Pulsating Flow of a Viscous Fluid over a Cavity Containing a Compressible Gas Bubble

A two-dimensional pulsating flow of a viscous fluid in a plane channel whose wall has rectangular microcavities partially or completely filled with a compressible gas is investigated. This problem formulation can clarify the friction reduction mechanism in a laminar sublayer of a turbulent viscous boundary layer flow over a textured stripped superhydrophobic surface containing periodically arranged rectangular micro-cavities filled with gas. It is assumed that the dimensions of the cavities are much smaller than the channel thickness. On the macroscale, the problem of one-dimensional unsteady viscous flow in a plane channel with no-slip conditions on the walls and a harmonic variation of the pressure difference is solved. The solution obtained in this way is used for formulating non-stationary in time and periodic in space boundary conditions for the flow on the scale of a chosen cavity (microscale), with the instantaneous volume of the gas bubble in the cavity depending on the instantaneous pressure over the cavity. The flow on the microscale near a cavity with a gas bubble occurs in the Stokes regime. The numerical solution is obtained using an original version of the boundary element method. A parametric numerical study of the flow field in a pulsating shear flow over a cavity with a compressible gas bubble is performed. The averaged parameters characterizing the effective 'velocity slip' of viscous fluid and the friction reduction in a pulsating flow over a stripped superhydrophobic surface are calculated.