基于方、矩形环管直接数值模拟结果的各向异性RANS湍流模型构建
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摘要
传统RANS湍流模型大多基于Boussinesq湍流涡粘本构模型,该本构模型是在研究半无限大平板流构型中得到的.然而该模型在向复杂几何构型湍流模拟的推广应用时遇到了极大的挑战,其中一般湍流各向异性运动的普遍性是问题的关键所在.在分析方、矩形环管充分发展湍流直接数值模拟结果的基础上,试图运用张量涡粘系数模型重构出可描述各向异性运动的RANS湍流模型.进而利用重构出的RANS模型对方、矩形环管内充分发展湍流进行计算,通过比较基于张量涡粘RANS模型计算结果与直接数值模拟结果和SSTk-ω模型结果,分别说明了所构建张量涡粘RANS模型的有效性和优越性.
Traditional RANS models were mostly based on Boussinesq's eddy viscosity constitutive model.The model was originally obtained when Boussinesq studied the flow past a semi-infinite flat-plate,and it is facing a great challenge when extending to generic turbulence with more complex geometry.The critical issue in the challenge is how to deal with turbulence's anisotropy that universally exists in almost all the turbulent phenomena.Based on the direct numerical simulation data of fully developed turbulence in square and rectangular annular duct flow,a tensor eddy-viscosity model is proposed to reconstruct the RANS model representing the anisotropy in turbulence.The new RANS model is applied to simulate fully-developed turbulence in square and rectangular annular duct,with its effectiveness and advantage demonstrated by comparing the results based on the new model to the DNS data and SSTk-ω model respectively.
Traditional RANS models were mostly based on Boussinesq's eddy viscosity constitutive model.The model was originally obtained when Boussinesq studied the flow past a semi-infinite flat-plate,and it is facing a great challenge when extending to generic turbulence with more complex geometry.The critical issue in the challenge is how to deal with turbulence's anisotropy that universally exists in almost all the turbulent phenomena.Based on the direct numerical simulation data of fully developed turbulence in square and rectangular annular duct flow,a tensor eddy-viscosity model is proposed to reconstruct the RANS model representing the anisotropy in turbulence.The new RANS model is applied to simulate fully-developed turbulence in square and rectangular annular duct,with its effectiveness and advantage demonstrated by comparing the results based on the new model to the DNS data and SSTk-ω model respectively.
引文
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[3] CHUNG S.Direct numerical simulation of turbulent concentric annular pipe flow Part 1:Flow field[J].International Journal of Heat and Fluid Flow,2002,23(4):426-440.
[4] XU H.Direct numerical simulation of turbulence in a square annular duct[J].Journal of Fluid Mechanics,2009,621:23-57.
[5] BHUSHAN S,BORSE M,WALTERS D K,et al.Analysis of turbulence generation and energy transfer mechanisms in boundary layer transition using direct numerical simulation[C]//ASME 2016 Fluids Engineering Division Summer Meeting Collocated with the ASME 2016 Heat Transfer Summer Conference and the ASME 2016,International Conference on Nanochannels, Microchannels,and Minichannels.2016:V01AT08A006.
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[8]葛铭纬,许春晓,黄伟希,等.基于壁面主动变形的湍流减阻控制研究[J].力学学报,2012,44(4):653-663.
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[11] XE F,SCHMITT O G.About Boussinesq s turbulent viscosity hypothesis:Historical remarks and a direct evaluation of its validity[J].Comptes Rendus Mecanique,2007,335(9):617-627.
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[13]徐弘一.方、矩形环管充分发展湍流Reynolds应力与能量谱直接数值模拟分析:对湍流本构关系的再认识[J].气体物理——理论与应用,2014,9(2):1-20.
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[15] JONES W P,LAUNDER B E.The prediction of laminarization with a two-equation model of turbulence[J].International Journal of Heat&Mass Transfer,1972,15(2):301-314.
[16] MALGE A,PAWAR P.Zonal two equation k-ωturbulence models for aerodynamic flows[J].Journal of Renewable&Sustainable Energy,2015,87(2):123-867.
[17] MENTER F R.Two-equation eddy-viscosity turbulence models for engineering applications[J].AIAA Journal,2012,32(8):1598-1605.
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[19]徐弘一,郭加宏.方型和矩型环管湍流直接数值模拟分析:I.平均流场,对直管道充分发展湍流边界层的再认识[J].中国科学:物理学力学天文学,2013,43(5):634-651.
[20]徐弘一.方,矩形环管湍流直接数值模拟分析:Ⅱ.雷诺应力场与平均能量谱,对传统湍流本构关系的再认识[J].中国科学:物理学力学天文学,2017,47(8):113-129.
[21]王振东,姜楠.湍流新涡粘模式的研究[J].科学通报,1994(13):1183-1186.
[22]王维,管新蕾,姜楠.湍流边界层各向异性张量模式的实验研究[J].实验流体力学,2013,27(5):11-15.
[23]王振东,姜楠.剪切湍流的涡黏张量模式[J].力学学报,1995,27(2):137-142.
[24] CARATI D,CABOT W.Anisotropic eddy viscosity models[R].Stanford,California,USA:Center for Turbulence Research,Stanford University and NASA,1996,22(1):147-148.
[25] NIECKELE A O,THOMPSON R L,MOMPEAN G.Anisotropic Reynolds stress tensor representation in shear flows using DNS and experimental data[J].Journal of Turbulence,2016,17(6):602-632.
[26]汤泓灏.基于直接数值模拟的方形环管湍流模型与近壁速度分析[D].上海:复旦大学,2016.
[27] SPEZIALE C G.On nonlinear kl and k-εmodels of turbulence[J].Journal of Fluid Mechanics,1987,178:459-475.
[28] SPEZIALE C G.Turbulence modeling for time-dependent RANS and VLES:A review[J].AIAA Journal,2012,36(2):173-184.
[29]符松.湍流模式——研究现状与发展趋势[J].应用基础与工程科学学报,1994,2(1):1-15.
[30] KIM J,MOIN P.Application of a fractional-step method to incompressible Navier-Stokes equations[J].Journal of Computational Physics,1985,59(2):308-323.
[31] XU H,YUAN W,KHALID M.Design of a high-performance unsteady Naiver-Stokes solver using a flexiblecycle additive-correction multigrid technique[J].Journal of Computational Physics,2005,209(2):504-540.
[32] LING J,KURZAWSKI A,TEMPLETON J.Reynolds averaged turbulence modelling using deep neural networks with embedded invariance[J].Journal of Fluid Mechanics,2016,807:155-166.
[33] KUTZ J N.Deep learning in fluid dynamics[J].Journal of Fluid Mechanics,2017,814:1-4.
[2] NIKITIN N V.Direct numerical modeling of three-dimensional turbulent flows in pipes of circular cross section[J].Fluid Dynamics,1994,29(6):749-758.
[3] CHUNG S.Direct numerical simulation of turbulent concentric annular pipe flow Part 1:Flow field[J].International Journal of Heat and Fluid Flow,2002,23(4):426-440.
[4] XU H.Direct numerical simulation of turbulence in a square annular duct[J].Journal of Fluid Mechanics,2009,621:23-57.
[5] BHUSHAN S,BORSE M,WALTERS D K,et al.Analysis of turbulence generation and energy transfer mechanisms in boundary layer transition using direct numerical simulation[C]//ASME 2016 Fluids Engineering Division Summer Meeting Collocated with the ASME 2016 Heat Transfer Summer Conference and the ASME 2016,International Conference on Nanochannels, Microchannels,and Minichannels.2016:V01AT08A006.
[6] WANG Y,TANG J,LIU C,et al.DNS study on volume vorticity increase in boundary layer transition[J].Transactions of Nanjing University of Aeronautics and Astronautics,2016,33(3):252-259.
[7] BARKLEY D,SONG B,MUKUND V,et al.The rise of fully turbulent flow[J].Nature,2015,526(7574):550-553.
[8]葛铭纬,许春晓,黄伟希,等.基于壁面主动变形的湍流减阻控制研究[J].力学学报,2012,44(4):653-663.
[9] STROH A.Control of spatially developing turbulent boundary layers for skin friction drag reduction[M].New York,USA:Springer International Publishing,2016.
[10] AHMADI S,ROCCON A,ZONTA F,et al.Turbulent drag reduction in channel flow with viscosity stratified fluids[J].Computers&Fluids,2018,176:260-265.
[11] XE F,SCHMITT O G.About Boussinesq s turbulent viscosity hypothesis:Historical remarks and a direct evaluation of its validity[J].Comptes Rendus Mecanique,2007,335(9):617-627.
[12] KOLMOGOROV A N.Mathematical models of turbulent motion of an incompressible viscous fluid[J].Russian Mathematical Surveys,2007,59(1):3.
[13]徐弘一.方、矩形环管充分发展湍流Reynolds应力与能量谱直接数值模拟分析:对湍流本构关系的再认识[J].气体物理——理论与应用,2014,9(2):1-20.
[14] BARDINA J,HUANG P,COAKLEY T,et al.Turbulence modeling validation[C]//28th Fluid Dynamics Conference.Snowmass Village,CO,USA:AIAA,1997:2121.
[15] JONES W P,LAUNDER B E.The prediction of laminarization with a two-equation model of turbulence[J].International Journal of Heat&Mass Transfer,1972,15(2):301-314.
[16] MALGE A,PAWAR P.Zonal two equation k-ωturbulence models for aerodynamic flows[J].Journal of Renewable&Sustainable Energy,2015,87(2):123-867.
[17] MENTER F R.Two-equation eddy-viscosity turbulence models for engineering applications[J].AIAA Journal,2012,32(8):1598-1605.
[18] MENTER F R,KUNTZ M,LANGTRY R.Ten years of industrial experience with the SST turbulence model[J].Turbulence,Heat and Mass Transfer,2003,4(1):625-632.
[19]徐弘一,郭加宏.方型和矩型环管湍流直接数值模拟分析:I.平均流场,对直管道充分发展湍流边界层的再认识[J].中国科学:物理学力学天文学,2013,43(5):634-651.
[20]徐弘一.方,矩形环管湍流直接数值模拟分析:Ⅱ.雷诺应力场与平均能量谱,对传统湍流本构关系的再认识[J].中国科学:物理学力学天文学,2017,47(8):113-129.
[21]王振东,姜楠.湍流新涡粘模式的研究[J].科学通报,1994(13):1183-1186.
[22]王维,管新蕾,姜楠.湍流边界层各向异性张量模式的实验研究[J].实验流体力学,2013,27(5):11-15.
[23]王振东,姜楠.剪切湍流的涡黏张量模式[J].力学学报,1995,27(2):137-142.
[24] CARATI D,CABOT W.Anisotropic eddy viscosity models[R].Stanford,California,USA:Center for Turbulence Research,Stanford University and NASA,1996,22(1):147-148.
[25] NIECKELE A O,THOMPSON R L,MOMPEAN G.Anisotropic Reynolds stress tensor representation in shear flows using DNS and experimental data[J].Journal of Turbulence,2016,17(6):602-632.
[26]汤泓灏.基于直接数值模拟的方形环管湍流模型与近壁速度分析[D].上海:复旦大学,2016.
[27] SPEZIALE C G.On nonlinear kl and k-εmodels of turbulence[J].Journal of Fluid Mechanics,1987,178:459-475.
[28] SPEZIALE C G.Turbulence modeling for time-dependent RANS and VLES:A review[J].AIAA Journal,2012,36(2):173-184.
[29]符松.湍流模式——研究现状与发展趋势[J].应用基础与工程科学学报,1994,2(1):1-15.
[30] KIM J,MOIN P.Application of a fractional-step method to incompressible Navier-Stokes equations[J].Journal of Computational Physics,1985,59(2):308-323.
[31] XU H,YUAN W,KHALID M.Design of a high-performance unsteady Naiver-Stokes solver using a flexiblecycle additive-correction multigrid technique[J].Journal of Computational Physics,2005,209(2):504-540.
[32] LING J,KURZAWSKI A,TEMPLETON J.Reynolds averaged turbulence modelling using deep neural networks with embedded invariance[J].Journal of Fluid Mechanics,2016,807:155-166.
[33] KUTZ J N.Deep learning in fluid dynamics[J].Journal of Fluid Mechanics,2017,814:1-4.