Hydrodynamics and heat convection in channels with vibrating walls
In this work a combined analytical and numerical study of the non-linear effects of transverse wall vibrations on fluid flows are presented. Streaming motions and their effect on heat and mass transfer are investigated for a viscous fluid confined in an infinite channel with flexible walls. The amplitude of vibration is small compared to the wavelength of the vibrating surface and a perturbation approach is utilized. A non-orthogonal coordinate system in which the wall is stationary is used in the analysis.
A standing wave operating on a fluid at rest induces streaming in cellular flow patterns. The non-dimensional frequency and channel half-width determine the structure of the generated flow, and the ability of these flows to mix viscous fluids by advection is investigated by computing the mean Lagrangian velocities and particle paths. Effective mixing is obtained for flows having channel half-widths of similar or lower order as the wavelength and for sufficiently high frequencies. The structure of the streaming flow is important for mixing.
The heat transfer through the channel is enhanced by the vibrations, especially for small channel half-widths as compared to the wavelength of the vibrating surface.
Travelling and standing waves operating on low Reynolds number channel flows affect the bulk flow through non-linear interactions. The largest hydrodynamic effects are found when forced oscillatory motions interact with eigenmodes of the unperturbed flow. In the vicinity of this resonance phenomenon the time-averaged flow rate decreases strongly for standing waves and for waves travelling in the direction of the flow in the channel. This effect is enhanced with increasing Reynolds numbers. Standing waves, furthermore, produce cellular flow structures for certain parameter ranges.