Groove optimization for drag reduction

Abstract

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.

New instability mode in a grooved channel

“…The stability characteristics of the optimal grooves are of interest, as such grooves provide the largest possible drag reduction (Mohammadi & Floryan 2013b). The shapes of such grooves depend on the type of constraints.…”

“…L e imβz , y U (z) = 1, (4.3a,b) and the groove height (S L,max ) and depth (S L,min ) are subject to constraints of the form (4.4a,b) In the case of equal-depth grooves, S L,max = S L,min = S. In the case of unequal-depth grooves, the height is set by (4.4a,b) while the depth is determined by the optimization process (Mohammadi & Floryan 2013b). The shape of the optimal, equal-depth grooves can be well approximated by a universal trapezoid with a 2 = b 2 = λ/8 and c 2 = d 2 = 3λ/8 (figure 23b).…”

Discovery of riblets in a bird beak (Rynchops) for low fluid drag

“…The samples were tested in the turbulent regime, because it was expected that riblets would not provide a drag reduction in laminar flow, similar to shark-inspired riblets [21,43]. This principle is shown in figure 8.…”

Spectrally-accurate algorithm for the analysis of flows in two-dimensional vibrating channels

“…The efficiency has been increased by an order of magnitude through the development of specialized solvers which account for the special structure of the coefficient matrix [38,39]. The method has been used to identify the laminar drag-reducing grooves [16][17][18][19][20] and to study the effects of various grooves on the flow stability [40][41][42][43][44][45][46]. This work is focused on the development of an efficient algorithm suitable for the analysis of changes in the pressure gradient required to drive a specified flow rate through a vibrating channel.…”

“…An analytical mapping of the irregular physical domain to a rectangular computational domain can help improve the accuracy at the cost of increased complexity of the field equations [13,14]. However, such mappings are available only for a limited class of geometries [1] and reconstruction of the coefficient matrix during each time step can add to the overall computational cost by a substantial margin [14][15][16][17][18][19][20].…”