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.

中文翻译：

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数值共形映射方法与几何分离姿态的关系：燃烧室内部流动模拟

本文介绍了二维燃烧室中流动分析的数值解决方案，该燃烧室有两个平行的进气口用于推进剂的进入，解决了许多相互依赖的不同问题：离散点内涡流影响的流动，速度受电池中流动状态的影响，燃烧问题受氧气和燃料从电池壁进入的影响。燃烧室的形状由方形截面和半圆形截面构成。该问题的数学模型包括一个不均匀的流函数拉普拉斯方程，该方程与部分微分质量守恒方程耦合，该方程受到壁面非侵入条件和壁面开口中已知质量值的影响。代数共形映射变换已用于建模复杂的单元格几何。通过对电流函数和质量计算使用迭代高斯-赛德尔方法获得解。与用于校准目的的另一种建模方法进行了比较；分别考虑每个几何成分，而在两个部分之间应用连续条件。网格类型为：（1）直角坐标在正方形部分中的均匀网格，以及（2）极坐标在均匀圆形中的网格。发现不同的初始猜测对最终解决方案没有影响，但是有根据的初始猜测会影响解决方案的时间收敛迭代次数。最后，研究了混合涡流对燃烧室中火焰前沿位置的影响。