A parametric study of flame propagation in hybrid rocket motors

Abstract

A numerical study of flame propagation in hybrid rocket motors is conducted using a two dimensional, two domain physics based mathematical model. The main objective of the study is to identify the important flow and heat transfer parameters that determine the rate of flame propagation in these motors. The mathematical model is comprised of unsteady energy equations for each domain (the gaseous oxidizer and the solid fuel) which are coupled through an energy balance equation at the fuel-oxidizer interface. The equation at the interface includes convective cooling by the incoming gaseous oxidizer and radiative heating from the flame front. It is hypothesized that these two competing modes of heat transfer determine the rate at which the fuel surface temperature increases at the upstream of the flame front. And this in turn determines the flame propagation rate in the motor. The nonlinear partial differential equations of the mathematical model are solved using an explicit finite-difference technique. An analytical stretching is used in the vertical direction of the computational domain to obtain a finer resolution near the interface. The equations are first transformed using this stretching and then linearized using the numerical technique. Finally, the numerical model is adopted for the simulation of flame propagation in a subscale hybrid rocket motor with a two dimensional planar configuration of HTPB and gaseous oxygen. Numerical results confirm the hypothesis that radiation is the dominating heat transfer mode in determining the fuel surface temperature and therefore the rate of flame propagation. Nomenclature Symbols A Arrhenius factor c specific heat E activation energy e internal energy h heat transfer coefficient k thermal conductivity n refractive index q radiation flux R gas constant R0 motor port radius rb fuel regression rate t time T temperature of gas u axial velocity v transverse velocity x axial coordinate x0 axial length y vertical coordinate y0 fuel thickness Greek Symbols /?« diffusion mean extinction coefficient e emmisivity y transmittivity factor u effective viscosity p density a Stephan Boltzman constant 8 boundary layer thickness £ transformed distance in x-direction rj transformed distance in y-direction Subscripts ab e f int o r s ablation effective flame interface initial radiative solid fuel Introduction Professor. Member, AIAA. Graduate Student. Presently with LMMSS. ^Propulsion Engineer. Member, ASME. ^Propulsion Engineer, Member, AIAA. Copyright © 1998 by Akyuzlu and et. al. Published by AIAA with permission. It has been observed in various subscale experiments conducted by Lockheed Martin and others that certain fuel configurations in hybrid rocket motors results in a chamber pressure (Pc) phenomena which is called a DC shift. It is well documented that these shifts can occur at different times within the tests. The DC shift in a motor can be either positive or negative. A large performance deficiency is found during the low Pc portion of the test exhibiting a DC shift. Other researchers have also identified this unexpected phenomena while testing standard motor configurations but have attributed it to random events or spontaneous eruptions of high frequency oscillations [1]. A detailed explanation of this phenomenon was given by Arves and Jones in a previous publication [2]. It was concluded that the experimentally observed anomalies in motor performance are the result of deficiencies in combustion and that analytical models are needed to predict and validate the proposed mechanisms of such phenomenon. Here, such an attempt is undertaken by using a physics based mathematical model. two zones, the solid fuel and the gaseous oxidizer. Each domain is two dimensional (planar configuration). There is a well defined interface between the fuel and the oxidizer where the heat and mass exchange occurs. The heat exchange at the interface is due to conduction, radiation, and ablation of the fuel. The gaseous oxidizer is assumed to be optically thick therefore it is taken to be a radiatively participating gas. The flow is assumed to be steady and incompressible (subsonic) but thermally unsteady.