Regularities of Physical Processes in Hybrid Solid-Propellant Rocket Engines

Abstract

Safety and economy of delivery of a payload into its intended orbit necessitate the continued improvement of engine design for rocket boosters. A possible compromise in the requirements implied by this need is connected with the use in space systems of hybrid solid-propellant engines (HSPEs) working with liquid or gaseous oxidizers. Physical notions about the processes taking place during combustion of propellants and about heat and mass exchange were generalized in the review in [1], which, however, lacks a methodical basis for an analysis of interior-ballistic and gasdynamic processes in hybrid engines covering the entire time of their functioning. This brings us to the fact that a number of aspects of the processes taking place in hybrid solid-propellant rocket engines have received very little attention. Therefore, the goal of the present paper is to model key features of the physical processes taking place in hybrid solid-propellant rocket engines. Since the working process of an HSFE includes various periods of operation (substantially non-steady-state launch-and-ignition, depressurization, and an extended period of quasi-steady-state burning), the most optimal model within the framework of a unified approach is precisely the non-steady-state model. For the quasi-steady-state case, modeling of non-steady-state processes is the basis of one of the most effective methods for solving interior ballistics problems – the so-called relaxation method [2]. Typical schemes of hybrid engines are shown in Fig. 1. The basic equations for calculating the working parameters of an HSPE are formulated for the scheme of the solution domain presented in Fig. 2. The dynamics of the gas-dynamic characteristics is investigated in three subdomains of average parameters (oxidizer tank and head and prenozzle volumes of the combustion chamber), and also in the subdomain of a one-dimensional description of flow in the burning fuel channel. We consider a mechanical mixture of gases with arbitrary number of components, these being the oxidizer, the combustion products of the flammable components, possibly a multicomponent grain of fuel, and products of the gasification of thermal-insulation materials. The mathematical model is formulated on the basis of assumptions [2, 3] in which the conservation laws are augmented by two specially constructed equations for calculating the variation of the thermodynamic parameters of the mixture (the gas constant R and the isobaric specific heat Cp), and also two equations for calculating the viscosity of the gas mixture μ. In addition, an equation for the mass fraction of oxidizer C is added, which together with the viscosity coefficient of the mixture is needed to concretize the right-hand sides of the equations – to calculate the burning rate, the friction density ffr, and the heat loss density q. The mathematical model takes account of the physical character of the combustion process in the HSPE – the dependence of the rate of gasification of the solid propellant on the mass flux density of the oxidizer blowing the combustion surface. The balance relations for the mass of the gas were constructed taking into account the expenditure