Prediction of asymmetric vortical flows around slender bodies using Navier-Stokes equations

Abstract

Steady and unsteady asymmetric vortical flows around slender bodies at high angles of attack are solved using the unsteady, compressible, this-layer Navier-Stokes equations. An implicit, upwind-biased, flux-difference splitting, finite-volume scheme is used for the numerical computations. For supersonic flows past point cones, the locally conical flow assumption has been used for efficient computational studies of this phenomenon. Asymmetric flows past a 5° semiapex-angle circular cone at different angles of attack, free-stream Mach numbers, and Reynolds numbers has been studied in responses to different sources of disturbances. The effects of grid fineness and computational domain size have also been investigated. Next, the responses of three-dimensional supersonic asymmetric flow around a 5° circular cone at different angles of attack and Reynolds numbers to short-duration sideslip disturbances are presented. The results show that flow asymmetry becomes stronger as the Reynolds number and angles of attack are increased. The asymmetric solutions show spatial vortex shedding which is qualitatively similar to the temporal vortex shedding of the unsteady locally conical flow. A cylindrical afterbody is also added to the same cone to study the effect of a cylindrical part on the flow asymmetry. One of the cases of flow over a cone-cylinder configuration is validated fairly well by experimental data.