Large-eddy simulation of boundary-layer separation and transition at a change of surface curvature

Abstract

Transition arising from a separated region of flow is quite common and plays an important role in engineering. It is difficult to predict using conventional models and the transition mechanism is still not fully understood. We report the results of a numerical simulation to study the physics of separated boundary-layer transition induced by a change of curvature of the surface. The geometry is a flat plate with a semicircular leading edge. The Reynolds number based on the uniform inlet velocity and the leading-edge diameter is 3450. The simulated mean and turbulence quantities compare well with the available experimental data.The numerical data have been comprehensively analysed to elucidate the entire transition process leading to breakdown to turbulence. It is evident from the simulation that the primary two-dimensional instability originates from the free shear in the bubble as the free shear layer is inviscidly unstable via the Kelvin–Helmholtz mechanism. These initial two-dimensional instability waves grow downstream with a amplification rate usually larger than that of Tollmien–Schlichting waves. Three-dimensional motions start to develop slowly under any small spanwise disturbance via a secondary instability mechanism associated with distortion of two-dimensional spanwise vortices and the formation of a spanwise peak–valley wave structure. Further downstream the distorted spanwise two-dimensional vortices roll up, leading to streamwise vorticity formation. Significant growth of three-dimensional motions occurs at about half the mean bubble length with hairpin vortices appearing at this stage, leading eventually to full breakdown to turbulence around the mean reattachment point. Vortex shedding from the separated shear layer is also observed and the ‘instantaneous reattachment’ position moves over a distance up to 50% of the mean reattachment length. Following reattachment, a turbulent boundary layer is established very quickly, but it is different from an equilibrium boundary layer.

A pressure-gradient mechanism for vortex shedding in constricted channels

“…V) resulting in the flapping. Note that the findings of Yang and Voke 43 and Deck and Thorigny 42 suggest that the cause of shear-layer flapping is due to convective instabilities in the shear layer.…”

A numerical method for solving the 3D unsteady incompressible Navier–Stokes equations in curvilinear domains with complex immersed boundaries

“…(10), which are expensive to compute and store and increase significantly the requirements for smoothness of the computational mesh as they involve second order derivatives of the metrics of the geometric transformation. FT-1 formulations have been proposed and applied to solve the incompressible Navier-Stokes equations, see for example [17,18], but because of the aforementioned difficulties such methods have not been widely used in the literature.…”

“…The volume fluxes are obtained by discretizing and solving their respective transport equations, which, for reasons that will soon become apparent, are formulated as follows: (16) where ℜ q (q = 1, 2, 3) denote the contravariant fluxes of the convective and viscous terms: (17) The key difference between the proposed method and the FT-2 approach is that the ℜ q terms at their respective surface centers are not obtained by discretizing the C and D terms at the surface centers (as required in approach FT-2 as shown in Eq. (14)) but are reconstructed by interpolation from the volume centers.…”

Dynamic pitching effect on a laminar separation bubble

“…Further numerical and experimental analyses by Yang and Voke (2001), Lang et al (2003) showed that transition is the result of amplification of K-H instabilities in the separated shear layer, which leads to the roll-up and subsequent shedding of large vortices at the rear part of the bubble. These results are supported by recent studies from, e.g.…”