Physical modelling of riblet performance in yawed and non-yawed flows
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2023-11
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Melbourne Authors
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Mechanical Engineering
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PhD thesis
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© 2024 Jeremy Zi-Jun Wong
Abstract
We introduce a viscous vortex model to predict the drag and heat transfer of riblets, eliminating the need for expensive direct numerical simulations (DNS) or experiments. The footprint of a typical quasi-streamwise vortex, in terms of the spanwise and wall-normal velocities, is extracted from smooth-wall DNS flow fields in close proximity to the surface. The extracted velocities are then averaged and used as boundary conditions in a Stokes-flow problem, wherein riblets with various cross-sectional shapes are embedded. Here, the same smooth-wall based boundary conditions can be used for riblets, as we observe from the DNSs that the quasi-streamwise vortices remain unmodified apart from an offset. In particular, the position of these vortices remain unpinned above small riblets. This smooth-wall-like behaviour persists up to the optimal size of riblets, and also up to a yaw angle of 15 degrees, enabling us to predict the riblet drag and heat transfer within these size and yaw-angle constraints. The present approach is compared with the protrusion height model of Luchini et al. (J. Fluid Mech., vol. 228, 1991, pp. 87–109), which is also based on a Stokes calculation, but represents the vortex with only a uniform spanwise velocity boundary condition. The key novelty of the viscous vortex model is the introduction of a non-zero wall-normal velocity component into the boundary condition. This approach induces transpiration at the riblet crests, as transpiration becomes relevant at increasing riblet sizes. Consequently, we show that the drag and heat-transfer prediction of the present model agree with our DNS data, as well as published data.
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drag reduction, turbulent boundary layer