Influence of wall shape on vortex formation in modulated channel flow

Authors:
Publisher website
Google Scholar
Abstract
The flow inside channels with periodic, wavy walls of arbitrary shape is considered numerically. Solutions are obtained using either a perturbation approach, for weak modulation amplitude, or a finite volume technique, for strong amplitude. The flow is examined for sinusoidal, arched and triangular modulation over a wide range of amplitude, wavelength and Reynolds number in the steady laminar regime. For weak wall modulation (ε<0.3, α<2, where ε and α are the dimensionless half-wave height and wavelength, respectively), it is found that the flow behavior along the modulated wall is of the boundary-layer type. As such, the critical Reynolds number, Re c , for separation for each modulation shape can be expressed as an explicit function of ε and α, while the location of separation and pressure distribution along the modulated wall scale with ε, α, and Re c . For strong modulations, the boundary layer model is no longer satisfactory to predict the flow behavior and deviations from the trends found for weaker modulations are observed. It is also shown that the driving force required to sustain a given flow rate increases as ε increases. For all modulation amplitudes, the sinusoidal wave shape is found to require the largest pressure gradient to maintain a given flow rate through the channel and, consequently, yields the highest friction factor. Finally, the existence of a stable recirculating flow regime is discussed in the light of earlier stability analyses.

This publication has 27 references indexed in Scilit: