Characterization of unsteady separation in a turbulent boundary layer: mean and phase-averaged flow

Abstract

A spatially developing turbulent boundary layer subject to a space- and time-dependent pressure gradient is analysed via large-eddy simulation. The unsteadiness is prescribed by imposing an oscillating suction–blowing velocity profile at the top boundary of the computational domain. The alternating favourable and adverse pressure gradients cause the flow to separate and reattach to the wall periodically. A range of reduced frequencies $k$ was investigated, spanning from a very rapid flutter-like motion to a slow, quasi-steady flapping. The Reynolds number based on the boundary-layer displacement thickness $\delta _o^{*}$ at the inflow plane is $Re_*=1000$ . Both time- and phase-averaged fields are analysed and results are compared with steady conditions. The reduced frequency $k$ has a significant effect on the transient flow-separation process. For high $k$ the separation bubble does not grow as thick as in the corresponding steady case, but the length of the bubble remains comparable; hysteresis is observed in the near-wall region. As $k$ is reduced, a threshold is met at which the separation bubble grows in the wall-normal direction. However, the length of the bubble is significantly reduced again when compared with the steady case. At this frequency, the region of slow-moving fluid generated by the flow reversal is advected downstream, causing a decorrelation between the forcing (the imposed free-stream velocity) and the velocity and pressure downstream of the separation bubble. Moreover, hysteresis effects are shifted away from the wall. At the lowest frequency a quasi-steady solution is approached; however, transient effects are still present in the backflow region.

Characterisation of unsteady separation in a turbulent boundary layer: Reynolds stresses and flow dynamics

“…The time-varying pressure distribution gives rise to transient flow separation, which, in some cases, leads to the advection and shedding of large-scale vortical structures; for instance, in the case of dynamic stall on a pitching airfoil (Simpson 1989;Rival & Tropea 2010;Williams et al 2015). An extensive literature review on the effects of steady (both adverse and favourable) pressure gradients on mean-flow quantities has been presented in Ambrogi, Piomelli & Rival (2022); the rest of this section will be devoted to the effects of steady and unsteady pressure gradients on higher-order moments. Subsequently, the main objectives of this investigation are described, followed by an outline of the rest of the paper.…”

“…As discussed in Ambrogi et al (2022), the onset of a transient separation process strongly influences the flow in the detachment region. In many cases, the slow-moving fluid region generated by the flow reversal is highly unstable, periodically advected downstream and out of the domain (Mullin, Greated & Grant 1980;Simpson 1989;Ambrogi et al 2022).…”

“…As discussed in Ambrogi et al (2022), the onset of a transient separation process strongly influences the flow in the detachment region. In many cases, the slow-moving fluid region generated by the flow reversal is highly unstable, periodically advected downstream and out of the domain (Mullin, Greated & Grant 1980;Simpson 1989;Ambrogi et al 2022). This particular flow configuration is difficult to achieve via experiments due to the complexity of the boundary conditions, and the required strength of the pressure gradients.…”

“…From a numerical point of view, the increasing computational resources available over recent years have made the literature on unsteady pressure-gradient flow simulations grow considerably. The reader is referred to Ambrogi et al (2022) for a complete review of past studies. Here we mention the work carried out by Wissink & Rodi (2003) who performed a direct numerical simulation (DNS) of a laminar separation bubble in the presence of an oscillating external flow.…”

“…In our recent characterisation of unsteady flow separation in a TBL (Ambrogi et al 2022), we described how the transient separation process is affected by the reduced frequency k, and shed light into the underlying physical characteristics associated with hysteresis and its effect on the local flow behaviour. We also pointed out commonalities between unsteady separation on a flat plate and the more complex dynamic-stall process on for instance a pitching airfoil; however, only mean and phase-averaged first-order quantities were examined, and many questions concerning the flow dynamics still remained open.…”