Streamwise-travelling viscous waves in channel flows.
Streamwise-travelling viscous waves in channel flows.
复制标题
河道流动中沿河道行进的粘性波。
DOI：
10.1007/s10665-018-9953-y
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发表时间：
2018
影响因子：
1.3
通讯作者：
Ricco P
中科院分区：
文献类型：
--
作者：
Ricco P
本文研究了不可压层流槽道中展向壁面速度的流向行波诱导的非定常粘性流动。属于这一类别的壁波已经发现了重要的实际应用，例如通过电渗和表面声学强迫的微流体流动操纵以及湍流壁边界流动中的壁摩擦的减少。得到了由经典的流向Poiffille流和抛物柱面函数描述的展向速度分布组成的解析解，该解依赖于体雷诺数R、标度流向波长和标度波相速度U。讨论了这些参数的各种组合的数值解。流动的边界层理论进行了研究，从而揭示了占主导地位的物理平衡和量化的厚度近壁展向流。文泽尔-克拉默斯-布里渊-杰弗里斯（WKBJ）理论也被用来获得一个解析解，这是有效的整个通道。对于小于或等于最大流向速度的正波速，通过WKBJ分析出现了转折点行为。在壁面和转折点之间，壁面法向粘性效应仅由壁面强迫驱动的对流来平衡，而在转折点和中心线之间，Poiffille对流平衡壁面法向扩散。在转折点处，Poiffille对流和壁面强迫对流相互抵消，从而导致恒定的粘性应力和WKBJ解的破裂。通过WKBJ复合展开和Langer方法分析了这种流态。Langer解比WKBJ复合解更简单、更精确，而后者量化了转折点区域的厚度。我们还讨论了如何通过表面声波强迫和电渗产生这些波，并提出了它们作为微流体流动混合装置的用途。对于电渗透的情况下，Helmholtz-Smoluchowski速度在德拜-休克尔层的边缘，这驱动了大量的电中性流，通过匹配的渐近展开。
The unsteady viscous flow induced by streamwise-travelling waves of spanwise wall velocity in an incompressible laminar channel flow is investigated. Wall waves belonging to this category have found important practical applications, such as microfluidic flow manipulation via electro-osmosis and surface acoustic forcing and reduction of wall friction in turbulent wall-bounded flows. An analytical solution composed of the classical streamwise Poiseuille flow and a spanwise velocity profile described by the parabolic cylinder function is found. The solution depends on the bulk Reynolds numberR, the scaled streamwise wavelength, and the scaled wave phase speedU. Numerical solutions are discussed for various combinations of these parameters. The flow is studied by the boundary-layer theory, thereby revealing the dominant physical balances and quantifying the thickness of the near-wall spanwise flow. The Wentzel–Kramers–Brillouin–Jeffreys (WKBJ) theory is also employed to obtain an analytical solution, which is valid across the whole channel. For positive wave speeds which are smaller than or equal to the maximum streamwise velocity, a turning-point behaviour emerges through the WKBJ analysis. Between the wall and the turning point, the wall-normal viscous effects are balanced solely by the convection driven by the wall forcing, while between the turning point and the centreline, the Poiseuille convection balances the wall-normal diffusion. At the turning point, the Poiseuille convection and the convection from the wall forcing cancel each other out, which leads to a constant viscous stress and to the break down of the WKBJ solution. This flow regime is analysed through a WKBJ composite expansion and the Langer method. The Langer solution is simpler and more accurate than the WKBJ composite solution, while the latter quantifies the thickness of the turning-point region. We also discuss how these waves can be generated via surface acoustic forcing and electro-osmosis and propose their use as microfluidic flow mixing devices. For the electro-osmosis case, the Helmholtz–Smoluchowski velocity at the edge of the Debye–Hückel layer, which drives the bulk electrically neutral flow, is obtained by matched asymptotic expansion.