Mechanisms of interaction between stationary crossflow instabilities and forward-facing steps

Abstract

We study the interaction between a stationary crossflow instability and forward-facing steps in a swept-wing boundary layer using Direct Numerical Simulations (DNS). The stationary primary crossflow mode is imposed at the inflow. Steps of several heights are modeled. Particular emphasis is placed on ensuring a fully stationary solution, in order to isolate the modulation of the primary instability at the step and the generation of stationary secondary perturbations. The main features of the base flow are step-induced flow reversal and secondary inflection points. When approaching the step, the incoming crossflow instability lifts up and passes over it. Additional perturbation streaks arise, which are accompanied by secondary stationary vortices that have the same spanwise wavenumber as the fundamental crossflow disturbance. For sufficiently high steps, secondary perturbation structures attain amplitude values comparable in magnitude to primary instability in the vicinity of the step. We propose metrics to quantify the impact of the step on the development of the crossflow disturbance upon interaction. Considering energy-based criteria, we find that the crossflow perturbation is amplified upstream of the step. Interestingly, the incoming primary crossflow instability undergoes strong stabilization immediately downstream of the largest step. The mechanisms revealed in this work provide a first insight into the possible causes of transition on swept wings due to forward-facing steps.

Unsteady interaction of crossflow instability with a forward-facing step

“…This behaviour is in agreement with previous experimental observations by Eppink (2020b) and Rius-Vidales & Kotsonis (2021). In addition, the numerical results of Casacuberta et al (2021) identified a series of near-wall perturbation streaks downstream of the FFS edge developing at the spanwise wavelength of the stationary CF vortices. Given that the wavelength of these secondary perturbations coincides with the primary CF disturbance, they manifest as a secondary peak near the wall superimposed on the disturbance profile as shown in Tufts et al (2017) and Eppink (2020b).…”

“…Nonetheless, recent numerical (e.g. Tufts et al 2017;Cooke et al 2019;Casacuberta, Hickel & Kotsonis 2021) and experimental (e.g. Duncan et al 2014b;Eppink 2018Eppink , 2020bRius-Vidales & Kotsonis 2020Groot & Eppink 2021) studies revealed numerous unresolved aspects essential to the understanding of the FFS-CFI interaction.…”

“…Numerical simulations by Casacuberta et al (2021) on the steady FFS-CFI interaction (i.e. simulating only stationary step-flow features) showed that as the primary CF disturbance reaches the FFS, it does not directly impinge on the step edge but instead lifts off the surface and passes over it.…”

“…large FFS at low-amplitude of the CF vortices) the identified near-wall peak can exceed the magnitude of the one corresponding to the primary CF disturbance. Thus, Casacuberta et al (2021) propose a set of metrics to adequately determine the growth of the primary CF disturbance in these conditions.…”

Secondary instabilities in swept-wing boundary layers: Direct Numerical Simulations and BiGlobal stability analysis

“…The DNS are carried out with INCA, a conservative finite-volume-based flow solver (Hickel and Adams, 2008, Hickel et al, 2014, Casacuberta et al, 2020. The free-stream evolution and the DNS setup considered in this work are identical to the ones presented in a recent article (Casacuberta et al, 2021). The highly refined computational grid for the current DNS computations has 6760, 576, and 72 points along the chordwise, wall-normal, and spanwise directions, respectively, and more than 70 grid points cover the inflow boundary-layer thickness.…”