Data-driven turbulence modeling studies have reached such a stage that the basic framework is settled,but several essential issues remain that strongly affect the performance.Two problems are studied in the current re...Data-driven turbulence modeling studies have reached such a stage that the basic framework is settled,but several essential issues remain that strongly affect the performance.Two problems are studied in the current research:(1)the processing of the Reynolds stress tensor and(2)the coupling method between the machine learning model and flow solver.For the Reynolds stress processing issue,we perform the theoretical derivation to extend the relevant tensor arguments of Reynolds stress.Then,the tensor representation theorem is employed to give the complete irreducible invariants and integrity basis.An adaptive regularization term is employed to enhance the representation performance.For the coupling issue,an iterative coupling framework with consistent convergence is proposed and then applied to a canonical separated flow.The results have high consistency with the direct numerical simulation true values,which proves the validity of the current approach.展开更多
In this paper the database obtained from LES is used to examine the algebraicturbulence model in Demuren and Rodi’s work. The results show that the prediction ofnormal Reynolas stresses and turbulence energy by means...In this paper the database obtained from LES is used to examine the algebraicturbulence model in Demuren and Rodi’s work. The results show that the prediction ofnormal Reynolas stresses and turbulence energy by means of turbulence modeling isbetter than that of shear Reynolde stresses. The comparison shows the LES methodcan be used to examine turbulence modelling.展开更多
We present the approaches to implementing the k-√k L turbulence model within the framework of the high-order discontinuous Galerkin(DG)method.We use the DG discretization to solve the full Reynolds-averaged Navier-St...We present the approaches to implementing the k-√k L turbulence model within the framework of the high-order discontinuous Galerkin(DG)method.We use the DG discretization to solve the full Reynolds-averaged Navier-Stokes equations.In order to enhance the robustness of approaches,some effective techniques are designed.The HWENO(Hermite weighted essentially non-oscillatory)limiting strategy is adopted for stabilizing the turbulence model variable k.Modifications have been made to the model equation itself by using the auxiliary variable that is always positive.The 2nd-order derivatives of velocities required in computing the von Karman length scale are evaluated in a way to maintain the compactness of DG methods.Numerical results demonstrate that the approaches have achieved the desirable accuracy for both steady and unsteady turbulent simulations.展开更多
The prediction of interfacial turbulence characteristics is one of the still challenging of two-phase stratified flow.The evaluation of some important parameters such as interfacial heat transfer coefficient based on ...The prediction of interfacial turbulence characteristics is one of the still challenging of two-phase stratified flow.The evaluation of some important parameters such as interfacial heat transfer coefficient based on turbulence kinetic energy and turbulence dissipation rate in some models,intensifies the importance of turbulence flow correct simulation.High gradient of velocity and turbulence kinetic energy at the interface of two-phase stratified flow leads to a major overestimation or underestimation of flow characteristics without any special treatment.Consideration of a source function of turbulence eddy frequency at the interface is one of the common solution employed in past researches.Although this solution remedies some shortcomings of traditional methods in smooth stratified flow,its application in wavy stratified flow needs the other modifications.The examination of turbulence characteristics near the free surface reveals that,in addition to turbulence eddy frequency,the other source function of turbulence kinetic energy should be considered near the free interface.So,a new source function of turbulence kinetic energy is proposed at the interface based on flow condition.This new method has been employed for Fabre et al.(1987)experiment designed for air/water stratified flow.The results of simulation have a good agreement with experimental data and turbulence characteristic can be captured near the free surface.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
Machine learning(ML)techniques have emerged as powerful tools for improving the predictive capabilities of Reynolds-averaged Navier-Stokes(RANS)turbulence models in separated flows.This improvement is achieved by leve...Machine learning(ML)techniques have emerged as powerful tools for improving the predictive capabilities of Reynolds-averaged Navier-Stokes(RANS)turbulence models in separated flows.This improvement is achieved by leveraging complex ML models,such as those developed using field inversion and machine learning(FIML),to dynamically adjust the constants within the baseline RANS model.However,the ML models often overlook the fundamental calibrations of the RANS turbulence model.Consequently,the basic calibration of the baseline RANS model is disrupted,leading to a degradation in the accuracy,particularly in basic wall-attached flows outside of the training set.To address this issue,a modified version of the Spalart-Allmaras(SA)turbulence model,known as Rubber-band SA(RBSA),has been proposed recently.This modification involves identifying and embedding constraints related to basic wall-attached flows directly into the model.It is shown that no matter how the parameters of the RBSA model are adjusted as constants throughout the flow field,its accuracy in wall-attached flows remains unaffected.In this paper,we propose a new constraint for the RBSA model,which better safeguards the law of wall in extreme conditions where the model parameter is adjusted dramatically.The resultant model is called the RBSA-poly model.We then show that when combined with FIML augmentation,the RBSA-poly model effectively preserves the accuracy of simple wall-attached flows,even when the adjusted parameters become functions of local flow variables rather than constants.A comparative analysis with the FIML-augmented original SA model reveals that the augmented RBSA-poly model reduces error in basic wall-attached flows by 50%while maintaining comparable accuracy in trained separated flows.These findings confirm the effectiveness of utilizing FIML in conjunction with the RBSA model,offering superior accuracy retention in cardinal flows.展开更多
Correcting wavefront distortion caused by atmospheric turbulence is crucial for atmospheric optics.To evaluate correction systems,a real and fast atmospheric turbulence time-evolving model is needed.We proposed a mode...Correcting wavefront distortion caused by atmospheric turbulence is crucial for atmospheric optics.To evaluate correction systems,a real and fast atmospheric turbulence time-evolving model is needed.We proposed a model for a time-evolving turbulence phase screen(PS)based on its fractal nature,which achieves scale transformation under time or space.According to fractional Brownian motion,an interpolation algorithm is proposed to enhance the spatio-temporal resolution of PS efficiently.Additionally,a grid-based time-evolving PS generation method is proposed combining the covariance matrix and temporal spectra.The results demonstrate that our method can efficiently generate time-evolving PS with high spatio-temporal resolution and accuracy,and the interpolation algorithm introduces a slight deviation of less than 2%,which has a minimal impact on the overall results.The fractal nature of atmospheric turbulence has enabled the generation of PS with high accuracy,efficiency,and flexibility.This advancement is meaningful for atmospheric turbulence simulation and related atmospheric optics fields.展开更多
With the rapid development of artificial intelligence techniques such as neural networks,data-driven machine learning methods are popular in improving and constructing turbulence models.For high Reynolds number turbul...With the rapid development of artificial intelligence techniques such as neural networks,data-driven machine learning methods are popular in improving and constructing turbulence models.For high Reynolds number turbulence in aerodynamics,our previous work built a data-driven model applicable to subsonic airfoil flows with different free stream conditions.The results calculated by the proposed model are encouraging.In this work,we aim to model the turbulence of transonic wing flows with fully connected deep neural networks,where there is less research at present.The proposed model is driven by two flow cases of the ONERA(Office National d'Etudes et de Recherches Aerospatiales)wing and coupled with the Navier-Stokes equation solver.Four subcritical and transonic benchmark cases of different wings are used to evaluate the model performance.The iteration process is stable,and final convergence is achieved.The proposed model can be used to surrogate the traditional Reynolds averaged Navier-Stokes turbulence model.Compared with the data calculated by the Spallart-Allmaras model,the results show that the proposed model can be well generalized to the test cases.The mean relative error of the drag coefficient at different sections is below 4%for each case.This work demonstrates that modeling turbulence by data-driven methods is feasible and that our modeling pattern is effective.展开更多
The emerging push of the differentiable programming paradigm in scientific computing is conducive to training deep learning turbulence models using indirect observations.This paper demonstrates the viability of this a...The emerging push of the differentiable programming paradigm in scientific computing is conducive to training deep learning turbulence models using indirect observations.This paper demonstrates the viability of this approach and presents an end-to-end differentiable framework for training deep neural networks to learn eddy viscosity models from indirect observations derived from the velocity and pressure fields.The framework consists of a Reynolds-averaged Navier–Stokes(RANS)solver and a neuralnetwork-represented turbulence model,each accompanied by its derivative computations.For computing the sensitivities of the indirect observations to the Reynolds stress field,we use the continuous adjoint equations for the RANS equations,while the gradient of the neural network is obtained via its built-in automatic differentiation capability.We demonstrate the ability of this approach to learn the true underlying turbulence closure when one exists by training models using synthetic velocity data from linear and nonlinear closures.We also train a linear eddy viscosity model using synthetic velocity measurements from direct numerical simulations of the Navier–Stokes equations for which no true underlying linear closure exists.The trained deep-neural-network turbulence model showed predictive capability on similar flows.展开更多
We introduce a framework for statistical inference of the closure coefficients using machine learning methods.The objective of this framework is to quantify the epistemic uncertainty associated with the closure model ...We introduce a framework for statistical inference of the closure coefficients using machine learning methods.The objective of this framework is to quantify the epistemic uncertainty associated with the closure model by using experimental data via Bayesian statistics.The framework is tailored towards cases for which a limited amount of experimental data is available.It consists of two components.First,by treating all latent variables(non-observed variables)in the model as stochastic variables,all sources of uncertainty of the probabilistic closure model are quantified by a fully Bayesian approach.The probabilistic model is defined to consist of the closure coefficients as parameters and other parameters incorporating noise.Then,the uncertainty associated with the closure coefficients is extracted from the overall uncertainty by considering the noise being zero.The overall uncertainty is rigorously evaluated by using Markov-Chain Monte Carlo sampling assisted by surrogate models.We apply the framework to the Spalart-Allmars one-equation turbulence model.Two test cases are considered,including an industrially relevant full aircraft model at transonic flow conditions,the Airbus XRF1.Eventually,we demonstrate that epistemic uncertainties in the closure coefficients result into uncertainties in flow quantities of interest which are prominent around,and downstream,of the shock occurring over the XRF1 wing.This data-driven approach could help to enhance the predictive capabilities of CFD in terms of reliable turbulence modeling at extremes of the flight envelope if measured data is available,which is important in the context of robust design and towards virtual aircraft certification.The plentiful amount of information about the uncertainties could also assist when it comes to estimating the influence of the measured data on the inferred model coefficients.Finally,the developed framework is flexible and can be applied to different test cases and to various turbulence models.展开更多
Flows experiencing laminarization and retransition are universal and crucial in many engineering applications.The objective of this study is to conduct an uncertainty quantification and sensitivity analysis of turbule...Flows experiencing laminarization and retransition are universal and crucial in many engineering applications.The objective of this study is to conduct an uncertainty quantification and sensitivity analysis of turbulence model closure coefficients in capturing laminarization and retransition for a rapidly contracting channel flow.Specifically,two commonly used turbulence models are considered:the Spalart-Allmaras(SA)one-equation model and the Menter Shear Stress Transport(SST)two-equation model.Thereby,a series of steady Reynolds Averaged Navier-Stokes(RANS)predictions of aero-engine intake acceleration scenarios are carried out with the purposely designed turbulence model closure coefficients.As a result,both SA and SST models fail to capture the retransition phenomenon though they achieve pretty good performance in laminarization.Using the non-intrusive polynomial chaos method,solution uncertainties in velocity,pressure,and surface friction are quantified and analyzed,which reveals that the SST model possesses much great uncertainty in the non-laminar regime,especially for the logarithmic law prediction.Besides,a sensitivity analysis is performed to identify the critical contributors to the solution uncertainty,and then the correlations between the closure coefficients and the deviations of the outputs of interest are obtained via the linear regression method.The results indicate that the diffusion-related constants are the dominant uncertainty contributors for both SA and SST models.Furthermore,the remarkably strong correlation between the critical closure coefficients and the outputs might be a good guide to recalibrate and even optimize the commonly used turbulence models.展开更多
The application of machine learning(ML)algorithms to turbulence modeling has shown promise over the last few years,but their application has been restricted to eddy viscosity based closure approaches.In this article,w...The application of machine learning(ML)algorithms to turbulence modeling has shown promise over the last few years,but their application has been restricted to eddy viscosity based closure approaches.In this article,we discuss the rationale for the application of machine learning with high-fidelity turbulence data to develop models at the level of Reynolds stress transport modeling.Based on these rationales,we compare different machine learning algorithms to determine their efficacy and robustness at modeling the different transport processes in the Reynolds stress transport equations.Those data-driven algorithms include Random forests,gradient boosted trees,and neural networks.The direct numerical simulation(DNS)data for flow in channels are used both as training and testing of the ML models.The optimal hyper-parameters of the ML algorithms are determined using Bayesian optimization.The efficacy of the above-mentioned algorithms is assessed in the modeling and prediction of the terms in the Reynolds stress transport equations.It was observed that all three algorithms predict the turbulence parameters with an acceptable level of accuracy.These ML models are then applied for the prediction of the pressure strain correlation of flow cases that are different from the flows used for training,to assess their robustness and generalizability.This explores the assertion that ML-based data-driven turbulence models can overcome the modeling limitations associated with the traditional turbulence models and ML models trained with large amounts of data with different classes of flows can predict flow field with reasonable accuracy for unknown flows with similar flow physics.In addition to this verification,we carry out validation for the final ML models by assessing the importance of different input features for prediction.展开更多
Flow characteristics around a wall-mounted square cylinder have been numerically simulated at aspect ratios (AR) ranging from 4 to 7 at Re =10 000. Four turbulence models have been compared in terms of drag coefficien...Flow characteristics around a wall-mounted square cylinder have been numerically simulated at aspect ratios (AR) ranging from 4 to 7 at Re =10 000. Four turbulence models have been compared in terms of drag coefficient (C_D). The closest result has been provided by two turbulence models, namely, k-ε Realizable and k ?ω Shear Stress Transport (SST). Hence, these models were utilized to present the flow patterns of pressure distributions, turbulent kinetic energy values, velocity magnitude values with streamlines, streamwise velocity components, crossstream velocity components and spanwise velocity components on different planes. Flow stagnation has been attained in front of the cylinder. Pressure values peaked for the upstream region. Over the cylinders, the tip vortex structure was dominant owing to the influence of the free end. Flow separation from the top front edge of the body has been obtained. The dividing streamline affected by the flow separation was highly effective in the wake region and moved nearer to the body when the aspect ratio was decreased;the reason was the wake shrinkage owing to the decreasing aspect ratio. Upwash and downwash have been seen in the cylinder wake. These two models presented similar flow patterns and drag coefficients. These drag coefficients are in good agreement with those in previous studies.展开更多
This review provides a comprehensive and systematic examination of Computational Fluid Dynamics(CFD)techniques and methodologies applied to the development of Vertical Axis Wind Turbines(VAWTs).Although VAWTs offer si...This review provides a comprehensive and systematic examination of Computational Fluid Dynamics(CFD)techniques and methodologies applied to the development of Vertical Axis Wind Turbines(VAWTs).Although VAWTs offer significant advantages for urban wind applications,such as omnidirectional wind capture and a compact,ground-accessible design,they face substantial aerodynamic challenges,including dynamic stall,blade-wake interactions,and continuously varying angles of attack throughout their rotation.The review critically evaluates how CFD has been leveraged to address these challenges,detailing the modelling frameworks,simulation setups,mesh strategies,turbulence models,and boundary condition treatments adopted in the literature.Special attention is given to the comparative performance of 2-D vs.3-D simulations,static and dynamic meshing techniques(sliding,overset,morphing),and the impact of near-wall resolution on prediction fidelity.Moreover,this review maps the evolution of CFD tools in capturing key performance indicators including power coefficient,torque,flow separation,and wake dynamics,while highlighting both achievements and current limitations.The synthesis of studies reveals best practices,identifies gaps in simulation fidelity and validation strategies,and outlines critical directions for future research,particularly in high-fidelity modelling and cost-effective simulation of urban-scale VAWTs.By synthesizing insights from over a hundred referenced studies,this review serves as a consolidated resource to advance VAWT design and performance optimization through CFD.These include studies on various aspects such as blade geometry refinement,turbulence modeling,wake interaction mitigation,tip-loss reduction,dynamic stall control,and other aerodynamic and structural improvements.This,in turn,supports their broader integration into sustainable energy systems.展开更多
The nozzle is a critical component responsible for generating most of the net thrust in a scramjet engine.The quality of its design directly affects the performance of the entire propulsion system.However,most turbule...The nozzle is a critical component responsible for generating most of the net thrust in a scramjet engine.The quality of its design directly affects the performance of the entire propulsion system.However,most turbulence models struggle to make accurate predictions for subsonic and supersonic flows in nozzles.In this study,we explored a novel model,the algebraic stress model k-kL-ARSM+J,to enhance the accuracy of turbulence numerical simulations.This new model was used to conduct numerical simulations of the design and off-design performance of a 3D supersonic asymmetric truncated nozzle designed in our laboratory,with the aim of providing a realistic pattern of changes.The research indicates that,compared to linear eddy viscosity turbulence models such as k-kL and shear stress transport(SST),the k-kL-ARSM+J algebraic stress model shows better accuracy in predicting the performance of supersonic nozzles.Its predictions were identical to the experimental values,enabling precise calculations of the nozzle.The performance trends of the nozzle are as follows:as the inlet Mach number increases,both thrust and pitching moment increase,but the rate of increase slows down.Lift peaks near the design Mach number and then rapidly decreases.With increasing inlet pressure,the nozzle thrust,lift,and pitching moment all show linear growth.As the flight altitude rises,the internal flow field within the nozzle remains relatively consistent due to the same supersonic nozzle inlet flow conditions.However,external to the nozzle,the change in external flow pressure results in the nozzle exit transitioning from over-expanded to under-expanded,leading to a shear layer behind the nozzle that initially converges towards the nozzle center and then diverges.展开更多
We review the concept of ‘‘equilibrium＇＇ in turbulence. It generally means a property of the energy spectrum, it can also be understood in terms of a scalar property, the Taylor–Kolmogorov formula relating the di...We review the concept of ‘‘equilibrium＇＇ in turbulence. It generally means a property of the energy spectrum, it can also be understood in terms of a scalar property, the Taylor–Kolmogorov formula relating the dissipation rate to the total energy and integral length scale. The implications of equilibrium and strong departure from equilibrium for turbulence modeling are stressed.展开更多
Three-dimensional corner separation is a common phenomenon that significantly affects compressor performance. Turbulence model is still a weakness for RANS method on predicting corner separation flow accurately. In th...Three-dimensional corner separation is a common phenomenon that significantly affects compressor performance. Turbulence model is still a weakness for RANS method on predicting corner separation flow accurately. In the present study, numerical study of corner separation in a linear highly loaded prescribed velocity distribution （PVD） compressor cascade has been investigated using seven frequently used turbulence models. The seven turbulence models include Spalart Allmaras model, standard k-e model, realizable k-e model, standard k-to model, shear stress transport k co model, v2-fmodel and Reynolds stress model. The results of these turbulence models have been compared and analyzed in detail with available experimental data. It is found the standard k-1： model, realizable k-e model, v2-f model and Reynolds stress model can provide reasonable results for predicting three dimensional corner separation in the compressor cascade. The Spalart-Allmaras model, standard k-to model and shear stress transport k-w model overesti- mate corner separation region at incidence of 0°. The turbulence characteristics are discussed and turbulence anisotropy is observed to be stronger in the corner separating region.展开更多
A growing interest has been devoted to the contra-rotating propellers （CRPs） due to their high propulsive efficiency, torque balance, low fuel consumption, low cavitations, low noise performance and low hull vibrati...A growing interest has been devoted to the contra-rotating propellers （CRPs） due to their high propulsive efficiency, torque balance, low fuel consumption, low cavitations, low noise performance and low hull vibration. Compared with the single-screw system, it is more difficult for the open water performance prediction because forward and aft propellers interact with each other and generate a more complicated flow field around the CRPs system. The current work focuses on the open water performance prediction of contra-rotating propellers by RANS and sliding mesh method considering the effect of computational time step size and turbulence model. The validation study has been performed on two sets of contra-rotating propellers developed by David W Taylor Naval Ship R ＆ D center. Compared with the experimental data, it shows that RANS with sliding mesh method and SST k-ω turbulence model has a good precision in the open water performance prediction of contra-rotating propellers, and small time step size can improve the level of accuracy for CRPs with the same blade number of forward and aft propellers, while a relatively large time step size is a better choice for CRPs with different blade numbers.展开更多
A variety of turbulence models were used to perform numerical simulations of heat transfer for hydrocarbon fuel flowing upward and downward through uniformly heated vertical pipes at supercritical pressure. Inlet temp...A variety of turbulence models were used to perform numerical simulations of heat transfer for hydrocarbon fuel flowing upward and downward through uniformly heated vertical pipes at supercritical pressure. Inlet temperatures varied from 373 K to 663 K, with heat flux rang- ing from 300 kW/m2 to 550 kW/m2. Comparative analyses between predicted and experimental results were used to evaluate the ability of turbulence models to respond to variable thermophysical properties of hydrocarbon fuel at supercritical pressure. It was found that the prediction performance of turbulence models is mainly determined by the damping function, which enables them to respond differently to local flow conditions. Although prediction accuracy for experimental results varied from condition to condition, the shear stress transport （SST） and launder and sharma models performed better than all other models used in the study. For very small buoyancy-influenced runs, the thermal-induced acceleration due to variations in density lead to the impairment of heat transfer occurring in the vicinity of pseudo-critical points, and heat transfer was enhanced at higher temperatures through the combined action of four thermophysical properties： density, viscosity, thermal conductivity and specific heat. For very large buoyancy- influenced runs, the thermal-induced acceleration effect was over predicted by the LS and AB models.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
基金This work was supported by the National Natural Science Foundation of China(91852108,11872230 and 92152301).
文摘Data-driven turbulence modeling studies have reached such a stage that the basic framework is settled,but several essential issues remain that strongly affect the performance.Two problems are studied in the current research:(1)the processing of the Reynolds stress tensor and(2)the coupling method between the machine learning model and flow solver.For the Reynolds stress processing issue,we perform the theoretical derivation to extend the relevant tensor arguments of Reynolds stress.Then,the tensor representation theorem is employed to give the complete irreducible invariants and integrity basis.An adaptive regularization term is employed to enhance the representation performance.For the coupling issue,an iterative coupling framework with consistent convergence is proposed and then applied to a canonical separated flow.The results have high consistency with the direct numerical simulation true values,which proves the validity of the current approach.
文摘In this paper the database obtained from LES is used to examine the algebraicturbulence model in Demuren and Rodi’s work. The results show that the prediction ofnormal Reynolas stresses and turbulence energy by means of turbulence modeling isbetter than that of shear Reynolde stresses. The comparison shows the LES methodcan be used to examine turbulence modelling.
基金supported by the National Natural Science Foundation of China(Grant Nos.92252201 and 11721202)the Fundamental Research Funds for the Central Universities.
文摘We present the approaches to implementing the k-√k L turbulence model within the framework of the high-order discontinuous Galerkin(DG)method.We use the DG discretization to solve the full Reynolds-averaged Navier-Stokes equations.In order to enhance the robustness of approaches,some effective techniques are designed.The HWENO(Hermite weighted essentially non-oscillatory)limiting strategy is adopted for stabilizing the turbulence model variable k.Modifications have been made to the model equation itself by using the auxiliary variable that is always positive.The 2nd-order derivatives of velocities required in computing the von Karman length scale are evaluated in a way to maintain the compactness of DG methods.Numerical results demonstrate that the approaches have achieved the desirable accuracy for both steady and unsteady turbulent simulations.
文摘The prediction of interfacial turbulence characteristics is one of the still challenging of two-phase stratified flow.The evaluation of some important parameters such as interfacial heat transfer coefficient based on turbulence kinetic energy and turbulence dissipation rate in some models,intensifies the importance of turbulence flow correct simulation.High gradient of velocity and turbulence kinetic energy at the interface of two-phase stratified flow leads to a major overestimation or underestimation of flow characteristics without any special treatment.Consideration of a source function of turbulence eddy frequency at the interface is one of the common solution employed in past researches.Although this solution remedies some shortcomings of traditional methods in smooth stratified flow,its application in wavy stratified flow needs the other modifications.The examination of turbulence characteristics near the free surface reveals that,in addition to turbulence eddy frequency,the other source function of turbulence kinetic energy should be considered near the free interface.So,a new source function of turbulence kinetic energy is proposed at the interface based on flow condition.This new method has been employed for Fabre et al.(1987)experiment designed for air/water stratified flow.The results of simulation have a good agreement with experimental data and turbulence characteristic can be captured near the free surface.
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supported by the National Natural Science Foundation of China(Grant Nos.12388101,12372288,U23A2069,and 92152301).
文摘Machine learning(ML)techniques have emerged as powerful tools for improving the predictive capabilities of Reynolds-averaged Navier-Stokes(RANS)turbulence models in separated flows.This improvement is achieved by leveraging complex ML models,such as those developed using field inversion and machine learning(FIML),to dynamically adjust the constants within the baseline RANS model.However,the ML models often overlook the fundamental calibrations of the RANS turbulence model.Consequently,the basic calibration of the baseline RANS model is disrupted,leading to a degradation in the accuracy,particularly in basic wall-attached flows outside of the training set.To address this issue,a modified version of the Spalart-Allmaras(SA)turbulence model,known as Rubber-band SA(RBSA),has been proposed recently.This modification involves identifying and embedding constraints related to basic wall-attached flows directly into the model.It is shown that no matter how the parameters of the RBSA model are adjusted as constants throughout the flow field,its accuracy in wall-attached flows remains unaffected.In this paper,we propose a new constraint for the RBSA model,which better safeguards the law of wall in extreme conditions where the model parameter is adjusted dramatically.The resultant model is called the RBSA-poly model.We then show that when combined with FIML augmentation,the RBSA-poly model effectively preserves the accuracy of simple wall-attached flows,even when the adjusted parameters become functions of local flow variables rather than constants.A comparative analysis with the FIML-augmented original SA model reveals that the augmented RBSA-poly model reduces error in basic wall-attached flows by 50%while maintaining comparable accuracy in trained separated flows.These findings confirm the effectiveness of utilizing FIML in conjunction with the RBSA model,offering superior accuracy retention in cardinal flows.
基金supported by the National Natural Science Foundation of China(Nos.62371437,62271463,and 62171424)the Fundamental Research Funds for the Central Universities(No.KY2470000006)the Innovation Program for Quantum Science and Technology(No.2021ZD0300701)。
文摘Correcting wavefront distortion caused by atmospheric turbulence is crucial for atmospheric optics.To evaluate correction systems,a real and fast atmospheric turbulence time-evolving model is needed.We proposed a model for a time-evolving turbulence phase screen(PS)based on its fractal nature,which achieves scale transformation under time or space.According to fractional Brownian motion,an interpolation algorithm is proposed to enhance the spatio-temporal resolution of PS efficiently.Additionally,a grid-based time-evolving PS generation method is proposed combining the covariance matrix and temporal spectra.The results demonstrate that our method can efficiently generate time-evolving PS with high spatio-temporal resolution and accuracy,and the interpolation algorithm introduces a slight deviation of less than 2%,which has a minimal impact on the overall results.The fractal nature of atmospheric turbulence has enabled the generation of PS with high accuracy,efficiency,and flexibility.This advancement is meaningful for atmospheric turbulence simulation and related atmospheric optics fields.
基金supported by the National Natural Science Foundation of China(Grant Nos.92152301,and 91852115)the National Numerical Wind tunnel Project(Grand No.NNW2018-ZT1B01).
文摘With the rapid development of artificial intelligence techniques such as neural networks,data-driven machine learning methods are popular in improving and constructing turbulence models.For high Reynolds number turbulence in aerodynamics,our previous work built a data-driven model applicable to subsonic airfoil flows with different free stream conditions.The results calculated by the proposed model are encouraging.In this work,we aim to model the turbulence of transonic wing flows with fully connected deep neural networks,where there is less research at present.The proposed model is driven by two flow cases of the ONERA(Office National d'Etudes et de Recherches Aerospatiales)wing and coupled with the Navier-Stokes equation solver.Four subcritical and transonic benchmark cases of different wings are used to evaluate the model performance.The iteration process is stable,and final convergence is achieved.The proposed model can be used to surrogate the traditional Reynolds averaged Navier-Stokes turbulence model.Compared with the data calculated by the Spallart-Allmaras model,the results show that the proposed model can be well generalized to the test cases.The mean relative error of the drag coefficient at different sections is below 4%for each case.This work demonstrates that modeling turbulence by data-driven methods is feasible and that our modeling pattern is effective.
文摘The emerging push of the differentiable programming paradigm in scientific computing is conducive to training deep learning turbulence models using indirect observations.This paper demonstrates the viability of this approach and presents an end-to-end differentiable framework for training deep neural networks to learn eddy viscosity models from indirect observations derived from the velocity and pressure fields.The framework consists of a Reynolds-averaged Navier–Stokes(RANS)solver and a neuralnetwork-represented turbulence model,each accompanied by its derivative computations.For computing the sensitivities of the indirect observations to the Reynolds stress field,we use the continuous adjoint equations for the RANS equations,while the gradient of the neural network is obtained via its built-in automatic differentiation capability.We demonstrate the ability of this approach to learn the true underlying turbulence closure when one exists by training models using synthetic velocity data from linear and nonlinear closures.We also train a linear eddy viscosity model using synthetic velocity measurements from direct numerical simulations of the Navier–Stokes equations for which no true underlying linear closure exists.The trained deep-neural-network turbulence model showed predictive capability on similar flows.
文摘We introduce a framework for statistical inference of the closure coefficients using machine learning methods.The objective of this framework is to quantify the epistemic uncertainty associated with the closure model by using experimental data via Bayesian statistics.The framework is tailored towards cases for which a limited amount of experimental data is available.It consists of two components.First,by treating all latent variables(non-observed variables)in the model as stochastic variables,all sources of uncertainty of the probabilistic closure model are quantified by a fully Bayesian approach.The probabilistic model is defined to consist of the closure coefficients as parameters and other parameters incorporating noise.Then,the uncertainty associated with the closure coefficients is extracted from the overall uncertainty by considering the noise being zero.The overall uncertainty is rigorously evaluated by using Markov-Chain Monte Carlo sampling assisted by surrogate models.We apply the framework to the Spalart-Allmars one-equation turbulence model.Two test cases are considered,including an industrially relevant full aircraft model at transonic flow conditions,the Airbus XRF1.Eventually,we demonstrate that epistemic uncertainties in the closure coefficients result into uncertainties in flow quantities of interest which are prominent around,and downstream,of the shock occurring over the XRF1 wing.This data-driven approach could help to enhance the predictive capabilities of CFD in terms of reliable turbulence modeling at extremes of the flight envelope if measured data is available,which is important in the context of robust design and towards virtual aircraft certification.The plentiful amount of information about the uncertainties could also assist when it comes to estimating the influence of the measured data on the inferred model coefficients.Finally,the developed framework is flexible and can be applied to different test cases and to various turbulence models.
基金co-supported by the Youth Program of the National Natural Science Foundation of China (No. 11902367)the Youth Program of Natural Science Foundation of Hunan Province, China (Nos. S2021JJQNJJ2519 and S2021JJQNJJ2716)the Science and Technology Research and Development plan of China National Railway Group, China (Nos. P2020J025 and P2021J036)
文摘Flows experiencing laminarization and retransition are universal and crucial in many engineering applications.The objective of this study is to conduct an uncertainty quantification and sensitivity analysis of turbulence model closure coefficients in capturing laminarization and retransition for a rapidly contracting channel flow.Specifically,two commonly used turbulence models are considered:the Spalart-Allmaras(SA)one-equation model and the Menter Shear Stress Transport(SST)two-equation model.Thereby,a series of steady Reynolds Averaged Navier-Stokes(RANS)predictions of aero-engine intake acceleration scenarios are carried out with the purposely designed turbulence model closure coefficients.As a result,both SA and SST models fail to capture the retransition phenomenon though they achieve pretty good performance in laminarization.Using the non-intrusive polynomial chaos method,solution uncertainties in velocity,pressure,and surface friction are quantified and analyzed,which reveals that the SST model possesses much great uncertainty in the non-laminar regime,especially for the logarithmic law prediction.Besides,a sensitivity analysis is performed to identify the critical contributors to the solution uncertainty,and then the correlations between the closure coefficients and the deviations of the outputs of interest are obtained via the linear regression method.The results indicate that the diffusion-related constants are the dominant uncertainty contributors for both SA and SST models.Furthermore,the remarkably strong correlation between the critical closure coefficients and the outputs might be a good guide to recalibrate and even optimize the commonly used turbulence models.
文摘The application of machine learning(ML)algorithms to turbulence modeling has shown promise over the last few years,but their application has been restricted to eddy viscosity based closure approaches.In this article,we discuss the rationale for the application of machine learning with high-fidelity turbulence data to develop models at the level of Reynolds stress transport modeling.Based on these rationales,we compare different machine learning algorithms to determine their efficacy and robustness at modeling the different transport processes in the Reynolds stress transport equations.Those data-driven algorithms include Random forests,gradient boosted trees,and neural networks.The direct numerical simulation(DNS)data for flow in channels are used both as training and testing of the ML models.The optimal hyper-parameters of the ML algorithms are determined using Bayesian optimization.The efficacy of the above-mentioned algorithms is assessed in the modeling and prediction of the terms in the Reynolds stress transport equations.It was observed that all three algorithms predict the turbulence parameters with an acceptable level of accuracy.These ML models are then applied for the prediction of the pressure strain correlation of flow cases that are different from the flows used for training,to assess their robustness and generalizability.This explores the assertion that ML-based data-driven turbulence models can overcome the modeling limitations associated with the traditional turbulence models and ML models trained with large amounts of data with different classes of flows can predict flow field with reasonable accuracy for unknown flows with similar flow physics.In addition to this verification,we carry out validation for the final ML models by assessing the importance of different input features for prediction.
文摘Flow characteristics around a wall-mounted square cylinder have been numerically simulated at aspect ratios (AR) ranging from 4 to 7 at Re =10 000. Four turbulence models have been compared in terms of drag coefficient (C_D). The closest result has been provided by two turbulence models, namely, k-ε Realizable and k ?ω Shear Stress Transport (SST). Hence, these models were utilized to present the flow patterns of pressure distributions, turbulent kinetic energy values, velocity magnitude values with streamlines, streamwise velocity components, crossstream velocity components and spanwise velocity components on different planes. Flow stagnation has been attained in front of the cylinder. Pressure values peaked for the upstream region. Over the cylinders, the tip vortex structure was dominant owing to the influence of the free end. Flow separation from the top front edge of the body has been obtained. The dividing streamline affected by the flow separation was highly effective in the wake region and moved nearer to the body when the aspect ratio was decreased;the reason was the wake shrinkage owing to the decreasing aspect ratio. Upwash and downwash have been seen in the cylinder wake. These two models presented similar flow patterns and drag coefficients. These drag coefficients are in good agreement with those in previous studies.
基金funded by Ministry of Higher Education Malaysia under the Fundamental Research Grant Scheme(FRGS/1/2024/TK10/UKM/02/7).
文摘This review provides a comprehensive and systematic examination of Computational Fluid Dynamics(CFD)techniques and methodologies applied to the development of Vertical Axis Wind Turbines(VAWTs).Although VAWTs offer significant advantages for urban wind applications,such as omnidirectional wind capture and a compact,ground-accessible design,they face substantial aerodynamic challenges,including dynamic stall,blade-wake interactions,and continuously varying angles of attack throughout their rotation.The review critically evaluates how CFD has been leveraged to address these challenges,detailing the modelling frameworks,simulation setups,mesh strategies,turbulence models,and boundary condition treatments adopted in the literature.Special attention is given to the comparative performance of 2-D vs.3-D simulations,static and dynamic meshing techniques(sliding,overset,morphing),and the impact of near-wall resolution on prediction fidelity.Moreover,this review maps the evolution of CFD tools in capturing key performance indicators including power coefficient,torque,flow separation,and wake dynamics,while highlighting both achievements and current limitations.The synthesis of studies reveals best practices,identifies gaps in simulation fidelity and validation strategies,and outlines critical directions for future research,particularly in high-fidelity modelling and cost-effective simulation of urban-scale VAWTs.By synthesizing insights from over a hundred referenced studies,this review serves as a consolidated resource to advance VAWT design and performance optimization through CFD.These include studies on various aspects such as blade geometry refinement,turbulence modeling,wake interaction mitigation,tip-loss reduction,dynamic stall control,and other aerodynamic and structural improvements.This,in turn,supports their broader integration into sustainable energy systems.
基金supported by the Zhejiang Provincial Key Research and Development Program of China(No.2020C01020).
文摘The nozzle is a critical component responsible for generating most of the net thrust in a scramjet engine.The quality of its design directly affects the performance of the entire propulsion system.However,most turbulence models struggle to make accurate predictions for subsonic and supersonic flows in nozzles.In this study,we explored a novel model,the algebraic stress model k-kL-ARSM+J,to enhance the accuracy of turbulence numerical simulations.This new model was used to conduct numerical simulations of the design and off-design performance of a 3D supersonic asymmetric truncated nozzle designed in our laboratory,with the aim of providing a realistic pattern of changes.The research indicates that,compared to linear eddy viscosity turbulence models such as k-kL and shear stress transport(SST),the k-kL-ARSM+J algebraic stress model shows better accuracy in predicting the performance of supersonic nozzles.Its predictions were identical to the experimental values,enabling precise calculations of the nozzle.The performance trends of the nozzle are as follows:as the inlet Mach number increases,both thrust and pitching moment increase,but the rate of increase slows down.Lift peaks near the design Mach number and then rapidly decreases.With increasing inlet pressure,the nozzle thrust,lift,and pitching moment all show linear growth.As the flight altitude rises,the internal flow field within the nozzle remains relatively consistent due to the same supersonic nozzle inlet flow conditions.However,external to the nozzle,the change in external flow pressure results in the nozzle exit transitioning from over-expanded to under-expanded,leading to a shear layer behind the nozzle that initially converges towards the nozzle center and then diverges.
文摘We review the concept of ‘‘equilibrium＇＇ in turbulence. It generally means a property of the energy spectrum, it can also be understood in terms of a scalar property, the Taylor–Kolmogorov formula relating the dissipation rate to the total energy and integral length scale. The implications of equilibrium and strong departure from equilibrium for turbulence modeling are stressed.
基金supported by the National Natural Science Foundation of China(No.51376001,No.51420105008,No.51306013,No.51136003)the National Basic Research Program of China(2012CB720205,2014CB046405)+2 种基金the Beijing Higher Education Young Elite Teacher Projectthe Fundamental Research Funds for the Central Universitiessupported by the Innovation Foundation of BUAA for Ph.D.Graduates
文摘Three-dimensional corner separation is a common phenomenon that significantly affects compressor performance. Turbulence model is still a weakness for RANS method on predicting corner separation flow accurately. In the present study, numerical study of corner separation in a linear highly loaded prescribed velocity distribution （PVD） compressor cascade has been investigated using seven frequently used turbulence models. The seven turbulence models include Spalart Allmaras model, standard k-e model, realizable k-e model, standard k-to model, shear stress transport k co model, v2-fmodel and Reynolds stress model. The results of these turbulence models have been compared and analyzed in detail with available experimental data. It is found the standard k-1： model, realizable k-e model, v2-f model and Reynolds stress model can provide reasonable results for predicting three dimensional corner separation in the compressor cascade. The Spalart-Allmaras model, standard k-to model and shear stress transport k-w model overesti- mate corner separation region at incidence of 0°. The turbulence characteristics are discussed and turbulence anisotropy is observed to be stronger in the corner separating region.
基金supported by the National Natural Science Foundation of China(Grant No.51079157)
文摘A growing interest has been devoted to the contra-rotating propellers （CRPs） due to their high propulsive efficiency, torque balance, low fuel consumption, low cavitations, low noise performance and low hull vibration. Compared with the single-screw system, it is more difficult for the open water performance prediction because forward and aft propellers interact with each other and generate a more complicated flow field around the CRPs system. The current work focuses on the open water performance prediction of contra-rotating propellers by RANS and sliding mesh method considering the effect of computational time step size and turbulence model. The validation study has been performed on two sets of contra-rotating propellers developed by David W Taylor Naval Ship R ＆ D center. Compared with the experimental data, it shows that RANS with sliding mesh method and SST k-ω turbulence model has a good precision in the open water performance prediction of contra-rotating propellers, and small time step size can improve the level of accuracy for CRPs with the same blade number of forward and aft propellers, while a relatively large time step size is a better choice for CRPs with different blade numbers.
基金funding support from National Natural Science Foundation of China (No.51406005)Defense Industrial Technology Development Program of China (No.B2120132006)
文摘A variety of turbulence models were used to perform numerical simulations of heat transfer for hydrocarbon fuel flowing upward and downward through uniformly heated vertical pipes at supercritical pressure. Inlet temperatures varied from 373 K to 663 K, with heat flux rang- ing from 300 kW/m2 to 550 kW/m2. Comparative analyses between predicted and experimental results were used to evaluate the ability of turbulence models to respond to variable thermophysical properties of hydrocarbon fuel at supercritical pressure. It was found that the prediction performance of turbulence models is mainly determined by the damping function, which enables them to respond differently to local flow conditions. Although prediction accuracy for experimental results varied from condition to condition, the shear stress transport （SST） and launder and sharma models performed better than all other models used in the study. For very small buoyancy-influenced runs, the thermal-induced acceleration due to variations in density lead to the impairment of heat transfer occurring in the vicinity of pseudo-critical points, and heat transfer was enhanced at higher temperatures through the combined action of four thermophysical properties： density, viscosity, thermal conductivity and specific heat. For very large buoyancy- influenced runs, the thermal-induced acceleration effect was over predicted by the LS and AB models.
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.
