Harmonic Balance Analysis of Blade Row Interactions in a Transonic Compressor
Harmonic Balance Analysis of Blade Row Interactions in a Transonic Compressor
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DOI：
10.2514/1.43879
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发表时间：
2010-03
影响因子：
1.9
通讯作者：
K. Ekici;K. Hall;R. Kielb
中科院分区：
文献类型：
--
作者：
K. Ekici;K. Hall;R. Kielb
本文应用谐波平衡技术分析了某进气道导叶与转子相互作用问题，并将计算结果与实验数据进行了比较。计算结果与实验结果吻合较好，表明该方法可以准确有效地模拟激波/叶片相互作用和非定常激波运动等强非线性周期流动。使用谐波平衡方法，无论实际叶片数量如何，每个叶片排都使用仅跨越单个叶片通道的计算网格进行建模。对于每个刀片行，存储了多个跨越单个时间段的子时间级解决方案。这些子时间级解通过欧拉（或Navier-Stokes）方程中的时间导数项相互关联，该项由伪谱算子近似，通过沿每排叶片计算域的周期边界的复周期性条件，以及叶片和转子之间的界面边界条件。将控制方程转换为谐波平衡形式消除了对时间的显式依赖。数学上，要解决的方程在形式上类似于稳定的欧拉（或纳维-斯托克斯）方程，附加的源项与不稳定的基本频率成正比。因此，传统的稳态计算流体动力学技术，包括局部时间步进和多网格加速，用于加速收敛，从而产生非常有效的非定常流解算器。
In this paper we apply the harmonic balance technique to analyze an inlet guide vane and rotor interaction problem, and compare the computed flow solutions to existing experimental data. The computed results, which compare well with the experimental data, demonstrate that the technique can accurately and efficiently model strongly nonlinear periodic flows, including shock/vane interaction and unsteady shock motion. Using the harmonic balance approach, each blade row is modeled using a computational grid spanning just a single blade passage regardless of the actual blade counts. For each blade row, several subtime level solutions that span a single time period are stored. These subtime level solutions are related to each other through the time derivative term in the Euler (or Navier―Stokes) equations, which is approximated by a pseudo-spectral operator, by complex periodicity conditions along the periodic boundary of each blade row's computational domain, and by the interface boundary conditions between the vane and rotor. Casting the governing equations in harmonic balance form removes the explicit dependence on time. Mathematically, the equations to be solved are similar in form to the steady Euler (or Navier―Stokes) equations with an additional source term proportional to the fundamental frequency of the unsteadiness. Thus, conventional steady-state computational fluid dynamics techniques, including local time stepping and multigrid acceleration, are used to accelerate convergence, resulting in a very efficient unsteady flow solver.