Foundations of the Blade-Vortex Interaction Problem: Structure and Behavior of Travelling Compressible Vortices

The structure of a compressible free vortex has been analyzed while undergoing convection in a quasi-uniform stream flow. Holographic interferograms several reveal radial density profiles of the vortex at different stages of its development during convection. A general mathematical expression is found which closely describes the distribution of density inside the vortex. By use of experimental data and the governing equations in an empiricaltheoretical analysis, an extended physical description of the vortex is developed. The time behavior of the density, determined from the experiments, allows the solution of the Continuity Equation and a distribution of the radial component of fluid velocity relative to the vortex center is obtained. The density information, supplemented by an independent determination of pressure is the used in the Radial Momentum Equation to obtain a distribution of the circumferential component of fluid velocity relative to the vortex center, thus completing the description of the radial dependence of the velocities inside the vortex. Furthermore, the calculated velocities are used to evaluate the magnitudes of the convective and diffusive terms of the Angular Momentum Equation, thus providing insight into the question of the relative effects of compressibility and viscosity on the internal structure and behavior of the vortex in terms of the distribution and transport of angular momentum.