Control of vortices over slender conical bodies - a theoretical and computational study

Abstract

Pneumatic controls of vortices over slender conical bodies at high angles of attack and low speeds are studied by a theoretical method developed by Cai, Liu, and Luo (J. of Fluid Mech., vol. 480, 2003, pp.65-94) and verified by Euler computations. The theoretical method is based on an eigenvalue analysis on the motion of the vortices under small perturbations, which pertains to the absolute-type of instability. Steady blowing and suction are simulated by sources and sinks. A modification of the original model to account for the effects of the vortex core is implemented. The theory predicts the positions of stationary conical vortices and their stability. The numerical solver is based on a multi-block, multigrid, finite-volume method and parallel code for the steady and unsteady Euler and Navier-Stokes equations implemented on overset grids. The Euler algorithm has strictly symmetric characteristics, is capable to capture stationary symmetric vortex flows, and can simulate the flow-instability developments under small asymmetric temporal disturbances. Conical slot suction and blowing with a small amount of mass-flow-rate are introduced to stabilize the originally unstable stationary symmetric vortex flow over a circular-cone and a flat-plate delta wing combination, and to manipulate the vortices over a delta wing symmetrically to increase/decrease normal force and antisymmetrically to produce rolling moment. The theoretical predictions agree well with the Euler computations. © 2004 by the authors.