Mitigation of Solid Booster Ignition over Pressure by Water Aerosol Sprays

Abstract

Interaction of acoustic waves with water aerosol layers is analyzed in the context of the problem of solid booster ignition overpressure suppression. In contrast to the conventional approach to ignition overpressure suppression, which aims at using water to quench the sources of the ignition overpressure waves, this study focuses on blocking the ignition overpressure wave propagation, using reflection and attenuation of the wave by the water aerosol layers. The study considers interaction of the waves with aerosol layers of large mass loading for varying sizes of the droplets. The size of the droplets is shown to substantially affect the mechanisms of interaction with the waves. The criteria for the crossover between different mechanisms are established as functions of the droplet size and the ignition overpressure wave parameters. The optimal parameters and designs for water aerosol sprays are proposed that maximize the ignition overpressure suppression. These results were obtained using the nozzle and the exhaust hole geometries similar to those of the space shuttle. Remarkably, it is found that various a priori reasonable designs of the aerosol and water sprays may increase the ignition overpressure impact on the vehicle, increasing the risk of vehicle damage. Nomenclature C D = drag coefficient C P = specific heat at constant pressure, J∕kg∕K c = sound velocity, m∕s d drop = droplet diameter, m f L = liquid volume fraction h = layer width, m j = mass flux, kg∕m 2 ∕s k = wave vector, 1∕m L D = thermodiffusion length, m M = million p = fluid pressure, Pa R g = gas constant, J∕kg∕K r drop = droplet radius, m T = fluid temperature, K T aer = transmission coefficient T wave = period of acoustic wave, s t = time, s u = gas velocity, m∕s α = attenuation coefficient, m −1 κ = thermal conductivity, W∕m∕K λ = wavelength, m μ = dynamic viscosity, Pa · s ν = frequency, Hz ρ = fluid mass density, kg∕m 3 σ = surface tension, N∕m σ st = Stefan-Boltzmann constant τ = typical time, s ω = angular frequency Subscripts aer = aerosol drop = droplet G = gas ign = ignition L = liquid s = surface, saturation v = vapor w = water 0 = initial state