Nonlinear optimal control of buoyancy-driven flow using direct-adjoint-looping method for various ventilation strategies

We consider the problem of optimally controlling turbulent buoyancy-driven flows in the built environment in the presence of a known time-varying disturbance. Using unsteady Reynolds-averaged equations (URANS), a Direct-Adjoint-Looping (DAL) implementation of the nonlinear optimal control problem yields time-varying values of temperature and velocity of the inlet flow that lead to `optimal' time-averaged temperature relative to appropriate objective functionals in a region of interest. As a test case, we consider a time-varying heat-source in a displacement ventilation scenario, where maintaining a certain temperature profile in the region is of significant practical value. Our results can inform optimal sensor and/or actuator placement tasks, as well as provide a way to obtain open loop control that results in robustness to unknown disturbances.