Applications of boundry vorticity dynamics to flow simulation, airfoil design, and flow control

This dissertation is dedicated to the study of applications of the boundary vorticity dynamics theoryThe vorticity generation mechanism from solid boundaries is studied firstThe development of a two-dimensional viscous solver and an airfoil inverse design tool is conducted next. Finally, a new flow control method called "BVF cutting" is introduced and tested.

Various source terms of the vorticity generation rate, i.e., boundary vorticity flux (BVF), are studied based on the tangential momentum balance on a solid surface. The direct connection between BVF and aerodynamic forces is rederived. The constraint of BVF imposed by the vorticity conservation is formulated and clarified.

Two aerodynamic tools are developed in terms of BVF: A numerical Navier-Stokes (N-S) solver for two-dimensional incompressible steady or unsteady flows by using stream function-vorticity variables, with the BVF as the Neumann boundary condition; and an inverse design tool to develop airfoils with improved performance, in which the BVF is used as the objective function in the Euler limit of a viscous flow. An extensive validation of the N-S solver is conducted, and examples of improved airfoils are given mainly for the purpose of enhancing their lift coefficients and delaying the stall angles of attack.

By reexamining the flow separation in terms of BVFtwo possible ways to imple- ment the BVF cutting method are examined, one of which is proved very effective. Enlightened by these, the most idealized objective for flow control is found. A principle for the perfect controlled flow and a guideline to judge the effectiveness of a flow control is proposed.