Evaluation of gray box thermostatic expansion valve mass flow models

Abstract

Thermostatic expansion valves (TXVs) are widely used in air-conditioning and commercial refrigeration systems. Accurate predictions of the refrigerant mass flow rate across a refrigeration cycle are desired in many engineering processes and applications such as a computer simulation model, for control purposes, or for fault detection and diagnostics (FDD). Several researchers have developed mass flow models for TXVs. This paper reviews and analyzes four gray-box TXV mass flow models in the literature and evaluates and compares their performance. Three of the models were developed for air-conditioners, but in the current work their applicability to refrigeration system modeling is assessed, with the use of normal and faulted laboratory data from a commercial walk-in cooler and a freezer. Model regression parameters are calculated during the training process with the use of parameter estimation techniques and a training dataset. The models are then used to predict the mass flow rates for several validation data points. Each of the models is found to perform well for the majority of the data points for the freezer, typically with errors below 10%, but application of the models to the cooler's dataset resulted in relatively large errors. The source of the model deviations includes the difficulty associated with the calculation of the TXV diaphragm force and the thermodynamic states of a two-phase refrigerant at the inlet of the valve. The presence of a liquid line receiver, which are common in refrigeration equipment, appears to cause some model deviation.