Numerical studies of the flow around an airfoil at low Reynolds number

Abstract

A study of the flow around airfoils at low-Reynolds numbers has been performed, by a combination of direct numerical simulation (DNS) and linear stability analysis. The behaviour of laminar separation bubbles formed on a NACA-0012 airfoil at Rec = 5 £ 104 and incidence 5± is investigated. Initially volume forcing is introduced in order to promote transition to turbulence. After obtaining sufficient data from this forced case, the explicitly added disturbances are removed and the simulation run further. With no forcing the turbulence is observed to 'self-sustain', with increased turbulence intensity in the reattachment region. A comparison of the forced and unforced cases shows that the forcing improves the aerodynamic performance whilst requiring little energy input. Linear stability analysis of the time-averaged flow field is performed, however no absolute instability is observed that could explain the presence of self sustaining turbulence. A series of simplified DNS are presented that illustrate a three-dimensional in-stability of the two-dimensional vortex shedding that occurs naturally. The instability leads to exponential growth in time at fixed streamwise locations, and a mechanism for its growth is proposed. The fact that this transition processis independent of upstream disturbances has implications for modelling separation bubbles. A further DNS, of a laminar separation bubble formed on a NACA-0012 airfoil at incidence 7± clearly exhibits sustained transition to turbulence via the proposed instability mechanism, and illustrates that the effect of a modest increase in airfoil incidence upon separation bubble behaviour appears slight in comparison to that of the addition of forcing. For all airfoil flows the transition/reattachment region of the separation bubble was observed to be a significant contributor to airfoil self-noise. Numerical simulations of the response of the time-averaged flowfield to small perturbations, intended to complement linear stability analysis, illustrate that for two dimensional cases in the range 5± · ® · 8:5± the time-averaged flowfield is unstable due to an acoustic feedback instability, whereby hydrodynamic disturbances convecting over the trailing edge generate upstream traveling acoustic waves, which ultimately generate further downstream travelling hydrodynamic disturbances. As the cycle repeats, the amplitude of both hydrodynamic instabilities and acoustic waves increases. It is suggested that an acoustic feedback loop of this type may act as a frequency selection mechanism for naturally occurring vortex shedding observed in two-dimensions.

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ORCID for Neil Sandham: orcid.org/0000-0002-5107-0944

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