Effects of riblet shape on drag reduction in turbulent flow

Abstract

Flow passing over the surface of vehicles creates significant skin-friction drag. The reduction of that drag through flow-control techniques, driven by environmental and financial incentives, has already received substantial attention by fluid mechanicians and will continue to be one of the prominent topics in the field. In this dissertation, we study turbulent flow over riblets, i.e. over tiny streamwise-aligned surface grooves that have the potential to reduce skin-friction drag compared to a smooth wall.

Small riblets with spacings of typically less than 20 viscous units (a few tens of micrometres on an aircraft fuselage in cruise conditions) are known to reduce skin-friction drag compared to a smooth wall, but larger riblets allow inertial-flow mechanisms to appear and cause drag reduction to break down. One of these mechanisms is a Kelvin-Helmholtz instability that Garcia-Mayoral & Jimenez (J. Fluid Mech., vol. 678, 2011, pp. 317-347) identified in turbulent flow over blade riblets. In order to evaluate its dependence on riblet shape and thus gain a broader understanding of the underlying physics, we employ the minimal-span channel concept for cost-efficient Direct Numerical Simulations of rough-wall flows (MacDonald et al., J. Fluid Mech., vol. 816, 2017, pp. 5-42). This allows us to investigate seven different riblet shapes and various viscous-scaled sizes between those of maximum drag reduction and significant drag increase for a total of 29 configurations. We verify that the small numerical domains capture all relevant physics by varying the domain size and by comparing to reference data from full-span channel flow. Specifically, we find that, in the previously identified spectral region occupied by drag-increasing Kelvin-Helmholtz rollers, the energy-difference relative to smooth-wall flow is not affected by the narrow domain, even though these structures have large spanwise extents. This allows us to evaluate the influence of the Kelvin-Helmholtz instability by comparing the flow fields over riblets to that over a smooth wall.

We find that in this data set only large sharp-triangular and blade riblets have a drag penalty associated with the Kelvin-Helmholtz instability and that the mechanism appears to be absent for blunt-triangular and trapezoidal riblets of any size. We therefore investigate two indicators for the occurrence of Kelvin-Helmholtz rollers in turbulent flow over riblets. First, we confirm for the different riblet shapes that the groove cross-sectional area in viscous units serves as a proxy for the wall-normal permeability that is necessary for the development of Kelvin-Helmholtz rollers. Additionally, we find that the occurrence of the instability correlates with a high momentum absorption at the riblet tips. The momentum absorption can be qualitatively predicted using Stokes flow.

We further investigate the drag characteristics of multi-scale riblets, i.e. trapezoidal grooves with a half-height riblet in the centre. Garcia-Mayoral & Jimenez (J. Fluid Mech., vol. 678, 2011, pp. 317-347) proposed to measure the riblet size by the square root of their cross-sectional area $\ell_g^+$, which scales the size of minimum drag for different fully open single-scale grooves. We find that $\ell_g^+$ is not the optimal description of the riblet size for multi-scale geometries. Upon investigating effects of the secondary riblet on the flow field and overall drag of the surface, we propose a generalised measure of the riblet size for multi-scale surfaces.