Stability and receptivity characteristics of a laminar separation bubble on an aerofoil

Abstract

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.

Response of a laminar separation bubble to impulsive forcing

“…Similarly to earlier studies (Häggmark et al 2001;Rist & Maucher 2002;Jones et al 2010;Marxen & Rist 2010;Yarusevych & Kotsonis 2017) the stability characteristics of the LSB mean flow field are investigated using linear stability theory (LST). The latter assumes local parallel flow and low amplitude wave-like disturbances.…”

“…However, in the upstream part of the LSB, α i may be approximated by a second order polynomial (e.g. Jones et al 2010, cf. figure 11).…”

“…The most common type of forcing is sinusoidal and periodic at the most unstable frequency of the separated shear layer, usually identified through linear stability theory (LST) analysis. This type of forcing has been introduced by various means including spanwise uniform wall oscillation (Alam & Sandham 2000;Marxen et al 2009), externally imposed acoustic excitation (Yarusevych et al 2007;Jones et al 2010) as well as DBD plasma actuation (Yarusevych & Kotsonis 2017). However, the majority of the previous studies considered the response of the LSB to continuous forcing.…”

Effects of free-stream turbulence intensity on laminar separation bubbles

“…The transition process begins with the amplification of small amplitude perturbations originating upstream through the receptivity process [12]. The initial growth of these disturbances is primarily two-dimensional and nearly exponential, and can be modelled by linear stability theory [13][14][15]. As the disturbances continue to grow, non-linear interactions begin to occur, and the shear layer rolls up into coherent spanwise oriented vortices [16][17][18].…”

Self-Noise Effects on Aerodynamics of Cambered Airfoils at Low Reynolds Number

“…Besides, the substantial reverse flow past the boundary-layer separation destabilizes the iterative approach to solve for an eigenvalue of the O-S equation. Alternatively, a more direct sensitivity study based on the forced Navier-Stokes equations, employed in [9,16], would be effective in these circumstances. Instead, we choose the flow field at relatively lower angle of attack, α = 6°, where no leading-edge separation occurs in both cases, to ensure the solution of the O-S equation.…”