Direct numerical simulations (DNS) of laminar separation bubbles on a NACA-0012 airfoil at Re c = 5 × 10 4 and incidence 5• are presented. 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. Classical linear stability analysis is performed upon the time-averaged flow field; however no absolute instability is observed that could explain the presence of self-sustaining turbulence. Finally, a series of simplified DNS are presented that illustrate a three-dimensional absolute instability of the twodimensional vortex shedding that occurs naturally. Three-dimensional perturbations are amplified in the braid region of developing vortices, and subsequently convected upstream by local regions of reverse flow, within which the upstream velocity magnitude greatly exceeds that of the time-average. The perturbations are convected into the braid region of the next developing vortex, where they are amplified further, hence the cycle repeats with increasing amplitude. The fact that this transition process is independent of upstream disturbances has implications for modelling separation bubbles.

No abstract

In the present paper, direct numerical simulation (DNS) studies of the compressible flow in the

Stability characteristics of aerofoil flows are investigated by linear stability analysis of time-averaged velocity profiles and by direct numerical simulations with time-dependent forcing terms. First the wake behind an aerofoil is investigated, illustrating the feasibility of detecting absolute instability using these methods. The time-averaged flow around an NACA-0012 aerofoil at incidence is then investigated in terms of its response to very low-amplitude hydrodynamic and acoustic perturbations. Flow fields obtained from both two- and three-dimensional simulations are investigated, for which the aerofoil flow exhibits a laminar separation bubble. Convective stability characteristics are documented, and the separation bubble is found to exhibit no absolute instability in the classical sense; i.e. no growing disturbances with zero group velocity are observed. The flow is however found to be globally unstable via an acoustic-feedback loop involving the aerofoil trailing edge as a source of acoustic excitation and the aerofoil leading-edge region as a site of receptivity. Evidence suggests that the feedback loop may play an important role in frequency selection of the vortex shedding that occurs in two dimensions. Further simulations are presented to investigate the receptivity process by which acoustic waves generate hydrodynamic instabilities within the aerofoil boundary layer. The dependency of the receptivity process to both frequency and source location is quantified. It is found that the amplitude of trailing-edge noise in the fully developed simulation is sufficient to promote transition via leading-edge receptivity.

Direct numerical simulations of the flow around a NACA-0012 aerofoil are conducted, employing an immersed boundary method to represent flat-plate trailing-edge extensions both with and without serrations. Properties of the turbulent boundary layer convecting over the trailing edge are similar for both cases. For cases with serrations, the trailing-edge noise produced by the flow over the aerofoil is observed to decrease in amplitude, and the frequency interval over which the noise reduction occurs differs depending on the serration length. The directivity and spanwise coherence of the trailing-edge noise appears largely unaffected by the serrations. The hydrodynamic behaviour in the vicinity of the trailing-edge extensions is investigated. The streamwise discontinuity imparted upon the turbulent flow by the straight trailing edge can clearly be observed in statistical quantities, whereas for the serrated case no spanwise homogeneous discontinuities are observed. The trailing-edge serrations appear to break up the larger turbulent structures convecting into the wake, and to promote the development of horseshoe vortices originating at the serrations themselves.