Analytical modeling of a spherical combustor including recirculation

Abstract

In order to predict rocket-engine performance and heat transfer, it is desirable that thelocal flow and thermal fields within a combustion chamber be completely determined. In a recent book, (Ref. 1), Spalding and his associates outline a numerical procedure for the solution of the flow and energy equations which allows the existence of recirculation, reacting gases (combustion), eddy mixing, and compressibility. The uniqueness of this approach lies in the transformation of the separate conservation equations—mass, stream function, vorticity, and energy—into one standard format, a nonlinear, elliptic, partial differential equation. This coupled system of P.D.E.'s is then solved by a finite-difference procedure, using the Gauss-Seidel iterative technique. Specifically, this program computes the complete flow and thermal field, including swirl velocities, for two-dimensional or axisymmetric flow. The only inputs required are the chamber geometry and propellant inlet conditions. Improvements to this program have been made at Bell Aerospace to allow for the injection ofdissimilar gases (oxygen and hydrogen) at extreme velocity differences (100 to 2400 fps). These results, which correlated quite well with experimental performance data for a cylindrical combustion chamber, ere presented in a previous paper (Ref. 2). More recently, a spherical combustion chamber with opposing propellant injection (reverse-flow combustor) has been evaluated for an attitude-control gaseous-rocket engine. The oxidizer has been injected with superimposed swirl velocity. The purpose of this paper is to present the methods used to adapt the modified Spalding computational technique to the reverse-flow combustion chamber.