Nonlinear Analysis of Unsteady Flows in Multistage Turbomachines Using Harmonic Balance
Nonlinear Analysis of Unsteady Flows in Multistage Turbomachines Using Harmonic Balance
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DOI：
10.2514/1.22888
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发表时间：
2007-05
期刊：
影响因子：
2.5
通讯作者：
K. Ekici;K. Hall
中科院分区：
文献类型：
--
作者：
K. Ekici;K. Hall
提出了一种用于分析多级涡轮机中二维线性（小扰动）和非线性非定常流的谐波平衡技术。本方法使用混合时域/频域方法，允许计算多级机器对叶片振动（颤振问题）和尾流相互作用（强迫响应问题）的非定常空气动力学响应。一般来说，流场可能具有多个彼此不是整数倍的激励频率，因此非定常流在时间上（有时）是非周期性的。使用我们的方法，我们使用跨越单个叶片通道的计算网格对每个叶片排进行建模。在每个刀片行中，我们存储了几个子时间级别的解决方案。对于时间上周期性的流，这些子时间级别跨越单个时间段。对于非周期性流，这些子时间级解所跨越的时间周期足够长以对非周期性流中包含的相关离散频率进行采样。在这两种情况下，这些子时间级解通过欧拉或纳维-斯托克斯方程和边界条件中的时间导数项相互关联；复杂的周期性条件连接叶片通道内的子时间水平，行间边界条件连接叶片排之间的解。所得到的离散方程在数学上是稳定的，因为时间导数已被伪谱算子取代，其中激励频率作为参数出现，可以使用多重网格加速技术非常有效地求解。在本文中，我们将该技术应用于颤振和尾流相互作用问题，并说明了相邻叶片排对叶片排非定常空气动力响应的影响。
A harmonic balance technique for the analysis of two-dimensional linear (small-disturbance) and nonlinear unsteady flows in multistage turbomachines is presented. The present method uses a mixed time-domain/frequency-domain approach that allows one to compute the unsteady aerodynamic response of multistage machines to both blade vibration (the flutter problem) and wake interaction (the forced response problem). In general, the flowfield may have multiple excitation frequencies that are not integer multiples of each other, so that the unsteady flow is (sometimes) aperiodic in time. Using our approach, we model each blade row using a computational grid spanning a single blade passage. In each blade row, we store several subtime level solutions. For flows that are periodic in time, these subtime levels span a single time period. For aperiodic flows, the temporal period spanned by these subtime level solutions is sufficiently long to sample the relevant discrete frequencies contained in the aperiodic flow. In both cases, these subtime level solutions are related to each other through the time-derivative terms in the Euler or Navier-Stokes equations and boundary conditions; complex periodicity conditions connect the subtime levels within a blade passage, and interrow boundary conditions connect the solutions among blade rows. The resulting discretized equations, which are mathematically steady because time derivatives have been replaced by a pseudospectral operator in which the excitation frequencies appear as parameters, can be solved very efficiently using multigrid acceleration techniques. In this paper, we apply the technique to both flutter and wake-interaction problems and illustrate the influence of neighboring blade rows on the unsteady aerodynamic response of a blade row.