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

Abstract

Convergent–divergent (C–D) riblets are known to induce large-scale secondary flow motion in laminar flow that may point to their potential for flow separation control and heat transfer enhancement. In this paper, a fully-developed pressure-driven laminar channel flow with C–D riblets is studied numerically. The effects of Reynolds number, riblet wavelength and riblet cross-sectional shape on the secondary flow and drag characteristics are investigated. An exact expression for the drag coefficient of this flow is derived based on the balance of kinetic energy principle for a rough-wall channel. Furthermore, the triple decomposition technique is used to identify the contribution to drag production from the mean velocity field, the small- and large-scale dispersive flow field. Our results show that the normalized drag increment starts to rise when the secondary flow begins to alter the velocity field across the span as the Reynolds number based on the channel height (ReH) increases above 100, a behavior which is very different from that of a laminar channel flow developing over homogeneous roughness in which the normalized drag increment is found to remain constant up to a much greater Reynolds number due to an absence of secondary flow. It is found that the drag produced by C–D riblets is predominantly caused by the wall-normal gradient of streamwise velocity. In addition, while the drag increment is predominantly caused by the mean and small-scale dispersive velocity at ReH≤100, the contribution from the large-scale dispersive velocity field increases rapidly with the Reynolds number and becomes dominant as ReH exceeds 400. It is also observed that the secondary flow scales with the riblet wavelength Λ, and its swirling strength peaks around Λ=1.25H, which is accompanied by a drag maxima at ReH≥400. Finally, among the three C–D riblet cross-sectional shape (rectangular, triangular and sinusoidal) examined here, the triangular riblet pattern is found to produce a secondary motion with a similar strength to the other two shapes but with less drag penalty.