THEORETICAL STUDY OF VORTEX SHEDDING FROM BODIES OF REVOLUTION UNDERGOING CONING MOTION

摘要

Based on experimental evidence of the existence of a steady asymmetric vortex system on a slender body in coning motion, a theoret-ical flow model for vortex shedding was developed using potential flow methods and slender-body theory. The model provides for the calculation of the strength and position of each of the two vortices representing the areas of concentrated vorticity in the crossflow plane and the resulting force distribution induced on the body. Initial vortex locations very close to the body must be prescribed to start the compu¬tation. For cylindrical bodies, the results for vortex motion and forces were found to be quite sensitive to the initial positions. In order to investigate the nature of the initial condition problem, a linearized analysis of the vortex motion very close to the body was performed. Linearization was found to decouple the motion of the two vortices, so that the paths of the vortices could be obtained, but the relative positions of the two vortices along their paths could not. Upon specializing the body to a cone, it was found that the full nonlinear solution rapidly converged to a unique solution for symmetrical initial conditions, but that the solution was again sensitive to initial asymmetry.nOn the basis of agreement with data for a cone and an ogive cylinder in lunar coning motion, the flow model developed is felt to describe reasonably accurately the nature of the vortex-like separated flow over the body and the vortex-induced force distribution. The windward vortex is shown to be somewhat further distant from the body than the leeward vortex and to be somewhat stronger than the leeward vortex over the forward portion of the body. These differences are shown to produce a side force to leeward and a stabilizing side moment in correspondence with the measured results.nThe theoretical results were found to be quite sensitive to the assumed location of the separation lines. Accurate knowledge of the location of separation is required before a truly predictive method can be developed.