Numerical conformal mapping method vs. geometrical separation attitude: Combustion motor chamber internal flow simulation

Abstract

This paper describes the numerical solution of flow analysis in a two‐dimensional combustion chamber with two parallel inlets aided for propellants entrance, addressing a number of different problems that depend on each other: the flow affected by a discrete point in‐cell vortex, the velocity affected by the flow regime in the cell, and the combustion problem affected by the oxygen and fuel entries from the cell walls. The shape geometry of the combustion chamber is made from a square section connected with a semi‐circular one. The mathematical model of the problem consists of an inhomogeneous stream function Laplace equation coupled to partial differential mass conservation equation subjected to a wall non‐intrusion condition and known mass values in the wall openings. Algebraic conformal mapping transformation has been used for modeling the complex cell geometry. The solution was obtained by using the iterative Gauss–Seidel method for both the current function and the mass calculation. Comparison with another modeling method for calibration purpose was performed; considering each geometrical component separately whereas continuous conditions were applied between the two sections. The grid types are: (1) a uniform grid in Cartesian coordinates in the square part, and (2) a uniform circular grid in polar coordinates. It was found that different initial guesses have not effect on the final solution, but an informed initial guess affects the solution time convergence iterations number to solve the problem. Finally, the effect of the mixing vortex on the location of the flame front in the chamber was investigated.