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本文用有限元法计算了固体发动机的响应函数。计算公式是在一步正向化学反应的阿累尼乌斯定律和由任意入射波的谐波声学扰动产生的压力耦合的基础上导出的。应用了在火焰区和分解区具有解析边界条件的多维非线性时间相关性方程。这些解析边界条件是用拉格朗日乘子法求得的。也包括在特殊介质中的辐射热传导。数值结果表明,所有变量(压力、密度、速度、温度、质量分数)在上游区的振荡特性是显著的,下游才逐渐趋向衰弱。数值结果还表明,辐射热传导在低频时对响应起阻尼作用,在高频时则起增大作用。
In this paper, the finite element method is used to calculate the response function of solid-state engine. The formula is derived based on the Arrhenius law of one-step forward chemical reactions and the pressure coupling resulting from the harmonic acoustic perturbation of any incident wave. A multi-dimensional nonlinear time-dependent equation with analytic boundary conditions in the flame zone and the decomposition zone is applied. These analytical boundary conditions are calculated by Lagrange multipliers. Radiative heat conduction in special media is also included. The numerical results show that the oscillation characteristics of all the variables (pressure, density, velocity, temperature, mass fraction) are significant in the upstream zone, and the downstream ones tend to weaken gradually. The numerical results also show that the radiative heat conduction dampens the response at low frequencies and increases at high frequencies.