Simple mathematical model for predicting the transient behaviour of an ice-bank system

Abstract

The time-variable performance of a Refrigerant 22 ice-bank system was simulated by a dynamic model which was derived by assuming that heat transfer was always the limiting process, and which thus ignored hydrodynamic processes. The model comprised four ordinary differential equations describing the position of the ice front, the water temperature, and the refrigerant evaporation and condensation temperatures, each of which was derived by energy balance, plus a number of algebraic equations. Measured plant performance was accurately predicted except immediately after start-up, and in circumstances in which the assumption that the dynamics of refrigerant flow did not exert any controlling influence on the overall process dynamics was inadequate (for example, when the thermostatic expansion valve operation becomes unstable). The model requires only data that should be readily available or can be easily estimated, and thus it is suitable for analyses in the design of ice bank systems to handle time-varying conditions. Simple dynamic models ignoring hydrodynamics can be adequate in circumstances where the main source of variation arises beyond the refrigeration circuit itself.