Numerical Simulation Of Low-speed And Low-Reynolds Number 2-D Flows Based On Method Of Pseudo Compressibility

Based on pseudo compressibility, two-dimensional low-speed flows are numerically simulated by solving Euler and Navier-Stokes equations. The pseudo-compressibility term is introduced to the continuity equation of incompressible governing equations, which results in a closed hyperbolic system of equations. Thus, the pressure field is coupled up with the velocity field while keeping zero velocity divergence. In this dissertation, finite volume method, explicit Runge-Kutta time-marching scheme and "dual-time stepping method" are employed to solve the governing equations. Both inviscid and viscous steady flows around two-dimensional cylinder, flat-plate and airfoils are simulated, and unsteady flows for airfoil in arbitrary motion are also calculated. The results are in reasonably good agreement with experimental data or other researcher's results, which demonstrate that the developed method is effective for solving low-speed flows.The main work of this dissertation is as follows:1. With introduction of pseudo compressibility, two-dimensional Euler Equations are derived. Referring to compressible method, central finite volume scheme is employed to develop a computational code. The eigenvalues ofJacobian matrix are derived and the stability condition is also presented. According to the Bernoulli equation, similar to compressible calculations, pressure damping is introduced to accelerate convergence. The calculations of inviscid flows around cylinder are taken as numerical examples which show good agreement with analytical solutions.2. Two-dimensional steady incompressible Navier-Stokes equations of laminar flows are derived by the method of Pseudo compressibility. The numerical results of low-Reynolds number flow around semi-infinite flat plate and airfoils are consistent with Blasius solutions and references' data.3. Unsteady incompressible Euler and Navier-Stokes equations are solved for two dimensional low-speed flows by the method of Pseudo compressibility. The time marching is based on "dual-time stepping method". The method is suitable for analysis of the problems of airfoil in arbitrary motion.4. For steady incompressible flows, the effects of Reynolds number and thickness of airfoils on the aerodynamic characteristics are studied.5. Effects of unsteady flows on the aerodynamic characteristics are also analyzed. The results of this dissertation are useful for the further investigations of three-dimensional flapping wing.The method given in this dissertation, as the computational results and analysis indicate, is correct and successful for simulating two-dimensional low-speed flows.Combined with blade element theory, the results can be used to evaluate aerodynamic characteristics of flapping wings, which are helpful for the initial design of micro rotary and flapping wing.