Self-consistent surface-temperature boundary condition for iquefying-fuel-based hybrid rockets internal-ballistics simulation

A novel methodology for the calculation of the surface temperature of liquefying fuels typically burned in hybrid rockets is proposed. This procedure stems from the formulation of a fuel in-depth pyrolysis model coupled with the resolution of the thermo-fluid-dynamic field in the rocket combustion chamber, which allows for the characterization of the unstable liquid layer formed on top of the fuel surface. The aim is the simulation of the internal ballistics of hybrid rocket engines fed by paraffin-based fuels without the need for parametrically assigning the surface temperature to match the experimental data as, indeed, required in the authors’ previous work. With the presented technique, surface temperature and fuel vaporization rate are calculated locally along the wall, and, with the integration of a liquid fuel entrainment model, which requires the tuning of just one parameter (i.e. the so-called entrainment factor), the fuel regression rate is determined. The overall numerical approach, upon the assumption that the liquid fuel is in the supercritical pressure regime, is based on the solution of the Reynolds-averaged Navier–Stokes equations for single-phase multicomponent turbulent reacting flow. A series of numerical simulations are carried out to unveil the effect of the oxygen mass flux, which allowed deriving an approximate analytical equation for the regression rate prediction. A set of hot fires of a laboratory-scale hybrid rocket are reproduced through single numerical simulations carried out on the fuel port average geometry in the burn to validate the computational model, showing deviations between the measured and predicted average regression rate less than 4.5%. In order to fairly match also the fuel consumption axial profile, transient numerical simulations over the entire engine firing are conducted with which the post-burn port shape is captured with maximum error of 8%.