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A semi-analytical solution for acoustic wave propagation in varying area ducts with mean flow

机译：不同区域管道中的声波传播的半分析解决方案，平均流量

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A semi-analytical solution for the propagation of plane acoustic waves in a varying area duct, sustaining a mean isentropic flow with axial gas property gradients, is developed. A second order differential equation (ODE) for acoustic pressure is derived from the linearised Euler equations in the frequency domain, by neglecting the communication between acoustic and entropy disturbances. This ODE has axially varying coefficients and is solved using an adaptive WKB approximation method, so that the obtained wave-like solution consists of separate amplitude and phase factors, expressed as the superposition of downstream and upstream propagating wave components. This solution is valid at sufficiently large frequencies, meaning the frequencies considered must be low enough to ensure a predominantly one-dimensional acoustic field with negligible diffusive effects, but large enough for WKB method validity. A test case representing a typical industrial gas turbine combustor outlet converging section with a high mean-flow acceleration is considered for validation. Analytical results are compared to numerical solutions of linearised Euler equations neglecting acoustic-entropy coupling (2LEE). When the limiting frequency criteria are satisfied, the semi-analytical solution agrees well with the 2LEE results at even flow Mach-numbers around 0.5.
机译：开发了一种半分析方法，用于在不同区域管道中进行平面声波的传播，使得具有轴向气体特性梯度的平均等熵流。用于声压的二阶微分方程（ODE）通过忽略声学和熵干扰之间的通信来源于频域中的线性化欧拉方程。该颂歌具有轴向变化的系数，并且使用自适应WKB近似方法进行解决，使得所获得的波状溶液由单独的幅度和相位因子组成，表示为下游和上游传播波部件的叠加。该解决方案在足够大的频率上有效，这意味着所考虑的频率必须足够低，以确保主要的一维声场，扩散效应可忽略不计，但足以用于WKB方法有效性。代表具有高平均流量加速度的典型工业燃气涡轮燃烧器出口会聚部分的测试箱被认为是验证。将分析结果与忽略声学熵联轴器（2LEE）的线性化欧拉方程的数值解。当满足限制频率标准时，半分析解决方案均匀地同意，甚至流动MACH系列甚至约为0.5。

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