A new statistical approach to identify critical mass flow rate in CO2 nozzles near saturation conditions

The pressing needs to increase efficiency in heat pumps require refined design of various system components. In common reverse cycles, the throttling valve performs pure energy dissipation, and therefore it is well suited to be replaced by technologies such as ejectors and turbines, to augment system performance. In both two-phase turbines and two-phase ejectors a supersonic convergent-divergent nozzle is commonly required, which is responsible for accelerating the refrigerant fluid from the high-pressure part (e.g. condenser) to the low pressure part (e.g. evaporator). In the design phase of these nozzles, the accurate prediction of the maximum mass flow rate, also known as the critical mass flow rate, is particularly complex due to the two-phase nature of the expansion. In this paper, a new statistical approach to determine the value of the critical mass flow rate for CO2, as refrigerant fluid, is presented and assessed. This approach is based on the MF (Massflow Factor) parameter, which well correlates the value of mass flow rate in sonic conditions. The relationship shown here is based on open experimental information and it is validated on data from the open literature and the industry. The relative error on critical flow rate is less than 15% in the validation range, placing this statistical approach at a level of accuracy comparable to other physical models. An example of design is provided in this paper to demonstrate the potential of the relationship found. This approach provides the designer with a straightforward and validated basis for a reliable preliminary design of expanding two-phase nozzles.