Groove optimization for drag reduction

Optimal shapes of laminar, drag reducing longitudinal grooves in a pressure driven flow have been determined. It has been shown that such shapes can be characterized using reduced geometry models involving only a few Fourier modes. Two classes of grooves have been studied, i.e., the equal-depth grooves, which have the same height and depth, and the unequal-depth grooves. It has been shown that the optimal shape in the former case can be approximated by a certain universal trapezoid. There exists an optimum depth in the latter case and this depth, combined with the corresponding groove shape, defines the optimal geometry; this shape is well-approximated by a Gaussian function. Drag reduction due to the use of the optimal grooves has been determined. The analysis has been extended to kinematically driven flows. It has been shown that in this case the longitudinal grooves always increase the flow resistance. (C) 2013 AIP Publishing LLC.