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arXiv 2007.16197physics.flu-dyn
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Re = 500,000时翼型层流分离泡的解析分析

Resolvent analysis of an airfoil laminar separation bubble at Re = 500,000

Chi-An Yeh, Stuart I. Benton, Kunihiko Taira, Daniel J. Garmann

摘要:

我们进行预解式分析,以检查层流分离泡(LSB)的扰动动力学,在弦基雷诺数为500,000和迎角为8度的NACA 0012翼型的前缘附近形成。随机奇异值分解被采用在本分析中,以减轻与高Re全球基流的计算成本。为了研究LSB上的局部物理,我们考虑使用指数折扣来限制允许不稳定性相对于基流发展的时间范围。通过折扣,频率上的增益分布准确地捕获从流动模拟获得的LSB上的频谱内容。峰值增益频率也同意以前的流动控制的结果抑制动态失速俯仰翼型。根据增益分布和模式结构,我们得出主要的能量放大机制是开尔文-亥姆霍兹不稳定性。除了贴现,我们还研究了空间窗口的使用强迫和响应。从响应窗口分析,我们发现,LSB服务的能量放大器的主要作用,与放大饱和的再附着点。输入窗口施加表面强迫的约束,结果表明,最佳的驱动器的位置是稍微上游的分离点。表面强迫模式还建议在表面切线方向上的最佳动量强迫,具有很强的单向性,这对于合成射流型致动器是理想的。这项研究证明了随机预解式分析在处理高雷诺数基流的强度,并呼吁注意基流不稳定性所需的护理。

英文摘要:

We perform resolvent analysis to examine the perturbation dynamics over the laminar separation bubble (LSB) that forms near the leading edge of a NACA 0012 airfoil at a chord-based Reynolds number of 500,000 and an angle of attack of 8 degrees. Randomized SVD is adopted in the present analysis to relieve the computational cost associated with the high-Re global base flow. To examine the local physics over the LSB, we consider the use of exponential discounting to limit the time horizon that allows for the instability to develop with respect to the base flow. With discounting, the gain distribution over frequency accurately captures the spectral content over the LSB obtained from flow simulation. The peak-gain frequency also agrees with previous flow control results on suppressing dynamic stall over a pitching airfoil. According to the gain distribution and the modal structures, we conclude that the dominant energy-amplification mechanism is the Kelvin-Helmholtz instability. In addition to discounting, we also examine the use of spatial windows for both the forcing and response. From the response-windowed analysis, we find that the LSB serves the main role of energy amplifier, with the amplification saturating at the reattachment point. The input window imposes the constraint of surface forcing, and the results show that the optimal actuator location is slightly upstream of the separation point. The surface-forcing mode also suggest the optimal momentum forcing in the surface-tangent direction, with strong uni-directionality that is ideal for synthetic-jet-type actuators. This study demonstrates the strength of randomized resolvent analysis in tackling high-Reynolds-number base flows and calls attention to the care needed for base-flow instabilities.

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