Numerical Research Of ALE Finite Volume Method For Calorically Perfect Gas/Chemical Nonequilibrium Gas Flow

Many flows have moving boundaries, e.g., the flapping and plunging of wing of bird, aeroelastic, store realease and internal-combustion engines. Comparing with flow with rigid boundaries, some special difficulties arising for numerical simulation of moving boundary flow. For internal-combustion engines, chemical reaction is also occurred, so the effect of chemical nonequilibrium has to be considered. Several issues of simulating calorically perfect gas and chemical nonequilibrium gas flow involving moving boundaries have been studied in this dissertation.ALE metheod is adopted to describe the motion of fluid. The current state of art of descretization method for NS equations with ALE description, the mesh deformation method and the solution method of chemical nonequilibrium flow are reviewed.A computer program has been developed to solve the compressible flow with moving boundaries based on the assumption of calorical perfect gas, and the spatial and temporal discretisation scheme, boundary conditions and turbulence models have been given in detail.We show that it is inadequate to assert if a method is DGCL satisfied only by examining whether the uniform flow is calculated accurately. In the framework of finite volume discretisation, we can prove in theory that all stable BDF schemes can maintain the designed accuracy and satisfy DGCL on moving mesh using the method proposed by Mavriplis; while Mavriplis’ s method is not able to keep time accuracy of their design on all of the time discrete scheme, Crank-Nicolsen scheme is taken as an example;the theoretical proofs are also verified through numerical experiments. A new version of AUSM-type scheme for ALE formulation is proposed. This new construction method has clear physical meaning, and numerical experiments prove the accuracy of this method.For the purpose of constructing a moving mesh method with high efficience and robustness, a moving submesh method, RBFs-MSA, is raised. The proposed algorithm is as robust as RBFs and much more robust than spring analogy, but is much more efficient than the latter two methods. By the test cases, it indicates that this new method can deal with the mesh deformation when the boundaries undergo large rotation, large displacement and large deformation, which prove its superior deformation ability and high efficiency.The verification of the algorithms of unstructured finite volume method for NS equation with ALE description has been made by several test cases. Usteady, viscous fows over fapping airfoils in a biplane conguration are computed on moving meshes as an application.In order to deal with the stiff problem of the numerical solution of chemical nonequilibrium flow introduced by the reaction source terms, a novel uncoupling algorithm is adopted. Based on the defined new energy variable and equivalent specific heat ratio, we can transfer the original governing equations of chemical nonequilibrium flow to equations which have the same form as the governing equations of calorical perfect gas flow. The transformed governing equations can be splitted into flow part and reacting part by standard Strang’s operator splitting method. For the calculation of the partial differential equations of flow part, the conventional algorithm which developed for calorically perfect gas can be applied directly only with minor modifications; for the calculation of the ordinary differential equations of reacting part, several existed stiff ode solvers can be used. One main advantage of this decoupling method is the easy utilization of any conventional algorithm which developed for solving the calorically perfect gas flow. To reflect this advantage of the novel decoupled algorithm, a high-order finite difference scheme and the ALE unstructured finite volume scheme have been extended to simulate the chemical nonequilibrium flow with this novel uncoupling algorithm. It’s demonstrated via simulation that geometrical configuration plays a definitive role in the unstable regime for shock induced combustion. Finally, A chemical reacting flow with moving boundary has been simulated.