湍流基于EMMS原理的介尺度建模
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摘要
工程湍流问题中往往存在湍动和非湍动(即层流)区域共存的特点,而传统湍流模型假定计算网格内流体总是处于充分湍流状态,忽视了流动中的层流部分,导致模拟的准确性不足.本文介绍基于能量最小多尺度(Energy Minimization Multi-Scale,EMMS)原理发展介尺度湍流模型,用于提升工程湍流模拟的预测性能;探索湍流中黏性和惯性控制机制通过竞争中的协调形成多尺度结构及稳定性条件;分析模型拓展的物理基础、数学表达及其验证与应用.文章初步认为,水力学中的最小和最大能耗率争论已久,EMMS湍流模型分析两者的基本假设,进而做出统一解释.最后,展望EMMS湍流模型仍需解决的问题以及湍流介尺度方法.
Turbulent flows in engineering are characterized by the coexistence of turbulent and non-turbulent fluids.Nonetheless,in traditional turbulence models,the laminar portion of the fluid flow is often neglected and constitutive laws are expressed to describe fully turbulent states within computational grids.This situation is perceived as a source of inaccuracies in modeling practical engineering flows.In this paper,a meso-scale turbulence model based on the principle of energy-minimization multi-scale model(EMMS) for improving the accuracy of turbulence modeling is presented.Then,the multi-scale structure and stability criterion originated from the compromise in competition between viscous and inertial control coordination mechanisms in turbulent flows are explored,and the physical basis of the model's extension,the mathematical expression,the verification and the application are also analyzed.Furthermore,the contradiction between the hypothesis of minimum energy dissipation rate and that of maximum energy dissipation rate in hydraulics can be interpreted in a unified framework of the EMMS-based turbulence model.Finally,some problems and challenges in the EMMS-based turbulence model and the development of the turbulence-based meso-sciences are also discussed.
Turbulent flows in engineering are characterized by the coexistence of turbulent and non-turbulent fluids.Nonetheless,in traditional turbulence models,the laminar portion of the fluid flow is often neglected and constitutive laws are expressed to describe fully turbulent states within computational grids.This situation is perceived as a source of inaccuracies in modeling practical engineering flows.In this paper,a meso-scale turbulence model based on the principle of energy-minimization multi-scale model(EMMS) for improving the accuracy of turbulence modeling is presented.Then,the multi-scale structure and stability criterion originated from the compromise in competition between viscous and inertial control coordination mechanisms in turbulent flows are explored,and the physical basis of the model's extension,the mathematical expression,the verification and the application are also analyzed.Furthermore,the contradiction between the hypothesis of minimum energy dissipation rate and that of maximum energy dissipation rate in hydraulics can be interpreted in a unified framework of the EMMS-based turbulence model.Finally,some problems and challenges in the EMMS-based turbulence model and the development of the turbulence-based meso-sciences are also discussed.
引文
1 Li J H,Hu Y,Yuan Q,et al.Chemical Engineering in 21st Century(in Chinese).Beijing:Chemical Industry Press,2004[李静海,胡英,袁权,等.展望21世纪的化学工程.北京:化学工业出版社,2004]
2 Li J H.Multi scale-modeling and Method of Energy Minimization for Particle-fluid Two-phase Flow(in Chinses).Dissertation for Doctoral Degree.Beijing:Institute of Chemical Metallurgy,Chinese Academy of Sciences,1987[李静海.两相流多尺度作用模型和能量最小方法.博士学位论文.北京:中国科学院化工冶金研究所,1987]
3 Li J H,Kwauk M.Particle-Fluid Two-Phase Flow:The Energy-Minimization Multi-Scale Method.Beijing:Metallurgical Industry Press,1994
4 Li J H,Ge W,Wang W,et al.From Multiscale Modeling to Meso-Science:A Chemical Engineering Perspective-Principles,Modeling,Simulation,and Application.London:Springer,2013
5 Zhao H.Multi-scale Modeling of Gas-liquid(slurry)Reactors(in Chinese).Dissertation for Doctoral Degree.Beijing:Institute of Process Engineering,Chinese Academy of Sciences,2006[赵辉.气液(浆)反应器的多尺度模拟.博士学位论文.北京:中国科学院过程工程研究所,2006]
6 Yang N,Wu Z,Chen J,et al.Multi-scale analysis of gas-liquid interaction and CFD simulation of gas-liquid flow in bubble columns.Chem Eng Sci,2011,66:3212-3222
7 Li J H,Zhang Z D,Ge W,et al.A simple variational criterion for turbulent flow in pipe.Chem Eng Sci,1999,54:1151-1154
8 Batchelor G K.An Introduction to Fluid Dynamics.Cambridge:Cambridge University Press,1967
9 White F M.Viscous Fluid Flow.New York:McGraw Hill International,1991
10 Li J H,Kwauk M.Exploring complex systems in chemical engineering-the multi-scale methodology.Chem Eng Sci,2003,58:521-535
11 Onsager L.Reciprocal relations in irreversible processes.Ⅰ.Phys Rev,1931,37:405-426
12 Nicolis G,Prigogine I.Self-Organization in Nonequilibrium Systems.New York:Wiley,1977
13 Helmholtz H.Zur theorie der stationaren strome in reibenden flüssigkeiten.In:Verh Des Nathrhist-Med Vereinszu Heidelberg Bd VS(1-7).Charleston:Nabu Press,1868.1:223-224
14 Korteweg D J.On a general theorem of the stability of the motion of a viscous fluid.Philos Mag Ser 5,1883,16:112-118
15 Rayleigh L.On the motion of a viscous fluid.Philos Mag Ser 6,1913,26:776-786
16 Malkus W V R.Outline of a theory of turbulent shear flow.J Fluid Mech,1956,1:521-539
17 Malkus W V R,Smith L M.Upper bounds on functions of the dissipation rate in turbulent shear flow.J Fluid Mech,1989,208:479-507
18 Bertram J.Maximum kinetic energy dissipation and the stability of turbulent Poiseuille flow.J Fluid Mech,2015,767:342-363
19 Wang L M.Discrete Simulation for Single-phase Complex Flows(in Chinese).Dissertation for Doctoral Degree.Beijing:Institute of Process Engineering,Chinese Academy of Sciences,2008[王利民.单相复杂流动的离散模拟.博士学位论文.北京:中国科学院过程工程研究所,2008]
20 Ge W,Chen F,Gao J,et al.Analytical multi-scale method for multi-phase complex systems in process engineering—Bridging reductionism and holism.Chem Eng Sci,2007,62:3346-3377
21 Yang C T,Song C S.Theory of minimum rate of energy dissipation.J Hydraul Div,1979,105:769-784
22 Yang C T,Song C S.Theory of minimum energy and energy dissipation rate.Encyclopedia Fluid Mech,1986,1:353-399
23 Huang W L.The law of maximum rate of energy dissipation on continuum dynamics(in Chinese).J Tsinghua Univ,1981,1:87-96[黄万里.连续介体动力学最大能量消散定律.清华大学学报,1981,1:87-96]
24 Ni J,Zhang R.Extremal hypotheses and their applications on river geometry studies(in Chinese).Hydrol-Sci Eng,1991:307-318[倪晋仁,张仁.河相关系中的极值假说及其应用.水利水运科学研究,1991:307-318]
25 Pope S B.Turbulent Flows.Cambridge:Cambridge University Press,2000
26 Moin P,Mahesh K.Direct numerical simulation:A tool in turbulence research.Annu Rev Fluid Mech,1998,30:539-578
27 Lesieur M,Metais O,Comte P.Large-Eddy Simulations of Turbulence.Cambridge:Cambridge University Press,2005
28 He G W,Rubinstein R,Wang L P.Effects of subgrid-scale modeling on time correlations in large eddy simulation.Phys Fluids,2002,14:2186-2193
29 Fox R O.Large-eddy-simulation tools for multiphase flows.Annu Rev Fluid Mech,2012,44:47-76
30 Spalart P R.Strategies for turbulence modelling and simulations.Int J Heat Fluid Flow,2000,21:252-263
31 Wilcox D C.Turbulence Modeling for CFD.Birmingham:DCW Industries Press,2006
32 Fu S.Progress in the study of nonlinear turbulence mdoelling(in Chinese).Adv Mech,1995,25:318-327[符松.非线性瑞流模式研究及进展.力学进展,1995,25:318-327]
33 Zhou H,Zhang H X.What is the essence of the so-called century lasting difficult problem in classic physics,the“problem of turbulence”?(in Chinese).Sci Sin-Phys Mech Astron,2012,42:445-447[周恒,张涵信.号称经典物理留下的世纪难题“湍流问题”的实质是什么?中国科学:物理学力学天文学,2012,42:445-447]
34 Zhang L,Qiu X P,Wang L M,et al.A stability condition for turbulence model:From EMMS model to EMMS-based turbulence model.Particuology,2014,16:142-154
35 Wang L M,Qiu X P,Zhang L,et al.Turbulence originating from the compromise-in-competition between viscosity and inertia.Chem Eng J,2016,300:83-97
36 Huang Y N,Chen Y S.On the discussion about the“What is essence of so-called century lasting difficult problem in classic physics,the“problem of turbulence”?”(in Chinese).Sci Sin-Phys Mech Astron,2012,42:445-447[黄永念,陈耀松.对《号称经典物理留下的世纪难题“湍流问题”的实质是什么?》一文的讨论.中国科学:物理学力学天文学,2012,42:445-447]
37 Li J H,Hu Y,Yuan Q.Mesoscience:Exploring old problems from a new angle(in Chinese).Sci Sin-Chem,2014,44:277-281[李静海,胡英,袁权.探索介尺度科学:从新角度审视老问题.中国科学:化学,2014,44:277-281]
2 Li J H.Multi scale-modeling and Method of Energy Minimization for Particle-fluid Two-phase Flow(in Chinses).Dissertation for Doctoral Degree.Beijing:Institute of Chemical Metallurgy,Chinese Academy of Sciences,1987[李静海.两相流多尺度作用模型和能量最小方法.博士学位论文.北京:中国科学院化工冶金研究所,1987]
3 Li J H,Kwauk M.Particle-Fluid Two-Phase Flow:The Energy-Minimization Multi-Scale Method.Beijing:Metallurgical Industry Press,1994
4 Li J H,Ge W,Wang W,et al.From Multiscale Modeling to Meso-Science:A Chemical Engineering Perspective-Principles,Modeling,Simulation,and Application.London:Springer,2013
5 Zhao H.Multi-scale Modeling of Gas-liquid(slurry)Reactors(in Chinese).Dissertation for Doctoral Degree.Beijing:Institute of Process Engineering,Chinese Academy of Sciences,2006[赵辉.气液(浆)反应器的多尺度模拟.博士学位论文.北京:中国科学院过程工程研究所,2006]
6 Yang N,Wu Z,Chen J,et al.Multi-scale analysis of gas-liquid interaction and CFD simulation of gas-liquid flow in bubble columns.Chem Eng Sci,2011,66:3212-3222
7 Li J H,Zhang Z D,Ge W,et al.A simple variational criterion for turbulent flow in pipe.Chem Eng Sci,1999,54:1151-1154
8 Batchelor G K.An Introduction to Fluid Dynamics.Cambridge:Cambridge University Press,1967
9 White F M.Viscous Fluid Flow.New York:McGraw Hill International,1991
10 Li J H,Kwauk M.Exploring complex systems in chemical engineering-the multi-scale methodology.Chem Eng Sci,2003,58:521-535
11 Onsager L.Reciprocal relations in irreversible processes.Ⅰ.Phys Rev,1931,37:405-426
12 Nicolis G,Prigogine I.Self-Organization in Nonequilibrium Systems.New York:Wiley,1977
13 Helmholtz H.Zur theorie der stationaren strome in reibenden flüssigkeiten.In:Verh Des Nathrhist-Med Vereinszu Heidelberg Bd VS(1-7).Charleston:Nabu Press,1868.1:223-224
14 Korteweg D J.On a general theorem of the stability of the motion of a viscous fluid.Philos Mag Ser 5,1883,16:112-118
15 Rayleigh L.On the motion of a viscous fluid.Philos Mag Ser 6,1913,26:776-786
16 Malkus W V R.Outline of a theory of turbulent shear flow.J Fluid Mech,1956,1:521-539
17 Malkus W V R,Smith L M.Upper bounds on functions of the dissipation rate in turbulent shear flow.J Fluid Mech,1989,208:479-507
18 Bertram J.Maximum kinetic energy dissipation and the stability of turbulent Poiseuille flow.J Fluid Mech,2015,767:342-363
19 Wang L M.Discrete Simulation for Single-phase Complex Flows(in Chinese).Dissertation for Doctoral Degree.Beijing:Institute of Process Engineering,Chinese Academy of Sciences,2008[王利民.单相复杂流动的离散模拟.博士学位论文.北京:中国科学院过程工程研究所,2008]
20 Ge W,Chen F,Gao J,et al.Analytical multi-scale method for multi-phase complex systems in process engineering—Bridging reductionism and holism.Chem Eng Sci,2007,62:3346-3377
21 Yang C T,Song C S.Theory of minimum rate of energy dissipation.J Hydraul Div,1979,105:769-784
22 Yang C T,Song C S.Theory of minimum energy and energy dissipation rate.Encyclopedia Fluid Mech,1986,1:353-399
23 Huang W L.The law of maximum rate of energy dissipation on continuum dynamics(in Chinese).J Tsinghua Univ,1981,1:87-96[黄万里.连续介体动力学最大能量消散定律.清华大学学报,1981,1:87-96]
24 Ni J,Zhang R.Extremal hypotheses and their applications on river geometry studies(in Chinese).Hydrol-Sci Eng,1991:307-318[倪晋仁,张仁.河相关系中的极值假说及其应用.水利水运科学研究,1991:307-318]
25 Pope S B.Turbulent Flows.Cambridge:Cambridge University Press,2000
26 Moin P,Mahesh K.Direct numerical simulation:A tool in turbulence research.Annu Rev Fluid Mech,1998,30:539-578
27 Lesieur M,Metais O,Comte P.Large-Eddy Simulations of Turbulence.Cambridge:Cambridge University Press,2005
28 He G W,Rubinstein R,Wang L P.Effects of subgrid-scale modeling on time correlations in large eddy simulation.Phys Fluids,2002,14:2186-2193
29 Fox R O.Large-eddy-simulation tools for multiphase flows.Annu Rev Fluid Mech,2012,44:47-76
30 Spalart P R.Strategies for turbulence modelling and simulations.Int J Heat Fluid Flow,2000,21:252-263
31 Wilcox D C.Turbulence Modeling for CFD.Birmingham:DCW Industries Press,2006
32 Fu S.Progress in the study of nonlinear turbulence mdoelling(in Chinese).Adv Mech,1995,25:318-327[符松.非线性瑞流模式研究及进展.力学进展,1995,25:318-327]
33 Zhou H,Zhang H X.What is the essence of the so-called century lasting difficult problem in classic physics,the“problem of turbulence”?(in Chinese).Sci Sin-Phys Mech Astron,2012,42:445-447[周恒,张涵信.号称经典物理留下的世纪难题“湍流问题”的实质是什么?中国科学:物理学力学天文学,2012,42:445-447]
34 Zhang L,Qiu X P,Wang L M,et al.A stability condition for turbulence model:From EMMS model to EMMS-based turbulence model.Particuology,2014,16:142-154
35 Wang L M,Qiu X P,Zhang L,et al.Turbulence originating from the compromise-in-competition between viscosity and inertia.Chem Eng J,2016,300:83-97
36 Huang Y N,Chen Y S.On the discussion about the“What is essence of so-called century lasting difficult problem in classic physics,the“problem of turbulence”?”(in Chinese).Sci Sin-Phys Mech Astron,2012,42:445-447[黄永念,陈耀松.对《号称经典物理留下的世纪难题“湍流问题”的实质是什么?》一文的讨论.中国科学:物理学力学天文学,2012,42:445-447]
37 Li J H,Hu Y,Yuan Q.Mesoscience:Exploring old problems from a new angle(in Chinese).Sci Sin-Chem,2014,44:277-281[李静海,胡英,袁权.探索介尺度科学:从新角度审视老问题.中国科学:化学,2014,44:277-281]