Modeling of Advective Heat Transfer in a Practical Building Atrium via Koopman Mode Decomposition

Abstract

This chapter develops a methodology for modeling of heat transfer dynamics in a building atrium via Koopman mode decomposition (KMD). We address the phenomenon of heat transfer due to movement of air inside an atrium, where the air slowly moves over the distance between individual rooms. The heat transfer is modeled as a heat advection equation with a vector-valued velocity coefficient and a nonlinear input term from heating, ventilation, and air-conditioning (HVAC) operations, which corresponds to a control variable. KMD is applied to the equation so that the heat transfer and HVAC operation are characterized in terms of frequencies and wavenumber vectors of Koopman modes (KMs). The velocity coefficient is then identified with a KM governing the heat transfer. The effectiveness of the modeling is demonstrated with measurement data on temperature field and HVAC operation of a practically used building. A possibility of how to use this modeling for control of heat transfer dynamics is discussed at the end of this chapter.