Riblet-generated flow mechanisms that lead to local breaking of Reynolds analogy

Abstract

We investigate the Reynolds analogy over riblets, namely the analogy between the fractional increase in Stanton number Ch and the fractional increase in the skin-friction coefficient Cf, 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 α=30∘,60∘,90∘, a trapezoid, a rectangle and a right triangle. The viscous-scaled riblet spacing varies between s+≈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 Ch than in Cf. 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 Cf than in Ch. Only the triangular riblets with α=30∘ 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.