Large-eddy simulation of laminar transonic buffet

Abstract

A large-eddy simulation of laminar transonic buffet on an airfoil at a Mach number $M=0.735$, an angle of attack $\unicode[STIX]{x1D6FC}=4^{\circ }$, a Reynolds number $Re_{c}=3\times 10^{6}$ has been carried out. The boundary layer is laminar up to the shock foot and laminar/turbulent transition occurs in the separation bubble at the shock foot. Contrary to the turbulent case for which wall pressure spectra are characterised by well-marked peaks at low frequencies ($St=f\cdot c/U_{\infty }\simeq 0.06{-}0.07$, where $St$ is the Strouhal number, $f$ the shock oscillation frequency, $c$ the chord length and $U_{\infty }$ the free-stream velocity), in the laminar case, there are also well-marked peaks but at a much higher frequency ($St=1.2$). The shock oscillation amplitude is also lower: 6 % of chord and limited to the shock foot area in the laminar case instead of 20 % with a whole shock oscillation and intermittent boundary layer separation and reattachment in the turbulent case. The analysis of the phase-averaged fields allowed linking of the frequency of the laminar transonic buffet to a separation bubble breathing phenomenon associated with a vortex shedding mechanism. These vortices are convected at $U_{c}/U_{\infty }\simeq 0.4$ (where $U_{c}$ is the convection velocity). The main finding of the present paper is that the higher frequency of the shock oscillation in the laminar regime is due to a different mechanism than in the turbulent one: laminar transonic buffet is due to a separation bubble breathing phenomenon occurring at the shock foot.

Modal Analysis of a Laminar-Flow Airfoil under Buffet Conditions at Re = 500,000

“…These modes can be interpreted in the light of other observations of higher frequencies on airfoils. Performing a large-eddy simulation of a supercritical laminar airfoil (OALT25) at α = 4 • and M = 0.735, but at a higher Reynolds number of Re = 3 • 10 6 , Dandois et al [43] reported shock motion (a permanent back and forth moving shock wave) at significantly higher Strouhal numbers (St = 1.2) compared to typical buffet frequencies, and linked it to a breathing phenomenon of the separation bubble associated with downstream convecting vortices. Similar phenomena were reported by Memmolo et al [17] analysing the V2C airfoil at α = 7 • and high Reynolds numbers using large-eddy simulation.…”

Analysis of a civil aircraft wing transonic shock buffet experiment

“…Whilst in these works the boundary layer is turbulent upstream of the SWBLI, noticeable differences have recently been reported under laminar flow conditions, where laminar-to-turbulent transition takes place in the region of the SWBLI. In this case, the shock undergoes smaller chordwise excursions confined to the shock foot, which oscillates at frequencies over an order of magnitude higher than fully turbulent interactions (Brion et al 2017;Dandois, Mary & Brion 2018). Direct numerical Analysis of a transonic wing shock buffet experiment 884 A1-3 simulation at moderate Reynolds number has revealed complex interaction between shock and pressure waves and boundary layers, with these flow features occurring at frequencies distinct from characteristic low-frequency lift fluctuations at St ≈ 0.1 (Zauner, De Tullio & Sandham 2019).…”

On some explicit local time stepping finite volume schemes for CFD

“…The present wall mesh resolution, ∆x + ≈ 25, ∆y + ≈ 1, ∆z + ≈ 8, is finer than that used in [26] and equivalent to that used in [30,31], in which grid converged results are presented for the same kind of flow: airfoil with laminar separation bubble and turbulent reattachment. As the numerical method employed in the present paper is the same as the one validated in [26,32,30,31,33,34] thanks to windtunnel experiment comparisons, we are confident that our results obtained with the classical RK3 scheme and a global timestep are physically correct for the specific set of Reynolds number and boundary conditions. Therefore the solution obtained with the classical RK3 explicit scheme is considered as a reference to assess the accuracy and efficiency of the proposed temporal scheme.…”