具有倾斜燃面的固体火箭发动机内流场解析解与数值解的分析比较

Analysis and comparison of analytical and numerical solutions of flow field in solid rocket motors with tapered sidewalls

运用解析方法与数值模拟方法,对具有倾斜燃面的固体火箭发动机内流场进行了研究。解析部分以二维不可压欧拉方程为基础,运用摄动法求解涡量-流函数非线性方程,得到了燃烧室内速度场、压力场及涡量场的解。数值模拟部分采用FLUENT软件中的层流模型与标准k-ε模型,针对不同雷诺数下的情况选择不同的模型,对该问题进行了数值模拟。主要研究了燃面倾斜角α与平直燃面长度L对燃烧室内流场的影响。结果表明,若不考虑倾斜效应,仅用平直燃面代替倾斜燃面,不仅会高估压降,而且会影响流场的其他参数,这种影响在加长燃烧室或大燃面倾斜角发动机中尤为突出。解析解与数值解基本吻合。

The flow field in solid rocket motors with tapered sidewalls was studied using both analytical method and numerical method. Based on incompressible Euler equation of two-dimensional flow, nonlinear vorticity-stream function equation was solved by using the method of perturbation in order to obtain the solutions of velocity field, pressure field and vorticity field. In the numerical part, the laminar model and standard k-ε model in FLUENT software were adopted to solve different problems at different Reynolds number separately. The results indicate that the influence of taper angle of sidewalls α and the length of straight sidewalls L is important, the pressure in chamber may be over estimated and the other parameters will be affected more remarkable without taking into account the taper angle, it is more obvious for longer chamber and larger burning sidewall. The numerical results are in agreement with the analytical solutions in the main.