Pub Date : 2011-01-24DOI: 10.1088/1468-5248/3/1/013
V. Kalaev, A. Zhmakin, E. Smirnov
We present the results of numerical simulation of three-dimensional unsteady turbulent melt convection duringCzo chralski (CZ) silicon crystal growth. A model combining the large-eddy simulation and Reynolds-averaged approaches has been developed to predict the contribution of unresolved turbulent motion. The model is examined for different growth conditions in an industrial CZ configuration. Data illustrating instantaneous and time-averaged behaviour of the melt are presented and compared with experimental observations. Thermal fluctuations in the melt are analysed with respect to spectral characteristics and compared with the temperature measurements performed by thermocouples and an optical sensor. This article was chosen from selected Proceedings of the Second International Symposium on Turbulence and Shear Flow Phenomena (KTH-Stockholm, 27-29 June 2001) ed E Lindborg, A Johansson, J Eaton, J Humphrey, N Kasagi, M Leschziner and M Sommerfeld.
本文给出了czo chralski (CZ)硅晶体生长过程中三维非定常熔体湍流对流的数值模拟结果。结合大涡模拟和雷诺平均方法建立了一个模型来预测未解湍流运动的贡献。该模型在工业CZ配置的不同生长条件下进行了检验。给出了熔体瞬时和时间平均行为的数据，并与实验观察结果进行了比较。根据光谱特性分析了熔体中的热波动，并与热电偶和光学传感器进行的温度测量进行了比较。本文选自第二届国际湍流和剪切流动现象研讨会论文集(KTH-Stockholm, 2001年6月27-29日)，作者E Lindborg, A Johansson, J Eaton, J Humphrey, N Kasagi, M Leschziner和M Sommerfeld。
{"title":"MODELING OF TURBULENT MELT CONVECTION DURING CZOCHRALSKI BULK CRYSTAL GROWTH","authors":"V. Kalaev, A. Zhmakin, E. Smirnov","doi":"10.1088/1468-5248/3/1/013","DOIUrl":"https://doi.org/10.1088/1468-5248/3/1/013","url":null,"abstract":"We present the results of numerical simulation of three-dimensional unsteady turbulent melt convection duringCzo chralski (CZ) silicon crystal growth. A model combining the large-eddy simulation and Reynolds-averaged approaches has been developed to predict the contribution of unresolved turbulent motion. The model is examined for different growth conditions in an industrial CZ configuration. Data illustrating instantaneous and time-averaged behaviour of the melt are presented and compared with experimental observations. Thermal fluctuations in the melt are analysed with respect to spectral characteristics and compared with the temperature measurements performed by thermocouples and an optical sensor. This article was chosen from selected Proceedings of the Second International Symposium on Turbulence and Shear Flow Phenomena (KTH-Stockholm, 27-29 June 2001) ed E Lindborg, A Johansson, J Eaton, J Humphrey, N Kasagi, M Leschziner and M Sommerfeld.","PeriodicalId":438618,"journal":{"name":"Proceeding of Second Symposium on Turbulence and Shear Flow Phenomena","volume":"95 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2011-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117209280","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2004-04-01DOI: 10.1108/09615530410517977
K. Nikas, H. Iacovides
This study is concerned with the computation of turbulent flow and heat transfer in U‐bends of strong curvature. Following the earlier studies within the authors' group on flows through round‐ended U‐bends, here attention is turned to flows through square‐ended U‐bends. Flows at two Reynolds numbers have been computed, one at 100,000 and the other at 36,000. In the heat transfer analysis, the Prandtl number was either 0.72 (air) or, in a further departure from our earlier studies, 5.9 (water). The turbulence modelling approaches examined, include a two‐layer and a low‐Re k‐e model, a two‐layer and a low‐Re version of the basic differential stress model (DSM) and a more recently developed, realisable version of the differential stress model that is free of wall‐parameters. For the low‐Re effective viscosity model (EVM) and DSMs, an alternative, recently proposed length‐scale correction term, independent of wall distance has also been tested. Even the simplest model employed – two‐layer EVM – reproduces the mean flow development with reasonable accuracy, suggesting that the mean flow development is mainly influenced by mean pressure rather than the turbulence field. The heat transfer parameters, on the other hand, show that only the low‐Re DSMs produce reliable Nusselt number predictions for both Prandtl numbers examined.
{"title":"THE COMPUTATION OF FLOW AND HEAT TRANSFER THROUGH SQUARE-ENDED U-BENDS, USING LOW-REYNOLDS-NUMBER MODELS","authors":"K. Nikas, H. Iacovides","doi":"10.1108/09615530410517977","DOIUrl":"https://doi.org/10.1108/09615530410517977","url":null,"abstract":"This study is concerned with the computation of turbulent flow and heat transfer in U‐bends of strong curvature. Following the earlier studies within the authors' group on flows through round‐ended U‐bends, here attention is turned to flows through square‐ended U‐bends. Flows at two Reynolds numbers have been computed, one at 100,000 and the other at 36,000. In the heat transfer analysis, the Prandtl number was either 0.72 (air) or, in a further departure from our earlier studies, 5.9 (water). The turbulence modelling approaches examined, include a two‐layer and a low‐Re k‐e model, a two‐layer and a low‐Re version of the basic differential stress model (DSM) and a more recently developed, realisable version of the differential stress model that is free of wall‐parameters. For the low‐Re effective viscosity model (EVM) and DSMs, an alternative, recently proposed length‐scale correction term, independent of wall distance has also been tested. Even the simplest model employed – two‐layer EVM – reproduces the mean flow development with reasonable accuracy, suggesting that the mean flow development is mainly influenced by mean pressure rather than the turbulence field. The heat transfer parameters, on the other hand, show that only the low‐Re DSMs produce reliable Nusselt number predictions for both Prandtl numbers examined.","PeriodicalId":438618,"journal":{"name":"Proceeding of Second Symposium on Turbulence and Shear Flow Phenomena","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129006742","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A direct numerical simulation is performed to examine the relationship between wall pressure fluctuations and near-wall streamwise vortices in a spatially developing turbulent boundary layer. It is found that wall pressure fluctuations are closely linked with the upstream quasistreamwise vortices in the buffer region. The maximum correlation occurs with the spanwise displacement from the location of wall pressure fluctuations. The space–time correlation reveals that wall pressure fluctuations lag behind streamwise vorticity in the upstream, while streamwise vorticity lag behind wall pressure fluctuations in the downstream. The contributions of high-amplitude wall pressure event to the turbulent energy production mechanism are examined by the quadrant analysis of Reynolds shear stress.
{"title":"RELATIONSHIP BETWEEN WALL PRESSURE FLUCTUATIONS AND STREAMWISE VORTICITY IN A TURBULENT BOUNDARY LAYER","authors":"Joongnyon Kim, Jung‐Il Choi, H. Sung","doi":"10.1063/1.1429964","DOIUrl":"https://doi.org/10.1063/1.1429964","url":null,"abstract":"A direct numerical simulation is performed to examine the relationship between wall pressure fluctuations and near-wall streamwise vortices in a spatially developing turbulent boundary layer. It is found that wall pressure fluctuations are closely linked with the upstream quasistreamwise vortices in the buffer region. The maximum correlation occurs with the spanwise displacement from the location of wall pressure fluctuations. The space–time correlation reveals that wall pressure fluctuations lag behind streamwise vorticity in the upstream, while streamwise vorticity lag behind wall pressure fluctuations in the downstream. The contributions of high-amplitude wall pressure event to the turbulent energy production mechanism are examined by the quadrant analysis of Reynolds shear stress.","PeriodicalId":438618,"journal":{"name":"Proceeding of Second Symposium on Turbulence and Shear Flow Phenomena","volume":"61 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2002-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115150759","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Statistics of the streamwise velocity component in fully-developed pipe flow are examined for Reynolds numbers in the range 5.5 x 10^4 < Re_D < 5.7 x 10^6. The second moment exhibits two maxima: one in the viscous sublayer is Reynolds-number dependent while the other, near the lower edge of the log region, is also Reynolds-number dependent and follows roughly the peak in Reynolds shear stress. The behaviour of both peaks is consistent with the concept of inactive motion which increases with increasing Reynolds number and decreasing distance from the wall. No simple scaling is apparent, and in particular, so-called "mixed" scaling is no better than wall scaling in the viscous sublayer and is actually worse than wall scaling in the outer region. The second moment is compared with empirical and theoretical scaling laws and some anomalies are apparent. The scaling of spectra using y, R and u_τ is examined. It appears that even at the highest Reynolds number, they exhibit incomplete similarity only: while spectra do collapse with either inner or outer scales for limited ranges of wave number, these ranges do not overlap. Thus similarity may not be described as complete and any apparent k_1^(-1) range does not attract any special significance and does not involve universal constants. It is suggested that this is because of the influence of inactive motion. Spectra also show the presence of very long structures close to the wall.
{"title":"REYNOLDS-NUMBER DEPENDENCE OF STREAMWISE VELOCITY FLUCTUATIONS IN TURBULENT PIPE FLOW","authors":"J. Morrison, W. Jiang, B. McKeon, A. Smits","doi":"10.2514/6.2002-574","DOIUrl":"https://doi.org/10.2514/6.2002-574","url":null,"abstract":"Statistics of the streamwise velocity component in fully-developed pipe flow are examined for Reynolds numbers in the range 5.5 x 10^4 < Re_D < 5.7 x 10^6. The second moment exhibits two maxima: one in the viscous sublayer is Reynolds-number dependent while the other, near the lower edge of the log region, is also Reynolds-number dependent and follows roughly the peak in Reynolds shear stress. The behaviour of both peaks is consistent with the concept of inactive motion which increases with increasing Reynolds number and decreasing distance from the wall. No simple scaling is apparent, and in particular, so-called \"mixed\" scaling is no better than wall scaling in the viscous sublayer and is actually worse than wall scaling in the outer region. The second moment is compared with empirical and theoretical scaling laws \u0000and some anomalies are apparent. The scaling of spectra using y, R and u_τ is examined. It appears that even at the highest Reynolds number, they exhibit \u0000incomplete similarity only: while spectra do collapse with either inner or outer scales for limited ranges of wave number, these ranges do not overlap. Thus similarity may not be described as complete and any apparent k_1^(-1) range does not attract any special significance and does not involve universal constants. It is suggested that this is because of the influence of inactive motion. Spectra also show the presence of very long structures close to the wall.","PeriodicalId":438618,"journal":{"name":"Proceeding of Second Symposium on Turbulence and Shear Flow Phenomena","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2002-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125073247","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2001-10-22DOI: 10.1088/1468-5248/2/1/015
X. Jiang, K. Luo
This paper describes a spatial direct numerical simulation (DNS) of the flow transition of a buoyant diffusion flame established on a rectangular nozzle with an aspect ratio of 2:1. Combustion is represented by a one-step finite-rate Arrhenius chemistry. Without applying external perturbations, large vortical structures develop naturally in the flow field due to buoyancy effects. The vortex dynamics of the rectangular buoyant reacting jet has been analysed. The interaction between density gradients and gravity initiates the flow vorticity in the cross-streamwise directions. The streamwise vorticity is mainly generated by the vortex stretching. Downstream of the reacting jet, a more disorganized flow regime characterized by small scales has been observed, following the breakdown of the large vortical structures due to three-dimensional vortex interactions. Analysis of the energy spectra shows that the spatially developing reacting jet has a tendency of transition to turbulence under the effects of combusti...
{"title":"SPATIAL DNS OF THE FLOW TRANSITION OF A RECTANGULAR BUOYANT REACTING FREE-JET","authors":"X. Jiang, K. Luo","doi":"10.1088/1468-5248/2/1/015","DOIUrl":"https://doi.org/10.1088/1468-5248/2/1/015","url":null,"abstract":"This paper describes a spatial direct numerical simulation (DNS) of the flow transition of a buoyant diffusion flame established on a rectangular nozzle with an aspect ratio of 2:1. Combustion is represented by a one-step finite-rate Arrhenius chemistry. Without applying external perturbations, large vortical structures develop naturally in the flow field due to buoyancy effects. The vortex dynamics of the rectangular buoyant reacting jet has been analysed. The interaction between density gradients and gravity initiates the flow vorticity in the cross-streamwise directions. The streamwise vorticity is mainly generated by the vortex stretching. Downstream of the reacting jet, a more disorganized flow regime characterized by small scales has been observed, following the breakdown of the large vortical structures due to three-dimensional vortex interactions. Analysis of the energy spectra shows that the spatially developing reacting jet has a tendency of transition to turbulence under the effects of combusti...","PeriodicalId":438618,"journal":{"name":"Proceeding of Second Symposium on Turbulence and Shear Flow Phenomena","volume":"502 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116180496","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract : As combustion chamber pressures increase in order to realize higher performance and efficiency in a wide range of propulsion applications, the injected fluid may experience ambient pressures which exceed the critical pressure of the injected propellants. For example, in the cryogenic liquid hydrogen/liquid oxygen Space Shuttle main engine, the thrust chamber pressure is more than 4 times larger then the critical pressure of oxygen. In these applications, the initial temperature of the injected oxygen can initially be below the critical temperature, and then undergo a transition to a supercritical temperature as the oxygen is mixed and burned in the combustion chamber.
{"title":"THE BEHAVIOR OF CRYOGENIC SHEAR LAYERS UNDER SUPERCRITICAL CONDITIONS","authors":"B. Chehroudi, R. Cohn, D. Talley","doi":"10.21236/ada409838","DOIUrl":"https://doi.org/10.21236/ada409838","url":null,"abstract":"Abstract : As combustion chamber pressures increase in order to realize higher performance and efficiency in a wide range of propulsion applications, the injected fluid may experience ambient pressures which exceed the critical pressure of the injected propellants. For example, in the cryogenic liquid hydrogen/liquid oxygen Space Shuttle main engine, the thrust chamber pressure is more than 4 times larger then the critical pressure of oxygen. In these applications, the initial temperature of the injected oxygen can initially be below the critical temperature, and then undergo a transition to a supercritical temperature as the oxygen is mixed and burned in the combustion chamber.","PeriodicalId":438618,"journal":{"name":"Proceeding of Second Symposium on Turbulence and Shear Flow Phenomena","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131376545","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The modeling capabilities of the Lagrangian Averaged Navier-Stokes-α equations (LANS-α) is investigated in statistically stationary three-dimensional homogeneous and isotropic turbulence. The predictive abilities of the LANS-α equations are analyzed by comparison with DNS data. Two different forcing techniques were implemented to model the energetics of the energy containing scales. The resolved flow is examined by comparison of the energy spectra of the LANS-α and the DNS computations; furthermore, the correlation between the vorticity and the eigenvectors of the rate of the resolved strain tensor is studied. We find that the LANS-α equations captures the gross features of the flow while the wave activity below a given scale α is filtered by the non- linear dispersion.
{"title":"NUMERICAL SIMULATIONS OF THE LAGRANGIAN AVERAGED NAVIER-STOKES (LANS-α) EQUATIONS","authors":"K. Mohseni, S. Shkoller, B. Kosović, J. Marsden","doi":"10.2514/6.2001-2645","DOIUrl":"https://doi.org/10.2514/6.2001-2645","url":null,"abstract":"The modeling capabilities of the Lagrangian Averaged Navier-Stokes-α equations (LANS-α) is investigated in statistically stationary three-dimensional \u0000homogeneous and isotropic turbulence. The predictive abilities of the LANS-α equations are analyzed \u0000by comparison with DNS data. Two different forcing \u0000techniques were implemented to model the energetics of the energy containing scales. The resolved flow \u0000is examined by comparison of the energy spectra of \u0000the LANS-α and the DNS computations; furthermore, the correlation between the vorticity and the \u0000eigenvectors of the rate of the resolved strain tensor \u0000is studied. We find that the LANS-α equations captures the gross features of the flow while the wave \u0000activity below a given scale α is filtered by the non- \u0000linear dispersion.","PeriodicalId":438618,"journal":{"name":"Proceeding of Second Symposium on Turbulence and Shear Flow Phenomena","volume":"63 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129693935","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"ADVANCED TURBULENCE MODELLING OF THE FLOW IN A GENERIC WING-BODY JUNCTION","authors":"M. Leschziner, D. Apsley","doi":"10.1615/tsfp2.330","DOIUrl":"https://doi.org/10.1615/tsfp2.330","url":null,"abstract":"","PeriodicalId":438618,"journal":{"name":"Proceeding of Second Symposium on Turbulence and Shear Flow Phenomena","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132214917","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"COMPARING CVS AND LES FILTERING FOR 3D HOMOGENEOUS TURBULENCE","authors":"M. Farge, K. Schneider, G. Pellegrino, A. Wray","doi":"10.1615/tsfp2.1020","DOIUrl":"https://doi.org/10.1615/tsfp2.1020","url":null,"abstract":"","PeriodicalId":438618,"journal":{"name":"Proceeding of Second Symposium on Turbulence and Shear Flow Phenomena","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2000-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116832147","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"H∞ CONTROL OF LINEAR GLOBAL INSTABILITY IN MODELS OF NON-PARALLEL WAKES","authors":"E. Lauga, T. Bewley","doi":"10.1615/tsfp2.1150","DOIUrl":"https://doi.org/10.1615/tsfp2.1150","url":null,"abstract":"","PeriodicalId":438618,"journal":{"name":"Proceeding of Second Symposium on Turbulence and Shear Flow Phenomena","volume":"123 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"120988256","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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