Modeling and performance simulation of a gas cooler for a C[O.sub.2] heat pump system
The outlet temperature of a gas cooler has a great effect on the efficiency of carbon dioxide heat pump systems. In order to obtain a small approach temperature difference at the gas cooler, a near-counterflow type heat exchanger has been proposed, and a larger heat transfer area is demanded. Therefore, the optimum design for gas coolers involving the analysis of trade-offs between heat transfer performance and cost is desirable. For this study, a simulation model has been developed for fin-and-tube type gas coolers, and an air-side heat transfer correlation is proposed. The developed model was confirmed by experimental results. The effects of geometric parameters, such as transverse tube spacing, longitudinal tube spacing, number of tube rows, and fin spacing, on the performance of heat exchangers were investigated using the developed model. This study suggests various simulation results for optimum design of gas coolers.
Due largely to the recent outbreak of environmental problems caused by global warming, many ongoing studies are aiming to adopt heat pump systems using carbon dioxide (C[O.sub.2]), a natural refrigerant. As shown in Figure 1, the critical temperature of carbon dioxide is lower than ambient air temperature, which acts as a heat sink. Thus, this refrigeration system is different from others using conventional refrigerants; the condensing process does not exist and hot gas refrigerant is cooled in a single-phase gas cooling process. In this study, a performance analysis model is proposed that uses a fin-and-tube heat exchanger as the gas cooler of a C[O.sub.2] heat pump system.
Hot C[O.sub.2] is introduced through the tubes of a fin-and-tube heat exchanger, and an air-cooling process takes place. For fin-and-tube heat exchangers, air-side thermal resistance is a great portion of the total thermal resistance. Thus, in order to improve the performance of the heat exchanger, it is crucial to enhance the performance of the air-side heat transfer. Consequently, it is very important to understand air-side heat transfer characteristics for the design of a fin-and-tube gas cooler. The overall heat transfer coefficient is calculated from heat exchanger performance test data and [epsilon]-NTU relations considering the shape of the heat exchanger and operating condition, and the air-side heat transfer coefficient can be obtained from the overall heat transfer coefficient. However, Youn et al. (2000) verified that the discrepancy in air-side heat transfer coefficients could be as much as 20% according to the choice of [epsilon]-NTU relation for data reduction.
In this study, the tube-by-tube method was used as a gas cooler model because thermodynamic and transport properties of C[O.sub.2] show large variations during the gas cooling process. This method is relatively simple, and accurate results can be obtained considering the variations of heat transfer characteristics of each tube. Therefore, the tube-by-tube method is also used for obtaining air-side heat transfer coefficients instead of the [epsilon]-NTU relation method. Measured air-side heat transfer coefficients can be expressed by the correlation of Reynolds number and Prandtl number. The effects of geometric parameters, such as transverse tube spacing, longitudinal tube spacing, the number of tube rows, and fin spacing, on the performance of heat exchangers were investigated using the developed model.
Cross-flow type fin-and-tube heat exchangers are widely used in air-conditioning systems. They are composed of circular tubes made of copper and aluminum fins that are adhered to each other by mechanical expansion of the tubes. While the refrigerant flows through the copper tubes, air travels in cross-direction through the fins. There are several ways of analyzing fin-and-tube heat exchangers; one involves using the [epsilon]-NTU relation deduced by Hiller and Glicksman (1976) and Fisher and Rice (1981). Another is the tube-by-tube method developed from the study of Domanski (1989). It is assumed that the air between steps is unmixed, and each tube is handled as an independent component. This method is simple and allows researchers to obtain accurate results. The model is widely applied in the analysis of air-cooled heat exchangers.
The heat transfer equation, using the mean temperature difference to each independent tube applied to pure cross-flow type heat exchangers (Domanski 1989), is shown below.
Q = U x A x [DELTA][T.sub.m] (1)
The enthalpy change of refrigerants in the heat transfer process can be expressed as
Q = [dot.m.sub.r] x ([i.sub.i] – [i.sub.e]). (2)
Since microfin tubes were used in this study, the heat transfer correlation by Han and Lee (2005) is used for obtaining the water- or refrigerant-side heat transfer coefficient. As the water-side heat transfer coefficient is 10 to 40 times greater than the air-side heat transfer coefficient, the effect of uncertainty of the water-side heat transfer coefficient on the overall heat transfer coefficient is negligible. By summing heat resistances between the refrigerant and the air, the overall heat transfer coefficient for a fin-and-tube unit can be expressed by Equation 3.
[FIGURE 1 OMITTED]
U = [[[A.sub.o]/[[h.sub.r][A.sub.r]]] + [[[A.sub.o]t]/[[A.sub.p,m][k.sub.p]]] + [[A.sub.o]/[[A.sub.p,o][h.sub.c]]] + [1/[[h.sub.o](1 – [[A.sub.f]/[A.sub.o]](1 – [phi]))]]] (3)
Here, fin efficiency is calculated from the method proposed by Schmidt (1945) and McQuiston and Parker (1982).
AIR-SIDE HEAT TRANSFER COEFFICIENT
Figure 2 shows the experimental apparatus measuring the performance of the heat exchanger. It is placed inside a thermal environment chamber where the temperature and humidity of the air are carefully controlled. Resistance temperature devices (RTDs) are installed to measure the air temperatures at the inlet and outlet of the heat exchanger, and wet-bulb temperatures are measured at the same temperature measuring points using RTDs wrapped in muslin and kept wet.
The airflow rate is measured using multi-nozzles, and a pressure transducer is used to measure the air-side pressure drop. A schematic diagram of the water circulation loop is shown in Figure 3. The loop is composed of a water tank, a mass flowmeter, pumps, a constant temperature bath, and the heat exchanger sample.
The inlet and outlet temperatures of the heat exchanger are measured with T-type thermocouples. The test conditions are listed in Table 1. Experiments were conducted by varying the frontal velocity of air and the mass flow rate of water while the other conditions of air and water were maintained as in Table 1. Experimental data are recorded on a computer using a data acquisition apparatus in a steady state.
A fin-and-tube heat exchanger has one row of tubes or more according to the application. There are various types of fins used for fin-and-tube heat exchangers, such as plate, wavy, louver, slit, and so on. Among them, slit and louver fins are commonly used due to their high performance. In this study, two types of fin-and-tube heat exchangers were used: one has two rows and the other has three rows (Figure 4). The outer diameter of the tube is 7 mm. The specifications of the fin-and-tube heat exchangers are listed in Table 2.
[FIGURE 2 OMITTED]
[FIGURE 3 OMITTED]
It is known that gas cooler performance decreases as a consequence of conduction through fins from hot inlet tubes to colder tubes. However, Pattersen et al. (1998) verified that performance could be enhanced using modified fins by a split between tube rows (in the direction of airflow). In this study, tested heat exchangers are composed of split fins, which are shown in Figure 4 as dotted lines between tube rows. Through preliminary tests, it was found that heat exchanger performance does not show significant variation according to temperature difference between air and water. Therefore, it is assumed that fin conduction effects are negligible in the split-fin configuration.
The air-side heat transfer rate is calculated from the inlet and outlet temperatures and mass flow rate of the air (Equation 4). The water-side heat transfer rate is calculated using Equation 5.
[FIGURE 4 OMITTED]
[Q.sub.a] = [dot.m.sub.a] x ([i.sub.a,e] – [i.sub.a,i]) (4)
[Q.sub.w] = [dot.m.sub.w] x ([i.sub.w,i] – [i.sub.w,e]) (5)
The air-side heat transfer coefficient is obtained by performance simulation using the tube-by-tube model presented previously. The heat transfer rate is calculated by the arithmetic mean of air-side and water-side heat transfer rates.
Based on the uncertainty analysis method proposed by Kline and McClintock (1953), uncertainties of heat transfer rate and air-side heat transfer coefficient are estimated to be about 5% and 10% at mean condition. However, the uncertainty of the heat transfer coefficient is found to be largely dependent on the tube-side heat transfer coefficient. The uncertainty of the air-side heat transfer coefficient is estimated to be about 19% at the lowest mass flow rate of the water condition. The uncertainty of the contact thermal resistance and tube-side heat transfer coefficient are assumed to be 10% and 6.4%, respectively, in this calculation (Han and Lee 2005).
The deviations of the heat transfer rates of water and air are within 5%. Fin efficiency obtained from the model is about 80%, and the air-side heat transfer correlation according to air velocity change is expressed as shown in Equation 6 and Figure 5.
Nu = C[Re.sub.D.sup.m][Pr.sup.1/3] (6)
Here, [Re.sub.D] is the Reynolds number for the tube diameter.
In order to verify the accuracy of the developed heat transfer correlation, performance simulation was carried out. The results of this simulation are compared to experimental results as shown in Figure 6. The simulation model predicts the heat transfer rate within 10%.
[FIGURE 5 OMITTED]
To verify whether the simulation model in this study could be applied to a C[O.sub.2] gas cooler, performance simulation was carried out using experimental results of a previous study on C[O.sub.2] gas coolers (Chang et al. 2005). Comparison of simulation results to experimental results is shown in Figure 7. The developed model describes the experimental results well and is suitable for the performance analysis of C[O.sub.2] gas coolers.
The performance of gas coolers has been evaluated using the developed heat exchanger model in this study; simulation conditions are listed in Table 3. Inlet temperature and frontal velocity of air and temperature, pressure, and mass flow rate of C[O.sub.2] are maintained constant throughout the performance simulation. The effects of geometric parameters, such as transverse tube spacing, longitudinal tube spacing, number of tube rows, and fin spacing, are investigated in comparison with the performance of the two-row heat exchanger listed in Table 2.
[FIGURE 6 OMITTED]
[FIGURE 7 OMITTED]
Variations in Heat Transfer Coefficient and Fin Efficiency
The air-side heat transfer coefficient is affected by the air conditions, fin shape, fin pitch, transverse tube pitch, and longitudinal tube pitch of the heat exchanger. As shown in Figure 8, according to the design parameters of the heat exchanger, variations in the heat transfer coefficient and fin efficiency are predicted using the heat transfer model of Wang et al. (1999). Heat transfer coefficients and fin efficiencies are normalized by the values of the reference geometric specifications listed in Table 2. The heat transfer coefficient decreases when either the fin pitch or the transverse tube pitch increases. The heat transfer coefficient decreases by 4% and 10% when there is a 30% increase in the fin pitch and the transverse tube pitch, respectively. The variation in the heat transfer coefficient caused by the longitudinal tube pitch is very small. Fin efficiency is not much affected by the fin pitch or the longitudinal tube pitch but decreases largely when the transverse tube pitch increases.
Because the air-side heat transfer correlation proposed in this study can be applied only to a given heat exchanger geometry, the correction factor f is used to calculate the air-side heat transfer coefficient with various geometric parameters. The normalized air-side heat transfer coefficient shown in Figure 8a is used as the correction factor.
[FIGURE 8 OMITTED]
h = f x h* (7)
In Equation 7, the * stands for the reference condition and h* is the heat transfer coefficient of the tested heat exchanger of Figure 4 at a given air and refrigerant condition.
Performance with Frontal Area
The heat transfer rate and the minimum temperature difference of refrigerant and air at the refrigerant outlet when frontal area is changed are shown in Figure 9. At reference conditions, the minimum temperature difference is very small, 2[degrees]C. A decrease of the frontal area brings an increase of the minimum temperature difference and a decrease of the heat transfer rate due to reductions of heat transfer area and airflow rate.
Performance with Number of Circuits
The performance analysis result regarding the number of circuits when the frontal area is constant is shown in Figure 10. Refrigerant supplied to the gas cooler is distributed to each circuit. If the number of circuits is 4, the refrigerant flowing in each circuit is 1/4 of the total refrigerant flow rate. The total mass flow rate of C[O.sub.2] is 70 g/s. If the number of circuits decreases, the mass flow rate of the refrigerant in each tube, the heat transfer coefficient, and the pressure drop of the refrigerant all increase. When refrigerant circuits are decreased from four to three, performance is decreased about 1%; when number of circuits is two, the pressure drop increases about 10 times and the heat transfer rate decreases dramatically by 10% compared to that of four circuits.
Performance with Geometric Parameters
The changes in heat transfer rate and air-side pressure drop according to variations of fin pitch, transverse tube pitch, and longitudinal tube pitch are shown in Figure 11. When fin pitch or transverse tube pitch increases, heat transfer rate decreases due to a reduction of the air-side heat transfer coefficient as shown in Figure 8. Contrarily, when longitudinal tube pitch increases, the heat transfer rate and pressure drop increase due to increased heat transfer area.
[FIGURE 9 OMITTED]
[FIGURE 10 OMITTED]
[FIGURE 11 OMITTED]
Through experiments using water, an air-side heat transfer correlation was developed and applied to the simulation of a gas cooler with various design parameters. The results are as follows:
* The decrease of frontal area brings an increase of minimum temperature difference and a decrease of heat transfer rate. A 20% decrease in frontal area results in only an 8% reduction of the heat transfer rate.
* When the number of circuits is decreased, the heat transfer rate decreases and the refrigerant pressure drop increases. Owing to increased mass flux of the refrigerant, refrigerant-side heat transfer is improved. This is a favorable effect on heat exchanger performance when the number of circuits is reduced. However, because the refrigerant pressure drop increases, the outlet enthalpy of C[O.sub.2] increases at the same outlet temperature of the gas cooler, which causes deterioration of gas cooler performance. When the number of circuits is two, the performance reduction due to the increased refrigerant pressure drop becomes greater than the performance improvement due to increased refrigerant-side heat transfer coefficient. Therefore, the optimum number of circuits is found to be three, considering equal flow distribution of refrigerant into each circuit.
* When fin pitch or transverse tube pitch increases, the heat transfer rate and the air-side pressure drop decrease. When longitudinal tube pitch increases, the heat transfer rate and the air-side pressure drop increase. To enhance heat exchanger performance with given frontal heat exchanger areas, the increase of longitudinal tube pitch can be considered.
The work presented in this study is part of the project “Development of High Efficient Cooling and Heating Systems Using the Natural Refrigerant of C[O.sub.2],” sponsored by the Ministry of Commerce, Industry and Energy in Korea. The authors are grateful for their support.
A = area, [m.sup.2]
f = correction factor
h = heat transfer coefficient, kW/[m.sup.2] x K
i = enthalpy, kJ/kg
k = thermal conductivity, kW/m x K
[dot.m] = mass flow rate, kg/s
NTU = number of transfer units
Nu = Nusselt number
Pr = Prandtl number
Q = heat transfer rate, kW
Re = Reynolds number
t = tube thickness, m
U = overall heat transfer coefficient, kW/[m.sup.2] x K
[DELTA][T.sub.m] = mean temperature difference, [degrees]C
[DELTA]P = pressure drop, Pa, kPa
[epsilon] = effectiveness
[phi] = fin efficiency
a = air
D = diameter
exp = experiment
f = fin
i = inlet
o = outlet
r, ref = refrigerant
sim = simulation
w = water
* = reference condition
Chang, Y.S, M.K. Lee, Y.S. Ahn, and Y. Kim. 2005. An experimental investigation on the performance of outdoor heat exchangers for heat pump using C[O.sub.2]. Korean Journal of Air-Conditioning and Refrigeration Engineering 17(2):101-109.
Domanski, P.A. 1989. EVSIM–An evaporator simulation model accounting for refrigerant and one-dimensional air, NISTIR-89-4133. Washington, DC: NIST.
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Young-Soo Chang, PhD
Min Seok Kim
Received September 22, 2006; accepted January 11, 2007
Young-Soo Chang is a senior research scientist and Min Seok Kim is a research scientist at the Thermal/Flow Control Research Center, Korea Institute of Science and Technology, Seoul, Korea.
Table 1. Experimental Test Conditions
Inlet Conditions Value
Air Temperature, [degrees]C 15
Relative humidity, % 60
Frontal velocity, m/s 0.5-2.5
Water Temperature, [degrees]C 35
Mass flow rate, g/s 15-100
Table 2. Geometric Dimensions of Heat Exchangers
Item 2 Rows 3 Rows
Tube outside diameter, mm 7 7
Tube thickness, mm 0.32 0.32
Number of rows 2 3
Transverse tube spacing, mm 21 21
Longitudinal tube spacing, mm 12.7 12.7
Fin material Al Al
Fin type louver louver
Louver angle, [degrees] 45 45
Louver height, mm 0.9 0.9
Fin thickness, mm 0.1 0.1
Fin spacing, mm 1.2 1.2
Tube type microfin tube microfin tube
Table 3. Simulation Conditions
Inlet Conditions Value
Air Temperature, [degrees]C 35
Relative humidity, % 40
Frontal velocity, m/s 1.5
C[O.sub.2] Temperature, [degrees]C 93.1
Pressure, kPa 9000
Mass flow rate, g/s 70
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