1. Introduction
One of the most widely used building heating and cooling equipments in resident in China is the air-cooling heat pump unit. And the compound condensation process (CCP) has been an industrial standard. It includes two parts: one is the water cooling + water cooling pattern and the other is the water cooling + air cooling pattern. Then the thermodynamic characteristic of the two condenser condensing system should be studied. There are several researches that have been published by our research group about the former one: a thermodynamic model of an irreversible Carnot Refrigerator with Heat Recovery (CRHR) working between two high temperature reservoirs (THTH and TRTR) and one low temperature heat reservoir (TLTL) has been established in this paper for optimization of allocation of heat transfer areas [1] . The finite time thermodynamics is used to set up the time series simulation model and the software CYCLEPAD is used for the simulation of the compound condensing process [2] . As a result, an upper bound of recoverable condensation heat for the compound condensing process is obtained which is in good agreement with experimental result. And the result is valuable and useful to optimization design of cooling and heating resource systems. The thermodynamic characteristic has been studied in the one stage decentralized chiller in south China with R22 [3] .
Due to the environment influence of the traditional refrigerant, the substitute refrigerant which has few or no destroy to the environment is developed. The R22 is the most widely used fluorocarbon refrigerant. Now, there are several substitute refrigerants. As a natural refrigerant, CO_{2} has become the hotspot of air-conditioner and heat pump because of its good characteristic. Because of the high heat transfer efficiency of the CO_{2}, the CO_{2} refrigerant system is more compact, and the flow resistance is relatively low, and the cooling capacity per unit volume is large, and the area of the heat transfer is reduced, especially with the research and developing of the micro-channel heat exchanger and the high efficiency compressor, and the space occupy ratio of the single stage cycle has deduced a lot [4] . The air-conditioner sample in the car based on CO_{2} trans-critical refrigerating cycle was developed by Prof. Lorentzen in Nova Technical University in last 90^{th} [5] . From 1994, many car industry companies in Europe, such as BMW, DAIMLERBNZ, VOLVO and Volkswagen combined with the universities and vehicle air conditioner manufacturers developed the CO_{2} vehicle air-conditioner system [6] . As to the family use CO_{2} air-conditional systems, they have been studied and developed by many researchers [7] . But most of them including CO_{2} automation air conditioner are using the traditional 4 components cycle of the basic refrigerating cycle. Because of the low critical temperature of carbon dioxide (31.1˚C), the working pressure far exceeds the sub-critical cycle. So the compression ratio is low, and the pressure gap is large, which brings problems to the design and sealing of components. At the same time, the exergy loss is very high in the throttle which makes the system efficiency lower than the ordinary refrigerant systems [8] . On the other hand, the cost of the components in the CO_{2} trans-critical refrigerating cycle is high. There are problems of high pressure resistance, high temperature resistance, prevention and curing the leak of CO_{2} and reduce friction. These problems are the bottleneck in applying the CO_{2} trans-critical refrigerating cycle [9] . The heating and cooling performance of the equipment has been compared with CO_{2} trans-critical, HFCs and R22: a performance evaluation of mini-channel parallel flow (MCPF) condenser in residential/commercial refrigeration system has been carried out in calorimeter room with wind tune. The field measurement and modeling results of COP’s for HFC and CO_{2} systems has been compared. The new CO_{2} systems have higher total COP than HFC systems for outdoor temperatures lower than about 24˚C. The modeling is used to calculate the annual energy use of HFC and new CO_{2} system in an average size supermarket in Stockholm. The result shows that the new CO_{2} systems use about 20% less energy than a typical HFC system [10] .
But thermodynamics analysis of the compound condensation process (CCP) with two separate cooling systems, including water-cooling + air-cooling systems, has been seldom investigated so far. Literatures most focus on the single refrigeration cycles. And there are some problems needed further investigation, for example, condensation heat recovery of typical air-cooling heat pump unit and its thermodynamic analysis, etc. So it is meaningful in improving the performance of the CCP system, bringing down the operation cost of the CO_{2} trans-critical CCP, developing the production with the natural refrigerant CO_{2} [11] . To analyze the performances of the CCP with R407C/R410A/CO_{2}, a thermodynamic model of two-condenser condensation and dynamic simulation of the air cooled heat pump is needed. The thermodynamic model of two-condenser condensation and the dynamic simulation would be developed. This paper presents a general simulation model for a system supplying sanitary hot water, heating, and cooling loads. A base case is defined, and the model is solved with MATLAB/SIMULINK software. The thermodynamic characteristic of the CCP with air cooled heat pump will be studied. The performance of HFC CCP refrigeration systems and alternative CO_{2} trans-critical solutions for air cooled heat pump will compare the performance with the R22 system.
2. Material and Methods
A air-cooling heat pump unit in resident in south China has been selected as the example. The refrigeration capacity is about 1 kW. The working fluid is R22/R407C/R410A. A sanitary hot water system has been added to the unit at July 2013. And it is part of the whole condensation process. The volume of the sanitary hot tank is 100 L. As shown in Table 1.
The high temperature refrigerant from the compressors passes the sanitary hot water supply system and the ordinary condenser in turn. The sanitary hot water system produces sanitary hot water about 7 kg・d^{−}^{1}. And the water temperature of the water tank that sent to user can reach to about 53˚C. A conventional system on a T-S diagram is illustrated in Figure 1, as show in Figure 1.
The heat recovery technique AC/HP system analysis is a compound-cooling mode which has been analysis in the paper published.
3. Theory/Calculation
3.1. The Mathematical Model of the CCP
The total condensation heat can be calculated by:
Table 1. The operating parameter of the CCP.
Figure 1. The T-S diagram of the air-cooling heat pump unit.
${Q}_{c}={{Q}^{\prime}}_{cond}+{Q}_{cond}$ (1)
${Q}_{c}$ is total condensation heat;
${{Q}^{\prime}}_{cond}$ is condensation heat of the sanitary hot water system;
${Q}_{cond}$ is condensation heat of the ordinary condenser.
3.2. The Mathematical Model of the Sanitary Hot Water System
The heat recovered by the sanitary hot water system
${Q}_{shw}$ is equal to the heat exhausted to the sanitary hot water system
${{Q}^{\prime}}_{cond}$ , so:
${{Q}^{\prime}}_{cond}={Q}_{shw}$ (2)
${Q}_{shw}$ is the heat recovered by the sanitary hot water system.
The exchanged heat of the sanitary hot water system is equal to the enthalpy drop from the state C to state X [12] :
${{\stackrel{\dot{}}{Q}}^{\prime}}_{cond}={H}_{C}-{\stackrel{\dot{}}{H}}_{x}$ (3)
${{\stackrel{\dot{}}{Q}}^{\prime}}_{cond}$ is the heat exhaust rate to sanitary hot water system [13] ;
${H}_{C}$ is enthalpy at state C;
${\stackrel{\dot{}}{H}}_{x}$ is enthalpy at state X;
They are changing corresponding to the heat exchanging condition.
The heat recovered by the sanitary hot water system is calculated by [14] .
${\stackrel{\dot{}}{Q}}_{shw}={c}_{p}\cdot {m}_{shw}\cdot \left({\stackrel{\dot{}}{T}}_{x}-{T}_{0}\right)$ (4)
${Q}_{shw}$ is the heat recovered by the sanitary hot water system;
${c}_{p}$ is special heat capacity of constant pressure;
${m}_{shw}$ is mass flow of sanitary hot water;
${\stackrel{\dot{}}{T}}_{x}$ is temperature of the sanitary hot water at the outlet of the sanitary hot water tank;
${T}_{0}$ is the initial temperature of the input sanitary hot water.
According to the Equation (3), we can get:
${H}_{C}-{\stackrel{\dot{}}{H}}_{X}={C}_{P}\cdot {m}_{shw}\cdot \left({\stackrel{\dot{}}{T}}_{X}-{T}_{0}\right)$ (5)
The irreversible exergy loss of the sanitary hot water system is [15] :
${\stackrel{\dot{}}{i}}_{shw}={m}_{ref}\cdot {T}_{0}\cdot \left({\stackrel{\dot{}}{S}}_{C}-{S}_{X}\right)+{m}_{shw}\cdot {T}_{0}\cdot \left({\stackrel{\dot{}}{S}}_{X}-{S}_{0}\right)$ (6)
${S}_{0}$ is the entropy of initial temperature of the input water;
${S}_{C}$ is entropy at the state C;
${\stackrel{\dot{}}{S}}_{X}$ is entropy at the state X.
The Equation (1), (5), and (6) constitute the mathematical model of the sanitary hot water system.
3.3. The Mathematical Model of the Ordinary Condenser
The
${Q}_{cond}$ is equal to the enthalpy drop of the refrigerant from state X to state 4' [16] .
${\stackrel{\dot{}}{Q}}_{cond}={\stackrel{\dot{}}{H}}_{X}-{H}_{{4}^{\prime}}$ (7)
${H}_{{4}^{\prime}}$ is enthalpy of the refrigerant at state 4'.
Then, the exergy loss of the ordinary condenser:
${\stackrel{\dot{}}{I}}_{cond}={m}_{ref}\cdot \left({\stackrel{\dot{}}{h}}_{X}-{h}_{{4}^{\prime}}\right)-{T}_{0}\left({\stackrel{\dot{}}{s}}_{x}-{s}_{{4}^{\prime}}\right)$ (8)
${\stackrel{\dot{}}{I}}_{cond}$ is exergy loss rate of the ordinary condenser;
${m}_{ref}$ is mass flow rate of refrigerant;
${s}_{{4}^{\prime}}$ is the entropy of state 4'.
The Equations (1), (7), and (8) constitute the mathematical model of the ordinary condenser.
The COP and
$\eta $ of the CCP are:
$\text{COP}=\frac{{\displaystyle {\sum}_{i=1}^{n}{\stackrel{\dot{}}{Q}}_{chwi}}+{\displaystyle {\sum}_{i=1}^{n}{\stackrel{\dot{}}{Q}}_{shw}}}{{\displaystyle {\sum}_{i=1}^{n}{\stackrel{\dot{}}{W}}_{i}}}$ (9)
$\eta =\frac{{\displaystyle {\sum}_{i=1}^{n}{\stackrel{\dot{}}{e}}_{chwi}}+{\displaystyle {\sum}_{i=1}^{n}{\stackrel{\dot{}}{e}}_{shw}}}{{\displaystyle {\sum}_{i=1}^{n}{\stackrel{\dot{}}{e}}_{w}}}$ (10)
COP is energy efficiency of the CCP system;
$\eta $ is exergy efficiency of the CCP system;
${Q}_{chw}$ is the cooling capacity of the chilled water produced;
${E}_{chw}$ is the exergy of the chilled water produced;
${Q}_{shw}$ is the heat of the sanitary hot water produced;
${E}_{shw}$ is the exergy of the sanitary hot water produced;
${E}_{w}$ is work input to the CCP.
The Equations (1), (5)-(10) constitute the mathematical model of the CCP.
3.4. The Simulation Model of CCP with Simulink
3.4.1. The Simulation Model of Hot Water Supply System
Let
${S}_{C}$ subtracts
${S}_{X}$ , then the result (
${S}_{C}-{S}_{X}$ ) multiplies
${T}_{0}$ and
${m}_{ref}$ . The block of exergy loss at refrigerant side
${T}_{0}\cdot {m}_{ref}\cdot \left({S}_{C}-{S}_{X}\right)$ can be gotten. Then do the result add the block of exergy loss at sanitary hot water side
${T}_{0}\cdot {m}_{shw}\cdot \left({S}_{X}-{S}_{0}\right)$ , the simulation model of exergy loss of the hot water supply system
${m}_{ref}\cdot {T}_{0}\cdot \left({S}_{C}-{S}_{X}\right)+{m}_{shw}\cdot {T}_{0}\cdot \left({S}_{X}-{S}_{0}\right)$ is gotten. The model shows the process of the refrigerant from state C to state X and the water temperature from
${T}_{0}$ to
${T}_{X}$ , see in Figure 2.
3.4.2. The Simulation Model of Ordinary Condenser
According to the outlet pressure of the compressor and the condensing temperature, the
${h}_{{4}^{\prime}}$ which is enthalpy of state 4',
${s}_{{4}^{\prime}}$ which is entropy of state 4' are gotten. And based on the
${T}_{X}$ calculated by the model of hot water system above, the
${h}_{X}$ and
${s}_{X}$ can be gotten. So the exergy loss of the condenser can be obtained. As shown in Figure 3. The model shows the process from state X to state 4' in Figure 1.
3.4.3. The Simulation Model of the CCP
The system simulation model consists of these models of compressor, sanitary hot water system, ordinary condenser, expansion valve and evaporator. The operating mode is supplying sanitary hot water and cooling simultaneously. The exergy loss of each component, the exergy of the sanitary hot water and the refrigerate load can be calculated and displayed, as shown in Figure 4.
Figure 2. The simulation model of the sanitary hot water system.
Figure 3. The simulation model of the ordinary condenser.
Figure 4. The system simulation model on the refrigerant-sanitary hot water mode.
3.5. The CO_{2} Trans-Critical CCP System
3.5.1. The Physical Model of the CO_{2} Trans-Critical CCP
A sanitary hot water set has been added in the CO_{2} trans-critical system, seen in Figure 5. It includes compressor, sanitary hot water set, gas-cooler, expansion valve and evaporator. The low pressure refrigerant gaseous has been compressed to high pressure gaseous refrigerant through the compressor (process 1-2), then exhaust heat to the sanitary hot water set at a constant pressure (process 2-3), the rest condensation heat was exhaust to the gas-cooler at a constant pressure (process 3-4), the next is throttling process by throttle (process 4-5), the last is heat absorption of the low pressure liquid refrigerant in the evaporator at a constant pressure (process 5-1).
Figure 5. The diagram of the CO_{2} trans-critical of CCP system.
3.5.2. The Mathematical Model of the CO_{2} Trans-Critical CPP
1) The mathematical model of the compressor
Because of the in-reversible of the compression process, there is entropy and exergy loss produced, according to the T-S diagram of the CO_{2}, seen in Figure 6, the mathematical model can be indicated by:
The work input of the compressor:
${W}_{a}=\left({h}_{2}-{h}_{1}\right)-\left({h}_{3}-{h}_{4}\right)$ (11)
In the equation,
${W}_{a}$ is work input of the compressor;
${h}_{1},{h}_{2},{h}_{3}$ and
${h}_{4}$ are specific enthalpy from state 1 to 4.
2) The mathematical model of the sanitary hot water set
The calculation period is the time of temperature increase of the hot water tank, which is from the initial temperature to the temperature that the user demand. To the number i cycle, the heat recovered and the exergy loss of the sanitary hot water set and the gas cooler can be calculated by the formula:
${Q}_{refi}={Q}_{shwi}+{Q}_{hroi}={m}_{ref}\cdot \left({h}_{2}-{h}_{xi}\right)$ (12)
The subscript i indicate the number i cycle of the sanitary hot water set, n is the total number of the cycle until the temperature of the sanitary hot water reached the user demand.
${Q}_{refi}$ is the heat exhaust by the refrigerant at cycle i,
${Q}_{hroi}$ is heat exhaust to the environment by the refrigerant,
${Q}_{shwi}$ is the heat that the sanitary hot water set absorbed in the cycle i [17] .
${m}_{ref}$ is the mass flow of the refrigerant CO_{2},
${h}_{Xi}$ is special enthalpy of the state X at cycle i.
${Q}_{shwi}$ can be calculated by:
${Q}_{shwi}={C}_{pw}\cdot {m}_{shw}\cdot \left({T}_{i}-{T}_{i-1}\right)$ (13)
${C}_{pw}$ is the specific heat of the refrigerant CO_{2} at a constant pressure;
${m}_{ref}$ is the mass flow of the sanitary hot water;
${T}_{i}$ is the temperature of the sanitary
Figure 6. The T-S diagram of the CO_{2} trans-critical of CCP system.
hot water at cycle i.
${T}_{0}$ is the initial temperature, 25˚C [18] . The heat exhaust to the environment is very small and it can be neglected, the heat absorbed by the sanitary hot water is equal to the enthalpy from state C to state X:
${Q}_{shwi}={H}_{2}-{H}_{Xi}$ (14)
${H}_{Xi}$ is the enthalpy of the state 2;
${H}_{Xi}$ is the enthalpy of the state X at cycle i, The initial temperature of
${X}_{0}$ is equal to
${T}_{0}$ , 25˚C, the temperature of the
${X}_{n}$ is 53˚C.
The exergy loss of the sanitary hot water set can be calculated by:
${I}_{shwi}={m}_{ref}\cdot {T}_{0}\cdot \left({s}_{Xi}-{s}_{3}\right)+{m}_{shw}\cdot {T}_{0}\cdot \left({s}_{i}-{s}_{i-1}\right)$ (15)
${I}_{shwi}$ is the exergy loss of the sanitary hot water set;
${s}_{Xi}$ is entropy of state X at cycle i;
${s}_{3}$ is entropy of state 3;
${s}_{i}$ is entropy of the sanitary hot water at cycle i;
${s}_{0}$ is the entropy of the initial sanitary hot water.
3) The mathematical model of the gas cooler
According to the T-S diagram in Figure 2, the CO_{2} from the saturated gas to saturated liquid, the dryness from 1 to 0, use the correlation Dobson, the heat transfer efficiency and pressure drop in the near critical area of the CO_{2} system can be calculated by [19] :
$h=0.023{R}_{el}^{0.8}{P}_{rl}^{0.4}\left(1+\frac{2.22}{{x}_{tt}^{0.89}}\right)\frac{\lambda}{d}$ (16)
${R}_{el}=\frac{G\cdot \left(1-x\right)\cdot d}{{\mu}_{l}}$ (17)
${P}_{rl}=\frac{{C}_{pl}{\mu}_{l}}{\lambda}$ (18)
${x}_{tt}={\left(\frac{1-x}{x}\right)}^{0.9}{\left(\frac{{\rho}_{v}}{{\rho}_{l}}\right)}^{0.5}{\left(\frac{{\mu}_{l}}{{\rho}_{v}}\right)}^{0.1}$ (19)
$\frac{\text{d}P}{\text{d}L}=\frac{32G}{{R}_{e}\cdot \rho \cdot d}$ (20)
In the equations,
$\lambda $ is the heat conduction efficiency, W・m^{−}^{1}∙k^{−}^{1},
${R}_{el}$ is the Reynard number of the liquid CO_{2},
${P}_{rl}$ is the prandtl number of the liquid CO_{2};
${x}_{tt}$ is the turbulence liquid;
${C}_{pl}$ is the specific heat of the CO_{2}, kj・kg^{−}^{1}・k^{−}^{1};
${\mu}_{l}$ is the kinetic viscosity of the CO_{2} kj∙m^{−}^{1}∙s^{−}^{1};
$\text{d}P/\text{d}L$ is the pressure drop of the per unit length along the horizontal pipe, bar∙m^{−}^{1}.
${R}_{e}$ is the Reynard number of the CO_{2};
$\rho $ is the mass density of the CO_{2}, kj∙m^{−}^{2}.
${I}_{condi}={m}_{ref}\cdot {i}_{condi}$ (21)
And:
${i}_{condi}=\left({h}_{Xi}-{h}_{3}\right)-{T}_{0}\left({s}_{Xi}-{s}_{3}\right)$ (22)
4) The mathematical model of the valve
The exergy loss of the expansion valve is defined by:
${I}_{exp}={T}_{0}\cdot {m}_{ref}\cdot \left({s}_{4}-{s}_{3}\right)$ (23)
5) The mathematical model of the evaporator
The heat absorb process is happened at the two phase area, and the evaporating pressure is very high, about 7 to 10 times of the ordinary evaporating one, and the physical characteristic is special, so the ebullition heat transfer characteristic is different with the normal refrigerant. So there is different demand in the construction design of the evaporator for the CO_{2} system [20] .
In the CO_{2} trans-critic water cooling + water cooling heat pump system , the construction of the evaporator is tube and shell, the flow path is double tube side and single shell side. The refrigerant vaporization and absorbed heat in the tube, the chilled water flows at the outside of the tube. There are assumptions: 1) it is steady-state operation; 2) there is no heat conduction at axial direction of the tube; 3) The heat loss is neglect; 4) the CO_{2} is one-dimensional flow along the axial direction in the tube; 5) the pressure drop is neglect in the chilled water side; 6) the flow and temperature of the CO_{2} and the chilled water is uniform distribution; 7) the outlet of the evaporator is statute.
When the heat loss is neglect, the heat absorbed of the CO_{2} in the evaporation is equal to the heat exhaust of the chilled water, according to the heat transfer formula:
1) The heat exhaust at the chilled water side:
${Q}_{ew}={m}_{ev}\times \left({h}_{ew,in}-{h}_{ew,out}\right)={m}_{ew}\times {C}_{p,ew}\times \left({T}_{ew,in}-{T}_{ew,out}\right)$ (24)
In the equation,
${Q}_{ew}$ is heat exhaust of the chilled water, W,
${m}_{ew}$ is mass flow of the chilled water, kg∙s^{−}^{1}, ew, in and ew, out are the entropy at inlet and out let of the chilled water, j∙kg^{−}^{1};
${C}_{p,ew}$ is the specific heat, j∙kg^{−}^{1}∙k^{−}^{1};
${T}_{ew,in}$ and
${T}_{ew,out}$ is the temperature at outlet and inlet of the chilled water, K.
2) The heat absorbed by the CO_{2}:
${Q}_{er}={m}_{er}\times \left({h}_{er,in}-{h}_{er,out}\right)$ (25)
In the equation, er is heat absorbed by CO_{2}, W; er, in and er, out are the enthalpy of the CO_{2} at inlet and outlet, j∙kg^{−}^{1}.
3) The total heat transferred:
${Q}_{r,w}={U}_{e}\times {A}_{z}\times \Delta {T}_{m}$ (26)
${Q}_{r,w}$ is the heat exchanged, W,
${U}_{e}$ is the heat transfer efficiency, W∙m^{−}^{2}∙k^{−}^{1};
${A}_{z}$ is the heat transfer area,
$\Delta {T}_{m}$ is logarithmic heat transfer temperature difference, K.
According to the energy balance equation:
${Q}_{ew}={Q}_{er}={Q}_{r,w}$ (27)
The exergy loss of the evaporator can be valued as:
${I}_{ev}={m}_{ref}\left[\left({h}_{4}-{h}_{1}\right)-{T}_{0}\left({s}_{4}-{s}_{1}\right)\right]+{m}_{ev,w}\left[\left({h}_{evwo}-{h}_{evwi}\right)-{T}_{0}\left({s}_{evwo}-{s}_{evwi}\right)\right]$ (28)
In the equation,
${I}_{ev}$ is exergy loss of the evaporator;
${m}_{ev,w}$ is the mass flow of the sanitary hot water;
${h}_{evwo}$ ,
${h}_{evwi}$ is enthalpy of sanitary hot water in and out;
${s}_{evwo}$ and
${s}_{evwi}$ are entropy of sanitary hot water in and out.
The range of the evaporating is from −5˚C to 5˚C.
3.5.3. The Simulation Model of the CCP System with CO_{2} Trans-Critical
1) The simulation model of the compressor
According to the evaporate temperature
${T}_{e}$ , the entropy of the state 1
${s}_{1}$ can be gotten. Then, the entropy of state 2
${s}_{2}$ can be calculated according to the condensation temperature
${T}_{c}$ . On the other hand, the
${h}_{1}$ ,
${h}_{2}$ and
$\left({h}_{2}-{h}_{1}\right)$ can be defined and calculated through the value of
${T}_{e}$ ,
${T}_{c}$ , and the compression efficiency of the compressor
${\eta}_{is.c}$ . Take the
$\left({h}_{2}-{h}_{1}\right)$ sublet the product of
${T}_{0}$ multi
$\left({s}_{2}-{s}_{1}\right)$ , the result is
$\left({h}_{2}-{h}_{1}\right)-{T}_{0}\cdot \left({s}_{2}-{s}_{1}\right)$ . At last, put the
$\left({h}_{2}-{h}_{1}\right)-{T}_{0}\left({s}_{2}-{s}_{1}\right)$ multi the mass flow of the refrigerant CO_{2}, the exergy loss of the compressor
${T}_{0}\cdot \left({h}_{2}-{h}_{1}\right)-{T}_{0}\cdot \left({s}_{2}-{s}_{1}\right)$ is gotten, seen in Figure 7 [21] .
2) The simulation model of the sanitary hot water set
Take the environment temperature 20˚C as the reference temperature, set the initial temperature of the sanitary hot water 20˚C [22] . According to the
Figure 7. The simulation model of the compressor.
condensation temperature and evaporation temperature, the entropy of the state 3 can be defined, then, the entropy of the state X can be calculated. Let the
${s}_{3}$ sublet
${s}_{x}$ , the result multi the initial temperature
${T}_{0}$ and the mass flow of the refrigerant
${m}_{ref}$ . The exergy loss of the refrigerant side
${m}_{ref}\cdot {T}_{0}\cdot \left({s}_{3}-{s}_{Xi}\right)$ can be gotten. On the other hand, the mass flow of the sanitary hot water
${m}_{shw}$ can be calculated according to the specific of the refrigerant CO_{2} and the initial temperature
${T}_{0}$ [22] . To the cycle i, take the result of (
${s}_{i}-{s}_{i-1}$ ) multi the reference temperature
${T}_{0}$ and mass flow of the sanitary hot water
${m}_{shw}$ , the exergy loss of the refrigerant side can be gotten. At last, let the exergy loss of the refrigerant side
${m}_{ref}\cdot {T}_{0}\cdot \left({s}_{3}-{s}_{Xi}\right)$ add the exergy loss of the water side
${m}_{shw}\cdot {T}_{0}\cdot \left({s}_{i}-{s}_{i-1}\right)$ , the exergy loss can be gotten, the simulation model can be seen in Figure 8.
3) The simulation model of the gas cooler
According to the exergy loss of the gas cooler
$\left({h}_{Xi}-{h}_{3}\right)-{T}_{0}\left({s}_{Xi}-{s}_{3}\right)$ , at first, the entropy and enthalpy of state 3 (s_{3}), (h_{3}) can be gotten. At the same time, the entropy and enthalpy of state X, s_{3}, h_{3} can be calculated, then through the operation with reference temperature
${T}_{0}$ and mass flow of the refrigerant CO_{2} (
${m}_{ref}$ ), the exergy loss of the gas cooler can be gotten. See in Figure 9.
The parameter input: the specific of the water is 4.2 kj∙kg^{−}^{1};
${m}_{shw}$ is mass flow of the sanitary hot water, it is 2.5 kg∙min^{−}^{1};
${T}_{0}$ is the environment temperature, 25˚C; the adjust parameter:
${m}_{ref}$ is the mass flow of the CO_{2}; condensation temperature
${T}_{C}$ is 100˚C [23] .
4) The simulation model of the valve
According to the exergy loss of the expansion valve:
${T}_{0}\cdot {m}_{ref}\cdot \left({s}_{4}-{s}_{3}\right)$ , at first, the entropy of state 4 (
${s}_{4}$ ) can be got through the condensation temperature (
${T}_{c}$ ); then, the entropy of state 3 (
${s}_{3}$ ) can be got through the evaporation temperature (
${T}_{e}$ ); at last, take the different of (
${s}_{4}-{s}_{3}$ ) multi the reference temperature (
${T}_{0}$ ) and mass flow of the refrigerant CO_{2} (
${m}_{ref}$ ). The simulation model of the expansion valve is show in Figure 10.
Figure 8. The simulation model of the sanitary hot water set.
Figure 9. The simulation model of the gas cooler.
5) The simulation model of the evaporator
According to the mathematical model of the evaporator, exergy loss of the evaporator is
${m}_{ref}\left[\left({h}_{4}-{h}_{1}\right)-{T}_{0}\left({s}_{4}-{s}_{1}\right)\right]+{m}_{ev,w}\left[\left({h}_{evwo}-{h}_{evwi}\right)-{T}_{0}\left({s}_{evwo}-{s}_{evwi}\right)\right]$ . The process of establish the simulation model: at first, according to the condensation and evaporation temperature, the entropy and enthalpy of state 1 and state 4 can be calculated; then, the entropy and enthalpy of inlet and outlet of the sanitary hot water can be defined and calculated. The simulation model can be seen in Figure 11.
6) The simulation model of the CCP with CO_{2}
The simulation model of CCP with CO_{2} include compressor, sanitary hot water set, air cooled condenser, expansion valve and evaporator. Connected the components to a system model by the MATLAB/SIMULINK software. This model can operate at traditional refrigerating mode (sanitary hot water set shut
Figure 11. The simulation model of the evaporator.
down) and compound condensation mode. The exergy loss of each component and other parameters can be calculated and displayed, seen in Figure 12.
4. Results
Tests of the experimental prototype have been made. The electrical energy input to the prototype compressor is about 1 kW. The charged working fluid is R22. Sanitary hot water tank capacity is 80 L. The rating flux of the water pump for circulation is 2.67 kg∙min^{−}^{1}. The maximal value of the lowest pressure of the compressor suction side is 0.5 MPa. The highest pressure of the compressor exit side is 1.8 MPa. The water flow and the temperature increasing of the sanitary hot water are assumed to be constant approximately. The energy and exergy efficiency of the system before and after retrofit were investigated. The test data of the operating parameters of the system are plotted in Figure 13 and Figure 14. The relationships of the exergy loss of the component vs. the condensation temperature and evaporation temperature can be seen from Figure 13 and Figure 14.
Figures 15-19 show the operation parameter of the CCP on the refrigeration-sanitary hot water mode. In Figure 15, the exergy loss of the sanitary hot water system is decrease from 0.8 kW to zero. And the exergy loss of the ordinary condenser increase from 1.4 to 1.6 kW. That is because the heat exchange amount reduces, so the exergy loss reduces accordingly; in the mean while, the heat exchange amount of the ordinary condenser increases, then the exergy loss of the ordinary condenser increases accordingly.
Figure 16 shows the aim exergy efficiency after retrofit and before retrofit. It is showed that the aim exergy efficiency improved 0.05 to 0.01. That is because the heat transfer temperature difference of the sanitary hot water reduce with the
Figure 12. The simulation model of the CCP system with CO_{2}.
Figure 13. The exergy loss of the component vs. the condensation temperature at the operation evaporation temperature 0˚C.
Figure 14. The exergy loss of the component vs. the evaporate temperature at the condensation temperature 40˚C.
Figure 15. The exergy loss of the air cooled condenser and the heat recovery equipment vs. the operation time (at ambient temperature 25˚C, condensation/evaporation temperature 40/0˚C).
Figure 16. The exergy efficiency vs. the operating time on the refrigerant-sanitary hot water temperature.
increase of the temperature sanitary hot water.
The heat recovered and the exergy efficiency reduce accordingly.
As show in Figure 17, the compare of the COP of CCP and traditional refrigerant mode with R407C, COP of the CCP is vary from 2.7 to 1.9, and the CCP of the traditional refrigerant mode with R407C is 1.9 - 1.8. The energy using situation has been improved; the thermodynamic characteristic has been increased. In a calculation period, the CCP declined with the operation time. That is because the heat exchange amount is reduced according to the decrease of the temperature gap. The trend is the same with Figure 17.
Figure 17. The COP of the CCP and the traditional refrigerant mode with R407C.
Figure 18. The COP of the R410A refrigerant-sanitary hot water mode vs. refrigerant mode.
As show in Figure 18, it compares the COP with the CCP and the traditional refrigerant mode with R410A. After retrofit, the COP is 3.3 - 2.3; it is 2.3 - 2.2 before retrofit. The energy using situation is improved, the performance of the COP is enhanced of the COP. the COP declined with the operation time. That is because the heat exchange amount is reduced according to the decrease of the temperature gap. The trend is the same with Figure 17.
As show in Figure 19, the COP of the R410A is about 0.3 - 0.5 higher than the
Figure 19. The COP of the CCP with R22/R407C/R410A.
R22 system, the R407C system is about 0.2 lower than the R22 system.
On the sanitary hot water model: the outlet temperature of the sanitary hot water tank of the CCP with the R407C and R410A is showed in Figure 20. The increase velocity of the temperature of the sanitary hot water of the R410A system is the fastest. To the temperature the user demand 47˚C, the R407C system needs about 27 mins, the R22 system needs about 40 mins, the R410A system needs about 52 mins.
Figure 21 shows the exergy efficiency vs. the temperature of the sanitary hot water that the user demand. The R410A system is 0.2 - 0.5 higher than the R22 system. And the R407C system is 0.5 - 0.1 lower than the R22 system.
The COP of the CO_{2} refrigerant mode vs. exhaust pressure. The COP declines with the increase of the exhaust pressure. It is about 3.6 at the exhaust pressure 8.5 MP_{a}, and declines to 3.3 at the exhaust temperature 10.0 MP_{a}.
Figure 23 shows the COP of CCP system with CO_{2} vs. the COP of CO_{2} refrigerant system. The COP of CCP system declines with the increase of the exhaust pressure. It is about 3.4 at the exhaust pressure 5 MP_{a}, and declines to about 2.4 at exhaust pressure 35 MP_{a}. While the COP of the CO_{2} refrigerant system stays about 2.3 - 2.3.
The COP of the CCP system with R22 and CO_{2} is showed in Figure 24, the CCP of CO_{2} system with is lower than the CCP of the R22 system.
From the Figure 25, the outlet temperature of the sanitary hot water tank, it shows that it needs 18 minutes to reach the temperature that the user demand. And the R22 system is about 30 minutes.
5. Discussion
The simulation model of the CCP with refrigerant R22/R407C/R410A/CO_{2} for periods of 18 - 30 minutes were built, the object is water cooling + air-cooling combined heat pump system for a typical resident in south China. The refrigeration
Figure 20. The temperature of the sanitary hot water tank vs. the operation time with R22/R407C/R410A.
Figure 21. The exergy efficiency vs. the temperature of the sanitary hot water with R22/R407C/R410A.
systems, the analysis method, and the required assumptions are explained in details. The CCP systems with R407C/R410A and CCP system with CO_{2} trans-critical were compared to the CCP system with R22 discussed in details. The different CCP systems are made comparable by looking at the different exergy loss versus the condensing temperatures and the temperature of the sanitary hot tank versus the operating time and the COP versus the operating time and the exhaust pressure and the exergy efficiency versus the temperature of the
Figure 22. The COP of the CO_{2} refrigerant mode vs. exhaust pressure.
Figure 23. The COP of CCP system with CO_{2} vs. the COP of CO_{2} refrigerant system.
sanitary hot tank. Theoretical modelling where the energy use of the CCP systems with HFC and CO_{2} trans-critical
in a period of the sanitary hot water increased to reach the user demand was calculated.
6. Conclusions
The COP and exergy efficiency of a period that the sanitary hot water increases to reach the temperature that the user demands were plotted. It is the CCP system with HFC and CO_{2} trans-critical in a typical resident. The total COP of the CCP system with R410A is about 3% - 5% higher than the CCP system with R22, and the CCP system of R407C is a little lower than the R22 system due to their thermal characteristics. To the CCP system of CO_{2} trans-critical, it has advantage
Figure 24. The COP of the CO_{2} system vs. the R22 system on the sanitary hot water + heating mode.
Figure 25. The outlet temperature of the sanitary hot water tank on the sanitary hot water mode with CO_{2}.
compared to the refrigerant mode. The trend is the same with the traditional refrigerant mode. On the sanitary hot water mode, the exergy efficiency of both CCP system with CO_{2} and R22 declines with the increase of the sanitary hot water temperature that the user demands. And it is the same with R407C and R410A. To reach the temperature of the sanitary hot water tank 53˚C, the CO_{2} trans-critic CCP system is 12 mins faster than the CCP system with R22. And the COP of the CCP system with CO_{2} trans-critical is higher than the CCP system with R22 at the sanitary hot water mode.
The detailed analysis done in this study proves that HFC and CO_{2} trans-critical CCP systems are more energy efficient solutions for residential than typical HFC and CO_{2} refrigeration systems in South of China. The analysis method and results presented in this study can be used to expand the analysis for different case studies in other climate conditions which will help verify the potential of HFC and CO_{2} trans-critical CCP solution in other countries.
Acknowledgements
The authors would like to thank the engineers, like Wei Zen, for their help in system experimentation. The authors are also grateful to the financial support of National Special Program of International Cooperation and Exchange (No. 2010DFB83650); Important and big Science Program of Hunan Province of China (Nos. 2008GK2016; 2010FJ1013); and thanks professor Jinyue Yan has given helpful advises.
Nomenclature