Quasi-Analytical Solution of Optimum and Maximum Depth of Transverse V-Groove for Drag Reduction at Different Reynolds Numbers

Abstract

Reducing the skin-friction drag of a vehicle is an important way to reduce carbon emissions. Previous studies have investigated the drag reduction mechanisms of transverse grooves. However, it is more practical to investigate which groove geometry is optimal at different inflow conditions for engineering. The purpose of this paper is to establish the physical model describing the relationship between the dimensionless depth (H+=Huτ/υ) of the transverse groove, the dimensionless inflow velocity (U∞+=U∞/uτ), and the drag reduction rate (η) to quasi-analytically solve the optimal and maximum transverse groove depth according to the Reynolds numbers. Firstly, we use the LES with the dynamic subgrid model to investigate the drag reduction characteristics of transverse V-grooves with different depths (h = 0.05~0.9 mm) at different Reynolds numbers (1.09×104~5.44×105) and find that H+ and U∞+ affect the magnitude of slip velocity (Us+), thus driving the variation of the viscous drag reduction rate (ην) and the increased rate of pressure drag (ηp). Moreover, the relationship between Us+, ην, and ηp is established based on the slip theory and the law of pressure distribution. Finally, the quasi-analytical solutions for the optimal and maximum depths are solved by adjusting Us+ to balance the cost (ηp) and benefit (ην). This solution is in good agreement with the present numerical simulations and previous experimental results.