Abstract

Abstract

No abstract

We study the flow above non-optimal riblets, specifically large drag-increasing and two-scale trapezoidal riblets. In order to reach large Reynolds numbers and large scale separation while retaining access to flow details, we employ a combination of boundary-layer hot-wire measurements and direct numerical simulation (DNS) in minimal-span channels. Although the outer Reynolds numbers differ, we observe fair agreement between experiments and DNS at matched viscous–friction-scaled riblet spacings $s^+$ in the overlapping physical and spectral regions, providing confidence that both data sets are valid. We find that hot-wire velocity spectra above very large riblets with $s^+ \gtrsim 60$ are depleted of near-wall energy at scales that are (much) greater than $s$ . Large-scale energy likely bypasses the turbulence cascade and is transferred directly to secondary flows of size $s$ , which we observe to grow in strength with increasing riblet size. Furthermore, the present very large riblets reduce the von Kármán constant $\kappa$ of the spanwise uniform mean velocity in a logarithmic layer and, thus, reduce the accuracy of the roughness-function concept, which we link to the near-wall damping of large flow structures. Half-height riblets in the groove, which we use as a model of imperfectly repeated (spanwise-varying) riblets, impede in-groove turbulence. We show how to scale the drag optimum of imperfectly repeated riblets based on representative measurements of the true geometry by solving inexpensive Poisson equations.

We investigate the Reynolds analogy over riblets, namely the analogy between the fractional increase in Stanton number $C_h$ and the fractional increase in the skin-friction coefficient $C_f$ , relative to a smooth surface. We investigate the direct numerical simulation data of Endrikat et al. (Flow Turbul. Combust., vol. 107, 2021, pp. 1–29). The riblet groove shapes are isosceles triangles with tip angles $\alpha = {30}^{\circ }, {60}^{\circ }, {90}^{\circ }$ , a trapezoid, a rectangle and a right triangle. The viscous-scaled riblet spacing varies between $s^+ \approx 10$ to $60$ . The global Reynolds analogy is primarily influenced by Kelvin–Helmholtz rollers and secondary flows. Kelvin–Helmholtz rollers locally break the Reynolds analogy favourably, i.e. cause a locally larger fractional increase in $C_h$ than in $C_f$ . These rollers induce negative wall shear stress patches which have no analogue in wall heat fluxes. Secondary flows at the riblets’ crests are associated with local unfavourable breaking of the Reynolds analogy, i.e. locally larger fractional increase in $C_f$ than in $C_h$ . Only the triangular riblets with $\alpha = {30}^{\circ }$ trigger strong Kelvin–Helmholtz rollers without appreciable secondary flows. This riblet shape globally preserves the Reynolds analogy from $s^+ = 21$ to $33$ . However, the other riblet shapes have weak or non-existent Kelvin–Helmholtz rollers, yet persistent secondary flows. These riblet shapes behave similarly to rough surfaces. They unfavourably break the global Reynolds analogy, and do so to a greater extent as $s^+$ increases.