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Structural ensemble dynamics based closure model for wall-bounded turbulent flow 被引量:11
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作者 Zhen-Su She Ning Hu You Wu State Key Laboratory for Turbulence and Complex Systems and Dept Mechanical and Aerospace Engineering,College of Engineering, Peking University,100871 Beijing, China 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2009年第5期731-736,共6页
Wall-bounded turbulent flow involves the development of multi-scale turbulent eddies, as well as a sharply varying boundary layer. Its theoretical descriptions are yet phenomenological. We present here a new framework... Wall-bounded turbulent flow involves the development of multi-scale turbulent eddies, as well as a sharply varying boundary layer. Its theoretical descriptions are yet phenomenological. We present here a new framework called structural ensemble dynamics (SED), which aims at using systematically all relevant statistical properties of turbulent structures for a quantitative description of ensemble means. A new set of closure equations based on the SED approach for a turbulent channel flow is presented. SED order functions are defined, and numerically determined from data of direct numerical simulations (DNS). Computational results show that the new closure model reproduces accurately the solution of the original Navier-Stokes simulation, including the mean velocity profile, the kinetic energy of the streamwise velocity component, and every term in the energy budget equation. It is suggested that the SED-based studies of turbulent structure builds a bridge between the studies of physical mechanisms of turbulence and the development of accurate model equations for engineering predictions. 展开更多
关键词 TURBULENCE Closure equation Channel flow structural ensemble dynamics
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Multi-layer analytic solution for k-ωmodel equations via a symmetry approach
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作者 Fan TANG Weitao BI Zhensu SHE 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI CSCD 2023年第2期289-306,共18页
Despite being one of the oldest and most widely-used turbulence models in engineering computational fluid dynamics(CFD),the k-ωmodel has not been fully understood theoretically because of its high nonlinearity and co... Despite being one of the oldest and most widely-used turbulence models in engineering computational fluid dynamics(CFD),the k-ωmodel has not been fully understood theoretically because of its high nonlinearity and complex model parameter setting.Here,a multi-layer analytic expression is postulated for two lengths(stress and kinetic energy lengths),yielding an analytic solution for the k-ωmodel equations in pipe flow.Approximate local balance equations are analyzed to determine the key parameters in the solution,which are shown to be rather close to the empirically-measured values from the numerical solution of the Wilcox k-ωmodel,and hence the analytic construction is fully validated.The results provide clear evidence that the k-ωmodel sets in it a multilayer structure,which is similar to but different,in some insignificant details,from the Navier-Stokes(N-S)turbulence.This finding explains why the k-ωmodel is so popular,especially in computing the near-wall flow.Finally,the analysis is extended to a newlyrefined k-ωmodel called the structural ensemble dynamics(SED)k-ωmodel,showing that the SED k-ωmodel has improved the multi-layer structure in the outer flow but preserved the setting of the k-ωmodel in the inner region. 展开更多
关键词 turbulence model k-ωmodel structural ensemble dynamics(SED) multilayer structure SYMMETRY
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New perspective in statistical modeling of wall-bounded turbulence 被引量:14
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作者 Zhen-Su She Xi Chen +1 位作者 You Wu Fazle Hussain 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2010年第6期847-861,共15页
Despite dedicated effort for many decades,statistical description of highly technologically important wall turbulence remains a great challenge.Current models are unfortunately incomplete,or empirical,or qualitative.A... Despite dedicated effort for many decades,statistical description of highly technologically important wall turbulence remains a great challenge.Current models are unfortunately incomplete,or empirical,or qualitative.After a review of the existing theories of wall turbulence,we present a new framework,called the structure ensemble dynamics (SED),which aims at integrating the turbulence dynamics into a quantitative description of the mean flow.The SED theory naturally evolves from a statistical physics understanding of non-equilibrium open systems,such as fluid turbulence, for which mean quantities are intimately coupled with the fluctuation dynamics.Starting from the ensemble-averaged Navier-Stokes(EANS) equations,the theory postulates the existence of a finite number of statistical states yielding a multi-layer picture for wall turbulence.Then,it uses order functions(ratios of terms in the mean momentum as well as energy equations) to characterize the states and transitions between states.Application of the SED analysis to an incompressible channel flow and a compressible turbulent boundary layer shows that the order functions successfully reveal the multi-layer structure for wall-bounded turbulence, which arises as a quantitative extension of the traditional view in terms of sub-layer,buffer layer,log layer and wake. Furthermore,an idea of using a set of hyperbolic functions for modeling transitions between layers is proposed for a quantitative model of order functions across the entire flow domain.We conclude that the SED provides a theoretical framework for expressing the yet-unknown effects of fluctuation structures on the mean quantities,and offers new methods to analyze experimental and simulation data.Combined with asymptotic analysis,it also offers a way to evaluate convergence of simulations.The SED approach successfully describes the dynamics at both momentum and energy levels, in contrast with all prevalent approaches describing the mean velocity profile only.Moreover,the SED theoretical framework is general,independent of the flow system to study, while the actual functional form of the order functions may vary from flow to flow.We assert that as the knowledge of order functions is accumulated and as more flows are analyzed, new principles(such as hierarchy,symmetry,group invariance,etc.) governing the role of turbulent structures in the mean flow properties will be clarified and a viable theory of turbulence might emerge. 展开更多
关键词 Wall turbulence Statistical modeling Structure ensemble dynamics Order function MULTI-LAYER
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神经网络增强SED-SL建模应用于翼型绕流湍流计算
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作者 黄文霄 刘溢浪 +2 位作者 毕卫涛 高毅卓 陈军 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2024年第3期72-86,共15页
本文采用SED-SL-RBF的新型建模方法,利用有限NACA机翼的空气动力学数据增强了SED-SL(壁湍流的结构系综动力学-应力长)模型,构建了机翼上湍流边界层的多层结构(MLS),并利用机器学习从实验数据中重建模型参数.该方法应用于九种不同类型的N... 本文采用SED-SL-RBF的新型建模方法,利用有限NACA机翼的空气动力学数据增强了SED-SL(壁湍流的结构系综动力学-应力长)模型,构建了机翼上湍流边界层的多层结构(MLS),并利用机器学习从实验数据中重建模型参数.该方法应用于九种不同类型的NACA机翼上的湍流,具有广泛的雷诺数和攻角范围.研究采用RBF(径向基函数)神经网络重建模型参数(l^(∞)_(0)和y^(∞)_(buf)),并将其应用于SED-SL的CFD数值计算.相较Menter SST湍流模型,SED-SL-RBF模型提升了在同样几何形状和流动条件下升力和阻力系数的预测精度.预测升力系数C_(L)的精确度超过了95%,而预测阻力系数C_(D)的误差则小于6 count.神经网络增强的SED-SL模型对压力场的预测精度也非常高.NACA 2421的MLS参数表现出不随攻角变化的相似性,并可视其为由雷诺数刻画的函数.该结果表明,NACA2421的MLS参数与失速前的攻角大小无关.该相似行为为模拟各种物理条件下的机翼流动提供了一种可行的方案.未来期望整合数据以揭示模型参数方面的模型内在差异,从而将SED-SL-RBF模型的适用性扩展到更广泛的流动场景. 展开更多
关键词 structural ensemble dynamics RANS model Turbulent boundary layer Machine learning Neural network
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Precise drag prediction of airfoil flows by a new algebraic model 被引量:4
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作者 Meng-Juan Xiao Zhen-Su She 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2020年第1期35-43,共9页
We report the results of accurate prediction of lift(C L)and drag(C D)coefficients of two typical airfoil flows(NACA0012 and RAE2822)by a new algebraic turbulence model,in which the eddy viscosity is specified by a st... We report the results of accurate prediction of lift(C L)and drag(C D)coefficients of two typical airfoil flows(NACA0012 and RAE2822)by a new algebraic turbulence model,in which the eddy viscosity is specified by a stress length(SL)function predicted by structural ensemble dynamics(SED)theory.Unprecedented accuracy of the prediction of C D with error of a few counts(one count is 10−4)and of C L with error under 1%-2%are uniformly obtained for varying angles of attack(AoA),indicating an order of magnitude improvement of drag prediction accuracy compared to currently used models(typically around 20 to 30 counts).More interestingly,the SED-SL model is distinguished with fewer parameters of clear physical meaning,which quantify underlying turbulent boundary layer(TBL)with a universal multi-layer structure,and is thus promising to be more easily generalizable to complex TBL.The use of the new model for the calibration of flow condition in experiment and the extraction of flow physics from numerical simulation data of aeronautic flows are discussed. 展开更多
关键词 Lift and drag coefficients Airfoil Flows Stress Length structural ensemble dynamics
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