Novel Technique for Reconstructing High-Frequency Transient Rocket Chamber-Pressure Measurements

Abstract

An algorithm for reconstructing transient rocket chamber pressures from attenuated time histories is presented. This method is presented as an alternative to traditional methods, in which motor pressures are sensed by transducers mounted close-coupled to the motor casing. This close-coupled installation presents several significant measurement issues, including potential structural weakening of chamber walls, overheating of the pressure sensing element, motor-case strain biasing of the sensing element, and resonance within the measurement port. A less complex, and consequently less risky, installation is to tap the case at desired locations using very small pressure ports and then transmit pressure from the port to a pressure transducer using a significant length of pneumatic transmission tubing. This installation allows the transducer to be mounted in a controlled environment and virtually eliminates any sensing errors due to motor-case strain. Very small pressure taps are far easier to integrate with motor-case walls and allow multiple longitudinal measurements to be obtained without significantly reducing the structural integrity of the motor case. The method, based on optimal deconvolution theory, amplifies attenuated pressure signals while rejecting additive noise. The method is validated using laboratory-derived data and then applied to reconstructing transient chamber pressure for a small-scale solid rocket motor. Nomenclature= characteristic velocity, m=s c = sonic velocity, m=s D = tube diameter, mm E = expectation operator G = optimal deconvolution function i = frequency index J = cost functional j = complex constant, 1 1=2 k = time index L = tube length, cm M = number of data points in record N = frequency-domain noise, kPa=s kNk 2 = measurement variance, kPa 2 n = discrete-time advance index P c = chamber pressure, kPa P L = frequency-domain response (sensed) pressure, kPa kP LL k 2 = measured pressure variance, kPa 2 . P 0 = frequency-domain input pressure to pneumatic tubing, kPa kP 0L k = covariance, kPa 2 . kP 00 k 2 = measured pressure variance, kPa 2 . p L = time-domain response pressure, kPa p 0 = time-domain input pressure to pneumatic tubing, kPatransducer volume, cm 3 x = longitudinal coordinate, cm z = discrete-frequency response variable, 1=s t = sample interval, s p = wave propagation factor = ratio of specific heats = damping ratio = time-domain noise function, kPa = dynamic viscosity, N s=m 2 = time-domain convolution function = polytropic exponent = fluid density, kg=m 3 0 = mean fluid density in tube, kg=m 3 = time lag or dummy variable, s, = frequency-domain convolution function ! = angular frequency, rad=s ! n = radian natural frequency, rad=ŝ = optimal estimate Subscripts I = imaginary component of complex number R = real component of complex number Superscript = complex conjugate

Closed-loop Dynamic Stall Control Using a Plasma Actuator

“…A model which corrects for attenuation and phase lag associated with pneumatic tubing was developed by Berg and Tijdeman [2] in the 1970s. This model has been improved over the years, most recently by Whitmore and Wilson [24].…”

“…The Berg and Tijdeman model is an ideal system that amplifies all attenuated frequencies, including frequencies often associated with high frequency noise in the measured signal. Whitmore and Wilson [24] extended the Berg and Tijdeman model by applying a Weiner filter in order to avoid the amplification of high frequency noise. The filter is given by…”

Transient thrust behavior of low‐aspect‐ratio rocket propulsion systems**

“…Whitmore et al [4] presented a novel technique to reconstruct high-frequency chamber pressure measurements in transient situations in which their analysis on the thrust force was based on the general thrust formula. Drummond [5] focused on transient thrust prediction for an ejector propulsion system using common thrust force formula too.…”

Flow structure of pressure transmission tube and its influence on unsteady pressure measuring results in compressible flow

“…To validate theoretical models [2][3][4][5] or apply the inverse correction method [7], experimental methods for the calibration of tube dynamic response have been developed [8][9][10][11][12]. In most calibration experiments, a sine-like periodic pressure signal is imposed as the input signal, and it is measured by two pressure transducers at the same time.…”