Optimal Control of Unsteady Flows Using a Discrete and a Continuous Adjoint Approach

Abstract

Part 5: Flow ControlInternational audienceWhile active flow control is an established method for controlling flow separation on vehicles and airfoils, the design of the actuation is often done by trial and error. In this paper, the development of a discrete and a continuous adjoint flow solver for the optimal control of unsteady turbulent flows governed by the incompressible Reynolds-averaged Navier-Stokes equations is presented. Both approaches are applied to testcases featuring active flow control of the blowing and suction type and are compared in terms of accuracy of the computed gradient

Optimal Flow Control and Topology Optimization Using the Continuous Adjoint Method in Unsteady Flows

“…10.6 stands for the contribution of jets on the forces acting upon the body, at the jets locations. A similar study, for a circular cylinder, can be found in [8].…”

“…It is about the optimal configuration of a set of pulsating jets activated at fixed locations along the perimeter of a square cylinder, to minimize the time-averaged drag. The velocity components of each jet are given by [8] and f m 0 = 0, where v ∞ is the infinite flow velocity and d is the side length of the square cylinder. The only design variables are the amplitudes A m .…”

“…This paper is dealing with the unsteady continuous adjoint [5][6][7][8] methods, where the adjoint PDEs are firstly derived and, then, discretized. The primal problem is governed by the unsteady flow equations and time-averaged performance metrics are used as objective functions.…”

On the proper treatment of grid sensitivities in continuous adjoint methods for shape optimization

“…The problem becomes much more pronounced in unsteady adjoint solvers, [5,6], 30 in which, for a time-averaged objective function, the SD computation must be repeated for each and every time-step. In the same problem, the cost of SI is still negligible.…”

Optimization of Airfoils Using the Adjoint Approach and the Influence of Adjoint Turbulent Viscosity

“…It can be seen from the analytical adjoint equations that the adjoint field develops backwards in time and upstream to the primal flow. A known disadvantage of the continuous adjoint approach is that it can produce inaccurate gradients in turbulent flows [8], because the adjoints to the turbulence parameters are often neglected. This is the so-called "frozen turbulence" assumption [9]: The same turbulent viscosity from the primal Navier-Stokes equations is used in the adjoint equations.…”