Numerical Methods For Hypersonic Flowfield With Magnetic Interference

A typical characteristic of hypersonic flow is the high temperature, which makes the air being decomposed and ionized, and local plasma flow formed around the aircraft, so the hypersonic flowfield is much more complicated than common flowfield. In this dissert, a new kind of numerical method based on unstructured meshes and upwind schemes for the Magnetohydrodynamics(MHD) equations and hypersonic chemical reacting equations is developed, and used to analyze the rules of advantageous interference made by the magnetic fields on the hypersonic plasma flows, which is helpful for hypersonic aircraft design.Firstly, classical theory and assumptions of MHD are studied to establish the theoretical base for numerical computation. The MHD equations are derived from the theory and governing equations of electromagnetics and hydrodynamics, along with the assumptions of MHD. Then characteristics and difficulties of MHD equations in numerical computation are discussed, and the emphases and difficulties of this dissert are presented.Secondly, numerical methods based on unstructured/hybrid meshes for multidimensional MHD equations developed in this dissert are presented in detail. Two different numerical methods are developed, which have some common points: 1)using the Finite Volume Method(FVM) for spatial discretization; 2) 5-stage explicit Runge-Kutta scheme is employed for the time integration; 3) using the hyperbolic divergence cleaning(HDC) method to get rid of the influence of divergence created during the simulating; 4)central scheme is used for the viscous fluxes;5)the Monotone Upstream-Centred Schemes for Conservation Laws(MUSCL) and the koren limiter are employed for the second order computation. The difference of the two methods lies in the computation of the convective fluxes: one approximates the fluxes using the Advection Upstream Splitting Method (AUSM), which has been modified for the multidimensional MHD equations; the other one is based on the restoration of homogeneity of the MHD equations, which makes the equations suitable for the upwind flux splitting method while remain the same results, and using the new flux vector splitting(FVS) method developed in this dissert, successfully realize the computation of multidimensional MHD equations using the upwind flux splitting method. Then numerical simulations are carried out to validate the correctness of the two methods. Afterwards, hypersonic nonequilibrium chemical reacting flows are numerically studied to validate the mathematical model used in this dissert of chemical reactions and the thermodynamic properties of high temperature air. Numerical method based on unstructured hybrid meshes for the hypersonic viscous nonequilibrium chemical reacting flows is developed. The inviscid fluxes are approximated using the VanLeer flux-splitting method, and the MUSCL approach with koren limiter is implemented to increase the numerical accuracy, and central scheme is employed for the viscous fluxes. The time integration is an explicit 5-stage Runge-Kutta scheme. Some modifications are made to the original VanLeer scheme for the speciality of hypersonic flow. Numerical results of the RAMC-II flight test model are shown and compared with the experimental data and limited references, which shows the correctness of the mathematical models of the hypersonic nonequilibrium chemical reactions employed in this dissert.Subsequently, numerical methods for hypersonic MHD flows with chemical nonequilibrium effects are investigated. The numerical methods presented above are implemented to compute the 2D idea MHD equations and chemical governing equations respectively, and a loosely coupled approach is implemented to merge the two parts of computation. In both of the parts, the AUSM scheme is implemented in the spatial discretization, and an explicit 5-stage Runge-Kutta scheme is used for the time integration. The chemical reacting model consists of 5 species and 5 reactions. Numerical simulation was carried out, and the result shows the feasibility of the numerical methods in simulating hypersonic MHD flows with nonequilibrium chemical reactions.At last, parallel algorithm of MHD equations on unstructured meshes using the Message Passing Interface(MPI) standard library on PC-CLUSTER system is investigated. To achieve high efficiency of message passing and ensure the conservation of fluxes on the interface between different subzones, domain decomposition technique based on unstructured hybrid mesh and a message passing method based on ghost cells is presented. A master/slave parallel mode is used for the parallel computation in consideration of load balance. A 2-D hypersonic MHD flow was numerically simulated using the parallel algorithm, and high parallel efficiency was achieved, which shows the feasibility of developing high efficient parallel algorithms for multidimensional MHD equations.