Stability of Flow in a Channel with Drag Reducing Grooves

Laminar flow in a channel with longitudinal grooves is analyzed. Grooves may have an arbitrary shape but do not affect the average channel opening. It is demonstrated that there exist groove shapes that reduce the laminar drag. It is shown that the reduced geometry model based on a single Fourier mode captures the relevant flow characteristics with an acceptable accuracy. The linear stability analysis is used to determine the range of flow conditions when the flow remains laminar. The same grooves represent a certain class of surface roughness, and its effect of the critical flow conditions is of interest. It is demonstrated that the short wavelength grooves destabilize the flow while the long wavelength grooves have an opposite effect. Stability characteristics of the optimal grooves that produce the largest possible drag reduction have also been determined.