Modeling and simulation of the transcritical CO2
heat pump system
Kai-Hsiang Lin
a,b, Cheng-Shu Kuo
c, Wen-Der Hsieh
c, Chi-Chuan Wang
a,*
aDepartment of Mechanical Engineering, National Chiao Tung University, Hsinchu 300, TaiwanbInstitute of Nuclear Energy Research, Taoyuan 325, Taiwan c
Green Energy Research Laboratories, Industrial Technology Research Institute, Hsinchu 310, Taiwan
a r t i c l e i n f o
Article history:Received 3 February 2013 Received in revised form 1 August 2013
Accepted 5 August 2013 Available online 13 August 2013 Keywords: Carbon dioxide Gas cooler System modeling COP Transcritical
a b s t r a c t
In this study, a CO2transcritical cycle model without imposing any excessive constraints
such as fixed discharge pressure and suction pressure is developed. The detailed geometrical variation of the gas cooler and the evaporator have been taken into account. The model is validated with the experimental measurements. Parametric influences on the CO2system with regard to the effect of dry bulb temperature, relative humidity, inlet water
temperature, compressor speed, and the capillary tube length are reported. The COP in-creases with the dry bulb temperature or the inlet relative humidity of the evaporator. Despite the refrigerant mass flowrate may be increased with the inlet water temperature, the COP declines considerably with it. Increasing the compressor speed leads to a higher heating capacity and to a much lower COP. Unlike those of the conventional sub-critical refrigerant, the COP of the transcritical CO2 cycle does not reveal a maximum value
against the capillary tube length.
ª 2013 Elsevier Ltd and IIR. All rights reserved.
Mode´lisation et simulation du syste`me de pompe a` chaleur au
CO2
transcritique
Mots cle´s : Dioxyde de carbone ; Refroidisseur de gaz ; Mode´lisation du syste`me ; Coefficient de performance ; Transcritique
1.
Introduction
The carbon dioxide refrigeration systems first appeared in 1850 and were used thereafter for a very long period of time. With the advent of the halocarbon refrigerants, natural re-frigerants like carbon dioxide were slowly phased out. How-ever, as is well known that the synthetic refrigerants, either CFC, HCFC, or HFC, cast significant impact on the
environment, thereby raising serious concerns to ban the utilization of the CFC/HCFC/HFC. Hence revisit of the natural refrigerants had caught a lot attention since 1990, and CO2is a
potential candidate for having advantages like environment friendliness, low price, non-flammability and non-toxicity. On the other hand, despite CO2has some drawbacks such as a
rather low critical temperature and an extremely high oper-ational pressure, Lorentzen and Pettersen (1993),Lorentzen
* Corresponding author. E474, 1001 University Road, Hsinchu 300, Taiwan. Tel.:þ886 3 5712121x55105; fax: þ886 3 5720634. E-mail addresses:ccwang@mail.nctu.edu.tw,ccwang@hotmail.com(C.-C. Wang).
w w w . i i fi i r . o r g
Available online at
www.sciencedirect.com
journal homepage: www.e lsevie r.com/locate/ijrefrig
0140-7007/$e see front matter ª 2013 Elsevier Ltd and IIR. All rights reserved.
Nomenclature
A surface area (m2)
Acapi cross section area in the capillary tube (m2)
Af fin area (m2)
Ao total surface area in the airside (m2)
Ap tube area (m2)
Api inside tube area (m2)
Apo outside tube area (tube outside surface area) (m2)
Apm mean tube area, given by
Apm¼ ðApo ApiÞ=ðlnðApo=ApiÞÞ (m2)
b0p slope of a straight line between the outside and inside tube wall temperature (J kg1K1) b0r slope of the air saturation curve at the mean
coolant temperature (J kg1K1)
b0w;m slope of the air saturation curve evaluated at the mean water film temperature on the
fin) (J kg1K1)
b0w;p slope of the air saturation curve evaluated at the mean water film (J kg1K1)
Bo boiling number
COP coefficient of performance Cp specific heat (J kg1K1) dcap capillary tube diameter (m)
di inner diameter of the inner tube of gas cooler (m)
dH hydraulic diameter of the annulus in the gas
cooler (m)
do outer diameter of the inner tube of gas cooler (m)
f friction factor
F correction factor
G mass flux (kg m2)
h heat transfer coefficient (W m2K1)
ho,w total heat transfer coefficient for wet external
fin (W m2K1)
I0 modified Bessel function of 1st kind, order 0
I1 modified Bessel function of 1st kind, order 1
i enthalpy (J kg1)
iai inlet enthalpy of air (J kg1)
iao outlet enthalpy of air (J kg1)
iri saturated air enthalpy evaluated at the refrigerant
inlet temperature (J kg1)
irm saturated air enthalpy evaluated at the average
refrigerant temperature (J kg1)
iro saturated air enthalpy evaluated at the refrigerant
outlet temperature (J kg1)
is,w,m saturated air enthalpy evaluated at the
condensate water film temperature (J kg1) Dim log mean enthalpy difference (J kg1)
K0 modified Bessel function of 2nd kind, order 0
K1 modified Bessel function of 2nd kind, order 1
k thermal conductivity (W m1K1)
kf thermal conductivity of the fin (W m1K1)
kc thermal conductivity of the CO2(W m1K1)
kp thermal conductivity of the tube (W m1K1)
kw thermal conductivity of the water (W m1K1)
L length of gas cooler (m)
LMTD log mean temperature difference (K) LMHD log mean enthalpy difference (J kg1)
_m mass flowrate (kg s1)
MT parameter defined in Eq.(19)(m1)
Ncom compressor speed, rev
n segment number
Nu Nusselt number
p pressure (Pa)
Pl longitudinal tube pitch (m)
Pt transverse tube pitch (m)
Pr Prandtl number
Q heat transfer rate (Watt)
rc radius of the tube collar (m)
req equilibrium radius for circular fin (m)
Re Reynolds number
RH relative humidity
T temperature (C)
Tp,i,m mean temperature of the inner tube wall of the
fin-and-tube evaporator (C)
Tp,o,m mean temperature of the outer tube wall of the
fin-and-tube evaporator (C)
Tr,m mean temperature of refrigerant coolant (CO2) (C)
U overall heat transfer coefficient (W m2K1) Tw,m mean temperature of the condensate water
film (C)
Uo,w overall heat transfer coefficient of the wet
surface (kg m2s1)
Vcom swept volume of the compressor (m3)
v specific volume (m3kg1)
W power consumption of the compressor (W)
x vapor quality
X LockharteMartinelli parameter
xp thickness of the tube (m)
yw thickness of the condensate water film (m)
z axial direction of the capillary tube (m) Greek letters
df thickness of the fin (m)
ε surface roughness in the capillary tube (m)
m dynamic viscosity (Pa s)
r density (kg m3)
f two-phase friction multiplier
hf,wet wet fin efficiency
hisen isentropic efficiency
hv volumetric efficiency Subscripts 1 saturated region 2 superheated region a air b bulk c carbon dioxide
c,i ith segment of carbon dioxide
dis discharge
db inlet dry bulb temperature
eva evaporator
f evaluated at film temperature
g gas
h heating
i ith segment of heat exchanger
(1994, 1995)andRiffat et al. (1996)had shown that the problem of the low critical temperature of the carbon dioxide can be effectively overcome by operating the system in the tran-scritical region. This had led to the revival of the CO2 as a
refrigerant and it is implemented as the transcritical carbon dioxide cycle with the condenser being replaced by a gas cooler.
There had been a number experimental studies associ-ated with the performance of the transcritical CO2system
(e.g. Stene, 2005; Cabello et al., 2008; Aprea and Maiorino, 2009). These studies provided valuable design information from the aspect of practical applications. For further ex-aminations of the transcritical behaviors of the CO2system,
some comprehensive system simulations with thermody-namics base and detailed component modeling may be helpful in practice. However, due to the transcritical nature of the CO2, the performance of the carbon dioxide system
will not be exactly the same as the conventional one. Hence the simulation models developed for the conven-tional systems cannot be directly employed to this system. There were some available system modeling concerning the system performance of the CO2 transcritical cycle as
tabulated in Table 1, including those by Kim et al. (2005), Yang et al. (2010), Sarker et al. (2004, 2006, 2009, 2010),
Yokoyama et al. (2007), Wang et al. (2009) and Yamaguchi
et al. (2011).
The abovementioned developed system model provided many in-depth contents about the transcritical features of the CO2system. Nevertheless the foregoing models all had
some excessive constraints in the simulation, such as con-stant suction superheat, suction pressure, discharge pres-sure, or a given compressor power. Yet some of the modeling is thermodynamics base and lacked some detailed influence of the heat exchangers (gas cooler or evaporator). Note that the actual system response normally floats when the oper-ating conditions of the heat exchangers vary. As a result, the actual response of the CO2system may not be so realistic due
to excessive constraints. Hence it is the main purpose of this study to propose a comprehensive system model to relax all these restrictions, and to include some detailed modeling of the heat exchangers, including gas cooler and the fin-and-tube heat exchanger, that can take into account the complex
variations of the geometrical parameters and inlet
conditions. in inlet l liquid phase o outlet s saturation sp single phase suc suction t total tp two phase v vapor phase w water wet wet
wb inlet wet bulb temperature
wall wall
Table 1e Comparisons of the available CO2system simulation model.
Study Gas cooler Evaporator Expansion
device model
Inner HX Excessive controlled
conditions
Kim et al. (2005) Water
Tube-in-tube
Water Tube-in-tube
Di ¼ 0 Yes Pdis, Tsup
Yang et al. (2010) Water
Shell-tube
Water Shell-and-tube
_
Wexp¼ Grði3 i4;isÞ hexp;is hexp;m
No Pdis
Sarker et al. (2006) Water
Tube-in-tube
Water Tube-in-tube
Di ¼ 0 Yes Maximum COP
Yokoyama et al. (2007) Water
Tube
Water Tube
Di ¼ 0 No _mCo2; Peva; Tci;gc
Yamaguchi et al. (2011) Water
Tube-in-tube
Air
Fin-and-tube
Di ¼ 0 Yes Wcom
Wang et al. (2009) Water
Tube-in-tube
Water Tube-in-tube
Di ¼ 0 No Maximum COP
Sarker et al. (2004) No description No description Di ¼ 0 Yes Teva, Tco,gc, Maximum COP
Sarker et al. (2009) Water
Tube-in-tube
Water Tube-in-tube
Di ¼ 0 No Pdis,
Degree of superheat
Sarker et al. (2010) Water
Tube-in-tube
Water Tube-in-tube
Di ¼ 0 No Pdis, Psuc
This study Water
Tube-in-tube
Air
Fin-and-tube
2.
Numerical method
The carbon dioxide heat pump system is shown inFig. 1and it is consisted of a gas cooler, an evaporator, a compressor, and an expansion device. Water is supplied to the gas cooler to absorb heat from CO2and the air at the ambient temperature
enters the fin-and-tube evaporator. The gas cooler is a double-pipe heat exchanger as shown inFig. 2(a) with a counter-flow arrangement (Fig. 2(b)) and a fin-and-tube heat exchanger having plain fin configuration inFig. 2(c) is used as the evap-orator. The expansion device in this study is a capillary tube as shown inFig. 2(d). Further details of the components modeling is summarized in the subsequent sections.
2.1. Gas cooler
The gas cooler is a double-pipe heat exchanger with the water flowing in the annulus and the CO2flowing counter-currently
along the inner tube as shown inFig. 2(a). Some basic as-sumptions for analyzing the gas cooler are summarized as follows:
1. The pressure drop of the water and the carbon dioxide in the heat exchangers and connecting pipes are negligible. 2. The heat transfer process for the water within the
gas-cooler is single-phase only.
3. Heat loss to the ambient is negligible.
With the tremendous property variation of the CO2at the
transcritical region, the gas cooler must be discretized into tiny segments and the energy conservation equations in every segment must be employed. A prior sensitivity analysis of the influence of the segments on the overall accuracy was per-formed, and a total of 65 segments were used in the simula-tion (Yu et al., 2012). A schematic showing the variation of the temperature of the CO2and the water is shown inFig. 2(b),
where the subscript c denotes the CO2and w represents the
water. The heat balance between the water and the CO2in
each segment i can be expressed by the following equations:
Qi¼ _mcCpc;iTc;i Tc;iþ1¼ _mwCpw;iTw;i Tw;iþ1: (1)
Qi¼ ðUAÞi ðLMTDÞi: (2)
The overall heat transfer coefficient is obtained from 1 UA¼ 1 hwAo;iþ lndo di 2pkwallLþ 1 hcAi;i: (3)
The physical properties of the CO2are a function of the local
pressure and temperature, and the properties of the water are related to the local temperature. The relevant properties are obtained from REFPROP 8.0 (2007). The heat transfer coeffi-cient of the CO2is based on the correlation ofDang and Hihara (2004), i.e. hc¼ Nuckc=di: (4) Nuc¼ fc 8 ðReb 1000ÞPrc 1:07 þ 12:7 ffiffiffifc 8 q Pr23 c 1 : (5) Carbon dioxide Water
(a) Schematic of the gas cooler – tube in tube heat exchanger.
Tc,1 Tc,2 Tc,3 Tw,1 Tw,2 Tw,3 Tc,i Tc,i +1 Tw,i Tw,i +1 CO Water
(b) Counter flow arrangement of the gas cooler.
(c) Schematic of the fin-and-tube evaporator.
Single phaseregion
Two phase region
Gas cooler
outlet Evaporator inlet
(d) Schematic of the capillary tube.
Fig. 2e Schematics of the major components (a), (b): gas cooler; (c): evaporator; and (d) capillary tube.
Gas cooler (water)
Evaporator (air)
Compressor Capillary tube
Fig. 1e Schematic diagram of the CO2system. (a)
Schematic of the gas cooler-tube in tube heat exchanger.(b) Counter flow arrangement of the gas cooler. (c) Schematic of the fin-and-tube evaporator. (d) Schematic of the capillary tube.
where Pr¼ 8 > > > > > > < > > > > > > : Cpb;cmb;c=kb;c; for Cpb;c Cp Cpb;cmb;c=kf;c; for Cpb;c< Cp and mb;c=kb;c mf;c=kf;c Cpb;cmf;c=kf;c; for Cpb;c< Cp and mb;c=kb;c < mf;c=kf;c : (6) Cp¼ ib;c iwall;c Tb;c Twall;c: (7) Reb¼ Gdi mb;c: (8) fc¼ ½1:82logðRebÞ 1:64-2: (9)
where the subscript b represents the evaluation at the bulk temperature, wall is evaluated at the wall temperature and f denotes the value at the film temperature. The film temper-ature, Tf, is defined as Tf¼ (Tbþ Twall)/2. In contrast, the heat
transfer coefficient for the water side, hw, is obtained via the Gnielinsk (1976)correlation: hw¼ Nuwkw=dH: (10) Nuw¼ fw 8 ðRew 1000ÞPrw 1:07 þ 12:7 ffiffiffiffifw 8 q Pr23 w 1 : (11) where fw¼ ½1:82logðRewÞ -1:64-2: (12) 2.2. Evaporator
Heat transfer in the airside of the evaporator involves both heat and mass transfer. Thus, the enthalpy-based method proposed byThrelkeld (1970)is adopted. The heat transfer rate in the evaporator is calculated as
Qeva¼ _maðiai iaoÞ: (13)
where iaiand iaoare the inlet and outlet enthalpy of the air
flow. The rating equation of the dehumidifying heat exchanger, according toThrelkeld (1970), is:
Qeva¼ UowAoFDim: (14)
where Uowis the enthalpy-based overall heat transfer
coeffi-cient, F is the correction factor and Dim is the log mean
enthalpy difference. For counter flow arrangement, Dim is
given as follows (Bump, 1963; Myers, 1967) Dim¼ði
ai iroÞ ðiao iriÞ
lniaiiro iaoiri
: (15)
The enthalpy-based overall heat transfer coefficient Uo,win
Eq.(14)is evaluated as (Wang et al., 1997):
Uo;w¼ 2 6 4b0rAo hiAp;iþ b0pxpAo kpAp;mþ 1 ho;w Ap;o b0 w;pAoþ Afhf;wet b0 w;mAo 3 7 5 1 : (16) where ho;w¼ Cpa1 b0w;mhc;oþ yw kw : (17)
Note that ywin Eq.(17)is the thickness of the condensate
water film. A constant of 0.005 inch of the condensate film was proposed byMyers (1967). In practice, yw=kw accounts only
0.5e5% comparing to Cpa=b0w;mhc;oand is often neglected by
previous investigators (Wang et al., 1997). As a result, this term is not included in the final analysis. The wet fin efficiency in Eq.(16)is calculated as:
hwet;f¼ 2rc MT r2 eq r2c K1ðMTrÞI1 MTreq K1 MTreq I1ðMTrcÞ K1MTreqI0ðMTrcÞ þ K0ðMTrcÞI1MTreq : (18) where MT¼ ffiffiffiffiffiffiffiffiffiffiffiffi 2ho;w kfdf s ¼ ffiffiffiffiffiffiffiffiffiffiffi 2hc;o kfdf s ffiffiffiffiffiffiffiffiffiffi b0 w;m Cpa s : (19)
rcis radius including collar and reqis the equivalent radius for
circular fin. For the present plate fin geometry, Threlkeld (1970)recommended the following approximation:
req¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffi pt pl p r : (20)
Notice that the evaluation of wet fin efficiency is quite controversy in the open literature. Interested readers should refer to the article byLin et al. (2001)for further discussion. The present study adopts the enthalpy-based wet fin effi-ciency. Also shown in Eq. (16), there are four quantities ðb0
w;m; b0w;p; b0p; and b0rÞ involving enthalpy-temperature ratios
that must be evaluated. The quantities of b0p; and b0rcan be
calculated as: b0r¼ is;p;i;m ir;m Tp;i;m Tr;m: (21) b0p¼iTs;p;o;m is;p;i;m p;o;m Tp;i;m: (22)
The values of b0w;p and b0w;m are the slope of the saturated enthalpy curve evaluated at the outer mean water film tem-perature that is at the base surface and at the fin surface. Without loss of generality, b0
w;pcan be approximated by the
slope of the saturated enthalpy curve evaluated at the base surface temperature (Wang et al., 1997). Unfortunately, there is no explicit way to determine b0
w;m, and it must be obtained
by trial and error procedures. The evaluation procedure is as follows:
(1) Assume a value of Tw,mand determine its corresponding
value of b0w;m.
(2) Obtain the overall heat transfer coefficient, ho,w, from Eq. (17).
(3) Evaluate the wet fin efficiency from Eq.(18).
(4) Calculate the enthalpy-based overall heat transfer coeffi-cient Uo,wfrom Eq.(16).
is;w;m¼ i Cp;aho;whwet;f b0 w;mhc;o 1 Uo;wAo " b0r hiAp;iþ xpb0p kpAp;m #! ði ir;mÞ: (23) (6) Determine Tw,m at is,w,m. If it is not the same with the
assumed value, assume a new value and repeat the procedure.
The detailed empirical correlations for various fin patterns of the sensible heat transfer coefficients hc,oin wet conditions
were summarized byWang (2000)andWang et al. (2001). In this study, the plain fin geometry is used for the simulation and experimentation. Note that the corresponding plain fin correlation is from Wang et al. (1997) since the present simulation range and geometry falls within the scope of the test ranges of their data. The applicable range of their corre-lation is as follows:
Pt(transverse pitch): 25.4 mm,
Pl(longitudinal pitch): 22 mm.
Nominal tube diameter (tube diameter): 9.52 mm. Frontal velocity: 0.3e4 m s1.
Relative humidity: 50e90%.
Calculation of the two-phase evaporation heat transfer coefficient is based on the Hihara and Tanaka correlation
(2000)applicable for in-tube evaporation of the CO2. i.e.
heva;c hlo ¼ C1 Boþ C2 1 Xtt 2=3 : (24)
Where C1 and C2 are the empirical coefficients
(C1¼ 1:4 104; C2¼ 0:93) and Xtt is the LockharteMartinelli (1949)variable, and is given by
Xtt¼ 1 x x 0:9 r g;c rl;c 0:5 m l;c mg;c !0:1 : (25)
hlois the heat transfer coefficient corresponding to the liquid
phase flowing at the total mass flowrate, calculated from the DittuseBoelter equation:
hlo¼ 0:023Re0:8l;cPr0:4l;c
kl;c
di :
(26) where kl,cis the liquid thermal conductivity of the CO2. Notice
that the two-phase CO2in the evaporator may fully evaporate
to become superheated vapor where only single phase heat transfer takes place. As a consequence, simulation of the evaporator must be divided into two regions, namely the two-phase region and the single two-phase region. The total heat transfer surface of the fin-and-tube heat exchanger A is equal to:
A¼ A1þ A2: (27)
Where the subscript 1 represents the two-phase evaporation region and 2 denotes the superheated single-phase region. The superheated single-phase heat transfer coefficient can be obtained from theGnielinsk (1976)correlation (Eq.(11)).
2.3. Capillary tube
The expansion process is via a capillary tube in which an isenthalpic process is fulfilled. A schematic of the capillary tube is shown in Fig. 2(d). The continuity and the energy equations are as follows:
_mc;o _mc;i¼ 0: (28)
_mc;oic;o _mr;iic;i¼ 0: (29)
As shown in Fig. 2(d), the capillary tube undergoes both single- and two-phase process. It is imperative to calculate the total pressure drop of the capillary tube. The pressure drop of single-phase region can be easily obtained. For the two-phase region, the homogenous two-phase flow model is adopted with the mean two-phase viscosity being evaluated as (McAdams et al., 1942): 1 mtp¼ 1 x ml þ x mg: (30) where x is the vapor quality and the subscripts tp, l, and g represents the two-phase, the saturated liquid, and the satu-rated vapor, respectively.
The variation of the pressure gradient in the two-phase region comprises the wall friction and the flow acceleration, and is calculated as (Agrawal et al., 2011):
dp dz¼ G 2 ftp v 2dcapþ dv dz : (31)
where p is the local pressure in the capillary tube, G is the mass flux, v is the specific volume, and dcapis the diameter of
the capillary tube. The two-phase friction factor is evaluated based on the Lin et al.’s correlation(1991):
ftp¼ ftpfsp v sp vtp : (32) ftp¼ 2 6 4 8=Retp 12 þA16 tpþ B16tp 3=2 8=Resp 12 þA16 spþ B16sp 3=2 3 7 5 1=12 1þ x v g vl 1 : (33) A¼ 2:457ln 1 7=Retp 0:9 þ 0:27ε=dcap ! ; B ¼37530 Retp : (34) Retp¼ Gdcap mtp : (35) where f is the Fanning friction factor, f is the two-phase frictional multiplier and the subscript sp represents the sin-gle phase and Re is the Reynolds number.
2.4. Compressor
The continuity and the energy equations of the compressor are as follows:
_mc;o _mc;i¼ 0: (36)
The isentropic efficiency hisenand the volumetric efficiency
hvare defined as follows:
hisen¼
ic;isen ic;i
ic;o ic;i : (38)
hv¼
_mc;i
rc;iVcomNcom:
(39) where Vcomis swept volume of the compressor, Ncomis the
compressor speed and rc,i is the inlet density into the
compressor. The volumetric efficiency hvand the isentropic
efficiency hisenare estimated from the correlations bySarkar et al. (2010): hv¼ 0:9207 0:0756 pdis psuc þ 0:0018 pdis psuc 2 : (40) hisem¼ 0:26 þ 0:7952 pdis psuc 0:2803 pdis psuc 2 þ 0:0414 pdis psuc 3 0:0022 pdis psuc 4 : (41) where pdisis the compressor discharge pressure, and psucis
the compressor suction pressure.
2.5. Numerical procedure
The system model is consisted of four major modules (compressor, capillary tube, gas cooler, and evaporator). Implementation of the system model requires the integration of the separate modules. The most influential design
Input Evaporator dimensions, Gas cooler dimensions, Capillary tube dimensions, Compressor data, Air inlet parameters and
water inlet parameters.
Initial guess: compressor inlet pressure
Guess: evaporator outlet temperature
Guess: compressor outlet pressure
Calculate: refrigeration mass flow rate
Calculate: gas cooler outlet conditions
Calculate: capillary tube outlet conditions
Capillary tube outlet pressure = compressor inlet
pressure?
Update compressor outlet
pressure
Evaporator heat balance?
Update compressor inlet conditions No No Outputs: state points, COP Yes Yes
Fig. 3e Flow chart for the simulation model. (a) Exterior (back view). (b) Exterior (front view). (c) Schematic of the system and sensor locations.
parameters are the refrigerant mass flowrate, the discharge pressure, the suction pressure, and the suction temperature before entering the compressor. However, these design pa-rameters are inter-connected. Thus, it is necessary to obtain these design parameters by iteration. The iteration of the system modeling requires the balance of the high pressure side (compressor, gas cooler, and the capillary tube) and the low pressure side (evaporator). Calculation was first per-formed in the compressor to obtain the CO2mass flowrate in
the high pressure side. The mass flowrate in the high pressure side is then used consecutively to obtain the exit condition of the gas cooler, the capillary tube, and the evaporator. The relevant exit conditions are then used to check whether the initial guesses were met. The solution algorithm can be seen fromFig. 3. Relevant procedures are summarized as follows:
a. (1) Input the geometrical parameters and the configura-tions of the major components (gas cooler, evaporator, capillary tube, and compressor speed).
(2) Prescribe the inlet conditions (the dry, wet bulb tem-perature and the frontal velocity) of the incoming air into the evaporator.
(3) Prescribe the inlet water condition into the gas cooler (inlet water temperature, and the mass flowrate) (3) Guess the inlet suction temperature, the suction
pressure, and the discharge pressure.
b. Based on the compressor model, evaluate the mass flow-rate _mc;comp across the compressor and the outlet state
(enthalpy and the discharge temperature) of the
compressor.
c. From the exit condition of the compressor as the inlet state of the CO2into the gas cooler, calculate the heat transfer
rate, pressure drop, and the exit state of the gas cooler. Note that due to the tremendous variation of the CO2
property, the gas cooler is further divided into tiny segments.
d. From the exit condition of the gas cooler and the mass flowrate, _mc;capi¼ _mc;comp, to estimate the exit pressure of
the capillary tube. If the exit evaporating pressure is not equal to the originally guessed suction pressure, repeat process a.
e. Based on the exist sate of the capillary tube, calculate the heat transfer rate, friction loss, and the exit state of the evaporator. Check the exit temperature and the capacity of the gas cooler against the summation of the evaporator capacity and the compressor work. If these values are not the same, readjust the initial guesses of suction tempera-ture and the gas cooler pressure. Repeat the process a to f until it converges.
g. End the system program and dump the calculated results.
3.
Experimental setup and verification of
experiments and simulation
An experimental CO2 system is made available to verify
the proposed model. The CO2 system contains a
semi-hermetic compressor (Danfoss TN 1410 reciprocating-type compressor), a gas-cooler, a capillary tube and a fin-and-tube evaporator. A layout of the instrumented test facility is
shown inFig. 4(a),(b) and (c) depicts the location of the mea-surements. A magnetic flowmeter is used to record the flow-rates of water in the gas cooler. The magnetic flowmeter was calibrated in advance with a calibrated accuracy of 0.002 L s1. Two absolute pressure transducers are installed at the inlet of
Table 2ae Specifications of the gas cooler used for experimental testing.
Description
Type of Heat exchanger Tube-in-tube
Inner tube CO2
Outer tube Water
ID of inner tube (mm) 12
OD of inner tube (mm) 18
ID of outer tube (mm) 27
Tube length (m) 2.58
Tube material Copper
Solder AISI 316
Fig. 4e Schematics of the experimental CO2refrigerated
cabinet and its components and measurements: (a) exterior (back view) (b) exterior (front view) (c) Schematic of the system and sensor locations. (a) COPh. (b) Heating
the gas cooler and evaporator with resolution up to 0.1 kPa. The inlet and outlet of the gas cooler and evaporator are measured by RTDs (Pt100U) having a calibrated accuracy of 0.1C. Some details of the geometric configurations of the gas cooler and the evaporator are shown inTable 2a and 2b. To verify the validity of the proposed simulation model of the transcritical CO2cycle, simulation results are then compared
with those measured results from the experiment. The simulation results are obtained based on the same conditions of the experimental conditions which are listed inTable 3. The compressor speed is equal to the rated value with the system COPhbeing defined as follows:
COPh¼
Qh
W (42)
where W is the power consumption of the compressor, and Qh
is the heating capacity of the gas cooler. Fig. 5shows the comparison of the predicted COPhand the heating capacity
against the measurements. As seen inFig. 5, the predicted results are in favorable agreements with the experimental results. The maximum difference between the predicted and measured COPh is 5.6% with a mean average difference of
2.2%. The results suggest the applicability of the proposed model. Hence, further detailed parametric calculations are made to explore the system response of the CO2transcritical
cycle. The standard condition used for calculations is shown inTable 4a and the detailed geometrical configurations of the major components used for simulations are tabulated in
Table 4b.
4.
Results and discussion
The effect of the dry bulb temperature on the system perfor-mance is shown inFig. 6. The corresponding mass flowrate of
-5% Calculated COP 2.0 2.5 3.0 3.5 4.0 4.5 Experimental COP 2.0 2.5 3.0 3.5 4.0 4.5 +5%
(a) COP
h.Calculate heating capacity (Watt)
700 800 900 1000 1100 1200
Experimental heating capacity ( Watt )
700 800 900 1000 1100 1200 +5% -5%
(b) Heating capacity.
Fig. 5e Comparison between the experimental measurements and simulations: (a) COPh; (b) Heatingcapacity. (a) Variation of CO2mass flowrate. (b) Variation of
system COPh. (c) Variation of suction and discharge
pressure. (d) Variation of heating capacity and power consumption.
Table 3e Test inlet conditions at the gas cooler and evaporator of the experimental run.
Variant Tdb (C) Twb (C) Tw,i (C) Vfr (m s1) _mw (kg s1) Run1 19.5 16.2 18.6 1.12 0.11 Run2 19.5 15.9 22.4 1.12 0.12 Run3 19.4 16.4 14.6 1.12 0.14 Run4 19 15.8 25.4 1.12 0.12 Run5 20.3 15.5 18.1 1.12 0.12 Run6 18.9 16.0 20.7 1.12 0.13 Run7 19.4 16.3 26.2 1.12 0.12 Run8 18.8 15.3 24.3 1.12 0.12 Run9 18.7 16.2 14.9 1.12 0.11 Run10 19.4 15.5 11.4 1.12 0.11 Run11 18.5 16.2 30.5 1.12 0.12 Run12 18.5 16.1 28.3 1.12 0.11
Table 2be Specifications of the fin-and-tube heat exchanger used for experimental testing. Description
Heat exchanger type Fin-and-tube heat exchanger
Transverse tube spacing (mm) 25.4
Longitudinal tube spacing (mm) 22
Outside tube diameter (mm) 9.52
Inside tube diameter (mm) 8.2
Tube material, tube arrangement Cu, staggered
Fin spacing (mm) 4
Fin thickness (mm) 0.15
Number of tube rows 5
Number of tubes per row 4
the CO2, the COPh, the suction pressure, the discharge
pres-sure, the heating capacity of the gas cooler, the cooling ca-pacity of the evaporator, and the power consumption vs. inlet dry bulb temperature at the evaporator is shown in the figure. The results show that the system COPhincreases with the rise
of the dry bulb temperature and the heating/cooling capacity of the gas cooler/evaporator also rise with the dry bulb tem-perature. However, the power consumption remains nearly the same. Moreover, the mass flowrate of the CO2 and the
pressure at the inlet and outlet of compressor tend to increase. The appreciable rise of mass flowrate of the CO2is the main
reason of increasing heating capacity and the COPh.On the
other hand, with a rise of the dry bulb temperature, it appears that the evaporation temperature is also increased, thereby leading to a rise of COPhand the heating/cooling capacity. This
is analogous to the conventional refrigerant system. Similar influence caused by raising the inlet frontal velocity is also seen in the figure. Despite the system performance is appre-ciably improved by raising the dry bulb temperature, the synchronous rise of the discharge pressure eventually place a upper limit on the dry bulb temperature due to the concerns of
the mechanical failure. The effect of the relative humidity on the system performance subject to the inlet dry bulb tem-perature of 20C and 30C are shown inFig. 7. The influence of the relative humidity is very similar to that of the dry bulb temperature. This is because the corresponding latent load rises when the relative humidity is increased, thereby leading to an appreciable rise of the evaporator temperature. Accordingly the increase of the relative humidity results in a higher discharge pressure and the system COPh. However, it
should be mentioned that the corresponding increase of the discharge pressure, suction pressure, and mass flowrate is less pronounced as compared to that of the dry bulb temper-ature. This is somehow expected for a fixed dry bulb tem-perature places an upper limit of the suction temtem-perature.
Fig. 8shows the effect of the inlet water temperature into the gas cooler on the system performance. The general system response subject to the inlet water temperature in the gas cooler is analogous to those of the dry bulb temperature. However, it appears that both of the system COPhand the
heating capacity are decreased with the rise of the inlet water temperature. The results are in line with the conventional refrigeration system that increasing the condensing temper-ature will result in a decrease of the system COPh. Notice that
raising the dry bulb temperature also leads to a rise of the discharge pressure at the gas cooler but it reveals a steady increase of the system COPh. The main reason for the
decreasing COPhwith respect to the effect of the inlet water
temperature is associated with the difference in CO2
refrig-erant mass flowrate as shown inFig. 8. When compared to the influence of the dry bulb temperature, it is found that the mass flowrate can be increased as much as 35% when the dry bulb temperature is increased from 15 to 30C. However, the rise of the mass flowrate is less than 8% when raising the water inlet temperature from 5 to 30C. The gigantic differ-ence gives rise to a decrease of the heating capacity and the system COPh. The other reason for decreasing COPhis
attrib-uted to the dramatic change of thermophysical properties around the pseudocritical temperature. The decreasing trends subject to the inlet water temperature are in line with some existing experimental measurements, e.g. Stene (2005) and
Goodman et al. (2011).Stene (2005)showed that the system COPhis almost linearly decreased against the rise of the water
coolant temperature, ranging from 12% to 25% when the inlet water temperature is raised from 5 to 30C. Analogous results were also reported byGoodman et al. (2011)who showed that the relative decline of the system COPh, is about 30e40% when
the inlet water temperature is raised from 5 to 35C. InFig. 8, one can also see that the relative decline of the system COPh
for _mw ¼ 0.2 kg s1 is more pronounced than that of
_mw¼ 0.08 kg s1despite _mw¼ 0.2 kg1gives a higher heating
capacity. This is attributed to a much better heat transfer performance of _mw¼ 0.2 kg s1in the gas cooler that leads to a
much lower pressure.
Fig. 9shows the effect of the compressor speed on the mass flowrate of the CO2, the system COP, the discharge pressure,
the suction pressure, the heat transfer capacity of the gas cooler and the evaporator, and the power consumption. The results show that the system COPhremarkably decreases with
the compressor speed despite appreciable increases of the mass flowrate and the heating capacity are encountered. The Table 4ae Standard simulation conditions.
Water Flow rate kg s1 0.11e0.14
Inlet temperature C 10e30
Air Frontal velocity m s1 1.12
Inlet dry bulb temperature C 18e20
Inlet wet bulb temperature C 15e17
Capillary tube Length m 5.0
Compressor Diameter mm 0.95
Speed rpm 3500
Capacity cc 1.5
Table 4be Geometrical configurations of the major components for simulation.
Water Mass flow rate kg s1 0.08e0.20
Inlet temperature C 5e30
Air Flow rate ms1 1.12
Inlet temperature (dry bulb) C 15e30 Inlet temperature (wet bulb) C 10e25
Capillary tube Length m 2.0
Compressor Diameter mm 1.8
Rotary speed rpm 3500
Capacity cc 14
Gas cooler Inner tube ID mm 12
Inner tube OD mm 18 Outer tube ID mm 27 Evaporator Length m 6.5 Height mm 677 Width mm 189.6 Tube diameter mm 7.35
Transverse tube spacing mm 25.4
Longitudinal tube spacing mm 19.05
Fin spacing mm 1.6
Fin thickness mm 0.115
Number of tube row 2
sharp decline in COPh is attributed to two major reasons.
Firstly, a higher compressor speed leads to a larger compres-sion ratio. In this case, the comprescompres-sion ratio varies from 1.8 to 3.2 as the compressor speed is increased from 1500 to 5000 rpm which suggests an approximately 15% decline of volumetric efficiency based on the evaluation from Eq.(40). On the other hand, the simultaneous increase of the discharge pressure and the decline of the suction pressure results in a considerable rise of the required compressor power. Conse-quently, a detectable deterioration of the COPh emerges.
Basically, the results are analogous to the conventional refrigeration system.
Fig. 10shows the effect of the length of capillary tube on the system performance. As shown in the figure, it appears that the system COPhshows a very slightly increases vs. the
capillary tube length. Notice that the variation of the discharge and suction pressure is similar to that of increasing compressor speed. However, the rise of the discharge pressure and the decline of suction pressure are much smaller than that in increasing the compressor speed. The variations of the Fig. 6e Effect of the dry bulb temperature on (a) CO2mass flow rate; (b) COPh; (c) discharge and suction pressure; (d) Heating
capacity and power consumption. Simulation is performed with RH[ 50%, Tw,i[ 10C, _mw[ 0.08 kg sL1, Lcap[ 2.0 m,
dcap[ 1.2 mm, Ncom[ 3500 rpm. (a) Variation of CO2mass flowrate. (b) Variation of system COPh. (c) Variation of suction
COPh with the capillary tube length differ from those
commonly observed in the conventional refrigeration system (e.g.Reddy et al., 2012). For a conventional refrigerant oper-ated in the sub-critical region with a given capillary tube diameter, normally a maximum COP is attainable for a specific capillary tube length. Yet a detectable decrease of the COP is encountered if the capillary tube length is increased further. However, it is found that in the present transcritical operation where the COPhreveals a continuous increase with respect to
the capillary tube length. Even though the amount of increase is relatively small, but it shows no sign of achieving a maximum COPhwhen the capillary tube length is increased
from 0.5 to 3.5 m. To explain this unusual characteristic, one must resort to the difference of the variation of the enthalpy subject to the vapor pressure between the present CO2and the
conventional refrigerant such as R-134a as shown inFig. 11. For a conventional refrigerant like R-134a, the pressure rise results in a smaller enthalpy change since the major heat transfer mechanism in the condenser is latent heat as shown in Fig. 11(b). For instance, a 28% decrease in latent heat is observed for R-134a when the pressure is increased from 3 to 3.5 MPa. On the other hand, the enthalpy decline from 8 MPa to 10 MPa for the CO2in transcritical operation in the
tem-perature span of 300e360 K is less than 4% as shown in Fig. 7e Effect of the relative humidity on (a) CO2mass flow rate; (b) COPh; (c) discharge and suction pressure; (d) Heating
capacity and power consumption. Simulations are performed at Vfr[ 1.1 m sL1, Twi[ 10C, _mw[ 0.2 kg sL1, Lcap[ 2.0 m,
dcap[ 1.2 mm, Ncom[ 3500 rpm. (a) Variation of CO2mass flowrate. (b) Variation of system COPh. (c) Variation of suction
Fig. 11(a). In addition, raising the discharge pressure of the CO2
also accompanies with a significant increase of the CO2
tem-perature, thereby the considerable rise of the temperature difference between the CO2and the water offsets the opposite
influences of moderate decrease of the mass flowrate of CO2.
In summary of these two effects (higher temperature differ-ence and a rather slight decrease in the enthalpy variation), the CO2system shows a slight increase of the heating
capac-ity. Moreover, a moderate decrease in the mass flowate for a
longer capillary tube length and a minor increase in the enthalpy change across the compressor bring about a nearly unchanged compressor power. In summary of the foregoing effects, the COPh shows a very slight increase against the
length of the capillary tube. Note that increasing the capillary tube length results in a higher discharge pressure and a lower suction pressure which is similar to that of increasing compressor speed. However, the mass flowrate in the former is decreasing while the latter is increasing. Yet the required Fig. 8e Effect of the water inlet temperature at the gas cooler on (a) CO2mass flow rate; (b) COPh; (c) discharge and suction
pressure; (d) Heating capacity and power consumption. Simulations are performed at Tdb[ 27C, Twb[ 20C,
Vfr[ 1.1 m sL1, Lcap[ 2.0 m, dcap[ 1.2 mm, Ncom[ 3500 rpm. (a) Variation of CO2mass flowrate. (b) Variation of system
compressor work in the former remains unchanged while it is appreciably increased in the latter. As a consequence, one can see a dramatic difference in COPhbetween these two cases.
5.
Concluding remarks
In this study a system model capable of handling the system response of a CO2transcritical cycle is proposed. Unlike some
existing system models applicable for the CO2, the present
model does not impose any excessive constraints such as fixed discharge pressure, suction pressure, and so on during the modeling. In addition, the complex configurations of the heat exchangers, including detailed geometrical variation of the gas cooler and fin-and-tube evaporator have been taken into account to make the simulation quite realistic. The sys-tem simulation is first compared with the experimental
measurements and good agreements between the simulation and the measurements are reported. For further examinations the system response of the CO2transcritical cycle, parametric
studies on the system performance with regard to the effect of dry bulb temperature, relative humidity in the evaporator, inlet water temperature at the gas cooler, compressor speed, and the capillary tube length are reported. The associated parametric influences on the CO2 transcritical system are
summarized in the following:
(1) The system COPh, and the heating capacity increases with
the rise of the inlet dry bulb temperature in the evaporator. However, the discharge pressure also rises considerably against the dry bulb temperature.
(2) The effect of the relative humidity in the evaporator on the system performance is similar to that of the dry bulb temperature. The system COPh, the heating capacity, and
Compressor speed ( rpm )
1500 2000 2500 3000 3500 4000 4500 5000
Refrigerant mass flow rate ( kgs
-1 ) 0.03 0.04 0.05 0.06 0.07
(a) Variation of CO mass flowrate.
2Compressor speed ( rpm ) 1500 2000 2500 3000 3500 4000 4500 5000 System COP 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5
(b) Variation of system COP
h.Compressor speed ( rpm ) 1500 2000 2500 3000 3500 4000 4500 5000 Pressure ( MPa ) 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 Discharge Pressure Suction Pressure
(c) Variation of suction and discharge pressure.
Compressor speed ( rpm )
1500 2000 2500 3000 3500 4000 4500 5000 Heat transfer rate and power consumption ( Watt )
0 2000 4000 6000 8000 10000 Gas cooler Evaporator Compressor
(d) Variation of heating capacity and power consumption
.Fig. 9e Effect of the compressor speed on (a) CO2mass flow rate; (b) COPh; (c) discharge and suction pressure; (d) Heating
capacity and power consumption. Simulation is performed with Tdb[ 27C, Twb[ 20C, Tw,i[ 10C, _mw[ 0.2 kg sL1,
Lcap[ 2.0 m, dcap[ 1.4 mm. (a) Variation of CO2mass flowrate. (b) Variation of system COPh. (a) Variation of suction and
the discharge pressure also increase with the rise of the relative humidity due to increase of latent loading but the increase is less pronounced as compared to that of the dry bulb temperature.
(3) It is found that the inlet water temperature at the gas cooler casts significant impact on this system perfor-mance. Despite the CO2mass flowrate may be increased
with the inlet water temperature, the system COPh
de-clines considerably with the inlet water temperature.
(4) The rise of the compressor speed will give rise to a higher heating capacity but it also leads to a much lower COPh due to a substantial increase of the compressor
work.
(5) Unlike those of the conventional sub-critical refrigerant, the system COPhdoes not reveal a maximum value against
the capillary tube length. This is mainly due to a much smaller enthalpy change for the CO2 transcritical
operation.
Fig. 10e Effect of the capillary tube length on (a) CO2mass flow rate; (b) COPh; (c) discharge and suction pressure; (d) Heating
capacity and power consumption. Simulation is performed with Tdb[ 27C, Twb[ 20C, Tw,i[ 20C, Vfr[ 1.1 m sL1,
Acknowledgments
This work is supported by the National Science Council of Taiwan under contract of 102-ET-E-009-006-ET. The financial support from the Bureau of Energy from the Ministry of Eco-nomic Affairs, Taiwan is also highly appreciated.
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