压气机叶栅非定常线性自回归气动降阶模型研究

Unsteady Linear Autoregressive Aerodynamic Reduced-Order- Model of Compressor Cascade

关键词:  压气机叶栅  降阶模型  非定常流动  带外输入自回归模型  动态气动边界

Key words:  Compressor cascade  Reduced-order-model  Unsteady flow  Autoregressive with exogenous input  Dynamic aerodynamic boundary

摘要:

为满足叶轮机械领域高效非定常气动计算的迫切需求，采用线性带外输入的自回归（ARX）理论建立了高亚声速压气机叶栅非定常气动性能降阶模型。该降阶模型构造简单，建立较为容易。通过逐渐增加输入/输出延迟阶数，可以获得较高精度的模型超参数。研究结果表明：降阶模型对线性非定常系统的气动参数响应具有较好的预测精度，但在部分无量纲总压一阶幅值比以及无量纲静压一阶相位角存在一定预测误差。非定常系统线性工况下，同一折合频率的气动参数的一阶幅值比和相位角基本不随攻角幅值的增加而变化。通过与具有泛化能力的非线性降阶模型比较，基于线性假设发展的ARX模型能获得更高精度的气动参数响应。

Abstract:

In order to meet the urgent needs of efficient unsteady aerodynamic calculation in the field of turbomachinery， a reduced-order model of unsteady aerodynamic performance of a typical high subsonic compressor cascade was established by using the linear autoregressive with exogenous input（ARX） theory. The reduced-order model had simple structure and was easier to build. The results show that the high-precision model hyper-parameter can be obtained by gradually increasing the delay order of input/output， which had better accuracy for the response of aerodynamic parameter of the linear unsteady system. However， some of the first-order amplitude ratios of the dimensionless total pressure and the first-order phase angle of the dimensionless static pressure had slight errors. The first-order amplitude ratio and phase angle of the aerodynamic parameters with the same reduced frequency has no variations with the increase of the angle of attack amplitude under the linear working condition of the unsteady system. Compared with the nonlinear reduced-order model with generalization ability， the ARX model developed based on the linear assumption can obtain higher-precision response aerodynamic parameter.