弯曲方管中三维湍流边界层的壁面模化大涡模拟
Wall-modeled large-eddy simulation of three-dimensional turbulent boundary layer in a bent square duct
AI总结：
本文通过弯曲方管内3DTBL的WMLES并对照实验，比较平衡、积分非平衡与PDE非平衡三种壁面模型，发现PDE模型显著改善壁面应力方向预测，而外区解基本不受模型影响。
摘要：
我们对弯曲方管底板上发展的压力驱动三维湍流边界层（3DTBL）开展了壁面模化大涡模拟（WMLES），以考察三种广泛使用的壁面模型的预测能力，即简单平衡应力模型、积分型非平衡模型和PDE非平衡模型。数值结果与Schwarz和Bradshaw的实验（J. Fluid Mech.（1994），第272卷，第183–210页）进行了比较。尽管三种壁面模型预测的壁面应力量级相当，但PDE非平衡壁面模型对壁面应力方向的预测要准确得多，其次是积分型非平衡壁面模型。研究表明，壁面模型给出的壁面应力方向具有可分离的贡献，分别来自平衡应力部分和积分非平衡效应，而各壁面模型对后者的建模方式有所不同。壁面模型解的三角图揭示了各壁面模型在表征流动方向沿壁面法向变化方面的不同能力。相反，外层LES解不受所用壁面模型类型的影响，因此所有壁面模型对外区平均统计量和湍流统计量给出几乎相同的预测。这可由涡量动力学以及产生平均三维性的无黏偏斜机制解释。最后，外层LES解被用于研究湍流的各向异性。与经典二维壁湍流不同，Reynolds应力各向异性随壁面距离增加表现出强烈的非单调行为。
英文摘要：
We conduct wall-modeled LES (WMLES) of a pressure-driven three-dimensional turbulent boundary layer (3DTBL) developing on the floor of a bent square duct to investigate the predictive capability of three widely used wall models, namely, a simple equilibrium stress model, an integral nonequilibrium model, and a PDE nonequilibrium model. The numerical results are compared with the experiment of Schwarz and Bradshaw (J. Fluid Mech. (1994), vol. 272, pp. 183-210). While the wall-stress magnitudes predicted by the three wall models are comparable, the PDE nonequilibrium wall model produces a substantially more accurate prediction of the wall-stress direction, followed by the integral nonequilibrium wall model. The wall-stress direction from the wall models is shown to have separable contributions from the equilibrium stress part and the integrated nonequilibrium effects, where how the latter is modeled differs among the wall models. The triangular plot of the wall-model solution reveals different capabilities of the wall models in representing variation of flow direction along the wall-normal direction. On the contrary, the outer LES solution is unaffected by the type of wall model used, resulting in nearly identical predictions of the mean and turbulent statistics in the outer region for all the wall models. This is explained by the vorticity dynamics and the inviscid skewing mechanism of generating the mean three-dimensionality. Finally, the LES solution in the outer layer is used to study the anisotropy of turbulence. In contrast to the canonical 2D wall turbulence, the Reynolds stress anisotropy exhibit strong non-monotonic behavior with increasing wall distance.
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