Turbulent flow over superhydrophobic surfaces with streamwise grooves
Turbulent flow over superhydrophobic surfaces with streamwise grooves
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DOI：
10.1017/jfm.2014.137
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发表时间：
2014-05-01
影响因子：
3.7
通讯作者：
Frohnapfel, B.
中科院分区：
文献类型：
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作者：
Tuerk, S.;Daschiel, G.;Frohnapfel, B.
我们研究了带有流向沟槽的超疏水表面(SHS)在完全发展的槽道湍流中对流动动力学和由此产生的减阻的影响。SHS被模拟为具有交替无滑移和自由滑移条件的平坦边界，并通过系统地改变流向沟槽的展向周期进行了一系列直接的数值模拟。在所有计算中，采用了恒定压力梯度条件，因此减阻效果表现为体积平均速度的增加。为了捕捉由非均匀边界条件引起的流动特性，将瞬时湍流分解为空间平均分量、相干分量和随机分量。观察到交替的无滑移和自由滑移边界条件导致了以相干流向涡为特征的Prandtl第二类二次流的产生。体积平均速度与不同的动力贡献，即有效滑移长度和滑面附加湍流损失之间的数学关系表明，体积平均速度的增加主要是由有效滑移长度决定的。对于较小的展向周期性流槽，湍流中的有效滑移长度与层流的解析解符合得很好。然而，一旦自由滑移区的展向宽度大于约20个壁面单位，由于底层湍流和二次流引起的混合，有效滑移长度从层流值显著减小。基于这些结果，我们开发了一个简单的模型，该模型可以估计在实际高雷诺数的湍流中由于SHS而产生的增益。
We investigate the effects of superhydrophobic surfaces (SHS) carrying streamwise grooves on the flow dynamics and the resultant drag reduction in a fully developed turbulent channel flow. The SHS is modelled as a flat boundary with alternating no-slip and free-slip conditions, and a series of direct numerical simulations is performed with systematically changing the spanwise periodicity of the streamwise grooves. In all computations, a constant pressure gradient condition is employed, so that the drag reduction effect is manifested by an increase of the bulk mean velocity. To capture the flow properties that are induced by the non-homogeneous boundary conditions the instantaneous turbulent flow is decomposed into the spatial-mean, coherent and random components. It is observed that the alternating no-slip and free-slip boundary conditions lead to the generation of Prandtl's second kind of secondary flow characterized by coherent streamwise vortices. A mathematical relationship between the bulk mean velocity and different dynamical contributions, i. e. the effective slip length and additional turbulent losses over slip surfaces, reveals that the increase of the bulk mean velocity is mainly governed by the effective slip length. For a small spanwise periodicity of the streamwise grooves, the effective slip length in a turbulent flow agrees well with the analytical solution for laminar flows. Once the spanwise width of the free-slip area becomes larger than approximately 20 wall units, however, the effective slip length is significantly reduced from the laminar value due to the mixing caused by the underlying turbulence and secondary flow. Based on these results, we develop a simple model that allows estimating the gain due to a SHS in turbulent flows at practically high Reynolds numbers.