Experimental Study and Performance Analysis of a Li-Br Single-Effect/Two-Stage Hybrid Absorption Chiller

Abstract

In order to maximize the use of low-temperature heat sources for refrigeration, a Li-Br absorption chiller combined with single-effect absorption refrigeration cycle and two-stage absorption refrigeration cycle (STAC) was developed. Experimental research on STAC was conducted on a prototype with a refrigeration capacity of 500 KW. A numerical model validated by experimental data was used to study the refrigeration performance of STAC under variable operating conditions. Compared to single-effect units and two-stage units, STAC demonstrates remarkable heat source conservation capability and adaptability to a broad spectrum of heat source temperatures. This advantage renders the STAC unit more adaptable to new energy or waste heat scenarios characterized by unstable heat sources. As the inlet temperature of the hot water increases, the temperature difference between the inlet and outlet of the hot water also increases. When the inlet temperature of the hot water is 70 °C, 90 °C and 120 °C, the temperature difference between the inlet and outlet of the hot water is 10 °C, 30 °C and 70 °C, respectively. Both increasing the inlet temperature of hot water and decreasing the temperature of cooling water will enhance the cooling capacity and coefficient of performance (COP) of STAC. As the flow rate of chilled water increases, the refrigeration capacity of STAC will also increase, but the COP will first increase and then decreases.

1. Introduction

Below 100 °C, low-grade thermal increase constitutes over 60% of the globally available heat energy [1,2]. Advancements in low-grade heat utilization technologies are crucial for enhancing overall energy efficiency and mitigating the challenges posed by fossil fuel supply depletion. Lithium bromide absorption refrigeration (AR) technology is regarded as a highly promising approach for low-grade heat recovery. In recent years, numerous studies have been conducted on Li-Br AR systems, which can be driven by either high-temperature or low-temperature heat sources. Depending on the heat source temperature, Li-Br AR units operate with different absorption cycles. Arranged in order of increasing heat source temperature, these include the two-stage absorption cycle (TSAC), single-effect absorption cycle (SEAC), and double-effect absorption cycle (DEAC) [3]. The TSAC is advantageous for utilizing low-temperature (70–80 °C) heat sources; however, it suffers from a low coefficient of performance (COP), typically below 0.4 [4,5]. In contrast, the SEAC and DEAC require heat source temperatures no lower than 90 °C and 150 °C, respectively, but offer significantly higher COPs. Specifically, the COP of SEAC ranges from 0.6 to 0.7, while that of DEAC exceeds 1.2 [6,7].

Numerous studies have focused on both lowering the heat source temperature and improving the COP of absorption refrigeration systems. Several novel low-temperature absorption refrigeration cycles have been developed and optimized based on the single-effect absorption cycle (SEAC) and two-stage absorption cycle (TSAC). Su et al. [8] provided a comprehensive review of recent research on basic and advanced absorption cycle configurations for low-grade energy recovery. The double-section absorption cycle (DSAC) is a novel configuration that connects two SEACs in series, sharing the same high- and low-temperature heat sources. DSAC can operate stably at lower evaporation temperatures, effectively increasing the temperature drop of the heat source while exhibiting reduced irreversible losses in the external cycle, thereby enabling more efficient utilization of low-grade heat. However, due to the increased number of components, the construction and operational costs of DSACs are substantially higher [9,10]. The compression-assisted absorption cycle (CAAC) is another innovative cycle that utilizes low-temperature heat sources for refrigeration. By integrating the absorption cycle with a vapor compression cycle, the absorption–compression cycle simultaneously harnesses the advantages of both cycles while mitigating their respective drawbacks, thus enhancing overall system performance [11,12,13]. Furthermore, the integration of membrane distillation with absorption refrigeration systems offers a novel strategy to address challenges associated with low-temperature heat-driven refrigeration [14,15]. Nevertheless, due to constraints imposed by operating conditions and membrane material performance parameters, system efficiency remains relatively low [16]. Improving system efficiency will therefore continue to be a key research focus for the foreseeable future.

In applications where obtaining heat sources incurs a cost, conserving heat sources directly translates into improved economic efficiency. Currently, most research on novel absorption refrigeration systems has focused on enhancing the coefficient of performance (COP) or lowering the required heat source temperature, with less attention paid to reducing heat source consumption. Only a limited number of studies have aimed at heat source conservation. Chen et al. [17] developed an absorption refrigeration cycle that combines the single-effect absorption cycle (SEAC) and the two-stage absorption cycle (TSAC), which can significantly reduce heat source usage. Wang et al. [18] designed a 1.5-effect absorption cycle, also a hybrid configuration of SEAC and TSAC. The performance of three configurations of the 1.5-effect cycle was analyzed. The results indicated that the configuration comprising a high-temperature single-effect sub-cycle and a low-temperature half-effect sub-cycle exhibited the best performance in terms of heat source conservation. The two studies mentioned above have not yet been validated experimentally and remain supported solely by theoretical calculations. Experimental research on the SEAC/TSAC hybrid cycle, with a primary focus on heat source conservation, currently represents a research gap.

To maximize the utilization of low-grade heat from heat sources, this study proposes a Li-Br composite absorption refrigeration cycle formed by connecting an SEAC and a TSAC in series on the heat source side. Based on this cycle, a single-effect/two-stage coupled Li-Br absorption chiller (STAC) with a refrigeration capacity of 500 kW was manufactured, and a corresponding numerical model was established. The refrigeration performance of the STAC was experimentally investigated under varying heat source conditions (hot-water temperature), environmental conditions (cooling-water temperature), and load conditions (chilled-water flow rate) through both experimental tests and numerical simulations. This experimental study fills the research gap in the relevant field.

2. Chiller Description

2.1. Configuration Design

This section provides a detailed description of the main components of the proposed STAC and their interconnecting pathways. As illustrated in Figure 1, the STAC primarily comprises 11 heat and mass transfer components and 4 pumps. Circled numbers denote the components and pumps, while uncircled numbers indicate the state points of the various fluids within the cycle. The single-effect generator (③) and single-effect condenser (④) are housed in the same chamber, separated by a centrally located louver. The solvent (water) vapor generated in the single-effect generator (③) can pass through the louver into the single-effect condenser (④). Similarly, the high-pressure generator (②) and high-pressure condenser (①) are also located in the same chamber. The low-pressure generator (⑤) and high-pressure absorber (⑥) share a common chamber, while the evaporator (⑦) and low-pressure absorber (⑧) are housed together in another chamber. No. 1 solution heat exchanger (⑨) is installed in the solution line between the high-pressure generator (②) and high-pressure absorber (⑥). No. 2 solution heat exchanger (⑩) is placed between the low-pressure generator (⑤) and low-pressure absorber (⑧). No. 3 solution heat exchanger (⑪) is positioned between the single-effect generator (③) and low-pressure generator (⑤). Pumps (⑫), (⑬), (⑭), and (⑮) are located beneath the low-pressure generator (⑤), low-pressure absorber (⑧), high-pressure absorber (⑥), and evaporator (⑦), respectively.

2.2. Fluid Circulation

In Figure 1, the solid line represents the hot-water flow path. Hot water first enters the single-effect generator (③), then flows into the low-pressure generator (⑤), and finally exits from the high-pressure generator (②). The hot water leaving the chiller returns to the heat source to absorb thermal energy before re-entering the cycle. The double-dotted line in Figure 1 denotes the cooling-water flow, which consists of two parallel streams. One stream of cooling water first enters the single-effect condenser (④), then passes through the high-pressure condenser (①), and subsequently exits. The other stream first enters the low-pressure absorber (⑧), then flows into the high-pressure absorber (⑥), and finally exits. The outflowing cooling water is directed to a cooling tower for heat dissipation and is subsequently reused. The dash-dotted line in Figure 1 indicates the chilled-water flow. Chilled water enters the evaporator (⑦) to be cooled and then returns to the air-conditioning terminals.

The solvent (water) flow is represented by the dotted line in Figure 1. During the solvent circulation process, water vapor is desorbed from both the single-effect generator (③) and the high-pressure generator (②). The vapor then enters the single-effect condenser (④) and high-pressure condenser (①), respectively, for condensation. The condensed water flows downward into the evaporator (⑦), where it is evaporated into vapor. The resulting vapor is subsequently absorbed into the Li-Br solution within the low-pressure absorber (⑧).

In the high-pressure solution circulation loop, the solution flow is indicated by the dashed line in Figure 1. The weak solution exits the high-pressure absorber (⑥) and is pumped into No. 1 solution heat exchanger (⑨) for preheating. It then enters the high-pressure generator (②) for desorption. The solution, now with an increased concentration, flows out of the high-pressure generator (②) and passes through No. 1 solution heat exchanger (⑨) for pre-cooling. It then returns to the high-pressure absorber (⑥) to absorb water vapor originating from the low-pressure generator (⑤).

In the low-pressure solution circulation loop, the solution flow is represented by the long dashed line. The weak solution exiting the low-pressure absorber (⑧) is pumped successively into No. 2 solution heat exchanger (⑩) and then No. 3 solution heat exchanger (⑪) for preheating. The preheated solution then enters the single-effect generator (③), where it desorbs water vapor, resulting in a gradual increase in both its concentration and temperature. The solution with increased concentration flows out of the single-effect generator (③) and subsequently enters No. 3 solution heat exchanger (⑪) for pre-cooling. The pre-cooled solution then enters the low-pressure generator (⑤), where it continues to desorb water vapor. The concentrated solution exiting the low-pressure generator (⑤) is pumped to No. 2 solution heat exchanger (⑩) for pre-cooling. It then enters the low-pressure absorber (⑧), where the concentrated solution absorbs water vapor from the evaporator (⑦). During this absorption process, the solution is cooled, and its concentration decreases. At this point, the low-pressure solution circulation loop completes a full cycle. Compared with the high-pressure solution circulation loop, the low-pressure solution circulation loop incorporates one additional generation process.

2.3. Refrigeration Cycle and State Parameters

Figure 2 illustrates the parameters of the various state points for the solution and solvent (water) in the proposed STAC refrigeration cycle, presented in terms of specific enthalpy and concentration. Each state point is defined by three parameters: temperature, pressure, and concentration. By calculating the thermodynamic parameters of each state point, it is possible not only to design the refrigeration unit (forward engineering) but also to predict and analyze its performance (reverse engineering). The curves labeled P_k, P_k′, P_m, and P_o in Figure 2 represent constant pressure lines. P_k denotes the pressure in the high-pressure condenser (and high-pressure generator). P_k′ denotes the pressure in the single-effect condenser (and single-effect generator). P_m denotes the pressure in the low-pressure generator (and high-pressure absorber) and is also referred to as the intermediate pressure. P_o denotes the pressure in the evaporator (and low-pressure absorber). The pressures are ranked in descending order as P_k > P_k′ > P_m > P_o.

The high-pressure solution circulation can be represented by the closed loop of state points 5→6→7→8→5. Point 5 represents the solution state before entering the high-pressure generator from the high-pressure absorber. Path 5→6 corresponds to the desorption of water vapor from the solution in the high-pressure generator. During this process, the solution pressure remains constant at P_k, the concentration increases from ω₁ to ω₂, and both specific enthalpy h and temperature increase. Path 6→7 represents the flow of solution from the high-pressure generator to the high-pressure absorber. In this process, the solution pressure decreases from P_K to P_m, specific enthalpy h and temperature decrease, while the concentration remains unchanged at ω₂. Path 7→8 describes the absorption of water vapor by the solution in the high-pressure absorber. The solution pressure remains constant at P_m, the concentration decreases from ω₂ to ω₁, and specific enthalpy h and temperature decrease further. Path 8→5 shows the flow of solution from the high-pressure absorber to the high-pressure generator. During this process, the solution pressure increases from P_m to P_K, specific enthalpy h and temperature increase, while the concentration remains constant at ω₁. In this closed loop, the solution circulates between two pressure levels (P_K and P_m) and two concentration levels (ω₁ and ω₂).

Compared with the high-pressure solution circulation, the low-pressure solution circulation is more complex. The low-pressure solution circulation consists sequentially of the state point loop 9→10→11→12→13→14. Paths 9→10 and 11→12 represent the solution desorption processes in the single-effect generator and the low-pressure generator, respectively. Paths 10→11 and 12→13 indicate the successive flow of the solution from the single-effect generator to the low-pressure generator and then to the low-pressure absorber. Paths 13→14 represents the solution absorption process in the low-pressure absorber. Paths 14→9 describes the flow process from the low-pressure absorber to the single-effect generator. In this closed loop, the solution circulates among three pressure levels (P_k′, P_m and P_o) and three concentration levels (ω₃, ω₄ and ω₅).

The solvent (water) circulation is represented by the points on the Y-axis. The state points 1, 1′, 2, 2′ 3, 3′, and 4′ sequentially represent: water in the evaporator, vapor in the evaporator, condensate in the single-effect condenser, vapor in the single-effect condenser, condensate in the high-pressure condenser, vapor in the high-pressure condenser, and vapor in the low-pressure generator.

2.4. Structure and Design Parameters

To evaluate the refrigeration performance of the STAC, a prototype with a cooling capacity of 500 kW was designed and manufactured. The structural configuration of the prototype is presented in Figure 3 and Figure 4, and its design parameters are summarized in

Table 1. Design parameters of the STAC prototype.

Design Parameters	Values
Rated refrigeration capacity (kW)	500
Inlet temperature of chilled water (°C)	15
Outlet temperature of chilled water (°C)	7
Mass flow of chilled water (kg/s)	14.94
Inlet temperature of cooling water (°C)	32
Outlet temperature of cooling water (°C)	37
Mass flow of cooling water (kg/s)	63.05
Inlet temperature of hot water (°C)	90
Outlet temperature of hot water (°C)	60
Mass flow of hot water (kg/s)	6.75
Mass flow of high-pressure solution (kg/s)	4.43
Mass flow of low-pressure solution (kg/s)	4.86
Mass flow of vapor (kg/s)	0.22
UA of evaporator (kW/K)	12.5
UA of condenser (kW/K)	9.4
UA of generator (kW/K)	11.6
UA of absorber (kW/K)	13.8
UA of solution heat exchanger (kW/K)	6.7
coefficient of performance (COP)	0.59
power supply	3 Φ-380 V-50 Hz
total electrical load (kW)	5.6
Adjustment range of refrigerating capacity	50~120%
Variable range of chilled-water flow rate	60~120%
Overall dimensions (mm)	5450 × 2170 × 3300

.

3. Numerical Simulation

Although prototype experimentation provides the most accurate and reliable means of evaluating the performance of the STAC developed in this study, the associated experimental time and cost are substantial, particularly when investigating variable operating conditions. Therefore, this research also developed a numerical model, which is primarily intended for studying STAC performance under variable operating conditions and for facilitating future design optimization of the STAC.

3.1. Governing Equations

The Li-Br STAC comprises 11 main components involved in heat and mass transfer. The heat and mass transfer processes of the solution or solvent within these components can be analyzed mathematically by formulating governing equations, which generally include the mass conservation equation, energy conservation equation, component conservation equation, and heat transfer calculation equation [19,20,21]. Before presenting the mathematical equations, the principal assumptions are outlined as follows:

• The working medium (Li-Br solution or water/steam) at each state point is in thermodynamic equilibrium, with uniform temperature and pressure.
• The system operates under steady-state conditions; all parameters (temperature, pressure, flow rate, concentration) are invariant with time.
• All heat exchange equipment and pipelines are assumed to have no heat loss.
• There is no pressure loss within pipelines, valves, or heat exchangers. The throttling process is considered isenthalpic.
• The heat transfer capacity of each heat exchanger can be evaluated using the lumped parameter method. Heat is transferred only in the radial direction within each heat exchanger, with no heat conduction along the flow direction.
• The working fluid in the evaporation, condensation, generation, and absorption processes is always in a saturated state.

These assumptions have been widely adopted and validated in the literature [22,23,24,25], yielding accurate modeling results. Based on the above assumptions, the governing equations for each component can be formulated as follows:

• High-pressure generator

  (1)

  Total mass conservation equation:

  $${\dot{m}}_{s,HG,in}={\dot{m}}_{s,HG,out}+{\dot{m}}_{v,HG}$$

  (1)

  (2)

  Lithium bromide mass conservation equation:

  $${\dot{m}}_{s,HG,in}{\omega }_{in}={\dot{m}}_{s,HG,out}{\omega }_{out}$$

  (2)

  (3)

  Energy conservation equation:

  $${\dot{m}}_{s,HG,in}{h}_{s,HG,in}+Q_{HG}={\dot{m}}_{s,HG,out}{h}_{s,HG,out}+{\dot{m}}_{v,HG}{h}_{v,HG}$$

  (3)

  (4)

  Calculation equation of heat exchange at hot-water side:

  $$Q_{HG}={\dot{m}}_{w,HG}{c}_w\left(T_{w.HG,in}-T_{w.HG,out}\right)$$

  (4)

2.

High-pressure condenser

(1)

Mass conservation equation:

$${\dot{m}}_{v,HC,in}={\dot{m}}_{l,HC,out}$$

(5)

(2)

Energy conservation equation:

$${\dot{m}}_{v,HC}{h}_{v.HC}={\dot{m}}_{l,HC}{h}_{l.HC}+Q_{HC}$$

(6)

(3)

Calculation equation of heat exchange at cooling-water side:

$$Q_{HC}={\dot{m}}_{w,HC}{c}_w\left(T_{w,HC,out}-T_{w,HC,in}\right)$$

(7)

3.

Single-effect generator

(1)

Total mass conservation equation:

$${\dot{m}}_{s,SG,in}={\dot{m}}_{s,SG,out}+{\dot{m}}_{v,SG}$$

(8)

(2)

Lithium bromide mass conservation equation:

$${\dot{m}}_{s,SG,in}{\omega }_{in}={\dot{m}}_{s,SG,out}{\omega }_{out}$$

(9)

(3)

Energy conservation equation:

$${\dot{m}}_{s,SG,in}{h}_{s,SG,in}+Q_{SG}={\dot{m}}_{s,SG,out}{h}_{s,SG,out}+{\dot{m}}_{v,SG}{h}_{v,SG}$$

(10)

(4)

Calculation equation of heat exchange at hot-water side:

$$Q_{SG}={\dot{m}}_{w,SG}{c}_w\left(T_{w.SG,in}-T_{w.SG,out}\right)$$

(11)

4.

Single-effect condenser

(1)

Mass conservation equation:

$${\dot{m}}_{v,SC,in}={\dot{m}}_{l,SC,out}$$

(12)

(2)

Energy conservation equation:

$${\dot{m}}_{v.SC}{h}_{v,SC}={\dot{m}}_{l,SC}{h}_{l,SC}+Q_{SC}$$

(13)

(3)

Calculation equation of heat exchange at cooling-water side:

$$Q_{SC}={\dot{m}}_{w,SC}{c}_w\left(T_{w,SC,out}-T_{w,SC,in}\right)$$

(14)

5.

High-pressure absorber

(1)

Total mass conservation equation:

$${\dot{m}}_{s,HA,out}={\dot{m}}_{s,HA,in}+{\dot{m}}_{v,HA}$$

(15)

(2)

Lithium bromide mass conservation equation:

$${\dot{m}}_{s,HA,in}{\omega }_{in}={\dot{m}}_{s,HA,out}{\omega }_{out}$$

(16)

(3)

Energy conservation equation:

$${\dot{m}}_{s,HA,in}{h}_{s,HA,in}+{\dot{m}}_{v,HA}{h}_{v,HA}={\dot{m}}_{s,HA,out}{h}_{s,HA,out}+Q_{HA}$$

(17)

(4)

Calculation equation of heat exchange at cooling-water side:

$$Q_{HA}={\dot{m}}_{w,HA}{c}_w\left(T_{w.HA,out}-T_{w.HA,in}\right)$$

(18)

6.

Low-pressure generator

(1)

Total mass conservation equation:

$${\dot{m}}_{s,LG,in}={\dot{m}}_{s,LG,out}+{\dot{m}}_{v,LG}$$

(19)

(2)

Lithium bromide mass conservation equation:

$${\dot{m}}_{s,LG,in}{\omega }_{in}={\dot{m}}_{s,LG,out}{\omega }_{out}$$

(20)

(3)

Energy conservation equation:

$${\dot{m}}_{s,LG,in}{h}_{s,LG,in}+Q_{LG}={\dot{m}}_{s,LG,out}{h}_{s,LG,out}+{\dot{m}}_{v,LG}{h}_{v,LG}$$

(21)

(4)

Calculation equation of heat exchange at hot-water side:

$$Q_{LG}={\dot{m}}_{w,LG}{c}_w\left(T_{w.LG,in}-T_{w.LG,out}\right)$$

(22)

7.

Low-pressure absorber

(1)

Total mass conservation equation:

$${\dot{m}}_{s,LA,out}={\dot{m}}_{s,LA,in}+{\dot{m}}_{v,LA}$$

(23)

(2)

Lithium bromide mass conservation equation:

$${\dot{m}}_{s,LA,in}{\omega }_{in}={\dot{m}}_{s,LA,out}{\omega }_{out}$$

(24)

(3)

Energy conservation equation:

$${\dot{m}}_{s,LA,in}{h}_{s,LA,in}+{\dot{m}}_{v,LA}{h}_{v,LA}={\dot{m}}_{s,LA,out}{h}_{s,LA,out}+Q_{LA}$$

(25)

(4)

Calculation equation of heat exchange at hot-water side:

$$Q_{LA}={\dot{m}}_{w,LA}{c}_w\left(T_{w.LA,out}-T_{w.LA,in}\right)$$

(26)

8.

Evaporator

(1)

Mass conservation equation:

$${\dot{m}}_{v,E,in}={\dot{m}}_{l,E,out}$$

(27)

(2)

Energy conservation equation:

$${\dot{m}}_{v.E}{h}_{v,E}={\dot{m}}_{l,E}{h}_{l,E}+Q_E$$

(28)

(3)

Calculation equation of heat exchange at cooling-water side:

$$Q_E={\dot{m}}_{w,E}{c}_w\left(T_{w,E,in}-T_{w,E,out}\right)$$

(29)

9.

No. 1 solution heat exchanger

(1)

Energy conservation equation:

$${\dot{m}}_{s.HG,out}\left(h_{s.HG,out}-h_{s.HA,in}\right)={\dot{m}}_{s.HA,out}\left(h_{s.HG,in}-h_{s.HA,out}\right)$$

(30)

(2)

Calculation equation of heat exchange

$$Q_{HE1}=K_{HE1}{A}_{HE1}\Delta T_{\log ,HE1}$$

(31)

10.

No. 2 solution heat exchanger

(1)

Energy conservation equation:

$${\dot{m}}_{s.LG,out}\left(h_{s.LG,out}-h_{s.LA,in}\right)={\dot{m}}_{s.LA,out}\left(h_{s.HE2,cold,out}-h_{s.LA,out}\right)$$

(32)

(2)

Calculation equation of heat exchange

$$Q_{HE2}=K_{HE2}{A}_{HE2}\Delta T_{\log ,HE2}$$

(33)

11.

No. 3 solution heat exchanger

(1)

Energy conservation equation:

$${\dot{m}}_{s.SG,out}\left(h_{s.SG,out}-h_{s.LG,in}\right)={\dot{m}}_{s.HE3,cold,in}\left(h_{s.SG,in}-h_{s.HE3,cold,in}\right)$$

(34)

(2)

Calculation equation of heat exchange

$$Q_{HE3}=K_{HE3}{A}_{HE3}\Delta T_{\log ,HE3}$$

(35)

In addition to the 11 main components described above, the pressurization process of the integral pumps within the unit also influences the overall system energy balance. Since the vacuum pump operates intermittently, it is excluded from the present analysis. Assuming negligible power losses in the pumps and modeling the pressurization process as isentropic compression, the power calculation equations for the pumps are given as follows:

• High-pressure generator pump

$$P_{HG,pump}={\rho }_{s,HA,out}g{\dot{m}}_{s,HA,out}{H}_{HA-HG}$$

(36)

2.

Single-effect generator pump

$$P_{SG,pump}={\rho }_{s,LA,out}g{\dot{m}}_{s,LA,out}{H}_{LA-SG}$$

(37)

3.

Low-absorber pump

$$P_{LA,pump}={\rho }_{s,LG,out}g{\dot{m}}_{s,LG,out}{H}_{LG-LA}$$

(38)

4.

Evaporator pump

$$P_{E,pump}={\rho }_{l,E,out}g{\dot{m}}_{l,E,out}{H}_{E-E}$$

(39)

The circulation ratio is defined as the mass of solution that must be circulated per kilogram of water vapor generated in the generator. Its defining equation is as follows:

$$f={\displaystyle \frac{{\dot{m}}_s}{{\dot{m}}_v}}$$

(40)

The vapor release range is defined as the concentration difference of the solution between the inlet and outlet of the generator. Since the total mass of Li-Br in the generator remains constant, the circulation ratio can also be expressed in terms of the Li-Br solution concentrations at the generator inlet and outlet, as follows:

$$f={\displaystyle \frac{{\omega }_{out}}{{\omega }_{out}-{\omega }_{in}}}$$

(41)

The circulation ratio of the high-pressure solution circulation:

$$f_{HG}={\displaystyle \frac{{\omega }_2}{{\omega }_2-{\omega }_1}}$$

(42)

The circulation ratio of the low-pressure solution circulation:

$$f_{SG}={\displaystyle \frac{{\omega }_5}{{\omega }_5-{\omega }_3}}$$

(43)

Since pump power consumption is nearly directly proportional to the circulation ratio, reducing the circulation ratio constitutes a core objective for system optimization, improving energy efficiency, and minimizing equipment size. In the numerical simulation conducted in this study, the circulation ratio is treated as a key variable. The high-pressure and low-pressure circulation ratios are coupled through the solution heat exchanger and the overall mass balance of the system.

The coefficient of performance of the absorption refrigeration system is defined as follows:

$$\eta ={\displaystyle \frac{Q_E}{Q_{SG}+Q_{HG}+Q_{LG}}}$$

(44)

3.2. Mathematical Model

Given the complexity of the coupled single-effect/two-stage absorption refrigeration cycle, this study employs the Newton–Raphson iteration method to solve the nonlinear equations and systems of equations involved. In the programming implementation, each component is treated as a modular unit. During computation, each input value yields a corresponding output result. The iteration variables are defined as follows: high-pressure condenser pressure P_k, single-effect condenser pressure P_k′, low-pressure generator pressure P_m, evaporator pressure P_o, high-pressure side circulation ratio f_HG, and low-pressure side circulation ratio f_SG. Each module is computed via a subroutine, after which the main program iteration proceeds until convergence is achieved.

• System global variable vector

$$X=\left[{\dot{m}}_{v,HG},{\dot{m}}_{v,SG},{\dot{m}}_{v,LG},{\dot{m}}_{v,E},{\dot{m}}_{s,HG},{\dot{m}}_{s,SG},P_{HG},P_{SG},P_{LG},P_E,{\omega }_{s,HG,out},{\omega }_{s,SG,out},{\omega }_{s,LG,out},T_{s,HA,in},T_{s,LA,in},T_{s,LG,in},T_{v,HC},T_{v,SC},Q_E,f_{HG},f_{SG},f_{LG},\eta \right]$$

(45)

where X is the system global variable vector containing 23 independent variables, including mass flow, pressure, concentration, temperature, refrigerating capacity, circulation ratio and coefficient of performance.

2.

Residual equation

• The equations of each component are converted into the form of residual equation as follows:

  $$F_i\left(X\right)=0$$

  (46)
• Therefore, the residual equations corresponding to the above independent variables are established

$$F_1\left(X\right)={\dot{m}}_{s,HG,in}-{\dot{m}}_{s,HG,out}-{\dot{m}}_{v,HG}$$

(47)

$$F_2\left(X\right)={\dot{m}}_{s,HG,in}{\omega }_{in}-{\dot{m}}_{s,HG,out}{\omega }_{out}$$

(48)

$$F_3\left(X\right)={\dot{m}}_{s,HG,in}{h}_{s,HG,in}+Q_{HG}-{\dot{m}}_{s,HG,out}{h}_{s,HG,out}-{\dot{m}}_{v,HG}{h}_{v,HG}$$

(49)

$$F_4\left(X\right)={\dot{m}}_{s,SG,in}-{\dot{m}}_{s,SG,out}-{\dot{m}}_{v,SG}$$

(50)

$$F_5\left(X\right)={\dot{m}}_{s,SG,in}{\omega }_{in}-{\dot{m}}_{s,SG,out}{\omega }_{out}$$

(51)

$$F_6\left(X\right)={\dot{m}}_{s,SG,in}{h}_{s,SG,in}+Q_{SG}-{\dot{m}}_{s,SG,out}{h}_{s,SG,out}-{\dot{m}}_{v,SG}{h}_{v,SG}$$

(52)

$$F_7\left(X\right)={\dot{m}}_{s,LG,in}-{\dot{m}}_{s,LG,out}-{\dot{m}}_{v,LG}$$

(53)

$$F_8\left(X\right)={\dot{m}}_{s,LG,in}{\omega }_{in}-{\dot{m}}_{s,LG,out}{\omega }_{out}$$

(54)

$$F_9\left(X\right)={\dot{m}}_{s,LG,in}{h}_{s,LG,in}+Q_{LG}-{\dot{m}}_{s,LG,out}{h}_{s,LG,out}-{\dot{m}}_{v,LG}{h}_{v,LG}$$

(55)

$$F_{10}\left(X\right)={\dot{m}}_{s,HA,out}-{\dot{m}}_{s,HA,in}-{\dot{m}}_{v,HA}$$

(56)

$$F_{11}\left(X\right)={\dot{m}}_{s,HA,in}{\omega }_{in}-{\dot{m}}_{s,HA,out}{\omega }_{out}$$

(57)

$$F_{12}\left(X\right)={\dot{m}}_{s,HA,in}{h}_{s,HA,in}+{\dot{m}}_{v,HA}{h}_{v,HA}-{\dot{m}}_{s,HA,out}{h}_{s,HA,out}-Q_{HA}$$

(58)

$$F_{13}\left(X\right)={\dot{m}}_{s,LA,out}-{\dot{m}}_{s,LA,in}-{\dot{m}}_{v,LA}$$

(59)

$$F_{14}\left(X\right)={\dot{m}}_{s,LA,in}{\omega }_{in}-{\dot{m}}_{s,LA,out}{\omega }_{out}$$

(60)

$$F_{15}\left(X\right)={\dot{m}}_{s,LA,in}{h}_{s,LA,in}+{\dot{m}}_{v,LA}{h}_{v,LA}-{\dot{m}}_{s,LA,out}{h}_{s,LA,out}-Q_{LA}$$

(61)

$$F_{16}\left(X\right)={\dot{m}}_{v.SC}{h}_{v,SC}-{\dot{m}}_{l,SC}{h}_{l,SC}-Q_{SC}$$

(62)

$$F_{17}\left(X\right)={\dot{m}}_{v,HC}{h}_{v.HC}-{\dot{m}}_{l,HC}{h}_{l.HC}-Q_{HC}$$

(63)

$$F_{18}\left(X\right)={\dot{m}}_{v.E}{h}_{v,E}-{\dot{m}}_{l,E}{h}_{l,E}-Q_E$$

(64)

$$F_{19}\left(X\right)={\dot{m}}_{s.HG,out}\left(h_{s.HG,out}-h_{s.HA,in}\right)-{\dot{m}}_{s.HA,out}\left(h_{s.HG,in}-h_{s.HA,out}\right)$$

(65)

$$F_{20}(X)={\dot{m}}_{s.LG,out}\left(h_{s.LG,out}-h_{s.LA,in}\right)-{\dot{m}}_{s.LA,out}\left(h_{s.HE2,cold,out}-h_{s.LA,out}\right)$$

(66)

$$F_{21}\left(X\right)={\dot{m}}_{s.SG,out}\left(h_{s.SG,out}-h_{s.LG,in}\right)-{\dot{m}}_{s.HE3,cold,in}\left(h_{s.SG,in}-h_{s.HE3,cold,in}\right)$$

(67)

$$F_{22}\left(X\right)={\displaystyle \frac{Q_E}{Q_{HG}+Q_{SG}+Q_{DG}}}$$

(68)

$$F_{23}\left(X\right)=f_{SG}-{\displaystyle \frac{{\omega }_5}{{\omega }_5-{\omega }_3}}$$

(69)

3.3. Program Flow

In the program flow, the first step is to input the specified parameters to define the external conditions and equipment parameters. The second step involves iterative calculations, which constitute the most critical process. The final step is to output the computational results. Within the iterative computation loop, each independent variable must first be assigned a reasonably appropriate initial value. Subsequently, the thermophysical parameters corresponding to each state point in the cycle—such as pressure, temperature, concentration, and enthalpy—are determined by calling a subroutine for calculating the thermophysical properties of the lithium bromide solution. The subsequent steps are, in order: constructing the residual equation, computing the Jacobian matrix, solving the linear equations, determining the step factor, updating the variables, and assessing convergence. The program flow chart is presented in Figure 5.

4. Performance Testing

This section provides a detailed description of the experimental setup for the STAC prototype, along with the definitions and calculation formulas for key performance parameters. The test results obtained under the designed operating conditions are presented. Furthermore, the computational model described in the preceding section is validated through comparison with the experimental results.

4.1. Testing Setup

Figure 6 presents a schematic diagram of the experimental setup used for testing the refrigeration performance of the STAC prototype. The setup consists of three water circuits, namely the hot-water circuit, the chilled-water circuit, and the cooling-water circuit. In each water circuit, the temperature of the water entering the STAC prototype is controlled by a thermostatic water bath, and the flow rate is regulated by a variable-frequency water pump. The hot-water thermostatic bath supplies heat to the generators, while the cooling-water thermostatic bath removes heat from the absorbers and condensers. The chilled-water thermostatic bath acts as an air-conditioning terminal, adding heat to the chilled water. The dashed lines in Figure 6 represent the solution circuits within the chiller. The measuring apparatus include five flow meters (Q1–Q5) and twelve temperature sensors (T1–T12). The parameters measured by these instruments are indicated in Figure 6. Detailed specifications of the main components and measuring instruments are provided in

Table 2. Main parameters of the components and measuring apparatus in the testing setup.

Name	Main Parameter
STAC prototype	See Table 1 for details
Hot-water thermostatic bath	Heating capacity: 2 MW
	Water temperature range: ambient temperature ~100 °C
	Control accuracy: ±0.5 °C
Chilled-water thermostatic bath	Water temperature range: 5~20 °C
	Control accuracy: ±0.5 °C
Cooling-water thermostatic bath	Water temperature range: 5~40 °C
	Control accuracy: ±0.5 °C
Hot-water pump	Flow range: 15~35 m3/h
	Adjustment accuracy: 10 RPM
	Liquid temperature range: −15~120 °C
Chilled-water pump	Flow range: 30~65 m3/h
	Adjustment accuracy: 10 RPM
	Liquid temperature range: −15~120 °C
Cooling-water pump	Flow range: 110~300 m3/h
	Adjustment accuracy: 10 RPM
	Liquid temperature range: −15~120 °C
Solution pump (Pump1, 2)	Flow range: 1~20 m3/h
	Adjustment accuracy: 5 RPM
	Liquid temperature range: 0~150 °C
Temperature sensor (T1~T12)	Temperature measuring range: −200~260 °C
	Measurement accuracy: ±0.1 °C
Water flow meters (Q1, Q2, Q3)	Maximum fluid temperature: 120 °C
	Flow measuring range: 10~300 m3/h
	Measurement accuracy: ±0.5%
Solution flow meters (Q4, Q5)	Maximum fluid temperature: 150 °C
	Flow measuring range: 0.5~10 m3/h
	Measurement accuracy: ±0.5%

.

4.2. Calculation Method

This study primarily investigates the relationship between external conditions (water temperature and mass flow rate) and the refrigeration performance of the STAC. Refrigeration performance is characterized by two key parameters: refrigeration capacity and coefficient of performance (COP). In addition, a comparative analysis of the refrigeration economy of the STAC is conducted. In this study, refrigeration economy is quantified as the refrigerating capacity per unit mass flow rate (RCPMF) of hot water. The definitions and calculation formulas for the various parameters involved in this test are provided as follows:

1.

Heating load

$$W_{heat}=q_1\cdot \left(t_1-t_4\right)\cdot C_w$$

(70)

where W_heat is the heating load provided by the hot water, kW; q₁ is the mass flow rate of hot water, kg/s; t₁ is the inlet temperature of hot water, °C; t₄ is the outlet temperature of hot water, °C; C_w is the specific heat of water, taken as 4.2 kJ/(kg·°C).

2.

Refrigeration capacity

$$W_{refri}=q_2\cdot \left(t_5-t_6\right)\cdot C_w$$

(71)

where W_refri is the refrigeration capacity provided by the chilled water, kW; q₂ is the mass flow rate of chilled water, kg/s; t₅ is the inlet temperature of chilled water, °C; t₆ is the outlet temperature of chilled water, °C.

3.

Heat dissipation capacity

$$W_{dissi}=q_3\cdot \left(t_{12}-t_7\right)\cdot C_w$$

(72)

where W_dissi is the heat dissipation capacity provided by the cooling water, kW; q₃ is the mass flow rate of cooling water, kg/s; t₇ is the inlet temperature of cooling water, °C; t₁₂ is the total return water temperature of cooling water, °C.

4.

Coefficient of performance

$$COP={\displaystyle \frac{W_{refri}}{W_{heat}}}$$

(73)

5.

Refrigeration capacity per unit mass flow

$$RCPMF={\displaystyle \frac{W_{refri}}{q_1}}$$

(74)

4.3. Measurement Uncertainty

For the performance experiment of absorption chillers, the most reliable choice for uncertainty evaluation is the GUM method (Guide to the Expression of Uncertainty in Measurement). It originates from an internationally recognized fundamental standard: ISO/IEC Guide 98-3:2008 [26]. The uncertainty of direct measured values and calculated values is determined by Formulas (75) and (76), respectively.

$$U_x={\displaystyle \frac{{\Delta }_x}{\sqrt{3}}}$$

(75)

where x is a direct measured value, U_x is the uncertainty of x, and Δ_x is the allowable error of the measuring equipment to test x.

$$U\left(y\right)={\displaystyle \frac{\sqrt{{\displaystyle \sum _{i=1}^N{\left(\frac{\partial f}{\partial x_i}\delta x_i\right)}^2}}}{y}}\times 100\%$$

(76)

where y is a calculated value, U (y) is the uncertainty of y, x_i is a direct measured value, f is the functional relationship between y and x_i, and δx_i is the uncertainty of x_i.

Based on Formulas (75) and (76), the measurement uncertainty can be calculated.

Table 3. Uncertainty of parameters.

No.	Parameters	Symbol	Unit	Uncertainty
1	Temperature	T	°C	±0.06 °C
2	Mass flow rate	q	kg/s	±0.3%
3	Heating load	Wheat	kW	±0.4%
4	Refrigeration capacity	Wrefri	kW	±0.4%
5	Heat dissipation capacity	Wdissi	kW	±0.4%
6	Coefficient of performance	COP		±0.5%
7	Refrigeration capacity per unit mass flow	RCPMF	kW/(kg/s)	±0.6%

lists the calculation results of parameter uncertainties, including directly measured parameters and calculated parameters.

4.4. Testing Results and Model Validation

To verify the functional feasibility and design accuracy of the STAC prototype, a performance test under design conditions was conducted in a professional refrigeration machine testing laboratory, as shown in Figure 7. A comparison between the test results and the design values is presented in

Table 4. The comparison between test results and design values of main parameters.

Main Design Parameters	Design Values	Test Results	Deviation Rate
t1 (°C)	90	90.5	0.5%
t4 (°C)	60	61.4	2.3%
q1 (kg/s)	6.75	6.81	0.8%
t7 (°C)	32	32.3	0.9%
t12 (°C)	37	36.7	0.8%
q3 (kg/s)	63.05	64.16	1.8%
t6 (°C)	7	7.5	4.6%
t5 (°C)	15	15.7	7.1%
q2 (kg/s)	14.94	15.21	1.5%
Wrefri (kW)	500	522.34	4.4%
COP	0.59	0.627	6.3%

. The test results confirm the feasibility of the single-effect/two-stage coupled refrigeration cycle developed in this study and indicate that the deviation between the actual performance of the prototype and the design values is within an acceptable range. Therefore, the test data obtained from this prototype can be used to validate and calibrate the numerical model described previously.

A simulation model of the STAC prototype was developed to investigate its refrigeration performance under off-design operating conditions. To enhance the predictive accuracy of the model, multiple experiments were conducted on the prototype under off-design conditions, and the experimental data were used to validate the model.

Table 5. The comparison between test results and model results of the STAC parameters.

Parameters	Design Condition		Off-Design Condition-1		Off-Design Condition-2
	Test Results	Model Results	Test Results	Model Results	Test Results	Model Results
t1 (°C)	90.5	90.5	120.2	120.2	70.4	70.4
t4 (°C)	61.4	59.8	50.6	51.7	60.1	60.5
q1 (kg/s)	6.81	6.81	1.83	1.83	14.78	14.78
t7 (°C)	32.3	31.3	31.8	31.8	32.1	32.1
t11 (°C)	36.7	36.5	35.1	34.6	37.5	38.2
q3 (kg/s)	64.16	64.16	63.61	63.61	42.03	42.03
t6 (°C)	7.5	7.3	9.2	9.5	7.1	6.8
t5 (°C)	15.7	15.7	17.3	17.3	15.6	15.6
q2 (kg/s)	15.21	15.21	10.11	10.11	7.64	7.64
Wrefri (kW)	522.34	535.08	343.98	331.24	272.71	282.33
%e of Wrefri		2.4%		3.7%		3.5%
COP	0.627	0.609	0.642	0.628	0.426	0.417
%e of COP		2.9%		2.2%		2.1%

presents the test results and model predictions under both design and off-design conditions. As shown in Table 5, the percentage error (%e) of the model for refrigeration capacity W_refri and COP falls within the ranges of 2.4–3.5% and 2.1–2.9%, respectively. The primary source of error is attributed to the inevitable heat losses encountered during the experiments, whereas the numerical simulation assumes ideal conditions with no heat losses from any heat exchange components or piping. Overall, this level of error is considered acceptable.

5. Results and Discussion

Given that the model has been validated with experimental data, it can be employed to predict the refrigeration performance of STAC units under varying external conditions. Furthermore, the model can also be utilized to assess the merits of STAC units in terms of heat source conservation.

5.1. Research on Refrigeration Performance Under Varying Operating Conditions

The STAC developed in this study is suitable for application as a solar-powered air-conditioning system. Owing to significant fluctuations in solar radiation, the temperature of the hot water produced by solar collectors also varies considerably. Changes in ambient temperature and humidity further affect the cooling-water temperature. Moreover, the refrigeration load varies with the cooling demand. For the STAC, all these variations manifest as changes in hot-water temperature, cooling-water temperature, and chilled-water flow rate. Therefore, investigating the refrigeration performance of the STAC under variable operating conditions is of substantial practical significance.

Given the complex coupling among the STAC components, experimental studies under varying operating conditions require considerable time and energy consumption. Consequently, the previously validated numerical model was employed to investigate the refrigeration performance of the STAC under various operating conditions, including variations in hot-water temperature, cooling-water temperature, and chilled-water mass flow rate.

Figure 8 illustrates the variations in refrigeration capacity (W_refri) and COP with respect to the inlet temperature of hot water (t₁) in the STAC. Under the given constraints of parameters q₁, q₂, t₅, and t₇, both W_refri and COP increase as t₁ rises. When t₁ increases from 70 °C to 120 °C, W_refri increases from 345 kW to 577 kW, and COP rises from 0.41 to 0.78. The simulation results indicate that, similar to other types of absorption chillers, raising the inlet temperature of hot water enhances the refrigeration performance of the unit. Specifically, increasing the hot-water temperature promotes refrigerant vapor generation in the generator and enhances refrigerant circulation, thereby improving the heat exchange capacity of the evaporator.

Figure 9 illustrates the effect of the cooling-water inlet temperature (t₇) on the refrigeration capacity (W_refri) and COP. As shown in Figure 9, both W_refri and COP exhibit a negative correlation with t₇. A lower t₇ is more favorable for improving W_refri and COP. When t₇ is at its minimum value of 22 °C, W_refri reaches its maximum of 615 kW, and COP attains its peak value of 0.66. As t₇ increases, both and COP decrease. At the maximum t₇ of 42 °C, W_refri and COP drop to their minimum values of 333 kW and 0.45, respectively. These results were computed under the given parameters (q₂, q₃, t₁, t₅). The cooling-water temperature directly affects the condensation pressure. A low cooling-water temperature leads to a low condensation pressure, which facilitates the condensation of the refrigerant from the generator.

The variation in chilled-water mass flow rate represents the change in refrigeration demand. The temperature of the chilled water generally needs to remain stable; therefore, the inlet temperature of the chilled water (t₅) is set to a specified value. According to the data presented in Figure 10, as q₂ increases from 9 kg/s to 19 kg/s, the refrigeration capacity W_refri continuously increases from 299 kW to 579 kW, while the COP initially rises from 0.51 to 0.58 and then decreases from 0.58 to 0.53.

5.2. Water-Saving Properties Analysis

Compared with single-effect and two-stage chillers, the STAC can utilize a larger temperature difference in the hot-water supply. Consequently, the STAC achieves greater conservation of heat source water. In this section, the previously defined RCPMF (see Equation (74)) is employed to analyze the water-saving characteristics of the system.

Shuangliang Company (Wuxi, China) and Broad Company (Changsha, China) are two major manufacturers of Li-Br refrigeration units. In this study, the hot-water mass flow rate (q₁) of commercial products from these two companies is used for comparison with the STAC (see

Table 6. Commercial products from major Li-Br refrigeration machine producers.

Chiller Type	Model Number	Producer	Wrefri (kW)	t1 (°C)	q1 (kg/s)	q2 (kg/s)	q3 (kg/s)
Single-effect chiller	RXZH2A	Shuangliang	540	85	24.42	25.83	49.17
	BDH98-500	Broad	512	98	16.61	17.47	40.28
Two-stage chiller	RXZIII-25ZH2M2	Shuangliang	500	72	34.11	23.89	67.22
	BDH8.6XII	Broad	525	70	16.78	25.08	75.25

). During model computations, the refrigeration capacity (W_refri) and the hot-water inlet temperature (t₁) of the STAC are set to be identical to those of the commercial products.

Figure 11 presents a comparison of the RCPMF values between the STAC and the four commercial units listed in Table 6. Arranged in ascending order, the RCPMF values of the STAC correspond to 134%, 295%, 313%, and 591% of those of the BDH8.6XII, RXZIII-ZH2M2, RXZH2A, and BDH98-500 units, respectively. As the inlet hot-water temperature (t₁) increases, the RCPMF value also rises. This result indicates that the STAC exhibits high water efficiency under high-temperature heat source conditions. In applications where the cost of the heat source water is high—such as with geothermal water—using the STAC as an air-conditioning refrigeration system offers considerable economic advantages over currently available commercial absorption chillers.

6. Conclusions

The STAC innovatively developed in this study is a composite lithium bromide absorption refrigeration system that couples a single-effect absorption cycle with a two-stage absorption cycle. The heat source water flows sequentially through the single-effect generator, the low-pressure generator, and the high-pressure generator, thereby maximizing the utilization of heat from the hot water. A STAC prototype with a refrigeration capacity of 500 kW was manufactured, and experiments conducted on the prototype verified the feasibility of its coupled cycle. To further investigate the refrigeration performance under off-design operating conditions, this paper also adopts a numerical simulation approach, which is more efficient and economical compared to experimental methods. Based on the experimental and numerical simulation results, the following conclusions can be drawn:

• The design temperature difference between the inlet and outlet of the hot water for the STAC is 30 °C (90 °C to 60 °C). This temperature difference can be extended to 70 °C (120 °C to 50 °C) when the hot-water flow rate is reduced and the inlet hot-water temperature is increased. Increasing the temperature difference between the inlet and outlet of the hot water enhances water conservation.
• The design inlet temperature of hot water for the STAC is 90 °C. The chiller remains operational even when the inlet hot-water temperature drops to 70 °C. Under this condition, the temperature difference between the inlet and outlet of the hot water is 10 °C (70 °C to 60 °C)
• Both the refrigeration capacity and the COP of the STAC increase with rising hot-water inlet temperature. When the hot-water inlet temperature increases from 70 °C to 120 °C, the refrigeration capacity increases from 296 kW to 577 kW, and the COP rises from 0.41 to 0.78. Conversely, the refrigeration capacity and COP exhibit a negative correlation with the cooling-water inlet temperature. As the cooling-water inlet temperature increases from 22 °C to 42 °C, the refrigeration capacity decreases from 615 kW to 333 kW, and the COP drops from 0.66 to 0.45.
• As the chilled-water mass flow rate increases from 9 kg/s to 19 kg/s, the refrigeration capacity increases from 299 kW to 579 kW, while the COP initially rises from 0.51 to 0.58 (reaching a peak at 15 kg/s) and then decreases from 0.58 to 0.53.
• Under the same refrigeration capacity and hot-water inlet temperature, the RCPMF values of the STAC are substantially higher than those of single-effect and two-stage refrigerators. Specifically, the RCPMF values of the STAC range from 134% to 591% of those of current commercial products, demonstrating that the STAC exhibits excellent water-saving performance.

Based on the aforementioned conclusions, it is observed that when the external conditions of the STAC chiller—including the inlet temperature of hot water, the inlet temperature of cooling water, and the flow rate of chilled water—undergo changes, the resulting variations in its cooling capacity and COP follow trends similar to those observed in single-effect and two-stage absorption refrigerators. However, the STAC demonstrates notable water conservation capability (as reflected by the RCPMF) and adaptability to a wide range of heat source temperatures (from 70 °C to 120 °C). This advantage makes the STAC unit more suitable for applications involving renewable energy or waste heat, where the heat source is often unstable.

Compared with single-effect and two-stage units, the STAC system comprises more components and involves more intricate coupling relationships, leading to higher manufacturing and maintenance costs, which constitute its primary drawback. Nevertheless, with the increasing utilization of unstable renewable energy sources, the market demand for such STAC units is expected to grow progressively. Looking ahead, leveraging artificial intelligence (AI) technology to address the control challenges of the STAC represents a key trend in the technological advancement of STAC systems.