论文标题
用于传热的准二维线性化欧拉方程的解决方案
A solution for the quasi-one-dimensional linearised Euler equations with heat transfer
论文作者
论文摘要
对声和/或熵波强迫的稳定传热的喷嘴的不稳定响应进行了建模。该方法基于准二维线性化的欧拉方程。这些方程是用三个变量来施放的，即无量纲质量，停滞温度和熵波动，它们在零频率下是系统的不变性，没有热传递。然后使用Magnus膨胀方法求解所得的微分方程的一阶系统，其中扰动参数是归一化频率和体积热传递。在这项工作中，对流量非分散性的度量（在这种情况下，稳定的传热）首次将其用作扩展参数。将溶液方法应用于亚临界和超临界流动案例的恒定热传递的收敛变化喷嘴，显示出与数值预测的良好一致性。据观察，喷嘴的声学和熵转移函数在很大程度上取决于频率和传热。
The unsteady response of nozzles with steady heat transfer forced by acoustic and/or entropy waves is modelled. The approach is based on the quasi-one-dimensional linearised Euler equations. The equations are cast in terms of three variables, namely the dimensionless mass, stagnation temperature and entropy fluctuations, which are invariants of the system at zero frequency and with no heat transfer. The resulting first-order system of differential equations is then solved using the Magnus expansion method, where the perturbation parameters are the normalised frequency and the volumetric heat transfer. In this work, a measure of the flow non-isentropicity (in this case the steady heat transfer) is used for the first time as an expansion parameter. The solution method was applied to a converging-diverging nozzle with constant heat transfer for both sub-critical and super-critical flow cases, showing good agreement with numerical predictions. It was observed that the acoustic and entropy transfer functions of the nozzle strongly depend on the frequency and heat transfer.
