Bluff -body flow simulations using vortex methods

Incompressible, viscous, two-dimensional unsteady flows over bluff bodies are simulated via the use of vortex methods. The vorticity domain is discretized into a number of Lagrangian point vortices. The vorticity transport equation is split into convection and diffusion parts, and each part is solved sequentially, rather than simultaneously, in each time step. The convection equation is solved using a “vortex-in-cell” method, and the diffusion equation is either simulated by a random walk method, or solved using a finite-difference ADI scheme. New vorticity is created on the body surface during each time step in order to satisfy the no-slip boundary condition. The no-flow boundary condition is satisfied through proper adjustment of the stream-function on the body surface. Impulsively started flow over an isolated circular cylinder is simulated, and early stages of flow development are studied. Also, the variation of force coefficients and vortex shedding frequency with Reynolds number for fully-developed flows are obtained. Transverse oscillations of a circular cylinder in a cross-flow are investigated, and a lock-in diagram is obtained. Effects of the frequency and amplitude of oscillation on force coefficients and Strouhal frequency are studied. In-line oscillations of a circular cylinder are also simulated, and a similar investigation is performed. Unsteady flow over elliptic cylinders at high angles of attack is simulated. A conformal transformation is used to map the body onto a unit circle, and computations are conducted in the transformed plane. Detailed information on the velocity and vorticity fields around stationary and pitching elliptic cylinders are given. The effects of several parameters on the flow field are investigated. The dynamic stall flow over a pitching NACA 0012 airfoil is simulated. A similar conformal transformation to that employed for the elliptic cylinder is also used in this case. The process of flow separation, vortex formation and release, and flow reattachment during pitching cycles are studied, through streamline and vorticity contour plots. Hysteresis loops for the force and pitching moment coefficients are obtained, and the effects of several parameters on the dynamic stall characteristics of the airfoil are investigated.