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

TL;DR

This paper presents an optimal control strategy for a separated boundary-layer flow over a bump, using augmented Lagrangian methods to stabilize the flow from a nonlinear state back to steady conditions with a single actuator.

Contribution

It introduces a novel control approach that decomposes slow and fast flow dynamics, enabling effective flow stabilization and baseflow modification with minimal actuators.

Findings

Control law effectively stabilizes the flow from nonlinear states.

Decomposition allows targeted control of baseflow and oscillations.

Method works for weakly unstable flow regimes without external noise.

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.