椭圆翼型动态失速流场模态分解与重构

Mode decomposition and reconstruction of dynamic stall flow field of an elliptic airfoil

  • 摘要: 为深入研究椭圆翼型动态失速特性、捕捉流场非定常结构,基于非定常雷诺平均纳维-斯托克斯方程(URANS),并通过SST k-ωγ-Reθt进行湍流建模,建立了一套适用于椭圆翼型流场模拟的数值方法。随后,对相对厚度为16%的椭圆翼型深度动态失速的工况进行了数值模拟,并在时域上对流场非定常特征、气动力系数变化规律进行了深入分析。通过动态模态分解技术(DMD)对速度和压力进行了特征提取,并以模态能量占比为理论基础,建立了共轭模态的截取方法,开展了流场重构与误差评估。结果表明,椭圆翼型在抬头侧前缘处产生的分离泡是其动态失速涡形成的重要征兆,各阶模态能有效描述动态失速的动力学特征,且与时域上的主要流动特征存在着一致性。在各阶模态之中,一阶模态为静态模态,体现出翼型深度失速的流动特征,而流场的非定常结构则来源于共轭模态的贡献。除去一阶模态,采用75%~95%能量占比的共轭模态重构流场能一定程度地反映气动力系数在时域上的变化规律,但无法准确描述精细的非定常细节。采用99%能量占比的共轭模态重构流场,虽然在翼型发生严重流动分离的时刻存在着较大的误差且在捕捉近壁分离泡的流动细节上精度有限,但在重构气动力系数上已具有较高的精度与较为有效的模型降维能力,在工程上具有应用价值。

     

    Abstract: In order to deeply understand the dynamic stall characteristics of elliptic airfoils and capture the main unsteady structures of the flow field, a numerical method suitable for simulating the flow field of elliptic airfoils was established based on unsteady Reynolds-averaged Navier-Stokes (URANS) equations and k-ω SST, γ-Reθt turbulence models. Subsequently, simulations were carried out for the case of deep dynamic stall of an elliptical airfoil with a relative thickness of 16%, and the unsteady characteristics of the flow field and the variations of aerodynamic coefficient were thoroughly discussed in the time domain. The characteristics of velocity and pressure fields were extracted by dynamic mode decomposition (DMD) technique, and the flow field reconstruction and error assessment were carried out by establishing truncation methods of conjugate modes based on the theory of mode energy proportion. The results show that the appearance of separation bubbles generated by the elliptic airfoil at the leading edge during the upstroke process is an important sign of the dynamic stall vortex formation. The modes of each order can effectively characterize the dynamics of dynamic stall, which are consistent with main flow features in the time domain. The conjugate modes contribute to the unsteady components of the flow field, while the first-order DMD mode reflects the uniform flow field showing characteristics of deep stall of the airfoil. Excluding the first-order mode, the reconstructed flow field using 75%-95% energy proportion of the conjugate modes can capture variations of the aerodynamic coefficients in the time domain to a certain extent, but fails to describe fine unsteady details accurately. Although the reconstructed flow field using 99% energy proportion of the conjugate modes has certain errors when the airfoil undergoes severe flow separation, and the accuracy in capturing fine flow details of near-wall separation bubbles remains limited, it still presents a decent accuracy in aerodynamic coefficient prediction and effectiveness in dimensionality reduction, showing its value in engineering applications.

     

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