Determination of Solid Propellant Admittances by the Impedance Tube Method

Abstract

The adaptation of the impedance tube technique for the measurement of solid propellant admittances and response functions is described. These quantities are needed for combustion stability analysis of solid rocket motors. The experimental set up consists of a tube with a disk of solid propellant sample placed at one end and a combination of an exhaust valve and an acoustic driver placed at the other end. Performing a test consists of turning on the acoustic driver to excite a standing wave of a predetermined frequency in the tube, ignition, and burnout of the solid propellant sample. During a test, acoustic pressure data is measured by fifteen pressure transducers distributed along a distance that includes, at least, two standing wave pressure minima. The data are transferred via a fast analog-to-digital converter to a minicomputer system for immediate storage and later analysis. The measured acoustic pressure amplitude and phase data are input into a newly developed data reduction procedure that is based upon the solution of the impedance tube wave equations, for the determination of the admittance and response function of the tested solid propellant sample and the acoustic energy losses in the gas phase. The paper presents results obtained in a series of tests conducted with an A-14 propellant. The paper demonstrates the capability of the developed experimental technique to determine simultaneously the acoustic characteristics of the flow inside the impedance tube and the admittance of the burning solid propellant for the duration of the experiment. Nomenclature A /y = defined in the Appendix C = constant defined in Eq. (8) c = velocity of sound, m/s cp - specific heat at constant pressure, kcal/kg K cv = specific heat at constant volume, kcal/kg K E = error function defined in Eq. (15),, (N/m 2)2 or Pa 2 F = losses due to viscosity and gas phase damping, kg/m2s2 G = gas phase bulk loss coefficient, kg/m3 s / = identity matrix M = Mach number m = mass flow rate per unit cross-sectional area, kg/m2 s p = pressure, N/m2 or Pa Q = volumetric heat source, kcal/m3 s mole R = gas constant, kcal/kg mole K r = burning rate, m/s s = entropy, kcal/kg K T = temperature, K; also transmission matrix defined in Eq. (10) TWQ = wall temperature at x = 0, K u = axial velocity, m/s Y = specific admittance, dimensionless Z = variable used to represent oscillatory quantities, defined by Eq. (6) ps = density of solid propellant, kg/m3 p = density, kg/m3 Superscripts (~) = variable describing a steady-state quantity ()' = variable describing a perturbation quantity