用于湍流减阻的黏弹性涂层的预解算子分析
Resolvent analysis to inform viscoelastic coatings for turbulent drag reduction
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中文总结 AI 辅助
该研究通过预解算子分析，发现不可压缩流动中黏弹性涂层减阻受流动诱导结构不稳定性限制，而超声速流动的高密度比提供了稳定窗口，为柔性壁减阻应用提供了理论依据。
中文摘要 AI 辅助
黏弹性柔性涂层提供了一种被动改变壁湍流的途径，但其减阻效果仍未明确。我们对线性黏弹性连续体上的湍流边界层开展预解算子分析，并将其应用于不可压缩水动力学和可压缩空气动力学零压力梯度湍流边界层，同时采用标准和涡黏性预解算子两种公式。在宽范围的储能模量E和涂层厚度H下，黏弹性表面会放大近壁循环型模态，同时使超大尺度运动（VLSMs）的预解算子增益衰减多达50%，二者共同作用导致雷诺应力降低。然而，对于代表水基不可压缩流动的密度匹配涂层，这些有利的作用带完全处于有效涂层对行波颤振呈线性不稳定的区域，使其在实际中无法实现。优化材料阻尼无法消除这种不稳定性，但为利用较弱的次优相互作用提供了途径。在超声速流动中，大的固液密度比（O(1000)）将有利相互作用转移到显著更高的模量，使可实现的湍流生成减弱至几个百分点。不过，最强的相互作用带处于线性稳定区域。这些结果表明，在不可压缩应用中，通过与高增益模态耦合实现的柔性壁减阻，根本上受流动诱导的结构不稳定性限制；而超声速流动的高密度比为实际涂层提供了窄得多但稳定的窗口。
英文摘要
Viscoelastic compliant coatings offer a passive route to modify wall-bounded turbulence; however, their effectiveness for drag reduction remains unresolved. We perform resolvent analysis of turbulent boundary layers over linear viscoelastic continuum, and apply it to incompressible hydrodynamic and compressible aerodynamic zero-pressure-gradient turbulent boundary layers, using both standard and eddy viscosity resolvent formulations. Across a wide range of storage modulus E and coating thickness H, viscoelastic surfaces amplify near-wall-cycle-type modes while also attenuating the resolvent gain of very large scale motions (VLSMs) by up to 50%, which together result in a reduction of Reynolds stress. For density-matched coatings representative of aqueous incompressible flows, however, these favorable bands lie entirely within the regime where the effective coatings are linearly unstable to traveling wave flutter, rendering them practically unrealizable. Optimizing material damping does not eliminate this but provides a pathway to use weaker sub-optimal interactions. In supersonic flow, the large solid-to-fluid density ratio (O(1000)) shifts the favorable interaction to substantially higher moduli, weakening the achievable reduction in turbulence production to a few percent. However, the strongest interaction band occurs in the linearly stable regime. These results suggest that compliant wall drag reduction via coupling with high gain modes is fundamentally constrained by flow-induced structural instabilities in incompressible applications, whereas the high density ratios of supersonic flow offer a much narrower but stable window for practical coatings.
