A comparison of moving-boundary and finite-volume formulations for transients in centrifugal chillers

Abstract

Dynamic models of vapor compression systems are useful tools in developing feedback controllers and are gaining increasing attention in recent years. The dominant dynamics are typically those of the evaporator and condenser, which are difficult to model. Accuracy and execution speed of system models therefore are highly dependent on the modeling approach of the heat exchangers. The two common approaches are the finite-volume (FV) and the moving-boundary (MB) methods. Both have been used successfully and reported in the literature, but there is little discussion presented for either choice. This paper presents the development and comparative study of shell-and-tube heat exchanger dynamic models using both the FV and the MB approaches. Detailed model formulations are provided and stability is demonstrated as components and within a complete centrifugal chiller system model. The system models are validated using data from a 300 kW R134a centrifugal chiller test stand. The FV formulation is found to be more robust through start-up and all load-change transients, but executes slower. The moving-boundary method can handle all load-change transients but start-up stability is more sensitive to compressor and expansion valve formulations. The moving-boundary formulation also executes about three times faster than the finite-volume while maintaining nearly identical accuracy. With the homogenous two-phase assumption, charge prediction is seen to be less accurate in the moving-boundary approach.