In recent years, as part of the focus on reducing the electric power consumption differential between day and night, considerable research on heat saving has been conducted. In particular, there has been extensive research on heat saving for ice production (latent heat saving) for the use of surplus electric power during the night. Consequently, latent heat saving technology has witnessed rapid development [1].

Over the past few years, several studies have been conducted on ice heat-saving technology, but these have been limited to static ice-making types of production in which ice is made on a heat transfer area. This static-type ice-making system has a serious weakness in that the increasing ice creates thermal resistance, thereby decreasing the coefficient of performance of the refrigerator over time.

Studies in this field include those by Kang [2], who studied the cooling coil model, Min [3], who studied the handling method of cooling load, and Lee [4], who investigated the phenomena of ice production around the cooling coil. In addition, Ahn [5] and Park [6] conducted research on the operating characteristics of ice-on-coil-type refrigeration. Furthermore, Jekel [7], Vick [8], and Nelson [9] developed theoretical models for the internal melting of ice-on-coil tanks. They modeled the ice cylinder as growing over the tube at the same speed in different directions during the charging process, while the water cylinder grew concentrically within the ice cylinder during discharge. Finally, Zhu [10] reported a dynamic simulation model for the internal melting of ice-on-coil tanks with built-in horizontal tubes.

In the present study, to support the development of ice-making systems that can exploit surplus electric power at night, the ice-making characteristics were experimentally investigated under various conditions; in particular, nondimensional analysis was conducted.

Following the experimental method of the conventional research of an author [11], in the present study, the coolant temperature was controlled in a constant temperature bath (volume = 22 L and T = −20–99 °C) and was pumped around the circulation pipe. A copper tube, which was attached to the center of a water bath (180 mm × 140 mm × 130 mm), was maintained at a constant temperature. Figure 1 shows the experimental apparatus used in the present study. The setup consists of a constant-temperature bath to ensure that the coolant remains at a constant temperature (30%vol solution of ethylene glycol, with a melting temperature of −12 °C), a coolant circulation pipe, a water bath made of acrylic resin, and a copper tube in the water bath as the test section.

Figure 1:  
Schematic of the experimental apparatus

The experimental conditions are listed in Table 1. The parameters are coolant temperature, initial water temperature, coolant flow rate, and the dimensions of the copper tube.

A scale for measuring the thickness of the produced ice was attached to the front panel of the water bath, and Vernier calipers were used to measure the ice thickness. Additionally, to minimize reading error, digital photography was used.

To measure the flow rate of the coolant, a flow meter was installed at the outlet of the coolant circulation pipe and T-type thermocouples (uncertainty = ±0.1 K) were installed at the inlet and outlet of the test section copper tube. In addition, the temperature of water in the water bath was measured by T-type thermocouples installed at 2-mm intervals in upward and downward directions.

The coolant temperature was controlled in the constant-temperature bath with refrigeration, and coolant was pumped through the circulation pipe in a closed loop. As a result, the temperature of the copper tube, which was attached to the center of the water bath, was maintained at a near-constant temperature.

Analysis of the thermal flow within the phase-change material is very difficult and complex. In this study, for nondimensional analysis, the temperature distribution in Figure 8 was assumed for the freezing phenomena of the material.

Figure 8:  
Cross section of the heat exchanger pipe and ice

In Figure 8, the temperature of the flowing coolant at the center of the copper tube is below freezing. Around the copper tube, ice had grown, and it is assumed that water surrounds the ice. The direction of thermal flow runs from the water to the coolant. Figure 9 indicates this mechanism as a thermal resistance model.

Figure 9:  
Thermal resistance model

For nondimensional analysis in this study, it is used reference about the freezing of water [12].

Based on these assumptions, the governing equations for the cylindrical system are

where αdenotes the thermal diffusivity.

The boundary conditions are

i)Case, r = r₂

ii)Case, r = r₃

where k_ice denotes the thermal conductivity of ice, ρ_ice is the density of ice, L_f is latent heat of the fusion of ice, and h_b is the convective heat transfer coefficient of the coolant.

The primary assumptions of the model are as follows:

• ⚫ Heat resistance of the copper tube is negligible.
• ⚫ The physical properties are constant.
• ⚫ At the freezing point of 0 °C, the liquid condition is T_l = T_fr, and 1/h_e = 0.
• ⚫ The coolant temperature T_∞ and the convective heat transfer coefficient h_b are constants.

When the potential temperature is T_fr − T_∞, the thermal flow rate per unit area is calculated as follows:

For freezing at r = r₃, the thermal flow rate serves to remove the latent heat of solidification:

where dr³/dt is the volume flow per unit area (in m³/hr∙m² at the growth surface), and ρ_iceL_f is the latent heat per unit area (in J/m³). Combining Equations (7) and (8) gives

The following equation describes the ice thickness and the freezing time, with variables r₃ and t taken from Equation (9):

The dimensionless parameters are defined as

Substituting these nondimensional parameters into Equation (10) gives

If the freezing process continues from t = t⁺ = 0 to time t, Equation (13) can be differentiated to give

or,

If the temperature of the liquid, T_l, is higher than the melting point and the convective heat transfer coefficient is h_e at the solid–liquid interface of the system, Equation (13) may written as

When nondimensional parameters are adopted, Equation (16) can be cast in a nondimensional form whose nondimensional parameters are

R+=hehb,T+=Tl-TfrTfr-T∞

where R⁺ is the nondimensional heat transfer rate, h_e is the convective heat transfer coefficient of the surrounding ice, h_b is the convective heat transfer coefficient of the coolant, T⁺ is the nondimensional temperature, and the remaining nondimensional parameters are the same as in Equation (13).

Figure 10 shows the level of ice production calculated from the experimental results according to the nondimensional parameters. With the potential-resistance ratio as R⁺T⁺, Figure 10 indicates the variation of nondimensional ice thickness as a function of nondimensional time.

Figure 10:  
Nondimensional correlation equation

The resulting nondimensional equation from the nondimensional analysis was produced as Equation (17) with a margin of error of ±14%. The range of application is R⁺T⁺ = 2.1–4.7.

In this study, a nondimensional analysis of a comparatively simple ice-on-coil-type ice-making system was performed. From this study, the following conclusion may be drawn: By using the experimental results, the nondimensional amount of ice production was described, with a margin of error of ±14%, as follows:

𝑅⁺𝑇⁺=0.063∙ln(𝑡⁺)+0.206
[range of application: R⁺T⁺ = 2.1–4.7]