Evaluation of Ultrasound Technique for Solid-Propellant Burning-Rate Response Measurements

Abstract

The development of an ultrasound technique for precisely measuring the instantaneous regression rate of a solid-rocket propellant under transient conditions is reviewed. The technique is used to measure the burning-rate response of several solid propellants to an oscillatory chamber pressure with a frequency of up to 300 Hz. This measurement is known as the propellant's pressure-coupled response function and is used as an input into rocket stability prediction models. The ultrasound waveforms are analyzed using cross-correlation and other digital signal processing techniques to determine burning rate. Digital methods are less prone to bias and offer greater exibility than other techniques previously used. The resulting data are corrected for compression effects. The effects of a changing thermal pro le on the measurement are discussed. Other phenomena that may corrupt the measurement, such as surface roughness, are also covered. Results of the experiments are compared to data from two other measurement techniques: a T-burner and a magnetic owmeter. Nomenclature A= quasi-steady gas-phase and solid-phase reaction layer, homogeneous, one-dimensional solid (QSHOD) parameter, .@ P r=@ T s / p A = amplitude, or envelope function a T = temperature shift factor B = QSHOD parameter, .@ P r=@ T 0 / p C = group velocity C 1 , C 2 = Williams-Landel-Ferry (see Refs. 28 and 51) constants, see Eq. (26) c = phase speed d = particle diameter f = frequency, or arbitrary function G = spectral density function, or shear modulus g = arbitrary function h = propellant height i = .¡1/ 1=2 K = bulk modulus k = wave number M = bulk longitudinal modulus n = QSHOD parameter, .@ P r=@ p/ T0 n s = QSHOD parameter, .@ P r=@ p/ Ts P = principal part p = pressure R = cross-correlationfunction R = response function P r = burning rate T = period, or temperature t = time u = particle displacement in wave equation w = integration variable x = distance ® = attenuation coef cient 1t = round-trip time 1x = propellant thickness ± = round-trip time ±² = experimental erroŗ = QSHOD condensed phase eigenvalue, de ned in Eq. (21) º = Poisson's ratio » = thermal boundary-layer thickness ½ = density Ä = nondimensional frequency ! = frequency j j = magnitude of a complex number arg ² = phase of a complex number h i = averaged quantity Subscripts eff = effective f = nal value i = imaginary part, or initial value r = real part s = surface 0 = reference value Accents and Superscripts O = composite signal N = steady-state quantity 0 = unsteady quantity Q = Hilbert transform of a signal

Magnetic Flowmeter Burner Measurement of a Solid Propellant Pressure-Coupled Imaginary Response

“…A value of 10.0 was the maximum real part of the response measured over 97 tests spread among six different propellant formulations over a pressure range from 2.0 to 7.0 MPa, but over the same tests, the measured values of the imaginary part ranged from the unrealistic values of 8:0 to 82.0. Although only the real part of the response is required to perform a stability analysis for a solid rocket motor, the imaginary part is of interest to compute the absolute magnitude of the response and for comparison to other response-measuring devices, such as the ultrasound burner, that are capable of measuring the imaginary part [5,6]. The absence of a scientific understanding of why the magnetic flowmeter burner is unable to accurately measure values of the imaginary part casts doubt on its ability to accurately measure the real part.…”