## 1 Introduction
[PERSON] et al. [15] numerically investigated the discharge process (melting) in an internal melt ice-on-coil ice storage system. The effect of some operational (inlet mass flow-rate and temperature) and geometrical (coil pitch, diameter, and height) parameters on the melting process were studied. Results revealed that increasing the inlet temperature or mass flowrate leads to enhanced melting rate. Additionally, the coil diameter has a predominant effect on the melting time. [PERSON] et al. [16] performed a three-dimensional numerical analysis to study the solidification process (charging) in a serpentine type ice storage system. Increasing the distance between two serpentine tube rows favors the ice formation. On the contrary, increasing the tube diameter is detrimental to the rate of ice formation. [PERSON] et al. [17] studied the solidification process in an IOCS system with a double helical coil. By increasing the pitch length (50%) and the inner and outer coils distance (33.34%), the ice formation is enhanced by 22.81% and 13.99%, respectively. [PERSON] et al. [18] modeled the melting and solidification processes of an internal melt IOCS using Simulink. The obtained results showed that as the coil diameter increases, the thermal efficiency of the system rises. [PERSON] and [PERSON] [19; 20] reported that the material and the arrangement of the thin layer ring have a higher effect on the ice formation than the thickness of the thin layer ring. [PERSON] et al. [21] performed two-dimensional simulations of the ice formation (solidification) around a bent tube. As the wall temperature increases, the ice formation rate decreases. A higher initial temperature of liquid PCM leads to higher solidified mass. [PERSON] et al. [22] investigated numerically the solidification process in an ice storage system. The considered system is the ice-on-coil type in which the ice is formed around the cold wall of the coil. The considered ice storage system is a two-dimensional square shell and different numbers of heat transfer fluid tubes. The influences of the tube diameter, the number and the arrangement of the tubes on the solidification process have been evaluated, showing that as the diameter of the tubes decreases or the number of tubes increases at constant mass flow-rate of the heat transfer fluid, ice formation speeds up. The staggered triangular arrangement results in faster ice formation in comparison with the in-line arrangement. Although previous investigations focused on the ice formation in an IOCS system, there is no specific research to systematically compare the ice formation in a shell and coil tube type of an ice-on-coil storage system with two different horizontal and vertical positions. In this field, only [PERSON] et al. [23] studied the melting and solidification processes of a phase change material inside a vertical and horizontal shell-and-tube energy storage system. However, their studied geometry was a double pipe heat exchanger, where the PCM was placed in the annulus and the heat transfer fluid flowed in the inner pipe. Hence, the present study intends to numerically investigate the charging process (solidification) in an ice-on-coil ice storage system. The considered ice storage system is of shell and tube type, and three kinds of tubes are investigated including a U-shaped single tube, a coil tube with an inner return line, and a coil tube with an outer return line. Three-dimensional transient numerical simulations are performed by ANSYS Fluent 18.2, to evaluate the effects of the tube type and the position of the ice storage (horizontal or vertical) on the solidification process.