1. Introduction
The challenge of global warming will increasingly change future energy transfer and conversion processes, with renewable energy being a key feature of a low/zero carbon future. The refrigeration industry has a large potential for carbon mitigation by upgrading to renewable and sustainable approaches. In 2016, the electricity consumption of space cooling was 2000 TWh worldwide, which accounted for nearly 18.5% of that in buildings. The electricity consumption of space cooling was 3% of global primary energy use [
1]. This electricity consumption was dramatically reduced by replacing it with low-grade heat.
Solar refrigeration is one of the most promising options [
2,
3]. Solar energy harvest technology has been rapidly developed, and mature technology is available in low temperature ranges (<240 °C) [
4]. Evacuated tube collectors and compound parabolic collectors provide fluid with temperatures of around 100 °C, which meets the heating requirement of absorption refrigeration [
4].
Absorption refrigeration utilises low-grade heat. The primary working pairs are ammonia/water and water/lithium bromide. Water/lithium bromide systems have been widely used because refrigerant purification is eased, leading to a high Coefficient of Performance (COP). However, the refrigeration temperature is limited by the freezing of water and must be kept above 0 °C. Water/lithium bromide systems are not suitable for high environment temperatures because of crystallisation [
5].
An ammonia/water system meets the sub-zero refrigeration demand and is applicable to high environment temperatures. The driving temperature is 70–120 °C for single-stage [
6,
7]. The main drawback is the low COP due to the ammonia rectification between the desorber and condenser. The developments of ammonia-based absorption systems are focused on COP improvement and application extension. The optimisation approaches have been comprehensively discussed in open literature, which mainly include adding components to the basic cycles, rearrangement of cycle configurations, using novel working pairs and adding surfactant to the working fluids [
6,
7,
8,
9]. The cycle configurations were investigated to improve the thermal efficiency and compactness:
Internal heat recovery: the heat of rectification, absorption and condensation was reused to preheat the strong solution instead of dissipating it into the environment. The temperature of the strong solution was lifted before entering the desorber so that the net heating load was reduced. The generator absorber heat exchange (GAX) cycle made use of the temperature overlap between the desorber and absorber. The overlapped heat was transferred from the absorber to desorber. The GAX component was introduced in two-stage cycles and is located in either the high-pressure circuit or low-pressure circuit. With multi-effect cycles, the condensation heat was recovered solely or was combined with absorption heat to generate refrigerant vapour [
5,
10]. Solution recirculation was used when the desorber and absorber had large temperature glides. The desorber was divided into two parts. The rich solution was heated internally in the first part by the vapour leaving the desorber, and was then externally heated in the second part. Similarly, the absorber was composed of the internally cooled part and externally cooled part. Another configuration was the stream separation. The rich solution leaving the absorber was separated into two streams, which flowed into the solution heat exchanger and rectifier, respectively [
11]. Internal heat recovery was restrained by the pinch point temperature difference. The optimal cycle configuration depends on the operating conditions and needed to be investigated individually [
12].
Size reduction: small-scale ammonia/water systems were developed so that the chillers were mobile or met the residential requirement. The heat and mass transfer devices were microscale and are non-commercial, thus new design methods were required [
13,
14]. A counter-current desorber purified the refrigerant vapour and reduced the rectifier load, which facilitates compact units. The accurate prediction of transport processes helped to optimise the system design [
15,
16].
Compression-assisted absorption: a booster compressor was integrated in the absorption cycle, and the system operated at three pressure levels. The compressor had two locations. A low-pressure compressor was located between the evaporator and absorber, which increased the absorption pressure or reduced the evaporation pressure. A high-pressure compressor was between the desorber and condenser, lowering the desorption pressure or increasing the condensation pressure. The compressor promoted the vapour generation and augmented the cooling capacity [
17,
18].
Ammonia/water absorption cycles have been widely investigated with experiments and numerical models [
19,
20]. The experimental research has mostly measured the overall cycle performance but has not captured operational issues in depth. For example, the water content of ammonia refrigerant deteriorates the performance. But the refrigerant mass concentration is seldom measured, which is important to quantify the performance deterioration. Numerical models have the potential to investigate the operation details, which include pinch point analysis, heat exchanger efficiency method and conductance (
UA) model. Pinch point analysis is used to design the cycle configurations, but cannot predict the performance of heat exchangers [
12,
21]. When pinch point or heat exchanger efficiency are used for analysis, the working fluids are usually assumed as saturated states at the outlet of heat exchangers, which do not reflect the actual operation [
22,
23].
The
UA model is close to the actual cycle [
5]. In simplified models, the
UA value is assumed to be constant, which is convenient for the preliminary design but is less accurate for off-design conditions [
13]. Solar driven absorption cycles cope with a varying heat source. Thus, the chiller should perform favourably, not only in optimum conditions, but also in a wide range of operating conditions. The mass flow rates and mass concentrations of the working fluids are functions of boundary conditions, which change the
UA value during off-design operation. The resulting variation of heat exchanger performance has not been fully investigated when integrated into a cycle. The heat transfer processes of absorption cycle include absorption, desorption, evaporation, condensation and single-phase heat transfer. The heat exchanger performance determines the operating parameters of absorption cycles. For example, the rich solution must be subcooled at the absorber outlet. The mass flow rates and mass concentrations of the rich solution are limited by the heat transfer performance of the absorber. Thus, a detailed analysis of heat exchanger performance is needed, which helps to locate the bottleneck of the thermodynamic performance.
In ammonia/water system, water is volatile and vaporises with the refrigerant. The importance of refrigerant purification has been widely recognised, while the discussion is mostly qualitative [
5,
24,
25]. Fernández-Seara et al. [
26] and Fernández-Seara and Sieres [
27] built a model of distillation columns and compared different configurations. Ammonia concentration in the vapour refrigerant directly affects the operating pressures and system COP, which was quantified with a simplified system model. Osman and Guo [
25] assumed that the rectifier has a constant efficiency. In other numerical models, the refrigerant is assumed to be pure ammonia [
23], or the rectification process is not considered [
22].
The water content in the ammonia refrigerant has a detrimental effect on cycle performance, bringing about a temperature glide during the phase change process at the condenser and evaporator [
5]. The saturation temperature of ammonia/water is higher than pure ammonia. For condensation, the temperature difference between the refrigerant and secondary fluid is increased, which promotes the heat transfer. But the temperature difference during evaporation is reduced. Moreover, water content in the ammonia refrigerant produces mass transfer resistance, which decreases the Heat Transfer Coefficients (HTCs) of condensation [
28]. Although the overall performances of ammonia/water absorption chillers have been widely reported, the influence of refrigerant impurity has not been evaluated quantitatively. In this paper, the variation of refrigerant impurity is quantified as a function of operating conditions, which explains the COP deterioration because of temperature glide and HTCs reduction.
In this study, a numerical model was developed for single-stage ammonia/water absorption chillers. The system was composed of Plate Heat Exchangers (PHEs), making the overall structure compact [
3,
7]. The off-design cycle model integrated detailed heat exchanger models. The variational heat exchanger performances were analysed with changing boundary conditions. The model was validated with experimental results. In the case studies of sub-zero refrigeration temperature, different cycle configurations were compared. The advantages of advanced cycles relative to a basic cycle depend on heat source temperatures. The mass flow rates and mass concentrations of the rich solution had major influences on the cooling capacity and COP, which were limited by the heat transfer performance of the absorber. The above-zero refrigeration temperature was also discussed. The heat sink temperature is the secondary fluid temperature of the absorber and condenser. A lower heat sink temperature improves the temperature driving force of the absorber so that the ammonia mass concentration can be increased.
2. Methodology
Figure 1 is the flow diagram of the basic cycle. The rich solution was heated by the heat source fluid at the desorber, where vapour of high ammonia concentration was generated. The vapour and poor solution flowed co-currently and left the desorber at the outlet (4 and 7). The vapour was partly condensed and was purified at the rectifier, where the heat was recovered by the rich solution. The reflux from the rectifier was mixed with the poor solution at the inlet of the Solution Heat Exchanger (SHE) (4 and 8). The vapour refrigerant was cooled by the heat sink fluid of the condenser. At the Refrigerant Heat Exchanger (RHE), the refrigerant was subcooled by the cold stream exiting the evaporator. Since the refrigerant was not pure ammonia, the evaporation was restrained by the temperature glide. The refrigerant left the evaporator as a two-phase fluid or superheated vapour, which was dependent on the refrigerant mass concentration. The remaining cooling capacity was recovered at the RHE. The refrigerant and poor solution were mixed when entering the absorber (14 and 6). At the absorber outlet, the rich solution was subcooled (1). The rich solution recovered heat from the refrigerant at the rectifier and from the poor solution at the SHE.
It was possible to improve the thermodynamic efficiency of the basic cycle by integrating a compressor, optimising refrigerant purification and augmenting internal heat recovery. In this paper, advanced cycles are discussed, and different configurations are compared, including a compression-assisted cycle, a cycle with counter-current desorber and a cycle with bypassed rich solution.
Figure 2 shows the flow diagram of the compression-assisted cycle. The refrigerant leaving the RHE flows into a compressor, and the pressure is raised. The system operates at three pressure levels. The evaporator and cold side of the RHE have low pressure. The absorber is middle pressure. The other heat exchangers are on the high pressure side. Consequently, the mass concentration of the rich solution can be increased at the absorber.
In
Figure 3, the solution and refrigerant vapour flow counter-currently at the desorber. The vapour leaving the desorber is in direct contact with the rich solution (4 and 7), and the vapour mass concentration is increased. The reflux from the rectifier flows back to the desorber inlet and is mixed with the rich solution (8 and 3).
At the SHE of the basic cycle, the rich solution had a larger mass flow rate than the poor solution. The pinch point temperature difference was at the cold end. In
Figure 4, a part of the rich solution is bypassed into the rectifier after the solution pump. The rest of the rich solution enters the SHE. The two parts of the rich solution are fully preheated and are mixed before flowing into the desorber (3 and 16).
2.1. Integrated Cycle and Heat Exchanger Models
The cycle was modelled by solving thermodynamic energy and mass balance equations and heat transfer equations.
Figure 5 is the schematic of the model structure. The input parameters are the mass flow rate and mass concentration of the rich solution, as well as the boundary conditions of the secondary fluids.
The operating pressures were dependent on the heat source and heat sink temperatures. The desorber had the same pressures as the condenser, which were both on the high-pressure side. The absorber and evaporator had the same pressure and were on the low-pressure side. For given boundary temperatures, the condensation pressure determines the temperature driving force of the desorber and condenser. Higher condensation pressure reduced the temperature driving force of the desorber but raised the temperature driving force of the condenser. Thus, a small amount of refrigerant was generated at the desorber, which was likely to be subcooled at the condenser. On the other hand, lower condensation pressure promotes the generation of the refrigerant at the desorber. But the temperature driving force of the condenser was small, and the refrigerant could not be fully condensed. According to experimental work, the condensation pressure is a function of heat source and heat sink temperatures [
13,
19]. Higher heat source or heat sink temperatures increase the condensation pressure. More refrigerant is generated at higher heat source temperatures, which increases the heat load of the condenser. The condensation pressure increases to transfer the heat load. When the heat sink temperature increases, the condensation pressure is increased to maintain the temperature driving force. In this study, the condensation pressure was determined so that the refrigerant was completely condensed at the condenser.
Similarly, the temperature driving forces of the evaporator and absorber are functions of the evaporation pressure. The evaporation pressure is restrained by the absorber. At low evaporation pressure, the absorber has a small temperature driving force, and the rich solution cannot be subcooled. Vapour accumulates at the outlet, which increases the evaporation pressure. When the evaporation pressure is high, the temperature driving force of the evaporator is small. The cooling capacity is reduced. In accordance with experimental work, the evaporation pressure increases with higher heat source and heat sink temperatures [
13,
20]. Higher heat source temperatures contribute to more refrigerant and increase the heat load of the absorber. Higher heat sink temperatures reduce the temperature driving force of the absorber. Consequently, the evaporation pressure is increased. In this study, the evaporation pressure was determined so that the rich solution was subcooled at the absorber outlet. In practice, liquid tanks should be installed at the outlets of the condenser and absorber to stabilise the operation, which do not affect the energy balance and are not shown in
Figure 1,
Figure 2,
Figure 3 and
Figure 4.
Detailed heat exchanger models were integrated with the cycle model. PHEs were used as the desorber, condenser, evaporator, SHE and absorber. The HTCs were calculated with the geometric parameters of the PHEs. Referring to
Figure 1,
Figure 2,
Figure 3 and
Figure 4, the enthalpies of the states 1, 3 and 13 (
h1,
h3 and
h13) were initialised by the cycle model and then iterated. The states of the downstream points were calculated as functions of the heat exchanger performance. For example, the outlet conditions of the desorber were calculated with state 3, the heat transfer area of the desorber and secondary fluid. Enthalpy instead of temperature was used as the iteration parameter. Enthalpy changes smoothly from superheated vapour to subcooled liquid. The calculated values of
h1,
h3 and
h13 using the heat exchanger models were compared with the estimated values that resulted from the cycle model. The iteration is finished when the values agree. Otherwise,
h1,
h3 and
h13 are updated. The iteration was implemented using the Matlab fsolve algorithm [
29]. The output parameters were the cycle COP, the heat loads of all the heat exchangers, the mass flow rate and mass concentration of the refrigerant, as well as the HTCs. The pressure drops in the heat exchangers were small and were neglected during the iteration. When the iteration was finished, the pressure drops were estimated separately.
2.2. Modelling Method
The model integrates thermodynamic mass and energy balance calculations and heat transfer prediction. It is based on the following assumptions:
The operation of the cycle is steady state.
The pressure drops of the working fluids in the heat exchangers do not affect the heat transfer performance. The absorber and evaporator have the same operating pressures except for the compression-assisted cycle. The desorber, rectifier, condenser and SHE have identical operating pressures. The pressure drops are determined after the heat transfer calculation is converged.
Higher heat source and heat sink temperatures increase the operating pressures, so that the refrigerant is completely condensed at the condenser and the rich solution is subcooled at the absorber outlet.
Referring to
Figure 1,
Figure 2 and
Figure 4, at the desorber and rectifier, states 4 and 8 are saturated liquid. States 7 and 9 are saturated vapour. State 7 is in equilibrium with state 4 (T7 = T4). T7 and T8 have a temperature difference of 10 K because of the mass transfer resistance (T7 = T8 + 10). This value is based on the investigation of small scale rectifiers [
16,
30]. Similarly, in the cycle of
Figure 3, states 17 and 8 are saturated liquid. States 7 and 9 are saturated vapour. State 7 has the same temperature as state 4 (T7 = T4). T7 and T8 have a temperature difference of 10 K (T7 = T8 + 10).
The working fluids and secondary fluids are uniformly distributed in the channels of the PHEs. The heat leakage to the environment is neglected.
The expansion valves do not restrain the mass flow rate of working fluid. The expansion processes are isenthalpic.
At the evaporator outlet, unevaporated liquid droplets are entrained by the vapour flow. No water is accumulated. In the following analysis, the ammonia refrigerant has more water content under larger mass flow rate, and the entrainment effects are stronger.
The thermodynamic model was derived from the mass, mass concentration and energy balances of the components. Equations (1)–(3) are the control equations. Equation (4) calculates the cycle COP. It is the ratio of the cooling capacity to the heating capacity and consumed power. For the compression-assisted cycle, the power consumption included the pump power and compressor power. For the other cycles, only the pump power was involved. The pump power was much smaller than the heating capacity. The efficiency of the solution pump was assumed to be 50% [
31]. Since the pump power was less than 2% of the heating capacity, the pump efficiency had a little effect on the cycle COP.
The counter current heat exchanger models used the log mean temperature difference (LMTD) method. In Equation (5), the actual heat transfer areas of PHEs consider the area enlargement of corrugated plates [
32]. The HTCs of the working fluids and secondary fluids are functions of the operating conditions. The working fluids have temperature glides, which is quantified by the LMTD in Equation (6).
The solution circulation ratio is the mass flow rate ratio of rich solution to refrigerant, which is calculated in Equation (7). It measures the amount of refrigerant generated per unit rich solution. The solution circulation ratio also indicates the imbalance between the rich and poor solutions at the SHE.
In absorption cycles, the heat transfer processes include the desorption and absorption of solutions, the condensation and evaporation of refrigerant, as well as single-phase heat transfer. Applicable correlations were selected for PHEs and were implemented in the model. The details of the correlations were provided in the
Appendix A.
The desorption heat transfer of ammonia/water was estimated by the correlation of Taboas et al. [
33,
34]. The desorption process had large mass flow rates and low vapour qualities. The nucleate boiling process was degraded by the mass transfer resistance. Convective boiling enhanced the heat transfer. Cerezo et al. [
35] proposed a heat transfer correlation for water-cooled bubble absorbers. The liquid and vapour flowed upward. The heat transfer was enhanced by lower solution mass concentration, lower cooling water temperature and higher operating pressure. The correlation of two-phase inlet was used in the present model.
Ammonia has a high thermal conductivity and a large two-phase density ratio, whose heat transfer of evaporation and condensation shows distinct characteristics from other refrigerants [
36]. Khan et al. [
37] developed a heat transfer correlation for ammonia evaporation. The heat transfer is dominated by convective boiling in the narrow channels. Tao and Infante Ferreira [
36] proposed a heat transfer correlation of ammonia condensation based on flow patterns. Convective condensation prevails for large liquid mass fluxes, while gravity-controlled condensation becomes noticeable for small liquid mass fluxes. The ammonia refrigerant contained a small amount of water. The temperature glide of evaporation reduced the temperature driving force and the heat transfer deteriorated. Although the temperature glide of condensation enlarged the temperature driving force, the HTC was degraded because of mass transfer resistance. The mixture degradation of condensation was quantified using the Silver [
38] and Bell and Ghaly [
39] method.
At SHE, the heat transfer took place between single-phase working fluids. At the desorber, condenser, evaporator and absorber, the secondary fluids are single-phase flows. Single-phase heat transfer was predicted using the correlation of Martin [
40].
The rectifier has a large temperature driving force. The UA value is small. In this paper, the rectifier was assumed to have a constant UA value. At the RHE, the cold fluid was the refrigerant from the evaporator and contained water, which has a sharp temperature change. The heat transfer of the RHE was calculated with a pinch point temperature difference of 5 K.
The pressure drops of the working fluids and secondary fluids in the heat exchangers were calculated after the cycle iteration was converged. The working fluid is in two-phase flow at the desorber, condenser, evaporator and absorber, which shows separated flow characteristics [
34,
37,
41]. The two-phase pressure drop was calculated with a separated flow correlation [
36]. Both pure ammonia and ammonia/water have a large two-phase density ratio. The mass transfer resistance of the mixture had a minor influence on pressure drops. The pressure drop correlation of pure ammonia is applicable for ammonia/water [
28]. The working fluid was single-phase flow at the SHE. The secondary fluids also flowed in single-phase. The pressure drop was predicted using the correlation of Martin [
40].
The thermodynamic properties of ammonia/water were calculated using Refprop, such as enthalpy, temperature, pressure, density and mass concentration [
42]. The transport properties of the mixture used Conde including thermal conductivity and dynamic viscosity [
43]. The fluid properties of aqueous solutions were determined by Melinder [
44].