Reduced order model for air temperature control in indoor spaces

Real-time control of comfort in indoor spaces needs models of temperature distribution and air-velocity velocityfield. Complete models, based on CFD, give this information but are improper for real-time calculations. Therefore, a reduced model is needed. This study proposesto reduce the dimension of a CFD model by first considering the velocity field fixed and solving only the energy balance equation, then putting this equation in the form of state-space and finally by reducing its orderby Proper Orthogonal Decomposition (POD). This algorithm was applied to a room equipped with a fan coil with an air jet having three patterns: sticking to the ceiling and reaching the opposite wall, falling before the opposite wall, and falling before reaching the ceiling.For the two-dimensional case, the reduced model was validated by comparison with CFD results for step inputs of temperature and air velocity. As the order of the reduced model is always smaller than 7, the energy balance equation may be solved in real time and integratedinto a control algorithm.