Performance of a tube-in-tube CO2 gas cooler

Performance of a tube-in-tube CO2

gas cooler

Pei-Yu Yu

, Kai-Hsiang Lin

, Wei-Keng Lin

, Chi-Chuan Wang

*

a_{Green Energy Research Laboratories, Industrial Technology Research Institute, Hsinchu 300, Taiwan} b

Department of Mechanical Engineering, National Chiao Tung University, EE474, 1001 University Road, Hsinchu 300, Taiwan

c

Department of Engineering and System Science, National TsingHua University, Hsinchu 300, Taiwan

a r t i c l e i n f o

Article history:

Received 8 December 2011 Received in revised form 5 June 2012

Accepted 18 June 2012 Available online 4 July 2012 Keywords: Carbon dioxide Gas cooler Heat exchanger Supercritical Pseudo-critical

a b s t r a c t

In this study, a tube-in-tube heat exchanger model applicable to supercritical CO2and

water was developed. The developed model is first validated with some existing measurements. Normally, the variation of the heat transfer rate for a constant-property working fluid shows a monotonic decrease from the inlet of minimum heat capacity flow rate (Cmin). By contrast, the CO2may present a local minimum and a local maximum

along the length of the heat exchanger, provided CO2passes through the pseudo-critical

temperature, and this phenomenon becomes more and more pronounced when the pressure is close to the critical pressure. In contrast, it is possible for a local maximum heat transfer rate to occur near the inlet of Cmineven when the CO2does not pass through the

pseudo-critical point. This happens when Cmin is on the water side and the property

variation of CO2is taken into account. The calculation also shows that the effect of the inlet

pressure on the variation of the CO2temperature is not as apparent as the effect of the inlet

pressure on the heat transfer rate, even when there is a significant change in the overall heat transfer coefficient, implying that the heat transfer characteristics of CO2near the

pseudo-critical region is similar to normal refrigerants, which show an invariant temper-ature at the condensation point. Hence, it would be beneficial to extend the influence of the pseudo-critical region when taking the heat transfer augmentation into consideration.

ª 2012 Elsevier Ltd and IIR. All rights reserved.

Performance d’un refroidisseur de gaz au CO2 a` double tube

1.

Introduction

The use of natural refrigerants for heating, ventilation, air-conditioning, and refrigeration applications has attracted much attention recently. Among the possible candidates, carbon dioxide (CO2) is regarded as one of the most promising

candidates because it is environmentally benign, nontoxic, and possesses comparatively good thermodynamic proper-ties. Carbon dioxide is also comparable to HCFC refrigerants and outperforms conventional refrigerants when it is used in hot water heaters and automobile air conditioners (Lorentzen and Pettersen, 1993;Lorentzen, 1994;Lorentzen, 1995). In CO2

* Corresponding author. Tel.:þ886 3 5712121x55105; fax: þ886 3 5720634. E-mail address:[email protected](C.-C. Wang).

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air-conditioning and heat pump systems, CO2rejects heat at

a pressure above the critical pressure (7.38 MPa) in the gas cooler without phase change. When the CO2 is at

super-critical pressures, some small fluid temperature and pres-sure variations may produce large changes in the thermo-physical properties, and this is especially pronounced when the temperature is near the critical point. The gigantic change in the thermophysical properties may result in significant deviations in both heat transfer and fluid flow behaviors.

In contrast, investigations associated with CO2are mainly

performed on either system performance (e.g., Austin and Sumathy, 2011;Goodman et al., 2011;Cecchinato et al., 2005) or the heat transfer characteristics between tubes and chan-nels (e.g.,Cheng et al., 2008;Dang and Hihara, 2004a, 2004b; Dang et al., 2007, 2008, 2010;Gao et al., 2007;Kim et al., 2008;

Liao and Zhao, 2002; Yun et al., 2005, 2007). There are

comparatively fewer studies concerning the overall perfor-mance of heat exchangers (gas coolers). The relevant studies on the performance of gas coolers are normally classified into two categoriesdair cooled and water cooleddand most studies were related to air-cooled systems (Asinaria et al., 2004;Chang and Kim, 2007;Park and Hrnjak, 2007;Zhao and

Ohadi, 2004; Zilio et al., 2007). Note that the dominant

thermal resistances for an air-cooled gas cooler mainly occur on the air side, and thus its performance is normally controlled by the air flow rather than the CO2, irrespective of

appreciable changes in the physical properties of CO2. In

contrast, comparatively fewer studies investigate the cooled gas cooler. The only studies investigating the water-cooled gas cooler were carried out by Fronk and Garimella

(2011a, 2011b)andWang and Hihara (2002). The former

con-ducted an analysis of the heat transfer mechanisms of a water-coupled gas cooler with a compact, multipass cross-counter flow of aluminum-brazed plate and a microchannel CO2gas cooler and validated the analysis with experimental

data. The later presented an analysis of a concentric coun-terflow heat exchanger by solving a set of complicated partial differential equations, including conservation of mass, momentum and energy equations, between CO2 and water

and considering the wall conduction in both the radial and axial directions. They found that the variation of the local heat flux revealed a local maximum within the heat exchanger due to the tremendous change in the specific heat of CO2.

For a typical gas cooler, irrespective of the inlet pressure, the temperature of CO2changes quite significantly along the

length of the heat exchanger and may pass through the pseudo-critical point, where an appreciable change in the heat capacity may occur. In addition, the effect of changes in the physical properties of CO2is even more severe for a

liquid-cooled gas cooler because the controlled thermal resistance could switch to the CO2side. Despite the considerable efforts

that were devoted in determining the heat transfer perfor-mance of CO2above the critical point, the existing studies of

liquid-cooled gas coolers are limited and complicated. Hence, it is the objective of this study to develop a simple heat exchanger model that is capable of investigating and analyzing the heat transfer behavior of a CO2tube-in-tube water-cooled

gas cooler subject to a given set of inlet conditions.

2.

Numerical method

The model heat exchanger is a double-pipe heat exchanger with water flowing in the annulus and CO2flowing

counter-currently in the tube. Fig. 1 is a schematic of the heat exchanger. Because considerable changes in the physical properties of CO2 may be encountered, especially near

pseudo-critical temperatures, the heat exchanger must be subdivided into many small segments. A prior sensitivity analysis of the influence of the segments was performed, and Nomenclature

A surface area (m2₎

C heat capacity flow rate (W K1) Cp specific heat (J kg1K1)

d diameter (m)

f friction factor

h heat transfer coefficient (W m2K1) i specific enthalpy (kJ kg1)

ID inner diameter (m) k conductivity (W m1K1) L tube length (m)

LMTD log mean temperature difference (K) _m mass flow rate (kg s1)

Mw mass flow rate for water (kg s1) Mc mass flow rate for CO2(kg s1)

Nu Nusselt number (hd k1) OD outer diameter (m)

P pressure (MPa)

Pr Prandtl number Q heat transfer rate (kW) R thermal resistance (C W1) Re Reynolds number (rud m1₎

T temperature (C) u velocity (m s1)

U overall heat transfer coefficient (W m2K1) Greek letters DT temperature difference (K) m viscosity (kg m1s1) r density (kg m3) Subscripts b bulk c carbon dioxide

c,i ith segment of carbon dioxide

f film

H hydraulic diameter

i inner

i ith segment of the heat exchanger max larger one

min smaller one

o outer

w water

wall wall

a total of 65 segments were used in the simulation. A sche-matic showing the variation of the temperature for CO2and

water is shown inFig. 1(b), where the subscript c denotes CO2

and w represents water. The heat balance between the water and the coolant in each segment i can be expressed by the following equations:

Qi¼ mcCpc;i
Tc;i Tc;iþ1¼ mwCpw;i
Tw;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 CO2are a function of the local

pressure and temperature, and the properties of water are related to the local temperature. The relevant properties are obtained fromREFPROP, 2007. The heat transfer coefficient of CO2is based on theDang and Hihara, 2004a, i.e.,

hc¼ Nuckc=d: (4) Nuc¼  fc 8  ðReb 1000ÞPr 1:07 þ 12:7 ffiffiffiffi fc 8 r ðPr2=3_{ 1Þ} : (5) where Pr¼ 8 < : Cpbmb=lb; for Cpb Cp Cp_bmb=lf; for Cpb< Cp and mb=lb mf=lf Cpbmf=lf; for Cpb< Cp and mb=lb< mf=lf : (6) Cp¼hb hwall Tb Twall: (7) Reb¼ Gdi mb : (8) fc¼ ½1:82 logðRebÞ  1:642: (9)

where the subscript b represents the bulk temperature, wall is evaluated at the wall temperature and f denotes a calculation at the film temperature. The film temperature, 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  ðRe  1000ÞPr 1:07 þ 12:7 ffiffiffiffiffi fw 8 r ðPr2=3_{ 1Þ} : (11) where fw¼ ½1:82 logðRewÞ  1:642: (12)

3.

Results and discussion

To validate the proposed model, the calculation is first compared with the measurements ofPitla et al. (2000).Pitla et al. (2000)conducted experiments exploiting a CO2

tube-in-tube heat exchanger with an ID of 0.00472 m and an OD of 0.00635 m for the inner tube. The ID for the outer tube is 0.01575 m. Their test conditions are tabulated inTable 1. Using the inlet conditions for their raw data, the calculated cooling capacity vs. their measurements is depicted inFig. 2. As seen, the calculations are in line with the experimental measure-ments, suggesting the applicability of the present modeling.

Fig. 3is a schematic showing the relevant influence of the local heat transfer rate as a function of position, starting at the inlet of the fluid where the minimum thermal capacitance rate (Cmin) occurs.Fig. 3(a) depicts a schematic showing the

local heat transfer rate vs. the dimensionless distance from the inlet of Cmin for a typical tube-in-tube heat exchanger

using a conventional, subcritical, single-phase fluid such as water/water. In general, the variation in the local heat transfer rate shows only monotonic variation, and the heat transfer rate peaks at the inlet of Cmin, regardless of whether Cminis on

Table 1 e Test conditions for Pitla et al. (2000). Variant TCO2;in (C) PCO2;in (MPa) Twater,in (C) Mc (kg s1) Mw (kg s1) Run1 121.2 9.44 20.8 0.01963 0.04011 Run2 126 11.19 24.2 0.0274 0.040497 Run3 73.3 13.33 36.12 0.02043 0.12914 Run4 123.5 10.8 27.21 0.02862 0.084087 Run5 107.2 8.11 24.2 0.0198 0.0455 Run6 123.4 8.98 22.3 0.02996 0.067864 Run7 118.3 7.79 21.2 0.02123 0.066434 Run8 115.8 8.60 18.9 0.03436 0.084087 Run9 114.9 8.76 18.9 0.03638 0.065091 Run10 113.4 9.50 15.9 0.03825 0.109052 Carbon dioxide flow direction Water flow Tc,1 Tc,2 Tc,3 Tw,1 Tw,2 Tw,3 Tc,i Tc,i +1 Tw,i Tw,i +1 CO₂ Water

a

b

Fig. 1 e (a) Schematic of the tube-in-tube heat exchanger and (b) Definition of the temperature for CO2and water

the hot side or the cold side, followed by a steady decrease from the inlet of Cmintoward the outlet. In an extreme case in

which Cmin¼ Cmax, the variation of the local heat transfer rate

remains unchanged, provided the overall heat transfer coef-ficient is unchanged, as shown inFig. 3(b).

Apart from the constant-property condition, appreciable changes in the thermophysical properties of CO2give rise to

some certain unique characteristics. Of course, the variation in the local heat transfer rate for a CO2 heat exchanger still

behaves quite similarly to the constant-property scenario (Fig. 3(a)) as long as the CO2does not pass the pseudo-critical

point. Aside from the conventional monotonic behavior, there are two special phenomena that may be seen for the CO2

heat exchanger, namely, a local minimum and a plateau

(Fig. 3(c)) and a local maximum may occur within the heat

exchanger (Fig. 3(d)). To illustrate these special phenomena, calculations are performed with a CO2 tube-in-tube heat

exchanger with an ID¼ 0.020 m and an OD ¼ 0.025 m for the inner tube and an ID¼ 0.050 m for the outer tube. The calcu-lations are made for inlet pressures of 12, 10, and 8 MPa. The inlet temperatures of CO2 and water are 382 K and 287 K,

respectively, while the mass flow rates for water and CO2are

both 0.5 kg s1. The variation of the local heat transfer rate as a function of the dimensionless tube length is shown in Fig. 4(a). As clearly seen in this figure, the CO2heat exchanger

shows a peculiar trend compared with that of constant-property fluids. The local heat transfer rate does not show a consistently monotonic decrease from the inlet of Cminalong

the length of the heat exchanger. Conversely, the local heat transfer rate first decreases to a local minimum, followed by a rise to a plateau, and finally decreases again toward the outlet. This strange phenomenon becomes more and more apparent when the inlet pressure is further reduced. In fact, a significant recovery of the local heat transfer rate is encountered for p¼ 8 MPa, despite the fact that the maximum temperature difference still occurs at the CO2inlet. To explain

this phenomenon, one must understand the variation of the specific heat capacity of CO2above the critical point, as shown

inFig. 4(b). For a given supercritical pressure, a sharp rise in the cp is seen at the so-called pseudo-critical temperature. In

practice, when cooling, the very hot CO2gas may inevitably

pass through this temperature. In this sense, a significant increase in cpis seen near this temperature, leading to an

increase in the heat transfer coefficient and a much larger overall heat transfer coefficient accordingly. This phenom-enon becomes even more pronounced when the pressure is further decreased as cpincreases near the critical point. As

a result, a significant recovery of the local heat transfer rate and a second maximum occur in the tube-in-tube heat exchanger. The temperature variation of CO2as a function of the tube

length is depicted inFig. 4(c). The effect of the inlet pressure on the variation of the CO2temperature is not as apparent as the

variation of the heat transfer rate, even when there is a signif-icant change in the overall heat transfer coefficient. One of the explanations involves the considerable increase in the heat capacity flow rate (C ) of the CO2 near the pseudo-critical

temperature. Based on a simple energy balance formula, Q¼ CcDT, it is not surprising that the variation of the CO2

temperature tends to show a very slowly decreasing trend adjacent to the pseudo-critical region when compared with the inlet or outlet region. Apparently, this phenomenon becomes more pronounced as the inlet pressure is decreased, thereby leading to intersections of the temperatures profiles along the length of the heat exchangers. The foregoing results imply that the heat transfer characteristics of CO2near the pseudo-critical

region resemble normal refrigerants, which show an invariant temperature at the condensation point.

In contrast, it is possible for a local maximum to occur near the inlet of Cmin (Fig. 3(d)) even when CO2 does not pass

through the pseudo-critical point. This occurs when Cminis on

the water side and the effect of the variable properties has

x/L ( from the inlet of Cmin ) Q

x/L ( from the inlet of Cmin ) Q

x/L ( from the inlet of Cmin )

Q Q

x/L ( from the inlet of Cmin )

a

b

d

c

Fig. 3 e Schematic of the variation of the local heat transfer rate for a tube-in-tube heat exchanger: (a) Constant property,Cmins Cmax; (b) Constant property,Cmin[ Cmax;

(c) CO2flow across the pseudo-critical point; and (d)

Variable property.

Calculated Q (Watts)

-15%

+15%

Fig. 2 e Comparison of the local heat transfer rate for the calculations andPitla et al.’s data (2000).

been accounted for. Basically, the recovery of the local heat transfer rate is quite small and could also be applicable to any working-fluid subject to the same conditions.

4.

Concluding remarks

The present study described a tube-in-tube heat exchanger model applicable for supercritical CO2and water. The

devel-oped model is validated with some existing measurements. In addition, a further calculation is made to examine the influ-ence of the inlet pressure of CO2on the heat transfer

perfor-mance. Normally, the variation of the local heat transfer rate for constant-property working fluids shows a monotonic decrease from the inlet of Cmin. Conversely the CO2 may

present a local minimum and a local maximum along the length of the heat exchanger, provided CO2passes through the

pseudo-critical temperature, and this phenomenon becomes more and more pronounced when the pressure is close to the critical pressure. The phenomenon is attributed to the significant increase in the specific heat of CO2 near the

pseudo-critical temperature. The calculation also shows that the effect of the inlet pressure on the variation of the CO2

temperature is not as apparent as the variation of the heat transfer rate, even when there is a significant change in the overall heat transfer coefficient. This is also associated with a considerable increase in the heat capacity flow rate of the

CO2near the pseudo-critical temperature. As a consequence,

the variation of the CO2 temperature tends to show a very

slow decreasing trend adjacent to the pseudo-critical region when compared with the inlet or outlet region. Apparently, this phenomenon becomes more pronounced as the inlet pressure is decreased, thereby leading to intersections of the temperatures profiles along the length of the heat exchangers. The foregoing results imply that the heat transfer character-istics of CO2near the pseudo-critical region resemble those of

normal refrigerants, which show an invariant temperature at the condensation point. Hence, it would be beneficial to expand the influence of the pseudo-critical region when considering heat transfer augmentation.

In contrast, it is possible for a local maximum heat transfer rate to occur near the inlet of Cmin, even when CO2does not

pass through the pseudo-critical point. This happens when Cminis on the water side and the variation in the CO2

prop-erties is taken into account.

Acknowledgments

The authors would like to express gratitude for the Energy R&D foundation funding from the Bureau of Energy of the Ministry of Economic, Taiwan, and the National Science Committee (NSC 100-ET-E-009-004-ET) of Taiwan.

x/L 0.0 0.2 0.4 0.6 0.8 1.0 Q (Watt) 0 200 400 600 800 1000 1200 p = 12 MPa , Mc = 0.05 kgs-1 , Mw = 0.5 kgs-1 p = 10 MPa , Mc = 0.05 kgs-1 , Mw = 0.5 kgs-1 p = 8 MPa , Mc = 0.05 kgs-1 , Mw = 0.5 kgs-1 x/L 0.0 0.2 0.4 0.6 0.8 1.0 0 10000 20000 30000 40000 p = 12MPa p = 10MPa p = 8MPa Cp ( J kg -1 K -1 ) x/L 0.0 0.2 0.4 0.6 0.8 1.0 Temperature (K) 280 300 320 340 360 380 400 p = 8 MPa , Mc = 0.05 kgs-1 , Mw = 0.5 kgs-1 p = 10 MPa , Mc = 0.05 kgs-1 , Mw = 0.5 kgs-1 p = 12 MPa , Mc = 0.05 kgs-1 , Mw = 0.5 kgs-1

a

b

c

Fig. 4 e Effect of the inlet pressure on (a) The variation of the local heat transfer rate vs. the dimensionless tube length, (b) The variation ofcpvs. the dimensionless tube length and (c) The variation of the CO2temperature vs. the dimensionless tube length.

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