Analysis of Injecting Wall Inclination on Segmented Solid Rocket Motor Instability

Abstract

The influence of solid propellant inclination angle was analyzed through small-scale setup simulations. Two injected blocks separated by thermal protection reproduced the main geometric solid rocket motor features, and a dual phenomenon driving interactions between the shear layer and injecting wall vortex-shedding phenomena was clearly identified at any inclination angle. A threshold angle level was also pinpointed, and it literally controls either the decrease of oscillation levels for small angles or the increase of the coupling energy involved. Under similar dynamic conditions, a decreasing factor of two was observed between 0 and 1:5 deg, whereas an even higher amplification factor was noted for 2 deg. Correlation coefficients and phase-averaged analysis have allowed the authors to clearly explain these opposed trends by depicting the wall and shear-layer interactions along the chamber. Nomenclature a = sound velocity, m=s f n na=2L = nth longitudinal acoustic mode, Hz H c = channel height, m H = nozzle height, m It u 02 v 02 p =aM = turbulence intensity L = channel length, m L v = distance between the obstacle and the nozzle location, m M q m =awH c = characteristic Mach number based on the mass flow rate M M=1 L v = H c tan = modified Mach number P = static pressure, Pa q m = total mass flow rate, kg=s R x 0 y 0 x 0 ty 0 t = x 02 t q y 02 t q = correlation coefficient of arbitrary functions of time x 0 and y 0 S x 0 s x 0 =x 02 = normalized power spectral density, Hz 1 s x 0 = power spectral density T = period, s U u=U 0 = normalized mean velocity in each section U 0 = characteristic velocity, m=s u = mean velocity in each section, m=s u, v = velocity component in X and Y directions, m=s w = channel width, m X, Y = nondimensional axis normalized by H c = angle of inclination = density, kg=m 3 = time delay, s z = vorticity normalized by U 0 =H c Superscripts 0 = fluctuating component = time averaged h i = phase averaged

Vorticity generation and acoustic resonance of simulated solid rocket motor chamber with high wave number wall injection

“…The first category of the computational and analytical results deals with the steady state flow solutions that is generated by a constant side wall mass injection (V rw = À1) from the upper side of the chamber. There are several recent experimental investigations through small-scale setup simulations for the solid rocket motor chamber by Nguyen et al [24] and Deng et al [25,26]. The experimental results for the steady state flow by the latter are compared with the current mathematical models in order to validate the computational approach for the steady state solution.…”

“…Finally, the generation and evolution of the vorticity at several times t = 8, 16,24, and 40 at n = 3 for the non-resonance frequency is presented in Fig. 17.…”