Numerical Simulation Of Unsteady Flows Past A Delta Wing By A 3-D Vortex Method

Unsteady flow around a delta wing, especially breaking down of the vortices generated from leading edge, is one of the most popular problems focused by the aerodynamic specialists. Since the flow past a delta wing is highly non-linear and complicated, almost all the existing turbulence models can not describe the unsteady phenomenon very well. Simulation of the unsteady flow with high Reynolds Number accurately is still a difficult problem. On the other hand, since vortex method has been well developed to solve the Navier-Stokes equation, it gradually becomes an important computational fluid dynamical method. Profit from the Lagrangian coordinate, present method is gridless. Thus, there is no numerical viscosity or numerical oscillation. As a direct calculating method, vortex method is one of the efficient ways to simulate unsteady separated flow fields.In this paper, a fast Lagrangian vortex method is used to simulate the incompressible unsteady flows past a delta wing. The governing equations of this method are the vorticity-streamfunction equation and the vorticity-transport equation. Discrete vortices are used to model the vorticity generation, accumulation and transport mechanisms. By tracking the position and the intensity of these vortex elements, the process of vortex field can be well described. Generalized Biot-Savart formula is the solution of vorticity- streamfunction equation, which governs the movement of vortex elements. The velocity field is computed by this formula combined with a fast multiple expansion algorithms. Based on the velocity field, the position of the elements at the next time step can be obtained. The intensity of the vortex elements are governed by the vorticity-transport equation. The viscous diffusion term in this equation is solved by the Particle Strength Exchange (PSE) method and the stretching term is solved by calculating the gradient of velocity directly. An advanced model for nascent vortices generating from the boundary is used, which satisfies the non-slip boundary condition perfectly. The pressure of the flow field is obtained by solving the Poisson equation, which is transformed by the original Navier-Stokes equation.The corresponding program was designed by FORTRAN code. Simulations of the process and breakdown of symmetric vortices produced by 80o swept delta wing and 40o swept delta wing at low Reynolds number are performed. It can be confirmed that the attack angles which produce the highest lift force are 25o and 42o, respectively. Besides, by analyzing the torque of the 80o swept delta wing, the minimum attack angle reducing rocking motion is about 23o.