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Optimized transcritical CO2 heat pumps: Performance comparison of capillary tubes against expansion valves
international journal of refrigeration 31 (2008) 388–395
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Optimized transcritical CO2 heat pumps: Performance comparison of capillary tubes against expansion valves Neeraj Agrawal, Souvik Bhattacharyya* Department of Mechanical Engineering, Indian Institute of Technology Kharagpur, Kharagpur 721302, India
article info
abstract
Article history:
A capillary tube based CO2 heat pump is unique because of the transcritical nature of the
Received 7 March 2007
system. The transcritical cycle has two independent parameters, pressure and tempera-
Received in revised form
ture, unlike the subcritical cycle. In the present study, a steady state simulation model
13 June 2007
has been developed to evaluate the performance of a capillary tube based transcritical
Accepted 17 August 2007
CO2 heat pump system for simultaneous heating and cooling at 73 C and 4 C, respectively
Published online 25 August 2007
against optimized expansion valve systems. Capillary tubes of various configurations having diameters of 1.4, 1.5 and 1.6 mm along with internal surface roughness of 0.001–
Keywords:
0.003 mm have been tested to obtain the optimum design and operating conditions. Sub-
Heat pump
critical and supercritical thermodynamic and transport properties of CO2 are calculated
Carbon dioxide
employing a precision in-house property code.
Transcritical cycle
It is observed that the capillary tube system is quite flexible in response to changes in am-
Comparison
bient temperature, almost behaving to offer an optimal pressure control. System perfor-
Expansion
mance is marginally better with a capillary tube at higher gas cooler exit temperature.
Tube
Capillary tube length turns out to be the critical parameter that influences system opti-
Capillary
mum conditions. A novel nomogram has been developed that can be employed as a guide-
Expansion valve
line to select the optimum capillary tube. ª 2007 Elsevier Ltd and IIR. All rights reserved.
Pompes a` chaleur au CO2 transcritique optimise´es : comparaison de la performance des capillaires et des de´tendeurs Mots cle´s : Pompe a` chaleur ; Dioxyde de carbone ; Cycle transcritique ; Comparaison ; De´tente ; Tube ; Capillaire ; De´tendeur
1.
Introduction
Carbon dioxide was the preferred refrigerant from the late 1800s particularly in on-board ship refrigeration. However,
with the advent of the synthetic halocarbon refrigerants, carbon dioxide rapidly went out of use due to its low critical temperature and high operating pressure problems. In the recent past, there has been a renewed interest in natural refrigerants
* Corresponding author. Tel.: þ91 3222 282904; fax: þ91 3222 255303. E-mail address: [email protected] (S. Bhattacharyya). 0140-7007/$ – see front matter ª 2007 Elsevier Ltd and IIR. All rights reserved. doi:10.1016/j.ijrefrig.2007.08.006
international journal of refrigeration 31 (2008) 388–395
Nomenclature A Ac d Dc f G h k kw Lc LMTD _ m Nu P Pr Q Re T, t u UA v vg,c vl,c VS x Xtt
heat transfer area (m2) inside cross-sectional area of capillary tube (m2) inner tube diameter (m) capillary tube inner diameter (m) friction factor mass flux (kg m2 s1) specific enthalpy (J kg1) thermal conductivity (W m1 K1) wall thermal conductivity (W m1 K1) capillary tube length (m) log mean temperature difference (K) mass flow rate (kg s1) Nusselt number pressure Prandtl number heat transfer (W) Reynolds number temperature (K and C) refrigerant flow velocity (m s1) overall heat transfer conductance (W K1) specific volume (m3 kg) specific volume of saturated vapour, capillary tube (m3 kg) specific volume of saturated liquid, capillary tube (m3 kg) compressor displacement rate (m3 s1) quality Lockhart–Martinelli factor
Greek symbols waterside heat transfer coefficient (W m2 K1) aw ar refrigerant side heat transfer coefficient (W m2 K1)
due to their benign environmental characteristics. CO2 is one of the few natural refrigerants, which is neither flammable nor toxic. Carbon dioxide finds its major application share in mobile air-conditioning and heat pumps for simultaneous heating and cooling (Kim et al., 2004), the latter due to the large temperature glide in the gas cooler. Capillary tubes are extensively used in small size refrigeration and air-conditioning systems. However, employing a capillary tube for CO2 transcritical heat pump systems is very different from subcritical systems; here temperature and pressure are two independent parameters unlike the subcritical cycle. There exists an optimum pressure for a given gas cooler outlet temperature where it exhibits the maximum COP due to the unique behavioural pattern of CO2 properties around the critical point and beyond (Kauf, 1999). It would be interesting to note whether an optimized capillary tube can be chosen leading to an optimized gas cooler pressure. Most of the reported simulation studies are for conventional vapour compression systems (Chen and Prasad, 1999; Prasertsan et al., 1996; Herbas et al., 1993). Only a few have been reported for transcritical CO2 systems, most of which are on systems employing a control valve as the expansion device. Ortiz et al. (2003) carried out CO2 system simulation to evaluate the performance of air-to-air-conditioners and heat pumps.
DL 3 hV his;c m ml;c mg;c r f
389
length segment (m) internal surface roughness (mm) compressor volumetric efficiency compressor isentropic efficiency dynamic viscosity (N m2 s) dynamic viscosity of saturated liquid, capillary tube (N m2 s) dynamic viscosity of saturated vapour, capillary tube (N m2 s) density (kg m3) two phase multiplier
Subscripts 1–5 state points of refrigerant c capillary tube dis compressor discharge ev evaporator g gas/vapour gc gas cooler i inner l liquid o outer ref/r refrigerant rb refrigerant at bulk temperature rw refrigerant at wall temperature sp single phase suc suction tp two phase w tube wall Superscript i segmental step
Casson et al. (2003) proposed a throttling system consisting of a differential valve, a separator and a thermostatic expansion valve to control the high side pressure optimally as well as to control the superheat. The proposed system showed an intrinsic self-adjusting capability that led to COP values quite close to the maximum level when a fixed suitable value of the differential pressure is chosen, even if the temperature of the secondary fluid varied largely. Recently, Sarkar et al. (2006) presented a simulation study on transcritical CO2 heat pump systems employing a controllable throttle valve as the expansion device and considering an isenthalpic expansion process. Madsen et al. (2005) carried out theoretical and experimental studies of capillary tubes in a transcritical CO2 refrigeration system. However, this simplified study did not include heat transfer, fluid flow and internal surface effects of the capillary tube. Lately, Zbigniew and Boguslaw (2006) reported studies on a non-adiabatic capillary tube based transcritical heat pump system. However, issues related to capillary tube optimization were not addressed. Zimmermann and Maciel (2006) presented test results on capillary tube optimization with respect to refrigerant charge for a glass door merchandiser operating on a CO2 transcritical cycle. However, secondary fluid temperature effects were not included in their study. In this paper, a steady state simulation model has
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international journal of refrigeration 31 (2008) 388–395
been developed to evaluate the system performance of a transcritical carbon dioxide heat pump system for simultaneous heating and cooling at 73 C and 4 C, respectively. An adiabatic capillary tube is modelled as an expansion device in the simulation including fluid flow and internal surface effects. Various capillary tube configurations have been compared to obtain the optimum combination. Furthermore, the performance of the transcritical CO2 heat pump system employing an optimized capillary tube has been compared with the previously reported (Sarkar et al., 2006) optimal system employing a controllable expansion valve to justify the choice of a capillary tube based system for transcritical CO2 heat pumps.
2.
Mathematical modelling
Fig. 1 shows the layout of a transcritical CO2 system showing the main components along with the corresponding cycle on the temperature–entropy plane. Water at ambient temperature is employed as the secondary fluid in both gas cooler and evaporator. For the entire study, gas cooler water outlet temperature Tgco and evaporator water outlet temperature Tevo are maintained at 73 C and 4 C, respectively, by controlling the mass flow rate. Both gas cooler and evaporator are double pipe counter flow heat exchangers, where the refrigerant flows through the inner tube and water flows through the outer annular space. The adiabatic capillary tube is modelled as an expansion device where expansion is not isenthalpic due to change in refrigerant velocity (Agrawal and Bhattacharyya, 2007). In the entire system, each component is modelled based on an energy balance. Both the heat exchangers and the capillary tube are discretized spatially to consider the lengthwise property variation and momentum and energy conservation equations have been employed to each segment. To simplify the analysis, the following assumptions were considered in the simulation: 1. 2. 3. 4.
Heat transfer with the ambient is negligible. Only single phase heat transfer occurs for secondary fluid. Compression process is adiabatic but not isentropic. Pressure drop on waterside and in connecting pipes is negligible. 5. Refrigerant is free from oil.
6. Heat transfer in the capillary tube is negligible. 7. Thermodynamic equilibrium (i.e. no metastable phenomenon) occurs in capillary tube flow. 8. Homogeneous and one-dimensional steady flow occurs through the capillary tube.
2.1.
Compressor
A reciprocating single stage compressor is used in the system. _ ref , is proportional to the displacement The mass flow rate, m rate and the volumetric efficiency and is inversely proportional to the specific volume of gas entering the compressor and is given by _ ref ¼ m
hV V_ S n1
(1)
where volumetric efficiency hV for the semi-hermetic compressor is estimated from the empirical relation available from the data reported (Ortiz et al., 2003): 2 Pdis Pdis (2) þ 0:0018 hV ¼ 0:9207 0:0756 Psuc Psuc Isentropic efficiency of the compressor is estimated by an empirical correlation (Ortiz et al., 2003) given by Pdis his;c ¼ 0:26 0:7952 Psuc 2 3 4 Pdis Pdis Pdis þ0:0414 0:0022 0:2803 Psuc Psuc Psuc
2.2.
ð3Þ
Gas cooler
As mentioned earlier, the gas cooler is segmented lengthwise to accommodate the property variation. Heat transfer in the ith segment of the gas cooler is expressed in terms of overall heat transfer coefficient as i ¼ ðUAÞigc ðLMTDÞigc Qgc
(4)
The overall heat transfer coefficient for the ith segment is calculated considering all the thermal resistances: ln do =di 1 1 1 ¼ þ þ (5) aw A w 2pDLkw ðUAÞigc ar Ar
Fig. 1 – (a) Schematic layout of a transcritical CO2 system and (b) the corresponding cycle on T–s plane.
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international journal of refrigeration 31 (2008) 388–395
Gnielinski correlation with the Pitla et al. (2002) modification, incorporating both bulk and wall properties, for supercritical in-tube carbon dioxide cooling is employed to calculate the heat transfer coefficient. Pitla correlation is given by Nurw þ Nurb krw (6) Nur ¼ 2 krb
ar ¼
Nur krb di
(7)
Nusselt number is calculated by Gnielinski correlation (Gnielinski, 1976) at the respective conditions: ðf =8 ðRe 1000ÞPr Nu ¼ 1=2 1:07 þ 12:7 f =8 Pr2=3 1
(8)
f ¼ ð0:79lnðReÞ 1:64Þ
Capillary tube
The capillary tube is discretized into a number of longitudinal elements (Fig. 2), to enable the sharp changes in CO2 property, particularly near the critical point, to be captured in the analysis. Principles of mass, energy, and momentum conservation are employed to each segment of the capillary tube. The conservation of mass for steady flow in an element of fluid is given by Ac uc ¼0 (16) d vc Neglecting the elevation difference and the heat transfer in and out of the tube, the energy conservation may be written as dhc þ
where f is calculated as 2
2.4.
(9)
The water side heat transfer coefficient is calculated by the well known Dittus–Boelter correlation.
G2c 2 dv ¼ 0 2 c
From the conservation of momentum equation, the difference in forces applied to the element of fluid due to drag and pressure difference on opposite ends of the element should be equal to that needed to accelerate the fluid and is expressed as dpc fc
2.3.
Evaporator
(17)
dLc uc Gc ¼ Gc duc Dc 2
(18)
Hence,
The evaporator is modelled in the same way as the gas cooler. However, due to the presence of two phase flow, the convective heat transfer coefficient has been calculated using Wattelet–Carlo correlation (Boewe et al., 2001):
( ) 2Dc drc rc 2 dpc dLc ¼ fc rc Gc
(19)
ar ¼ Fal
(10)
Lin friction factor (Lin et al., 1991) is used to calculate the two phase friction factor: vsp;c (20) ftp;c ¼ ftp;c fsp;c vtp;c
kl al ¼ 0:023 Re0:8 Pr0:4 l di l
(11)
where 2
ftp;c
F ¼ 1 þ 1:925X0:83 tt
(12)
Similar to the gas cooler model, Dittus–Boelter correlation is employed to calculate the waterside heat transfer coefficient. The refrigeration side pressure drop for the ith segment is estimated by G2ev;r 2 DLev fr ð1 xÞ2 f ðDPev;r Þ ¼ 4 di 2 rl l i
(21)
where
where Xtt is the Lockhart–Martinelli factor given by 0:9 0:5 0:1 1x rv ml Xtt ¼ x rl mv
12 3=2 31=12 16 þ A16 tp;c þ Btp;c vg;c ¼ 4 1 1 þ xc 12 3=2 5 vl;c 8 16 þ A16 sp;c þ Bsp;c Resp;c 8 Retp;c
(13)
Atp;c ¼ 2:457 ln
7 Retp;c
Retp;c ¼
0:9
1 þ0:273=Dc
; Btp;c ¼
37; 530 ; Retp;c
G c Dc mtp;c
The McAdams model (McAdams et al., 1942) is employed to estimate the two phase viscosity: 1 ð1 xc Þ xc ¼ þ mtp;c ml;c mg;c
(22)
The friction factor fr and two phase multiplier fl are expressed as fr ¼ 0:0791Re0:25 l
(14)
and !1=2 fl ¼
1:376 þ
ð7:242=X1:655 Þ tt
where Xtt is the Lockhart–Martinelli factor.
(15) Fig. 2 – Longitudinal discretization for the capillary tube.
392
3.
international journal of refrigeration 31 (2008) 388–395
Numerical methodology
A computer code has been developed for the steady state simulation to evaluate the system performance of a transcritical carbon dioxide heat pump system for simultaneous heating and cooling at 73 C and 4 C, respectively, employing various configurations of an adiabatic capillary tube. Subcritical and supercritical thermo-physical and transport properties of CO2 are estimated employing a precision property code CO2PROP developed locally (Sarkar et al., 2004). Both the gas cooler and the capillary tube are susceptible to abrupt property variation of CO2 near the critical region. To capture these abrupt changes, both the capillary tube and the gas cooler are discretized longitudinally. To yield greater accuracy, the evaporator is spatially discretized as well. Each segment of gas cooler and evaporator is modelled considering them to be a counter flow heat exchanger. As shown in the flow-chart (Fig. 3), a certain
Input: Evaporator dimensions (di, do, Di, Lev), Gas cooler dimensions (di, do, Di, Lgc), Compressor data; Vs, N, Water: tevi, tgci, . mevw or tevo, mgcw or tgco, ΔTsucsuperheat Capillary geometry: D, ε. Guess: Capillary length (Lc) Guess: evaporator outlet pressure (P6)
Guess: gas cooler pressure (Pdis)
Calculate: mass flow rate, mref
Input evaporator model Calculate P5, x5, h4 Input gas cooler model Calculate find P3, t3 Input capillary tube model Calculate Lc*, x*5
If: Lc = L*c
No
Update Pdis
Yes No If: x5 = x*5
Update P6
Yes Optimum COP
No
Update Lc
Yes Output: state points, COPmax, Pdis, Lc L* = Simulated capillary tube length, x* = Refrigerant quality at exit of the simulated capillary tube
Fig. 3 – Flow-chart for the simulation model.
diameter and internal surface roughness are chosen for a capillary tube and mass flow rate of water and suction superheat are chosen as well. Initially capillary tube length is selected and discharge and evaporator pressures are guessed and the code solves iteratively for state point and system performance. It may be noted that the gas cooler pressure is estimated based on the chosen capillary tube length. Unlike a controllable throttle valve based system, gas cooler pressure is not an independent parameter with the capillary tube based system once the tube length is specified. Length of the capillary tube is selected based on the optimum system COP.
4.
Results and discussion
Performance of the system being studied for simultaneous heating and cooling applications is evaluated based on system COPs for various conditions and capillary geometry. Results are presented for the combined length of 25 m of the evaporator and gas cooler of standard stainless steel inner tube of 9.525 mm OD and outer tube of 14.097 mm ID. Capillary tubes in the range of 1.4–1.6 mm ID and having 0.001–0.003 mm internal surface roughness are employed in the study. Capillary tubes having ID smaller than 1.4 mm lead to choking and this sets the limiting condition for selection of optimal tube length. A Dorin (model TCS 111H) CO2 compressor with a rated speed of 2900 rpm is chosen for the system. Internal heat exchanger is not used in the analysis. However, suction superheat is taken as 10 C within the evaporator. About 8–10% evaporator length is utilised for suction superheat. Results are generated for the compressor rated speed of 2900 rpm while water inlet temperature varied from 20 C to 40 C and heat exchanger area ratio (gas cooler-to-evaporator) varied between 1 and 3. Fixing the water outlet temperature in gas cooler and evaporator at 73 C and 4 C, respectively, the simulated mass flow rate of water is calculated for each water inlet temperature to suit the heat transfer requirement as per the design of gas cooler and evaporator. Results from the present simulation model are compared with the published results from Madsen et al. (2005) for the specified capillary tubes with Dc ¼ 2 mm, Lc ¼ 2/4 m, Dc ¼ 1 mm, Lc ¼ 2 m, and Dc ¼ 1.8 mm, Lc ¼ 3 m. The evaporator pressure, gas cooler exit temperature and the high pressure are taken as 35 bar, 40 C and 100 bar, respectively. For all the chosen capillary tubes, internal surface roughness 3 is taken as 0.00576 mm. Experimentally measured refrigerant mass flow rates closely match predicted mass flow rates of the model presented here (Fig. 4). Variation of performance parameters with area ratio and capillary tube diameter for an internal tube roughness of 0.0015, a water inlet temperature of 30 C and a compressor speed of 2900 rpm has been studied through the simulation code and is exhibited in a nomogram (Fig. 5). It may be observed that with increase in area ratio, cooling output reduces due to decrease in refrigerant mass flow rate due to decrease in suction density at lower optimum discharge pressures. This may be attributed to the fact that at higher area ratio, gas cooler outlet temperature decreases and that causes the evaporator pressure to decrease as well for a given capillary tube. Consequently, refrigerant mass flow rate decreases
393
0.05
System COP
0.04
0.03
0.02
3.75
123
3.72
120
3.69
117
3.66
114
3.63
system COP Gas cooler pressure
0.01 Madsen et al. (2005) Our model
3.6 1.5
1.9
2.3
2.7
111
Gas cooler pressure (bar)
Theoretical refrigerant mass flow rate (kg/s)
international journal of refrigeration 31 (2008) 388–395
108 3.1
Capillary tube length (m)
0 0
0.01
0.02
0.03
0.04
0.05
Measured refrigerant mass flow rate (kg/s)
Fig. 4 – Validation of the present model with the results of Madsen et al. (2005).
due to decrease in suction density at a lower evaporator pressure. With decrease in evaporator pressure, gas cooler pressure also decreases. Hence, as shown in Fig. 5, system COP first increases and then decreases with a peak value of 3.72 at a gas cooler-to-evaporator area ratio of 1.5 for all the chosen capillary tubes; this trend is very similar to that reported earlier (Sarkar et al., 2006) for an expansion valve. At higher area ratio, capillary tube length increases for a chosen diameter, due to decrease in refrigerant mass flow rate (Fig. 5). The nomogram presented here is expected to help design the system better. For example, when the water inlet temperature is 30 C at a compressor speed of 2900 rpm, to attain a maximum COP of 3.72, an 1.6 m long and 1.4 mm ID capillary tube is required
Fig. 6 – Variation of COP and gas cooler pressure with capillary tube length at Dc [ 1.5 mm, 3 [ 0.0015 mm and area ratio [ 1.5.
at an area ratio 1.5, and the system is expected to yield a cooling output of 4.75 kW with a refrigerant mass flow rate of 0.0287 kg s1. All these system operating condition information is extracted from a simple diagram given here as a nomogram, as is illustrated in Fig. 5. As exhibited in Fig. 6, COP first increases with capillary length increase to reach a peak and then decreases. However, gas cooler pressure increases monotonically. Near the peak, COP variation is flat, implying that beyond a certain length, the gain in COP is not very appreciable. Hence it is recommended that for a chosen capillary tube diameter and internal surface roughness, capillary tube length should be selected on the basis of optimum COP.
Fig. 5 – Nomogram depicting the variation of performance parameters with area ratio and capillary diameter at 3 [ 0.0015 mm, compressor speed [ 2900 rpm and Twi [ 30 8C.
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international journal of refrigeration 31 (2008) 388–395
5.2
4.2
Table 1 – Variation of heat exchanger water mass flow rate with inlet temperature
4.9
3.8
4.3 4
3.6 System COP (Exp. valve) Dc = 1.4 mm, Lc = 1.4 m Dc = 1.5 mm, Lc = 2.1 m Dc = 1.6 mm, Lc = 3.0 m Cooling capacity (Exp. valve)
3.4
3.7 3.4
1 2 3 4 5
Water inlet temperature ( C)
Water mass flow rate (kg/min) Gas cooler
Evaporator
2.27 2.43 2.63 2.89 3.24
4.64 3.33 2.54 2.01 1.62
20 25 30 35 40
3.1
3.2 20
25
30
35
40
Water inlet temperature (°C) Fig. 7 – Capillary tube and expansion valve performance comparison at varying water inlet temperature and various capillary tube configurations with 3 [ 0.002 mm. Water inlet temperature is subjected to change with ambient condition. For a chosen capillary tube, it is desired that the system would run optimally even with varying water inlet temperature. This needs to be inspected carefully employing the simulation code. The effect of water inlet temperature at a compressor speed of 2900 rpm, and an optimum area ratio of 1.5 with various capillary tube configurations is shown in Figs. 7 and 8. Fig. 7 shows the variation of COP and cooling capacity with respect to water inlet temperature and various ID and length combination capillary tubes of internal surface roughness 0.002 mm. Table 1 shows the various water mass flow rates in the gas cooler and the evaporator for typical test runs with a capillary tube diameter of 1.5 mm having a surface roughness of 0.002 mm. As the water inlet temperature increases, mass flow rate of water in gas cooler increases while in evaporator it decreases for constant water outlet temperatures of 73 C and 4 C, respectively. It is observed that for all the chosen capillary tubes, the system operates very nearly at the optimum level at all the water inlet temperatures. The
Mass flow rate (Exp. Valve) Dc = 1.4, Lc = 1.4 Dc = 1.5, Lc = 2.1 Dc = 1.6, Lc = 3.0 Optimal gas cooler pressure (Exp. valve)
0.03
0.0296
reference optimum performance is chosen to be that of the corresponding heat pump system employing a controllable expansion valve instead of a capillary tube. It can also be observed that COP decreases with increase in water inlet temperature due to rise in gas cooler exit temperature causing degradation in heat transfer properties. Fig. 8 shows that the gas cooler pressure, which is not an independent parameter in case of the capillary tube, remains close to the optimum pressure obtained with an expansion valve at all the water inlet temperatures and for all the chosen capillary tube lengths. There is a marginal change in refrigerant mass flow rate with varying water inlet temperature. However, the gas cooler pressure increases rapidly with increase in water inlet temperature (Fig. 8). This system behaviour with the capillary tube and with varying water inlet temperature (in varying ambient temperature) shows that the capillary based system is at least as good as the controllable expansion valve based system. This is quite encouraging since there has been a good amount of scepticism in whether a capillary tube based system would perform as well when there is an issue of setting the optimum gas cooler pressure for all CO2 transcritical system heat pumps. Fig. 9 shows that as water temperature increases, compressor work in an expansion valve based system also increases due to increase in gas cooler pressure. A very similar trend is also exhibited by the heat pump using a capillary tube as the expansion device. It is also observed that the optimum capillary length increases rapidly with
124 3.55 121
118 0.0292 115 0.0288 112
Gas cooler pressure (bar)
Refrigerant mass flow rate (kg/s)
Test run
Compressor work (kW)
System COP
4.6
Cooling capacity (kW)
4
Compressor work (Exp. Valve) Dc = 1.4, Lc = 1.4 Dc = 1.5, Lc = 2.1 Dc = 1.6, Lc = 3.0
3.5 3.45 3.4 3.35 3.3
109
0.0284 20
25
30
35
40
Water inlet temperature (°C) Fig. 8 – Mass flow rate and gas cooler pressure comparison between capillary and expansion valve based systems with respect to water inlet temperature.
3.25 20
25
30
35
40
Water inlet temperature (°C) Fig. 9 – Variation of compressor work with respect to water inlet temperature for capillary tube and expansion valve based systems.
international journal of refrigeration 31 (2008) 388–395
in this study that capillary tubes can be a fairly effective expansion device in smaller CO2 based transcritical heat pump systems where the system is able to operate optimally with varying ambient conditions within a limited range.
Optimum capillary tube length (m)
3.8 roughness = 0.001 mm roughness = 0.0015 mm roughness = 0.002 mm roughness = 0.003 mm
3.4 3 2.6
references 2.2 1.8 1.4 1.4
1.45
1.5
1.55
1.6
Capillary tube diameter (mm) Fig. 10 – Optimum capillary tube length variation with capillary tube diameter and internal surface roughness.
increase in capillary tube diameter. However, internal surface roughness effect is less significant on optimum capillary length for the chosen diameters (Fig. 10). It may be noted that change in optimum capillary tube length is more significant at lower internal surface roughness values due to the fact that beyond a certain value of 3=Dc ratio, friction factor depends only on the size of the roughness elements. It is observed that installation of a proper capillary tube length replacing an expansion valve will result in a natural adjustment of the gas cooler pressure, so that the system balance always shifts to a favourable COP direction. At all the chosen water inlet temperatures, system operates at balance conditions using a proper capillary tube length as the expansion device. This novel finding regarding capillary tube based CO2 heat pumps augurs well for such systems, particularly for the smaller sized ones.
5.
395
Conclusions
The steady state performance of a transcritical CO2 heat pump system for simultaneous heating and cooling employing an adiabatic capillary tube has been compared with a nonconventional optimal system using a controllable expansion valve. For the transcritical cycle, pressure and temperature are independent parameters and system behaviour is not expected to be the same as in a conventional subcritical system employing a capillary tube as the expansion device. Capillary tube length turns out to be the deciding parameter to enable the system to run optimally. Length of the capillary tube should be selected on the basis of optimum gas cooler pressure for a given tube diameter. It is observed that the optimum area ratio value of 1.5 is almost the same for a controllable expansion valve and for all the chosen capillary tubes. A nomogram with capillary tube diameter as an independent parameter and COP, capillary tube length and refrigerant mass flow rate as output has been presented. Capillary tube based system is shown to be quite flexible regarding changes in ambient temperature, almost behaving to offer an optimal pressure control just like the controllable expansion valve. System performance is marginally better with a capillary tube at higher gas cooler exit temperature. It has been shown
Agrawal, N., Bhattacharyya, S., 2007. Adiabatic capillary tube flow of carbon dioxide in a transcritical heat pump cycle. Int. J. Energy Res. 31 (11), 1016–1030. Boewe, D.E., Bullard, C.W., Harjnak, P.S., 2001. Contribution of internal heat exchanger to transcritical R744 cycle performance. ASHRAE Trans. 2, 189–198. Chen, Q., Prasad, R.C., 1999. Simulation of a vapour-compression refrigeration cycles using HFC 134a and CFC 12. Int. Commun. Heat Mass Transfer 26 (4), 513–521. Casson, V., Cecchinato, L., Corradi, M., Fornasieri, E., Sergio, G., Minetto, S., Zamboni, L., Zilio, C., 2003. Optimization of the throttling system in a CO2 refrigerating machine. Int. J. Refrigeration 26 (8), 926–935. Gnielinski, V., 1976. New equations for heat and mass transfer in turbulent pipe and channel flow. Int. Chem. Eng. 16 (2), 359–366. Herbas, T.B., Berlinck, E.C., Uriu, C.A.T., Marques, R.P., Parise, J.A.R., 1993. Steady state simulation of vapour compression heat pumps. Int. J. Energy Res. 17, 801–816. Kim, M., Pettersen, J., Bullard, C.W., 2004. Fundamental process and system design issues in CO2 vapor compression systems. Prog. Energy Combust. Sci. 30, 119–174. Kauf, F., 1999. Determination of the optimum high pressure for transcritical CO2 refrigeration cycles. Int. J. Thermal Sci. 38 (4), 325–330. Lin, S., Kwok, C.C.K., Li, R.Y., Chen, Z.H., Chen, Z.Y., 1991. Local friction pressure drop during vaporization of R-12 through capillary tubes. Int. J. Multiphase Flow 17 (1), 95–102. Madsen, K.B., Poulsen, C.S., Wiesenfarth, M., 2005. Study of capillary tubes in a transcritical CO2 refrigeration system. Int. J. Refrigeration 28, 1212–1218. McAdams, W.H., Woods, W.K., Bryan, R.L., 1942. Vaporization inside horizontal tubes: II. Benzene–oil mixtures. Trans. ASME 64, 193. Ortiz, T.M., Li, D., Groll, A.E., 2003. Evaluation of the Performance Potential of CO2 as a Refrigerant in Air-to-Air Conditioner and Heat Pumps: System Modelling and Analysis. ARTI final report no. 21CR/610-10030. Prasertsan, S., Saen-saby, P., Ngamstritrakul, P., Prateepchaikul, G., 1996. Heat pump dryer. Part 1: simulation of the model. Int. J. Energy Res. 20, 1067–1079. Pitla, S.S., Groll, E.A., Ramadhyani, S., 2002. New correlation to predict the heat transfer coefficient during in-tube cooling of turbulent supercritical CO2. Int. J. Refrigeration 25, 887–895. Sarkar, J., Bhattacharyya, S., Ram Gopal, M., 2006. Simulation of a transcritical CO2 heat pump cycle for simultaneous cooling and heating applications. Int. J. Refrigeration 29, 735–743. Sarkar, J., Bhattacharyya, S., Ram Gopal, M., 2004. Optimization of transcritical CO2 heat pump cycle for simultaneous cooling and heating applications. Int. J. Refrigeration 27, 830–838. Zbigniew, K., Boguslaw, B., 2006. Study of capillary tube applications in a transcritical heat pump system. Arch. Thermodyn. 27 (4), 123–146. Zimmermann, A.J.P., Maciel, R.A., 2006. Discharge pressure optimization for CO2 transcritical cycle using capillary tube. In: Proceedings of International Refrigeration and Air Conditioning Conference, Purdue.
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Optimized transcritical CO2 heat pumps: Performance comparison of capillary tubes against expansion valves Neeraj Agrawal, Souvik Bhattacharyya* Department of Mechanical Engineering, Indian Institute of Technology Kharagpur, Kharagpur 721302, India
article info
abstract
Article history:
A capillary tube based CO2 heat pump is unique because of the transcritical nature of the
Received 7 March 2007
system. The transcritical cycle has two independent parameters, pressure and tempera-
Received in revised form
ture, unlike the subcritical cycle. In the present study, a steady state simulation model
13 June 2007
has been developed to evaluate the performance of a capillary tube based transcritical
Accepted 17 August 2007
CO2 heat pump system for simultaneous heating and cooling at 73 C and 4 C, respectively
Published online 25 August 2007
against optimized expansion valve systems. Capillary tubes of various configurations having diameters of 1.4, 1.5 and 1.6 mm along with internal surface roughness of 0.001–
Keywords:
0.003 mm have been tested to obtain the optimum design and operating conditions. Sub-
Heat pump
critical and supercritical thermodynamic and transport properties of CO2 are calculated
Carbon dioxide
employing a precision in-house property code.
Transcritical cycle
It is observed that the capillary tube system is quite flexible in response to changes in am-
Comparison
bient temperature, almost behaving to offer an optimal pressure control. System perfor-
Expansion
mance is marginally better with a capillary tube at higher gas cooler exit temperature.
Tube
Capillary tube length turns out to be the critical parameter that influences system opti-
Capillary
mum conditions. A novel nomogram has been developed that can be employed as a guide-
Expansion valve
line to select the optimum capillary tube. ª 2007 Elsevier Ltd and IIR. All rights reserved.
Pompes a` chaleur au CO2 transcritique optimise´es : comparaison de la performance des capillaires et des de´tendeurs Mots cle´s : Pompe a` chaleur ; Dioxyde de carbone ; Cycle transcritique ; Comparaison ; De´tente ; Tube ; Capillaire ; De´tendeur
1.
Introduction
Carbon dioxide was the preferred refrigerant from the late 1800s particularly in on-board ship refrigeration. However,
with the advent of the synthetic halocarbon refrigerants, carbon dioxide rapidly went out of use due to its low critical temperature and high operating pressure problems. In the recent past, there has been a renewed interest in natural refrigerants
* Corresponding author. Tel.: þ91 3222 282904; fax: þ91 3222 255303. E-mail address: [email protected] (S. Bhattacharyya). 0140-7007/$ – see front matter ª 2007 Elsevier Ltd and IIR. All rights reserved. doi:10.1016/j.ijrefrig.2007.08.006
international journal of refrigeration 31 (2008) 388–395
Nomenclature A Ac d Dc f G h k kw Lc LMTD _ m Nu P Pr Q Re T, t u UA v vg,c vl,c VS x Xtt
heat transfer area (m2) inside cross-sectional area of capillary tube (m2) inner tube diameter (m) capillary tube inner diameter (m) friction factor mass flux (kg m2 s1) specific enthalpy (J kg1) thermal conductivity (W m1 K1) wall thermal conductivity (W m1 K1) capillary tube length (m) log mean temperature difference (K) mass flow rate (kg s1) Nusselt number pressure Prandtl number heat transfer (W) Reynolds number temperature (K and C) refrigerant flow velocity (m s1) overall heat transfer conductance (W K1) specific volume (m3 kg) specific volume of saturated vapour, capillary tube (m3 kg) specific volume of saturated liquid, capillary tube (m3 kg) compressor displacement rate (m3 s1) quality Lockhart–Martinelli factor
Greek symbols waterside heat transfer coefficient (W m2 K1) aw ar refrigerant side heat transfer coefficient (W m2 K1)
due to their benign environmental characteristics. CO2 is one of the few natural refrigerants, which is neither flammable nor toxic. Carbon dioxide finds its major application share in mobile air-conditioning and heat pumps for simultaneous heating and cooling (Kim et al., 2004), the latter due to the large temperature glide in the gas cooler. Capillary tubes are extensively used in small size refrigeration and air-conditioning systems. However, employing a capillary tube for CO2 transcritical heat pump systems is very different from subcritical systems; here temperature and pressure are two independent parameters unlike the subcritical cycle. There exists an optimum pressure for a given gas cooler outlet temperature where it exhibits the maximum COP due to the unique behavioural pattern of CO2 properties around the critical point and beyond (Kauf, 1999). It would be interesting to note whether an optimized capillary tube can be chosen leading to an optimized gas cooler pressure. Most of the reported simulation studies are for conventional vapour compression systems (Chen and Prasad, 1999; Prasertsan et al., 1996; Herbas et al., 1993). Only a few have been reported for transcritical CO2 systems, most of which are on systems employing a control valve as the expansion device. Ortiz et al. (2003) carried out CO2 system simulation to evaluate the performance of air-to-air-conditioners and heat pumps.
DL 3 hV his;c m ml;c mg;c r f
389
length segment (m) internal surface roughness (mm) compressor volumetric efficiency compressor isentropic efficiency dynamic viscosity (N m2 s) dynamic viscosity of saturated liquid, capillary tube (N m2 s) dynamic viscosity of saturated vapour, capillary tube (N m2 s) density (kg m3) two phase multiplier
Subscripts 1–5 state points of refrigerant c capillary tube dis compressor discharge ev evaporator g gas/vapour gc gas cooler i inner l liquid o outer ref/r refrigerant rb refrigerant at bulk temperature rw refrigerant at wall temperature sp single phase suc suction tp two phase w tube wall Superscript i segmental step
Casson et al. (2003) proposed a throttling system consisting of a differential valve, a separator and a thermostatic expansion valve to control the high side pressure optimally as well as to control the superheat. The proposed system showed an intrinsic self-adjusting capability that led to COP values quite close to the maximum level when a fixed suitable value of the differential pressure is chosen, even if the temperature of the secondary fluid varied largely. Recently, Sarkar et al. (2006) presented a simulation study on transcritical CO2 heat pump systems employing a controllable throttle valve as the expansion device and considering an isenthalpic expansion process. Madsen et al. (2005) carried out theoretical and experimental studies of capillary tubes in a transcritical CO2 refrigeration system. However, this simplified study did not include heat transfer, fluid flow and internal surface effects of the capillary tube. Lately, Zbigniew and Boguslaw (2006) reported studies on a non-adiabatic capillary tube based transcritical heat pump system. However, issues related to capillary tube optimization were not addressed. Zimmermann and Maciel (2006) presented test results on capillary tube optimization with respect to refrigerant charge for a glass door merchandiser operating on a CO2 transcritical cycle. However, secondary fluid temperature effects were not included in their study. In this paper, a steady state simulation model has
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been developed to evaluate the system performance of a transcritical carbon dioxide heat pump system for simultaneous heating and cooling at 73 C and 4 C, respectively. An adiabatic capillary tube is modelled as an expansion device in the simulation including fluid flow and internal surface effects. Various capillary tube configurations have been compared to obtain the optimum combination. Furthermore, the performance of the transcritical CO2 heat pump system employing an optimized capillary tube has been compared with the previously reported (Sarkar et al., 2006) optimal system employing a controllable expansion valve to justify the choice of a capillary tube based system for transcritical CO2 heat pumps.
2.
Mathematical modelling
Fig. 1 shows the layout of a transcritical CO2 system showing the main components along with the corresponding cycle on the temperature–entropy plane. Water at ambient temperature is employed as the secondary fluid in both gas cooler and evaporator. For the entire study, gas cooler water outlet temperature Tgco and evaporator water outlet temperature Tevo are maintained at 73 C and 4 C, respectively, by controlling the mass flow rate. Both gas cooler and evaporator are double pipe counter flow heat exchangers, where the refrigerant flows through the inner tube and water flows through the outer annular space. The adiabatic capillary tube is modelled as an expansion device where expansion is not isenthalpic due to change in refrigerant velocity (Agrawal and Bhattacharyya, 2007). In the entire system, each component is modelled based on an energy balance. Both the heat exchangers and the capillary tube are discretized spatially to consider the lengthwise property variation and momentum and energy conservation equations have been employed to each segment. To simplify the analysis, the following assumptions were considered in the simulation: 1. 2. 3. 4.
Heat transfer with the ambient is negligible. Only single phase heat transfer occurs for secondary fluid. Compression process is adiabatic but not isentropic. Pressure drop on waterside and in connecting pipes is negligible. 5. Refrigerant is free from oil.
6. Heat transfer in the capillary tube is negligible. 7. Thermodynamic equilibrium (i.e. no metastable phenomenon) occurs in capillary tube flow. 8. Homogeneous and one-dimensional steady flow occurs through the capillary tube.
2.1.
Compressor
A reciprocating single stage compressor is used in the system. _ ref , is proportional to the displacement The mass flow rate, m rate and the volumetric efficiency and is inversely proportional to the specific volume of gas entering the compressor and is given by _ ref ¼ m
hV V_ S n1
(1)
where volumetric efficiency hV for the semi-hermetic compressor is estimated from the empirical relation available from the data reported (Ortiz et al., 2003): 2 Pdis Pdis (2) þ 0:0018 hV ¼ 0:9207 0:0756 Psuc Psuc Isentropic efficiency of the compressor is estimated by an empirical correlation (Ortiz et al., 2003) given by Pdis his;c ¼ 0:26 0:7952 Psuc 2 3 4 Pdis Pdis Pdis þ0:0414 0:0022 0:2803 Psuc Psuc Psuc
2.2.
ð3Þ
Gas cooler
As mentioned earlier, the gas cooler is segmented lengthwise to accommodate the property variation. Heat transfer in the ith segment of the gas cooler is expressed in terms of overall heat transfer coefficient as i ¼ ðUAÞigc ðLMTDÞigc Qgc
(4)
The overall heat transfer coefficient for the ith segment is calculated considering all the thermal resistances: ln do =di 1 1 1 ¼ þ þ (5) aw A w 2pDLkw ðUAÞigc ar Ar
Fig. 1 – (a) Schematic layout of a transcritical CO2 system and (b) the corresponding cycle on T–s plane.
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international journal of refrigeration 31 (2008) 388–395
Gnielinski correlation with the Pitla et al. (2002) modification, incorporating both bulk and wall properties, for supercritical in-tube carbon dioxide cooling is employed to calculate the heat transfer coefficient. Pitla correlation is given by Nurw þ Nurb krw (6) Nur ¼ 2 krb
ar ¼
Nur krb di
(7)
Nusselt number is calculated by Gnielinski correlation (Gnielinski, 1976) at the respective conditions: ðf =8 ðRe 1000ÞPr Nu ¼ 1=2 1:07 þ 12:7 f =8 Pr2=3 1
(8)
f ¼ ð0:79lnðReÞ 1:64Þ
Capillary tube
The capillary tube is discretized into a number of longitudinal elements (Fig. 2), to enable the sharp changes in CO2 property, particularly near the critical point, to be captured in the analysis. Principles of mass, energy, and momentum conservation are employed to each segment of the capillary tube. The conservation of mass for steady flow in an element of fluid is given by Ac uc ¼0 (16) d vc Neglecting the elevation difference and the heat transfer in and out of the tube, the energy conservation may be written as dhc þ
where f is calculated as 2
2.4.
(9)
The water side heat transfer coefficient is calculated by the well known Dittus–Boelter correlation.
G2c 2 dv ¼ 0 2 c
From the conservation of momentum equation, the difference in forces applied to the element of fluid due to drag and pressure difference on opposite ends of the element should be equal to that needed to accelerate the fluid and is expressed as dpc fc
2.3.
Evaporator
(17)
dLc uc Gc ¼ Gc duc Dc 2
(18)
Hence,
The evaporator is modelled in the same way as the gas cooler. However, due to the presence of two phase flow, the convective heat transfer coefficient has been calculated using Wattelet–Carlo correlation (Boewe et al., 2001):
( ) 2Dc drc rc 2 dpc dLc ¼ fc rc Gc
(19)
ar ¼ Fal
(10)
Lin friction factor (Lin et al., 1991) is used to calculate the two phase friction factor: vsp;c (20) ftp;c ¼ ftp;c fsp;c vtp;c
kl al ¼ 0:023 Re0:8 Pr0:4 l di l
(11)
where 2
ftp;c
F ¼ 1 þ 1:925X0:83 tt
(12)
Similar to the gas cooler model, Dittus–Boelter correlation is employed to calculate the waterside heat transfer coefficient. The refrigeration side pressure drop for the ith segment is estimated by G2ev;r 2 DLev fr ð1 xÞ2 f ðDPev;r Þ ¼ 4 di 2 rl l i
(21)
where
where Xtt is the Lockhart–Martinelli factor given by 0:9 0:5 0:1 1x rv ml Xtt ¼ x rl mv
12 3=2 31=12 16 þ A16 tp;c þ Btp;c vg;c ¼ 4 1 1 þ xc 12 3=2 5 vl;c 8 16 þ A16 sp;c þ Bsp;c Resp;c 8 Retp;c
(13)
Atp;c ¼ 2:457 ln
7 Retp;c
Retp;c ¼
0:9
1 þ0:273=Dc
; Btp;c ¼
37; 530 ; Retp;c
G c Dc mtp;c
The McAdams model (McAdams et al., 1942) is employed to estimate the two phase viscosity: 1 ð1 xc Þ xc ¼ þ mtp;c ml;c mg;c
(22)
The friction factor fr and two phase multiplier fl are expressed as fr ¼ 0:0791Re0:25 l
(14)
and !1=2 fl ¼
1:376 þ
ð7:242=X1:655 Þ tt
where Xtt is the Lockhart–Martinelli factor.
(15) Fig. 2 – Longitudinal discretization for the capillary tube.
392
3.
international journal of refrigeration 31 (2008) 388–395
Numerical methodology
A computer code has been developed for the steady state simulation to evaluate the system performance of a transcritical carbon dioxide heat pump system for simultaneous heating and cooling at 73 C and 4 C, respectively, employing various configurations of an adiabatic capillary tube. Subcritical and supercritical thermo-physical and transport properties of CO2 are estimated employing a precision property code CO2PROP developed locally (Sarkar et al., 2004). Both the gas cooler and the capillary tube are susceptible to abrupt property variation of CO2 near the critical region. To capture these abrupt changes, both the capillary tube and the gas cooler are discretized longitudinally. To yield greater accuracy, the evaporator is spatially discretized as well. Each segment of gas cooler and evaporator is modelled considering them to be a counter flow heat exchanger. As shown in the flow-chart (Fig. 3), a certain
Input: Evaporator dimensions (di, do, Di, Lev), Gas cooler dimensions (di, do, Di, Lgc), Compressor data; Vs, N, Water: tevi, tgci, . mevw or tevo, mgcw or tgco, ΔTsucsuperheat Capillary geometry: D, ε. Guess: Capillary length (Lc) Guess: evaporator outlet pressure (P6)
Guess: gas cooler pressure (Pdis)
Calculate: mass flow rate, mref
Input evaporator model Calculate P5, x5, h4 Input gas cooler model Calculate find P3, t3 Input capillary tube model Calculate Lc*, x*5
If: Lc = L*c
No
Update Pdis
Yes No If: x5 = x*5
Update P6
Yes Optimum COP
No
Update Lc
Yes Output: state points, COPmax, Pdis, Lc L* = Simulated capillary tube length, x* = Refrigerant quality at exit of the simulated capillary tube
Fig. 3 – Flow-chart for the simulation model.
diameter and internal surface roughness are chosen for a capillary tube and mass flow rate of water and suction superheat are chosen as well. Initially capillary tube length is selected and discharge and evaporator pressures are guessed and the code solves iteratively for state point and system performance. It may be noted that the gas cooler pressure is estimated based on the chosen capillary tube length. Unlike a controllable throttle valve based system, gas cooler pressure is not an independent parameter with the capillary tube based system once the tube length is specified. Length of the capillary tube is selected based on the optimum system COP.
4.
Results and discussion
Performance of the system being studied for simultaneous heating and cooling applications is evaluated based on system COPs for various conditions and capillary geometry. Results are presented for the combined length of 25 m of the evaporator and gas cooler of standard stainless steel inner tube of 9.525 mm OD and outer tube of 14.097 mm ID. Capillary tubes in the range of 1.4–1.6 mm ID and having 0.001–0.003 mm internal surface roughness are employed in the study. Capillary tubes having ID smaller than 1.4 mm lead to choking and this sets the limiting condition for selection of optimal tube length. A Dorin (model TCS 111H) CO2 compressor with a rated speed of 2900 rpm is chosen for the system. Internal heat exchanger is not used in the analysis. However, suction superheat is taken as 10 C within the evaporator. About 8–10% evaporator length is utilised for suction superheat. Results are generated for the compressor rated speed of 2900 rpm while water inlet temperature varied from 20 C to 40 C and heat exchanger area ratio (gas cooler-to-evaporator) varied between 1 and 3. Fixing the water outlet temperature in gas cooler and evaporator at 73 C and 4 C, respectively, the simulated mass flow rate of water is calculated for each water inlet temperature to suit the heat transfer requirement as per the design of gas cooler and evaporator. Results from the present simulation model are compared with the published results from Madsen et al. (2005) for the specified capillary tubes with Dc ¼ 2 mm, Lc ¼ 2/4 m, Dc ¼ 1 mm, Lc ¼ 2 m, and Dc ¼ 1.8 mm, Lc ¼ 3 m. The evaporator pressure, gas cooler exit temperature and the high pressure are taken as 35 bar, 40 C and 100 bar, respectively. For all the chosen capillary tubes, internal surface roughness 3 is taken as 0.00576 mm. Experimentally measured refrigerant mass flow rates closely match predicted mass flow rates of the model presented here (Fig. 4). Variation of performance parameters with area ratio and capillary tube diameter for an internal tube roughness of 0.0015, a water inlet temperature of 30 C and a compressor speed of 2900 rpm has been studied through the simulation code and is exhibited in a nomogram (Fig. 5). It may be observed that with increase in area ratio, cooling output reduces due to decrease in refrigerant mass flow rate due to decrease in suction density at lower optimum discharge pressures. This may be attributed to the fact that at higher area ratio, gas cooler outlet temperature decreases and that causes the evaporator pressure to decrease as well for a given capillary tube. Consequently, refrigerant mass flow rate decreases
393
0.05
System COP
0.04
0.03
0.02
3.75
123
3.72
120
3.69
117
3.66
114
3.63
system COP Gas cooler pressure
0.01 Madsen et al. (2005) Our model
3.6 1.5
1.9
2.3
2.7
111
Gas cooler pressure (bar)
Theoretical refrigerant mass flow rate (kg/s)
international journal of refrigeration 31 (2008) 388–395
108 3.1
Capillary tube length (m)
0 0
0.01
0.02
0.03
0.04
0.05
Measured refrigerant mass flow rate (kg/s)
Fig. 4 – Validation of the present model with the results of Madsen et al. (2005).
due to decrease in suction density at a lower evaporator pressure. With decrease in evaporator pressure, gas cooler pressure also decreases. Hence, as shown in Fig. 5, system COP first increases and then decreases with a peak value of 3.72 at a gas cooler-to-evaporator area ratio of 1.5 for all the chosen capillary tubes; this trend is very similar to that reported earlier (Sarkar et al., 2006) for an expansion valve. At higher area ratio, capillary tube length increases for a chosen diameter, due to decrease in refrigerant mass flow rate (Fig. 5). The nomogram presented here is expected to help design the system better. For example, when the water inlet temperature is 30 C at a compressor speed of 2900 rpm, to attain a maximum COP of 3.72, an 1.6 m long and 1.4 mm ID capillary tube is required
Fig. 6 – Variation of COP and gas cooler pressure with capillary tube length at Dc [ 1.5 mm, 3 [ 0.0015 mm and area ratio [ 1.5.
at an area ratio 1.5, and the system is expected to yield a cooling output of 4.75 kW with a refrigerant mass flow rate of 0.0287 kg s1. All these system operating condition information is extracted from a simple diagram given here as a nomogram, as is illustrated in Fig. 5. As exhibited in Fig. 6, COP first increases with capillary length increase to reach a peak and then decreases. However, gas cooler pressure increases monotonically. Near the peak, COP variation is flat, implying that beyond a certain length, the gain in COP is not very appreciable. Hence it is recommended that for a chosen capillary tube diameter and internal surface roughness, capillary tube length should be selected on the basis of optimum COP.
Fig. 5 – Nomogram depicting the variation of performance parameters with area ratio and capillary diameter at 3 [ 0.0015 mm, compressor speed [ 2900 rpm and Twi [ 30 8C.
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international journal of refrigeration 31 (2008) 388–395
5.2
4.2
Table 1 – Variation of heat exchanger water mass flow rate with inlet temperature
4.9
3.8
4.3 4
3.6 System COP (Exp. valve) Dc = 1.4 mm, Lc = 1.4 m Dc = 1.5 mm, Lc = 2.1 m Dc = 1.6 mm, Lc = 3.0 m Cooling capacity (Exp. valve)
3.4
3.7 3.4
1 2 3 4 5
Water inlet temperature ( C)
Water mass flow rate (kg/min) Gas cooler
Evaporator
2.27 2.43 2.63 2.89 3.24
4.64 3.33 2.54 2.01 1.62
20 25 30 35 40
3.1
3.2 20
25
30
35
40
Water inlet temperature (°C) Fig. 7 – Capillary tube and expansion valve performance comparison at varying water inlet temperature and various capillary tube configurations with 3 [ 0.002 mm. Water inlet temperature is subjected to change with ambient condition. For a chosen capillary tube, it is desired that the system would run optimally even with varying water inlet temperature. This needs to be inspected carefully employing the simulation code. The effect of water inlet temperature at a compressor speed of 2900 rpm, and an optimum area ratio of 1.5 with various capillary tube configurations is shown in Figs. 7 and 8. Fig. 7 shows the variation of COP and cooling capacity with respect to water inlet temperature and various ID and length combination capillary tubes of internal surface roughness 0.002 mm. Table 1 shows the various water mass flow rates in the gas cooler and the evaporator for typical test runs with a capillary tube diameter of 1.5 mm having a surface roughness of 0.002 mm. As the water inlet temperature increases, mass flow rate of water in gas cooler increases while in evaporator it decreases for constant water outlet temperatures of 73 C and 4 C, respectively. It is observed that for all the chosen capillary tubes, the system operates very nearly at the optimum level at all the water inlet temperatures. The
Mass flow rate (Exp. Valve) Dc = 1.4, Lc = 1.4 Dc = 1.5, Lc = 2.1 Dc = 1.6, Lc = 3.0 Optimal gas cooler pressure (Exp. valve)
0.03
0.0296
reference optimum performance is chosen to be that of the corresponding heat pump system employing a controllable expansion valve instead of a capillary tube. It can also be observed that COP decreases with increase in water inlet temperature due to rise in gas cooler exit temperature causing degradation in heat transfer properties. Fig. 8 shows that the gas cooler pressure, which is not an independent parameter in case of the capillary tube, remains close to the optimum pressure obtained with an expansion valve at all the water inlet temperatures and for all the chosen capillary tube lengths. There is a marginal change in refrigerant mass flow rate with varying water inlet temperature. However, the gas cooler pressure increases rapidly with increase in water inlet temperature (Fig. 8). This system behaviour with the capillary tube and with varying water inlet temperature (in varying ambient temperature) shows that the capillary based system is at least as good as the controllable expansion valve based system. This is quite encouraging since there has been a good amount of scepticism in whether a capillary tube based system would perform as well when there is an issue of setting the optimum gas cooler pressure for all CO2 transcritical system heat pumps. Fig. 9 shows that as water temperature increases, compressor work in an expansion valve based system also increases due to increase in gas cooler pressure. A very similar trend is also exhibited by the heat pump using a capillary tube as the expansion device. It is also observed that the optimum capillary length increases rapidly with
124 3.55 121
118 0.0292 115 0.0288 112
Gas cooler pressure (bar)
Refrigerant mass flow rate (kg/s)
Test run
Compressor work (kW)
System COP
4.6
Cooling capacity (kW)
4
Compressor work (Exp. Valve) Dc = 1.4, Lc = 1.4 Dc = 1.5, Lc = 2.1 Dc = 1.6, Lc = 3.0
3.5 3.45 3.4 3.35 3.3
109
0.0284 20
25
30
35
40
Water inlet temperature (°C) Fig. 8 – Mass flow rate and gas cooler pressure comparison between capillary and expansion valve based systems with respect to water inlet temperature.
3.25 20
25
30
35
40
Water inlet temperature (°C) Fig. 9 – Variation of compressor work with respect to water inlet temperature for capillary tube and expansion valve based systems.
international journal of refrigeration 31 (2008) 388–395
in this study that capillary tubes can be a fairly effective expansion device in smaller CO2 based transcritical heat pump systems where the system is able to operate optimally with varying ambient conditions within a limited range.
Optimum capillary tube length (m)
3.8 roughness = 0.001 mm roughness = 0.0015 mm roughness = 0.002 mm roughness = 0.003 mm
3.4 3 2.6
references 2.2 1.8 1.4 1.4
1.45
1.5
1.55
1.6
Capillary tube diameter (mm) Fig. 10 – Optimum capillary tube length variation with capillary tube diameter and internal surface roughness.
increase in capillary tube diameter. However, internal surface roughness effect is less significant on optimum capillary length for the chosen diameters (Fig. 10). It may be noted that change in optimum capillary tube length is more significant at lower internal surface roughness values due to the fact that beyond a certain value of 3=Dc ratio, friction factor depends only on the size of the roughness elements. It is observed that installation of a proper capillary tube length replacing an expansion valve will result in a natural adjustment of the gas cooler pressure, so that the system balance always shifts to a favourable COP direction. At all the chosen water inlet temperatures, system operates at balance conditions using a proper capillary tube length as the expansion device. This novel finding regarding capillary tube based CO2 heat pumps augurs well for such systems, particularly for the smaller sized ones.
5.
395
Conclusions
The steady state performance of a transcritical CO2 heat pump system for simultaneous heating and cooling employing an adiabatic capillary tube has been compared with a nonconventional optimal system using a controllable expansion valve. For the transcritical cycle, pressure and temperature are independent parameters and system behaviour is not expected to be the same as in a conventional subcritical system employing a capillary tube as the expansion device. Capillary tube length turns out to be the deciding parameter to enable the system to run optimally. Length of the capillary tube should be selected on the basis of optimum gas cooler pressure for a given tube diameter. It is observed that the optimum area ratio value of 1.5 is almost the same for a controllable expansion valve and for all the chosen capillary tubes. A nomogram with capillary tube diameter as an independent parameter and COP, capillary tube length and refrigerant mass flow rate as output has been presented. Capillary tube based system is shown to be quite flexible regarding changes in ambient temperature, almost behaving to offer an optimal pressure control just like the controllable expansion valve. System performance is marginally better with a capillary tube at higher gas cooler exit temperature. It has been shown
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