Fully connected neural networks(FCNNs)have been developed for the closure of subgrid-scale(SGS)stress and SGS heat flux in large-eddy simulations of compressible turbulent channel flow.The FCNNbased SGS model trained ...Fully connected neural networks(FCNNs)have been developed for the closure of subgrid-scale(SGS)stress and SGS heat flux in large-eddy simulations of compressible turbulent channel flow.The FCNNbased SGS model trained using data with Mach number Ma=3.0 and Reynolds number Re=3000 was applied to situations with different Mach numbers and Reynolds numbers.The input variables of the neural network model were the filtered velocity gradients and temperature gradients at a single spatial grid point.The a priori test showed that the FCNN model had a correlation coefficient larger than 0.91 and a relative error smaller than 0.43,with much better reconstructions of SGS unclosed terms than the dynamic Smagorinsky model(DSM).In a posteriori test,the behavior of the FCNN model was marginally better than that of the DSM in predicting the mean velocity profiles,mean temperature profiles,turbulent intensities,total Reynolds stress,total Reynolds heat flux,and mean SGS flux of kinetic energy,and outperformed the Smagorinsky model.展开更多
The incompressible models for the pressure-strain correlation are unable to correctly predict the turbulence flows evolving with significant compressibility. Huang and Fu use a damping function of the turbulent Mach n...The incompressible models for the pressure-strain correlation are unable to correctly predict the turbulence flows evolving with significant compressibility. Huang and Fu use a damping function of the turbulent Mach number to modify two numerical coefficients of the incompressible model for the pressure strain developed by Launder, Reece and Rodi. This model predicts the spreading rate and the shear stress behavior in compressible turbulent mixing well. However, the model does not show the well-known compressibility effects on the compressible homogenous shear flow. In the present work, the model of Huang-Fu is revised, all resulting model coefficients become dependent on the turbulent Mach number, the gradient Mach number and the convective Mach number. The proposed model is tested in different compressible turbulent homogeneous shear flow and mixing layers cases. In general, the predicted results from the proposed model are in an acceptable agreement with DNS and experiment data.展开更多
A numerical simulation of shock wave turbulent boundary layer interaction induced by a 24° compression corner based on Gao-Yong compressible turbulence model was presented.The convection terms and the diffusion t...A numerical simulation of shock wave turbulent boundary layer interaction induced by a 24° compression corner based on Gao-Yong compressible turbulence model was presented.The convection terms and the diffusion terms were calculated using the second-order AUSM(advection upstream splitting method) scheme and the second-order central difference scheme,respectively.The Runge-Kutta time marching method was employed to solve the governing equations for steady state solutions.Significant flow separation-region which indicates highly non-isotropic turbulence structure has been found in the present work due to intensity interaction under the 24° compression corner.Comparisons between the calculated results and experimental data have been carried out,including surface pressure distribution,boundary-layer static pressure profiles and mean velocity profiles.The numerical results agree well with the experimental values,which indicate Gao-Yong compressible turbulence model is suitable for the prediction of shock wave turbulent boundary layer interaction in two-dimensional compression corner flows.展开更多
This work is to study a role of the fluctuating density gradient in the compressible flows tbr the computational fluid dynamics （CFD）. A new anisotropy tensor with the fluctuating density gradient is introduced, and...This work is to study a role of the fluctuating density gradient in the compressible flows tbr the computational fluid dynamics （CFD）. A new anisotropy tensor with the fluctuating density gradient is introduced, and is used for an invariant modeling technique to model the turbulent density gradient correlation equation derived from the continuity equation. The modeling equation is decomposed into three groups proportional to the mean velocity, proportional to the mean strain rate, and proportional to the mean density. The characteristics of the correlation in a wake are extracted from the results by the two dimensional direct simulation, and shows the strong correlation with the vortices in the wake near the body. Thus, it can be concluded that the correlation of the density gradient is a significant parameter to describe the quick generation of the turbulent property in the compressible flows.展开更多
The modeling of turbulence,especially the high-speed compressible turbulence encountered in aerospace engineering,has always being a significant challenge in terms of balancing efficiency and accuracy.Most traditional...The modeling of turbulence,especially the high-speed compressible turbulence encountered in aerospace engineering,has always being a significant challenge in terms of balancing efficiency and accuracy.Most traditional models typically show limitations in universality,accuracy,and reliance on past experience.The stochastic multi-scale models show great potential in addressing these issues by representing turbulence across all characteristic scales in a reduced-dimensional space,maintaining sufficient accuracy while reducing computational cost.This review systematically summarizes advances in methods related to a widely used and refined stochastic multi-scale model,the One-Dimensional Turbulence(ODT).The advancements in formulations are emphasized for stand-alone incompressible ODT models,stand-alone compressible ODT models,and coupling methods.Some diagrams are also provided to facilitate more readers to understand the ODT methods.Subsequently,the significant developments and applications of stand-alone ODT models and coupling methods are introduced and critically evaluated.Despite the extensively recognized effectiveness of ODT models in low-speed turbulent flows,it is crucial to emphasize that there is still a research gap in the field of ODT coupling methods that are capable of accurately and efficiently simulating complex,three-dimensional,high-speed compressible turbulent flows up to now.Based on an analysis of the advantages and limitations of existing ODT methods,the recent advancement in the conservative compressible ODT model is considered to have provided a promising approach to tackle the modeling challenges of high-speed compressible turbulence.Therefore,this review outlines several recommended new research subjects and challenging issues to inspire further research in simulating complex,three-dimensional,high-speed compressible turbulent flows using ODT models.展开更多
We establish a deconvolutional artificial-neural-network(D-ANN)approach in large-eddy simulation(LES)of compressible turbulent flow.Filtered variables in the neighboring locations are taken as the inputs of D-ANN to r...We establish a deconvolutional artificial-neural-network(D-ANN)approach in large-eddy simulation(LES)of compressible turbulent flow.Filtered variables in the neighboring locations are taken as the inputs of D-ANN to recover original(unfiltered)variables,including density,momentum and pressure.The scale-similarity form is adopted to reconstruct subfilter-scale(SFS)terms.The proposed D-ANN models can give better a priori predictions of the sub-filter stress and heat flux than the classical approximate-deconvolution method(ADM)and the velocity-gradient model(VGM).The predicted SFS terms with the D-ANN models have correlation coefficients larger than 98.4%and relative errors smaller than 18%.In the a posteriori analysis,the D-ANN model compares against the implicit LES(ILES),the dynamic-Smagorinsky model(DSM),and the dynamic-mixed model(DMM).The D-ANN model predicts better than these classical models for velocity spectra,statistical properties of SFS kinetic energy flux and velocity increments.The turbulence statistics and transient velocity divergence are also accurately reconstructed.The type of explicit filter and the impact of compressibility do not significantly affect a posteriori accuracy of the D-ANN model.Results showthat the proposed D-ANN approach has a great potential in developing highly accurate SFS models for large-eddy simulation of complex compressible turbulent flow.展开更多
The Spalart-Allmaras （S-A） turbulence model, the shear-stress transport （SST） turbulence model and their compressibility corrections are revaluated for hypersonic compression comer flows by using high-order differ...The Spalart-Allmaras （S-A） turbulence model, the shear-stress transport （SST） turbulence model and their compressibility corrections are revaluated for hypersonic compression comer flows by using high-order difference schemes. The compressibility effect of density gradient, pressure dilatation and turbulent Mach number is accounted. In order to reduce confusions between model uncertainties and discretization errors, the formally fifth-order explicit weighted compact nonlinear scheme （WCNS-E-5） is adopted for convection terms, and a fourth-order staggered central difference scheme is applied for viscous terms. The 15° and 34° compression comers at Mach number 9.22 are investigated. Numerical results show that the original SST model is superior to the original S-A model in the resolution of separated regions and predictions of wall pressures and wall heat-flux rates. The capability of the S-A model can be largely improved by blending Catris＇ and Shur＇s compressibility corrections. Among the three corrections of the SST model listed in the present paper, Catris＇ modification brings the best results. However, the dissipation and pressure dilatation corrections result in much larger separated regions than that of the experiment, and are much worse than the original SST model as well as the other two corrections. The correction of turbulent Mach number makes the separated region slightly smaller than that of the original SST model. Some results of low-order schemes are also presented. When compared to the results of the high-order schemes, the separated regions are smaller, and the peak wall pressures and peak heat-flux rates are lower in the region of the reattachment points.展开更多
A new compressibility modification k-ε model,including shock unsteadiness effect and the previous compressibility modification of pressure dilatation and dilatational dissipation rate,was developed with a simple form...A new compressibility modification k-ε model,including shock unsteadiness effect and the previous compressibility modification of pressure dilatation and dilatational dissipation rate,was developed with a simple formulation for numerical simulation in supersonic complex turbulent flows.The shock unsteadiness effect was modeled by inhibiting turbulent kinetic energy production in the governing equations of turbulent kinetic energy and the turbulent kinetic energy dissipation rate.Sarkar's correction models were employed accounting for the dilatational compressibility effects in the new model.Two types of flows,the free supersonic mixing layers and complex supersonic flow with transverse injection were simulated with different flow conditions.Comparisons with experimental data of the free supersonic mixing layers showed that the new compressibility modification k-ε model significantly inhibited the excessive growth of turbulent kinetic energy and improved predictions.On the supersonic mixing layer flows,prediction results with the new model were in close agreement with experimental data,accurately predicting the decreasing trend of the mixing layer spreading rate with the increase of the convective Mach number.Due to the complicated flow field with flow separation,shock unsteadiness modification inhibited excessive growth of the turbulent kinetic energy in shock regions and wider shock regions are predicted,thereby significantly improving results of the flow with a strong separation forecast.The flow separation was stronger,which was the primary modification effect of the new model.Predictions accord with experimental results even in strong separation flows.展开更多
A finite-difference Total Variation Diminishing （TVD） numerical simulation model for coupling the Reynolds Averaged Navier-Stokes （RANS） equations, pressure-relative continuity equation and various k-εturbulence ...A finite-difference Total Variation Diminishing （TVD） numerical simulation model for coupling the Reynolds Averaged Navier-Stokes （RANS） equations, pressure-relative continuity equation and various k-εturbulence models was developed to solve the incompressible flow based on the pseudo-compressibility method. The hyperbolicity of all these equations was studied and the discretization of the fully coupling equations with all the primal variables and source terms were made in this article. Numerical simulation for modeling the flow around a ground-mounted square rib was implemented and validated by comparing with the published wind tunnel experimental data. It is shown that such a numerical simulation method with a proper turbulence model has a very good accuracy to simulate the flow around a surface-mounted rib. It is concluded that the Renormalization Group （RNG） and Chen-Kim k-εturbulence models have much better ability to predict the characteristics of the vortex structure and flow separation than the standard k-εmodel.展开更多
This paper concerns the theoretical and experimental modelling of the flat wall,highly heated,compressible turbulent boundary layer.Its final objective is to develop a numerical Navier-Stokes solver and to conclude on...This paper concerns the theoretical and experimental modelling of the flat wall,highly heated,compressible turbulent boundary layer.Its final objective is to develop a numerical Navier-Stokes solver and to conclude on its capability to correctly represent complex aerothermic viscous flows near the wall.The paper presents a constructed numerical method with particular attention given to the turbulence modelling at low Reynolds number and comparisons with supersonic and transonic experimental data.For the transonic experiment,very high wall temperature(Tw=1100K)is realized.The method of this difficult experimental set up is discussed.The comparison between experimental and computational data conducts to the first conclusion and gives some indications for the future work.展开更多
基金Financial support provided by the National Natural Science Foundation of China(Grant Nos.11702042 and 91952104)。
文摘Fully connected neural networks(FCNNs)have been developed for the closure of subgrid-scale(SGS)stress and SGS heat flux in large-eddy simulations of compressible turbulent channel flow.The FCNNbased SGS model trained using data with Mach number Ma=3.0 and Reynolds number Re=3000 was applied to situations with different Mach numbers and Reynolds numbers.The input variables of the neural network model were the filtered velocity gradients and temperature gradients at a single spatial grid point.The a priori test showed that the FCNN model had a correlation coefficient larger than 0.91 and a relative error smaller than 0.43,with much better reconstructions of SGS unclosed terms than the dynamic Smagorinsky model(DSM).In a posteriori test,the behavior of the FCNN model was marginally better than that of the DSM in predicting the mean velocity profiles,mean temperature profiles,turbulent intensities,total Reynolds stress,total Reynolds heat flux,and mean SGS flux of kinetic energy,and outperformed the Smagorinsky model.
文摘The incompressible models for the pressure-strain correlation are unable to correctly predict the turbulence flows evolving with significant compressibility. Huang and Fu use a damping function of the turbulent Mach number to modify two numerical coefficients of the incompressible model for the pressure strain developed by Launder, Reece and Rodi. This model predicts the spreading rate and the shear stress behavior in compressible turbulent mixing well. However, the model does not show the well-known compressibility effects on the compressible homogenous shear flow. In the present work, the model of Huang-Fu is revised, all resulting model coefficients become dependent on the turbulent Mach number, the gradient Mach number and the convective Mach number. The proposed model is tested in different compressible turbulent homogeneous shear flow and mixing layers cases. In general, the predicted results from the proposed model are in an acceptable agreement with DNS and experiment data.
文摘A numerical simulation of shock wave turbulent boundary layer interaction induced by a 24° compression corner based on Gao-Yong compressible turbulence model was presented.The convection terms and the diffusion terms were calculated using the second-order AUSM(advection upstream splitting method) scheme and the second-order central difference scheme,respectively.The Runge-Kutta time marching method was employed to solve the governing equations for steady state solutions.Significant flow separation-region which indicates highly non-isotropic turbulence structure has been found in the present work due to intensity interaction under the 24° compression corner.Comparisons between the calculated results and experimental data have been carried out,including surface pressure distribution,boundary-layer static pressure profiles and mean velocity profiles.The numerical results agree well with the experimental values,which indicate Gao-Yong compressible turbulence model is suitable for the prediction of shock wave turbulent boundary layer interaction in two-dimensional compression corner flows.
文摘This work is to study a role of the fluctuating density gradient in the compressible flows tbr the computational fluid dynamics （CFD）. A new anisotropy tensor with the fluctuating density gradient is introduced, and is used for an invariant modeling technique to model the turbulent density gradient correlation equation derived from the continuity equation. The modeling equation is decomposed into three groups proportional to the mean velocity, proportional to the mean strain rate, and proportional to the mean density. The characteristics of the correlation in a wake are extracted from the results by the two dimensional direct simulation, and shows the strong correlation with the vortices in the wake near the body. Thus, it can be concluded that the correlation of the density gradient is a significant parameter to describe the quick generation of the turbulent property in the compressible flows.
基金cosupported by the National Natural Science Foundation of China(No.12202487)。
文摘The modeling of turbulence,especially the high-speed compressible turbulence encountered in aerospace engineering,has always being a significant challenge in terms of balancing efficiency and accuracy.Most traditional models typically show limitations in universality,accuracy,and reliance on past experience.The stochastic multi-scale models show great potential in addressing these issues by representing turbulence across all characteristic scales in a reduced-dimensional space,maintaining sufficient accuracy while reducing computational cost.This review systematically summarizes advances in methods related to a widely used and refined stochastic multi-scale model,the One-Dimensional Turbulence(ODT).The advancements in formulations are emphasized for stand-alone incompressible ODT models,stand-alone compressible ODT models,and coupling methods.Some diagrams are also provided to facilitate more readers to understand the ODT methods.Subsequently,the significant developments and applications of stand-alone ODT models and coupling methods are introduced and critically evaluated.Despite the extensively recognized effectiveness of ODT models in low-speed turbulent flows,it is crucial to emphasize that there is still a research gap in the field of ODT coupling methods that are capable of accurately and efficiently simulating complex,three-dimensional,high-speed compressible turbulent flows up to now.Based on an analysis of the advantages and limitations of existing ODT methods,the recent advancement in the conservative compressible ODT model is considered to have provided a promising approach to tackle the modeling challenges of high-speed compressible turbulence.Therefore,this review outlines several recommended new research subjects and challenging issues to inspire further research in simulating complex,three-dimensional,high-speed compressible turbulent flows using ODT models.
基金This research was supported by the National Nat542 ural Science Foundation of China(Grants 91952104,92052301 and 91752201).
文摘We establish a deconvolutional artificial-neural-network(D-ANN)approach in large-eddy simulation(LES)of compressible turbulent flow.Filtered variables in the neighboring locations are taken as the inputs of D-ANN to recover original(unfiltered)variables,including density,momentum and pressure.The scale-similarity form is adopted to reconstruct subfilter-scale(SFS)terms.The proposed D-ANN models can give better a priori predictions of the sub-filter stress and heat flux than the classical approximate-deconvolution method(ADM)and the velocity-gradient model(VGM).The predicted SFS terms with the D-ANN models have correlation coefficients larger than 98.4%and relative errors smaller than 18%.In the a posteriori analysis,the D-ANN model compares against the implicit LES(ILES),the dynamic-Smagorinsky model(DSM),and the dynamic-mixed model(DMM).The D-ANN model predicts better than these classical models for velocity spectra,statistical properties of SFS kinetic energy flux and velocity increments.The turbulence statistics and transient velocity divergence are also accurately reconstructed.The type of explicit filter and the impact of compressibility do not significantly affect a posteriori accuracy of the D-ANN model.Results showthat the proposed D-ANN approach has a great potential in developing highly accurate SFS models for large-eddy simulation of complex compressible turbulent flow.
基金Foundation items： National Basic Research Program of China （2009CB723801） National Natural Science Foundation of China （11072259）
文摘The Spalart-Allmaras （S-A） turbulence model, the shear-stress transport （SST） turbulence model and their compressibility corrections are revaluated for hypersonic compression comer flows by using high-order difference schemes. The compressibility effect of density gradient, pressure dilatation and turbulent Mach number is accounted. In order to reduce confusions between model uncertainties and discretization errors, the formally fifth-order explicit weighted compact nonlinear scheme （WCNS-E-5） is adopted for convection terms, and a fourth-order staggered central difference scheme is applied for viscous terms. The 15° and 34° compression comers at Mach number 9.22 are investigated. Numerical results show that the original SST model is superior to the original S-A model in the resolution of separated regions and predictions of wall pressures and wall heat-flux rates. The capability of the S-A model can be largely improved by blending Catris＇ and Shur＇s compressibility corrections. Among the three corrections of the SST model listed in the present paper, Catris＇ modification brings the best results. However, the dissipation and pressure dilatation corrections result in much larger separated regions than that of the experiment, and are much worse than the original SST model as well as the other two corrections. The correction of turbulent Mach number makes the separated region slightly smaller than that of the original SST model. Some results of low-order schemes are also presented. When compared to the results of the high-order schemes, the separated regions are smaller, and the peak wall pressures and peak heat-flux rates are lower in the region of the reattachment points.
基金Supported by the National Natural Science Foundation of China (Grant No.50776085)
文摘A new compressibility modification k-ε model,including shock unsteadiness effect and the previous compressibility modification of pressure dilatation and dilatational dissipation rate,was developed with a simple formulation for numerical simulation in supersonic complex turbulent flows.The shock unsteadiness effect was modeled by inhibiting turbulent kinetic energy production in the governing equations of turbulent kinetic energy and the turbulent kinetic energy dissipation rate.Sarkar's correction models were employed accounting for the dilatational compressibility effects in the new model.Two types of flows,the free supersonic mixing layers and complex supersonic flow with transverse injection were simulated with different flow conditions.Comparisons with experimental data of the free supersonic mixing layers showed that the new compressibility modification k-ε model significantly inhibited the excessive growth of turbulent kinetic energy and improved predictions.On the supersonic mixing layer flows,prediction results with the new model were in close agreement with experimental data,accurately predicting the decreasing trend of the mixing layer spreading rate with the increase of the convective Mach number.Due to the complicated flow field with flow separation,shock unsteadiness modification inhibited excessive growth of the turbulent kinetic energy in shock regions and wider shock regions are predicted,thereby significantly improving results of the flow with a strong separation forecast.The flow separation was stronger,which was the primary modification effect of the new model.Predictions accord with experimental results even in strong separation flows.
文摘A finite-difference Total Variation Diminishing （TVD） numerical simulation model for coupling the Reynolds Averaged Navier-Stokes （RANS） equations, pressure-relative continuity equation and various k-εturbulence models was developed to solve the incompressible flow based on the pseudo-compressibility method. The hyperbolicity of all these equations was studied and the discretization of the fully coupling equations with all the primal variables and source terms were made in this article. Numerical simulation for modeling the flow around a ground-mounted square rib was implemented and validated by comparing with the published wind tunnel experimental data. It is shown that such a numerical simulation method with a proper turbulence model has a very good accuracy to simulate the flow around a surface-mounted rib. It is concluded that the Renormalization Group （RNG） and Chen-Kim k-εturbulence models have much better ability to predict the characteristics of the vortex structure and flow separation than the standard k-εmodel.
基金supported jointly by the Centre National de la Recherche Scientifiquethe Korea Science and Engineering Foundation
文摘This paper concerns the theoretical and experimental modelling of the flat wall,highly heated,compressible turbulent boundary layer.Its final objective is to develop a numerical Navier-Stokes solver and to conclude on its capability to correctly represent complex aerothermic viscous flows near the wall.The paper presents a constructed numerical method with particular attention given to the turbulence modelling at low Reynolds number and comparisons with supersonic and transonic experimental data.For the transonic experiment,very high wall temperature(Tw=1100K)is realized.The method of this difficult experimental set up is discussed.The comparison between experimental and computational data conducts to the first conclusion and gives some indications for the future work.
