Computer experiments related to chemical propulsion

Abstract

I. Introduction T HE use of high-speed computers has played an increasingly important role in the analysis of problems relating to chemical propulsion. In many cases the is merely used for the straightforward evaluation of the analytical expressions resulting from theoretical analysis; however, in an increasing number of problems the has played a central and indispensable role, being used as an apparatus to test theoretical models of the phenomenon under study. The use of such computer experiments'7 to study problems related to chemical propulsion forms the subject of the present survey. It is proposed that a experiment be defined as a theoretical analysis in which the use of the plays the central role in evaluating the consequences of the mathematical model of the physical phenomenon or process being studied. All such experiments involve first a formulation of the problem, second the development of a numerical scheme for solving the equations describing the process in question, then the actual computations, which would generally be impossible without modern high-speed computers, and finally an evaluation and interpretation of the results. The boundary between what can be classed as a experiment and a straightforward calculation will be somewhat arbitrary. Computer experiments take several different forms. In certain cases the physics of the problem is completely understood; however, the mathematical equations describing the phenomenon in question are intractable to analytical solution without the use of severe assumptions. Then high-speed computers are used to numerically evaluate the consequences of the equations. The calculations, made by Fromm 1 and others, of viscous flows over obstacles, and resulting in movies of the computed flow solutions, provide an outstanding example of this type of experiment. In other problems the detailed physics or the value of key physical constants may be uncertain. Thus, for example, reaction rate constant values needed to compute nonequilibrium gas flows may be known only to an accuracy of several orders of magnitude. Such problems are sometimes approached by developing a mathematical model that includes all possible factors of importance. Computer experiments or extensive calculations are then made to establish which factors are important, and which can be ignored. Duff's2 calculations of detonation structure which were carried out for several possible values of the key reaction rate constant provide an early example of this type of experiment.