Optimal control of a separated boundary-layer flow over a bump

Abstract

The optimal control of a globally unstable two-dimensional separated boundary layer over a bump is considered using augmented Lagrangian optimization procedures. The present strategy allows of controlling the flow from a fully developed nonlinear state back to the steady state using a single actuator. The method makes use of a decomposition between the slow dynamics associated with the baseflow modification, and the fast dynamics characterized by a large scale oscillation of the recirculation region, known as flapping. Starting from a steady state forced by a suction actuator located near the separation point, the baseflow modification is shown to be controlled by a vanishing suction strategy. For weakly unstable flow regimes, this control law can be further optimized by means of direct-adjoint iterations of the nonlinear Navier-Stokes equations. In the absence of external noise, this novel approach proves to be capable of controlling the transient dynamics and the baseflow modification simultaneously.

Nonlinear Observer for the turbulent wake of a square cylinder

“…The value of the high gain θ is chosen quite small in order to avoid sensitivity issues (in particular with respect to the output noise), to lessen the peaking effect and make the system performance effective (Fig 1) despite noise on the state dynamics. When the state feedback stabilizes x 1 to zero for t ∈ [10,15] s, the singularity is avoided using the fake outputs to preserve the mapping Φ invertibility. The choice of a quite small ε = 0.001 for (18) allows to modify the system only for a short period, yet at the price of the convergence of the estimated growth rate to zero instead of the nominal value x 3 = 2.…”

“…In this framework, the wake flow behind a cylinder is a well documented flow where the primary instability is a Hopf-type bifurcation which, in the laminar regime, is known to reach a finite amplitude and saturate to a limit cycle. The saturation process was highlighted in [11], [12], [3], [13] by the interaction between the vortex shedding mode and the steady state, which induces a shift of the flow, also known as shift mode [14], [15]. While the vortex shedding mode is characterized by a growth rate and a frequency mode, the shift mode only possesses a decay rate which varies with the growth rate and both are strongly coupled [14], [15].…”

“…The saturation process was highlighted in [11], [12], [3], [13] by the interaction between the vortex shedding mode and the steady state, which induces a shift of the flow, also known as shift mode [14], [15]. While the vortex shedding mode is characterized by a growth rate and a frequency mode, the shift mode only possesses a decay rate which varies with the growth rate and both are strongly coupled [14], [15]. In the case of a cylinder, the shift mode is associated with a shortening recirculation region and is directly related to the magnitude of the vortex shedding, the latter being dependent on the Reynolds number.…”

Superhydrophobic surfaces to reduce form drag in turbulent separated flows

“…In absence of SHSs, the bump is known to make the flow separate, creating a strong shear layer emanating from the separation point and producing a recirculating region [33][34][35] . The configuration, with no SHSs has been extensively investigated using classical statistical tools of turbulence theory [36][37][38][39][40][41] .…”

Particles in turbulent separated flow over a bump: Effect of the Stokes number and lift force

“…The bump makes the flow separate, creating a strong shear layer and recirculating region, [48][49][50] . The configuration is nonetheless still accessible to classical statistical tools and turbulence theory for the detailed study of turbulence dynamics, [51][52][53][54] . To the best of our knowledge, this is the first simulation of such a configuration laden with particles at a friction Reynolds number of 900 over the bump.…”