Numerical Analysis of Port Diameter Effect on Hybrid Rocket Fuel Regression Rate with Axial Injection

Abstract

Numerical simulations of the flowfield in a hybrid rocket motor are carried out with a Reynolds averaged Navier-Stokes solver including detailed gas surface interaction modeling based on surface mass and energy balances. Results are compared with several test data obtained from two dedicated test campaigns conducted with static firings of a laboratoryscaled hybrid rocket in which gaseous oxygen is fed into axisymmetric hydroxyl-terminated polybutadiene cylindrical grains through an axial conical subsonic nozzle. A first numerical rebuilding of all of the firing tests has been performed to validate the model, highlighting its prediction capabilities and modeling limits. Despite the several geometrical simplifications, which allowed relatively modest grid sizes to be used and efficient parametrical analysis to be performed, the presented CFD approach is fairly able to capture the main features of the motor internal ballistics both in terms of average chamber pressure and regression rate trends with oxidizer mass flux and port diameter. Computed flowfields showed the establishment of a significant recirculation region at the motor head end, which promotes propellant mixing, and raises the fuel regression rate. Numerical simulations, supported by the experimental results, demonstrated the main role played by the characteristics of this particular injection configuration in determining the fuel regression rate spatial distribution and trend, and clarified the mechanism for which the port diameter has a direct influence on the fuel regression. Nomenclaturē m = time-averaged mass flow rate, kg/ṡ ω i = species source term in control surface, kg/m 2 · ṡ m = mass blowing rate per unit area, kg/m 2 · ṡ q = heat flux, W/m 2 r = regression rate, m/ṡ w i = species source term in control volume, kg/m 3 · s η = inward (from solid to gas) coordinate normal to surface ρ = density, kg/m 3 D im = effective diffusion coefficient, m 2 /s h = enthalpy, J/kg k = thermal conductivity, W/m · K M = molecular weight of the species, kg/kmole N = number of species p = pressure, N/m 2 T = temperature, K v = velocity component normal to surface, m/s y = mass fraction y + = dimensionless wall distance Subscripts f = fuel i = species s = solid material w = wall Superscripts = average in time and spacê = average in space