Fast simulation of temperature distribution in air conditioned rooms by using proper orthogonal decomposition

Real-time control of air conditioning needs dynamic models of temperature distribution and air velocity field in rooms. Complete models, based on computational fluid dynamics (CFD), give this information, but they are too time-consuming for real-time applications. Therefore, a reduced model is needed. In mixed convection, when the air temperature has negligible variations, the velocity field may be considered fixed. In this case, the size of a CFD model may be reduced by solving only the energy balance equation, then putting this equation in the form of state-space and finally by reducing its order by proper orthogonal decomposition (POD). This algorithm was applied to a room equipped with a fan coil. Four fixed airflow fields, corresponding to negligible air temperature variation, were considered, resulting in four airflow patterns: the air jet sticks to the ceiling and reaches the opposite wall, the air jet falls before reaching the opposite wall, the air jet reaches the ceiling without extending along it, and the air jet falls before reaching the ceiling. The reduced model obtained from these airflow patterns was validated by comparing with CFD results for step variation of inlet temperature. As the order of the reduced model is always lower than seven, it may be used for real-time control applications.