Combustion Instability Involving Vortex Shedding in Hybrid Rocket Motors

Abstract

Hybrid rocket motors usually have an aft-mixing chamber in order to improve combustion efficiency. The presence of a sudden expansion at the exit of the fuel port determines the formation of vortices, whose vigourous burning may drive acoustic waves in the chamber. The shedding of vortices itself is then affected by the flow fluctuations, producing a well-known feedback loop. A reduced-order model, introduced by Matveev and Culick in 2003, is here used to analyze this phenomenon. It is assumed that vortex burning is localized in space and time, and a kicked oscillator model is utilized. A one-dimensional model proposed by the authors is used to determine the values of the eingenacoustic modes and corresponding damping coefficients. Numerical results are compared to experimental data. I. Nomenclature a = speed of sound D = port area diameter G = nondimensional parameter H = Laplace transform k = wave number L = Laplace transform operator L 1 = nozzle entrance coordinate N = number of modes p' = pressure fluctuation p 0 = undisturbed pressure Q = heat addition Sr = Strouhal number t = time u = velocity u' = velocity fluctuation = mean velocity x = longitudinal coordinate α = damping coefficient η = mode amplitude ψ = wave form Γ = circulation ω = angular frequency Subscripts i = mode number j = vortex number n = mode number 1 Professor, Dipartimento di Ingegneria Meccanica e Aerospaziale, C.so Duca degli Abruzzi 24. Senior Member AIAA.