Rotational inviscid flow in laterally burning solid-propellant rocket motors

Abstract

A theoretical analysis to determine the effects of mass addition on the inviscid but rotational and compressible flowfield in a porous duct with the injection rate dependent on the local pressure is performed for large ratios of length-to-duc t diameter. The problem of describing the flow is reduced to the solution of a single integral equation. The ratio of specific heat 7, and a constant pressure exponent u, measuring the dependence of the rate of mass injection on the local pressure, are the parameters of the solutions. The integral equation is solved numerically, and parametric results are presented for 7, varying from 1 to f and for n varying from 0 to 1. A choking phenomenon is exhibited at a critical length of the duct in the vicinity of which the Mach number approaches unity. The choking condition, which is relevant to the operation of nozzleless solid-propellant rocket motors, is obtained parametrically in the present study and compared with corresponding results for irrotational, quasi-one-dimensional flow. The rotationality reduces the choking pressure. Nomenclature A = cross-sectional area of the duct a = radius of the duct C = average speed-of-sound in the fluid cp = the specific heat of the fluid at constant pressure h = half-height of channel 7sp = specific impulse of the motor K = constant prefactor in the burning-rate law for the propellant / = length of the duct M = Mach number m = mass burning rate of the propellant n = pressure exponent in the burning-rate law for the propellant P = nondimensional pressure p/pQ p = dimensional pressure R - ratio of the specific impulse obtained by assuming quasi-one-dimensional flow to the specific impulse obtained by assuming rotational flow r = dimensional radial coordinate 5 = perimeter of the duct T - temperature t = time u = axial component of the velocity Vw = injection velocity v = radial component of the velocity X — nondimensional axial strained coordinate defined in Eq. (23) x = dimensional axial coordinate y = distance normal to.the propellant surface y = ratio of specific heat A =. boundary-layer thickness 8 = gas-phase flame standoff distance 17 = dimensional transverse coordinate in channel flow p pp = gas density = propellant density = function related to entropy