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

Abstract

The large-eddy simulation technique was used to investigate the dynamics of unsteady flow separation on a flat-plate turbulent boundary layer. The unsteadiness was generated by imposing an oscillating, wall-normal velocity profile at the top of the computational domain, and a range of reduced frequencies ( $k$ ), from a very rapid flutter-like motion to a slow quasi-steady oscillation, was studied. Ambrogi et al. (J. Fluid Mech., vol. 945, 2022, A10) showed that the reduced frequency greatly affects the transient separation process, and at a frequency $k=1$ , the separation region became unstable and was advected periodically out of the domain. In this paper, we discuss the causes of the observed advection process and the effects of the unsteadiness on the second moments. The time evolution of turbulent kinetic energy, for instance, reveals that an advection-like phenomenon is also present at a very low reduced frequency, but its dynamic behaviour is completely different from that of the intermediate frequency ( $k=1$ ). At the intermediate frequency the entire recirculation region is advected downstream, keeping its shape. The advected structure is rotational in nature, and moves at constant speed. In contrast, in the low-frequency case the advected fluid originates at the reattachment point, and the structure is shear-dominated. Particle pathlines reflect the fact that the flow at the low frequency is quasi-steady-state, but show peculiar differences at the intermediate frequency, in which the flow response to the freestream forcing depends on the particle positions in the wall-normal direction.

Evaluation of Turbulence Models in Unsteady Separation

“…Ambrogi et al [8] examined a turbulent boundary layer subjected to an unsteady freestream APG strong enough to cause separation. They studied a range of frequencies, and observed hysteresis effects that were confined to a thin region near the wall at high frequencies, but extended away from the wall for lower values of k. They further investigated the shedding of the recirculation region [22] which they found was associated with the entrainment of near-wall fluid with high turbulent kinetic energy (TKE) into the shear layer, which led to the persistence of this shear layer as it was advected downstream.…”

“…This work aims at evaluating consistently the capabilities of the three most commonly used one-and two-equation turbulence models to predict unsteady flow separation in a turbulent boundary layer, taking advantage of the simulations recently carried out by Ambrogi et al [8,22]. The physical phenomena observed by these authors and described above are expected to be difficult to model, making these configurations challenging test cases.…”

“…However, the physical phenomena present here are also present in many more complex configurations (as discussed in Refs. [8,22]); for this reason, the present setup has been used in numerous studies of separated flows [5,32,33]. The use of a simpler geometry, furthermore, allows us to compare the URANS results with those of a high-fidelity LES in a rigorous manner, which is the final objective of this study.…”

“…The height of the bubble is minimum at high frequency and largest at the lowest one. At the intermediate frequency, the recirculation bubble is advected downstream, almost as a solid body (see [22] for a discussion of the causes of this phenomenon). At Φ = 90 • , the advected region is exiting the domain.…”