Drag reduction by riblets has been a field of intensive research. However, there is no agreement on the efficiency and mechanism of drag reduction of three-dimensional riblets. Besides, due to the multi-scale problem brought by the coexistence of microstructure and macroscopic flow field, there is no effective approach yet for the numerical calculation of the drag reduction effect when riblets are applied on an actual macroscopic object underwater. This paper first studies drag reduction of three-dimensional riblets. Then, a drag calculation method for macroscopic objects with microstructure surfaces is proposed. The method has been utilized for calculating NACA 0030 airfoil with scalloped riblets and the calculation results are compared with those of direct calculation. The results show that, the algorithm well estimates the effect of the microstructure on the drag of macroscopic objects and can significantly shorten the calculation time.


Riblets, as an easily realizable passive drag reduction technique has been a field of intensive research due to its significant impact on energy saving and extensive engineering applications in aeronautics and marine. Walsh et al. (1982, 1984), Bechert et al. (1985, 1986) and Wilkinson et al. (1987, 1988) undertook detailed experimental research on the drag reduction effect of riblets and the optimization of cross-sectional shape. To understand the mechanisms of riblet drag reduction, experiments of Suzuki and Kasagi(1994), Djenidi and Antonia(1996), Park and Wallace(1994), Lee and Lee(2001), and numerical simulation of Choi et al. (1993), Chu and Karniadakis (1993) and Goldstein et al. (1995) have studied the flow structure near the riblets.

However, the above studies mainly focus on two-dimensional riblets with uniform cross-section. Studies on three-dimensional riblets are much fewer, and there is no agreement on the efficiency and mechanism of drag reduction of three-dimensional riblets.

Experimental study by Wen et al. (2014) found that three-dimensional riblets of sharkskin is hydrodynamically beneficial. But experimental study by Wilkinson et al. (1988) and Bechert et al. (1997) found no improvement in drag reduction of segmented blade riblets and staggered trapezoidal blade riblets compared with two-dimensional riblets. Boomsma and Sotiropoulos(2016) performed direct numerical simulation on three-dimensional riblets of sharkskin, and found that the drag increased compared with a flat plate without sharkskin riblets.

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