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
Based on multiple parallel short molecular dynamics simulation trajectories, we designed the reweighted ensem- ble dynamics （RED） method to more efficiently sample complex （biopolymer） systems, and to explore thei...Based on multiple parallel short molecular dynamics simulation trajectories, we designed the reweighted ensem- ble dynamics （RED） method to more efficiently sample complex （biopolymer） systems, and to explore their hierarchical metastable states. Here we further present an improvement to depress statistical errors of the RED and we discuss a few keys in practical application of the RED, provide schemes on selection of basis functions, and determination of the free parameter in the RED. We illustrate the application of the improvements in two toy models and in the solvated alanine dipeptide. The results show the RED enables us to capture the topology of multiple-state transition networks, to detect the diffusion-like dynamical behavior in an entropy-dominated system, and to identify solvent effects in the solvated peptides. The illustrations serve as general applications of the RED in more complex biopolymer systems.展开更多
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
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
In recent years,convolutional neural networks(CNNs)have achieved great success in image classification.However,CNN models usually have complex network structures that tend to cause some related problems,such as redund...In recent years,convolutional neural networks(CNNs)have achieved great success in image classification.However,CNN models usually have complex network structures that tend to cause some related problems,such as redundancy of network parameters,low training efficiency,overfitting,and weak generalization ability.To solve these problems and improve the accuracy of flower classification,the advantages of CNNs were combined with those of ensemble learning and a method was developed for the dynamic ensemble selection of CNNs.First,MobileNet models pre-trained on a public dataset were transferred to flower datasets to train thirteen different MobileNet classifiers,and a resampling strategy was used to enhance the diversity of individual models.Second,the thirteen classifiers were sorted by a classifier sorting algorithm,before ensemble selection,to avoid an exhaustive search.Finally,with the credibility of recognition results,a classifier subset was dynamically selected and integrated to identify the flower species from their images.To verify the effectiveness,the proposed method was used to classify the images of five flower species.The accuracy of the proposed method was 95.50%,an improvement of 1.62%,3.94%,22.04%,13.77%,and 0.44%,over those of MobileNet,Inception-v1,ResNet-50,Inception-ResNet-v2,and the linear ensemble method,respectively.In addition,the performance of the proposed method was compared with five other methods for flower classification.The experimental results demonstrated the accuracy and robustness of the proposed method.展开更多
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
基金supported by the National Natural Science Foundation of China (90716008)the MOST under 973 project (2009CB724100)
文摘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.
基金Project supported by the National Natural Science Foundation of China(Grant No.11175250)
文摘Based on multiple parallel short molecular dynamics simulation trajectories, we designed the reweighted ensem- ble dynamics （RED） method to more efficiently sample complex （biopolymer） systems, and to explore their hierarchical metastable states. Here we further present an improvement to depress statistical errors of the RED and we discuss a few keys in practical application of the RED, provide schemes on selection of basis functions, and determination of the free parameter in the RED. We illustrate the application of the improvements in two toy models and in the solvated alanine dipeptide. The results show the RED enables us to capture the topology of multiple-state transition networks, to detect the diffusion-like dynamical behavior in an entropy-dominated system, and to identify solvent effects in the solvated peptides. The illustrations serve as general applications of the RED in more complex biopolymer systems.
基金the National Numerical Wind Tunnel(No.NNW2019ZT1-A03)the National Natural Science Foundation of China(Nos.91952201,11372008,and 11452002)。
文摘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.
基金supported by the National Natural Science Foundation of China(90716008)the National Basic Research Program of China(2009CB724100).
文摘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.
基金the National Key R&D Program of China(Grant No.2019YFD1101100)the National Natural Science Foundation of China(Grant No.61403035)the Science&Technology Innovation Ability Construction Project of Beijing Academy of Agriculture and Forestry Science(Grant No.KJCX20211003)。
文摘In recent years,convolutional neural networks(CNNs)have achieved great success in image classification.However,CNN models usually have complex network structures that tend to cause some related problems,such as redundancy of network parameters,low training efficiency,overfitting,and weak generalization ability.To solve these problems and improve the accuracy of flower classification,the advantages of CNNs were combined with those of ensemble learning and a method was developed for the dynamic ensemble selection of CNNs.First,MobileNet models pre-trained on a public dataset were transferred to flower datasets to train thirteen different MobileNet classifiers,and a resampling strategy was used to enhance the diversity of individual models.Second,the thirteen classifiers were sorted by a classifier sorting algorithm,before ensemble selection,to avoid an exhaustive search.Finally,with the credibility of recognition results,a classifier subset was dynamically selected and integrated to identify the flower species from their images.To verify the effectiveness,the proposed method was used to classify the images of five flower species.The accuracy of the proposed method was 95.50%,an improvement of 1.62%,3.94%,22.04%,13.77%,and 0.44%,over those of MobileNet,Inception-v1,ResNet-50,Inception-ResNet-v2,and the linear ensemble method,respectively.In addition,the performance of the proposed method was compared with five other methods for flower classification.The experimental results demonstrated the accuracy and robustness of the proposed method.
文摘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.
