른쪽에 표시되고 그래프로 표시됩니다.
Expanded Active Simulation Control
능동 시뮬레이션 제어(ASC) 는 Probe로 지정한 부분의 흐름 정보를 기반으로 시뮬레이션을 제어하는 데 매우 유용합니다. 이번 릴리스에서 ASC는 일반 이력 데이터, 플럭스 표면 및 sampling volumes의 흐름 정보를 기반으로 추가 제어를 허용하도록 확장되었습니다.
포인트 프로브에 비해 플럭스 표면 및 샘플링 볼륨의 장점 중 하나는 포인트 기반이 아닌 표면 또는 볼륨에 대해 평균화된 정보를 제공할 수 있다는 것입니다. 어떤 상황에서는 표면 기반 및 볼륨 기반 정보가 시뮬레이션에서 관심 있는 동작을 더 잘 나타낼 수 있습니다.
이 새로운 기능을 통해 사용자는 다음을 수행할 수 있습니다.
제어 볼륨의 온도가 임계값을 초과하거나 아래로 떨어지면 시뮬레이션을 종료합니다.
샘플링 볼륨의 난류 에너지를 기반으로 노즐에서 충전 속도를 제어합니다.
자속 평면의 평균 속도를 기반으로 출력 주파수를 제어합니다.
샘플링 볼륨의 채우기 비율이 사용자가 지정한 값에 도달하면 시뮬레이션을 종료합니다.
이 예에서 극저온 탱크 공급 파이프의 펌프(진한 회색 직사각형)는 일정한 유속으로 추진제 탱크에서 액체 산소를 끌어옵니다. 액체 산소가 배출됨에 따라 얼리지의 압력이 지정된 값 아래로 떨어질 때 활성 시뮬레이션 제어에 의해 질량/운동량 소스(상단의 회색 막대)가 트리거됩니다. 얼리지 압력이 지정된 값 이상으로 상승하면 가압이 꺼집니다.
VOF to Particles
FLOW-3D 에서 복잡한 자유표면을 추적하는 VOF 방법의 정확성과 견고성은 유체 입자와 결합하여 향상되었습니다. VOF 입자라고 하는 새로운 입자 종류는 VOF 기능 대신 사용되어, 계산 영역에서 작은 유체 인대와 액적을 추적하여 유체 부피와 운동량을 더 잘 보존할 수 있습니다. 중력 제어 프로세스에서 더 높은 시간 단계 크기도 예상할 수 있습니다. VOF 유체는 특정 조건이 충족되면 특정 시간과 위치에서 자동으로 VOF 입자로 변환됩니다. 그런 다음 입자 모션은 Lagrangian 입자 모델을 사용하여 계산되고 입자는 유체에 다시 들어갈 때 VOF 표현으로 다시 변환됩니다.
입자에 대한 VOF
Axial Pump Model
FLOW-3D의 새로운 Axial Pump Model을 통해 사용자는 시뮬레이션에서 Axial Pump의 실제 효과를 구현할 수 있습니다. 펌프 동작과 관련하여 두 가지 옵션이 있습니다. 첫 번째 옵션은 유체가 지정된 속도로 이동하도록 펌프를 통한 체적 유량 또는 유속을 규정하는 것입니다. 이 옵션은 펌프에 작동 유량이 제공될 때 적합합니다. 두 번째 옵션은 펌프 성능 곡선을 기반으로 펌프 작동에 대한 보다 완전한 정의를 제공합니다. 이 경우 사용자는 펌프 성능 곡선의 선형 근사치를 정의하여 펌프를 통과하는 유량이 펌프 전체의 압력 강하에 따라 달라지도록 할 수 있습니다. 이 구성에서 펌프의 일반적인 동작은 다음과 같이 표시됩니다.
GUI의 팬/임펠러 구성요소GUI의 축 펌프 구성 요소
Droplet/Bubble Source Model | 액적/기포 소스 모델
FLOW-3D 는 처음 개발된 이후 로 표면 장력 작용에 따라 진화하는 유체 모양을 시뮬레이션하기 위해 노즐 및 기타 오리피스 모양에서 분사되는 액적을 모델링하는 데 사용되었습니다. 그러나 기판에 대한 액적의 영향만 관심이 있기 때문에 노즐을 떠날 때 액적의 모양을 시뮬레이션할 필요가 없는 경우가 있습니다. 또한, 유체에서 기포의 이동을 모델링하는 것은 흥미로울 수 있지만 기포의 시작은 아닙니다. 새로운 액적/기포 소스 모델은 이와 같은 경우에 유용합니다.
이 예에서 액적 소스는 원형 패턴으로 이동하면서 액적을 10m/s의 속도로 다공성 매체로 아래쪽으로 토출하여 링 모양 디자인을 만듭니다.
사용자 인터페이스에서 액적/기포 소스 설정
Simulation Templates
새로운 시뮬레이션 템플릿은 자유 표면이 있는 하나의 유체에 대해 비압축성 흐름 또는 2개의 유체 압축성 시뮬레이션과 같은 주어진 모델링 프레임워크를 기반으로 중요한 매개변수를 미리 로드합니다. 새로운 시뮬레이션이 생성되면 FLOW-3D 에서 가장 일반적으로 모델링된 사례를 다루는 6개의 템플릿이 포함된 대화 상자가 사용자에게 표시됩니다 . ‘없음’ 옵션을 사용하면 고급 사용자가 특수 수치 설정을 적용할 수 있도록 빈 슬레이트로 시작할 수 있습니다. 템플릿을 사용하면 모델 설정 프로세스를 신속하게 처리하고 사용자가 실수를 하거나 매개변수 정의를 잊어버리는 것을 방지할 수 있습니다.
GUI의 새로운 시뮬레이션 템플릿
추가 솔버 기능
추가 솔버 기능에는 비뉴턴 유체에 대한 Herschel-Bulkley 모델 및 분해되기 쉬운 유체 영역에 대한 질량 보존을 개선하기 위한 기체-공동 변환, 다중 이벤트 동작 및 이벤트 옵션 지원을 포함한 확장된 질량-운동량 소스 프로브 이벤트가 포함됩니다. 동반된 공기의 부피 분율과 용질 농도에 대한 것입니다.
Herschel-Bulkley 모델활성 시뮬레이션 질량 운동량 소스 이벤트
GUI 개선
WSIWYN 설계 접근 방식을 사용한 간소화된 GUI 개선에는 재설계된 물리 및 초기 조건 대화 상자, 더 쉽고 빠르며 오류 없는 시뮬레이션 설정을 위해 재설계된 출력 및 지오메트리 위젯이 포함됩니다.
초기 조건 위젯
초기 조건 위젯은 초기 유체 및 기체 영역 설정을 개선하여 더 쉽고 빠르게 만듭니다. 새로운 디자인에서는 전역, 영역 및 포인터 개체가 별도의 탭에 배치되어 설정을 훨씬 더 명확하게 볼 수 있습니다.
초기 조건 – 지역초기 조건 – 정수압초기 조건 – 포인터
출력 위젯
재설계된 출력 위젯을 통해 사용자는 시뮬레이션 결과 파일에서 어떤 출력을 사용할 수 있는지 정확히 확인할 수 있으며, 하나의 간결한 보기에서 다시 시작 및 선택한 데이터 출력을 명확히 알 수 있습니다.
재설계된 공간 출력 위젯출력 위젯 – 지오메트리 데이터공간 데이터가 기록될 때 출력을 강제 실행하면 기록 및 공간 데이터 출력에 대한 동기화된 출력이 사용자에게 제공됩니다.
대화형 지오메트리 생성 및 편집
대화형 지오메트리 생성 및 편집 기능이 그 어느 때보다 향상되었으며 이제 다음이 포함됩니다.
회전, 이동 및 크기 조정을 포함한 새로운 대화형 도구 선택이 가능합니다.
작업을 클릭하고 수정할 지오메트리를 선택하여 회전, 이동 또는 크기 조정 모드를 시작합니다.
위쪽 화살표 아이콘을 클릭하거나 ESC 키를 누르면 일반 선택 모드로 돌아갑니다.
Geometry Widget
기하학 위젯은 이제 다양한 속성 그룹을 결합하고 관련 항목을 함께 배치하는 WYSIWYN 디자인 접근 방식을 사용하여 더 쉽고 빠르게 탐색할 수 있습니다.
지오메트리 위젯
Easier Access to Help
이제 물리 대화 상자 내에서 클릭 한 번으로 관련 문서, 자습서 및 도움말 다이어그램에 액세스할 수 있습니다.
물리학 대화상자
간소화된 물리 대화 상자
사용자가 시뮬레이션을 더 빠르게 설정하고 설정 오류를 줄일 수 있도록 많은 물리 대화 상자가 간소화되었습니다.
Bubble and phase change modelAir entrainment modelDrift flux model
마이크로 컴퓨터 단층 촬영 검사 특성을 가진 Si 다공성 프리폼에 AlSi12 합금의 침투에 대한 실험적 연구 및 수치 시뮬레이션
Ruizhe LIU1 and Haidong ZHAO1,³ 1National Engineering Research Center of Near-Net-Shape Forming for Metallic Materials, South China University of Technology, Guangzhou 510640, China
Abstract
전분 함량(10, 20 및 30%)과 입자 크기(20, 50 및 90 m)가 다른 실리콘 입자 예비 성형체는 압축 성형 및 열처리를 통해 제작되었습니다. 프리폼의 기공 특성은 고해상도(³1 m) 3차원(3D) X선 마이크로 컴퓨터 단층 촬영(V-CT)으로 검사되었습니다. AlSi12 합금의 프리폼으로의 침투는 진공 보조 압력 침투 장치에서 800 °C 및 400 kPa의 조건에서 서로 다른 압력 적용 시간(3, 8 및 15초)으로 수행되었습니다. 고해상도(³500 nm) 수직 주사 백색광 간섭 프로파일로미터를 사용하여 복합 재료의 전면을 감지했습니다. Navier-Stokes 방정식을 기반으로 하는 ¯-CT 검사에서 실제 기공 형상을 고려하여 침투를 미시적으로 시뮬레이션했습니다. 그 결과 전분 함량과 입자크기가 증가할수록 복합재료의 표면적이 증가하는 것으로 나타났다. 전분 함량과 비교하여 입자 크기는 전면 표면적에 더 많은 영향을 미칩니다. 시뮬레이션에서 침투가 진행됨에 따라 액체 AlSi12의 압력이 감소했습니다. 복합재의 잔류 기공은 침투와 함께 증가했습니다. 실험 및 시뮬레이션 결과에 따르면 침투 방향을 따라 더 큰 압력 강하가 복합 재료의 더 많은 잔류 기공을 유도합니다.
Silicon particle preforms with different starch contents (10, 20 and 30%) and particle sizes (20, 50 and 90 ¯m) were fabricated by compression mold forming and heat treatment. The pore characteristics of preforms were inspected with a high-resolution (³1 ¯m) three-dimensional (3D) X-ray micro-computed tomography (¯-CT). The infiltration of AlSi12 alloys into the preforms were carried out under the condition of 800 °C and 400 kPa with different pressure-applied times (3, 8 and 15 s) in a vacuum-assisted pressure infiltration apparatus. A highresolution (³500 nm) vertical scanning white light interfering profilometer was used to detect the front surfaces of composites. The infiltration was simulated at micro-scale by considering the actual pore geometry from the ¯- CT inspection based on the Navier-Stokes equation. The results demonstrated that as the starch content and particle size increased, the front surface area of composite increased. Compared with the starch content, the particle size has more influence on the front surface area. In the simulation, as the infiltration progressed, the pressure of liquid AlSi12 decreased. The residual pores of composites increased with infiltration. According to the experiment and simulation results, a larger pressure drop along the infiltration direction leads to more residual pores of composites.
Fig. 1. Size distributions of Si particles.Fig. 2. Schematic of different locations of composites.Fig. 3. Three-dimensional geometry with the reconstruction
technology, enmeshment and infiltration parameters of Si preforms: (a) geometry, and (b) meshes and flow direction.
Fig. 4. Number-based frequencies of effective pore radius and throat radius: (a) effective pore radius of
preforms with the 50 ¯m particles, (b) effective throat radius of preforms with the 50 ¯m particles, (c) effective
pore radius of preforms with the 20 % starches, and (d) effective throat radius of preforms with the 20 % starches.Fig. 5. 3D topological morphologies of front surfaces of composites: (a) 50 ¯m-10 %, (b) 50 ¯m-20 %,
(c) 50 ¯m-30 %, (d) 20 ¯m-20 %, and (e) 90 ¯m-20 %.Fig. 6. Schematic of capillary tube.Fig. 8. Pressure distribution during the infiltration of preform with the 50 ¯m particles and 20 % starches:
(a) 25 % filled, (b) 57 % filled, and (c) 99 % filled.Fig. 9. Pressure distributions of liquid AlSi12 during the infiltration of preforms: (a) different fill fractions, (b) different starch
contents, and (c) different particle sizes.Fig. 10. Metallographs of composites: (a) different locations of composite with the 20 ¯m particles and 20 %
starches, and (b) different locations of composite with the 90 ¯m particles and 20 % starches.Fig. 11. Area fractions of residual pores of composites: (a) 50 ¯m (different starch contents), and (b) 20 %
(different particle sizes).
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측면 분기기(흡입구)의 상류 측에서 흐름 분리는 분기기 입구에서 와류를 일으키는 중요한 문제입니다. 이는 흐름의 유효 폭, 출력 용량 및 효율성을 감소시킵니다. 따라서 분리지대의 크기를 파악하고 크기를 줄이기 위한 방안을 제시하는 것이 필수적이다. 본 연구에서는 분리 구역의 치수를 줄이기 위한 방법으로 7가지 유형의 거칠기 요소를 분기구 입구에 설치하고 4가지 다른 배출(총 84번의 실험을 수행)과 함께 3개의 서로 다른 베드 반전 레벨을 조사했습니다. 또한 3D CFD(Computational Fluid Dynamics) 모델을 사용하여 분리 영역의 흐름 패턴과 치수를 평가했습니다. 결과는 거칠기 계수를 향상시키면 분리 영역 치수를 최대 38%까지 줄일 수 있는 반면, 드롭 구현 효과는 사용된 거칠기 계수를 기반으로 이 영역을 다르게 축소할 수 있음을 보여주었습니다. 두 가지 방법을 결합하면 분리 영역 치수를 최대 63%까지 줄일 수 있습니다.
Flow separation at the upstream side of lateral turnouts (intakes) is a critical issue causing eddy currents at the turnout entrance. It reduces the effective width of flow, turnout capacity and efficiency. Therefore, it is essential to identify the dimensions of the separation zone and propose remedies to reduce its dimensions. Installation of 7 types of roughening elements at the turnout entrance and 3 different bed invert levels, with 4 different discharges (making a total of 84 experiments) were examined in this study as a method to reduce the dimensions of the separation zone. Additionally, a 3-D Computational Fluid Dynamic (CFD) model was utilized to evaluate the flow pattern and dimensions of the separation zone. Results showed that enhancing the roughness coefficient can reduce the separation zone dimensions up to 38% while the drop implementation effect can scale down this area differently based on the roughness coefficient used. Combining both methods can reduce the separation zone dimensions up to 63%.
Turnouts or intakes are amongst the oldest and most widely used hydraulic structures in irrigation networks. Turnouts are also used in water distribution, transmission networks, power generation facilities, and waste water treatment plants etc. The flows that enter a turnout have a strong momentum in the direction of the main waterway and that is why flow separation occurs inside the turnout. The horizontal vortex formed in the separation area is a suitable place for accumulation and deposition of sediments. The separation zone is a vulnerable area for sedimentation and for reduction of effective flow due to a contracted flow region in the lateral channel. Sedimentaion in the entrance of the intake can gradually be transfered into the lateral channel and decrease the capacity of the higher order channels over time (Jalili et al. 2011). On the other hand, the existence of coarse-grained materials causes erosion and destruction of the waterway side walls and bottom. In addition, sedimentation creates conditions for vegetation to take root and damage the waterway cover, which causes water to leak from its perimeter. Therefore, it is important to investigate the pattern of the flow separation area in turnouts and provide solutions to reduce the dimensions of this area.
The three-dimensional flow structure at turnouts is quite complex. In an experimental study by Neary & Odgaard (1993) in a 90-degree water turnout it was found that the secondary currents and separation zone varies from the bed to the water surface. They also found that at a 90-degree water turnout, the bed roughness and discharge ratio play a critical role in flow structure. They asserted that an explanation of sediment behavior at a diversion entrance requires a comprehensive understanding of 3D flow patterns around the lateral-channel entrance. In addition, they suggested that there is a strong similarity between flow in a channel bend and a diversion channel, and that this similarity can rationalize the use of bend flow models for estimation of 3D flow structures in diversion channels.
Some of the distinctive characteristics of dividing flow in a turnout include a zone of separation immediately near the entrance of the lateral turnout (separation zone), a contracted flow region in the branch channel (contracted flow), and a stagnation point near the downstream corner of the junction (stagnation zone). In the region downstream of the junction, along the continuous far wall, separation due to flow expansion may occur (Ramamurthy et al. 2007), that is, a separation zone. This can both reduce the turnout efficiency and the effective width of flow while increasing the sediment deposition in the turnout entrance (Jalili et al. 2011). Installation of submerged vanes in the turnout entrance is a method which is already applied to reduce the size of flow separation zones. The separation zone draws sediments and floating materials into themselves. This reduces effective cross-section area and reduces transmission capacity. These results have also been obtained in past studies, including by Ramamurthy et al. (2007) and in Jalili et al. (2011). Submerged vanes (Iowa vanes) are designed in order to modify the near-bed flow pattern and bed-sediment motion in the transverse direction of the river. The vanes are installed vertically on the channel bed, at an angle of attack which is usually oriented at 10–25 degrees to the local primary flow direction. Vane height is typically 0.2–0.5 times the local water depth during design flow conditions and vane length is 2–3 times its height (Odgaard & Wang 1991). They are vortex-generating devices that generate secondary circulation, thereby redistributing sediment within the channel cross section. Several factors affect the flow separation zone such as the ratio of lateral turnout discharge to main channel discharge, angle of lateral channel with respect to the main channel flow direction and size of applied submerged vanes. Nakato et al. (1990) found that sediment management using submerged vanes in the turnout entrance to Station 3 of the Council Bluffs plant, located on the Missouri River, is applicable and efficient. The results show submerged vanes are an appropriate solution for reduction of sediment deposition in a turnout entrance. The flow was treated as 3D and tests results were obtained for the flow characteristics of dividing flows in a 90-degree sharp-edged, junction. The main and lateral channel were rectangular with the same dimensions (Ramamurthy et al., 2007).
Keshavarzi & Habibi (2005) carried out experiments on intake with angles of 45, 67, 79 and 90 degrees in different discharge ratios and reported the optimum angle for inlet flow with the lowest flow separation area to be about 55 degrees. The predicted flow characteristics were validated using experimental data. The results indicated that the width and length of the separation zone increases with the increase in the discharge ratio Qr (ratio of outflow per unit width in the turnout to inflow per unit width in the main channel).
Abbasi et al. (2004) performed experiments to investigate the dimensions of the flow separation zone at a lateral turnout entrance. They demonstrated that the length and width of the separation zone decreases with the increasing ratio of lateral turn-out discharge. They also found that with a reducing angle of lateral turnout, the length of the separation zone scales up and width of separation zone reduces. Then they compared their observations with results of Kasthuri & Pundarikanthan (1987) who conducted some experiments in an open-channel junction formed by channels of equal width and an angle of lateral 90 degree turnout, which showed the dimensions of the separation zone in their experiments to be smaller than in previous studies. Kasthuri & Pundarikanthan (1987) studied vortex and flow separation dimensions at the entrance of a 90 degree channel. Results showed that increasing the diversion discharge ratio can reduce the length and width of the vortex area. They also showed that the length and width of the vortex area remain constant at diversion ratios greater than 0.7. Karami Moghaddam & Keshavarzi (2007) analyzed the flow characteristics in turnouts with angles of 55 and 90 degrees. They reported that the dimensions of the separation zone decrease by increasing the discharge ratio and reducing the turnout angle with respect to the main channel. Studies about flow separation zone can be found in Jalili et al. (2011), Nikbin & Borghei (2011), Seyedian et al. (2008).
Jamshidi et al. (2016) measured the dimensions of a flow separation zone in the presence of submerged vanes with five arrangements (parallel, stagger, compound, piney and butterflies). Results showed that the ratio of the width to the length of the separation zone (shape index) was between 0.2 and 0.28 for all arrangements.
Karami et al. (2017) developed a 3D computational fluid dynamic (CFD) code which was calibrated by measured data. They used the model to evaluate flow pattern, diversion ratio of discharge, strength of the secondary flow, and dimensions of the vortex inside the channel in various dikes and submerged vane installation scenarios. Results showed that the diversion ratio of discharge in the diversion channel is dependent on the width of the flow separation area in the main channel. A dike, perpendicular to the flow, doubles the ratio of diverted discharge and reduces the suspended sediment load compared with the base-line situation by creating outer arch conditions. In addition, increasing the longitudinal distance between vanes increases the velocity gradient between the vanes and leads to a more severe erosion of the bed near the vanes.Figure 1VIEW LARGEDOWNLOAD SLIDE
Laboratory channel dimensions.
Al-Zubaidy & Hilo (2021) used the Navier–Stokes equation to study the flow of incompressible fluids. Using the CFD software ANSYS Fluent 19.2, 3D flow patterns were simulated at a diversion channel. Their results showed good agreement using the comparison between the experimental and numerical results when the k-omega turbulence viscous model was employed. Simulation of the flow pattern was then done at the lateral channel junction using a variety of geometry designs. These improvements included changing the intake’s inclination angle and chamfering and rounding the inner corner of the intake mouth instead of the sharp edge. Flow parameters at the diversion including velocity streamlines, bed shear stress, and separation zone dimensions were computed in their study. The findings demonstrated that changing the 90° lateral intake geometry can improve the flow pattern and bed shear stress at the intake junction. Consequently, sedimentation and erosion problems are reduced. According to the conclusions of their study, a branching angle of 30° to 45° is the best configuration for increasing branching channel discharge, lowering branching channel sediment concentration.
The review of the literature shows that most of the studies deal with turnout angle, discharge ratio and implementation of vanes as techniques to reduce the area of the separation zone. This study examines the effect of roughness coefficient and drop implementation at the entrance of a 90-degree lateral turnout on the dimensions of the separation zone. As far as the authors are aware, these two variables have never been studied as a remedy to decrease the separation zone dimensions whilst enhancing turnout efficiency. Additionally, a three-dimensional numerical model is applied to simulate the flow pattern around the turnout. The numerical results are verified against experimental data.
The experiments were conducted in a 90 degree dividing flow laboratory channel. The main channel is 15 m long, 0.5 m wide and 0.4 m high and the branch channel is 3 m long, 0.35 m wide and 0.4 m high, as shown in Figure 1. The tests were carried out at 9.65 m from the beginning of the flume and were far enough from the inlet, so we were sure that the flow was fully developed. According to Kirkgöz & Ardiçlioğlu (1997) the length of the developing region would be approximantly 65 and 72 times the flow depth. In this study, the depth is 9 cm, which makes this condition.
Both the main and lateral channel had a slope of 0.0003 with side walls of concrete. A 100 hp pump discharged the water into a stilling basin at the entrance of the main flume. The discharge was measured using an ultrasonic discharge meter around the discharge pipe. Eighty-four experiments in total were carried out at range of 0.1<Fr<0.4 (Froude numbers in main channel and upstream of turnout). The depth of water in the main channel in the experiments was 9 cm, in which case the effect of surface tension can be considered; according to research by Zolghadr & Shafai Bejestan (2020) and Zolghadr et al. (2021), when the water depth is more than 6 cm, the effect of surface tension is reduced and can be ignored given that the separation phenomenon occurs in the boundary layer, the height of the roughness creates disturbances in growth and development of the boundary layer and, as a result, separation growth is also faced with disruption and its dimensions grow less compared to smooth surfaces. Similar conditions occur in case of drop implementation. A disturbance occurs in the growth of the boundary layer and as a result the separation zone dimensions decrease. In order to investigate the effect of roughness coefficient and drop implementation on the separation zone dimensions, four different discharges (16, 18, 21, 23 l/s) in subcritical conditions, seven Manning (Strickler) roughness coefficients (0.009, 0.011, 0.017, 0.023, 0.028, 0.030, 0.032) as shown in Figure 2 and three invert elevation differences between the main channel and lateral turnout invert (0, 5 and 10 cm) at the entrance of the turnout were considered. The Manning roughness coefficient values were selected based on available and feasible values for real conditions, so that 0.009 is equivalent to galvanized sheet roughness and selected for the baseline tests. 0.011 is for concrete with neat surface, 0.017 and 0.023 are for unfinished and gunite concrete respectively. 0.030 and 0.032 values are for concrete on irregular excavated rock (Chow 1959). The roughness coefficients were created by gluing sediment particles on a thin galvanized sheet which was installed at the upstream side of the lateral turnout. The values of roughness coefficients were calculated based on the Manning-Strickler formula. For this purpose, some uniformly graded sediment samples were prepared and the Manning roughness coefficient of each sample was determined with respect to the median size (D50) value pasted into the Manning-Strickler formula. Some KMnO4 was sifted in the main channel upstream to visualize and measure the dimensions of the separation zone. Consequently, when KMnO4 approached the lateral turnout a photo of the separation zone was taken from a top view. All the experiments were recorded and several photos were taken during the experiment after stablishment of steady flow conditions. The photos were then imported to AutoCAD to measure the separation zone dimensions. Because all the shooting was done with a high-definition camera and it was possible to zoom in, the results are very accurate.Figure 2VIEW LARGEDOWNLOAD SLIDE
Roughness plates.
The velocity values were also recorded by a one-dimensional velocity meter at 15 cm distance from the turnout entrance and in transverse direction (perpendicular to the flow direction).
The water level was also measured by depth gauges with a accuracy of 0.1 mm, and velocity in one direction with a single-dimensional KENEK LP 1100 with an accuracy of ±0.02 m/s (0–1 m/s), ± 0.04 m/s (1–2 m/s), ± 0.08 m/s (2–4 m/s), ±0.10 m/s (4–5 m/s).
Numerical simulation
ListenA FLOW-3D numerical model was utilized as a solver of the Navier-Stokes equation to simulate the three-dimensional flow field at the entrance of the turnout. The governing equations included continuity momentum equations. The continuity equation, regardless of the density of the fluid in the form of Cartesian coordinates x, y, and z, is as follows:
(1)where u, v, and w represent the velocity components in the x, y, and z directions, respectively; Ax, Ay, and Az are the surface flow fractions in the x, y, and z directions, respectively; VF denotes flow volume fraction; r is the density of the fluid; t is time; and Rsor refers to the source of the mass. Equations (2)–(4) show momentum equations in x, y and z dimensions respectively :
(2)
(3)
(4)where Gx, Gy, and Gz are the accelerations caused by gravity in the x, y, and z directions, respectively; and fx, fy, and fz are the accelerations caused by viscosity in the x, y, and z directions, respectively.
The turbulence models used in this study were the renormalized group (RNG) models. Evaluation of the concordance of the mentioned models with experimental studies showed that the RNG model provides more accurate results.
Two blocks of mesh were used to simulate the main channels and lateral turnout. The meshes were denser in the vicinity of the entrance of the turnout in order to increase the accuracy of computations. Boundary conditions for the main mesh block included inflow for the channel entrance (volumetric flow rate), outflow for the channel exit, ‘wall’ for the bed and the right boundary and ‘symmetry’ for the top (free surface) and left boundaries (turnout). The side wall roughness coefficient was given to the software as the Manning number in surface roughness of any component. Considering the restrictions in the available processor, a main mesh block with appropriate mesh size was defined to simulate the main flow field in the channel, while the nested mesh-block technique was utilized to create a very dense solution field near the roughness plate in order to provide accurate results around the plates and near the entrance of the lateral turnout. This technique reduced the number of required mesh elements by up to 60% in comparison with the method in which the mesh size of the main solution field was decreased to the required extent.
The numerical outputs are verified against experimental data. The hydraulic characteristics of the experiment are shown in Table 1.Table 1
During the experiments, the dimensions of the separation zone were recorded with an HD camera. Some photos were imported to AutoCad software. Then, the separation zones dimensions were measured and compared in different scenarios.
At the beginning, the flow pattern in the separation zone for four different hydraulic conditions was studied for seven different Manning roughness coefficients from 0.009 to 0.032. To compare the obtained results, roughness of 0.009 was considered as the base line. The percentage of reduction in separation zone area in different roughness coefficients is shown in Figure 3. According to this figure, by increasing the roughness of the turnout side wall, the separation zone area ratio reduces (ratio of separation zone area to turnout area). In other words, in any desired Froud number, the highest dimensions of the separation zone area are related to the lowest roughness coefficients. In Figure 3, ‘A’ is the area of the separation zone and ‘Ai’ represents the total area of the turnout.Figure 3VIEW LARGEDOWNLOAD SLIDE
Effect of roughness on separation zone dimensions.
It should be mentioned that the separation zone dimensions change with depth, so that the area is larger at the surface than near the bed. This study measured the dimensions of this area at the surface. Figure 4 show exactly where the roughness elements were located.Figure 5VIEW LARGEDOWNLOAD SLIDE
Comparison of separation zone for n=0.023 and n=0.032.
Figure 5 shows images of the separation zone at n=0.023 and n=0.032 as examples, and show that the separation area at n=0.032 is smaller than that of n=0.023.
The difference between the effect of the two 0.032 and 0.030 roughnesses is minor. In other words, the dimensions of the separation zone decreased by increasing roughness up to 0.030 and then remained with negligable changes.
In the next step, the effect of intake invert relative to the main stream (drop) on the dimensions of the separation zone was investigated. To do this, three different invert levels were considered: (1) without drop; (2) a 5 cm drop between the main canal and intake canal; and (3) a 10 cm drop between the main canal and intake canal. The without drop mode was considered as the control state. Figure 6 shows the effect of drop implementation on separation zone dimensions. Tables 2 and 3 show the reduced percentage of separation zone areas in 5 and 10 cm drop compared to no drop conditions as the base line. It was found that the best results were obtained when a 10 cm drop was implemented.Table 2
Decrease percentage of separation zone area in 5 cm drop
Fr
n=0.011
n=0.017
n=0.023
n=0.028
n=0.030
n=0.032
0.08
10.56
11.06
25.27
33.03
35.57
36.5
0.121
7.66
11.14
11.88
15.93
34.59
36.25
0.353
1.38
2.63
8.17
14.39
31.20
31.29
0.362
3
11.54
19.56
25.73
37.89
38.31
Table 3
Decrease percentage of separation zone area in 10 cm drop
Effect of drop implementation on separation zone dimensions.
The combined effect of drop and roughness is shown in Figure 7. According to this figure, by installing a drop structure at the entrance of the intake, the dimensions of the separation zone scales down in any desired roughness coefficient. Results indicated that by increasing the roughness coefficient or drop implementation individually, the separation zone area decreases up to 38 and 25% respectively. However, employing both techniques simultaneously can reduce the separation zone area up to 63% (Table 4). The reason for the reduction of the dimensions of the separation zone area by drop implementation can be attributed to the increase of discharge ratio. This reduces the dimensions of the separation zone area.Table 4
Reduction in percentage of combined effect of roughness and 10 cm drop
Combined effect of roughness and drop on separation zone dimensions.
This method increases the discharge ratio (ratio of turnout to main channel discharge). The results are compatible with the literature. Some other researchers reported that increasing the discharge ratio can scale down the separation zone dimensions (Karami Moghaddam & Keshavarzi 2007; Ramamurthy et al. 2007). However, these researchers employed other methods to enhance the discharge ratio. Drop implementation is simple and applicable in practice, since there is normally an elevation difference between the main and lateral canal in irrigation networks to ensure gravity flow occurance.
Table 4 depicts the decrease in percentage of the separation zone compared to base line conditions in different arrangements of the combined tests.Figure 8VIEW LARGEDOWNLOAD SLIDE
Velocity profiles for various roughness coefficients along turnout width.
A comparison between the proposed methods introduced in this paper and traditional methods such as installation of submerged vanes, and changing the inlet geometry (angle, radius) was performed. Figure 8 shows the comparison of the results. The comparison shows that the new techniques can be highly influential and still practical. In this research, with no change in structural geometry (enhancement of roughness coefficient) or minor changes with respect to drop implementation, the dimensions of the separation zone are decreased noticeably. The velocity values were also recorded by a one-dimensional velocity meter at 15 cm distance from the turnout entrance and in a transverse direction (perpendicular to the flow direction). The results are shown in Figure 9.Figure 9VIEW LARGEDOWNLOAD SLIDE
Effect of roughness on separation zone dimensions in numerical study.
This study examined the flow patterns around the entrance of a diversion channel due to various wall roughnesses in the diversion channel. Results indicated that increasing the discharge ratio in the main channel and diversion channel reduces the area of the separation zone in the diversion channel.Figure 10VIEW LARGEDOWNLOAD SLIDE
Comparision of the vortex area (software output) for three roughnesses (0.009, 0.023 and 0.032).A laboratory and numerical error rate of 0.2605 was calculated from the following formula,
where Uexp is the experimental result, Unum is the numerical result, and N is the number of data.
Figure 9 shows the effect of roughness on separation zone dimensions in numerical study. Figure 10 compares the vortex area (software output) for three roughnesses, 0.009, 0.023 and 0.032 and Figure 11 shows the flow lines (tecplot output) that indicate the effect of roughness on flow in the separation zone. Numerical analysis shows that by increasing the roughness coefficient, the dimensions of the separation zone area decrease, as shown in Figure 10 where the separation zone area at n=0.032 is less than the separation zone area at n=0.009.Figure 11VIEW LARGEDOWNLOAD SLIDE
Comparison of vortex area in 3D mode (tecplot output) with two roughnesses (a) 0.009 and (b) 0.032.Figure 12VIEW LARGEDOWNLOAD SLIDE
Velocity vector for flow condition Q1/422 l/s, near surface.
The velocities intensified moving midway toward the turnout showing that the effective area is scaled down. The velocity values were almost equal to zero near the side walls as expected. As shown in Figure 12 the approach vortex area velocity decreases. Experimental and numerical measured velocity at x=0.15 m of the diversion channel compared in Figure 13 shows that away from the separation zone area, the velocity increases. All longitudinal velocity contours near the vortex area are distinctly different between different roughnesses. The separation zone is larger at less roughness both in length and width.Figure 13VIEW LARGEDOWNLOAD SLIDE
This study introduces practical and feasible methods for enhancing turnout efficiency by reducing the separation zone dimensions. Increasing the roughness coefficient and implementation of inlet drop were considered as remedies for reduction of separation zone dimensions. A data set has been compiled that fully describes the complex, 3D flow conditions present in a 90 degree turnout channel for selected flow conditions. The aim of this numerical model was to compare the results of a laboratory model in the area of the separation zone and velocity. Results showed that enhancing roughness coefficient reduce the separation zone dimensions up to 38% while the drop implementation effect can scale down this area differently based on roughness coefficient used. Combining both methods can reduce the separation zone dimensions up to 63%. Further research is proposed to investigate the effect of roughness and drop implementation on sedimentation pattern at lateral turnouts. The dimensions of the separation zone decreases with the increase of the non-dimensional parameter, due to the reduction ratio of turnout discharge increasing in all the experiments.
This method increases the discharge ratio (ratio of turnout to main channel discharge). The results are compatible with the literature. Other researchers have reported that intensifying the discharge ratio can scale down the separation zone dimensions (Karami Moghaddam & Keshavarzi 2007; Ramamurthy et al. 2007). However, they employed other methods to enhance the discharge ratio. Employing both techniques simultaneously can decrease the separation zone dimensions up to 63%. A comparison between the new methods introduced in this paper and traditional methods such as installation of submerged vanes, and changing the inlet geometry (angle, radius) was performed. The comparison shows that the new techniques can be highly influential and still practical. The numerical and laboratory models are in good agreement and show that the method used in this study has been effective in reducing the separation area. This method is simple, economical and can prevent sediment deposition in the intake canal. Results show that CFD prediction of the fluid through the separation zone at the canal intake can be predicted reasonably well and the RNG model offers the best results in terms of predictability.
A 3D numerical model of heat transfer and fluid flow of molten pool in the process of laser wire deposition was presented by computational fluid dynamics technique. The simulation results of the deposition morphology were also compared with the experimental results under the condition of liquid bridge transfer mode. Moreover, they showed a good agreement. Considering the effect of recoil pressure, the morphology of the deposit metal obtained by the simulation was similar to the experiment result. Molten metal at the wire tip was peeled off and flowed into the molten pool, and then spread to both sides of the deposition layer under the recoil pressure. In addition, the results of simulation and high-speed charge-coupled device presented that a wedge transition zone, with a length of ∼6 mm, was formed behind the keyhole in the liquid bridge transfer process, where the height of deposited metal decreased gradually. After solidification, metal in the transition zone retained the original melt morphology, resulting in a decrease in the height of the tail of the deposition layer.
Keywords
LWD, CFD, liquid bridge transfer, fluid dynamics, wedge transition zone
Fluid Thermodynamic Simulation of Ti-6Al-4V Alloy in Laser Wire DepositionFluid Thermodynamic Simulation of Ti-6Al-4V Alloy in Laser Wire Deposition
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Using an improved Carreau constitutive model, a numerical simulation of the casting process of a type of solid propellant slurry vacuum plate casting was carried out using the Flow3D software. Through the flow process in the orifice flow channel and the combustion chamber, the flow velocity of the slurry passing through the plate flow channel was quantitatively analyzed, and the viscosity, shear rate, and leveling characteristics of the slurry in the combustion chamber were qualitatively analyzed and predicted. The pouring time, pouring quality, and flow state predicted by the numerical simulation were verified using a visual tester consisting of a vacuum plate casting system in which a pouring experiment was carried out. Studies have shown that HTPB three-component propellant slurry is a typical yielding pseudoplastic fluid. When the slurry flows through the flower plate and the airfoil, the fluid shear rate reaches its maximum value and the viscosity of the slurry decreases. The visual pouring platform was built and the experiment was controlled according to the numerically-calculated parameters, ensuring the same casting speed. The comparison between the predicted casting quality and the one obtained in the verification test resulted in an error less than 10 %. Moreover, the error between the simulated casting completion time and the process verification test result was also no more than 10 %. Last, the flow state of the slurry during the simulation was consistent with the one during the experimental test. The overall leveling of the slurry in the combustion chamber was adequate and no relatively large holes and flaws developed during the pouring process.
개선된 Carreau 구성 모델을 사용하여 FLOW-3D 소프트웨어를 사용하여 고체 추진제 슬러리 진공판 유형의 Casting Process에 대한 수치 시뮬레이션을 수행했습니다. 오리피스 유로와 연소실에서의 유동과정을 통해 판 유로를 통과하는 슬러리의 유속을 정량적으로 분석하고, 연소실에서 슬러리의 점도, 전단율, 레벨링 특성을 정성적으로 분석하하고, 예측하였습니다.
타설시간, 타설품질, 수치해석으로 예측된 유동상태는 타설실험을 수행한 진공판주조시스템으로 구성된 비주얼 테스터를 이용하여 검증하였습니다.
연구에 따르면 HTPB 3성분 추진제 슬러리는 전형적인 생성 가소성 유체입니다. 슬러리가 플라워 플레이트와 에어포일을 통과할 때 유체 전단율이 최대값에 도달하고 슬러리의 점도가 감소합니다.
시각적 주입 플랫폼이 구축되었고 동일한 주조 속도를 보장하기 위해 수치적으로 계산된 매개변수에 따라 실험이 제어되었습니다. 예측된 casting 품질과 검증 테스트에서 얻은 품질을 비교한 결과 10 % 미만의 오류가 발생했습니다.
또한 모의 casting 완료시간과 공정검증시험 결과의 오차도 10 % 이하로 나타났습니다.
마지막으로 시뮬레이션 중 슬러리의 흐름 상태는 실험 테스트 시와 일치하였다. 연소실에서 슬러리의 전체 레벨링은 적절했으며 주입 과정에서 상대적으로 큰 구멍과 결함이 발생하지 않았습니다.
Figure 1. The equipment used in the vacuum flower-plate pouring
process.Figure 2. Calculation model.Figure 3. Grid block division unit.Figure 4. Circular section of the speed cloud.Figure 5. Viscosity and shear rate distribution cloud pattern flowing
through the plate holes.Figure 6. Circular section of the viscosity and shear-rate clouds.Figure 7. Volume fraction cloud chart at different time.Figure 8. Experimental program.Figure 9. Emulation experimental device.Figure 10. Visualization of the flow state of the pulp inside the tester.
References
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해저 지반에 설치되는 인공어초는 유속 및 수심이 동일한 경우라도 지반 조건에 따라 세굴 패턴이 크게 차이나는 경우가 있다. 따라서 본 연구에서는 모래, 실트 및 점토 등과 같이 다양한 해저 지반에 설치하는 인공어초의 지반공학적 안정성을 평가하고자 Flow-3D를 이용하여 세굴 해석을 수행하였다. 수치해석 결과 지반 입경이 작을수록 인공어초 주변에서 발생하는 세굴량이 커지며, 평형상태에 도달하는 시간이 더 오래 걸리는 결과를 보였다. 반면 입경이 커질수록 세굴량이 작아지며, 세굴된 지반 입자가 인공어초 후면부에 퇴적되는 결과를 보였다. 또한 최대 세굴심도와 입경은 비선형적인 관계를 나타내었다. 특히 세립토에서 최대 세굴심도가 크게 증가하였다.
Artificial reef-installed seabeds may have significantly different scouring patterns depending on the ground conditions, such as the soil particle size, even though the flow velocity and water depth are similar. In this study, the scour characteristics of the ground were determined using Flow-3D to evaluate the geotechnical stability of artificial reefs installed on various seabeds, such as sand, silt, and clay. The analysis results indicated that the smaller the particle size of the soil, the larger the amount of scour that occurs around the artificial reef and the longer it takes to reach an equilibrium state. However, eroded soil particles were deposited on the rear part of the artificial reef as the soil particle size increased. The maximum scour depth and average particle size showed a non-linear relationship. In particular, the maximum scour depth increased significantly in fine-grained soils.
레이저 분말 베드 퓨전(L-PBF) 적층 제조(AM)는 우수한 기계적 특성으로 그물 모양에 가까운 복잡한 부품을 생산할 수 있습니다. 그러나 빌드 실패 및 다공성과 같은 결함으로 이어지는 원치 않는 잔류 응력 및 왜곡이 L-PBF의 광범위한 적용을 방해하고 있습니다.
L-PBF의 잠재력을 최대한 실현하기 위해 잔류 변형, 용융 풀 및 다공성 형성을 예측하는 다중 규모 모델링 방법론이 개발되었습니다. L-PBF의 잔류 변형 및 응력을 부품 규모에서 예측하기 위해 고유 변형 방법을 기반으로 하는 다중 규모 프로세스 모델링 프레임워크가 제안됩니다.
고유한 변형 벡터는 마이크로 스케일에서 충실도가 높은 상세한 다층 프로세스 시뮬레이션에서 추출됩니다. 균일하지만 이방성인 변형은 잔류 왜곡 및 응력을 예측하기 위해 준 정적 평형 유한 요소 분석(FEA)에서 레이어별로 L-PBF 부품에 적용됩니다.
부품 규모에서의 잔류 변형 및 응력 예측 외에도 분말 규모의 다중물리 모델링을 수행하여 공정 매개변수, 예열 온도 및 스패터링 입자에 의해 유도된 용융 풀 변동 및 결함 형성을 연구합니다. 이러한 요인과 관련된 용융 풀 역학 및 다공성 형성 메커니즘은 시뮬레이션 및 실험을 통해 밝혀졌습니다.
제안된 부품 규모 잔류 응력 및 왜곡 모델을 기반으로 경로 계획 방법은 큰 잔류 변형 및 건물 파손을 방지하기 위해 주어진 형상에 대한 레이저 스캐닝 경로를 조정하기 위해 개발되었습니다.
연속 및 아일랜드 스캐닝 전략을 위한 기울기 기반 경로 계획이 공식화되고 공식화된 컴플라이언스 및 스트레스 최소화 문제에 대한 전체 감도 분석이 수행됩니다. 이 제안된 경로 계획 방법의 타당성과 효율성은 AconityONE L-PBF 시스템을 사용하여 실험적으로 입증되었습니다.
또한 기계 학습을 활용한 데이터 기반 프레임워크를 개발하여 L-PBF에 대한 부품 규모의 열 이력을 예측합니다. 본 연구에서는 실시간 열 이력 예측을 위해 CNN(Convolutional Neural Network)과 RNN(Recurrent Neural Network)을 포함하는 순차적 기계 학습 모델을 제안합니다.
유한 요소 해석과 비교하여 100배의 예측 속도 향상이 달성되어 실제 제작 프로세스보다 빠른 예측이 가능하고 실시간 온도 프로파일을 사용할 수 있습니다.
Laser powder bed fusion (L-PBF) additive manufacturing (AM) is capable of producing complex parts near net shape with good mechanical properties. However, undesired residual stress and distortion that lead to build failure and defects such as porosity are preventing broader applications of L-PBF. To realize the full potential of L-PBF, a multiscale modeling methodology is developed to predict residual deformation, melt pool, and porosity formation. To predict the residual deformation and stress in L-PBF at part-scale, a multiscale process modeling framework based on inherent strain method is proposed.
Inherent strain vectors are extracted from detailed multi-layer process simulation with high fidelity at micro-scale. Uniform but anisotropic strains are then applied to L-PBF part in a layer-by-layer fashion in a quasi-static equilibrium finite element analysis (FEA) to predict residual distortion and stress. Besides residual distortion and stress prediction at part scale, multiphysics modeling at powder scale is performed to study the melt pool variation and defect formation induced by process parameters, preheating temperature and spattering particles. Melt pool dynamics and porosity formation mechanisms associated with these factors are revealed through simulation and experiments.
Based on the proposed part-scale residual stress and distortion model, path planning method is developed to tailor the laser scanning path for a given geometry to prevent large residual deformation and building failures. Gradient based path planning for continuous and island scanning strategy is formulated and full sensitivity analysis for the formulated compliance- and stress-minimization problem is performed.
The feasibility and effectiveness of this proposed path planning method is demonstrated experimentally using the AconityONE L-PBF system. In addition, a data-driven framework utilizing machine learning is developed to predict the thermal history at part-scale for L-PBF.
In this work, a sequential machine learning model including convolutional neural network (CNN) and recurrent neural network (RNN), long shortterm memory unit, is proposed for real-time thermal history prediction. A 100x prediction speed improvement is achieved compared to the finite element analysis which makes the prediction faster than real fabrication process and real-time temperature profile available.
Figure 1.1: Schematic Overview of Metal Laser Powder Bed Fusion Process [2]Figure 1.2: Commercial Powder Bed Fusion SystemsFigure 1.3: Commercial Metal Components Fabricated by Powder Bed Fusion Additive Manufacturing: (a) GE Fuel Nozzle; (b) Stryker Hip Biomedical Implant.Figure 2.1: Proposed Multiscale Process Simulation FrameworkFigure 2.2: (a) Experimental Setup for In-situ Thermocouple Measurement in the EOS M290 Build Chamber; (b) Themocouple Locations on the Bottom Side of the Substrate.Figure 2.3: (a) Finite Element Model for Single Layer Thermal Analysis; (b) Deposition LayerFigure 2.4: Core-skin layer: (a) Surface Morphology; (b) Scanning Strategy; (c) Transient Temperature Distribution and Temperature History at (d) Point 1; (e) Point 2 and (f) Point 3Figure 2.5: (a) Scanning Orientation of Each Layer; (b) Finite Element Model for Micro-scale Representative Volume Figure 2.6: Bottom Layer (a) Thermal History; (b) Plastic Strain and (c) Elastic Strain Evolution HistoryFigure 2.7: Bottom Layer Inherent Strain under Default Process Parameters along Horizontal Scanning PathFigure 2.8: Snapshots of the Element Activation ProcessFigure 2.9: Double Cantilever Beam Structure Built by the EOS M290 DMLM Process (a) Before and (b)
After Cutting off; (c) Faro Laser ScanArm V3 for Distortion MeasurementFigure 2.10: Square Canonical Structure Built by the EOS M290 DMLM ProcessFigure 2.11: Finite Element Mesh for the Square Canonical and Snapshots of Element Activation ProcessFigure 2.12: Simulated Distortion Field for the Double Cantilever Beam before Cutting off the Supports: (a) Inherent Strain Method; (b) Simufact Additive 3.1Figure 3.10: Snapshots of Temperature Profile for Single Track in Keyhole Regime (P = 250W and V = 0.5m/s) at the Preheating Temperature of 100 °Cs) at the Preheating Temperature of 500 °CFigure 3.15: Melt Pool Cross Section Comparison Between Simulation and Experiment for Single Track
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Optimization of Solar CCHP Systems with Collector Enhanced by Porous Media and Nanofluid
Navid Tonekaboni,1Mahdi Feizbahr,2 Nima Tonekaboni,1Guang-Jun Jiang,3,4 and Hong-Xia Chen3,4
Abstract
태양열 집열기의 낮은 효율은 CCHP(Solar Combined Cooling, Heating, and Power) 사이클의 문제점 중 하나로 언급될 수 있습니다. 태양계를 개선하기 위해 나노유체와 다공성 매체가 태양열 집열기에 사용됩니다.
다공성 매질과 나노입자를 사용하는 장점 중 하나는 동일한 조건에서 더 많은 에너지를 흡수할 수 있다는 것입니다. 이 연구에서는 평균 일사량이 1b인 따뜻하고 건조한 지역의 600 m2 건물의 전기, 냉방 및 난방을 생성하기 위해 다공성 매질과 나노유체를 사용하여 태양열 냉난방 복합 발전(SCCHP) 시스템을 최적화했습니다.
본 논문에서는 침전물이 형성되지 않는 lb = 820 w/m2(이란) 정도까지 다공성 물질에서 나노유체의 최적량을 계산하였다. 이 연구에서 태양열 집열기는 구리 다공성 매체(95% 다공성)와 CuO 및 Al2O3 나노 유체로 향상되었습니다.
나노유체의 0.1%-0.6%가 작동 유체로 물에 추가되었습니다. 나노유체의 0.5%가 태양열 집열기 및 SCCHP 시스템에서 가장 높은 에너지 및 엑서지 효율 향상으로 이어지는 것으로 밝혀졌습니다.
본 연구에서 포물선형 집열기(PTC)의 최대 에너지 및 엑서지 효율은 각각 74.19% 및 32.6%입니다. 그림 1은 태양 CCHP의 주기를 정확하게 설명하기 위한 그래픽 초록으로 언급될 수 있습니다.
The low efficiency of solar collectors can be mentioned as one of the problems in solar combined cooling, heating, and power (CCHP) cycles. For improving solar systems, nanofluid and porous media are used in solar collectors. One of the advantages of using porous media and nanoparticles is to absorb more energy under the same conditions. In this research, a solar combined cooling, heating, and power (SCCHP) system has been optimized by porous media and nanofluid for generating electricity, cooling, and heating of a 600 m2 building in a warm and dry region with average solar radiation of Ib = 820 w/m2 in Iran. In this paper, the optimal amount of nanofluid in porous materials has been calculated to the extent that no sediment is formed. In this study, solar collectors were enhanced with copper porous media (95% porosity) and CuO and Al2O3 nanofluids. 0.1%–0.6% of the nanofluids were added to water as working fluids; it is found that 0.5% of the nanofluids lead to the highest energy and exergy efficiency enhancement in solar collectors and SCCHP systems. Maximum energy and exergy efficiency of parabolic thermal collector (PTC) riches in this study are 74.19% and 32.6%, respectively. Figure 1 can be mentioned as a graphical abstract for accurately describing the cycle of solar CCHP.
1. Introduction
Due to the increase in energy consumption, the use of clean energy is one of the important goals of human societies. In the last four decades, the use of cogeneration cycles has increased significantly due to high efficiency. Among clean energy, the use of solar energy has become more popular due to its greater availability [1]. Low efficiency of energy production, transmission, and distribution system makes a new system to generate simultaneously electricity, heating, and cooling as an essential solution to be widely used. The low efficiency of the electricity generation, transmission, and distribution system makes the CCHP system a basic solution to eliminate waste of energy. CCHP system consists of a prime mover (PM), a power generator, a heat recovery system (produce extra heating/cooling/power), and thermal energy storage (TES) [2]. Solar combined cooling, heating, and power (SCCHP) has been started three decades ago. SCCHP is a system that receives its propulsive force from solar energy; in this cycle, solar collectors play the role of propulsive for generating power in this system [3].
Increasing the rate of energy consumption in the whole world because of the low efficiency of energy production, transmission, and distribution system causes a new cogeneration system to generate electricity, heating, and cooling energy as an essential solution to be widely used. Building energy utilization fundamentally includes power required for lighting, home electrical appliances, warming and cooling of building inside, and boiling water. Domestic usage contributes to an average of 35% of the world’s total energy consumption [4].
Due to the availability of solar energy in all areas, solar collectors can be used to obtain the propulsive power required for the CCHP cycle. Solar energy is the main source of energy in renewable applications. For selecting a suitable area to use solar collectors, annual sunshine hours, the number of sunny days, minus temperature and frosty days, and the windy status of the region are essentially considered [5]. Iran, with an average of more than 300 sunny days, is one of the suitable countries to use solar energy. Due to the fact that most of the solar radiation is in the southern regions of Iran, also the concentration of cities is low in these areas, and transmission lines are far apart, one of the best options is to use CCHP cycles based on solar collectors [6]. One of the major problems of solar collectors is their low efficiency [7]. Low efficiency increases the area of collectors, which increases the initial cost of solar systems and of course increases the initial payback period. To increase the efficiency of solar collectors and improve their performance, porous materials and nanofluids are used to increase their workability.
There are two ways to increase the efficiency of solar collectors and mechanical and fluid improvement. In the first method, using porous materials or helical filaments inside the collector pipes causes turbulence of the flow and increases heat transfer. In the second method, using nanofluids or salt and other materials increases the heat transfer of water. The use of porous materials has grown up immensely over the past twenty years. Porous materials, especially copper porous foam, are widely used in solar collectors. Due to the high contact surface area, porous media are appropriate candidates for solar collectors [8]. A number of researchers investigated Solar System performance in accordance with energy and exergy analyses. Zhai et al. [9] reviewed the performance of a small solar-powered system in which the energy efficiency was 44.7% and the electrical efficiency was 16.9%.
Abbasi et al. [10] proposed an innovative multiobjective optimization to optimize the design of a cogeneration system. Results showed the CCHP system based on an internal diesel combustion engine was the applicable alternative at all regions with different climates. The diesel engine can supply the electrical requirement of 31.0% and heating demand of 3.8% for building.
Jiang et al. [11] combined the experiment and simulation together to analyze the performance of a cogeneration system. Moreover, some research focused on CCHP systems using solar energy. It integrated sustainable and renewable technologies in the CCHP, like PV, Stirling engine, and parabolic trough collector (PTC) [2, 12–15].
Wang et al. [16] optimized a cogeneration solar cooling system with a Rankine cycle and ejector to reach the maximum total system efficiency of 55.9%. Jing et al. analyzed a big-scale building with the SCCHP system and auxiliary heaters to produced electrical, cooling, and heating power. The maximum energy efficiency reported in their work is 46.6% [17]. Various optimization methods have been used to improve the cogeneration system, minimum system size, and performance, such as genetic algorithm [18, 19].
Hirasawa et al. [20] investigated the effect of using porous media to reduce thermal waste in solar systems. They used the high-porosity metal foam on top of the flat plate solar collector and observed that thermal waste decreased by 7% due to natural heat transfer. Many researchers study the efficiency improvement of the solar collector by changing the collector’s shapes or working fluids. However, the most effective method is the use of nanofluids in the solar collector as working fluid [21]. In the experimental study done by Jouybari et al. [22], the efficiency enhancement up to 8.1% was achieved by adding nanofluid in a flat plate collector. In this research, by adding porous materials to the solar collector, collector efficiency increased up to 92% in a low flow regime. Subramani et al. [23] analyzed the thermal performance of the parabolic solar collector with Al2O3 nanofluid. They conducted their experiments with Reynolds number range 2401 to 7202 and mass flow rate 0.0083 to 0.05 kg/s. The maximum efficiency improvement in this experiment was 56% at 0.05 kg/s mass flow rate.
Shojaeizadeh et al. [24] investigated the analysis of the second law of thermodynamic on the flat plate solar collector using Al2O3/water nanofluid. Their research showed that energy efficiency rose up to 1.9% and the exergy efficiency increased by a maximum of 0.72% compared to pure water. Tiwari et al. [25] researched on the thermal performance of solar flat plate collectors for working fluid water with different nanofluids. The result showed that using 1.5% (optimum) particle volume fraction of Al2O3 nanofluid as an absorbing medium causes the thermal efficiency to enhance up to 31.64%.
The effect of porous media and nanofluids on solar collectors has already been investigated in the literature but the SCCHP system with a collector embedded by both porous media and nanofluid for enhancing the ratio of nanoparticle in nanofluid for preventing sedimentation was not discussed. In this research, the amount of energy and exergy of the solar CCHP cycles with parabolic solar collectors in both base and improved modes with a porous material (copper foam with 95% porosity) and nanofluid with different ratios of nanoparticles was calculated. In the first step, it is planned to design a CCHP system based on the required load, and, in the next step, it will analyze the energy and exergy of the system in a basic and optimize mode. In the optimize mode, enhanced solar collectors with porous material and nanofluid in different ratios (0.1%–0.7%) were used to optimize the ratio of nanofluids to prevent sedimentation.
2. Cycle Description
CCHP is one of the methods to enhance energy efficiency and reduce energy loss and costs. The SCCHP system used a solar collector as a prime mover of the cogeneration system and assisted the boiler to generate vapor for the turbine. Hot water flows from the expander to the absorption chiller in summer or to the radiator or fan coil in winter. Finally, before the hot water wants to flow back to the storage tank, it flows inside a heat exchanger for generating domestic hot water [26].
For designing of solar cogeneration system and its analysis, it is necessary to calculate the electrical, heating (heating load is the load required for the production of warm water and space heating), and cooling load required for the case study considered in a residential building with an area of 600 m2 in the warm region of Iran (Zahedan). In Table 1, the average of the required loads is shown for the different months of a year (average of electrical, heating, and cooling load calculated with CARRIER software).Table 1The average amount of electric charges, heating load, and cooling load used in the different months of the year in the city of Zahedan for a residential building with 600 m2.
According to Table 1, the maximum magnitude of heating, cooling, and electrical loads is used to calculate the cogeneration system. The maximum electric load is 96 kW, the maximum amount of heating load is 62 kW, and the maximum cooling load is 118 kW. Since the calculated loads are average, all loads increased up to 10% for the confidence coefficient. With the obtained values, the solar collector area and other cogeneration system components are calculated. The cogeneration cycle is capable of producing 105 kW electric power, 140 kW cooling capacity, and 100 kW heating power.
2.1. System Analysis Equations
An analysis is done by considering the following assumptions:(1)The system operates under steady-state conditions(2)The system is designed for the warm region of Iran (Zahedan) with average solar radiation Ib = 820 w/m2(3)The pressure drops in heat exchangers, separators, storage tanks, and pipes are ignored(4)The pressure drop is negligible in all processes and no expectable chemical reactions occurred in the processes(5)Potential, kinetic, and chemical exergy are not considered due to their insignificance(6)Pumps have been discontinued due to insignificance throughout the process(7)All components are assumed adiabatic
Schematic shape of the cogeneration cycle is shown in Figure 1 and all data are given in Table 2.
Figure 1Schematic shape of the cogeneration cycle.Table 2Temperature and humidity of different points of system.
Based on the first law of thermodynamic, energy analysis is based on the following steps.
First of all, the estimated solar radiation energy on collector has been calculated:where α is the heat transfer enhancement coefficient based on porous materials added to the collector’s pipes. The coefficient α is increased by the porosity percentage, the type of porous material (in this case, copper with a porosity percentage of 95), and the flow of fluid to the collector equation.
Collector efficiency is going to be calculated by the following equation [9]:
Total energy received by the collector is given by [9]
In the last step based on thermodynamic second law, exergy efficiency has been calculated from the following equation and the above-mentioned calculated loads [9]:
3. Porous Media
The porous medium that filled the test section is copper foam with a porosity of 95%. The foams are determined in Figure 2 and also detailed thermophysical parameters and dimensions are shown in Table 3.
Figure 2Copper foam with a porosity of 95%.Table 3Thermophysical parameters and dimensions of copper foam.
In solar collectors, copper porous materials are suitable for use at low temperatures and have an easier and faster manufacturing process than ceramic porous materials. Due to the high coefficient conductivity of copper, the use of copper metallic foam to increase heat transfer is certainly more efficient in solar collectors.
Porous media and nanofluid in solar collector’s pipes were simulated in FLOW-3D software using the finite-difference method [27]. Nanoparticles Al2O3 and CUO are mostly used in solar collector enhancement. In this research, different concentrations of nanofluid are added to the parabolic solar collectors with porous materials (copper foam with porosity of 95%) to achieve maximum heat transfer in the porous materials before sedimentation. After analyzing PTC pipes with the nanofluid flow in FLOW-3D software, for energy and exergy efficiency analysis, Carrier software results were used as EES software input. Simulation PTC with porous media inside collector pipe and nanofluids sedimentation is shown in Figure 3.
Figure 3Simulation PTC pipes enhanced with copper foam and nanoparticles in FLOW-3D software.
3.1. Nano Fluid
In this research, copper and silver nanofluids (Al2O3, CuO) have been added with percentages of 0.1%–0.7% as the working fluids. The nanoparticle properties are given in Table 4. Also, system constant parameters are presented in Table 4, which are available as default input in the EES software.Table 4Properties of the nanoparticles [9].
System constant parameters for input in the software are shown in Table 5.Table 5System constant parameters.
The thermal properties of the nanofluid can be obtained from equations (18)–(21). The basic fluid properties are indicated by the index (bf) and the properties of the nanoparticle silver with the index (np).
The density of the mixture is shown in the following equation [28]:where ρ is density and ϕ is the nanoparticles volume fraction.
The specific heat capacity is calculated from the following equation [29]:
The thermal conductivity of the nanofluid is calculated from the following equation [29]:
The parameter β is the ratio of the nanolayer thickness to the original particle radius and, usually, this parameter is taken equal to 0.1 for the calculated thermal conductivity of the nanofluids.
The mixture viscosity is calculated as follows [30]:
In all equations, instead of water properties, working fluids with nanofluid are used. All of the above equations and parameters are entered in the EES software for calculating the energy and exergy of solar collectors and the SCCHP cycle. All calculation repeats for both nanofluids with different concentrations of nanofluid in the solar collector’s pipe.
4. Results and Discussion
In the present study, relations were written according to Wang et al. [16] and the system analysis was performed to ensure the correctness of the code. The energy and exergy charts are plotted based on the main values of the paper and are shown in Figures 4 and 5. The error rate in this simulation is 1.07%.
Figure 4Verification charts of energy analysis results.
Figure 5Verification charts of exergy analysis results.
We may also investigate the application of machine learning paradigms [31–41] and various hybrid, advanced optimization approaches that are enhanced in terms of exploration and intensification [42–55], and intelligent model studies [56–61] as well, for example, methods such as particle swarm optimizer (PSO) [60, 62], differential search (DS) [63], ant colony optimizer (ACO) [61, 64, 65], Harris hawks optimizer (HHO) [66], grey wolf optimizer (GWO) [53, 67], differential evolution (DE) [68, 69], and other fusion and boosted systems [41, 46, 48, 50, 54, 55, 70, 71].
At the first step, the collector is modified with porous copper foam material. 14 cases have been considered for the analysis of the SCCHP system (Table 6). It should be noted that the adding of porous media causes an additional pressure drop inside the collector [9, 22–26, 30, 72]. All fourteen cases use copper foam with a porosity of 95 percent. To simulate the effect of porous materials and nanofluids, the first solar PTC pipes have been simulated in the FLOW-3D software and then porous media (copper foam with porosity of 95%) and fluid flow with nanoparticles (AL2O3 and CUO) are generated in the software. After analyzing PTC pipes in FLOW-3D software, for analyzing energy and exergy efficiency, software outputs were used as EES software input for optimization ratio of sedimentation and calculating energy and exergy analyses.Table 6Collectors with different percentages of nanofluids and porous media.
In this research, an enhanced solar collector with both porous media and Nanofluid is investigated. In the present study, 0.1–0.5% CuO and Al2O3 concentration were added to the collector fully filled by porous media to achieve maximum energy and exergy efficiencies of solar CCHP systems. All steps of the investigation are shown in Table 6.
Energy and exergy analyses of parabolic solar collectors and SCCHP systems are shown in Figures 6 and 7.
Figure 6Energy and exergy efficiencies of the PTC with porous media and nanofluid.
Figure 7Energy and exergy efficiency of the SCCHP.
Results show that the highest energy and exergy efficiencies are 74.19% and 32.6%, respectively, that is achieved in Step 12 (parabolic collectors with filled porous media and 0.5% Al2O3). In the second step, the maximum energy efficiency of SCCHP systems with fourteen steps of simulation are shown in Figure 7.
In the second step, where 0.1, −0.6% of the nanofluids were added, it is found that 0.5% leads to the highest energy and exergy efficiency enhancement in solar collectors and SCCHP systems. Using concentrations more than 0.5% leads to sediment in the solar collector’s pipe and a decrease of porosity in the pipe [73]. According to Figure 7, maximum energy and exergy efficiencies of SCCHP are achieved in Step 12. In this step energy efficiency is 54.49% and exergy efficiency is 18.29%. In steps 13 and 14, with increasing concentration of CUO and Al2O3 nanofluid solution in porous materials, decreasing of energy and exergy efficiency of PTC and SCCHP system at the same time happened. This decrease in efficiency is due to the formation of sediment in the porous material. Calculations and simulations have shown that porous materials more than 0.5% nanofluids inside the collector pipe cause sediment and disturb the porosity of porous materials and pressure drop and reduce the coefficient of performance of the cogeneration system. Most experience showed that CUO and AL2O3 nanofluids with less than 0.6% percent solution are used in the investigation on the solar collectors at low temperatures and discharges [74]. One of the important points of this research is that the best ratio of nanofluids in the solar collector with a low temperature is 0.5% (AL2O3 and CUO); with this replacement, the cost of solar collectors and SCCHP cycle is reduced.
5. Conclusion and Future Directions
In the present study, ways for increasing the efficiency of solar collectors in order to enhance the efficiency of the SCCHP cycle are examined. The research is aimed at adding both porous materials and nanofluids for estimating the best ratio of nanofluid for enhanced solar collector and protecting sedimentation in porous media. By adding porous materials (copper foam with porosity of 95%) and 0.5% nanofluids together, high efficiency in solar parabolic collectors can be achieved. The novelty in this research is the addition of both nanofluids and porous materials and calculating the best ratio for preventing sedimentation and pressure drop in solar collector’s pipe. In this study, it was observed that, by adding 0.5% of AL2O3 nanofluid in working fluids, the energy efficiency of PTC rises to 74.19% and exergy efficiency is grown up to 32.6%. In SCCHP cycle, energy efficiency is 54.49% and exergy efficiency is 18.29%.
In this research, parabolic solar collectors fully filled by porous media (copper foam with a porosity of 95) are investigated. In the next step, parabolic solar collectors in the SCCHP cycle were simultaneously filled by porous media and different percentages of Al2O3 and CuO nanofluid. At this step, values of 0.1% to 0.6% of each nanofluid were added to the working fluid, and the efficiency of the energy and exergy of the collectors and the SCCHP cycle were determined. In this case, nanofluid and the porous media were used together in the solar collector and maximum efficiency achieved. 0.5% of both nanofluids were used to achieve the biggest efficiency enhancement.
In the present study, as expected, the highest efficiency is for the parabolic solar collector fully filled by porous material (copper foam with a porosity of 95%) and 0.5% Al2O3. Results of the present study are as follows:(1)The average enhancement of collectors’ efficiency using porous media and nanofluids is 28%.(2)Solutions with 0.1 to 0.5% of nanofluids (CuO and Al2O3) are used to prevent collectors from sediment occurrence in porous media.(3)Collector of solar cogeneration cycles that is enhanced by both porous media and nanofluid has higher efficiency, and the stability of output temperature is more as well.(4)By using 0.6% of the nanofluids in the enhanced parabolic solar collectors with copper porous materials, sedimentation occurs and makes a high-pressure drop in the solar collector’s pipe which causes decrease in energy efficiency.(5)Average enhancement of SCCHP cycle efficiency is enhanced by both porous media and nanofluid 13%.
Nomenclature
:
Solar radiation
a:
Heat transfer augmentation coefficient
A:
Solar collector area
Bf:
Basic fluid
:
Specific heat capacity of the nanofluid
F:
Constant of air dilution
:
Thermal conductivity of the nanofluid
:
Thermal conductivity of the basic fluid
:
Viscosity of the nanofluid
:
Viscosity of the basic fluid
:
Collector efficiency
:
Collector energy receives
:
Auxiliary boiler heat
:
Expander energy
:
Gas energy
:
Screw expander work
:
Cooling load, in kilowatts
:
Heating load, in kilowatts
:
Solar radiation energy on collector, in Joule
:
Sanitary hot water load
Np:
Nanoparticle
:
Energy efficiency
:
Heat exchanger efficiency
:
Sun exergy
:
Collector exergy
:
Natural gas exergy
:
Expander exergy
:
Cooling exergy
:
Heating exergy
:
Exergy efficiency
:
Steam mass flow rate
:
Hot water mass flow rate
:
Specific heat capacity of water
:
Power output form by the screw expander
Tam:
Average ambient temperature
:
Density of the mixture.
Greek symbols
ρ:
Density
ϕ:
Nanoparticles volume fraction
β:
Ratio of the nanolayer thickness.
Abbreviations
CCHP:
Combined cooling, heating, and power
EES:
Engineering equation solver.
Data Availability
For this study, data were generated by CARRIER software for the average electrical, heating, and cooling load of a residential building with 600 m2 in the city of Zahedan, Iran.
Conflicts of Interest
The authors declare that they have no conflicts of interest.
Acknowledgments
This work was partially supported by the National Natural Science Foundation of China under Contract no. 71761030 and Natural Science Foundation of Inner Mongolia under Contract no. 2019LH07003.
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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.
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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 tubeA novel investigation of the thermoacoustic field inside a Rijke tube
References
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실제 작동 조건에서 석탄 연소 회전 시멘트 가마의 클링커 형성은 방사선에 대한 Monte Carlo 방법, 가마 벽의 에너지 방정식에 대한 유한 체적 코드 및 클링커에 대한 화학 반응을 포함한 에너지 보존 방정식 및 종에 대한 새로운 코드. 기상의 온도 장, 벽으로의 복사 열유속, 가마 및 클링커 온도에 대한 예측 간의 반복적인 절차는 내부 벽 온도의 분포를 명시적으로 예측하는 데 사용됩니다. 여기에는 열 흐름 계산이 포함됩니다. 수갑. 가스와 가마 벽 사이의 주요 열 전달 모드는 복사에 의한 것이며 내화물을 통해 환경으로 손실되는 열은 입력 열의 약 10%이고 추가로 40%는 장입 가열 및 클링커 형성. 예측은 실제 규모의 시멘트 가마에서 경험과 제한된 측정을 기반으로 한 경향과 일치합니다.
키워드
산업용 CFD, 로타리 가마, 클링커 형성, 복사 열전달, Industrial CFD, Rotary kilns, Clinker formation, Radiative heat transfer
1 . 소개
시멘트 산업은 에너지의 주요 소비자이며, 미국에서 산업 사용자의 총 화석 연료 소비량의 약 1.4%를 차지하며 [1] 일반적인 비에너지 사용량은 제조된 클링커 1kg당 약 3.2MJ [2] 입니다. CaCO 3 → CaO + CO 2 반응이 일어나기 때문입니다., 클링커 형성의 첫 번째 단계는 높은 흡열성입니다. 시멘트 가마에서 에너지를 절약하기 위한 현재의 경향은 일반적으로 길이가 약 100m이고 직경이 약 5m인 회전 실린더인 가마를 떠나는 배기 가스로부터 에너지를 보다 효율적으로 회수하는 것과 저열량 연료의 사용에 중점을 둡니다. 값. 2-5초 정도의 화염 체류 시간을 허용하고 2200K의 높은 온도에 도달하는 회전 가마의 특성은 또한 시멘트 가마를 유기 폐기물 및 용제에 대한 상업용 소각로에 대한 경쟁력 있는 대안으로 만듭니다 [3]. 클링커의 형성이 이러한 2차 액체 연료의 사용으로 인한 화염의 변화로부터 어떤 식으로든 영향을 받지 않도록 하고, 대기 중으로 방출되는 오염 물질의 양에 대한 현재 및 미래 제한을 준수할 수 있도록, 화염 구조의 세부 사항과 화염에서 고체 충전물로의 열 전달을 더 잘 이해할 필요가 있습니다.
최근 시멘트 가마 4 , 5 , 6 , 7 에서 유동장 및 석탄 연소의 이론적 모델링복사 열 전달을 포함한 전산 유체 역학(CFD) 코드를 사용하여 달성되었습니다. 이러한 결과는 시멘트 가마에 대한 최초의 결과였으며 화염 길이, 산소 소비 등과 관련하여 실험적으로 관찰된 경향을 재현했기 때문에 그러한 코드가 수용 가능한 정확도로 대규모 산업용 용광로에 사용될 수 있음을 보여주었습니다. 킬른과 클링커는 포함하지 않았고, 벽온도의 경계조건은 가스온도와 용액영역의 열유속에 영향을 미치므로 계산에 필요한 경계조건은 예측하지 않고 실험적 측정에 기초하였다. 기상에 대한 CFD 솔루션은 앞으로의 주요 단계이지만 회전 가마를 포괄적으로 모델링하는 데만으로는 충분하지 않습니다.
내화물의 열 전달과 전하에 대한 세부 사항은 다양한 저자 8 , 9 , 10 , 11에 의해 조사되었습니다 . 충전물(보통 잘 혼합된 것으로 가정)은 노출된 표면에 직접 복사되는 열 외에도 전도에 의해 가마 벽에서 가열됩니다. 가장 완전한 이론적 노력에서, 가마 벽 (내화물)에 대한 3 차원 열전도 방정식을 해결하고, 두 개 또는 세 개의 인접하는 영역으로 한정 한 좌표 축 방향에서 어느 방사선 방사선 열전달 영역 모델과 결합 [ 10] 또는 자세히 해결 [11]. 그러나 클링커 형성 중에 일어나는 화학 반응은 고려되지 않았고 기체 상이 균일한 온도로 고정되어 필요한 수준의 정확도로 처리되지 않았습니다.
최종적으로 연소에 의해 방출되는 에너지(일부)를 받는 고체 전하가 화학 반응을 거쳐 최종 제품인 클링커를 형성합니다. 이것들은 [12]에 설명된 주요 특징에 대한 단순화된 모델과 함께 시멘트 화학 문헌에서 광범위한 조사의 주제였습니다 . 그 작업에서, 고체 온도 및 조성의 축 방향 전개를 설명하는 odes가 공식화되고 해결되었지만, 전하에 대한 열유속 및 따라서 클링커 형성 속도를 결정하는 가스 및 벽 온도는 1차원으로 근사되었습니다. 자세한 화염 계산이 없는 모델.
화염, 벽 및 장입물에 대한 위의 이론적 모델 중 어느 것도 회전식 가마 작동을 위한 진정한 예측 도구로 충분하지 않다는 것이 분명합니다. 국부 가스 온도(CFD 계산 결과 중 하나)는 벽 온도에 크게 의존합니다. 클링커 형성은 에너지를 흡수하므로 지역 가스 및 벽 온도에 따라 달라지며 둘 다 화염에 의존합니다. 벽은 화염에서 클링커로의 순 열 전달에서 “중개자” 역할을 하며, 내화재 두께에 따라 환경으로 피할 수 없는 열 손실이 발생합니다. 이러한 상호 의존성은 가마의 거동에 중요하며 개별 프로세스를 개별적으로 계산하는 데 중점을 두었기 때문에 문헌에서 발견된 수학적 모델로는 다루기 어렵습니다.
본 논문에서 우리는 위에 설명된 유형의 세 가지 개별 모델을 결합하여 수행되는 회전식 시멘트 가마에서 발생하는 대부분의 공정에 대한 포괄적인 모듈식 모델을 제시합니다. 우리 작업은 4 , 5 , 6 , 7 에서와 같이 석탄 연소를 위한 다차원 CFD 코드로 기체 상태를 처리합니다 . 10 , 11 에서와 같이 가마 벽의 3차원 열전도 방정식을 풉니다 . 9 , 12 와 유사한 모델로 잘 혼합된 전하 온도 및 조성을 해결합니다.. 3개의 모듈(화염, 벽, 전하)은 내화물에 입사하는 열유속의 축 분포에 대해 수렴이 달성될 때까지 반복적으로 계산됩니다. 충전 온도 및 구성. 따라서 이전 작업에 비해 현재의 주요 이점은 완전성에 있습니다. 이는 가스-킬른-클링커 시스템의 다양한 부분에서 에너지 흐름의 정량화를 통해 킬른 작동에 대한 더 나은 이해를 가능하게 하고 여기에서 사용된 방법을 건조 및 소각과 같은 다른 회전 킬른 응용 분야에 적용할 수 있게 합니다.
이 문서의 특정 목적은 회전식 시멘트 가마에 대한 포괄적인 모델을 제시하고 화염에서 클링커로의 에너지 플럭스와 가마에서 열 손실을 정량화하는 것입니다. 이 문서의 나머지 부분은 다음과 같이 구성됩니다. 2장 에서는 다양한 모델과 해법을 제시하고 3장 에서는 그 결과를 제시하고 논의한다 . 여기에는 본격적인 회전식 시멘트 가마의 제한된 측정값과의 비교가 포함됩니다. 이 논문은 가장 중요한 결론의 요약으로 끝납니다.
2 . 모델 공식화
2.1 . 개요
Fig. 1 은 시멘트 로터리 킬른의 단면을 보여준다. 가마의 회전은 전하의 움직임을 유도하여 후자를 대략적으로 잘 혼합되도록 합니다 [10] , 여기에서 채택할 가정입니다. 우리는 이 코팅을 클링커와 유사한 물리적 특성의 고체 재료로 모델링하여 가마 내화물에 부착된 클링커의 존재를 허용할 것입니다. 우리는 이 층의 두께가 가마를 따라 균일하다고 가정합니다. 이것은 아마도 지나치게 단순화한 것일 수 있지만 관련 데이터를 사용할 수 없습니다. 모델 설명을 진행하기 전에 그림 2 에 개략적으로 표시된 회전식 가마의 다양한 에너지 흐름을 이해하는 것이 중요합니다 .
석탄 연소에 의해 방출되는 에너지(단위 시간당)( Q 석탄 )는 배기 가스(Δ H 가스 )와 함께 가마 밖으로 흘러 가마 벽에 직접 복사( Q rad ) 및 대류( Q conv )됩니다. 공급 및 배기 덕트( Q rad,1 + Q rad,2 ) 에 대한 축 방향의 복사에 의해 작은 부분이 손실됩니다 . 전하 가마 시스템은 복사( Q rad ) 및 대류( Q conv )에 의해 가스로부터 에너지(Δ H cl )를 흡수 하고 주변으로 열을 잃습니다( Q손실 ). 전체 에너지 균형에서 개별 항의 계산, 즉(1a)큐석탄=ΔH가스-Q라드-Q전환-Q일, 1-Q일, 2,(1b)큐라드+Q전환=ΔH클+Q손실여기에서 다음 섹션에 설명된 대로 가스, 가마 및 클링커에 대한 이산화 에너지를 국부적으로 해결함으로써 수행됩니다.
2.2 . CFD 코드
가스 운동량, 종 농도 및 에너지의 Favre 평균 방정식은 표준 k – ε 모델을 사용하여 방사 모듈(RAD-3D)과 함께 상업적으로 이용 가능한 축대칭 CFD 코드(FLOW-3D)에 의해 해결됩니다. [13] . 기하학이 실제로 3차원이고 벽 온도의 각도 분포가 존재하지만 합리적인 시간과 현재 워크스테이션에서 완전한 3으로 솔루션을 얻을 수 있도록 기체상을 축대칭으로 취급합니다. -D를 요구하는 해상도로 계산하려면 슈퍼컴퓨터에 의존해야 합니다. FLOW-3D에서 사용되는 다양한 하위 모델의 일부 기능과 벽 경계 조건에 대한 특수 처리는 다음과 같습니다.
2.2.1 . 석탄 연소
Rossin-Rammler 크기 분포(45μm 평균 직경, 1.3 지수 [6] )를 따르는 석탄 입자 는 CPU 시간을 줄이기 위해 솔루션 영역(즉, 확률적 구성 요소 없이)에서 결정론적으로 추적되었지만 분산을 과소 평가하는 단점이 있습니다 . 14] . 입자는 2-반응 모델에 따라 휘발되도록 허용되었고 휘발성 연소는 무한히 빠른 것으로 간주되었습니다. 석탄 연소에 대한 설명의 세부 사항은 FLOW-3D에서 석탄 휘발 및 열분해의 “표준” 상수 집합이 합리적인 결과를 제공하고 Ref. [5] .
2.2.2 . 복사와 대류
가스의 복사 강도는 RAD-3D 모듈을 사용하여 80,000개의 입자로 Monte-Carlo 방법으로 계산되었습니다. 가마는 반경 방향으로 7개, 축 방향으로 19개(크기가 0.1 × 1.0 m와 0.2 × 5.0 m 사이)로 불균일한 구역으로 나뉘었으며 각 구역 에서 방사선 강도가 균일하다고 가정했습니다. 방사선 모듈의 출력은 내부적으로 FLOW-3D에 대한 유체 계산에 인터페이스되고 외부적으로 벽 및 클링커에 대한 코드에 인터페이스되었습니다( 섹션 2.3 섹션 2.4 참조). 방사선 패키지의 이산화된 구역은 CFD 그리드의 셀보다 훨씬 커야 하므로 구역에 온도 평균이 형성될 수 있는 많은 셀이 포함될 수 있다는 점을 이해하는 것이 중요합니다. 상대적으로 조잡한 복사 구역의 분해능과 Monte-Carlo 방법의 통계적 특성은 구역의 복사 열유속이 더 미세한 구역화 및 더 많은 입자로 몇 번의 실행에 의해 결정된 바와 같이 최대 약 10%까지 부정확할 수 있음을 의미합니다. 또한 경계면에 입사하는 열유속은 영역 크기보다 미세한 분해능으로 결정할 수 없으므로 복사 열유속은 벽에 인접한 19개 영역 각각의 중심에서만 계산됩니다. 0.15m -1 의 흡수 계수는 Ref.[11] . 엄밀히 말하면, 흡수 계수는 국부적 가스 조성과 온도의 함수이므로 균일하지 않아야 합니다. 그러나 가스 조성은 가마의 일부만 차지하는 화염 내에서만 변 하므로( 3절 참조 ) 균일한 흡수 계수를 가정하는 것이 합리적입니다. 또한, 현재 버전의 소프트웨어는 FLOW-3D의 반복 프로세스 동안 이 요소의 자동 재조정을 허용하지 않습니다. 여기서 로컬 가스 특성이 계산되므로 일정하고 균일한 흡수 계수가 필요합니다.
최종적으로, 벽에서 대류 열전달이 플로우 3D 패키지에서 표준 출력 표준 “벽 기능”제형에 혼입 난류 경계층에 대한 식에 기초하고,의 속도 경계 조건과 유사한 K – ε 모델. FLOW-3D 및 RAD-3D에서 입력으로 사용하고 출력으로 계산된 다양한 양은 그림 3에 개략적으로 표시 됩니다.
2.2.3 . 그리드
반경 방향 47개, 축 방향 155개 노드를 갖는 불균일한 격자를 사용하였으며 격자 독립성 연구를 수행한 결과 충분하다고 판단하였다. 유사한 크기의 그리드도 Refs에서 적절한 것으로 밝혀졌습니다. 4 , 5 , 6 , 7 . 매우 높은 축 방향 및 소용돌이 속도로 인해 석탄 버너 유정에 가까운 지역을 해결하기 위해 특별한 주의를 기울였습니다. HP 715/100MHz 워크스테이션에서 이 그리드의 일반적인 CPU 시간은 10시간이었습니다.
2.2.4 . 경계 조건
벽 온도에 대한 경계 조건은 기체상 및 복사 솔버 모두에 필요하다는 것을 인식하는 것이 중요합니다. 아래에서는 4 , 5 , 6 , 7 을 규정하기 보다는 축대칭 그리드에 대한 이 온도 분포를 예측하는 대략적인 방법을 설명합니다 .
내벽 온도 T w ( R in , x , ϕ ) 의 각도 분포 가 알려져 있다고 가정합니다 . 그런 다음 전체 3차원 문제를 “동등한” 축대칭 문제로 줄이기 위해 가상의 내벽 온도 T RAD ( x )는(2)2πε에티4라드(x) = ε클∫0ㄷ티4클(엑스)디ϕ + ε에∫ㄷ2π티4에(아르 자형~에, x, ϕ)디ϕ”효과적인” 경계 조건으로 사용할 수 있습니다. T RAD ( x )는 방위각으로 평균화된 “복사 가중” 온도입니다. 필요한 경계 조건으로 이 온도를 사용하는 것은 복사가 열 전달을 지배한다는 기대에 의해 동기가 부여됩니다(후반부 확인, 섹션 3.4 ). 따라서 전체 3차원 문제와 이 “유효한” 축대칭 문제에서 가스에서 가마로의 전체 에너지 흐름은 거의 동일할 것으로 예상됩니다. 식 의 사용 (2) 축대칭 코드로 기체상 및 복사장을 계산할 수 있으므로 엔지니어링 워크스테이션을 사용하여 문제를 다루기 쉽습니다.
고려되는 가마의 규모와 온도에서 가스는 광학적으로 두꺼운 것으로 간주될 수 있습니다. 솔루션(나중에 제시됨)은 평균 경로 길이(즉, “광자”의 모든 에너지가 흡수되기 전의 평균 길이)가 약 3.2m임을 보여주며, 이는 가마 내경 4.1m보다 작습니다. 이것은 내벽에 입사하는 복사 플럭스가 국부적 벽과 가스 온도에 강하게 의존하고 더 먼 축 또는 방위각 위치에서 벽의 온도에 약하게만 의존함을 의미합니다. 이것은 기체상에 사용된 축대칭 근사에 대한 신뢰를 줍니다. 그것은 또한 Refs의 “구역 방법”을 의미합니다. 8 , 9 , 10표면에 입사하는 방사선이 1-2 구역 길이보다 더 먼 축 위치와 무관한 것으로 간주되는 경우에는 충분했을 것입니다.
2.3 . 가마 온도
내부 소성로 표면 온도 T w ( R in , x , ϕ )는 Eq. 에서 필요합니다 . (2) 및 가마 벽 에너지 방정식의 솔루션 결과의 일부입니다. 각속도 ω로 회전하는 좌표계 에서 후자는 [10] 이 됩니다 .(3)ω∂(ϱ에씨피티에)∂ϕ=1아르 자형∂∂아르 자형에게에아르 자형∂티에∂아르 자형+1아르 자형2∂∂ϕ에게에∂티에∂ϕ+∂∂엑스에게에∂티에∂엑스경계 조건에 따라(3a)r=R~에,Θ<ϕ⩽2π:에게∂티에∂아르 자형=q라드(x)+q전환(엑스),(3b)r=R~에, 0 <ϕ⩽Θ:에게∂티에∂아르 자형=qw–cl(x, ϕ) = hw–cl티클(x)-T에(아르 자형~에, x, ϕ),(3c)r=R밖, 0 <ϕ⩽2π:.케이∂티에∂아르 자형=h쉿티쉿-T∞+ ε쉿티4쉿-T4∞.
전도도, 밀도 및 비열용량에 대한 값은 실제 가마에 사용되는 내화물 재료에 대한 제조업체 정보에서 가져옵니다 [15] . 외부 쉘 온도 T sh = T w ( R out , x , ϕ )는 x 및 ϕ 에 따라 달라질 수 있습니다 .
위 방정식에 대한 몇 가지 의견이 있습니다. 에서는 식. (3a) 에서 열유속의 방위각 의존성이 제거되었습니다. 이전에 언급했듯이 흐름은 광학적으로 두꺼운 것으로 간주됩니다. 즉, 화염이 너무 방사되고 너무 넓기 때문에 벽면 요소가 화염을 가로질러 반대쪽 벽을 “보지” 않습니다. 따라서 q rad ( x , ϕ ) 의 계산은 다른 각도 위치로부터의 복사를 포함할 필요 없이 T 가스 ( r , x ) 및 로컬 T w ( R in , x , ϕ )를 기반으로 할 수 있습니다. 여기부터 qrad ( x )는 Eq. 의 방위각 평균 온도를 기반으로 하는 축대칭 RAD-3D 솔루션에서 가져옵니다 . (2) , 결과적인 q rad ( x )는 어떤 의미에서 방위각으로 평균된 열유속입니다. 식 따라서 (3a) 는 우리가 이 열유속을 모든 ϕ 에 등분포한다는 것을 의미합니다 . Eq 에서 q rad 의 각도 변화를 무시한다는 점에 유의하십시오 . (3a) 는 Refs. [10] 또는 [11] 이 우선되어야 합니다.
소성로와 장입물 사이의 열전달 계수 h w-cl 은 소성로의 에너지 흐름과 온도를 정확하게 예측하는 데 중요하지만 잘 알려져 있지 않습니다. 500 W / m의 전형적인 값 이 K는 여기에 제시된 결과 사용되고있다 [8] . 계산된 T w ( r , x , ϕ ) 및 T RAD ( x) 이 계수의 선택에 따라 달라지지만 예측은 질적으로 변하지 않습니다. 껍질에서 대기로의 열 전달은 복사와 별도로 강제 및 자연 대류를 통해 발생합니다. 자연 대류에 대한 열전달 계수는 Ref. [11] , 현재 조건에서 약 5 W/m 2 K의 일반적인 값 을 사용합니다. 그러나 쉘에 불어오는 외부 팬은 과열을 피하기 위해 산업에서 종종 사용되며 이러한 효과는 총 h sh =30 W/m 2 K 를 사용하여 여기에서 모델링 되었습니다. 방사율에는 다음 값이 사용되었습니다. ε w = ε cl = 0.9 및 ε sh = 0.8.
식 (3) 은 가마의 방사형 기울기가 훨씬 더 가파르기 때문에 방위각 및 축 전도를 무시한 후 명시적 유한 체적 방법으로 해결되었습니다. 방사형으로 50개 노드와 축 방향으로 19개 노드가 있는 균일하지 않은 그리드가 사용되었으며 회전으로 인한 화염에 주기적으로 노출되는 표면으로 인해 발생하는 빠른 온도 변화를 따르기 위해 내부 표면에서 적절한 방사형 분해능이 사용되었습니다. 동일한 이유로 사용 된 작은 단계(Δ ϕ = π /100)는 가마의 큰 열 관성과 함께 가마 벽 온도가 수렴되도록 하기 위해 2시간 정도의 CPU 시간이 필요했습니다.
2.4 . 수갑
가마에 대한 모델의 마지막 부분은 클링커 온도 및 조성 보존 방정식에 관한 것으로, 축 방향 기울기만 고려하고 전도는 무시합니다.(4)씨피V클디(ϱ클티클)디엑스=−엘wclㄷㅏ클∫0ㄷ큐w–cl(x, ϕ)디ϕ +엘gclㅏ클큐라드(x)+q전환(엑스)−∑나Nsp아르 자형나시간0, 나는에프+씨피티,(5)V클디(ϱ클와이나)디엑스=r나,(6)V클디ϱ클디엑스=−r무엇2,여기서 A cl 은 속도 V cl 로 흐르는 전하가 덮는 단면적 이며 둘 다 일정하다고 가정하고 L gcl =2 R in sin( Θ /2) 전하로 덮인 섹터의 현( 그림 1 ) , L WCL = Θ R 에서는 , N SP 화학 종의 수와 r에 난을 (kg / m의 형성 속도 순 3 종의) I를 . 전하의 밀도는 Eq를 감소시킵니다 . (6) CO 2 에 대한 질량 손실로 인한하소하는 동안 초기 값은 총 질량 유량이 ϱ cl V cl A cl 과 같도록 선택되었습니다 . 참고 ρ (CL)이 있다 하지 전하 느슨하게 포장 된 입자로 이루어지는 것으로 생각 될 수있는 바와 같이, 충전 재료 밀도하지만 벌크 밀도. 우리는 또한 전하의 실제 입상 흐름 패턴을 조사하는 것보다 적은 것은 모델의 신뢰성에 크게 추가되지 않는 임시 설명 [10] 이라고 믿기 때문에 전하의 전도를 무시 합니다. 전하는 CaCO 3 , CaO, SiO 2 , Al 2 O 3 , Fe 로 구성된 것으로 가정합니다.2 O 3 , C2S, C3S, C3A 및 C4AF로, 마지막 4종은 클링커화 중에 형성된 복합 염에 대해 시멘트 화학자가 사용하는 특수 표기법으로 표시됩니다. 다음과 같은 화학 반응을 가정합니다 [12] .
(나)
CaCO3→높은+무엇2
k = 108특급(−175728/RT)
(Ⅱ)
높은+2SiO2→C2S
k = 107특급(−240000/RT)
(Ⅲ)
높은+C2S→C3S
k = 109특급(−420000/RT)
(IV)
3높은+로2그만큼3→C3A
k = 108특급(−310000/RT)
(V)
4높은+로2그만큼3+철2그만큼3→Q4AF
k = 108특급(−330000/RT)
상기 시행 착오에 의해 선택되는 아 레니 우스 식에 사용되는 사전 지수 인자 및 활성화 온도는 카코에 대한 활성화 에너지를 제외하고, 가마의 출구에서의 전하의 예상 조성물을 얻었다 (3) 에서 촬영 한 분해 참조 [16] . 우리는 이러한 반응이 임시 모델임을 강조합니다. 실제로 고체상의 화학반응은 다양한 종의 결정들 사이의 계면에서 일어나며 확산이 제한적 이지만 [17] , 클링커 화학에 대한 상세한 처리는 본 연구의 범위를 벗어난다.
클링커 형성의 마지막 단계로 간주되는 반응 (III)은 고온에서 액상이 존재할 때만 발생합니다. 클링커의 용융은 액체 분획 Y fus 에 대해서도 해결함으로써 모델링되었습니다 .(7)엘소란V클디(ϱ클와이소란)디엑스=RHS의식(4)만약 T의 CL이 융해 온도와 같거나보다 커진다 T의 FUS 와 T의 FUS 의 = 1560 K. 상한 Y의 FUS = 0.3 수행 하였다 [17] 상기 식을. (7) 무시되었다.
상미분 방정식, , , , , Gear 방식과 통합되었습니다. 가마 온도에 대한 유한 체적 코드( 2.3절 )와 클링커에 대한 코드는 반복적으로 해결되었으며( 그림 4 ), 이는 벽 클링커 열유속 q w–cl ( x , ϕ ).
2.5 . 최종 커플링
전체 문제(가스, 가마, 장입)는 반복 방식으로 해결되었습니다. T RAD 의 균일한 분포에서 시작 하여 기체상은 q rad ( x ) 및 q conv ( x ) 의 축 분포를 제공하도록 해결되었습니다 . 이것들은 다음에서 사용되었습니다., , , , , 그 솔루션의 새로운 추정 결과 T RAD ( X 통해) 식. (2) . 그런 다음 FLOW3D-RAD3D 실행이 6차 다항식 피팅의 계수 형태로 프로그램에 도입된 새로운 경계 조건으로 반복되었습니다. 의 연속 추정치 사이에 0.5 미만의 밑에 이완 인자 T RAD ( X)는 벽 온도에 대한 복사 열유속의 민감도가 크기 때문에 필요한 것으로 밝혀졌습니다. 일반적으로 HP 715 워크스테이션에서 10일 정도의 총 CPU 시간에 해당하는 내벽 온도(연속 반복이 40K 이상 변하지 않을 때 정의됨)의 수렴을 달성하기 위해 이러한 단계 사이에 약 10번의 반복이 필요했습니다. . 그림 5 는 균일한 값(1600K)에서 시작하여 최종 프로파일까지 T RAD ( x ) 의 수렴 이력을 보여줍니다 .
2.6 . 가마 조건
사용된 일부 매개변수에 대한 작동 조건 및 값은 표 1 표 2 표 3에 나와 있습니다. 이 값은 시멘트 회전 가마의 전형입니다.
표 1 . 공기 및 석탄 입자 입구 조건
축
수송
소용돌이
중고등 학년
석탄
m (kg/s)
2.253
1.759
2.910
45.930
4.0
유 (m/s)
77.1
36.5
76.1
12.73
36.5
V (m/s)
−20.7
0
63.9
0
0
W (m/s)
0
0
112.8
0
0
티 (케이)
318
383
318
1273
383
표 2 . 클링커 조성(질량 분율)
밀가루
가마 입구
가마 출구
m (kg/s)
50.374
39.815
32.775
티 (케이)
−
1100
1785
CACO 3
0.7947
0.40218
0
높은
0
0.33801
0.0229
그런가 2
0.1434
0.18143
0
알 2 O 3
0.0349
0.0442
0
철 2 O 3
0.0270
0.03416
0
C2S
0
0
0.1808
C3S
0
0
0.5981
C3A
0
0
0.0731
Q4AF
0
0
0.1242
소성 인자
0
0.6
1.0
소성 계수 카코의 비율을 3 의 CaO로 변환 된 FARINE있다.
표 3 . 재료 속성 및 기타 매개변수
ω (래드/초)
0.5
V의 CL (m / s)
0.035
T ∞ (K)
300
h sh (W/m 2 K)
30
h w–cl (W/m 2 K)
500
ε w , ε cl
0.9
ε 쉬
0.8
C의 P (클링커) (킬로 / kg K)
1.5
ϱ cl (kg/m 3 )
1200
L fus (kJ/kg)
418.4
c p (벽) (kJ/kg K)
1.5
ϱ w (kg/m 3 )
1600–3000
k는 w (W / m K)
0.6–3.0
석탄 열 방출(kJ/kg)
25475
3 . 결과 및 토론
이 섹션에서는 먼저 화염 구조에 대한 정보와 함께 예측된 공기역학적 패턴의 세부사항을 제시합니다. 소성로 내화물의 온도 분포와 클링커 조성의 변화를 설명합니다. 이 섹션은 가마의 전체 에너지 균형과 가능한 모델 개선에 대한 논의로 끝납니다.
3.1 . 화염 구조
그림 6 은 명확성을 위해 방사상 좌표가 과장된 온도의 등고선 플롯을 보여줍니다. 석탄은 주입 지점에서 약 1m 지점에서 약간 축에서 벗어나 점화되며 최대 화염 온도(약 2400K)는 경험에 따라 약 40m 하류에서 도달합니다 [15] . 완전한 입자 소진에 대한 가장 긴 시간은 버너에서 45m에 해당하는 약 1.4초였습니다. 방사형 온도 프로파일( 그림 7 ) 은 온도의 상당한 불균일성이 있음을 보여주지만 출구 프로파일이 본질적으로 평평해짐에 따라 하류에서 감소합니다. 또한 벽에 인접한 가스가 더 차가운 열 경계층이 존재한다는 것이 분명합니다.석탄 노즐에서 최대 30m까지 벽보다 이것은 이 영역에서 대류에 의한 열 전달이 음(즉, 기체 쪽으로)임을 의미하며, 3.4절 에서 더 자세히 논의된 지점 입니다.
버너 출구 바로 하류에 길이가 약 1 버너 직경인 재순환 구역이 있는데( 그림 8 ), 여기에서 화염이 더 하류에서 발화하기 때문에 소용돌이 안정화 화염 [7] 에서와 같이 화염 안정화에 기여하지 않습니다 . 그러나 액체 연료를 사용할 때는 중요할 수 있으므로 버너에 가까운 그리드의 세부 사항을 강조해야 합니다. 버너에서 처음 몇 미터는 매우 높은 전단력과 높은 난류 에너지 생산을 포함하며 이것이 그리드 미세 조정을 강조하는 또 다른 이유입니다. 휘발성 물질 연소 영역( x =10m, r =1m) 에서 k 및 ε 의 일반적인 예측 값 은 24.3 및 142m 2 /s입니다.3 , 각각. 대규모 난류 시간은 171ms이고 Kolmogorov 시간 규모는 1.1ms입니다. 휘발성 물질의 연소는 0.1ms(일반적인 탄화수소 연료) 정도의 시간 규모에서 발생하며, 이는 가마의 소규모 난류 시간보다 10배 더 짧습니다. 따라서 이 흐름에서 연소에 대한 유한 속도 동역학을 포함할 필요는 없으며 “혼합 연소” 근사가 합리적입니다.
3.2 . 가마 온도 분포
중심선에서 계산된 가스 온도, 온도 T RAD ( x ) 및 클링커 온도는 그림 9 에서 비교됩니다 . 최고 가스 온도는 25~40m 사이에 위치하며 내화 내부 표면 온도도 최고점입니다. 클링커는 놀랍게도 가마에서 나오기 전 마지막 몇 미터 동안 벽보다 뜨겁 습니다. 복사에 의해 내화물에 입사하는 열유속은 대류에 의한 것보다 1-2 배 더 높으며( 그림 10 ) 가마의 처음 10m에 대한 총 열 전달 은 가스를 향 합니다. 이 관찰의 중요성은 나중에 논의됩니다.
대류로 인한 에너지 플럭스는 화염에서 가마까지의 전체 에너지 플럭스의 매우 작은 부분인 것으로 밝혀졌습니다( 그림 10 ). 여기서 예측된 대류의 작은 기여는 Ref. [11] . 그 작업에서 대류 열 전달 계산에 사용된 가스 온도는 가마 단면의 평균이었고 따라서 축 근처에 있는 화염의 기여로 인해 벽 부근의 온도보다 훨씬 높았습니다. . 여기에서 우리는 온도와 가스 속도 및 난류 운동 에너지의 국부적 값을 기반으로 하는 보다 정확한 열전달 계수를 사용했기 때문에 보다 정확한 결과를 기대합니다.
예측된 벽 온도는 모든 방향에서 불균일합니다. Fig. 11 은 가마가 회전함에 따라 화염에 노출되었을 때 벽이 가스에 의해 연속적으로 가열되고 클링커에 열을 공급하여 냉각되는 것을 보여준다. 이것은 약 100K의 일반적인 각도 온도 변화를 갖는 대부분의 가마 길이에 해당됩니다. 대조적으로 버너에 가까우면 벽 은 (0 < ϕ < π /2) 동안 클링커에서 열을 얻고 다음으로 열을 잃 습니다. 노출될 때의 가스( π /2 < ϕ < 2 π ). 벽과 클링커 온도가 같으면서 방위각 변화가 없는 경우가 발생할 수 있습니다( 그림 11 , x = 17.5m). 이 온도 변화가 작은 것으로 간주될 수 있지만 벽에서 클링커까지의 열유속을 계산하는 위치에 있으려면 전체 3차원 내벽 온도 분포를 계산해야 합니다(0 < ϕ 범위에서 발생 < π /2).
그림 12 는 ϕ에 독립적인 외부(쉘) 온도와 함께 고체의 큰 비열로 인해 각도 방향의 변화 영역이 벽으로 약 1cm만 확장됨을 보여줍니다( 그림 12b) .. 벽 온도 방사 분포는 가스 온도, 입사 방사선 및 내화 재료의 특성이 변하기 때문에 축 방향 거리에 따라 달라집니다. 정확한 예측을 위해서는 내화물에 부착된 클링커 코팅의 두께에 대한 정확한 지식이 필요합니다. 여기에서 우리는 이 코팅을 클링커와 유사한 물성을 가진 균일한 두께의 재료로 취급했습니다. 그러나 이 코팅층의 실제 물리적 특성과 두께 분포에 관한 실험 데이터를 사용하여 예측의 신뢰성이 향상될 것입니다.
마지막으로, 그림 13 은 외부 쉘 온도가 화염 영역에서 최고조에 달하고 대략적으로 실험 경향을 따른다는 것을 보여줍니다 [15] . 외부 가마 외피는 다양한 강철 두께, 방사율(외피 착색으로 인한) 및 열 전달 계수(송풍기 간격으로 인한)를 갖고 가마는 가변 내화 두께(에 의한 침식으로 인해)를 갖기 때문에 정확한 비교는 의미가 없습니다. 클링커), 여기에 사용된 가정과 반대입니다. 전체 규모 가마는 또한 차등 코팅 및 내화 침식으로 인한 최대 ±100K의 쉘 온도 각도 변동을 보여줍니다 [15] . 따라서 우리는 그림 13 의 일치 가 실제 가마의 복잡성을 고려할 때 예상할 수 있는 만큼 우수 하다고 믿습니다 .
이 섹션에 제시된 예측은 가마 내부의 열 전달 경로에 대한 다음 그림을 뒷받침합니다. 대부분의 가마 길이에서 장입물은 화염으로부터의 복사와 벽으로부터의 열 전도에 의해 가열되고 있습니다. 장입물이 내화물보다 더 차갑기 때문입니다. 가마가 회전함에 따라 내화물은 화염에 노출될 때 열을 얻고 이를 클링커에 공급합니다( 그림 11 ). 벽의 이 “재생” 작용은 Refs. 9 , 10 및 현재 결과에서 재현되었습니다. 그러나 버너 근처에서 반대 에너지 흐름이 발생합니다( 그림 11 , 작은 x). 여기의 가스는 아직 충분히 뜨겁지 않아 내화물이나 장입물에 에너지를 공급하지 않습니다. 이 영역에서 벽은 다가오는 전하에 의해 열을 얻으므로 고체가 없을 때보다 더 뜨겁게 유지됩니다. 벽과 전하가 대류와 복사에 의해 가스에 열을 공급합니다. 우리는 이것을 “음의 재생” 작용으로 식별할 수 있으며 가마의 더 높은 온도 영역( x > 15m) 에서 클링커에 의해 흡수된 에너지에 의해 유지됩니다 . 전반적으로 클링커는 x > 15 m 에서 열을 흡수 하고 0 < x < 15 m 에서 일부를 가스로 되돌려 줍니다.
이 상호 작용은 간단하지 않으며 쉽게 예상할 수 없습니다. 이는 예를 들어 고체를 액체 연료로 대체하여 화염을 수정하면 열유속 분포를 변경하여 최종 클링커 온도에 중대한 영향을 미칠 수 있음을 의미합니다. 현재의 포괄적인 모델이 제공하는 세부 사항은 가마에서 이러한 변화를 평가하는 데 도움이 될 것입니다.
3.3 . 클링커 온도 및 조성
클링커 온도( 그림 9 )는 가장 높은 화염 온도에 도달하는 축 방향 위치에서 거의 최고조에 달하며 클링커는 약 1780K에서 킬른에 존재하며 이는 시멘트 킬른에서 실험 측정값에 가까운 값입니다 [15] . 초기 및 최종 클링커 조성은 표 2 에 나와 있으며 실제 가마에서 작동 값에 가깝습니다 [15] . 다양한 클링커 성분의 축방향 분포( 그림 14 )는 완전한 하소를 위해 고체 유입구에서 약 25m, C2S, C3A 및 C4AF 생성을 위해 추가로 10m가 소요됨을 보여줍니다. 첫 번째 액체상은 x 에서 발견됩니다.=50m이고 액화는 경험과 일치하는 예측인 매우 직후에 완료됩니다 [17] . 클링커화 반응(R-III)은 모델에서 액체가 나타날 때 시작되는 것으로 가정되었으며, 그림 14 에서 클링커화에는 나머지 길이의 거의 전체가 완료되어야 한다는 것이 분명 합니다. 예측은 전체적으로 시멘트 가마 운영의 경험과 일치하며 여기에 사용된 화학적 및 물리적 매개변수가 현실적인 값을 가지고 있음을 의미합니다.
3.4 . 글로벌 에너지 균형
전지구적 에너지 균형은 기체상(FLOW-3D 및 RAD-3D에 의한)과 소성로 장입 시스템에 대한 솔루션에서 쉽게 계산할 수 있으며 표 4 에 나와 있습니다. CFD 코드는 방사 모듈과 함께 에너지를 약 2%까지 절약합니다. 작은 것으로 간주되는 이 오류는 주로 RAD-3D의 영역 이산화와 Monte-Carlo 계산의 유한한 입자 수로 인해 발생하는 오류에 기인하며 CPU 시간을 희생하여 개선할 수 있습니다. 소성로-클링커 계산의 정확도는 더 나쁩니다. 소성로-클링커 시스템에 입력되는 에너지의 약 10% 오류( Q rad + Q conv )입니다. 이는 수렴된 솔루션이 식 (3) , 그리고 보다 정확한 암시적 솔버에 의해 개선될 수 있습니다.
시멘트 회전식 가마의 에너지 사용에 관한 몇 가지 흥미로운 결론은 표 4 의 결과를 통해 얻을 수 있습니다 . 연소에 의해 방출되는 에너지의 약 40%는 전하 가열 및 클링커 형성에 필요하고 약 10%는 내화물을 통해 대기로 손실됩니다. 나머지의 대부분은 본질적으로 배기 가스와 함께 소성로 밖으로 흐릅니다. 이 중 일부는 소성로 외부의 예비 하소기 및 사이클론에서 회수됩니다. 내부 가마 벽과 장입 온도를 자세히 다루는 여기에 제시된 포괄적인 모델에 의존하지 않고는 국지적 가스 온도를 정확하게 예측하고 이에 따라 향후 연구에서 오염 물질 형성을 예측하는 것이 불가능하다는 것이 분명합니다.
3.5 . 논의
여기에 제시된 회전식 시멘트 가마 작동에 대한 포괄적인 모델의 결과는 합리적이며 실험적으로 관찰된 경향을 재현합니다. 이전 모델링 작업에 비해 이 작업의 주요 이점은 가마에서 발생하는 대부분의 물리적 프로세스를 포함한다는 점입니다. 특히, 가스 온도와 클링커로의 열유속 및 이에 따른 클링커 형성을 결정하는 데 가장 중요한 양인 내벽 온도는 실험 데이터를 사용하여 규정된 것이 아니라 예측되었습니다. 이 특정 기능은 현재 모델을 진정한 예측형으로 만듭니다.
우리는 전체 3차원 문제를 공기역학에 대한 “동등한” 축대칭 문제로 줄이는 방법을 포함했습니다( 식 (2) ). 이를 통해 현재 워크스테이션에서 솔루션을 얻을 수 있습니다. 모델의 모듈식 특성, 즉 공기역학, 복사, 가마 및 장입에 대한 별도의 코드는 해당 모듈만 수정하면 다른 회전 가마 응용 프로그램(예: 소각 및 건조)에도 사용할 수 있음을 의미합니다. 예를 들어, 고형 폐기물의 소각은 현재 코드로 모델링할 수 있지만 적절한 화학, .
실험 데이터와의 상세한 비교는 이용 가능한 측정이 거의 없고 현지 시멘트 회사에서 제공한 경험적 데이터로 제한되어 매우 어렵습니다 [15] . 비교는 앞서 지적한 바와 같이 출구 클링커 조성과 온도가 산업적 경험( 표 2 ) 이내 이고, 배기 가스 조성은 공장 굴뚝에서 측정된 값에 가깝고(“가짜 공기” 희석을 허용한 후), 가마 외피 온도는 측정 범위 내에 있습니다( 그림 13 ). 이 동의는 모델이 프로세스의 정확한 표현임을 시사합니다.
더 높은 정확도의 예측을 달성하려면 모델의 다양한 부분에서 개선이 필요합니다. 내화물의 정확한 두께(즉, 내화물과 부착된 클링커)를 설정해야 합니다. 이는 가마 벽을 통해 주변으로 열 손실이 발생하여 외부 쉘 온도에 영향을 미치기 때문입니다. 새 내화물이 있는 가마에서 쉘 온도 측정과 자세한 비교가 이루어져야 합니다(불균일한 코팅 두께가 방지되도록). 벽 재료의 물리적 특성(열용량, 밀도, 전도도)의 적절한 값을 사용해야 합니다. 가장 큰 불확실성은 클링커 코팅의 가정된 특성에 관한 것입니다. 내벽 표면의 방사율과 가스의 흡수 계수를 더 자세히 조사해야 합니다. 가마에 입사하는 복사 열유속에 영향을 미치므로 벽 온도에 영향을 줄 수 있습니다. 클링커의 온도는 사용된 비열 용량에 따라 달라지므로 정확한 평가에 각별한 주의가 필요합니다. 화염의 국지적 온도와 종 구성에 대한 지식은 CFD 코드를 검증하는 데 매우 유용할 것이지만 그러한 적대적인 환경에서 측정은 분명히 달성하기 매우 어렵습니다. 마지막으로 클링커 화학 및 전하 이동은 개선할 수 있는 영역입니다. 그러한 적대적인 환경에서의 측정은 분명히 달성하기 매우 어렵습니다. 마지막으로 클링커 화학 및 전하 이동은 개선할 수 있는 영역입니다. 그러한 적대적인 환경에서의 측정은 분명히 달성하기 매우 어렵습니다. 마지막으로 클링커 화학 및 전하 이동은 개선할 수 있는 영역입니다.
이러한 모든 잠재적 개선과 모델과 관련된 불확실성에도 불구하고 가마의 모든 에너지 경로가 적절한 세부 사항으로 모델링되었기 때문에 전체 동작은 최소한 질적으로 정확합니다. 클링커 출구 구성, 쉘 온도 및 배기 가스 구성과 같은 중요한 양은 허용 가능한 정확도로 예측됩니다. 이 모델은 버너, 연료 유형, 품질 및 수량, 예비 하소 수준( 표 2 ) 또는 고형물 유량 등의 변경과 같은 많은 상황에서 산업계에 매우 유용할 것으로 예상됩니다 . 소성로 운영자는 최종 클링커 구성이 여전히 허용 가능하고 현재의 포괄적인 모델이 이 방향에 도움이 될 수 있는지 확인해야 합니다.
4 . 결론
실제 작동 조건에서 석탄 연소 회전 시멘트 가마의 클링커 형성은 석탄 화염과 가마 사이의 열 교환, 가마와 역류 고체 사이의 열 교환, 고형물을 최종 제품(클링커)으로 변환합니다. 방사선에 대한 Monte-Carlo 방법을 포함하는 축대칭 CFD 코드(상용 패키지 FLOW-3D)가 기상에 사용되었습니다. 가마 벽의 온도는 유한 체적 열전도 코드로 계산되었으며 클링커에 대한 종 및 에너지 보존 방정식도 공식화 및 해결되었습니다. 기체 온도 필드에 대한 예측 사이의 반복적인 절차, 벽에 대한 복사 열 유속, 가마 및 클링커 온도는 실험에서 이러한 정보를 사용한 이전 모델링 노력과 달리 내벽 온도 분포를 명시적으로 계산하는 데 사용되었습니다. 접선 좌표에 대한 통합은 CFD 코드에 필요한 경계 조건으로 사용되는 “유효” 내벽 온도의 축 분포를 초래했습니다. 이 절차를 통해 클링커로의 열 흐름 계산이 가능하고 축대칭 CFD 코드로 3차원 문제를 대략적으로 처리할 수 있습니다. CFD 코드에 필요한 경계 조건으로 사용됩니다. 이 절차를 통해 클링커로의 열 흐름 계산이 가능하고 축대칭 CFD 코드로 3차원 문제를 대략적으로 처리할 수 있습니다. CFD 코드에 필요한 경계 조건으로 사용됩니다. 이 절차를 통해 클링커로의 열 흐름 계산이 가능하고 축대칭 CFD 코드로 3차원 문제를 대략적으로 처리할 수 있습니다.
결과는 복사가 가스와 가마 벽 사이의 대부분의 열 전달을 설명하는 반면 내화물을 통한 환경으로의 열 손실은 입력 열의 약 10%를 설명한다는 것을 보여줍니다. 화학 반응과 충전물의 가열은 연소 에너지의 약 40%를 흡수합니다. 따라서 이러한 사항을 반드시 고려해야 합니다. 예측은 실제 규모의 시멘트 가마에서 얻은 경험과 측정값을 기반으로 한 경향과 일치합니다.
감사의 말
이 작업은 과학 및 기술을 위한 그리스 사무국 프로젝트 EPET-II/649의 자금 지원을 받았습니다. Mr.P에게 진심으로 감사드립니다. 시멘트 가마에 관한 지침 및 데이터는 그리스 TITAN SA의 Panagiotopoulos에게 문의하십시오.
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2 Also at Department of Chemical Engineering, University of Patras, Greece.
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 2. (a) Scanning electron microscopy images of Ti6Al4V powder particles and (b) simulated powder bed using
discrete element modellingFigure 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 msFigure 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 msFigure 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 msFigure 8. Transformation from shallow depth melt flow to deep keyhole formation when laser power increased from
(a) 170 W to (b) 200 WFigure 9. Stream traces and laser beam multiple reflections in deep keyhole melt flow modeFigure 10. A comparison between analytical and CFD simulation results for peak thermal distribution value in the deep
keyhole formationFigure 11. A comparison among experiments [49], CFD and analytical simulations for deep keyhole
top width and bottom width
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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.
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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. 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, respectivelyFig. 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. 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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a State Key Laboratory of Hydraulics and Mountain River Engineering, College of Water Resource and Hydropower, Sichuan University, Chengdu, 610065, China
b State Key Laboratory of Hydraulics and Mountain River Engineering, Sichuan University, College Of Water Resource and Hydropower, Chengdu, 610065, China
c 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
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
Keywords
Additive manufacturing, Laser powder bed fusion, Numerical modelling, Transient region
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.
Fig.1 Schematic diagram of the novel cytometric deviceFig.2 Overview of the cytometric device fabrication processFig.3 The fabricated micro cytometric device Fig. 4 Experiment setup for focusing performanceFig.5 Horizontal focusing images of two devices with and without stepsFig.6 Channel cross-section fluorescence images for different step heights
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.
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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.
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 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 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 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 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.
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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.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 mmSeparation 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).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.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
Edward P. Furlani is deceased.
Affiliations
Department of Chemical and Biomolecular Engineering, ETSIIT, University of Cantabria, Avda. Los Castros s/n, 39005, Santander, SpainJenifer Gómez-Pastora, Eugenio Bringas & Inmaculada Ortiz
Flow Science, Inc, Santa Fe, New Mexico, 87505, USAIoannis H. Karampelas
Department of Chemical and Biological Engineering, University at Buffalo (SUNY), Buffalo, New York, 14260, USAEdward P. Furlani
Department of Electrical Engineering, University at Buffalo (SUNY), Buffalo, New York, 14260, USAEdward P. Furlani
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 particlesHierarchical grain refinement during the laser additive manufacturing of Ti-6Al-4V alloys by the addition of micron-sized refractory particles Fig1Hierarchical grain refinement during the laser additive manufacturing of Ti-6Al-4V alloys by the addition of micron-sized refractory particles Fig2Hierarchical grain refinement during the laser additive manufacturing of Ti-6Al-4V alloys by the addition of micron-sized refractory particles Fig3Hierarchical grain refinement during the laser additive manufacturing of Ti-6Al-4V alloys by the addition of micron-sized refractory particles Fig4Hierarchical grain refinement during the laser additive manufacturing of Ti-6Al-4V alloys by the addition of micron-sized refractory particles Fig5Hierarchical grain refinement during the laser additive manufacturing of Ti-6Al-4V alloys by the addition of micron-sized refractory particles Fig6Hierarchical grain refinement during the laser additive manufacturing of Ti-6Al-4V alloys by the addition of micron-sized refractory particles Fig7
a Department of Mechanical Engineering, Technical University of Denmark, Building 425, Lyngby, Denmark
b 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-FigOn the role of the powder stream on the heat and fluid flow conditions during Directed Energy Deposition of maraging steel-Fig2On the role of the powder stream on the heat and fluid flow conditions during Directed Energy Deposition of maraging steel-Fig3On the role of the powder stream on the heat and fluid flow conditions during Directed Energy Deposition of maraging steel-Fig4On the role of the powder stream on the heat and fluid flow conditions during Directed Energy Deposition of maraging steel-Fig5On the role of the powder stream on the heat and fluid flow conditions during Directed Energy Deposition of maraging steel-Fig6On the role of the powder stream on the heat and fluid flow conditions during Directed Energy Deposition of maraging steel-Fig7On the role of the powder stream on the heat and fluid flow conditions during Directed Energy Deposition of maraging steel-Fig8On the role of the powder stream on the heat and fluid flow conditions during Directed Energy Deposition of maraging steel-Fig9On the role of the powder stream on the heat and fluid flow conditions during Directed Energy Deposition of maraging steel-Fig10On the role of the powder stream on the heat and fluid flow conditions during Directed Energy Deposition of maraging steel-Fig11
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.
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.
(1)
(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:
(3)where CDIS1, CDIS2, and CDIS3 are dimensionless parameters and the user can modify them. The diffusion of dissipation, Diff ɛ, is
(4)where u, v 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
(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:
(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
(7)
(8)
(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.
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).
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.
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)
d0
q (m3s−1)
dc/h (–)
1
50
18.6
0.06
0.045
0.1
2.6
2
50
18.6
0.06
0.082
0.235
4.6
3
50
30.0
0.06
0.045
0.1
2.6
4
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).
Figure3 The 3D computational domain model (50–18.6) slope change, and boundary condition for (50–30 slope change) model.
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.
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.
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.
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 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.
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.
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.
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.
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.
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.
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.
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.
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
processFig. 2 3D computational domain used for single-track
simulationFig. 3 Temperature-dependent material properties of Ti-6Al-4V
Fig. 4 Powder and substrate melting during laser applicationFig. 5 Melt region formed after complete melting and
solidificationFig. 6 Melt pool boundary comparison between the experiment
[25] and the simulation
Fig. 7 Equilibrium points during the formation of vapor column
[27]Fig. 8 Multiple reflection vectors from the keyhole wallFig. 9 (a) Velocity field, keyhole profile, and breakage of the
keyhole to form bubble and (b) 2D temperature and velocity
field along the longitudinal sectionFig. 10 Fluid flow in the transverse direction during keyhole
meltingFig. 11 Melt pool boundary compared with the experiment [21]
for 195 W laser power and 400 mm/s scan speedFig. 12 Melt region formed after complete melting and
solidificationFig. 13 2D images of the pores formed at the beginning of the
single track and their 3D-rendered morphologyFig. 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/sFig. 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/sFig. 18 Melt region with different level of power with LED of
0.4 J/mm
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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.
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.
![Fig. 1. (a) Dimensions of the casting with runners (unit: mm), (b) a melt flow simulation using Flow-3D software together with Reilly's model[44], predicted that a large amount of bifilms (denoted by the black particles) would be contained in the final casting. (c) A solidification simulation using Pro-cast software showed that no shrinkage defect was contained in the final casting.](https://flow3d.co.kr/wp-content/uploads/Fig.-1.-a-Dimensions-of-the-casting-with-runners.png)
![Fig. 1. (a) Dimensions of the casting with runners (unit: mm), (b) a melt flow simulation using Flow-3D software together with Reilly's model[44], predicted that a large amount of bifilms (denoted by the black particles) would be contained in the final casting. (c) A solidification simulation using Pro-cast software showed that no shrinkage defect was contained in the final casting.](https://ars.els-cdn.com/content/image/1-s2.0-S2213956721001791-gr1_lrg.jpg)
![Figure 1.1: Schematic Overview of Metal Laser Powder Bed Fusion Process [2]](https://flow3d.co.kr/wp-content/uploads/Figure-1.1-Schematic-Overview-of-Metal-Laser-Powder-Bed-Fusion-Process-2.png)
![Figure 11. A comparison among experiments [49], CFD and analytical simulations for deep keyhole top width and bottom width](https://flow3d.co.kr/wp-content/uploads/Figure-11.-A-comparison-among-experiments-49-CFD-and-analytical-simulations-for-deep-keyhole-top-width-and-bottom-width.png)
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.
Model, the Two-Equation Renormalization-Group (RNG) Model and large Eddy Simulation Model (
it solves an additional transport equation:
, 
, 
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
: 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:
: the turbulent length scale.
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.
![Fig. 6 Melt pool boundary comparison between the experiment [25] and the simulation](https://www.flow3d.co.kr/wp-content/uploads/Fig.-6-Melt-pool-boundary-comparison-between-the-experiment-25-and-the-simulation.png)
![Fig. 7 Equilibrium points during the formation of vapor column [27]](https://www.flow3d.co.kr/wp-content/uploads/Fig.-7-Equilibrium-points-during-the-formation-of-vapor-column-27.png)
![Fig. 11 Melt pool boundary compared with the experiment [21] for 195 W laser power and 400 mm/s scan speed](https://www.flow3d.co.kr/wp-content/uploads/s-scan-speed.png)
![Fig. 14 Pore number and volume from a different level of power with LED = 0.4 J/mm [29]](https://www.flow3d.co.kr/wp-content/uploads/mm-29.png)
![Fig. 16 Intensity dependence in the relationship between vapor column and evaporation pressure [27]](https://www.flow3d.co.kr/wp-content/uploads/Fig.-16-Intensity-dependence-in-the-relationship-between-vapor-column-and-evaporation-pressure-27.png)
