The effect of convergent-divergent riblets on laminar wall-bounded flows

Convergent-divergent (C-D) riblets are a type of bio-inspired surface pattern, and have begun to receive research attention in recent years, due to their potential in skin friction reduction and flow separation control. In this thesis, the effect of C-D riblets on the secondary flow, flow separation and drag characteristics in laminar wall-bounded flows is studied via numerical simulations. Firstly, a systematic investigation of the effect of riblet height, wavelength and yaw angle on the secondary flow in a laminar boundary layer developing over a C-D riblet section is undertaken. Large scale secondary flow is observed in cross-stream planes which displays downward/upward motions over the diverging/converging lines. The exact structure of the secondary flow depends on the relative size of riblet height and wavelength to the local boundary layer thickness, and three different patterns are observed. With the increase of wavelength, the average strength of the secondary flow per unit area exhibits a peak around a ratio between wavelength and local boundary layer thickness of 1. As the yaw angle increases, the strength of the secondary flow reaches to the peak value at a yaw angle of 45deg. Secondly, the effects of C-D riblets on momentum transfer enhancement and the extent of flow separation zone are examined by applying a section of C-D riblets upstream of a backward-facing rounded ramp in a laminar channel flow. In comparison with the baseline case, flow separation is delayed and the reattachment occurs earlier, leading to a smaller separation zone around the diverging line. The opposite phenomena occur around the converging line. A minimum riblet height of 3.75% of the channel height is required to produce a net reduction in the separation zone. As riblet spacing s increases with fixed riblet height h, a maximum strength of the secondary flow and a maximum reduction in the separation zone are obtained at s/h=4. Thirdly, the effect of C-D riblets on drag characteristics is studied by proposing an exact expression for the drag coefficient in laminar channel flows with wall roughness, whereby the drag is decomposed into contributions from different components of the velocity gradient tensor in the flow field. Furthermore, the triple decomposition technique is used to identify the contribution to drag production from the mean velocity field, the riblet- and wavelength-scale dispersive flow field. The normalized drag increment starts to rise when the Reynolds number is large enough to enable the secondary flow to alter the streamwise velocity across the span. While the normalized drag increment is predominantly caused by the mean and small-scale dispersive velocity at low Reynolds number, the contribution from the large-scale dispersive velocity field increases rapidly with the Reynolds number and gradually becomes dominant. Among C-D riblets with rectangular, triangular and sinusoidal cross-sectional shapes, the triangular riblet pattern is found to produce a secondary motion with a similar strength with less drag penalty. Finally, a theoretical derivation is presented to prove that drag reduction cannot be achieved by applying wall roughness structures onto the smooth inner walls of streamwise-periodic steady incompressible laminar channel/pipe flows at the same volume flow rate. It is shown that wall roughness produces a higher drag due to two factors: a) wall roughness induces other non-zero velocity gradient terms in addition to the wall-normal/radial gradient of streamwise velocity that exist in a smooth channel/pipe flow; b) the profile of streamwise velocity in the wall-normal/radial direction deviates from the parabolic profile that produces the minimum kinetic energy loss at the same volume flow rate.