An assessment of heat transfer through fins in a fin-and-tube gas cooler for transcritical carbon dioxide cycles.

In C[O.sub.2] transcritical refrigeration cycles, fin-and-tube coils are still considered possible gas cooling devices due to their lower cost when compared with recent aluminium minichannel heat exchangers. In spite of the very high working pressures, an off-the-shelf coil with four ranks of 3/8 in. (9.52 mm) copper tube and louvered fins was found suitable to work with high R-744 pressures and has been studied as a gas cooler in a test rig built for testing carbon dioxide (C[O.sub.2]) equipment operating with air as a secondary fluid. The test rig consists of two closed-loop air circuits acting as heat sink and heat source for the gas cooler and evaporator, respectively. The tested refrigerating circuit consists of two tube-and-fin heat exchangers as the gas cooler and the evaporator, a back-pressure valve as the throttling device, a double-stage compound compressor equipped with an oil separator, and an intercooler. A full set of thermocouples, pressure transducers, and flowmeters allows measurement and recording of all the main parameters of the C[O.sub.2] cycle, enabling heat balance to be performed for both air side and refrigerant side.

Tests focused on two different gas coolers, with continuous and cut fins, and on two different circuit arrangements. Tests on each heat exchanger were run at three different inlet conditions, for both C[O.sub.2] and air. A simulation model was developed for this type of heat exchanger and three models (Dang and Hihara 2004; Gnielinski 1976; Pitla et al. 2002) proposed for the C[O.sub.2] supercritical cooling heat transfer coefficients were implemented and compared in the code.

The model results are compared with the experimental data for the finned coil; emphasis is given to the effect of heat conduction through fins between adjacent tube ranks on system efficiency. In the paper, the experimental results for transcritical C[O.sub.2] entering the gas cooler at 87.0[degrees]C (7.911 MPa), 97.6[degrees]C (8.599 MPa), and 107.8[degrees]C (9.102 MPa) with air inlet temperatures of 20.3[degrees]C, 21.5[degrees]C, and 23.0[degrees]C, respectively, are presented. By using a coil with fins modified to reduce the heat conduction, a 3.7% to 5.6% heat flux improvement was gained. This improvement can be clearly translated in terms of coefficient of performance (COP), since a low value of the C[O.sub.2] temperature at its outlet increases the cooling capacity. Considering a reference cycle with the same operating conditions, a 5.7% to 6.6% increase of COP can be obtained.

INTRODUCTION

Due to the necessity of decreasing the greenhouse effect, new fluids need to be investigated as refrigerants. Carbon dioxide (C[O.sub.2]) seems promising because of its environmental friendliness and some excellent thermodynamic and transport properties, such as high specific heat, high thermal conductivity, and low viscosity. The "traditional" finned coil heat exchangers still can be considered an opportunity for C[O.sub.2] transcritical cycles. The gas cooling process needs to be investigated, taking into account two points of view: the great variation of thermophysical properties and the large decrease in temperature occurring along the heat exchanger. Very poor evidence is provided in the open literature to the study of finned coil gas coolers (GCs) with "macro" tubes (i.e., the internal diameter of the pipe is larger than 3 mm). Recently, Hwang et al. (2005) proposed an experimental and numerical study of a three-row finned coil GC with 7.9 mm outside diameter.

For this research, a set of tests was conducted and experimental results were compared with numerical predictions obtained through a finite volume simulation software.

Although simulation results gained by our software have been found to be in agreement with experimental results for a large number of refrigerants and test conditions, a systematic deviation was seen using C[O.sub.2]. Therefore, some correlations to predict C[O.sub.2] heat transfer coefficient were tested, but the heat conduction along the heat exchanger, which has not been considered by the software, was deemed to be the most important cause of the disagreement in results. This kind of phenomenon is not considered by the simulation software at the moment, and very poor evidence is given to this problem by papers available in the open literature. Furthermore, it seems to be relevant only to finned coil heat exchangers, since it was shown to be unimportant in microchannel heat exchangers (Asinari et al. 2004).

TEST RIG DESCRIPTION AND UNCERTAINTY ANALYSIS

The C[O.sub.2] circuit (Figure 1) carries out a double compression with gas intercooling between the two compression stages and single throttling, and it is equipped with an internal heat exchanger. The compressor is a two-stage semi-hermetic reciprocating unit running at 1450 rpm (50 Hz). The nominal volumetric flow rate of the low-pressure stage (one cylinder) is 3.0 [m.sup.3]/h, while that of the second stage is 1.74 [m.sup.3]/h (volume ratio 1.7). The lubricant is a PAG oil 46 ISO grade.

The compressor power input is recorded with an electronic transducer (with an accuracy of [+ or -]0.5% of the reading value).

The intercooler (IC) heat flow is rejected to a water loop. The cooling water inlet temperature and flow rate are controlled through an auxiliary circuit (temperature stability [+ or -]0.05[degrees]C). The IC is a copper tube-in-tube heat exchanger with the C[O.sub.2] flowing inside three pipes (4 mm ID, 6 mm OD) fed in parallel and inserted into a 20 mm ID (22 mm OD) copper tube. The water flows inside the outer tube in countercurrent to the C[O.sub.2]. The IC was designed for a 1[degrees]C temperature approach between the two fluids. The water volumetric flow rate is measured with an electromagnetic flow meter (accuracy [+ or -]0.2% of the reading value).

The internal heat exchanger used was a copper-steel 10 m long tube-in-tube heat exchanger with the high-pressure fluid flowing inside three pipes (6 mm ID, 8 mm OD) fed in parallel and inserted into a 21 mm ID (26.7 mm OD) steel tube. The low-pressure C[O.sub.2] flows inside the outer tube in countercurrent to the high-pressure C[O.sub.2]. The internal heat exchanger was designed for a 2[degrees]C temperature approach between the two fluids. The throttling device used in the tests was a back-pressure valve; this allows the operator to set and keep constant the GC outlet pressure.

The C[O.sub.2] circuit is equipped with an oil separator. A special accumulator with sight glasses is inserted for visual inspection of the oil returning to the compressor crankcase. A metering valve is also installed to control the lubricant level in the compressor and to avoid any hot gas bypass through the oil drainage.

Air is the external fluid for both the GC and the evaporator. For the tests reported here, finned coils with round copper tubes (8.22 mm ID, 9.52 mm OD) are employed. The aluminium fins are louvered with 2.1 mm fin spacing. The face area for both exchangers is 500 x 500 mm. Air temperature at the inlet of each heat exchanger is controlled by way of two separated closed-loop wind tunnels. The air duct layout was designed through computational fluid dynamics simulation targeted at getting very uniform velocity and temperature distribution over the entire heat exchanger face area. The centrifugal fans are equipped with inverters to adjust the volumetric flow rate that is measured with ISA 1932, AISI 316L nozzles with pressure taps integrated in the nozzle body. The nozzles were installed according to EN-ISO Standard 5167 (ISO 2005). Air pressure drop through the nozzles is measured by a strain gauge pressure transducer with an accuracy of [+ or -]1 Pa, while air temperature downstream the nozzles is recorded with a thermocouple. In this way, according to EN-ISO Standard 5167, the estimated accuracy in volumetric flow rate [dot.V] measurement is [+ or -]0.8% of the reading.

[FIGURE 1 OMITTED]

The air in the closed loop serving the GC is reconditioned by a cooling finned coil fed with water kept at an inlet constant temperature in an auxiliary circuit equipped with a commercial chiller and control system. The air inlet temperature to the GC is then kept at the desired value by electrical heaters, proportional-integral-derivative (PID) controlled. Another PID feedback loop is used to control the air dry-bulb temperature at the evaporator inlet by compensating the C[O.sub.2] system cooling power with electrical heating. The air temperature stability thus achieved in steady-state conditions was [+ or -]0.05[degrees]C. Nine thermocouples are placed, evenly distributed, just before the GC inlet. Since the large temperature change of the C[O.sub.2] through the gas cooling process leads to a scattered distribution of the air temperature across the outlet section (depending on the C[O.sub.2] pipe arrangement in the finned coil), an air mixer is placed after the GC and the air temperature is measured again by nine thermocouples placed after the air mixer. The same thermocouple arrangement was used for the evaporator.

C[O.sub.2] temperatures are measured with thermocouples placed inside mixing chambers at the inlet and outlet of each heat exchanger. A thermocouple is also placed at the IC water inlet, whereas the water temperature change across the IC is measured with a four-junction type T thermopile.

All the thermocouples for air and C[O.sub.2] are T type; the complete measuring chain, including the multimeter and the [+ or -]0.01[degrees]C reference ice point, was calibrated against a Pt100 thermometer of [+ or -]0.02[degrees]C accuracy. Thus, an accuracy of [+ or -]0.05[degrees]C is estimated for all the temperature measurements.

R-744 pressures are recorded with strain-gauge transducers at the outlet of each heat exchanger and inside the compressor's second-stage (high pressure) suction chamber. The accuracy is [+ or -]1 kPa for evaporator and compressor chamber pressures and [+ or -]2 kPa for GC pressures, according to the calibration report from the manufacturer. Differential pressure transducers were used for pressure drop recording across the GC, the evaporator, and the IC (accuracy [+ or -]400 Pa).

C[O.sub.2] mass flow rate is measured by a Coriolis mass flowmeter placed upstream of the throttling valve. The claimed accuracy is [+ or -]0.1% of the reading. IC water volumetric flow rate was measured by an electromagnetic meter (accuracy [+ or -]0.2% of the reading).

All the measurements are real-time acquired and elaborated. The particular layout of the air tunnels and the accuracy of the instruments led to a heat balance error for each component and for the complete system lower than [+ or -]1%.

According to Moffat's (1988) suggestion, a "single sample uncertainty analysis" was considered for the air velocity w and for the heat flux q.

In general, the uncertainty in a variable y depending on N independent variables ([x.sub.i]) with uncertainties [delta][x.sub.i] is estimated through Equation 1:

[delta]y = [[N.summation over (i = 1)] ([partial derivative]y/[[partial derivative][x.sub.i]]] [delta][x.sub.i])[.sup.2]][.sup.0.5] (1)

In particular, with

w = [dot.V]/S, (2)

it is

[delta]w = [([1/S][delta][dot.V])[.sup.2] + (-[[dot.V]/[S.sup.2]][delta]S)[.sup.2]][.sup.0.5]. (3)

The heat flux q, air side, is

q = [rho][dot.V][c.sup.p]([t.sub.air, out] - [t.sub.air, in]). (4)

Since a gas-cooling application is considered, air can be treated as dry air (no dehumidification), so the air density [rho] is evaluated through the following ideal gas relationship (ASHRAE 2005):

[rho] = p/0.2871(t + 273.15) (5)

Furthermore, a constant value for the specific heat capacity [c.sub.p] = 1006 J x k[g.sup.-1] x [K.sup.-1] was considered.

So it comes out that

[delta]p = [([1/0.2871(t + 273.15)][delta]p)[.sup.2] + (-[0.2871p/(0.2871(t + 273.15))[.sup.2]][delta]t)[.sup.2]][.sup.5], (6)

and therefore,

[delta][rho] = [([dot.V][c.sub.p]([t.sub.air, out] - [t.sub.air, in])[delta]p)[.sup.2] + ([rho][c.sub.p]([t.sub.air, out] - [t.sub.air, in])[delta][dot.V])[.sup.2] + ([square root of (2)][rho] [dot.V][c.sub.p][delta]t)[.sup.2]][.sup.0.5]. (7)

The "single point" estimated uncertainties are listed in Tables 1 and 2.

The heat flux, C[O.sub.2] side, can be expressed as follows:

[q.sub.CO.sub.2] = [dot.m.sub.CO.sub.2]([h.sub.CO.sub.2,out] - [h.sub.CO.sub.2, in]) (8)

Using Equation 1, the related uncertainty is

[delta][q.sub.CO.sub.2] = [(([h.sub.C[O.sub.2], out] - [h.sub.C[O.sub.2], in])[delta][dot.m.sub.CO.sub.2)[.sup.2] + [dot.m.sub.CO.sub.2] [delta]([h.sub.C[O.sub.2], out] - [h.sub.C[O.sub.2], in]))[.sup.2]].sup.0.5]. (9)

As already mentioned, a Coriolis mass flowmeter with 0.1% of the reading accuracy is used for [dot.m.sub.CO.sub.2]. REFPROP v. 7.0 (NIST 2002) is used for enthalpy calculations. It is well known that

[h.sub.CO.sub.2] = f[p, t], (10)

so, in general, enthalpy calculation uncertainty is affected by

* temperature measurement accuracy,

* pressure measurement accuracy, and

* accuracy of the enthalpy calculation approach used for Equation 10.

The evaluation of the last contribution is outside the purpose of this paper; reference should be made to Span and Wagner's (1996) data, since REFPROP v. 7.0 modeling is based on their measurements for the implementation of the Helmholtz approach to Equation 10. In this paper, only the effects of T and p accuracy on [delta]h are taken into consideration. According to Moffat (1998), a "sequential perturbation" method is applied by using the REFPROP code. Considering a temperature measuring accuracy of [+ or -]0.05[degrees]C and a pressure measuring accuracy of [+ or -]2 kPa, the estimated accuracy for the C[O.sub.2] side heat flow rate is reported in Table 2. The reader may appreciate that the difference between air-side and C[O.sub.2]-side heat fluxes is always below 1% of the air-side heat flux.

GAS COOLER DESCRIPTION

Three different heat exchangers were tested, dubbed A, B, and C throughout the paper. The main characteristics of the three finned coils are listed in Table 3. Coils A and B, as depicted in Figure 2a, are identical but for the fins. Referring to Figure 3, in coil B, the fins in adjacent tube rows are separated (cut) along line DE. This expedient contributes to reducing heat conduction between adjacent tube rows. Coil C presents the same fin arrangement as coil B, with different tube layout, as shown in Figure 2b. A simple scheme of the fin type used is given in Figure 3.

SIMULATION MODEL FOR THE FINNED COIL

The heat transfer analysis has been applied to the case of a finned coil GC by developing a dedicated simulation model. Since the flow configuration of a finned coil does not conform to the elementary and well-known parallel or counterflow patterns, the heat transfer area is subdivided into a three-dimensional array of cells that conforms to the true flow pattern of the air and of the refrigerant streams. Each tube is divided into cells and the total volume, in the form of a parallelepiped, is subdivided into individual nodes, each including a small stretch of tube and the related fins.

The numerical approach to the definition of the circuits is accomplished by means of two arrays, one for the refrigerant [PR(N)] and one for the air [PA(N)]. Each element of the preceding refrigerant (PR) vector indicates the index of the node preceding the N-node, along the refrigerant flow.

[FIGURE 2 OMITTED]

[FIGURE 3 OMITTED]

As described for the refrigerant, the preceding air (PA) value PA(N) represents the air-side node preceding the N-node according to the airflow direction.

This simple approach allows a finned coil to be solved regardless of how complicated the layout of the tube circuits is. For thermal performance determination, the refrigerant temperature and pressure at the GC outlet are calculated by an iterative procedure, the airflow rate and its inlet temperature being known, as well as the refrigerant pressure, temperature, and flow rate at the GC inlet. The well-known secant method is employed.

The refrigerant and air-side heat transfer coefficients are also input parameters in the program. The model can deal with C[O.sub.2] in transcritical conditions; in this case, the heat transfer coefficient is calculated from equations described in the literature, such as Gnielinski's (1976) equation, Pitla et al.'s (2002) equation, and Dang and Hihara's (2004) equation.

The friction factor is calculated by the Colebrook-White equation, while pressure drops in the curves are locally accounted for by adding an equivalent tube length equal to 50 times the tube diameter.

The air-side heat transfer coefficient, including surface efficiency, was evaluated experimentally by feeding the coils with a water flow at a temperature higher than ambient air temperature. An overall heat transfer coefficient U was evaluated from Equation 11, q being the measured heat flux, [A.sub.0] the external heat transfer area, and [DELTA][T.sub.lm] the countercurrent logarithmic mean temperature difference. U is defined by Equation 12:

q = U[A.sub.0][DELTA][T.sub.lm] (11)

1/U = [[A.sub.o]/[A.sub.i]][1/[h.sub.i]] + [[A.sub.o]/[A.sub.i]][[r.sub.i]/k]ln([r.sub.o]/[r.sub.i]) + [1/[[eta].sub.o]][1/[h.sub.o] (12)

where r is the radius, h is the heat transfer coefficient, [eta] is the finned surface efficiency, k is the tube thermal conductivity, i means internal, and o means external; [h.sub.i] was evaluated with the Gnielinski equation, so it was possible to obtain [[eta].sub.o][h.sub.o] from Equation 12.

It's worth noting that the investigated finned coils display four tube-side passes, with air in cross-flow. According to Kays and London (1998), the efficiency of this configuration is almost identical to pure counterflow configuration. The consistency of the [[eta].sub.o][h.sub.o] experimental values obtained through Equations 11 and 12 was evaluated by comparison with the ([[eta].sub.o][h.sub.o])[.sub.calc] values calculated according to the Wang et al. (1999) model. All the experimental values were predicted by the Wang et al. model within [+ or -]10% (deviation defined as 100 x [([[eta].sub.o][h.sub.o])[.sub.exp] - ([[eta.sub.o][h.sub.o])[.sub.calc]]/([[eta].sub.o][h.sub.o])[.sub.calc]).

The thermodynamic and thermophysical properties of R-744 in the calculations are obtained from the database REFPROP v. 7.0 by NIST (2002).

A more detailed description of the simulation model is provided by Casson et al. (2002).

COMPARISON BETWEEN NUMERICAL AND EXPERIMENTAL RESULTS

Coil A performance was compared with that of B and C at several operating conditions. In this paper, three different working pressures are analyzed from 7.9 MPa to 9.1 MPa. The pressure range mentioned was considered particularly meaningful because in these working conditions the R-744 Prandtl number is recognized to undergo the most "dramatic" variation. The test conditions to evaluate the GC performance are listed in Table 1.

Three sets of tests were conducted at the mentioned conditions, and the experimental results obtained are summarized in Table 2.

In order to analyze the fluid temperature distribution in the heat exchangers, a set of thermocouples was inserted along one circuit of the finned coil, as illustrated in Figure 4. The thermocouples were attached to the outside surface of 15 U-bends using a silicone-based heat transfer compound to improve the thermal contact to the surface. The thermocouple distribution is shown in Figure 2a for coils A and B and in Figure 2b for coil C. Every thermocouple and its corresponding U-bend were suitably insulated for the environment. Referring to test number 3 for coil A, the temperature profile is shown in Figure 4, where the temperature measurements are numbered according to what is shown in Figure 2a.

The solid line shown in Figure 4 relates to the temperature profile obtained by the numerical simulation. In each test with coil A, a significant difference between the predicted temperatures and measured values was observed. Although the approach and the temperature values are different between tests at different refrigerant and air inlet conditions, in the first row of the heat exchanger (0%-25% of the total surface), the measured temperature values are always lower than the calculated ones, while they are higher in the last three rows (25%-100%).

Several C[O.sub.2] heat transfer coefficient correlations were tested but without any significant change in the prediction (see Table 4). All C[O.sub.2]-specific correlations usually refer to the Gnielinski correlation that was chosen as the reference for the simulation software to evaluate the temperature profile and the heat flux. The other correlations were selected considering the different approaches to the heat transfer coefficient evaluation. Pitlas's correlation makes use of an average between Nusselt numbers referred to bulk and wall temperatures, while Dang and Hihara's correlation uses a film temperature to evaluate C[O.sub.2] properties and therefore the heat transfer coefficient.

Different correlations don't give rise to different results because the heat transfer resistance is chiefly concentrated on the air side in finned coils. Therefore, the C[O.sub.2]-side heat transfer coefficient estimation model doesn't seem to be as important as the air-side coefficient estimation. Starting from the previous considerations, the reason for the difference between predicted and measured values must lie in a phenomenon associated with the gas cooling process and not modeled by the numerical code.

[FIGURE 4 OMITTED]

Unlike condensation or evaporation processes, in which the fluid temperature is almost uniform in a large part of the heat exchanger, the gas cooling process involves a significant temperature glide along the heat exchanger. In particular, the C[O.sub.2] temperature gradient is higher in the first 20% of the heat transfer area (following the R-744 flow direction). Therefore, it seems reasonable to consider the thermal conduction from the first high-temperature tubes to the adjacent low-temperature tubes through the continuous fins as the most important factor responsible for performance penalization and temperature profile disagreement in finned coils. As a consequence of the conductive heat transfer from hotter to colder tubes, the efficiency of the heat exchanger deviates from the ideal counterflow behavior.

To confirm this hypothesis, the continuous fins were cut to eliminate the thermal conduction from any tube row to the adjacent ones. In this way, a separated row finned coil was tested (dubbed B in Table 2). A 3.7% to 5.6% heat flow rate improvement was gained, as can be seen in Table 2, while Figure 5 shows a better agreement of the B temperature profile as compared with the A profile. In the first row of the coil (0%-25%) the temperature values increased, while in the second part of the heat exchanger the temperatures decreased approaching the simulation profile. This is consistent with a decrease in thermal conduction.

This improvement can be clearly transferred in terms of COP, since a low value of the C[O.sub.2] temperature at the GC outlet increases the cooling capacity. Using the "cut-configuration," a 5.7% to 6.6% increase in COP can be obtained, considering a reference cycle with the same operating conditions. The reference cycle considered is the simplest kind of transcritical C[O.sub.2] system using single-stage compression, without the presence of a suction line heat exchanger. The compressor is simulated with constant isentropic efficiency equal to 0.6. Isobaric processes except for compression and throttling were considered, with -10[degrees]C evaporation temperature and 5[degrees]C vapor superheating. Furthermore, a higher COP improvement can be reached by an optimization of the GC pressure.

The C configuration represented in Figure 2b was chosen for a second set of tests to limit the thermal conduction between the two circuits along the vertical direction. Basically, from a geometric point of view, the two circuits were symmetrically fed, to reduce the thermal conduction in the horizontal middle cross section of the heat exchanger.

Referring to the comparison between the C configuration and the B configuration, Figure 6 shows a slightly better approach just in the first tube row (high temperature zone), while in the other three tube rows the measured temperatures are almost the same, and the overall thermal performance is also the same.

[FIGURE 5 OMITTED]

[FIGURE 6 OMITTED]

These experimental results are evidence that the thermal bridge through fins contributes to penalize heat transfer because of the thermal conduction between different tube rows, not between tubes in the same row.

Asinari et al. (2004) pointed out a negligible effect of conduction through fins in minichannel air-cooled GCs. It is worth noting that the flow arrangement plays a key role in this respect. Usually minichannel GCs are arranged as a single slab heat exchanger with C[O.sub.2] flowing in multistream with several pipes in parallel (in Asinari et al. [2004], a three pass arrangement in the unique rank with 13, 11, and 10 tubes in parallel, respectively, was analyzed). In this configuration, the heat conduction through fins is only significant in the region of flow inversion caused by the manifolds. In fact, a marked wall temperature difference is only present between the adjacent pipes in the flow inversion portion of the heat exchanger, whereas the other tubes fed in parallel within the same C[O.sub.2] pass are affected by very similar temperature fields, if the air velocity is assumed to be fairly uniform over the whole face area. According to temperature measurements presented in this paper, in the investigated finned coil at least 12 tubes of the first rank are directly set into contact through the fins with tubes having the wall temperature lower by at least 15[degrees]C (and in some cases by up to 35[degrees]C), according to Figures 4-6. From the same figures it is evident that the largest temperature change occurs in the first tube rank: the temperature profile is much more "flat" starting from the second down to the fourth rank. So the "cut-configuration" (coils B and C) interrupts the thermal bridge between the "higher wall temperature" first rank and the "lower wall temperature" part of the finned coil. The "separated" first rank behaves like a single-slab heat exchanger, from the point of view of conduction through fins. In the "cut-configuration" only the first three tubes of each circuit (following the C[O.sub.2] flow from the entrance) in the first rank are in direct contact through the fins with tubes having wall temperature differences higher than 5[degrees]C from the preceding pipe. Thus, the effect of thermal conduction of the first rank arrangement on the overall efficiency of the heat exchanger is expected (and proved experimentally by comparison of the performances of coils B and C) to be negligible.

CONCLUSIONS

Experimental tests and numerical analysis on two identical finned coils, one with continuous fins and the other with separated fins in each tube row, indicates that "internal" heat conduction through the fins is an important factor in finned coil C[O.sub.2] gas coolers. This fact is strictly linked to the high-temperature variation of C[O.sub.2] during the gas cooling process in a transcritical refrigeration cycle. The improvement in temperature approach between C[O.sub.2] outlet temperature and air inlet temperature was found to increase the efficiency of the refrigerating cycle. This point offers a quite promising technological opportunity, since it is easy to build a coil with fins separated among different rows.

Future work will be aimed at developing a more detailed code that also takes into account the heat conduction through the fins; this will be a fundamental tool for the optimized design of finned coil gas coolers.

ACKNOWLEDGMENT

This research was carried out with the financial support of the Italian Department for Education under the frame of the research programme PRIN-COFIN 2004.

NOMENCLATURE 

Symbols

A = heat transfer area

[c.sub.p] = specific heat

[delta]y = uncertainty in the result, generic

h = heat transfer coefficient

[[eta].sub.0] = finned surface efficiency

k = tube thermal conductivity

q = heat flux

r = tube radius

[rho] = density

N = number of elements in a sample

p = pressure

S = finned coil face area

t = temperature

[DELTA][T.sub.lm] = log mean temperature difference 

U = overall heat transfer coefficient

[dot.V] = volumetric airflow rate

w = air velocity

[x.sub.i] = generic ith variable

[delta][x.sub.i] = uncertainty in [x.sub.i]

Subscripts

i = internal

in = inlet

o = external

out = outlet

calc = calculated

REFERENCES

ASHRAE. 2005. 2005 ASHRAE Handbook--Fundamentals. Atlanta: American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc.

Asinari, P., L. Cecchinato, and E. Fornasieri. 2004. Effects of thermal conduction in microchannel gas coolers for carbon dioxide. Int. J. Refrig. 27(6):577-86.

Casson, V., A. Cavallini, L. Cecchinato, D. Del Col, L. Doretti, E. Fornasieri, L. Rossetto, and C. Zilio. 2002. Performance of finned coil condensers optimized for new HFC refrigerants. ASHRAE Transactions 108(2):517-28.

Dang, C., and E. Hihara. 2004. In-tube cooling heat transfer of supercritical carbon dioxide. Part 1. Experimental measurement. Int. J. Refrig. 27(7):736-47.

ISO. 2005. EN-ISO Standard 5167-1, Measurement of Fluid Flow by Means of Pressure Differential Devices. Geneva: International Organization for Standardization.

Gnielinski, V. 1976. New equations for heat and mass transfer in turbulent pipe and channel flow. Int. Chem. Eng. 16(2):359-67.

Hwang, Y., R. Radermacher, D.-H. Jin, and J.W. Hutchins. 2005. Performance measurement of C[O.sub.2] heat exchangers. ASHRAE Transactions 111(2):306-16.

Kays, W.M., and A.L. London. 1998. Compact Heat Exchangers. Malabar: Krieger Publishing Company.

Moffat, R.J. 1988. Describing the uncertainties in experimental results. Exp. Thermal Fluid Sc. 1:3-17.

NIST. 2002. REFPROP, version 7.0. Boulder, CO: National Institute of Standards and Technology.

Pitla, S.S., E.A. Groll, and S. Ramadhyani. 2002. New correlation to predict the heat transfer coefficient during in-tube cooling of turbulent supercritical C[O.sub.2]. Int. J. Refrig. 25(7):887-95.

Span, R., and W. Wagner. 1996. New equation of state for carbon dioxide covering the fluid region from the triple-point temperature to 1100 K at pressures up to 800 MPa. J. Phys. Chem. Ref. Data 25(6):1509-96.

Wang, C.-C., C.-J. Lee, C.-T. Chang, and S.-P. Lin. 1999. Heat transfer and friction correlation for compact louvered fin-and-tube heat exchangers. Int. J. Heat and Mass Transfer 42:1945-56.

Claudio Zilio, PhD

Luca Cecchinato, PhD

Marco Corradi, PhD

Giovanni Schiochet

Received September 1, 2006; accepted January 12, 2007

Claudio Zilio is an assistant professor, Luca Cecchinato and Marco Corradi are post-doctoral researchers, and Giovanni Schiochet is a PhD student with the Dipartimento di Fisica Tecnica, Universita di Padova, Padova, Italy.

Table 1. Test Conditions

      C[O.sub.2] Inlet      C[O.sub.2] Inlet         C[O.sub.2] Mass
Test  Pressure, MPa         Temperature, [degrees]C  Flow Rate, kg/h

1     7.911 [+ or -] 0.002   87.0 [+ or -] 0.05      169.0 [+ or -] 0.2
2     8.599 [+ or -] 0.002   97.6 [+ or -] 0.05      167.1 [+ or -] 0.2
3     9.102 [+ or -] 0.002  107.8 [+ or -] 0.05      166.4 [+ or -] 0.2

Test  Air Inlet Temperature, [degrees]C  Air Inlet Velocity, m/s

1     20.3 [+ or -] 0.05                 1.59 [+ or -] 0.01
2     21.5 [+ or -] 0.05                 1.59 [+ or -] 0.01
3     23.0 [+ or -] 0.05                 1.61 [+ or -] 0.01

Table 2. Experimental Results

              C[O.sub.2] Outlet   Air Outlet
Finned        Temperature,        Temperature,        Approach,
Coil    Test  [degrees]C          [degrees]C          [degrees]C

A       1     33.0 [+ or -] 0.05  39.5 [+ or -] 0.05  12.7 [+ or -] 0.05
        2     33.1 [+ or -] 0.05  42.7 [+ or -] 0.05  11.6 [+ or -] 0.05
        3     33.1 [+ or -] 0.05  45.1 [+ or -] 0.05  10.1 [+ or -] 0.05
B       1     32.1 [+ or -] 0.05  40.6 [+ or -] 0.05  11.8 [+ or -] 0.05
        2     31.1 [+ or -] 0.05  43.7 [+ or -] 0.05   9.6 [+ or -] 0.05
        3     30.9 [+ or -] 0.05  46.0 [+ or -] 0.05   7.9 [+ or -] 0.05
C       1     32.1 [+ or -] 0.05  40.8 [+ or -] 0.05  11.8 [+ or -] 0.05
        2     31.0 [+ or -] 0.05  43.8 [+ or -] 0.05   9.5 [+ or -] 0.05
        3     31.0 [+ or -] 0.05  46.2 [+ or -] 0.05   7.9 [+ or -] 0.05

Finned        Heat Flow Rate         Heat Flow Rate
Coil    Test  (C[O.sub.2] Side), kW  (Air Side), kW

A       1      9.0 [+ or -] 0.05      9.0 [+ or -] 0.1
        2     10.1 [+ or -] 0.06     10.2 [+ or -] 0.1
        3     10.9 [+ or -] 0.06     10.8 [+ or -] 0.1
B       1      9.5 [+ or -] 0.05      9.5 [+ or -] 0.1
        2     10.6 [+ or -] 0.06     10.6 [+ or -] 0.1
        3     11.3 [+ or -] 0.07     11.2 [+ or -] 0.1
C       1      9.5 [+ or -] 0.05      9.5 [+ or -] 0.1
        2     10.7 [+ or -] 0.06     10.6 [+ or -] 0.1
        3     11.1 [+ or -] 0.07     11.2 [+ or -] 0.1

Table 3. Specifications of the Heat Exchangers

Heat exchanger           Gas cooler
Type                     Finned coil
Dimension (W x H)        500 x 500 mm
Number of circuits       2
Number of tubes per row  20
Number of rows           4
Refrigerant path         Vertical, countercurrent
Tube pitch               25 mm
Row pitch                19 mm
Geometry                 Staggered tubes
Fin pitch                2.1 mm
Fin thickness            0.1 mm
Fin type                 Louver aluminium (Figure 3)
Tube outside diameter    9.52 mm
Tube thickness           0.65 mm
Tube type                Smooth

Table 4. Simulation Results Using Three Different Correlations

                     Gnielinski (1976)         Pitla et al. (2002)
Correlation  C[O.sub.2] Outlet             C[O.sub.2] Outlet
Test         Temperature,       Heat Flow  Temperature,       Heat Flow
             [degrees]C         Rate, kW   [degrees]C         Rate, kW

1            32.2                9.5       32.2                9.5
2            31.0               10.6       31.0               10.6
3            30.7               11.3       30.7               11.3

                   Dang and Hihara (2004)
Correlation  C[O.sub.2] Outlet        Heat Flow
Test         Temperature, [degrees]C  Rate, kW

1            32.3                      9.5
2            31.2                     10.6
3            30.9                     11.2