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Theoretical analysis on optimal configurations of heat exchanger and compressor in a two-stage compression air source heat pump system
Accepted Manuscript Title: Theoretical analysis on optimal configurations of heat exchanger and compressor in a two-stage compression air source heat pump system Author: Yunxiang Li, Jianlin Yu PII: DOI: Reference:
S1359-4311(15)01395-2 http://dx.doi.org/doi: 10.1016/j.applthermaleng.2015.11.132 ATE 7429
To appear in:
Applied Thermal Engineering
Received date: Accepted date:
7-9-2015 27-11-2015
Please cite this article as: Yunxiang Li, Jianlin Yu, Theoretical analysis on optimal configurations of heat exchanger and compressor in a two-stage compression air source heat pump system, Applied Thermal Engineering (2015), http://dx.doi.org/doi: 10.1016/j.applthermaleng.2015.11.132. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Theoretical analysis on optimal configurations of heat exchanger and compressor in a two-stage compression air source heat pump system Yunxiang Li, Jianlin Yu Department of Refrigeration & Cryogenic Engineering, School of Energy and Power Engineering, Xi’an Jiaotong University, Xi’an 710049, China
Highlights > Optimization of a flash tank cycle based heat pump system is conducted. >The optimal thermal conductance allocations are obtained under given conditions. >The system heating capacities are affected by thermal conductance allocation. > There exists an optimal compressor displacement ratio for optimum system COP. Abstract This paper presents an optimum system configuration analysis for a flash tank cycle (FTC) based two-stage compression air source heat pump system using a developed theoretical model with lumped parameter method. The analysis is carried out with respect to the thermal conductance allocation of total heat-exchanger inventory (condenser and evaporator) as well as the volume ratio of low-pressure compressor to high-pressure compressor in the system. The analysis results indicate that the heating coefficient of performance (COP) of the heat pump system can be maximized by optimally allocating the thermal conductance inventory of the two heat exchangers. Moreover, there also exists an optimal compressor volumetric displacement ratio, corresponding to the optimum system COP, when the cooling capacity of system is specified. The effects of main operation parameters on the configuration parameters and optimal performances have been discussed. The obtained results may provide some guides for the FTC based air source heat pump system optimization. Keywords: Air source heat pump; Performance optimization; Thermal conductance; Two-stage compression
Corresponding author. Tel: +86-29-82668738. Fax: +86-29-82668725. Email: [email protected] 1
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Nomenclature C O P heating coefficient of performance -1
-1
c p specific heat (J kg K ) -1
h specific enthalpy (kJ kg ) -1
m mass flow rate (kg s ) P pressure (kPa)
Q heat transfer rate (kW)
r
volumetric displacement ratio of low-pressure compressor to high-pressure
compressor t
temperature (℃) -1
UA thermal conductance (kW K ) V v
volumetric displacement (m3 s-1) specific volume (m3 kg-1)
W power (kW)
Greek symbols
adiabatic exponent
effectiveness factor of heat exchanger efficiency allocation ratio
Subscripts 2
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a air c condenser side d
discharge
e evaporator side f
fluid
h
high
i
inlet
l
low intermediate
m
max
maximum
o outlet opt r
optimal
refrigerant
s isentropic v volumetric
1. Introduction Over the past years, the air source heat pumps have attracted a great deal of attention for their merits of energy-saving and environmental protection [1, 2]. But when they operate at low ambient temperatures, several problems, such as the reduction in the heating capacity and heating coefficient of performance (COP), high compressor discharge temperature, etc., cause some application limitations. In this case, the development of air source heat pumps with higher performances and wider operating temperature range has become a major challenge. For the issues regarding performance degradation of air source heat pumps, some solutions to enhance the heating performance and reliability of the heat pump have been studied, including 3
Page 3 of 25
refrigerant injection technique, two-stage compression systems and cascade system [3-9]. The use of those methods provides more opportunities to apply air source heat pumps in cold regions. Traditionally, two-stage compression systems consisting of two individual compressors have received much attention for refrigeration applications [10-13]. However, they have also been well justified to improve the heating performance of systems for air source heat pump applications in cold climates. Neeraj et al. [14] carried out optimization studies of two-stage transcritical carbon dioxide heat pump cycles, and indicated the flash gas bypass system yields the best performance among the three two stage cycles analyzed. Arif and Hilmi [15] also conducted the second law analysis for a two-stage compression transcritical CO2 heat pump cycle, and identified the main factors that affect the two-stage compression transcritical CO2 system efficiency. Bertsch and Groll [16] investigated an air-source two-stage heat pump using R410A as the refrigerant, and experimentally verified that the heat pump is able to operate at ambient temperatures between -30 ℃ and 10 ℃ with supply water temperatures of up to 50℃. Kwon et al. [17] evaluated a two-stage compression heat pump system for district heating utilizing waste energy, and obtained the system performance characteristics under various operating conditions. Cao et al. [18] analyzed different high-temperature two-stage heat pump systems for low-grade waste heat recovery, and showed that the two-stage heat pump system with flash tank was preferred. Overall, two-stage compression systems could be a good alternative to avoid the performance deterioration of air source heat pumps in cold climates, and those relevant researches can drive their development in low temperature ambient application. For two-stage compression heat pump systems, there are two typical cycle 4
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configurations, i.e. flash tank cycle (FTC), and internal heat exchanger cycle (IHXC) [19]. Among these two cycles, the FTC has received more attention in recent years. Basically, previous researches on the FTC are mainly focused on the cycle performance improvement, component optimization or cycle control strategies. In fact, these issues are closely related to the system configurations of FTC. As is well known, the FTC system mainly consists of a flash tank，two compressors, a evaporator and a condenser. The configuration for the FTC systems is particularly involved in the parameters of compressor and heat exchangers, such as the heat exchange area or thermal conductance of heat exchangers and compressor displacement volume [19, 27], which play a key influence on overall system performance. To make effective use of the FTC, it is necessary to explore the relationship between the configuration parameters and the main performance parameters. In this paper, we present an analytical model with lumped parameter method for a FTC based air source heat pump air conditioner. In the model, heat exchanger thermal conductance inventory is considered as a constraint condition for configuring the FTC system [20]. Based on the developed model, the performance and optimum design conditions of the FTC system are analyzed in detail for different configuration parameters and operating conditions. Furthermore we analyzed the relationship of the optimal compressor volumetric displacement ratio and the optimal thermal conductance allocation at different heat exchanger thermal conductance inventory. And the influences of the different refrigerant on system optimal compressor volumetric displacement ratio are investigated. The objective of this work is to provide some theoretical guidance for the optimal design and operation of air source heat pump using the FTC systems. 2. Analytical model of the FTC system 5
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The schematic diagram of the FTC system is shown in Fig.1 (a), where the system consists of two compressors, a condenser, a flash tank, two expansion valves and an evaporator. The cycle system includes two circuits: a main refrigerant circuit and a bypass refrigerant circuit. The main circuit refrigerant flow is circulated by the low-pressure compressor through the high-pressure compressor, the condenser, the high pressure expansion valve, the flash tank, the low pressure expansion valve and the evaporator, whereas the bypass circuit flow is circulated by the flash tank through the high- pressure compressor, the condenser, the high pressure expansion valve. Fig. 1(b) shows the detailed working process of the FTC system on pressure-enthalpy diagram. In the condenser, high pressure superheated refrigerant vapor from the highpressure compressor (state 4) is cooled to the saturated or subcooled liquid (state 5) by secondary fluid (indoor air); The refrigerant liquid is expanded through the high pressure expansion valve, and then the two-phase refrigerant at an intermediate pressure (state 6) enters into the flash tank, in which it is separated into the two phase refrigerant include the saturated liquid (state 7) and saturated vapor (state 8). On the one hand, after the saturated liquid passes through the low pressure expansion valve, it is heated by outdoor air in the evaporator to be a saturated or superheated vapor (state 1) and then flows into the low-pressure compressor. On the other hand, after the saturated vapor from the flash tank mixes with the superheating refrigerant vapor (state 2) at the outlet of the low- pressure compressor, the vapor mixture (state 3) is compressed by the high- pressure compressor and then enters to the condenser. For modelling the FTC based air source heat pump system, the condenser and the evaporator were modeled by using the
-NTU method, and two compressors were
modeled based on the efficiency of method, for simulations. Furthermore the following assumptions are made: 6
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(1) Refrigerant pressure drops are neglected in the evaporator, the condenser and inlet or outlet of the compressors; (2) Mixing process of refrigerant at the outlet of the low- pressure compressor occurs at a constant intermediate pressure; (3) Refrigerant leaving from the condenser and the evaporator is saturated liquid and saturated vapor, respectively; (4) No heat losses to the environment from the system; (5) The throttling processes in the expansion valves are isenthalpic. Based on the assumptions above, the heating capacity of the condenser can be obtained as （1）
Q c c m fc c pfc ( t c t fci )
where m fc and c pfc are the mass flow rate and specific heat of the heated fluid in the condenser; t c is the condensing temperature, and t fci is the temperature of the fluid heated, at the inlet of the condenser; c is the heat exchanger effectiveness of the condenser, which can be given by Eqs. (2) and (3), c 1 exp ( U c Ac / m fc c pfc )
c
（2）
t fco t fci
（3）
t c t fci
where
U c Ac
is the thermal conductance of condenser, and t fco is the temperature of
the fluid heated, at the outlet of the condenser. It should be noted that when calculating the heating capacity of the condenser using the above Eq. (1) (including Eqs. (2) and (3)), the influence of the condenser superheat section is actually neglected. However, this simplicity may be appropriate because several literatures indicate that sufficient accuracy can be achieved for screening purposes when using an
-NTU model since the inherent errors of over
predicting the conductance in the effectiveness calculations and under predicting 7
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the temperature difference in the heat exchanger calculations tend to compensate each other [21, 22]. In addition, based on the energy conservation, the heating capacity of the condenser can be also written as Q c m rc ( h4 h5 )
（4）
where m rc is the mass flow rate of refrigerant in the condenser, h4 and h5 are refrigerant specific enthalpies of inlet and outlet of the condenser. Similarly, the heat transfer rate of the evaporator can be obtained as Q e e m ae c pae ( t aei t e )
（5）
and Q e m re ( h1 h9 )
（6）
where m re and m ae are the mass flow rates of refrigerant and air of the evaporator, h9
and h1 are refrigerant specific enthalpies at the inlet and outlet of the evaporator;
t e is the evaporating temperature, and t aei is the air temperature at the inlet of the
evaporator; c p ae is the air specific heat in the evaporator, e is the heat exchanger effectiveness of the evaporator, which can be given by Eqs. (7) and (8), e 1 exp( U e Ae / m ae c pae )
e
t aei t aeo
（7） （8）
t a ei t e
where U e Ae is the thermal conductance of the evaporator, and t aeo is the air temperature at the outlet of the evaporator. The total input power of compressors can be obtained, W
m re ( h2 s
sl
h1 )
m rc ( h4 s
sh
h3 )
（9）
where h1 and h3 are the refrigerant specific enthalpies at the inlet of the low and high- pressure compressors, respectively; h 2 s and h 4 s are the refrigerant specific enthalpies at the outlet of the low and high- pressure compressors under the isentropic 8
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processes; h3 is calculated by the energy balance as given in Eq. (10). h3 h8 q 6 h2 (1 q 6 )
（10）
where h8 is the specific enthalpy of saturated refrigerant vapor in the flash tank, and q 6 is the vapor quality of two phase refrigerant in the flash tank.
In addition, the isentropic efficiencies of the low and high- pressure compressors, sl and sh , can be calculated by Eqs. (11) and (12) [19], sl 1.41(1 e sh 1.41(1 e
where P2
P1
p 2 / p1 0.30 0.21
) 0.52 ln( p 2 / p1 1)
（11）
) 0.52 ln( p 4 / p 3 1)
（12）
p 4 / p 3 0.30 0.21
and P3 are the inlet pressures of the low and high- pressure compressors,
and P4 are the outlet pressures of the low and high- pressure compressors,
respectively. The refrigerant mass flow rates of the low and high- pressure compressors can be calculated by Eqs. (13) and (14), m re
m rc
vlV l v1
（13）
vhV h
（14）
v3
where V l and V h are the volumetric displacements of the low and high- pressure compressors; v1 and v 3 are the refrigerant specific volumes at the inlet of the low and high- pressure compressors; vl and vh are volumetric efficiencies of the low and high- pressure compressors, which are determined by Eqs. (15) and (16) [19]. vl 0.025( p 2 / p1 ) 1.02
（15）
（16） Based on the mass balance, the refrigerant mass flow rate of the high- pressure
vh 0 .0 2 5( p 4 / p 3 ) 1.02
compressor can be also written as
9
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m rc
m re
（17）
1 q
The volumetric displacement ratio between the low- pressure compressor and the high- pressure compressor is written as r
Vl
（18）
Vh
It is well known that the total thermal conductance is usually constrained to be finite on both the evaporator side and condenser side for a real air source heat pump system [23]. In order to maximize the performances of the system, it makes sense to consider the total thermal conductance as a design constraint, which is a fundamental design aspect in any real air source heat pump system. Thus, it is assumed that the total thermal conductance is constrained as （19）
U A U c Ac U e Ae C onstant
where
UA
is the total thermal conductance. Note that for a specified
UA ,
there
should be a thermal conductance allocation ratio between two heat exchangers, which represents the configuration relationship between the two heat exchangers. The configuration relationship between the thermal conductance of the two heat exchangers will play a key influence on overall system performance. The allocation of
UA
U e Ae U A
U c Ac (1 )UA
between the evaporator side and condenser side is written as （20） （21）
In general, introducing the thermal conductance allocation ratio is to examine the effect of the configuration relationship between the two heat exchangers on the system performance COP, and then try to find the optimal configuration of the two heat exchangers for obtaining a maximum COP at other 10
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given conditions. In following sections, the above model is used for analyzing the configuration optimization of a FTC based air source heat pump air conditioner (ASHPAC) system. Analyses are made with respect to specified volumetric displacements of two compressors or cooling capacity of the system. The optimum configuration parameters, including the and r , and system performances are evaluated under given operation and constraint conditions. An outline of the calculation procedure for the solution of the above model is shown in Fig2. It applied to compute that the variations of the
and Q c with at different
COP
UA .
The calculation procedures
of other cases are similar to those in Fig 2, and need not be repeated here. 3. Simulation results and discussion Recently, the refrigerant R32 used in commercial ASHPACs has attracted much attention due to its relative safety and good environmental friendly properties [24, 25]. And R290 has also become a promising refrigerant used in small domestic ASHPACs to replace the refrigerant R22. Hence, three kinds of refrigerants R22, R32 and R290 are selected as the working fluids of an ASHPAC system to conduct relevant system performance simulations and configuration parameter comparison among systems with different refrigerant. The simulation program is written in Fortran Language, and the required refrigerant properties are calculated by using the property subroutines of REFPROP 8.0 [26]. The relevant configuration parameters of the system are assumed as V l 8.24 10 4 kW K 1 .
3
m s
1
,
V h 4.92 10 4
3
m s
1
, and the
UA
ranging from 0.5 to 0.8
The indoor and outdoor air specific heat is assumed as
c pfc 1 0 0 5 J kg
1
K
1
c pae 1004 J kg
1
K
1
,
, respectively. Considering the FTC based ASHPACs are mainly
applied in the regions with cold climates, simulations are conducted based on winter 11
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operating condition. Hence, inlet temperature of outdoor air is assumed as t aei 7 ℃. The inlet temperature of indoor air is assumed as t fci 20 ℃. The mass flow rate of m fc 0.2
indoor and outdoor air is assumed as
kg s
1
, m ae 0.26
kg s
1
,
respectively. Fig.3 shows the variations of the
COP
and Q c with the , at different
where the refrigerant R32 is used in the ASHPAC system. It can be seen that the
UA ,
COP
of the system first increases and then decreases with increasing , which means that there exists a maximum
COP
at the o p t when fixing the
UA .
Furthermore, Fig.3
shows the system COPmax increases from 3.16 to 3.52 when the UA ranges from 0.5 to 1
0.8 kW K . The main reason for this case is that larger UA could lead to a higher evaporating temperature and a lower condensing temperature, resulting in smaller heat transfer temperature difference in both evaporator and condenser. This implies the irreversible losses in the system are reduced, and hence the system with increasing COPmax
UA .
As increasing the
UA ,
increases
however, the increasing tendency of
slows down. For example, the COPmax is increased by 5% when the 1
ranges from 0.5 to 0.6 kW K , while the UA
COPmax
COPmax
UA
is only increased by 3% when the
1
ranges from 0.7 to 0.8 kW K . The results indicate that the increase of
UA
to
improve the system COP should be properly considered in association with the cost of heat exchangers. On the other hand, it is seen from the figure that the system monotonically increasing function of at a constant increasing , the thermal conductance of condenser
UA .
U c Ac
Qc
is a
The reason is that as decreases and that of
evaporator U e Ae increases, which leads to the increases of t c and t e eventually. In this case, the increase of t c results in the decreasing in the specific heating capacity 12
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( h4 h5 ). Meanwhile, the p m also increases (as shown in Fig. 4), which leads to the increase of m rc due to the decease of v 3 . For both reasons above, the system Q c eventually shows an increasing tendency with . When the is changed from 0.25 1
to 0.5, the Q c increase by 12% - 19% at the UA in the range of 0.5 - 0.8 kW K . Fig.4 shows the variations of the optimal thermal conductance allocation o p t and the corresponding system intermediate pressure p m with increasing be found that the o p t increases from 0.37 to 0.40 when the
UA
UA .
It can
changes from 0.5 to
0.8 kW K . Obviously, the o p t is smaller than 0.5 at the given conditions, which 1
means that the thermal conductance of the evaporator that of the condenser
U c Ac
should be smaller than
U e Ae
. Furthermore, the o p t increases with the
UA ,
which
means that the thermal conductance allocated at the evaporator side should be increased at a larger
UA .
These results indicate that the performances of a ASHPAC
can be maximized by proper allocating between
U e Ae
and
U c Ac
an important thermal optimization principle, because the
UA
. This allocation is is finite and is
considered to be a significant constraint parameter in the ASHPAC designing. In addition, it can be found that the p m increases from 916.6 to 1001.6 UA
kP a
when the
1
ranges from 0.5 to 0.8 kW K . This results from the effect of two aspects.
Firstly, as increasing UA, the system t e increases, but the t c decreases. Furthermore, when the o p t increases from 0.37 to 0.40, the
U e Ae
increases, and the
U c Ac
decreases, which leads to the increase of t e and t c . In this case, the increments in t e and t c reach 3.45 ℃ and 1.24 ℃ , respectively. Correspondingly, the saturation
13
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temperature t s ( p m ) at intermediate pressure increases from 3.79 to 6.68 ℃ , as shown in Fig.5. Thus, the system p m shows an increasing tendency with rising Moreover, the p m and the t e show similar variation trend with the
UA .
UA
.
The main
reason for this is that the t e plays dominant influence on the p m compared with the t c [27].
Figs. 6 shows the variations of the
COP
and discharge temperature t d
with the , for the single-stage and two-stage compression systems, respectively, where the refrigerant is R32 and the
UA
1
is fixed at 0.6 kW K . It can be seen
that when the is changed from 0.25 to 0.5, the
COP
of two-stage compression
system increase by 72% - 69% over that of the single-stage compression system. Furthermore, Fig.6 shows the t d of two-stage compression system varies from 112.6 to 115.1 ℃ when the ranges from 0.25 to 0.5. It is greatly lower than that of the single-stage compression system. When the kW K 1
, the variations of the
is 0.5, 0.7 and 0.8
UA
and t d of single-stage and two-stage
COP
compression system are similar to that in Fig. 6. To sum up, the two-stage compression system is more favorable in terms of the
COP
increase and the
reduction of the discharge temperature. Fig.7 shows the variations of the
COP
and Q c with the at different m fc , 1
where the refrigerant is R32 and the U A is fixed at 0.6 kW K . It can be seen that the maximum
COP
that corresponds to the optimal allocation of the U A inventory
can be obtained at different m fc . The
COPmax
increases from 2.37 to 3.63 when the
m fc ranges from 0.1 to 0.3 k g s 1 . When the m fc ranges from 0.1 to 0.2 k g s 1 , the 14
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COPmax
is increased by 40%, while the COPmax is only increased by 9%, when the
m fc ranges from 0.2 to 0.3 k g s 1 . Thus, as the increase of m fc , the increasing
tendency of COPmax weakens. From the figure, it is also observed that the o p t 1
increases from 0.32 to 0.38 when the m fc ranges from 0.1 to 0.3 k g s . Obviously, the thermal conductance allocated at the evaporator side should be increased as increasing the m fc . In addition, it can be seen that the resulting Q c increases monotonically with the , and decreases monotonically as the m fc increases. Note that further increasing m fc does not significantly affects Q c . Overall, The variations of the optimal performance coefficient and heating capacity with respect to the m fc and should be considered compromisingly for optimally configuring the system parameters. Fig.8 further shows the variations of the
COP
and Q c with the at different
m ae . It can be seen that the COP curves for m ae and are similar to those in Fig.
7. Unlike the effect of m fc , however, the Q c increases with increasing m ae at a constant x. This means that the increase of m ae can be beneficial to increasing COPmax
and Q c at the o p t when the U A is specified. In addition, it is found that
the o p t increases from 0.31 to 0.38, when the m ae ranges from 0.06 to 0.26 k g s . 1
Considering the analysis results in both Fig. 7 and 8, it is clear that choosing the appropriate m ae and m fc is important, when designing an optimal ASHPAC system. Fig.9 shows the variations of COPmax and o p t with increasing t aei at different t fci , where the refrigerant is R32 and the
UA
is fixed at 0.6 kW K 1 . It
15
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can be seen that when the t aei is changed from -20 to 10 ℃ , the system COPmax is increased by 23% and 22% at the t fci of 20 and 24
℃,
respectively. Fig.9 shows
that as increasing t fci the system COPmax decreases at a constant t aei , which is due to the fact that the system t c increases with increasing t fci . From the figure, it is also observed that the o p t decreases from 0.40 to 0.34 when the t aei ranges from -20 to 10 ℃ . It means that the thermal conductance allocated at the evaporator side should be increased when the ASHPAC systems are applied in the regions with the lower outdoor temperatures. In addition, Fig.9 shows that the o p t has the same values for different t fci , when the t aei is specified. It means that the indoor air temperature almost has no influence on the allocation of the thermal conductance between the evaporator side and condenser side. Furthermore, simulation results show that when the t aei is changed from 10 to -20 ℃ , the discharge temperature t d at the o p t ℃
at the t fci of 20
℃.
increases from 101.8 to 129.7
It means that when the ASHPAC system uses refrigerant
R32, the outdoor temperature cannot be lower than -20 ℃ . As seen above, the previous optimization analysis of heat exchangers configuration is conducted for specifying the volumetric displacements of two compressors. In addition to that, it is usually necessary to specify a certain cooling capacity in the design of an ASHPAC system. In this case, optimization studies for the ASHPAC system, based on its cooling capacity duty, should be performed by considering both heat exchanger and compressor volumetric displacement configurations. Thus, the optimal configurations of heat exchangers and compressor 16
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volumetric displacements are analyzed at the specified cooling capacity in the following simulations. Fig.10 shows the variations of the COPmax at the o p t and the corresponding with increasing kW K
1
r
, where the refrigerant is R32 and the
r
r
Qe
are fixed at 0.7
, which means that there exists an
with respect to an optimum value of the
the other hand, it is seen from the figure that the function of
at a constant
r
UA
pm
COPmax when
fixing the
UA .
On
is a monotonically increasing
. Furthermore, the system optimal configuration
parameters including the o p t , ropt and the corresponding different
and
and 2.6 k W , respectively. It can be seen that the system COPmax firstly
increases and then decreases with increasing optimal
UA
pm
C O Pm ax,o ,
p m ,o and Q c,o at
are listed in Table 1. It can be found that the o p t increases from 0.37
UA
to 0.41 and the ropt decreases from 1.69 to 1.59 when the 0.8 kW K 1 . This means that when the
Qe
UA
increases from 0.6 to
is specified, the thermal conductance
allocated at the evaporator side should be increased at a larger
UA ,
whereas the ratio
between the volumetric displacements of both low and high-pressure compressor should be decreased. In addition, it should be mentioned that when from 0.6 to 0.8 kW K 1 , the
C O Pm ax,o
UA
increases
and p m ,o are increased by 13.9% and 2%, and
the Q c,o is decreased by 5.5% under the condition of ropt . Figs. 11 and 12 further show the variations of the COPmax at the o p t and the corresponding the
UA
COPmax
and
Qe
and the
pm
with
r
, at the refrigerant of R22 and R290, respectively, where
are fixed at 0.7 kW K 1 and 2.6 k W . It can be seen that both the pm
curves for
r
are similar to those in Fig. 10. Thus there also 17
Page 17 of 25
exist the ro p t with respect to an optimum value of the COPmax and the corresponding optimal
pm
in the ASHPAC system using the refrigerant R22 and R290.
Furthermore, it can be found from Table.2 that the system ro p t has an equal value of 1.63, when refrigerants R32 and R290 are used in the ASHPAC system, but when the system uses the refrigerant R22, the ro p t is 1.71. It means that when the refrigerant R22 is replaced by the R32 and R290 in the ASHPAC system, the volumetric displacement ratio of low-pressure compressor to high-pressure compressor should be decreased. Table 2 further shows that the o p t of the system using R32 and R290 are slightly less and larger than that of the system using R22, at the ro p t . Obviously, the thermal conductance allocated at the evaporator side should be decreased when the system uses refrigerant R32 to replace R22, while it should be increased when the refrigerant R290 is used in the system. Moreover, the p m ,o of the system using R32 shows an obvious increase compared with that of the system using R22. On the contrary, the system using R290 yields lower p m ,o . 4. Conclusions In the study, a theoretical model with lumped parameter method is presented for the optimization of a FTC based air source heat pump air conditioner. The influences of the thermal conductance allocation ratio on system
COP
and the heating capacity
are investigated based on the model. Theoretical analysis results indicate that under the given conditions, there exist optimal thermal conductance allocation ratios corresponding to the maximum
COP
of the ASHPAC system. And the system
heating capacities always increase with the increasing thermal conductance allocation ratio. And then the effects of the main parameters on the determination of the optimal thermal conductance allocation ratio are discussed. When the total thermal 18
Page 18 of 25
conductance ranges from 0.5 to 0.8 kW K 1 , the optimal allocation ratios vary in the ranges of 0.37 - 0.40. In addition, the optimal allocation ratios increase from 0.32 to 0.38 and from 0.31 to 0.38 at the mass flow rate of the fluid heated ranging from 0.1 to 0.3 kg s -1 , and the mass flow rate of air in the evaporator ranging from 0.06 to 0.26 kg s 1 , respectively.
Moreover, the analysis results indicate that there exist the
optimal volumetric displacement ratios with respect to maximizing the system COPmax under the given conditions. When R22 is replaced by the R32 and R290 in the ASHPAC system, the optimal volumetric displacement ratios should be reduced in order to achieve the highest system COPmax . To sum up, the study provides some theoretical guidance for the optimization of ASHPAC system. Certainly, further experimental studies on optimizing the system should also be performed to offer useful validation for residential and commercial applications in the next step. References [1]. K. J. Chua, S. K. Chou, W. M. Yang. Advances in heat pump systems: A review, Appl. Energy 87 (2010) 3611-3624. [2]. W. Wang, Y. C. Feng, J. H. Zhu, L. T. Li, Q. C. Guo, W. P. Lu. Performances of air source heat pump system for a kind of mal-defrost phenomenon appearing in moderate climate conditions, Appl. Energy 112 (2013) 1138-1145. [3]. J. Heo, M. W. Jeong, C. Baek, Y. Kim. Comparison of the heating performance of air-source heat pumps using various types of refrigerant injection, Int. J. Refrig 34 (2011) 444-453. [4]. X. Xu, Y. Hwang, R. Radermacher. Refrigerant injection for heat pumping/air conditioning systems: Literature review and challenges discussions, Int. J. Refrig 34 (2011) 402-415. [5]. S. Xu, G.Y. Ma. Experimental study on two-stage compression refrigeration/heat 19
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pump system with dual-cylinder rolling piston compressor, Appl. Therm. Eng 62 (2014) 803-808. [6]. S. Jiang, S. Wang, X. Jin, T. F. Zhang. A general model for two-stage vapor compression heat pump systems, Int. J. Refrig 51 (2015) 88-102. [7]. H. W. Jung, H. Kang, W. J. Yoon, Yongchan Kim. Performance comparison between a single-stage and a cascade multi-functional heat pump for both air heating and hot water supply, Int. J. Refrig 36 (2 013) 1431-1441. [8]. H. Park, D. H. Kim, M. S. Kim. Performance investigation of a cascade heat pump water heating system with a quasi-steady state analysis, Energy 63(2013) 283-294. [9]. J. H. Wu, Z. G. Yang, Q. H. Wu, Y. J. Zhu. Transient behavior and dynamic performance of cascade heat pump water heater with thermal storage system, Appl. Energy 91(2012) 187-196. [10].
C. Nikolaidis, D. Probert. Exergy-method analysis of a two-stage
vapour-compression refrigeration-plants performance, Appl. Energy 60(1998) 241-256. [11].
E. Torrella, R. Llopis, R. Cabello. Experimental evaluation of the inter-stage
conditions of a two-stage refrigeration cycle using a compound compressor, Int. J. Refrig 32(2009) 307-315. [12].
L. Cecchinato, M. Chiarello, M. Corradi, E. Fornasieri, S. Minetto, P.
Stringari, C. Zilio.
Thermodynamic analysis of different two-stage transcritical
carbon dioxide cycles, Int. J. Refrig 32 (2009) 1058 - 1067. [13].
A. A. Safa, A. S. Fung, R. Kumar. Performance of two-stage variable
capacity air source heat pump: Field performance results and TRNSYS simulation, Energ Buildings 94 (2015) 80–90. 20
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[14].
N. Agrawal, S. Bhattacharyya, J. Sarkar. Optimization of two-stage
transcritical carbon dioxide heat pump cycles, Int. J. Therm. Sciences 46 (2007) 180-187. [15].
A. E. zgür , H. C. Bayrakc. Second law analysis of two-stage compression
transcritical CO2 heat pump cycle, Int. J. Energ. Res 32(2008)1202-1209. [16].
S. S. Bertsch, E. A. Groll. Two-stage air-source heat pump for residential
heating and cooling applications in northern U.S. climates, Int. J. Therm. Sciences 31 (2008) 1282 -1292. [17].
O. Kwon, D. Cha, C. Park. Performance evaluation of a two-stage
compression heat pump system for district heating using waste energy, Energy 57 (2013) 375-381. [18].
Q. C. Xing, W. W. Yang, F. Zhou, Y. L. He. Performance analysis of
different high-temperature heat pump systems for low-grade waste heat recovery, Appl. Therm. Eng 71 (2014) 291-300. [19].
A. Redón, E. Navarro-Peris , M. Pitarch, J. Gonzálvez-Macia, J. M. Corberán,
Analysis and optimization of subcritical two-stage vapor injection heat pump systems, Appl. Energy 124 (2014) 231-240. [20].
B. JAN, J. V. C. VARGAS, M. SOKOLOV. Optimal allocation of a
heat-exchanger inventory in heat driven refrigerators, Inter. J. Heat and Mass T. 38(1995) 2997-3004. [21].
S. S. Bertsch, E. A. Groll. Two-stage air-source heat pump for
residential heating and cooling applications in northern U.S. climates, Int. J. Refrig 31 (2008) 1282 -1292. [22].
S.A. Klein, Design consideration for refrigeration cycles, Int. J. Refrig.
15 (1992) 181–185. 21
Page 21 of 25
[23].
A. Bejan. Entropy generation minimization: the new thermodynamics of
finite-size devices and finite-time processes, J. Appl. Phys 79 (1996) 1191-1218. [24].
S. X. Xu, G. Y. Ma, Q. Liu, Z. L. Liu. Experiment study of an enhanced
vapor injection refrigeration/heat pump system using R32, Int. J. Therm. Sciences 68(2013)103-109. [25].
S. Mancin, D. D. Col, L. Rossetto. R32 partial condensation inside a brazed
plate heat exchanger, Int. J. Refrig 36(2013) 601-611. [26].
E. W. Lemmon, M. L. Huber, M. O. McLinden. 2007. NIST Thermodynamic
and Transport Properties of Refrigerants and Refrigerant Mixtures (REFPROP) Version 8.0. NIST. [27].
X. Jin, S. G. Wang, T. F. Zhang, F. Zu. Intermediate pressure of two-stage
compression system under different conditions based on compressor coupling model, Int. J. Refrig 35(2012) 827-840.
22
Page 22 of 25
Figure Captions Fig. 1 (a) Schematic diagram of air source heat pump system (b) p-h diagram of the cycle LC—low- pressure compressor HC—high- pressure compressor CON—condenser EVA —evaporator FL —flash tank HPT —high pressure throttle
LPT —low pressure throttle
Fig. 2 Flowchart of the calculation procedure Fig.3. The variations of the
and
COP
Fig.4. The variations of the
opt
Qc
with at different
and p m at different
UA
Fig.5. The variations of the t c , t e and t s ( p m ) at different Figs.6. The comparison of the
UA
for R32 UA
for R32
and t p with the
COP
for R32
between the
one-stage and two-stage compression system for R32 Fig.7. The variations of the
COP
and
Qc
with at different m fc for R32
Fig.8. The variations of the
COP
and
Qc
with at different m ae for R32
Fig.9. The variations of the
C O Pm ax
and
opt
with t aei at different t fci for R32
Fig.10. The variations of the
C O Pm ax
and p m with
r
for R32
Fig.11. The variations of the
C O Pm ax
and p m with
r
for R22
Fig.12. The variations of the
C O Pm ax
and p m with
r
for R290
23
Page 23 of 25
Tables Table1 The opt , ro p t , C O Pm ax ,o , p m ,o and Q c,o at different UA for R32 -1 UA (KWK )
opt
ro p t
C O Pm ax ,o
p m ,o (kPa)
0.6 0.7 0.8
0.37 0.39 0.41
1.69 1.63 1.59
3.10 3.33 3.53
931.35 940.39 949.68
Q c,o
(kW)
3.84 3.71 3.63
24
Page 24 of 25
Table 2 The opt , ro p t , C O Pm ax, o , p m ,o and Q c,o for different refrigerant
Refrigerant
opt
ro p t
C O Pm ax, o
p m ,o (kPa)
R32
0.39
1.63
3.33
940.39
3.71
R22
0.4
1.71
3.49
576.65
3.64
R290
0.41
1.63
3.57
551.01
3.61
Q c,o
(kW)
25
Page 25 of 25
S1359-4311(15)01395-2 http://dx.doi.org/doi: 10.1016/j.applthermaleng.2015.11.132 ATE 7429
To appear in:
Applied Thermal Engineering
Received date: Accepted date:
7-9-2015 27-11-2015
Please cite this article as: Yunxiang Li, Jianlin Yu, Theoretical analysis on optimal configurations of heat exchanger and compressor in a two-stage compression air source heat pump system, Applied Thermal Engineering (2015), http://dx.doi.org/doi: 10.1016/j.applthermaleng.2015.11.132. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Theoretical analysis on optimal configurations of heat exchanger and compressor in a two-stage compression air source heat pump system Yunxiang Li, Jianlin Yu Department of Refrigeration & Cryogenic Engineering, School of Energy and Power Engineering, Xi’an Jiaotong University, Xi’an 710049, China
Highlights > Optimization of a flash tank cycle based heat pump system is conducted. >The optimal thermal conductance allocations are obtained under given conditions. >The system heating capacities are affected by thermal conductance allocation. > There exists an optimal compressor displacement ratio for optimum system COP. Abstract This paper presents an optimum system configuration analysis for a flash tank cycle (FTC) based two-stage compression air source heat pump system using a developed theoretical model with lumped parameter method. The analysis is carried out with respect to the thermal conductance allocation of total heat-exchanger inventory (condenser and evaporator) as well as the volume ratio of low-pressure compressor to high-pressure compressor in the system. The analysis results indicate that the heating coefficient of performance (COP) of the heat pump system can be maximized by optimally allocating the thermal conductance inventory of the two heat exchangers. Moreover, there also exists an optimal compressor volumetric displacement ratio, corresponding to the optimum system COP, when the cooling capacity of system is specified. The effects of main operation parameters on the configuration parameters and optimal performances have been discussed. The obtained results may provide some guides for the FTC based air source heat pump system optimization. Keywords: Air source heat pump; Performance optimization; Thermal conductance; Two-stage compression
Corresponding author. Tel: +86-29-82668738. Fax: +86-29-82668725. Email: [email protected] 1
Page 1 of 25
Nomenclature C O P heating coefficient of performance -1
-1
c p specific heat (J kg K ) -1
h specific enthalpy (kJ kg ) -1
m mass flow rate (kg s ) P pressure (kPa)
Q heat transfer rate (kW)
r
volumetric displacement ratio of low-pressure compressor to high-pressure
compressor t
temperature (℃) -1
UA thermal conductance (kW K ) V v
volumetric displacement (m3 s-1) specific volume (m3 kg-1)
W power (kW)
Greek symbols
adiabatic exponent
effectiveness factor of heat exchanger efficiency allocation ratio
Subscripts 2
Page 2 of 25
a air c condenser side d
discharge
e evaporator side f
fluid
h
high
i
inlet
l
low intermediate
m
max
maximum
o outlet opt r
optimal
refrigerant
s isentropic v volumetric
1. Introduction Over the past years, the air source heat pumps have attracted a great deal of attention for their merits of energy-saving and environmental protection [1, 2]. But when they operate at low ambient temperatures, several problems, such as the reduction in the heating capacity and heating coefficient of performance (COP), high compressor discharge temperature, etc., cause some application limitations. In this case, the development of air source heat pumps with higher performances and wider operating temperature range has become a major challenge. For the issues regarding performance degradation of air source heat pumps, some solutions to enhance the heating performance and reliability of the heat pump have been studied, including 3
Page 3 of 25
refrigerant injection technique, two-stage compression systems and cascade system [3-9]. The use of those methods provides more opportunities to apply air source heat pumps in cold regions. Traditionally, two-stage compression systems consisting of two individual compressors have received much attention for refrigeration applications [10-13]. However, they have also been well justified to improve the heating performance of systems for air source heat pump applications in cold climates. Neeraj et al. [14] carried out optimization studies of two-stage transcritical carbon dioxide heat pump cycles, and indicated the flash gas bypass system yields the best performance among the three two stage cycles analyzed. Arif and Hilmi [15] also conducted the second law analysis for a two-stage compression transcritical CO2 heat pump cycle, and identified the main factors that affect the two-stage compression transcritical CO2 system efficiency. Bertsch and Groll [16] investigated an air-source two-stage heat pump using R410A as the refrigerant, and experimentally verified that the heat pump is able to operate at ambient temperatures between -30 ℃ and 10 ℃ with supply water temperatures of up to 50℃. Kwon et al. [17] evaluated a two-stage compression heat pump system for district heating utilizing waste energy, and obtained the system performance characteristics under various operating conditions. Cao et al. [18] analyzed different high-temperature two-stage heat pump systems for low-grade waste heat recovery, and showed that the two-stage heat pump system with flash tank was preferred. Overall, two-stage compression systems could be a good alternative to avoid the performance deterioration of air source heat pumps in cold climates, and those relevant researches can drive their development in low temperature ambient application. For two-stage compression heat pump systems, there are two typical cycle 4
Page 4 of 25
configurations, i.e. flash tank cycle (FTC), and internal heat exchanger cycle (IHXC) [19]. Among these two cycles, the FTC has received more attention in recent years. Basically, previous researches on the FTC are mainly focused on the cycle performance improvement, component optimization or cycle control strategies. In fact, these issues are closely related to the system configurations of FTC. As is well known, the FTC system mainly consists of a flash tank，two compressors, a evaporator and a condenser. The configuration for the FTC systems is particularly involved in the parameters of compressor and heat exchangers, such as the heat exchange area or thermal conductance of heat exchangers and compressor displacement volume [19, 27], which play a key influence on overall system performance. To make effective use of the FTC, it is necessary to explore the relationship between the configuration parameters and the main performance parameters. In this paper, we present an analytical model with lumped parameter method for a FTC based air source heat pump air conditioner. In the model, heat exchanger thermal conductance inventory is considered as a constraint condition for configuring the FTC system [20]. Based on the developed model, the performance and optimum design conditions of the FTC system are analyzed in detail for different configuration parameters and operating conditions. Furthermore we analyzed the relationship of the optimal compressor volumetric displacement ratio and the optimal thermal conductance allocation at different heat exchanger thermal conductance inventory. And the influences of the different refrigerant on system optimal compressor volumetric displacement ratio are investigated. The objective of this work is to provide some theoretical guidance for the optimal design and operation of air source heat pump using the FTC systems. 2. Analytical model of the FTC system 5
Page 5 of 25
The schematic diagram of the FTC system is shown in Fig.1 (a), where the system consists of two compressors, a condenser, a flash tank, two expansion valves and an evaporator. The cycle system includes two circuits: a main refrigerant circuit and a bypass refrigerant circuit. The main circuit refrigerant flow is circulated by the low-pressure compressor through the high-pressure compressor, the condenser, the high pressure expansion valve, the flash tank, the low pressure expansion valve and the evaporator, whereas the bypass circuit flow is circulated by the flash tank through the high- pressure compressor, the condenser, the high pressure expansion valve. Fig. 1(b) shows the detailed working process of the FTC system on pressure-enthalpy diagram. In the condenser, high pressure superheated refrigerant vapor from the highpressure compressor (state 4) is cooled to the saturated or subcooled liquid (state 5) by secondary fluid (indoor air); The refrigerant liquid is expanded through the high pressure expansion valve, and then the two-phase refrigerant at an intermediate pressure (state 6) enters into the flash tank, in which it is separated into the two phase refrigerant include the saturated liquid (state 7) and saturated vapor (state 8). On the one hand, after the saturated liquid passes through the low pressure expansion valve, it is heated by outdoor air in the evaporator to be a saturated or superheated vapor (state 1) and then flows into the low-pressure compressor. On the other hand, after the saturated vapor from the flash tank mixes with the superheating refrigerant vapor (state 2) at the outlet of the low- pressure compressor, the vapor mixture (state 3) is compressed by the high- pressure compressor and then enters to the condenser. For modelling the FTC based air source heat pump system, the condenser and the evaporator were modeled by using the
-NTU method, and two compressors were
modeled based on the efficiency of method, for simulations. Furthermore the following assumptions are made: 6
Page 6 of 25
(1) Refrigerant pressure drops are neglected in the evaporator, the condenser and inlet or outlet of the compressors; (2) Mixing process of refrigerant at the outlet of the low- pressure compressor occurs at a constant intermediate pressure; (3) Refrigerant leaving from the condenser and the evaporator is saturated liquid and saturated vapor, respectively; (4) No heat losses to the environment from the system; (5) The throttling processes in the expansion valves are isenthalpic. Based on the assumptions above, the heating capacity of the condenser can be obtained as （1）
Q c c m fc c pfc ( t c t fci )
where m fc and c pfc are the mass flow rate and specific heat of the heated fluid in the condenser; t c is the condensing temperature, and t fci is the temperature of the fluid heated, at the inlet of the condenser; c is the heat exchanger effectiveness of the condenser, which can be given by Eqs. (2) and (3), c 1 exp ( U c Ac / m fc c pfc )
c
（2）
t fco t fci
（3）
t c t fci
where
U c Ac
is the thermal conductance of condenser, and t fco is the temperature of
the fluid heated, at the outlet of the condenser. It should be noted that when calculating the heating capacity of the condenser using the above Eq. (1) (including Eqs. (2) and (3)), the influence of the condenser superheat section is actually neglected. However, this simplicity may be appropriate because several literatures indicate that sufficient accuracy can be achieved for screening purposes when using an
-NTU model since the inherent errors of over
predicting the conductance in the effectiveness calculations and under predicting 7
Page 7 of 25
the temperature difference in the heat exchanger calculations tend to compensate each other [21, 22]. In addition, based on the energy conservation, the heating capacity of the condenser can be also written as Q c m rc ( h4 h5 )
（4）
where m rc is the mass flow rate of refrigerant in the condenser, h4 and h5 are refrigerant specific enthalpies of inlet and outlet of the condenser. Similarly, the heat transfer rate of the evaporator can be obtained as Q e e m ae c pae ( t aei t e )
（5）
and Q e m re ( h1 h9 )
（6）
where m re and m ae are the mass flow rates of refrigerant and air of the evaporator, h9
and h1 are refrigerant specific enthalpies at the inlet and outlet of the evaporator;
t e is the evaporating temperature, and t aei is the air temperature at the inlet of the
evaporator; c p ae is the air specific heat in the evaporator, e is the heat exchanger effectiveness of the evaporator, which can be given by Eqs. (7) and (8), e 1 exp( U e Ae / m ae c pae )
e
t aei t aeo
（7） （8）
t a ei t e
where U e Ae is the thermal conductance of the evaporator, and t aeo is the air temperature at the outlet of the evaporator. The total input power of compressors can be obtained, W
m re ( h2 s
sl
h1 )
m rc ( h4 s
sh
h3 )
（9）
where h1 and h3 are the refrigerant specific enthalpies at the inlet of the low and high- pressure compressors, respectively; h 2 s and h 4 s are the refrigerant specific enthalpies at the outlet of the low and high- pressure compressors under the isentropic 8
Page 8 of 25
processes; h3 is calculated by the energy balance as given in Eq. (10). h3 h8 q 6 h2 (1 q 6 )
（10）
where h8 is the specific enthalpy of saturated refrigerant vapor in the flash tank, and q 6 is the vapor quality of two phase refrigerant in the flash tank.
In addition, the isentropic efficiencies of the low and high- pressure compressors, sl and sh , can be calculated by Eqs. (11) and (12) [19], sl 1.41(1 e sh 1.41(1 e
where P2
P1
p 2 / p1 0.30 0.21
) 0.52 ln( p 2 / p1 1)
（11）
) 0.52 ln( p 4 / p 3 1)
（12）
p 4 / p 3 0.30 0.21
and P3 are the inlet pressures of the low and high- pressure compressors,
and P4 are the outlet pressures of the low and high- pressure compressors,
respectively. The refrigerant mass flow rates of the low and high- pressure compressors can be calculated by Eqs. (13) and (14), m re
m rc
vlV l v1
（13）
vhV h
（14）
v3
where V l and V h are the volumetric displacements of the low and high- pressure compressors; v1 and v 3 are the refrigerant specific volumes at the inlet of the low and high- pressure compressors; vl and vh are volumetric efficiencies of the low and high- pressure compressors, which are determined by Eqs. (15) and (16) [19]. vl 0.025( p 2 / p1 ) 1.02
（15）
（16） Based on the mass balance, the refrigerant mass flow rate of the high- pressure
vh 0 .0 2 5( p 4 / p 3 ) 1.02
compressor can be also written as
9
Page 9 of 25
m rc
m re
（17）
1 q
The volumetric displacement ratio between the low- pressure compressor and the high- pressure compressor is written as r
Vl
（18）
Vh
It is well known that the total thermal conductance is usually constrained to be finite on both the evaporator side and condenser side for a real air source heat pump system [23]. In order to maximize the performances of the system, it makes sense to consider the total thermal conductance as a design constraint, which is a fundamental design aspect in any real air source heat pump system. Thus, it is assumed that the total thermal conductance is constrained as （19）
U A U c Ac U e Ae C onstant
where
UA
is the total thermal conductance. Note that for a specified
UA ,
there
should be a thermal conductance allocation ratio between two heat exchangers, which represents the configuration relationship between the two heat exchangers. The configuration relationship between the thermal conductance of the two heat exchangers will play a key influence on overall system performance. The allocation of
UA
U e Ae U A
U c Ac (1 )UA
between the evaporator side and condenser side is written as （20） （21）
In general, introducing the thermal conductance allocation ratio is to examine the effect of the configuration relationship between the two heat exchangers on the system performance COP, and then try to find the optimal configuration of the two heat exchangers for obtaining a maximum COP at other 10
Page 10 of 25
given conditions. In following sections, the above model is used for analyzing the configuration optimization of a FTC based air source heat pump air conditioner (ASHPAC) system. Analyses are made with respect to specified volumetric displacements of two compressors or cooling capacity of the system. The optimum configuration parameters, including the and r , and system performances are evaluated under given operation and constraint conditions. An outline of the calculation procedure for the solution of the above model is shown in Fig2. It applied to compute that the variations of the
and Q c with at different
COP
UA .
The calculation procedures
of other cases are similar to those in Fig 2, and need not be repeated here. 3. Simulation results and discussion Recently, the refrigerant R32 used in commercial ASHPACs has attracted much attention due to its relative safety and good environmental friendly properties [24, 25]. And R290 has also become a promising refrigerant used in small domestic ASHPACs to replace the refrigerant R22. Hence, three kinds of refrigerants R22, R32 and R290 are selected as the working fluids of an ASHPAC system to conduct relevant system performance simulations and configuration parameter comparison among systems with different refrigerant. The simulation program is written in Fortran Language, and the required refrigerant properties are calculated by using the property subroutines of REFPROP 8.0 [26]. The relevant configuration parameters of the system are assumed as V l 8.24 10 4 kW K 1 .
3
m s
1
,
V h 4.92 10 4
3
m s
1
, and the
UA
ranging from 0.5 to 0.8
The indoor and outdoor air specific heat is assumed as
c pfc 1 0 0 5 J kg
1
K
1
c pae 1004 J kg
1
K
1
,
, respectively. Considering the FTC based ASHPACs are mainly
applied in the regions with cold climates, simulations are conducted based on winter 11
Page 11 of 25
operating condition. Hence, inlet temperature of outdoor air is assumed as t aei 7 ℃. The inlet temperature of indoor air is assumed as t fci 20 ℃. The mass flow rate of m fc 0.2
indoor and outdoor air is assumed as
kg s
1
, m ae 0.26
kg s
1
,
respectively. Fig.3 shows the variations of the
COP
and Q c with the , at different
where the refrigerant R32 is used in the ASHPAC system. It can be seen that the
UA ,
COP
of the system first increases and then decreases with increasing , which means that there exists a maximum
COP
at the o p t when fixing the
UA .
Furthermore, Fig.3
shows the system COPmax increases from 3.16 to 3.52 when the UA ranges from 0.5 to 1
0.8 kW K . The main reason for this case is that larger UA could lead to a higher evaporating temperature and a lower condensing temperature, resulting in smaller heat transfer temperature difference in both evaporator and condenser. This implies the irreversible losses in the system are reduced, and hence the system with increasing COPmax
UA .
As increasing the
UA ,
increases
however, the increasing tendency of
slows down. For example, the COPmax is increased by 5% when the 1
ranges from 0.5 to 0.6 kW K , while the UA
COPmax
COPmax
UA
is only increased by 3% when the
1
ranges from 0.7 to 0.8 kW K . The results indicate that the increase of
UA
to
improve the system COP should be properly considered in association with the cost of heat exchangers. On the other hand, it is seen from the figure that the system monotonically increasing function of at a constant increasing , the thermal conductance of condenser
UA .
U c Ac
Qc
is a
The reason is that as decreases and that of
evaporator U e Ae increases, which leads to the increases of t c and t e eventually. In this case, the increase of t c results in the decreasing in the specific heating capacity 12
Page 12 of 25
( h4 h5 ). Meanwhile, the p m also increases (as shown in Fig. 4), which leads to the increase of m rc due to the decease of v 3 . For both reasons above, the system Q c eventually shows an increasing tendency with . When the is changed from 0.25 1
to 0.5, the Q c increase by 12% - 19% at the UA in the range of 0.5 - 0.8 kW K . Fig.4 shows the variations of the optimal thermal conductance allocation o p t and the corresponding system intermediate pressure p m with increasing be found that the o p t increases from 0.37 to 0.40 when the
UA
UA .
It can
changes from 0.5 to
0.8 kW K . Obviously, the o p t is smaller than 0.5 at the given conditions, which 1
means that the thermal conductance of the evaporator that of the condenser
U c Ac
should be smaller than
U e Ae
. Furthermore, the o p t increases with the
UA ,
which
means that the thermal conductance allocated at the evaporator side should be increased at a larger
UA .
These results indicate that the performances of a ASHPAC
can be maximized by proper allocating between
U e Ae
and
U c Ac
an important thermal optimization principle, because the
UA
. This allocation is is finite and is
considered to be a significant constraint parameter in the ASHPAC designing. In addition, it can be found that the p m increases from 916.6 to 1001.6 UA
kP a
when the
1
ranges from 0.5 to 0.8 kW K . This results from the effect of two aspects.
Firstly, as increasing UA, the system t e increases, but the t c decreases. Furthermore, when the o p t increases from 0.37 to 0.40, the
U e Ae
increases, and the
U c Ac
decreases, which leads to the increase of t e and t c . In this case, the increments in t e and t c reach 3.45 ℃ and 1.24 ℃ , respectively. Correspondingly, the saturation
13
Page 13 of 25
temperature t s ( p m ) at intermediate pressure increases from 3.79 to 6.68 ℃ , as shown in Fig.5. Thus, the system p m shows an increasing tendency with rising Moreover, the p m and the t e show similar variation trend with the
UA .
UA
.
The main
reason for this is that the t e plays dominant influence on the p m compared with the t c [27].
Figs. 6 shows the variations of the
COP
and discharge temperature t d
with the , for the single-stage and two-stage compression systems, respectively, where the refrigerant is R32 and the
UA
1
is fixed at 0.6 kW K . It can be seen
that when the is changed from 0.25 to 0.5, the
COP
of two-stage compression
system increase by 72% - 69% over that of the single-stage compression system. Furthermore, Fig.6 shows the t d of two-stage compression system varies from 112.6 to 115.1 ℃ when the ranges from 0.25 to 0.5. It is greatly lower than that of the single-stage compression system. When the kW K 1
, the variations of the
is 0.5, 0.7 and 0.8
UA
and t d of single-stage and two-stage
COP
compression system are similar to that in Fig. 6. To sum up, the two-stage compression system is more favorable in terms of the
COP
increase and the
reduction of the discharge temperature. Fig.7 shows the variations of the
COP
and Q c with the at different m fc , 1
where the refrigerant is R32 and the U A is fixed at 0.6 kW K . It can be seen that the maximum
COP
that corresponds to the optimal allocation of the U A inventory
can be obtained at different m fc . The
COPmax
increases from 2.37 to 3.63 when the
m fc ranges from 0.1 to 0.3 k g s 1 . When the m fc ranges from 0.1 to 0.2 k g s 1 , the 14
Page 14 of 25
COPmax
is increased by 40%, while the COPmax is only increased by 9%, when the
m fc ranges from 0.2 to 0.3 k g s 1 . Thus, as the increase of m fc , the increasing
tendency of COPmax weakens. From the figure, it is also observed that the o p t 1
increases from 0.32 to 0.38 when the m fc ranges from 0.1 to 0.3 k g s . Obviously, the thermal conductance allocated at the evaporator side should be increased as increasing the m fc . In addition, it can be seen that the resulting Q c increases monotonically with the , and decreases monotonically as the m fc increases. Note that further increasing m fc does not significantly affects Q c . Overall, The variations of the optimal performance coefficient and heating capacity with respect to the m fc and should be considered compromisingly for optimally configuring the system parameters. Fig.8 further shows the variations of the
COP
and Q c with the at different
m ae . It can be seen that the COP curves for m ae and are similar to those in Fig.
7. Unlike the effect of m fc , however, the Q c increases with increasing m ae at a constant x. This means that the increase of m ae can be beneficial to increasing COPmax
and Q c at the o p t when the U A is specified. In addition, it is found that
the o p t increases from 0.31 to 0.38, when the m ae ranges from 0.06 to 0.26 k g s . 1
Considering the analysis results in both Fig. 7 and 8, it is clear that choosing the appropriate m ae and m fc is important, when designing an optimal ASHPAC system. Fig.9 shows the variations of COPmax and o p t with increasing t aei at different t fci , where the refrigerant is R32 and the
UA
is fixed at 0.6 kW K 1 . It
15
Page 15 of 25
can be seen that when the t aei is changed from -20 to 10 ℃ , the system COPmax is increased by 23% and 22% at the t fci of 20 and 24
℃,
respectively. Fig.9 shows
that as increasing t fci the system COPmax decreases at a constant t aei , which is due to the fact that the system t c increases with increasing t fci . From the figure, it is also observed that the o p t decreases from 0.40 to 0.34 when the t aei ranges from -20 to 10 ℃ . It means that the thermal conductance allocated at the evaporator side should be increased when the ASHPAC systems are applied in the regions with the lower outdoor temperatures. In addition, Fig.9 shows that the o p t has the same values for different t fci , when the t aei is specified. It means that the indoor air temperature almost has no influence on the allocation of the thermal conductance between the evaporator side and condenser side. Furthermore, simulation results show that when the t aei is changed from 10 to -20 ℃ , the discharge temperature t d at the o p t ℃
at the t fci of 20
℃.
increases from 101.8 to 129.7
It means that when the ASHPAC system uses refrigerant
R32, the outdoor temperature cannot be lower than -20 ℃ . As seen above, the previous optimization analysis of heat exchangers configuration is conducted for specifying the volumetric displacements of two compressors. In addition to that, it is usually necessary to specify a certain cooling capacity in the design of an ASHPAC system. In this case, optimization studies for the ASHPAC system, based on its cooling capacity duty, should be performed by considering both heat exchanger and compressor volumetric displacement configurations. Thus, the optimal configurations of heat exchangers and compressor 16
Page 16 of 25
volumetric displacements are analyzed at the specified cooling capacity in the following simulations. Fig.10 shows the variations of the COPmax at the o p t and the corresponding with increasing kW K
1
r
, where the refrigerant is R32 and the
r
r
Qe
are fixed at 0.7
, which means that there exists an
with respect to an optimum value of the
the other hand, it is seen from the figure that the function of
at a constant
r
UA
pm
COPmax when
fixing the
UA .
On
is a monotonically increasing
. Furthermore, the system optimal configuration
parameters including the o p t , ropt and the corresponding different
and
and 2.6 k W , respectively. It can be seen that the system COPmax firstly
increases and then decreases with increasing optimal
UA
pm
C O Pm ax,o ,
p m ,o and Q c,o at
are listed in Table 1. It can be found that the o p t increases from 0.37
UA
to 0.41 and the ropt decreases from 1.69 to 1.59 when the 0.8 kW K 1 . This means that when the
Qe
UA
increases from 0.6 to
is specified, the thermal conductance
allocated at the evaporator side should be increased at a larger
UA ,
whereas the ratio
between the volumetric displacements of both low and high-pressure compressor should be decreased. In addition, it should be mentioned that when from 0.6 to 0.8 kW K 1 , the
C O Pm ax,o
UA
increases
and p m ,o are increased by 13.9% and 2%, and
the Q c,o is decreased by 5.5% under the condition of ropt . Figs. 11 and 12 further show the variations of the COPmax at the o p t and the corresponding the
UA
COPmax
and
Qe
and the
pm
with
r
, at the refrigerant of R22 and R290, respectively, where
are fixed at 0.7 kW K 1 and 2.6 k W . It can be seen that both the pm
curves for
r
are similar to those in Fig. 10. Thus there also 17
Page 17 of 25
exist the ro p t with respect to an optimum value of the COPmax and the corresponding optimal
pm
in the ASHPAC system using the refrigerant R22 and R290.
Furthermore, it can be found from Table.2 that the system ro p t has an equal value of 1.63, when refrigerants R32 and R290 are used in the ASHPAC system, but when the system uses the refrigerant R22, the ro p t is 1.71. It means that when the refrigerant R22 is replaced by the R32 and R290 in the ASHPAC system, the volumetric displacement ratio of low-pressure compressor to high-pressure compressor should be decreased. Table 2 further shows that the o p t of the system using R32 and R290 are slightly less and larger than that of the system using R22, at the ro p t . Obviously, the thermal conductance allocated at the evaporator side should be decreased when the system uses refrigerant R32 to replace R22, while it should be increased when the refrigerant R290 is used in the system. Moreover, the p m ,o of the system using R32 shows an obvious increase compared with that of the system using R22. On the contrary, the system using R290 yields lower p m ,o . 4. Conclusions In the study, a theoretical model with lumped parameter method is presented for the optimization of a FTC based air source heat pump air conditioner. The influences of the thermal conductance allocation ratio on system
COP
and the heating capacity
are investigated based on the model. Theoretical analysis results indicate that under the given conditions, there exist optimal thermal conductance allocation ratios corresponding to the maximum
COP
of the ASHPAC system. And the system
heating capacities always increase with the increasing thermal conductance allocation ratio. And then the effects of the main parameters on the determination of the optimal thermal conductance allocation ratio are discussed. When the total thermal 18
Page 18 of 25
conductance ranges from 0.5 to 0.8 kW K 1 , the optimal allocation ratios vary in the ranges of 0.37 - 0.40. In addition, the optimal allocation ratios increase from 0.32 to 0.38 and from 0.31 to 0.38 at the mass flow rate of the fluid heated ranging from 0.1 to 0.3 kg s -1 , and the mass flow rate of air in the evaporator ranging from 0.06 to 0.26 kg s 1 , respectively.
Moreover, the analysis results indicate that there exist the
optimal volumetric displacement ratios with respect to maximizing the system COPmax under the given conditions. When R22 is replaced by the R32 and R290 in the ASHPAC system, the optimal volumetric displacement ratios should be reduced in order to achieve the highest system COPmax . To sum up, the study provides some theoretical guidance for the optimization of ASHPAC system. Certainly, further experimental studies on optimizing the system should also be performed to offer useful validation for residential and commercial applications in the next step. References [1]. K. J. Chua, S. K. Chou, W. M. Yang. Advances in heat pump systems: A review, Appl. Energy 87 (2010) 3611-3624. [2]. W. Wang, Y. C. Feng, J. H. Zhu, L. T. Li, Q. C. Guo, W. P. Lu. Performances of air source heat pump system for a kind of mal-defrost phenomenon appearing in moderate climate conditions, Appl. Energy 112 (2013) 1138-1145. [3]. J. Heo, M. W. Jeong, C. Baek, Y. Kim. Comparison of the heating performance of air-source heat pumps using various types of refrigerant injection, Int. J. Refrig 34 (2011) 444-453. [4]. X. Xu, Y. Hwang, R. Radermacher. Refrigerant injection for heat pumping/air conditioning systems: Literature review and challenges discussions, Int. J. Refrig 34 (2011) 402-415. [5]. S. Xu, G.Y. Ma. Experimental study on two-stage compression refrigeration/heat 19
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pump system with dual-cylinder rolling piston compressor, Appl. Therm. Eng 62 (2014) 803-808. [6]. S. Jiang, S. Wang, X. Jin, T. F. Zhang. A general model for two-stage vapor compression heat pump systems, Int. J. Refrig 51 (2015) 88-102. [7]. H. W. Jung, H. Kang, W. J. Yoon, Yongchan Kim. Performance comparison between a single-stage and a cascade multi-functional heat pump for both air heating and hot water supply, Int. J. Refrig 36 (2 013) 1431-1441. [8]. H. Park, D. H. Kim, M. S. Kim. Performance investigation of a cascade heat pump water heating system with a quasi-steady state analysis, Energy 63(2013) 283-294. [9]. J. H. Wu, Z. G. Yang, Q. H. Wu, Y. J. Zhu. Transient behavior and dynamic performance of cascade heat pump water heater with thermal storage system, Appl. Energy 91(2012) 187-196. [10].
C. Nikolaidis, D. Probert. Exergy-method analysis of a two-stage
vapour-compression refrigeration-plants performance, Appl. Energy 60(1998) 241-256. [11].
E. Torrella, R. Llopis, R. Cabello. Experimental evaluation of the inter-stage
conditions of a two-stage refrigeration cycle using a compound compressor, Int. J. Refrig 32(2009) 307-315. [12].
L. Cecchinato, M. Chiarello, M. Corradi, E. Fornasieri, S. Minetto, P.
Stringari, C. Zilio.
Thermodynamic analysis of different two-stage transcritical
carbon dioxide cycles, Int. J. Refrig 32 (2009) 1058 - 1067. [13].
A. A. Safa, A. S. Fung, R. Kumar. Performance of two-stage variable
capacity air source heat pump: Field performance results and TRNSYS simulation, Energ Buildings 94 (2015) 80–90. 20
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[14].
N. Agrawal, S. Bhattacharyya, J. Sarkar. Optimization of two-stage
transcritical carbon dioxide heat pump cycles, Int. J. Therm. Sciences 46 (2007) 180-187. [15].
A. E. zgür , H. C. Bayrakc. Second law analysis of two-stage compression
transcritical CO2 heat pump cycle, Int. J. Energ. Res 32(2008)1202-1209. [16].
S. S. Bertsch, E. A. Groll. Two-stage air-source heat pump for residential
heating and cooling applications in northern U.S. climates, Int. J. Therm. Sciences 31 (2008) 1282 -1292. [17].
O. Kwon, D. Cha, C. Park. Performance evaluation of a two-stage
compression heat pump system for district heating using waste energy, Energy 57 (2013) 375-381. [18].
Q. C. Xing, W. W. Yang, F. Zhou, Y. L. He. Performance analysis of
different high-temperature heat pump systems for low-grade waste heat recovery, Appl. Therm. Eng 71 (2014) 291-300. [19].
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heat-exchanger inventory in heat driven refrigerators, Inter. J. Heat and Mass T. 38(1995) 2997-3004. [21].
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[23].
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22
Page 22 of 25
Figure Captions Fig. 1 (a) Schematic diagram of air source heat pump system (b) p-h diagram of the cycle LC—low- pressure compressor HC—high- pressure compressor CON—condenser EVA —evaporator FL —flash tank HPT —high pressure throttle
LPT —low pressure throttle
Fig. 2 Flowchart of the calculation procedure Fig.3. The variations of the
and
COP
Fig.4. The variations of the
opt
Qc
with at different
and p m at different
UA
Fig.5. The variations of the t c , t e and t s ( p m ) at different Figs.6. The comparison of the
UA
for R32 UA
for R32
and t p with the
COP
for R32
between the
one-stage and two-stage compression system for R32 Fig.7. The variations of the
COP
and
Qc
with at different m fc for R32
Fig.8. The variations of the
COP
and
Qc
with at different m ae for R32
Fig.9. The variations of the
C O Pm ax
and
opt
with t aei at different t fci for R32
Fig.10. The variations of the
C O Pm ax
and p m with
r
for R32
Fig.11. The variations of the
C O Pm ax
and p m with
r
for R22
Fig.12. The variations of the
C O Pm ax
and p m with
r
for R290
23
Page 23 of 25
Tables Table1 The opt , ro p t , C O Pm ax ,o , p m ,o and Q c,o at different UA for R32 -1 UA (KWK )
opt
ro p t
C O Pm ax ,o
p m ,o (kPa)
0.6 0.7 0.8
0.37 0.39 0.41
1.69 1.63 1.59
3.10 3.33 3.53
931.35 940.39 949.68
Q c,o
(kW)
3.84 3.71 3.63
24
Page 24 of 25
Table 2 The opt , ro p t , C O Pm ax, o , p m ,o and Q c,o for different refrigerant
Refrigerant
opt
ro p t
C O Pm ax, o
p m ,o (kPa)
R32
0.39
1.63
3.33
940.39
3.71
R22
0.4
1.71
3.49
576.65
3.64
R290
0.41
1.63
3.57
551.01
3.61
Q c,o
(kW)
25
Page 25 of 25