Secondary flow in a laminar boundary layer developing over convergent-divergent riblets

Abstract

Convergent-divergent (C-D) riblets are a type of bio-inspired surface pattern. They are known to induce secondary flow in a boundary layer that may point to their potential for surface friction drag reduction and flow separation control. In this paper, a systematic investigation of the effect of riblet height, wavelength and yaw angle on the secondary flow in a flat-plate laminar boundary layer developing over a C-D riblet section is undertaken.The large-scale secondary flow in the cross-stream plane belongs to Prandtl's first kind, and is induced by the spanwise velocity generated by the yawed riblet passages. The exact structure of this secondary flow depends on the relative size of riblet height and wavelength to the local boundary layer thickness, and three different patterns are observed within the range of parameters examined. As the wavelength increases, the strength of the secondary flow increases firstly and then levels off at large wavelengths, whereas the average strength per unit area exhibits a peak around a ratio between wavelength and local boundary layer thickness of 1. As the yaw angle increases from 20 o to 70 o , the strength of the secondary flow exhibits a parabolic trend and achieves a maximum around a yaw angle of 45 o . The findings from this work can be used to inform the choice of riblet geometry for maximizing the strength of the secondary flow in a given boundary layer flow.

Current state and future trends in boundary layer control on lifting surfaces

“…Raayai-Ardakani and McKinley 38 numerically investigated how geometrical parameters of denticles as well as Re affect drag reduction. Guo et al 39,40 describe systematic computations undertaken to examine the effects of riblet geometry (height, wavelength, and yaw angle illustrated in Figure 1(c)) on the strength of the generated secondary flow as well as the extent of the flow separation zone. The authors report the suppression of the LSB, but not the net reduction in the total pressure losses, although they point out that further research is possible.…”

Energy-based drag decomposition analyses for a turbulent channel flow developing over convergent–divergent riblets

“…They are a type of spanwise heterogeneous roughness patterns which mimic the surface structures found on sharks' skin 1 and on the secondary flight bird feathers 2 . C-D riblets have received an increasing amount of research attention in recent years [3][4][5][6][7] , and they have been found to be capable of mitigating flow separation 8,9 .…”

Drag decomposition of laminar channel flows developing over convergent–divergent riblets

“…Convergent-divergent (C-D) riblets are a type of spanwise heterogeneous surface roughness pattern which is inspired by the micro-scale patterns found on sharks' skin around their sensory receptors and hearing sensors [1], and on the secondary flight feathers of birds [2]. This type of roughness pattern began to receive research attentions in recent years [3,4,5,6,7], due to its potential applications in friction drag reduction [2] and flow separation control [8,9]. The spanwise heterogeneity of C-D riblets is brought about by periodic spanwise switching in the orientation of inclined grooves (see Fig.…”

“…1). Due to their special surface pattern arrangement, C-D riblets are capable of inducing a spanwise surface flow directing from the diverging line to the converging line, leading to formation of a large-scale secondary flow motion (or roll mode) in both laminar [7,10] and turbulent boundary layers [4,6] despite their height and spacing being typically an order of magnitude smaller than the local boundary layer thickness.…”

“…The secondary flow has been observed to cause a spanwise redistribution of flow field which results in an increased streamwise velocity and a thinner boundary layer in the region of down-welling, and the opposite occurs around the region of upwelling [3,4,10]. Guo et al [7] carried out a parametric study of the effects of riblet geometry, including riblet height, yaw angle and wavelength, on the characteristics of roll mode. While changing riblet height had the strongest impact on the roll mode, with taller riblets generating a stronger roll mode as expected, a yaw angle of 45 o or a wavelength of about one boundary layer thickness was found to give rise to a stronger roll mode when the other parameters were kept unchanged [7].…”