后掠平板边界层的横流线性稳定性和广义共振分析

Crossflow linear stability and generalized resonance analysis of the boundary-layer flow over swept flat plates

摘要

横流不稳定主导了后掠机翼表面前缘附近的边界层湍流转捩，因此其稳定性分析对于通过层流控制实现飞行器的减阻、降噪以及热防护至关重要。本研究采用基于有限雷诺数理论的线性稳定性分析，研究了Falkner-Skan-Cooke边界层和后掠平板边界层的不稳定特征。通过在不同压力梯度边界层求解Orr-Sommerfeld方程和Rayleigh方程揭示了黏性、无黏在横流不稳定中所起的作用，并且基于三波共振和Bragg散射的广义共振机理，给出了能够高效触发横流边界层不稳定的壁面粗糙元和定常扰动模态的特定波数。

Abstract

Crossflow instability dominates the laminar-turbulent transition in the boundary layer near the leading edge of the surfaces of swept wings. Therefore, its stability analysis is crucial for achieving drag reduction, noise reduction, and thermal protection through laminar flow control. In this paper, linear stability analysis based on finite Reynolds number theory is used to study the unstable eigenmodes of Falkner-Skan-Cooke and swept-flat plate boundary layers. By solving the Orr-Sommerfeld equations and Rayleigh equation in boundary layers with different pressure gradients, the roles of viscosity and inviscid effects in crossflow instability are revealed. And based on the generalized resonance mechanism of three wave resonance and Bragg scattering, this article provides specific wave numbers of wall roughness elements and steady-state disturbance modes that can efficiently trigger the instability of crossflow boundary layer. The results of this stability analysis in this article can provide useful reference for transition prediction and laminar flow control in crossflow boundary layers.

关键词

横流边界层 / 流动稳定性 / 广义共振 / 线性稳定性理论 / 湍流转捩

Key words

crossflow boundary layer / hydrodynamic stability / generalized resonance / linear stability theory / turbulent transition

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基金资助

国家自然科学基金资助项目(12072164)

国家自然科学基金资助项目(12102361)