| The growth in computing power over the past several decades has allowed computational fluid dynamics(CFD)to become one of the primary predictive tools in engineering and scientific research.As the numerical simulations capabilities become more complex,the accuracy and reliability of turbulence modeling has gained more and more attention.Therefore,we focus on turbulence modeling,and conducted a thorough study on the accuracy and reliability of turbulence modeling from both theoretical analysis and numerical methods aspects.The core content of this work involves the development of CFD code,the improvement of time-marching algorithm,the realization of turbulence modeling method,the research of uncertainty quantification,the study on CFD verification and validation,as well as the study of transonic buffeting using the above methods.These works can be summarized as follows:1.We have developed a Navier–Stokes flow solver for targeting high-performance computing platforms(HPC),it paralleled by MPI programming model.Non-blocking communications are used to overlap computation with communication and exploit possible performance gains.The performance of this solver been demonstrated on the TH-1A HPC,results show it able to obtain in excess of 93% parallel efficiency(480 cores used).2.An acceleration technique using a reduced-order model is presented to speed up the convergence of a Navier-Stokes solver for viscous problems.This technique uses a limited number of solution corrections as snapshots to form a projection basis through dynamic mode decomposition.The projection basis is employed to transform the original high order system of governing equations to a reduced order system,which is then used to generate an improved solution that drives the convergence faster.Three viscous flow cases,including both 2D airfoil and 3D wing,were conducted to assess the performance of the proposed acceleration technique.The roles of snapshot selection parameters including quantity and span were also evaluated with these test cases.The proposed convergence acceleration technique is found to be an effective approach to accelerate the convergence of a Navier-Stokes solver,and it shows a satisfactory performance in a wide range of snapshot selection parameters.Besides,this method does not depend on the time integration method or data format and is thus straightforward to implement in a Navier-Stokes solver with hybrid unstructured mesh.3.We have proposed a methodology to improve the computational efficiency of unsteady flow simulations with dual time stepping scheme.The methodology is developed on the combination of dynamic mode extrapolation and dual time stepping scheme.It accelerates the convergence speed of the inner iterations by using dynamic mode extrapolation to provide an initial solution for each physical time step.The validation and verification are demonstrated by three cases,including unsteady flow past a stationary circular cylinder at Re=200,transonic flow over periodic and non-periodic pitching NACA 0012 airfoil and buffeting flow around NASA(SC)-0714 airfoil.For comparison,Lagrange extrapolation initial condition and natural initial condition are also applied.The results confirm that the proposed methodology is very successful in reducing computational time for both incompressible and transonic unsteady flow.4.Turbulence modeling has been discussed in detail.A full Reynolds stress model(RSM),as well as the SA and SST turbulence model,are implemented into our CFD solver,its numerical stability was improved by approximating the eigenvalue of source term during time-marching.In addition,the hybrid LES/RANS method was also studied.We have introduced the RSM into hybrid LES/RANS method by a modification to the original length scale,this length scale is defined by the modeled Reynolds stresses as well as wall distance.To meet the needs of refined turbulence simulation,LES method was also developed and explore the definition of filter scale on unstructured grids.Finally,various turbulence models at different levels of complexity were implemented.The RANS method includes three turbulence models: SA,SST and RSM;the LES method has three sub-grid models: Smagorinsky,dynamic Smagorinsky and WALE;DES,DDES and IDDES are successfully implemented(available for SA,SST and RSM).All of these methods have been verified by a series of standard test cases.5.Efforts have been made to verify and validate the turbulence modeling,a range of test cases have been conducted.Those test cases cover from simple two-dimensional airfoils to the most complex configuration of high-lift aircraft;The freestream range from low-speed incompressible flows to transonic flows,and the complexity of flowfield ranges from steady high-angle-of-attack flow to unsteady vortex shedding and shock boundary layer interaction.Results show that the current CFD solver meets the requirements of mesh convergence and the spatial discretization accuracy is second order.It also found that RSM and RSM-IDDES methods present natural superiority compared to the two equations turbulence models when simulating a flow with large scale flow separation or streamline curvature effects,as it is physically the more complete model.This especially true in DES,when the flow features of interest are the result of anisotropy in the Reynolds stresses,RSM-IDDES models show a better performance compared to the SST based IDDES model.6.To demonstrate the verification and validation,we have studied the uncertainties in turbulence simulations.Firstly,the origin of uncertainties in CFD computation and their description methods were discussed.Then we used the non-intrusive probabilistic collection method to investigate the aleatory uncertainties,which arise from intrinsic variability of a process,e.g.,inflow conditions.We used eigenspace perturbation methodology to estimate this epistemic uncertainty,which involves modeled terms,e.g.,the eddy viscosity.It was found that the epistemic uncertainty caused by the eddy viscosity hypothesis mainly affects the prediction of the viscous flow in the boundary layer,while the aleatory uncertainties of the incoming flow mainly affects the prediction of the external flow.Besides,when flow structure is not too complex,the traditional turbulence model shows high reliability.However,in the case of a relatively complex flow,the flow shows highly sensitive to the above-mentioned uncertainties.Both the experimental and the calculation results have a large dispersion,which means the statistical solution of turbulence simulation can be established by means of uncertain quantitative analysis method.7.An investigation on transonic shock buffet instability mechanism by applying a combination of numerical simulations and dynamic mode decomposition(DMD)is presented.The unsteady flow simulations over OAT15 A and NASA(SC)-0714 supercritical airfoil were performed,results are validated based on experimental data and analyzed by DMD.The analysis results show that the unsteadiness onset of flow is closely related to the instability of shear layers located between the separation and freestream.To study the unsteady aerodynamic loads associated with transonic buffet flow around a launcher,delayed detached-eddy simulations of a hammerhead configuration have been conducted at transonic Mach numbers.Results show that the mechanism involves a sequence of vortex,which is shed downstream,merges together,and ultimately impinges on the wall leading to large fluctuations.Besides,the cross-spectral analysis also revealed that the subsequent large scale and low frequency vortex shedding of the developed shear layer provides a strong influence on the flows around cone-cylinder conjunction.At the end,vortex-induced vibration of the NASA tandem cylinders was numerically simulated by using the RSM-IDDES method,results are compared with numerical data and available experiments.It was found that this hybrid method performed reasonably well,and shows better results when compared to the results obtained with SST based IDDES model. |
