Application Research Of High-order Weighted Compact Nonlinear Schemes In Subsonic/Transonic Separated Flows

The predicted results of any flow simulations depend on the accuracy of the underly-ing representation of the flow physics and the accuracy of the numerical methods for solv-ing the corresponding equations.This thesis aims at the simulations of separated flows in CFD at subsonic and transonic conditions and pays close attention to both high-order numerical methods and advanced turbulence models.A relatively complete hybrid RAN-S/LES framework is established finally,which is based on high-order WCNS methods and covers both first-order and second-order closures.On the one hand,this thesis is devoted to the study of high-order methods.Accuracy verification and cost evaluation methods are summarized and developed.Moreover,by using these methods,the advantage of the WCNSs in computing efficiency is proved.For the turbulence models,especially for the 7-equations Reynold-stress model,their high-order discretization process is carried out.A solution can be obtained robustly with the uniform high-order accuracy between the turbulence equations and the RANS equations.Moreover,by some benchmark cases the essentiality of the uniformity is indicated.On the other hand,this thesis foucses on the application of advanced turbulence mod-els.In particular,we derive the fundamental dynamical equations that are depended by the hybrid RANS/LES method.The reason that the hybrid method has been successful in engineering and the gap between the hybrid method and LES method are explained.More-over,the relatively complete hybrid RANS/LES framework is established,which covers both first-order and second-order closures.Under this framework and from a physical point of view,the link as well as diversity among deffirent scale resolving approaches,such as DES,SAS and so on,is investigated.A high-order application study of the DES method combined with?-Re_?transition model is carried out and a detailed contrastive analysis is performed in single cylinder and rod-airfoil cases.The results indicate that the high-order DES with transition model can approach the effect of the traditional LES method at moderate Reynolds numbers and give a better agreement with experiment data than the original DES without transition model.Subsequently,a variant of high-order DES method based on SSG/LRR-?Reynolds-stress model is carried out and applicated to NACA airfoil and deltawing cases.The results show that the SSG/LRR-DES can not only maintain the good performance of the traditional DES method in the large scale separation problems,but can also improve the prediction of complex separation problems,such as the critical stall of airfoil and the critical vortex-breakdown of a delta wing.