Resolvent-based study of compressibility effects on supersonic turbulent boundary layers
Resolvent-based study of compressibility effects on supersonic turbulent boundary layers
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基于求解的超音速湍流边界层压缩性效应研究
DOI：
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发表时间：
2019
影响因子：
3.7
通讯作者：
B. McKeon
中科院分区：
文献类型：
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作者：
H. J. Bae;Scott T. M. Dawson;B. McKeon
McKeon和Sharma（J. Fluid Mech.，第658卷，2010年，pp. 336-382）应用于超音速湍流边界层以研究Morkovin假设的有效性，该假设假定零压力梯度湍流边界层中的高速湍流结构与不可压缩边界层中的高速湍流结构基本相同。本文研究了马赫数为2 ~ 4的绝热壁面条件下超音速零压力梯度湍流边界层。预解式分析突出了波参数空间中超音速湍流边界层的两个不同区域：相对超音速区域和相对亚音速区域。在相对超音速的区域中，流动相对于自由流是超音速的，预解模态显示与不可压缩状态中不存在的马赫波辐射一致的结构。在相对亚音速区域，我们表明，低秩近似的预解算子是一个有效的近似的完整的系统和模型预测的响应模式表现出普遍的和几何自相似的行为，通过半局部尺度变换。此外，与半局部标度，我们表明，预解模式遵循相同的标度律，其不可压缩的对应物在该区域，这对建模和预测的湍流高速壁有界流动的影响。我们还表明，热力学变量表现出相似的模式形状的流向速度模式，支持强雷诺类比。最后，我们证明了主预解模式可以用来捕捉动量和热力学涨落之间的能量分布。
The resolvent formulation of McKeon & Sharma (J. Fluid Mech., vol. 658, 2010, pp. 336–382) is applied to supersonic turbulent boundary layers to study the validity of Morkovin’s hypothesis, which postulates that high-speed turbulence structures in zero-pressure-gradient turbulent boundary layers remain largely the same as their incompressible counterparts. Supersonic zero-pressure-gradient turbulent boundary layers with adiabatic wall boundary conditions at Mach numbers ranging from 2 to 4 are considered. Resolvent analysis highlights two distinct regions of the supersonic turbulent boundary layer in the wave parameter space: the relatively supersonic region and the relatively subsonic region. In the relatively supersonic region, where the flow is supersonic relative to the free-stream, resolvent modes display structures consistent with Mach wave radiation that are absent in the incompressible regime. In the relatively subsonic region, we show that the low-rank approximation of the resolvent operator is an effective approximation of the full system and that the response modes predicted by the model exhibit universal and geometrically self-similar behaviour via a transformation given by the semi-local scaling. Moreover, with the semi-local scaling, we show that the resolvent modes follow the same scaling law as their incompressible counterparts in this region, which has implications for modelling and the prediction of turbulent high-speed wall-bounded flows. We also show that the thermodynamic variables exhibit similar mode shapes to the streamwise velocity modes, supporting the strong Reynolds analogy. Finally, we demonstrate that the principal resolvent modes can be used to capture the energy distribution between momentum and thermodynamic fluctuations.
影响因子：
3.7
作者：
McKeon, B. J.;Sharma, A. S.
通讯作者：
Sharma, A. S.