Advanced model for a non-adiabatic capillary tube considering both subcooled liquid and non-equilibrium two-phase states of R-600a

Previous empirical correlations have largely failed to predict the mass flow rate variations of R-600a during the transient pull-down operation of household refrigerators. This shortcoming is attributed to the fact that these correlations were developed for specific thermodynamic states of the refrigerant at the capillary inlet, whereas the thermodynamic state varies during transient operations, particularly involving non-equilibrium two-phase states. To address these limitations, a novel model has been developed. This model comprises two distinct sub-models corresponding to the refrigerant state at the capillary tube inlet: one for the subcooled liquid state and the other for the non-equilibrium two-phase state. These sub-models are integrated to account for the transitions in the thermodynamic state of R-600a at the capillary inlet. The integrated model demonstrates excellent agreement with observed variations in the R-600a mass flow rate during the pull-down operation of actual refrigerators. The mean absolute percentage error between the measured and estimated mass flow rates is approximately 10 % over the entire period of pull-down operations tested under various environmental conditions.