Three-dimensional flow in rotating rocket motor nozzles

Abstract

A procedure used to calculate the effects of rocket motor rotation on the subsonic/transonic flowfield in axisymmetric rocket motor nozzles is presented. The governing equations for the unsteady three-dimensional flow of an ideal, in viscid fluid in thermodynamic equilibrium are derived in a noninertial reference frame. The governing equations are integrated numerically using MacCormack's explicit finite difference method. The boundary conditions are applied using Kentzer's method. The present technique is used to provide an accurate, steady, supersonic, initial-value surface for an existing method-of-characteristics analysis for steady three-dimensional supersonic flow. The steady supersonic initial-value surface is obtained as the asymptotic solution for large time of the unsteady subsonic/transonic flow analysis. This procedure can also be used to calculate the effects of inlet flow misalignment on the subsonic/transonic flowfield in nozzles. NomenclatureM =Mach number p = static pressure r L 0,z = coordinates R, f -position vectors, inertial and noninertial reference frames, respectively t = time v_ = velocity component V -velocity vector X = body force vector p = density oj = angular acceleration vector Subscripts M = relative to the missile TV = relative to the nozzle r,0,z -components XYZ, xyz = inertial and noninertial reference frames, respectively IntroductionT HE objective of this investigation 1 ' 2 was to develop an analysis and a computer program to predict the unsteady three-dimensional subsonic/transonic flowfields that occur in the inlets and throats of axisymmetric rocket motor nozzles, including the effects of rotation and inlet flow misalignment. The results of the present method can be used to provide an accurate steady supersonic initial-value surface (IVS) for an existing method-of-characteristics (MOC) analysis of the steady supersonic flowfield in the diverging portion of the nozzle. 3 One technique for generating the maneuvering torque for a fast response system is to rotate the supersonic portion of the propulsive nozzle to create a thrust misalignment and a corresponding turning torque. In the analysis of such a system, two questions arise: 1) how much missile turning torque is generated by a specified amount of nozzle rotation, and 2)