An adjoint-based temperature boundary optimal control approach for turbulent buoyancy-driven flows

Abstract

Abstract This paper deals with the adjoint optimal control for turbulent buoyancy-driven flows. The aim of this optimal control problem is to obtain a desired velocity profile and enhance the turbulence intensity in a well defined region by controlling the fluid temperature on domain boundaries and consequently the buoyancy forces. The fluid is assumed to be incompressible within the Boussinesq approximation, while turbulence is considered by coupling the Wilcox k-ω model with the Reynolds Averaged energy and Navier Stokes equations. The state, adjoint and control equations are derived by employing the Lagrangian multipliers method. The optimality system is solved with a finite elements code where a steepest descent algorithm has been implemented in order to find the optimal boundary control parameter. Numerical results are reported to show the robustness of the method in solving strongly-coupled optimality systems with a large number of unknowns.