Analysis of acoustic waves in a cold-flow rocket.

Abstract

A promising method for determining the losses in a rocket chamber during (combustioninstability is based on acoustic measurements at room temperature. This method permits the losses to be determined from experiments in a small-scale model of the actual chamber. The calculations presented here treat the acoustics of a chamber with mean flow; they are intended to be used in the design of such experiments and in the interpretation of data. NomenclatureA = admittance at boundary, defined by Eq. (9) a = sonic velocity D = tan 2 ft + 20 tanfi + X t t -unit axial vector / = dimensional frequency; also nonhomogeneous part of pressure boundary equation [Eq. (8)] h = nonhomogeneous part of pressure wave equation [Eq. (7)]k -nondimensional wave number for steady oscillations, 6>L/a ki = nondimensional wave number for purely axial mode classical oscillations kN = nondimensional wave number for classical mode oscillations I = axial mode number (ki/ir) Mo = magnitude of Mach number perturbation at head end of chamber N = X tan 2 ft -26 tanfi + 1 n = normal unit vector r = dimensionless radius, r/L S c = cross-sectional area of chamber S p = nozzle entrance area s = dimensionless entropy, v\ -P'/P t = time; nondimensional following Eq. (2) [(real time)/ (£/«)] X = square of the absolute value of complex nondimensional nozzle admittance, X = A* 2 + 0 2 Z -dimensionless head-end impedance, 17/M 0 ' t\ = nondimensional pressure, p'/yp 0 = imaginary part of nondimensional nozzle admittance A = imaginary part of k p -real part of nondimensional nozzle admittance <f > = a. + ip; tanh<£ = -A n 12 = real part of k n = nondimensional frequency, fl/(l -M c ) 2

Nozzle Damping in Solid Rocket Instabilities

“…13. One of the main conclusions of this study was that the impedance tube method appears to be the most suitable method for the measurement of nozzle admittances.…”

“…These data can then be used to determine the nozzle admittance at the resonant frequency by a procedure described in Ref. 13. This method suffers from most of the shortcomings that limit the applicability of waveattenuation methods.…”

Reduced Order Modeling Approach to Combustion Instabilities of Liquid Rocket Engines

“…In a rocket engine these are thermal, viscous, turbulent dissipation mechanisms and energy transport driven out of the geometric domain across the nozzle. Admittance has been extensively studied theoretically and experimentally ( [27][28][29][30][31]) and it is still today the subject of ongoing investigations. Thermal dissipation is the process by which a part of acoustic energy is converted into thermal energy.…”