Direct numerical simulation of a non-equilibrium three-dimensional turbulent boundary layer over a flat plate
Direct numerical simulation of a non-equilibrium three-dimensional turbulent boundary layer over a flat plate
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DOI：
10.1017/jfm.2020.488
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发表时间：
2020-09
影响因子：
3.7
通讯作者：
H. Abe
中科院分区：
文献类型：
--
作者：
H. Abe
摘要采用直接数值模拟方法研究了平板上方空间发展的非平衡三维湍流边界层。由于表面跨向速度的突然施加，目前的流动是一种‘剪切驱动’的3DTBL。特别注意了横流和雷诺数的影响。在数值模拟中，使用了三个入口动量厚度雷诺数$R{e_{{\theta_0}=300$、600和900，以及几个值${W_S}$。目前最大的${W_S}$是自由气流速度${U_0}$的两倍，与Lohmann(Trans.《流体工程》，第98卷，1976年，第354-363页)。施加${W_S}$后，平均流向涡度逐渐远离壁面传播，在壁面上，平均流向速度差与无粘性偏斜(即三维)有密切关系。在3DTBL下游站，表面摩擦系数出现近平台区，其大小本质上取决于${W_S}$。然而，对于U线上的平均流向速度来说，接近附生状态的过程是缓慢的，因为在U线上的雷诺剪切应力不能有效地从平均流中提取能量。随着雷诺数的增加，平均速度值趋于符合对数定律，但von Kármán常数大于二维湍流边界层。同时，由于横流，倾倒的u形构造占主导地位，并且随着雷诺数的增加而变得更加突出。在统计上，后者在y/δ99=0.2时相对于y呈线性增长，这表明横流产生了自相似行为。
Abstract Direct numerical simulations (DNS) are used to examine a spatially developing non-equilibrium three-dimensional turbulent boundary layer (3DTBL) over a flat plate. The present flow is a ‘shear-driven’ 3DTBL owing to a sudden imposition of a surface spanwise velocity ${W_S}$. Particular attention is given to the effects of cross-flow and Reynolds number. In the DNS, three values of the inlet momentum thickness Reynolds number, $R{e_{{\theta _0}}} = 300$, 600 and 900, are used with several values of ${W_S}$. The present largest ${W_S}$ is twice the free-stream velocity ${U_0}$, comparable to the maximum value of the spinning cylinder experiment by Lohmann (Trans. ASME I: J. Fluids Engng, vol. 98, 1976, pp. 354–363). After imposing ${W_S}$, the mean streamwise vorticity ${\overline \varOmega _x}$ increasingly propagates away from the wall where there is close relationship between a deficit of mean streamwise velocity and inviscid skewing (i.e. three-dimensionality). At a downstream station of a 3DTBL, near-plateaus appear in the skin friction coefficients where the magnitudes depend intrinsically on ${W_S}$. The approach to the collateral state is, however, slow for mean streamwise velocity $\overline U$ where the Reynolds shear stress $\overline {uv}$ extracts energy from the mean flow inefficiently. As the Reynolds number increases, the mean velocity magnitude ${Q_r}$ tends to show the log law but with a larger von Kármán constant than in a two-dimensional turbulent boundary layer. Instantaneously, toppling u structures dominate owing to cross-flow and become more prominent with increasing Re. Statistically, the latter spanwise length scale increases linearly with respect to y below y/δ99 = 0.2, which indicates that cross-flow yields a self-similar behaviour.