Thermodynamic Performance and Parametric Analysis of an Ice Slurry-Based Cold Energy Storage System

Abstract

Subcooling-based ice slurry production faces challenges in terms of energy efficiency and operational stability, which limit its applications for large-scale cold energy storage. A thermodynamic model is established to investigate the effects of key control parameters, including evaporation temperature, condensation temperature, subcooling degree, water flow rate, type of refrigerant, and adiabatic compression efficiency. The results show that using the refrigerant R161 achieves the highest energy efficiency, indicating that R161 is the optimal refrigerant in this research. When the evaporation and condensation temperatures are −10 °C and 30 °C, respectively, the system achieves the maximum comprehensive performance coefficient of 2.43. Moreover, under a flow velocity of 0.8 m/s and a temperature of 0.5 °C, the system achieves a peak ice production rate of 45.28 kg/h. A high water temperature and high flow velocity would significantly degrade the system’s ice production capacity. This research provides useful guidance for the design, optimization, and application of ice slurry-based cold energy storage systems.

1. Introduction

Rapid industrialization has made the imbalance between energy supply and demand in China increasingly prominent. The national power demand is tight, and optimizing power dispatching and improving energy utilization efficiency have become urgent problems to be solved. The electricity consumption pattern in China presents obvious fluctuations. During the peak hours of the day, the power grid load is close to the limit, while during the off-peak hours of the night, the power resources are not fully utilized [1,2]. The efficient operation of air conditioning and refrigeration systems has become a reliable way to enhance energy conservation and emission reduction efforts. Hence, the application potential of cold storage technology has become increasingly prominent.

An ice slurry is a two-phase solid–liquid mixture containing tiny suspended ice crystal particles, which can be stored in ice storage tanks for future use or directly pumped for cooling purposes [1]. When the ice slurry is delivered to an environment with a heat load, the ice crystal particles, which have a large specific surface area and latent heat of phase change, work together with the cold water to absorb heat and rapidly cool the environment. The ice slurry has a high cooling release rate and storage density and strong flow and heat exchange capacity, and its utilization could significantly reduce the use of pipe material and energy consumption in applications such as cold-storage air conditioning, centralized cooling and heating, and food refrigeration [2]. The key to the development of ice slurry cold-storage technology is to achieve continuous and stable slurry preparation [3].

Table 1. Comparison among different ice slurry preparation methods [3,4,5].

Method	Advantage	Disadvantage
Wall scraping	No ice blockage possibility; Stable performance	Complex system; Expensive scraper replacement
Direct contact	Low heat transfer resistance	Ice blockage in nozzles
Vacuum refrigeration	Vapor condensation	Airtightness and vacuum requirements; Corrosion
Subcooling	Simple system; Low investment and operating costs	Ice blockage in subcooler

presents a comparison of different ice slurry preparation methods. The comparison of various methods reveals that the subcooling method has obvious advantages in terms of system structure, heat exchange efficiency, and ice production cost [4,5].

Subcooling refers to the state when a fluid is cooled to a temperature below its freezing point and does not undergo phase change. Researchers have studied aspects such as the establishment of subcooling release models, stability control of the ice-making process, and system performance analysis and optimization of subcooling preparation technology. Li et al. [6] established a cooperative domain model to describe the dynamic phase transition process between subcooled water and amorphous ice, providing a new idea for the occurrence of ice–water phase transition in subcooling release. Mahato et al. [7] incorporated convection, sedimentation, interfacial resistance, and permeability into a macroscopic model to simulate solidification and multiphase convective transport during the formation of ice slurry. Tiwari et al. [8] considered the solidification of aqueous solutions and multiphase convection; simulated the flow field, temperature, and distribution of solid components; conducted solidification experiments of ice slurry formation; and analyzed the influence of process parameters on performance indicators of ice slurry formation. Hellmuth et al. [9] established the advanced subcooled water state equation, analyzed the subcooled water nucleation rate using classical nucleation theory, and theoretically explained the nucleation principle of subcooled release. Using molecular simulations, Ashbaugh et al. [10] concluded that the enthalpy and entropy values of hydrophobic hydration exhibit minimum values in subcooled water, explaining the fundamental principle of the subcooled water phase transition from the perspective of thermodynamic parameters. Du et al. [11], based on the population equilibrium model, concluded that the temperature change in water from the subcooled state to the phase equilibrium state was consistent with the growth of ice crystal size. Each of these systems has, to some extent, highlighted the same issue: ice slurry production still requires considerable time. In a specific device, interference is applied to remove the subcooling of the metastable subcooled water, causing ice crystals to form continuously. The subcooling method achieves the preparation of the ice slurry based on the principle of water subcooling crystallization, as shown in Figure 1: (1) the water is cooled to the subcooled state; (2) the subcooled water releases the subcooled state to become the ice slurry; (3) the ice slurry is separated into ice and water, the ice is stored for future use, and the water is sent into the next cycle [12]. The commonly used methods of subcooling release include shock and collision, ultrasonic vibration, and local low temperature [13]. Shock and impact can instantly change the momentum and flow state of water, causing the subcooled water to suddenly heat up, phase change to occur, and the subcooled state to be released. Ultrasonic vibration creates microbubbles in the subcooled water through cavitation, and the collapse of the bubbles releases high temperatures, high pressures, and shock waves, promoting the release of the subcooled state [14]. Local low temperatures are produced using small electronic refrigeration devices at temperatures far below that of the subcooled water, which is cooled for subcooling release.

Ultrasonic waves can promote the release of subcooled water from the subcooled state, shortening the ice-making time and reducing energy consumption. Saclier et al. [15] used a model of ice nucleation induced by acoustic cavitation to effectively predict the amount of ice nucleation under different acoustic pressures and degrees of undercooling. The ultrasonic cavitation effect generates microbubbles in the subcooled water, triggers heterogeneous nucleation, and promotes subcooling release. The extremely high pressure generated in the final stage of the acoustic cavitation bubble collapse raises the equilibrium freezing temperature of the water, promoting ice nucleation. Hu et al. [13] found that the degree of subcooling is a key influencing factor for the degree of subcooling release. The greater the degree of subcooling, the higher the degree of subcooling release, while the effects of ultrasonic power and subcooling dwell time on the degree of subcooling release are very small. Due to the randomness of ice crystal nucleation, the occurrence of ice blockage is difficult to control, which seriously affects the stable operation of the undercooled ice slurry preparation system. The factors that affect the occurrence of ice blockage include the degree of subcooling, the flow state, the content of impurity particles, and the ultrasonic parameters. Ahmadkermaj et al. [16] found that a rotating flow field makes the distribution of ice crystals more uniform on the cross-section of the pipe, which can reduce the deposition of ice crystals and suppress the occurrence of ice blockage. Okawa et al. [17] suggested that impurity particles in water significantly reduce the undercooling degree required for nucleation, and that reducing the total contact area between particles and water can effectively prevent ice blockage. Asaoka et al. [18] found that an increase in subcooling degree could significantly increase the rate of ice crystal nucleation. By reducing the temperature gradient on the heat exchange wall of the subcooler, the area with excessive local subcooling could be significantly reduced, maintaining the stable operation of the ice-making system. Based on the above analysis, the inlet water flow rate should be maintained in the range of 0.8 to 2.0 m/s, the inlet water temperature changes kept within 0.5 to 1.0 °C, the ultrasonic parameters limited to within 30 to 35 kHz, the average subcooling at the outlet of the subcooler should be controlled within 1 to 3 °C, and the temperature gradient on the heat exchange wall of the subcooler should be appropriately reduced. The experimental study of Wang et al. [19] showed that ultrasonic waves with specific parameters can increase the crystallization rate of subcooled water, effectively reduce the subcooling degree required for nucleation, and improve the energy efficiency of ice making.

In this study, the design of an indirect ice slurry preparation system is completed based on the theory of ice crystal nucleation and the principle of undercooling ice making. This proposed system includes a vapor-compression refrigeration cycle for subcooling realization, a heat-transfer cycle for preventing ice blockage, and an ice-making cycle relying on the ultrasonic crystal promotion. Using the process simulation software Aspen Plus V11, a thermodynamic model of the subcooled indirect cooling ice slurry preparation system is established. The effects of the main control parameters evaporation temperature, condensation temperature, subcooling degree, subcooler inlet water flow rate and temperature, refrigerant type, and adiabatic compression efficiency on the system performance are investigated. This study provides pragmatic information that helps achieve efficient and stable operation in ice-storage systems.

2. System Description

2.1. System Configuration

According to the undercooling ice-making method, an indirect cooling ice slurry preparation system is proposed, consisting of a refrigeration cycle, a secondary refrigerant cycle, and an ice-making cycle (from left to right). Compared with direct cooling, the addition of the secondary refrigerant cycle causes additional energy loss, but it can extend the stable ice-making time and improve the ice-making performance. Although pure water has a lower impurity particle content than tap water, and its usage can prolong the stable ice-making time, tap water is still used for economic benefits. The overall process of the ice slurry preparation system is shown in Figure 2.

(1) The refrigeration cycle. A single-stage vapor compression refrigeration cycle is used to provide cooling for the entire ice slurry preparation system. The main components include a piston compressor, an electronic expansion valve, a water-cooled condenser, and a shell-and-tube evaporator. The low-pressure superheated refrigerant vapor produced in the evaporator is drawn into the compressor, which consumes external work to compress the refrigerant to condensing pressure and then sends it to the condenser. In the condenser, the high-temperature refrigerant vapor is cooled by circulating cooling water and condensed into a high-pressure subcooled liquid. When throttling from the condensing pressure to the evaporation pressure in the expansion valve, part of the liquid absorbs its heat and vaporizes, reducing the temperature. The liquid refrigerant in the low-pressure gas–liquid two-phase mixture continues to absorb heat and evaporate in the evaporator, and it is appropriately superheated to prevent compressor liquid strike, cooling the secondary refrigerant to the required temperature.

(2) The secondary refrigerant cycle. This cycle uses a 40% volume fraction of ethylene glycol aqueous solution as the coolant, with a freezing point of −24.3 °C at ambient pressure. By having a lower freezing point than the evaporation temperatures expected at the evaporator of the refrigeration cycle, the secondary refrigerant does not freeze during system operation, which is a key requirement for the system operability and lifetime. The secondary refrigerant is pumped into the evaporator by the solution pump to exchange heat with the refrigerant. The refrigerant then transfers the cold energy to the ethylene glycol solution, which then enters the subcooler to exchange heat with the water, the ice-making medium, gradually cooling the water until it is subcooled. The secondary refrigerant is pumped back to the evaporator by the solution pump for another cycle operation.

(3) The ice-making cycle. The shell-and-tube subcooler is the core device of the ice-making cycle, using tap water as the ice-making medium. Compared with plate heat exchangers, the flow channels in shell-and-tube heat exchangers are relatively wide and less likely to be blocked by ice. The fluids flowing in the tube side and shell side are relatively independent. Even if ice crystals appear in a certain area, they will not spread rapidly to the entire heat-exchange surface, reducing the risk of the subcooler being damaged by freezing. The water initially separated by the bottom filter in the ice slurry storage tank carries a small amount of ice slurry particles. After being processed by the ice crystal removal device, the cooling water is pumped to the subcooler, where it is cooled by the ethylene glycol solution and reaches the subcooled state. Ignoring the heat loss, the cooling load required to cool tap water to a certain degree of subcooling is the cooling capacity output from the evaporator of the refrigeration cycle. Then, the subcooled state is removed by ultrasonic crystal promoters, generating ice crystal particles. When the ice slurry enters the storage tank, it undergoes ice–water separation. The solid ice is stored in the tank for standby, and the cooling water returns to the subcooler to achieve dynamic and continuous ice slurry preparation.

2.2. Refrigerant and Secondary Refrigerant

In this paper, the ice slurry preparation system utilizes a secondary refrigerant to reduce the impact of the temperature fluctuation of the refrigerant on the subcooling degree of the outflow of the subcooler and to reduce the risk of ice blockage in this equipment due to direct heat exchange between the low-temperature refrigerant and the water. The selection of the working medium includes the refrigerant and the secondary refrigerant.

The refrigerant circulates in the system and continuously exchanges energy with the outside through changes in its thermal state. Hydrochlorofluorocarbons with a high ozone depletion potential (ODP) must be banned. Currently, hydrochlorofluorocarbons and natural refrigerants have become the main substitutes [20]. R161, R290, R1270, and R32, which have an ODP of 0, are all acceptable alternatives to R22, effectively addressing the problem of ozone depletion. The flammability and photofog effect value of R161 are far lower than those of hydrocarbons, making it safer to use in refrigeration systems. Therefore, R161 is chosen as the first refrigerant medium, and the other three refrigerants are used for comparisons to study the effects of refrigerant types on the performance of ice slurry preparation systems.

The secondary refrigerant in the circulating flow first acquires cold energy by heat exchange with the refrigerant in the evaporator; then, the low-temperature fluid is pumped to the subcooler, and the cold energy is delivered to the cooled ice-making medium. Water, inorganic salt solutions, and organic liquids are all commonly used secondary refrigerants. Inorganic salt solutions have a lower freezing point and are suitable for use as coolants in medium- and low-temperature refrigeration systems, but they are corrosive. Especially when in contact with air, acidic dilute salt solutions are highly corrosive to metal materials. Ethylene glycol aqueous solution is a colorless, odorless liquid that is slightly corrosive to metals, chemically stable, and non-electrolytic. It has a high ignition point, is not easy to burn, has high safety, and is easy to transport. It has low volatility and evaporation rate, and the freezing temperature can be adjusted by changing its concentration ratio. Therefore, ethylene glycol solution is chosen as the secondary refrigerant in this research.

3. Methodology

3.1. Basic Assumptions

For simplicity, the following assumptions are made: (1) The entire system is in a stable state, and the changes in kinetic and potential energy of the circulating working medium are negligible. (2) The heat loss between the equipment/pipelines within the system and the external environment is neglected. (3) All heat exchangers perform counter-current heat exchange, with heat transfer temperature differences and pressure losses of the flows. (4) The low-pressure vapor at the outlet of the evaporator is superheated, the high-pressure liquid at the outlet of the condenser is subcooled, and the water at the outlet of the subcooler is in a subcooled state. (5) The secondary refrigerant at the outlet of the evaporator and the subcooler is saturated liquid, with no freezing or evaporation. (6) The throttling process is isenthalpic. (7) The refrigerant compression process is not ideal isentropic compression, but the adiabatic compression efficiency of the compressor remains constant. (8) The pressure and heat transfer losses in the connecting pipes and the power consumption of the circulating cooling water are neglected. (9) There is no leakage of the working medium and no non-condensable gas in the whole system.

3.2. Balance Equations

Following is the mass conservation equation:

$${\displaystyle \sum m_{in}}={\displaystyle \sum m_{out}}$$

(1)

where $\sum m_{in}$ and $\sum m_{out}$ are the mass flow rates of all streams flowing into and out of components, kg/s, respectively.

According to the first law of thermodynamics, ignoring changes in kinetic and potential energy, the energy balance equation for a stable flow system is as follows:

$$Q+P=q_m(h_{out}-h_{in})$$

(2)

where Q and P are the heat and work input to the system per unit time, q_m is the mass flow rate flowing in or out of the system, h is the specific enthalpy of the working medium, and the subscripts in and out indicate the fluid entering and leaving the system, respectively. The energy balance equations of the equipment are given in

Table 2. Balance equations.

Device	Energy Balance Equation
Compressor	$P_c={\displaystyle \frac{P_0}{{\eta }_{c,s}{\eta }_m}}={\displaystyle \frac{q_{mr}(h_{2s}-h_1)}{{\eta }_{c,s}{\eta }_m}}={\displaystyle \frac{q_{mr}(h_2-h_1)}{{\eta }_m}}$
Condenser	$Q_k=q_{mr}(h_2-h_3)=Q_{mw}(t_{out}-t_{in})$
Evaporator	$Q_e=q_{mr}(h_1-h_4)=q_{mr}(h_1-h_3)$
Valve	$h_3=h_4$
Subcooler	$Q_c=q_{mw}{c}_{pw}(t_9-t_{10})=q_{mz}{c}_{pz}(t_8-t_7)=Q_e$

, and the parameters and nomenclatures are shown in

Table 3. Parameters and nomenclature.

Nomenclature	Parameter	Unit
h4	Specific enthalpy of the outflow of the valve	kJ/kg
h2s	Theoretical specific enthalpy of the outflow of the compressor	kJ/kg
h2	Actual specific enthalpy of the outflow of the compressor	kJ/kg
h3	Specific enthalpy of the outflow of the condenser	kJ/kg
h1	Specific enthalpy of the outflow of the evaporator	kJ/kg
qmr	Mass flow rate of refrigerant	kg/s
qmz	Mass flow rate of secondary refrigerant	kg/s
qmw	Mass flow rate of tap water	kg/s
Qmw	Mass flow rate of circulating cooling water	kg/s
tin	Inlet temperature of circulating cooling water	°C
tout	Outlet temperature of circulating cooling water	°C
t7	Inlet temperature of subcooler	°C
t8	Outlet temperature of subcooler	°C
cpz	Specific heat at constant pressure of secondary refrigerant	kJ/(kg·°C)
t9	Inlet temperature of tap water	°C
t10	Outlet temperature of tap water	°C
ηc,s	Adiabatic compression efficiency of compressor	%
ηb	Efficiency of ethylene glycol solution pump	%
ηm	Drive efficiency of compressors and solution pump	%
Pc	Actual power consumption for adiabatic compression	kW
P0	Theoretical power consumption for adiabatic compression	kW
Pb	Power consumption of ethylene glycol solution pump	kW
Pw	Power consumption of water pump	kW
Qk	Heat load of condenser	kJ
Qe	Cooling capacity output from evaporator	kW
Qc	Heat load of subcooler	kW
cpw	Specific heat at constant pressure of water	kJ/(kg·°C)

.

The coefficient of performance (COP) is the ratio of the cooling capacity obtained to the total energy consumption of the equipment. The energy-consuming equipment in the system includes the compressor in the refrigeration cycle, the solution pump in the secondary refrigeration cycle, the ultrasonic crystal promoter, and the water pump in the ice-making cycle. Then, the combined coefficient of performance (COP_Z) of the ice slurry preparation system is given as follows:

$$CO{P}_Z={\displaystyle \frac{Q_c}{P_Z}}={\displaystyle \frac{Q_c}{P_c+P_{zw}}}={\displaystyle \frac{Q_e}{P_c+P_b+P_g+P_w}}$$

(3)

where P_Z is the total energy consumption of the ice slurry preparation system, P_zw is the energy consumption of the non-cooling unit (P_zw = P_b + P_g + P_w), and P_g represents the energy consumption of the ultrasonic crystal promoter, in kW.

Both the production amount of ice and the energy consumption per unit of ice are important indicators for measuring the ice-making performance of the system [13]. The theoretical calculation equation for the ice production rate is given as Equation (4). The ice production rate, M_ice (kg/h), refers to the mass of solid ice in the ice slurry per unit of time. The energy consumption per unit W_m (kWh/kg) refers to the ratio of the total energy consumed to the mass of solid ice. The smaller the value, the higher the ice-making energy efficiency. It can be defined as follows:

$$M_{ice}={\displaystyle \frac{c_{pw}\mathsf{\Delta }{T}_g{q}_{mw}}{\gamma }}\times 3600={\displaystyle \frac{c_{pw}{q}_{mw}\left(t_n-t_{10}\right)}{\gamma }}\times 3600$$

(4)

$$W_m={\displaystyle \frac{P_Z}{M_{ice}}}$$

(5)

where ΔT_g is the subcooling degree of the outlet water (ΔT_g = t_n − t₁₀), °C; γ is the latent heat of solid ice melting, approximately 334 kJ/kg; t_n is the freezing point of water, 0 °C.

3.3. Simulation Model and Validation

At first, REFPROP is selected as the physical property method. The isentropic compression is specified for the compressor. The efficiency of the solution pump is fixed at a constant value. The outlet pressure of the compressor and the solution pump are specified, but the performance of the water pump is determined using the characteristic curve. The HeatX module is selected for both the evaporator and the subcooler (also for the condenser), and the calculation mode is shortcut (simple design). Considering that both equipment components are shell-and-tube heat exchangers, the pressure drop is set within 10 to 30 kPa. The overall heat transfer coefficient is calculated using the phase method and the constant U method. The expansion valve is selected as an adiabatic flash at the specified outlet pressure.

An experimental platform for indirect subcooled ice making is established to study the effects of parameters such as condensing temperature and inlet water flow rate on system performance [21]. For comparison, the same operational parameters in the literature are employed: refrigerant mass flow rate of 70 kg/h, condensation temperature of 30–45 °C, liquid subcooling degree of 3 °C, evaporation temperature of −15 °C, effective superheat degree of 5 °C, adiabatic compression efficiency of 80%, inlet water temperature of 0.5 °C of the subcooler, inlet water flow rate of 2.6 m³/h. R161 is selected as the refrigerant, and a 40% volume fraction of ethylene glycol solution is used as the secondary refrigerant. The overall performance coefficient of the system and the variations in ice production rate at different condensing temperatures are obtained, and the results are shown in

Table 4. Model validation.

Condenser Temperature (°C)	COPZ		Relative Errors	Mice (kg/h)		Relative Errors
	Present Study	Reference [21]		Present Study	Reference [21]
30	2.208	2.221	0.6%	48.454	48.408	0.1%
35	2.008	1.989	1.0%	46.062	46.153	0.2%
40	1.830	1.814	0.9%	43.635	43.626	0.1%
45	1.670	1.663	0.4%	41.166	41.241	0.2%

. The results in this work are compared with the experimental results. It can be found that the differences between the present research and the literature are within the acceptable range, proving that the established model of the ice slurry preparation system in this research is accurate and reliable.

4. Results and Discussion

4.1. Design Condition

The main control parameters include the refrigeration cycle parameters (evaporation temperature, condensation temperature, vapor overheating degree, liquid subcooling degree, compressor efficiency, refrigerant type) and the ice-making cycle parameters (inlet water flow rate and temperature of the subcooler). The effects of the above variables on the overall performance coefficient of the ice-making system, the amount of ice produced, and the energy consumption per unit of ice are studied. Based on the ambient environment and the requirements of the ice slurry preparation, the specific design conditions are provided in

Table 5. Parameter specifications.

Parameter	Design Value	Range	Unit
Evaporation temperature, t0	−14	−22~−10, with an interval of 3	°C
Overheating degree, Δtr	5	1.5, 5, 8.5	°C
Condenser temperature, tk	36	30~45, with an interval of 3	°C
Subcooling degree, Δtg	5	1, 4, 7	°C
Compressor efficiency, ηc,s	85%	75, 85, 95	%
Water inflow velocity, uw	1.2	0.8~1.8, with an interval of 0.2	m/s
Refrigerant	/	R161, R290, R1270, R32	/
Inflow temperature of cooler, t9	0.5	0.5, 0.8, 1.1	°C
Refrigerant mass flow rate, qmr	60	/	kg/h
Temperature difference of secondary coolant, Δtz	3	/	°C

. According to the literature [16,17,18,19], under ultrasonic vibration conditions of 33 kHz and 360 W, the overall performance of the ice slurry preparation system is optimal when the outlet subcooling is within 1–2.5 °C. Therefore, in this study, an ultrasonic crystal promoter working at this condition is used as the subcooling release device. When investigating the combined impact of two parameters on system performance, the remaining parameters remain constant. The variation range for each control parameter is also given. Through process simulation, a detailed system performance analysis is conducted using the established model of the undercooled indirect cooling ice-making system.

4.2. Performance Analysis

(1)

Effects of the condenser temperature and subcooling degree

The condensation temperature and the subcooling degree of high-pressure liquid refrigerant are selected as the control parameters to form 18 working conditions. The effects of t_k and Δt_g on the system cooling capacity, comprehensive performance coefficient, and ice-making capacity are investigated, as shown in Figure 3. When the subcooling degree of liquid refrigerant is constant, t_k increases in the refrigeration cycle pressure–enthalpy diagram, the process line of evaporation remains unchanged, but the condensation process line increases. The enthalpy h₃ of the high-pressure refrigerant liquid at the outlet of the condenser increases, and the enthalpy h₁ of the superheated vapor at the outlet of the evaporator remains unchanged; hence, the difference h₁ − h₃ decreases, and the cooling capacity decreases accordingly. The compressor exhaust pressure p₂ increases with the increase in t_k, the pressure ratio increases, the enthalpy h₂ of the high-pressure vapor at the compressor outlet increases, and the specific work of compression h₂ − h₁ increases; hence, the compressor energy consumption P_c increases, the system total energy consumption increases, and the overall performance coefficient decreases. Under the condition of constant condensing temperature, Δt_g increases; the left side of the throttling process line is prolonged in the pressure–enthalpy diagram; h₃ decreases, but h₁ remains unchanged; the cooling capacity per unit increases; and the system cooling capacity increases. Since the compression process line remains the same, the energy consumption of the compressor is not affected by Δt_g, and the change in P_Z with subcooling degree can be ignored, so the COP_Z of the system increases with the increase in subcooling degree of the high-pressure liquid.

Figure 4 shows the effects of condensing temperature and subcooling on the system’s ice-making capacity and the energy consumption per unit of ice. When the condensing temperature is raised while Δt_g is constant, the cooling capacity transferred from the refrigerant in the evaporator to the ethylene glycol solution decreases, the amount of cooling Q_c used to cool the tap water decreases, and hence, the undercooling degree of the outlet water decreases. When the inlet water flow is constant, the amount of ice produced is reduced due to the decrease in ΔT_g. In general, the total energy consumption of the system increases with the increase in t_k, so the energy consumption per unit increases with the increase in condensing temperature. When t_k remains constant, increasing the subcooling degree of the refrigerant liquid increases the cooling capacity, P_Z remains almost constant, the subcooling degree of the water at the outlet of the subcooler and the system’s ice-making capacity increase, and W_m goes down.

(2)

Effects of the evaporation temperature and overheating degree

The effects of evaporation temperature t₀ and superheating degree of low-pressure vapor Δt_r on the overall energy efficiency and ice-making capacity are investigated, and the results are shown in Figure 5 and Figure 6. The effects of evaporation temperature and vapor superheat on the system’s cooling capacity and overall performance coefficient are studied. For the same vapor superheat, as t₀ increases, the condensation process line in the refrigeration cycle pressure–enthalpy diagram remains unchanged, but the evaporation process line moves upward. The enthalpy h₃ of the high-pressure liquid refrigerant at the outlet of the condenser remains unchanged. The specific enthalpy of saturated vapor increases with temperature, but the change is small. When t₀ rises, the enthalpy h₁ of superheated vapor at the evaporator outlet increases, the cooling capacity per unit h₁ − h₃ increases, and Q_e increases. The increase in evaporation temperature raises the evaporation pressure, but the condensing pressure is the same. The pressure ratio of the compressor decreases, the adiabatic compression work P_c decreases, and the total energy consumption decreases. Therefore, the overall performance coefficient of the ice-making system increases with the increase in t₀. At the same evaporation temperature, the effective superheat of the vapor increases, the inlet temperature t₁ and enthalpy h₁ increase, but h₃ remains unchanged, and the cooling capacity per unit and Q_e increase accordingly. With the compression ratio remaining constant, the exhaust temperature t₂ increases as t₁ rises, the compression process line in the pressure–enthalpy diagram shifts to the right, and the slope decreases. The adiabatic compression specific work h₂ − h₁, which is enclosed by the coordinate axes, increases, increasing the total energy consumption. But the increase in cooling capacity, ΔQ_e, is greater than the increase in total energy consumption, ΔP_Z; hence, the overall performance coefficient increases with Δt_r. Since the total energy consumption of the system increases with Δt_r but decreases with t₀, the change in evaporation temperature has a more significant impact on the coefficient of performance.

The effects of t_r and Δt₀ on the system’s ice-making and energy consumption per unit are obtained, as depicted in Figure 6. At the same steam superheating degree, as t₀ increases, the cooling capacity Q_e output by the evaporator increases, and the subcooling degree of the water at the outlet of the subcooler and the system’s ice-making capacity increase. The main reasons are as follows: although the temperature of the secondary refrigerant at the inlet of the subcooler rises with the increase in t₀, the amount of cold energy carried by the ethylene glycol solution increases. When the inlet water flow and temperature remain unchanged, the amount of cold energy Q_c used to cool the tap water increases. The ice production is proportional to the inlet water flow rate of the subcooler and the degree of subcooling at the outlet. An increase in ΔT_g increases the ice-making capacity. In general, it can be concluded that the total energy consumption of the system decreases as t₀ increases, so the energy consumption per unit for ice making decreases as t₀ increases. At the same evaporation temperature, an increase in the effective superheat of the vapor leads to an increase in the amount of cold energy that the secondary refrigerant obtains in the evaporator. ΔT_g increases, and the system’s ice production capacity M_ice increases. While the total energy consumption increases with Δt_r, W_m slightly decreases with the increase in steam superheating degree because the increase in ice production capacity, ΔM_ice, is greater than the increase in total energy consumption, ΔP_Z.

(3)

Effects of the condensation/evaporation temperature

Based on the obtained results, the condensation temperature and evaporation temperature play important roles in the performance optimization of the ice slurry preparation system. Therefore, this section selects evaporation temperature (within the range from −18 to −10 °C with intervals of 4 °C) and condensation temperature (30 to 46 °C, interval: 4 °C) as the control parameters. This section focuses on the effect of the temperature difference between the condensation and evaporation temperatures, Δt = t_k − t₀, on the system performance, and compares the influences of t_k and t₀ on ice-making system performance. The simulation results are shown in Figure 7 and Figure 8. When the condensation temperature drops or the evaporation temperature rises, the temperature difference decreases. The heat absorption of the refrigerant in the evaporator increases, and at the same time, the heat release resistance in the condenser decreases. The heat exchange efficiency increases, making the refrigeration cycle more efficient. In the pressure–enthalpy diagram, the condensation and evaporation process lines become closer, the entire refrigeration cycle flattens, and the cooling capacity per unit h₁ − h₃ increases. The compression ratio of the compressor p_k/p₀ decreases, the adiabatic compression specific work h₂ − h₁ decreases, and the power consumption of the compressor decreases. The cooling capacity of the system increases, but the total energy consumption decreases. Hence, the coefficient of performance increases as Δt decreases. The secondary refrigerant transfers the cooling capacity to the ice-making medium to achieve subcooling. The subcooling degree of the outlet water increases with Q_e, and the ice production capacity increases accordingly. The ice-making energy consumption per unit is the ratio of the ice production to the total energy consumption. As M_ice increases and P_Z decreases, W_m decreases, and the ice-making capacity of the system increases. At an evaporation temperature of −10 °C and a condenser temperature of 30 °C, with the rest of the operational parameters under the design conditions, the coefficient of performance COP_Z of the ice slurry preparation system reaches the maximum value of 2.43. Compared with the published literature [21], this value is 9.5% higher than the maximum value of 2.22 in the literature, indicating an improved energy efficiency and a better cold storage performance of the proposed system.

When t_k and t₀ change with the same interval, the increase in cooling capacity ΔQ_e is smaller when increasing t₀ compared with that when the condensing temperature drops. From the perspective of refrigerant characteristics and the principle of the refrigeration cycle, the specific enthalpy of the high-pressure subcooled liquid decreases when t_k decreases, and the enthalpy of the low-pressure superheated vapor increases when t₀ increases. However, the increase in h₁ is insignificant compared with the decrease in h₃, and the cooling capacity per unit increases significantly when t_k decreases. The refrigerant in the condenser is better cooled after the condensing pressure is lowered, and the flash gas produced during throttling is reduced. It can absorb heat more effectively when it returns to the evaporator, thereby increasing the cooling capacity. When the evaporation temperature rises, the reduction in compressor energy consumption, ΔP_c, is greater, resulting in a larger reduction in total system energy consumption than the value when t_k is lowered. The main reason is that an increase in t₀ can significantly reduce the compression ratio, reducing compressor power consumption. At the same time, the evaporation pressure rises, the density of compressor inflow increases, and at the same mass flow rate q_mr, the gas volume to be compressed is reduced, and P_c is further reduced. Since the increase in cooling capacity is greater than the increase in total energy consumption, to improve the overall performance coefficient of the system, the effect of decreasing t_k is stronger than that of increasing t₀.

In addition, since the increase in cooling capacity is greater when t_k is reduced than when t₀ is increased, the increase in the subcooling degree of water at the subcooler outlet is larger, and the growth trend of ice production capacity is steeper, as shown in Figure 8. At t₀ of −10 °C, when t_k drops from 46 °C to 30 °C, the ice production capacity increases from 37.23 to 43.88 kg/h. Although the total energy consumption decreases more as the evaporation temperature rises, the decrease in t_k leads to a significant increase in the ice production capacity, which has a slightly greater impact on W_m. In summary, when the condensing temperature is lowered or the evaporation temperature is improved to reduce the temperature difference, the ice-making capacity of the system is enhanced, the energy consumption per unit is reduced, and the entire ice-making system is more energy-efficient. Therefore, in the actual operation of the current system, the condensation temperature should be lowered as much as possible, provided that the lowest non-freezing temperature requirement for the subcooler is met. However, in actual systems, the increase in evaporation temperature is limited by a variety of factors, while the decrease in condensation temperature could be relatively large. So, maintaining a low condensing temperature has obvious advantages in optimizing the ice-making performance of the system.

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Effects of the water inflow velocity

As the core component for achieving water subcooling, the inlet parameters of the subcooler directly affect the subcooling degree of the outlet water and thereby influence the ice-making capacity of the system. Therefore, the inlet water temperature and flow rate are selected as control variables, and the other parameters remain unchanged (the cooling capacity Q_e, the heat transfer capacity Q_c of the subcooler, and the power consumption of the compressor and solution pump remain unchanged). This section focuses on the effects of the inlet water temperature and flow rate of the subcooler on the system’s ice-making capacity and energy consumption per unit, as shown in Figure 9. As described in this figure, a decrease in inlet water flow rate leads to a reduction in pump power P_w, a decrease in total system energy consumption, and an increase in COP_Z. However, inlet water temperature does not affect P_Z and P_w. When t₉ changes, the system’s cooling capacity, energy consumption, and overall performance coefficient remain the same.

When the inlet water temperature of the subcooler is the same, u_w increases, the flow rate of tap water increases, the average subcooling degree at the outlet decreases, and the amount of ice produced decreases. Based on the fundamental principle that ultrasonic waves promote the nucleation of subcooled water, the analysis is conducted from three directions: ultrasonic cavitation effect, liquid micro-disturbance, and heat transfer. An increase in u_w enhances convective heat transfer of water in the subcooler, making the temperature distribution of the subcooled water more uniform, and liquid micro-disturbance enhances the uniform nucleation of the subcooled water. However, the cooling time of the water in the subcooler is shortened, and the large flow rate of tap water leads to insufficient heat exchange, resulting in a lower heat exchange efficiency of the subcooler. At the same time, the rapid inflow of tap water takes away the energy generated by the cavitation bubbles, reduces the residence time of the cavitation bubbles, disperses the cavitation effect area of the ultrasonic waves, weakens the cavitation intensity of the ultrasonic waves, and reduces the cavitation efficiency. The combined effect causes the outlet water subcooling to decrease, M_ice to decrease, and u_w to increase. The total energy consumption and the energy consumption per unit increase.

The refrigeration cycle parameters remain unchanged, and the cooling capacity transferred by the secondary refrigerant to the water remains unchanged. According to the heat exchange equation of the subcooler, when the inlet water flow rate is constant, the heat exchange temperature drop, Δt_w = t₉ − t₁₀ = ΔT_g + t₉, of the tap water in the subcooler is fixed. An increase in t₉ leads to a decrease in the subcooling degree of the outlet water and a reduction in M_ice due to the decrease in ΔT_g, and the total energy consumption remains unchanged; then, the energy consumption per unit increases with the increase in t₉. In addition, at u_w = 0.8 m/s and t₉ = 0.5 °C, the system’s ice-making capacity reaches the highest value of 45.28 kg/h, which is higher than those values in previous studies [19,21]. The combined effect of increasing u_w and t₉ leads to a reduction in the system’s ice-making capacity. At u_w = 1.8 m/s and t₉ = 1.1 °C, the ice-making energy consumption per unit is about 4.8 times that at the maximum M_ice condition, reaching the maximum value of 0.26 kWh/kg. High flow rate and high water temperature should be avoided as much as possible.

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Effects of the compressor efficiency

The adiabatic compression efficiency of the compressor (75%, 85%, and 95%) is selected as the first variable. The evaporation temperature, which has a significant influence on energy consumption in the refrigeration cycle, is selected as the secondary variable. The effects of adiabatic compression efficiency on the performance of the ice slurry preparation system are analyzed, as shown in Figure 10. When the evaporation temperature remains constant, the adiabatic compression efficiency of the compressor, η_c,s, increases, the refrigerant evaporation is almost unaffected, and the cycle cooling capacity remains unchanged. But when η_c,s becomes higher, the compression process of the refrigerant is closer to isentropic compression. The inflow enthalpy h₁ remains unchanged, the exhaust temperature decreases, the enthalpy h₂ of the high-pressure vapor at the compressor outlet decreases, the adiabatic compression specific work h₂ − h₁ decreases, and hence, the compressor energy consumption goes down. The parameters of the ice-making cycle are also constant, the energy consumption of the non-refrigeration unit is unchanged, the total energy consumption of the system is reduced because P_c is lower, and the coefficient of performance is improved. At this point, if t₀ is increased, the pressure ratio of the compressor and the inflow volume rate of the refrigerant are significantly reduced, P_c and P_Z are further reduced, and COP_Z is effectively enhanced.

As shown in Figure 11, an increase in refrigeration capacity leads to an increase in the subcooling degree of outlet water, and the ice-making capacity of the system increases with the increase in t₀. However, the variation lines of the ice production capacity for different compressor efficiencies are the same, and M_ice remains constant as η_c,s increases. It is mainly because when the adiabatic compression efficiency increases, the cold energy of the secondary refrigerant transferred to the water in the subcooler remains unchanged. According to the heat transfer equation and the ice production calculation equation, the inlet water flow rate and temperature are fixed, the outlet undercooling degree remains constant, and the ice-making capacity remains the same. The energy consumption per unit decreases with the increase in η_c,s, and if reducing t₀ at the same time, the value of W_m can be further reduced. When t₀ = −22 °C and the other parameters are under standard conditions, η_c,s increases from 75% to 95%, and W_m decreases accordingly by 0.106 kWh/kg. That is, when t₀ is lower, improving the performance of the compressor is more beneficial for decreasing the energy consumption per unit.

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Effects of the refrigerant type

Four acceptable alternatives to the traditional refrigerant R22 are selected as the working fluids for the ice slurry preparation system: R161, R290, R1270, and R32. The ice-making cycle parameters are kept constant, and the flow rates of the four refrigerants are equal. The effects of the refrigerant types on the system performance are investigated for different evaporation and condensation temperatures. As shown in Figure 12 and Figure 13, when the evaporation temperature rises or the condensation temperature drops, the refrigeration capacity increases, the compressor energy consumption decreases, the total energy consumption of the system decreases, and the COP_Z increases. The system’s cooling capacity and overall performance coefficient can be obtained in the descending order of R161 > R1270 > R290 > R32. This is because R161 has a higher specific enthalpy variation with changing temperatures, higher latent heat of vaporization and thermal conductivity, and larger cooling capacity per unit mass. When operating under the same conditions, the refrigerant R161 can absorb heat more effectively in the evaporator and has a better cooling effect in the condenser. The efficiency of the entire refrigeration cycle is enhanced, resulting in a greater cooling output. Although R32 has a large specific heat capacity at constant pressure, it has poor thermodynamic cycle characteristics, the lowest cooling capacity per unit, and obvious disadvantages in terms of cooling capacity and COP_Z. Compared with refrigerants R1270 and R290, although R161 has a lower operating pressure range, its compression ratio is slightly higher, and its exhaust temperature is also higher, resulting in slightly higher energy consumption for compressor operation. But the increase in the system’s total energy consumption, ΔP_Z, is lower than the increase in the cooling capacity, ΔQ_e; hence, the overall performance coefficient of the ice-making system is still the highest when R161 is used as the refrigerant.

The ice production capacity M_ice is mainly affected by the subcooling degree of the water at the outlet of the subcooler. According to the balance equation of the subcooler, at the same inlet water flow rate and temperature, the greater the degree of subcooling at the outlet, the greater the ice-making capacity. At this point, if the increase in energy consumption during the refrigerant compression process is much lower than the increase in ice-making capacity, the energy consumption per unit is reduced. The ice-making efficiency and energy efficiency are improved. At standard operating conditions, the M_ice of R161 is 7.60%, 4.81%, and 18.73% higher than that of R290, R1270, and R32, respectively. The corresponding values of W_m are 6.09%, 4.58%, and 16.14% lower in sequence. As shown in Figure 14 and Figure 15, the ice production capacity of the system can be obtained as R161 > R1270 > R290 > R32, and the energy consumption per unit can be obtained as R161 < R1270 < R290 < R32. Therefore, when operating under the simulated conditions, the system can achieve the highest cooling capacity, coefficient of performance, and ice production capacity by using R161 as the refrigerant. By using a suitable refrigerant, higher thermodynamic performance can be achieved under the same conditions. The conversion efficiency of high-quality energy, such as electrical or mechanical energy, can also be improved.

5. Conclusions

This paper focuses on the problems of low ice-making energy efficiency and poor stability of the undercooled ice slurry preparation system. Based on the ice-making principle, an ice slurry preparation system consisting of a refrigeration cycle, a secondary refrigerant cycle, and an ice-making cycle is designed to study the influence of the various control parameters on the system performance. The main conclusions are as follows:

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Appropriately increasing the evaporation temperature, the overheating degree of the low-pressure vapor, and the subcooling degree of the high-pressure liquid, and maintaining a lower condensation temperature, can increase the system’s refrigeration capacity, overall performance coefficient, and ice production capacity and reduce the energy consumption per unit of ice. At t₀ = −10 °C and t_k = 30 °C, the coefficient of performance of the ice-making system reaches the maximum value of 2.43. When t_k is reduced, the cooling capacity per unit increases significantly, and the heat exchange efficiency of the refrigerant in the evaporator and condenser improves significantly. The ice-making capacity of the system increases from 37.23 to 43.88 kg/h when t₀ = −10 °C, and t_k reduces from 46 °C to 30 °C. In actual ice-making systems, the increase in evaporation temperature is limited by multiple factors, and lowering the condensation temperature is more effective for improving system performance.

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Reducing the inlet water flow rate can prolong the cooling time of the water in the subcooler, intensify the ultrasonic cavitation effect, and improve cavitation efficiency. At the same time, lowering the inlet water temperature can reduce the loss of cooling capacity used to overcome the sensible heat of water and increase the subcooling degree of the outlet water, thereby improving the ice-making efficiency and energy efficiency of the system and achieving efficient and stable ice making. At u_w = 0.8 m/s and t₉ = 0.5 °C, the system’s ice-making capacity reaches a maximum of 45.28 kg/h. In addition, the increases in the inlet water temperature and flow rate of the subcooler promote each other in reducing the system’s ice-making capacity. At u_w = 1.8 m/s and t₉ = 1.1 °C, the ice-making energy consumption per unit is approximately 4.8 times that at the M_ice maximum operating condition, reaching the highest energy consumption per unit of 0.26 kWh/kg. High water temperature and high flow rate should be avoided.

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The overall performance coefficient of the system can be significantly improved by improving the adiabatic compression efficiency. When t₀ = −22 °C, increasing the η_c,s from 75% to 95% decreases W_m by 0.106 kWh/kg. Improving the compressor performance at lower t₀ is more beneficial for improving the system’s ice-making energy efficiency.

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When comparing the effects of refrigerants R161, R290, R1270, and R32 on the system performance, the system using R161 achieves the highest cooling capacity, coefficient of performance, and ice-making capacity. The proper selection of refrigerants not only enhances the high-quality energy conversion but also optimizes the ice-making performance of the system.