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Investigation of Görtler vortices in high-speed boundary layers via an efficient numerical solution to the non-linear boundary region equations
Theoretical and Computational Fluid Dynamics ( IF 3.4 ) Pub Date : 2021-07-03 , DOI: 10.1007/s00162-021-00576-w
Omar Es-Sahli 1 , Adrian Sescu 1 , Mohammed Afsar 2 , Yuji Hattori 3
Affiliation  

Streamwise vortices and the associated streaks evolve in boundary layers over flat or concave surfaces due to disturbances initiated upstream or triggered by the wall surface. Following the transient growth phase, the fully developed vortex structures become susceptible to inviscid secondary instabilities resulting in early transition to turbulence via ‘bursting’ processes. In high-speed boundary layers, more complications arise due to compressibility and thermal effects, which become more significant for higher Mach numbers. In this paper, we study Görtler vortices developing in high-speed boundary layers using the boundary region equations (BRE) formalism, which we solve using an efficient numerical algorithm. Streaks are excited using a small transpiration velocity at the wall. Our BRE-based algorithm is found to be superior to direct numerical simulation (DNS) and ad hoc nonlinear parabolized stability equation (PSE) models. BRE solutions are less computationally costly than a full DNS and have a more rigorous theoretical foundation than PSE-based models. For example, the full development of a Görtler vortex system in high-speed boundary layers can be predicted in a matter of minutes using a single processor via the BRE approach. This substantial reduction in calculation time is one of the major achievements of this work. We show, among other things, that it allows investigation into feedback control in reasonable total computational times. We investigate the development of the Görtler vortex system via the BRE solution with feedback control parametrically at various freestream Mach numbers \(M_\infty \) and spanwise separations \(\lambda \) of the inflow disturbances.



中文翻译:

通过非线性边界区域方程的有效数值解研究高速边界层中的 Görtler 涡

由于上游启动或壁面触发的扰动,流向涡流和相关条纹在平坦或凹面的边界层中演变。在瞬态生长阶段之后,完全发展的涡流结构变得容易受到无粘性的二次不稳定性的影响,从而通过“爆裂”过程过早过渡到湍流。在高速边界层中,由于可压缩性和热效应而产生更多的复杂性,这对于更高的马赫数变得更加重要。在本文中,我们使用边界区域方程 (BRE) 形式研究了在高速边界层中发展的 Görtler 涡旋,我们使用有效的数值算法对其进行求解。使用壁上较小的蒸腾速度激发条纹。我们基于 BRE 的算法被发现优于直接数值模拟 (DNS) 和临时非线性抛物线稳定性方程 (PSE) 模型。BRE 解决方案比完整 DNS 的计算成本更低,并且比基于 PSE 的模型具有更严格的理论基础。例如,可以通过 BRE 方法使用单个处理器在几分钟内预测高速边界层中 Görtler 涡流系统的完整开发。计算时间的大幅减少是这项工作的主要成就之一。我们表明,除其他外,它允许在合理的总计算时间内研究反馈控制。我们通过 BRE 解决方案研究 Görtler 涡流系统的发展,并在各种自由流马赫数下参数化地进行反馈控制\(M_\infty \)和流入扰动的展向分离\(\lambda \)

更新日期:2021-07-04
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