Based On Approximate Boundary Conditions Of The Wing Transonic Euler Equation, Numerical Simulation,

This dissertation studies and proposes an efficient method for solving steady and unsteady transonic Euler Equations for the flow over wing by assuming the wing being thin and undergoing small deformation. Wall boundary conditions are implemented on non-moving mean wall positions, meanwhile the first-order approximate boundary conditions are used in Euler equations on stationary Cartesian grids. The method needn't the generation of moving body-fitted grids along with the pitching of wing in unsteady flow, thus it need less demand on CPU time and can be easily deployed in any fluid-structure interaction problem. The first-order approximate boundary conditions are used in solving the Euler equations and the results are compared with the Euler solutions using the exact boundary conditions and known experimental data. It is shown that the first-order wall boundary conditions are adequate to represent wing of typical thicknesses with small deformation.The main aspects of this dissertation are as follows:1. Stationary Cartesian grids are generated by using one-dimensional stretching functions in every direction and grids are clustered in local part of leading and trailing points.2. 2-D Euler equations' approximate boundary conditions are induced. 3-D Euler equations' approximate boundary conditions are established based on 2-D and are validated by numerical simulation.3. The numerical simulation of airfoil's steady and unsteady Euler equations is accomplished based on 2-D approximate boundary conditions. The results of cases are in good agreement with the Euler solutions using the exact boundary conditions and known experimental data. The correctness of the method in this dissertation is validated.4. The numerical simulation of wing's steady and unsteady Euler equations is accomplished based on 3-D approximate boundary conditions. Through the numerical calculations of ONERA M6 wing. LANN wing and a rectangular wing, the correctness and validity of the numerical simulation of Euler equation using the approximate boundary conditions on 3-D flow are validated.Cell-center finite volume method spatial derivatives, implicit dual-time temporalderivatives and 5-step Runge-Kutta scheme are adopted in the solution of unsteady flow. The techniques of local time stepping and implicit residual smoothing are used to increase the convergence rate.