Bach Jacob S, Bruus Henrik
Department of Physics, Technical University of Denmark, DTU Physics Building 309, DK-2800 Kongens Lyngby, Denmark.
J Acoust Soc Am. 2018 Aug;144(2):766. doi: 10.1121/1.5049579.
The acoustic fields and streaming in a confined fluid depend strongly on the viscous boundary layer forming near the wall. The width of this layer is typically much smaller than the bulk length scale set by the geometry or the acoustic wavelength, which makes direct numerical simulations challenging. Based on this separation in length scales, the classical theory of pressure acoustics is extended by deriving a boundary condition for the acoustic pressure that takes viscous boundary-layer effects fully into account. Using the same length-scale separation for the steady second-order streaming, and combining it with time-averaged short-range products of first-order fields, the usual limiting-velocity theory is replaced with an analytical slip-velocity condition on the long-range streaming field at the wall. The derived boundary conditions are valid for oscillating cavities of arbitrary shape and wall motion, as long as both the wall curvature and displacement amplitude are sufficiently small. Finally, the theory is validated by comparison with direct numerical simulation in two examples of two-dimensional water-filled cavities: The well-studied rectangular cavity with prescribed wall actuation, and a more generic elliptical cavity embedded in an externally actuated rectangular elastic glass block.
受限流体中的声场和流动强烈依赖于在壁面附近形成的粘性边界层。该层的宽度通常远小于由几何形状或声波波长设定的主体长度尺度，这使得直接数值模拟具有挑战性。基于这种长度尺度上的差异，通过推导一个充分考虑粘性边界层效应的声压边界条件，对经典压力声学理论进行了扩展。对于稳态二阶流动，采用相同的长度尺度差异，并将其与一阶场的时间平均短程乘积相结合，用壁面上长程流动场的解析滑移速度条件取代了通常的极限速度理论。只要壁面曲率和位移幅值足够小，所推导的边界条件对于任意形状和壁面运动的振荡腔都是有效的。最后，通过与二维充水腔的两个例子中的直接数值模拟进行比较，验证了该理论：一个是经过充分研究的具有规定壁面驱动的矩形腔，另一个是嵌入外部驱动的矩形弹性玻璃块中的更一般的椭圆形腔。
