Flowfield Computations in Rotating Propulsive Nozzles

Abstract

AN analysis is presented for calculating the flowfield and the forces and moments acting on the supersonic section of a propulsive nozzle during both nozzle and vehicle rotations. The governing equations are derived in a noninertial reference frame attached to the nozzle for the most general case where the nozzle has both angular velocity and acceleration with respect to the vehicle and the vehicle has both angular velocity and acceleration as well as linear acceleration with respect to Earth. The resulting equations are placed in characteristi c form for steady, three-dimensional, nonequilibrium, chemically reacting, supersonic flow. A production computer program was developed to compute the flowfield using a second-order, three-dimensional, bicharacteristic method. Examples are presented to illustrate the type of results that can be expected. Contents A common method of thrust vector control for solid propellant rocket motors is based on rotating the nozzle, thus generating side forces and torques due to the change in direction of the gas flowfield. In most applications, the rate of rotation and nozzle flow rates are such that the forces due to the angular motion are relatively small and may be ignored. However, for fast response systems using very large nozzles and high chamber pressures, the gasdynamic forces due to angular motion of the nozzle and/or vehicle may be significant. The angular motion of the nozzle and/or vehicle causes the flowfield to become three-dimensional even if the nozzle geometry is axisymmetric. Thus, to determine the flowfield requires using a three-dimensional algorithm. The objective of this study was to develop an analysis for calculating the flowfield and the forces and moments acting in a propulsive nozzle during nozzle and vehicle rotations. The approach consisted of expanding an existing computerized analysis for steady, three-dimensional, nonequilibrium, chemically reacting, supersonic flow to include momentum equation terms due to nozzle and vehicle rotations. The existing computer program was based on the work of Ransom et al. 1 and Cline and Hoffman.2 The governing equations were derived for the most general case where the nozzle has both angular velocity and acceleration as well as linear acceleration with respect to Earth. A numerical integration