Mathematical modeling of CO₂ based heat pumping systems

CO₂ based heat pumping systems have in recent years received considerable focus world-wide. Now, attention has been turned toward heating and cool- ing of larger, non-residential buildings. With plate heat exchanger’s now becoming available for CO₂, this natural refrigerant becomes a real alterna- tive for larger applications, considering both efficiency and economy.

However, research and design tools have not been readily available to fully design optimized systems for larger buildings. Simulation-aided design is particularly valuable for CO₂ systems, as existing conventional systems can- not be used with good results. However, the special properties of CO₂ both increase the need for discretization of component models, and require more complex fundamental equations for thermophysical properties. Because of this, circuit simulations with CO₂ are considerably slower compared to sim- ulation of conventional refrigerant systems, to the extent that it is limiting the ability to design optimal CO₂ systems.
In this work, an existing circuit simulation tool, CSIM, has been extended and modified to be suited for efficient design and optimization of heat pump- ing systems with complex-configuration plate heat exchangers. The modification of CSIM performed in this work includes a versatile and configurable plate heat exchanger model, and a general method to handle more complex fluid stream configurations. The new model can describe the local behav- ior in individual, parallel flowing, plate channels, including asymmetric heat transfer, pressure drop and mass flow distribution.
Implemented into CSIM, this model can be used to predict the system per- formance impact due to local behavior in the component. A demonstration simulation case was carried out, comparing the predicted system performance using a simple uniform model, and the new advanced plate heat exchanger model. The results showed that the additional information in the new plate heat exchanger model could have a large impact on the predicted system performance.
A profiling of CSIM simulations on six test cases revealed that approxi- mately 99.85% of the time was consumed calculating thermophysical prop- erties for CO₂. To increase the simulation performance, a new, considerably faster thermophysical library (FTL) for CO₂ has been developed and implemented. FTL is based on linear interpolation in lookup tables containing pre-calculated values of CO₂ properties. Through careful design of extract- ing functions and table grid, even the highly non-linear properties around the critical point was described with acceptable accuracy.
A test suite was performed, focusing on the accuracy and calculation speed compared to the reference equation of state. Overall, simulation results showed only very minuscule differences, but the simulation time was on av- erage reduced from 945 seconds to 2.2 seconds, a reduction of 99.77%. This considerable reduction in simulation time will facilitate the more advanced component and system models needed to optimize CO₂ system design.