Nonlinear optimal control strategies for buoyancy-driven flows in the built environment

Abstract We consider the problem of optimally controlling turbulent buoyancy-driven flows in the built environment, focusing on a model test case of displacement ventilation with a time-varying heat source. The flow is modeled using the unsteady Reynolds-averaged equations (URANS). A direct-adjoint-looping 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. The resulting dynamics of both ‘filling’ and ‘intruding’ added layers due to a time-varying source and inlet flow are discussed. The robustness of the optimal solution is demonstrated. It is found that for large enough values of time horizon the optimal steady solution is recovered, while for intermediate values a non-trivial deviation from this optimal steady state design is achieved. The computational framework is flexible, and can be applied to several problems of interest in optimal design and control of indoor airflow.

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