Modeling and experimental evaluation of parallel flow micro channel condensers

Modeling and experimental evaluation of parallel flow micro channel condensers

J. M. Saiz Jabardo^I; W. G. Mamani^II

^IUniversidade de São Paulo – USP Escola de Engenharia de São Carlos-EESC Departamento de Engenharia Mecânica Laboratório de Refrigeração Av. Trabalhador São-carlense, 400 – Centro 13560-250 São Carlos , SP. Brazil [e-mail]

^IIUniversidad Privada Boliviana – UPB Facultad de Ingeniería y Arquitectura Carrera de Ingeniería de Petróleo y Gas Natural Casilla 3967, Cochabamba. Bolivia [e-mail]

ABSTRACT

This paper reports results obtained in a theoretical and experimental study involving micro channel/louvered fin condensers for automotive applications. A simulation model has been developed based upon three zones related to the thermodynamic states of the refrigerant in the condenser. Experiments with condensers have been performed in a set up developed for thermal performance evaluations of automotive air conditioning systems. Comparisons between simulation model and experimental results for refrigerant HFC-134a have been performed with respect to three important condenser parameters: heat rejection rate, refrigerant pressure drop and overall heat transfer coefficient. It has been shown that model results for the particular tested condenser compare very well with the experimental data, with deviations being within an acceptable range.

Keywords: Parallel flow condenser, micro channels, automotive, air conditioning systems

Introduction

Tight limitations in space and weight of automobile air conditioning condensers, in addition to high thermal performance requirements has led manufacturers to develop new and ingenious geometries. One of such geometries, which is prevailing in present days, is made of blades of extruded aluminum micro channels (typical dimension of the order of 1 mm), with the space between blades being filled with louvered fins. Blades are brazing soldered to vertical headers where the refrigerant is distributed to the micro channels, as shown in Fig. 1. One of the main advantages of the micro channel condenser is the distribution of the refrigerant through a higher area, what enhances the heat transfer performance. A schematic representation of a louvered surface of the kind considered in this study is shown in Fig. 2 along with the main geometric parameters.

Several coils simulation programs have been developed in the past, though most of them do not deal with the parallel micro channel type of heat exchanger. Noteworthy is the simulation program developed by the Oak Ridge National Laboratory in comprehensive study involving "air to air heat pumps", Fischer and Rice (1983). In fact, the model proposed herein has been based upon that program. The basic procedure consists in dividing the coil into three regions: the superheated vapor, the change of phase, and the subcooled liquid regions. Despite the intensive research being carried out around the world regarding the heat transfer mechanisms prevailing in parallel flow micro channels condensers, not many studies have been published in the open literature about their overall performance. One such study has been conducted by Rahman Ali (1995), who developed a mathematical model for a parallel flow micro channel condenser as part of a comprehensive research involving the simulation of an automobile air conditioning system. Lee and Yoo (2000) followed a similar approach modeling a parallel flow micro channel condenser as part of a simulation program of an automobile air conditioning refrigeration circuit. By dividing the condenser into single-phase and phase-change regions, Lee and Yoo were able to model their condenser in a quite accurate manner, considering the obtained results as compared with their experimental counterparts.

Present paper reports the development of a computer simulation program of a parallel flow micro channel condenser and its validation through results from an experimental set up. The experimental bench has been developed from actual parts and components of an automobile air conditioning system and has been operated under typical field conditions.

Nomenclature

A = Area (m²)

A_cs = Fin cross section area in m_f (m²)

C = Heat capacity, m cp (W/K)

C_f = Friction factor

C^* = C_min/Cmax

cp = Specific heat (J/kg.K)

D = Diameter, (m)

Fp = Fin pitch (m)

G = Mass velocity (kg/m²s)

h = Heat transfer coefficient (W/m²K)

h_average = Condensing average heat transfer coefficient (W/m²K)

Hc = Dimension as in Fig.1 (m)

hf = Fin length (m)

hm = Tube height (m)

i = Enthalpy (J/kg)

j = Colburn factor, Nu/(RePr^1/3)

k = Thermal conductivity (W/mK)

L = Length (m)

Lc = Dimension as in Fig.1 (m)

L_f = Fin corrected length (m)

Lp = Louver pitch (m)

L1 = Louver length (m)

m = Mass flow rate (kg/s)

m_f = Fin effectiveness parameter given by [h_aA_cs/(k_fd_f)]0.5

NTU = Number of Transfer Units

p = Pressure (Pa)

Pr = Prandt Number

Q_c = Condenser heat rejection rate (kW)

Re = Reynolds number

T = Temperature (K)

TEV = Thermostatic expansion valve

U = Overall heat transfer coefficient (kW/m²K)

V_a = Face velocity of the air (m/s)

wm = Tube depth (m)

x = Quality

X_tt = Martinelli Parameter

Greek Symbols

D = Deviation

Dp = Pressure drop, (Pa)

DT = Temperature difference, (K)

d = Thickness (m)

e = Heat exchanger effectiveness

f = Two phase flow multiplier

r = Density (kg/m³)

h = Overall effectiveness of finned surfaces

h_{f =} Individual fin effectiveness

q = Louver angle (deg)

m = Dynamic viscosity [kg/(m s)]

Subscripts

a = Air

c = Refers to either cool fluid, condenser or condensation

e = External

eq = Equivalent

f = Fin

ffa = Refers to minimum free flow area

g = Refer to either gas or vapor

h = Hydraulic diameter, hot fluid

i = Internal

l = Liquid or liquid in the mixture

lo = Refers to the total mass flow rate flowing as liquid

Lp = Refers to fin dimension Lp

r = Refrigerant

Description of the Experimental Bench

A schematic description of the experimental set up is shown in Fig. 3. The experimental bench was made of equipment and components from a commercial auto air conditioning system arranged in a way that field operating conditions could adequately be reproduced in the laboratory. The compressor was capacity controlled that operates in such a way to keep the suction pressure constant at approximately 2 bar. It was driven by an electric motor coupled to a frequency converter to allow for rotational speed control so that experiments could be performed covering the actual range of speeds. The cooling coil, installed in its actual casing, was a standard aluminum tube and fins whereas the expansion device was a thermostatic expansion valve used in the auto air conditioning industry. Thermal load was imposed by both, mixing the return with ambient air, and by electrically heating the incoming air. The condensing air was provided by a twin fan arrangement installed as in the actual vehicle and run by their original motors with electrical power provided by a regular 12 V automobile battery. The condenser/fan arrangement was installed at the downstream far end of a small wind tunnel constructed for that purpose, as shown in Fig. 3. The incoming air temperature was adjusted by a coil of electrical heaters installed at the entrance of the wind tunnel and controlled by a voltage converter. A double screen was installed at mid way in the tunnel in order to further rectify the air stream.

The flow rate of air was measured by two different procedures: the calorimetric and by mapping out the cross section with an electronic Pitot tube. A Coriolis type meter measured the mass flow rate of refrigerant. Pressures and temperatures along the refrigeration circuit were measured and monitored in locations shown in Fig. 2. Analog signals from transducers were processed by a data acquisition system from Strawberry Tree, USA. Accuracy of measurements were as follows: (a) temperature (measured with T thermocouples): ± 0,7°C ; (b) pressure: ± 20 kPa ; (c) mass flow rate: 0,15% of full scale. Further details of experimental procedures can be found in Ianella (1998).

Condenser Model

The condenser simulation model assumes that the heat transfer surface is divided into three regions associated to the state of the refrigerant: superheated vapor, condensing and subcooled liquid. Refrigerant and air total flow rates, and the entrance conditions of the refrigerant and air are assumed to be known. Each region is considered as an independent heat exchanger with the total air flow being distributed for each region according to the procedure described below. The state of the refrigerant at the exit of one region corresponds to the inlet of the succeeding one, as shown in Fig. 4.

The overall heat transfer coefficient for each region is determined by assuming negligibly small the combined thermal resistance due to fouling, heat conduction in tube wall, and metal contact. The following equation can then be written:

where h is the overall effectiveness of the finned surface, given by

h = 1 – (A_f/A_e)(1-h_f)

The internal value for h is one, since the surface of the micro channels is assumed to be smooth, with no fins on it. The louvered air side fins are assumed as plane with rectangular profile whose effectiveness is given by the following equation:

h_f = tanh(m_f L_f)/(m_f L_f)

Heat Transfer Correlations

(a) Refrigerant Side

The refrigerant side involves three distinct regions characterized by the thermodynamic state: superheated, condensing and subcooled. Two remarks must be made at this point regarding the refrigerant side:

(1) Mixed oil effects have been disregarded in the present approach. Oil was certainly mixed with the refrigerant in all the experiments since no oil separator was used in the discharge of the compressor, as it is usual in automobile air conditioning systems. The oil mass concentration in all the experiments was limited to a maximum of 2.5 %, determined from the density of the refrigerant in the liquid line. This figure was considered low enough to cause any significant effect in the condenser performance.

(2) Correlations for the heat transfer coefficient are strongly dependent upon the mass velocity. Contrary to what happens in standard coil condensers, the refrigerant flow area might vary between passes in the parallel flow micro channel ones, affecting the value of the mass velocity, and, as a result, the heat transfer coefficient. This variation must be introduced in the simulation program in such a way that the heat transfer correlations are adequately adjusted. In the condenser simulated herein, the refrigerant flow area remains essentially constant and so does the mass velocity, G.

Regarding the single-phase heat transfer coefficient, Mamani and Saiz Jabardo (2000) have found that correlations for standard size tubes are equally applicable with acceptable results to a micro channel geometry like the one considered in the present study. The well-known Dittus and Boelter (1930) correlation, Eq. (2), was used in the present version of the simulation program due to its simplicity and accuracy though others such as the one by Gnielinski (1976) have been tested with satisfactory results.

It must be noted that the single-phase regions occur in an area of limited extent in the condenser. This is not so with the condensing region which occurs in most of the heat transfer area. As a result some care must be exercised when dealing with this region. Several correlations developed for standard tube size have been considered such as the ones by Akers et al (1959), Shah (1979), and others. The obtained results were surprisingly satisfactory considering the doubts raised recently by several authors about their adequacy to condensation in micro channels. Correlations developed for the condensation of refrigerants in micro channels have also been tested using the simulation program. One of such correlations is that proposed by Yang and Webb (1996a), with satisfactory results when used along with the present simulation model. However, considering that experimental data for refrigerant R-134a were available involving a similar channel geometry, a correlation for the local heat transfer coefficient was obtained by curve fitting these data, Mamani (2001). Curve fitting was performed in terms of a dimensionless heat transfer coefficient and a modified version of the Martinelli parameter, evaluated from a Blasius type of correlation for the friction coefficient. The resulting correlation is as follows:

where

X_tt = G [(1-x)/x]^0.875

and

G = (r_g/r_l)^0.5 (m_l/m_g)^0.125

h_l is the single-phase heat transfer coefficient corresponding to the liquid of the mixture flowing in the micro channel. The condensing heat transfer coefficient in Eq. (3) depends upon the quality (local correlation), requiring the evaluation of an average coefficient extensive to the condensing region. This has been accomplished by assuming a constant heat flux along this region, what allows for the shifting of the dependent variable from length to quality in the integral of the local heat transfer coefficient. The resulting equation for the condensing average heat transfer coefficient is as follows:

where

C = 0.555+0.528/G^0.976

(b) Air side

The air side thermal resistance is generally the dominant one in the overall condenser resistance given by Eq. (1). This requires an accurate evaluation of the air side heat transfer coefficient in order to obtain a satisfactory performance of the simulation program. In the past fifty years a significant number of publications have addressed the heat transfer problem related to the flow of gases through compact heat exchangers channels, including some textbooks such as the one by Kays and London (1984) and, more recently, the one by Webb (1994). The complexity of the air passageway between fins in air cooled condensers makes the development of a generalized correlation for heat transfer a rather cumbersome problem. Chang and Wang (1997) have recently tried to develop such correlation for different fin geometries, including those considered in this study. The proposed correlation for the air side heat transfer coefficient is given in terms of the typical Colburn factor, j, and includes a complex product of dimensionless geometric factors besides the Reynolds number, assuming the following form:

In contrast with the relative complexity of the Chang and Wang correlation, the one proposed by Rahman Ali (1995) for the air side heat transfer coefficient is strikingly simple:

It must be noted that this correlation has been empirically obtained for the air side geometry considered in this study, i. e. louvered fins brazed on flat blades. Figure 5 presents the variation of the Colburn factor with the air face velocity according to both correlations, Eqs. (5) and (6). Face velocity has been used in this plot instead of the Reynolds number since in each correlation this number is based upon different characteristic dimension. Figure 4 clearly displays minor differences between results from both correlations, with deviations being in the range between 8 and 10%. In addition to directly comparing the correlations, comparisons have been performed through the simulation program run for different operating conditions, the results showing negligibly small deviations. As a result, the Rahman Ali correlation for the air side heat transfer coefficient has been chosen, since, besides its simple form, it is reasonably accurate.

Refrigerant Pressure Drop

The refrigerant pressure drop affects the temperature distribution along the condenser, and, as a result, its thermal performance. On the other hand, the air pressure drop, which is an independent parameter, does not affect the thermal performance of the condenser, since, in this case, the air flow rate (or face velocity) was kept constant and equal to that promoted by the twin fan system. As a result, its evaluation has not been considered in the present simulation.

Single-phase pressure drop in the superheated and subcooled regions is determined from the Yang and Webb (1996b) correlation,

Dp = 2C_f (G² L / r D)

where

This is an empirical correlation developed for micro channel flow of halocarbon refrigerants. As pointed out by Mamani and Saiz Jabardo (2000), correlations developed for standard size tubes have proven to be inadequate for channels of the size considered in this study.

Two distinct effects cause the pressure drop in the condensing region: friction and acceleration (inertia). Few studies have focused on friction effects in micro channels in the past. Yang and Webb (1996b) is one of such studies. It introduces an empirical equivalent friction factor based upon experimental data involving the condensation of halocarbon refrigerants in channels of reduced size. The final form of the correlation is as follows:

Dp =2C_{f eq} (G_eq² L / r_l D)

where

(C_{f eq} / C_f)=0.435Re_eq^0.12

and

is the equivalent Reynolds number based on the mass velocity, G_eq.

In the present case, friction effects are evaluated through an empirical correlation for the two-phase flow multiplier, f_l, developed by curve fitting experimental results obtained by Mamani (2001) in terms of the Martinelli parameter, X_tt,

As in the case of the heat transfer coefficient, Eq. (9) is a local correlation and requires the evaluation of the average two-phase flow multiplier over the condensing region, which, in this case, assumes the following closed form:

Inertia effects are neglected in the single-phase regions due to the relatively minor refrigerant density changes that occur in these sections of the condenser. The state of the refrigerant changes from saturated vapor to saturated liquid in the condensing region. Thus inertia effects can not be ignored, due to the significant density variation that occurs in this region. Inertia contribution to the total pressure drop in the condensing region can thus be evaluated as

It must be noted that inertia effects in the condensing region tend to reduce the pressure drop due to the deceleration experienced by the refrigerant.

Pressure drop effects in the headers, and inlets and exits of the micro channels are neglected in the condenser model.

Heat Exchanger Overall Analysis

Each of the three regions of the condenser has been considered as an independent heat exchanger, and the (e, NTU) procedure has been used for thermal performance analysis. According to this procedure, the heat exchanger effectiveness is defined as

The Number of Transfer Units, NTU, is defined as the ratio between the product (UA) and the minimum of the thermal capacities of both fluids. The following (e, NTU) correlations have been adopted in the condenser model:

(a) single phase regions, cross flow with both fluids unmixed arrangement,

(b) condensing region, the refrigerant temperature is assumed constant and equal to the saturation temperature at the average pressure in the region,

In this case, NTU is evaluated in terms of the thermal capacity of the air, C_a.

Overall energy balances must complement (e, NTU) correlations in each region. The following equations are considered for that purpose in the model:

(a) Air side

(b) Refrigerant side

(b1) Single phase regions

(b2) Condensing region

(c) Overall condenser

Numerical Procedure

The set of equations that constitute the condenser mathematical model has been solved through the software Engineering Equation Solver, EES, from F-Chart, USA. In addition to providing solutions for systems of algebraic (and differential) equations, the software incorporates transport properties of several substances including a number of halocarbon refrigerants.

The numerical solution proceeds as shown in the block diagram of Fig. 6. Further details of the adopted procedure can be found in Mamani (1997), a summary of it is as follows:

(1) Reading input parameters: Condenser geometry, inlet air and refrigerant temperatures and pressures, mass flow rate of refrigerant and face velocity of the air.

(2) Thermal evaluation of the superheated region:

(a) Determination of the overall heat transfer coefficient and pressure drop

(b) Determination of the other parameters through an iterative procedure. Initially, the mass flow rate of air corresponding to this region is assumed to be equal to 10% of the overall air mass flow rate.

(c) Evaluation of the refrigerant pressure drop.

(d) Evaluation of the air capacity, C_a, along with C_min , e, and the NTU for the region. It must be noted that the actual heat transfer rate for the region is known, since the inlet and outlet temperatures of the refrigerant are available.

(e) Evaluation of the product (UA) and area of the region from NTU.

(f) With the external heat transfer area, the mass flow rate of air for that region can be determined as

(g) The obtained mass flow rate is compared to the initially assumed value, step (b). If the deviation is within 1% or less, the program proceeds to step (3), otherwise to step (b) to start the calculation over again.

(3) Thermal evaluation of the condensing region: Once the superheated region has been solved, the condensing one is started following a similar procedure. The initial assumption for the air mass flow rate for this region is 80% of the overall mass flow rate.

(4) Thermal evaluation of the subcooled region: The procedure for the subcooled region is simpler since the mass flow rate of air can easily be determined as the difference between the overall mass flow rate and the combined flow rate of previous regions.

(5) Closure: The exit average air temperature is evaluated by adiabatically mixing the exit air from the three regions along with the total refrigerant pressure drop and the condenser heat transfer. The overall heat transfer coefficient extensive to the full condenser will be discussed in connection with the experimental results.

Discussion of Results

Results from the proposed model have been compared with those obtained from an actual condenser tested in the experimental set up described herein. The particular condenser of this study is that of the type described in Figs. 1 and 2, with micro channels of square cross section. The geometry of the condenser is detailed in Tables 1 and 2, where the micro channels and fins along with the overall dimensions are presented.

A face velocity of the cooling air of 3 m/s was maintained throughout the tests, corresponding to the flow rate provided by the twin fan system, as mentioned before.

Results have been compared in terms of three important physical parameters of the condenser: heat rejection rate, refrigerant pressure drop, and heat transfer coefficient. Figures 7 (a) and ^(b) present the comparison between experimental and simulated results of the first two parameters. Data points correspond to ranges of input parameters indicated in the figure caption. It can be noted that both the condenser heat rejection rate and refrigerant pressure drop, compare very well. It must be stressed that results involve a relatively wide range of input parameters, what makes them yet more significant. Regarding the pressure drop, neglecting effects of headers, and inlet and exit of the micro channels has not significantly affected simulation model results since they compare well with the experimental ones. In fact, data dispersion in ^{Fig. 7 (b)} is in the range between –3% and + 6%, which is a clear indication that the effect of the neglected parameters over the simulation model is of limited extent.

According to the simulation procedure, the product of the overall heat transfer coefficient by the heat transfer area is determined for each of the three condenser regions. The overall (UA)_c product, extensive to the full condenser, is determined by assuming that the refrigerant is at the average condensing temperature (saturation temperature at the average condenser pressure) and the exit temperature of the air is uniform. It must be noted that these are the conditions assumed in the experimental (UA)_c product evaluation, as suggested in succeeding paragraphs. As a result, for each operating condition, the (UA)_c product can be determined according to the following equation:

For the range of operating conditions, summarized in the caption of Fig. 8, the calculated (UA)_c product varies from a minimum of 728.6 W/K to a maximum of 844.6 W/K, corresponding to a variation of 15.9%, as shown in the plot of Fig. 8. The average value of (UA)_c, corresponding to the set of operating conditions of Fig. 8, is equal to 784.9 W/K.

In the condenser industry the heat rejection rate is usually correlated in terms of the difference between the average condensing temperature, corresponding to the average refrigerant pressure in the condenser, and the inlet air temperature, also known as "approaching temperature difference". Figure 9 displays this type of plot involving superimposed experimental and simulation model results. It can be noted that both sets of data points are aligned over straight lines passing through the origin with slopes as indicated in the figure. The deviation of the simulated slope with respect to the experimental one is of the order of 1.79%. Neglecting the effects of the superheated vapor and subcooled liquid regions, as if the refrigerant underwent solely a condensing process, it can be shown, Stoecker and Saiz Jabardo (2002), that the slope of the straight line, R, is given by the following correlation:

Thus, given that the mass flow rate of air is known and constant, the product (UA) can be determined from Eq. (21). This U value corresponds to the average overall heat transfer coefficient extensive to the range of input parameters. Values of (UA)_c from experimental and simulated results are respectively equal to 789.0 W/K and 823.6 W/K. The simulated value of (UA) deviates 4.39% from the experimental, a rather low figure considering that the simulation model includes independently obtained heat transfer and pressure drop correlations and does not present any empirically adjusted coefficient. Finally, it is interesting to note that the simulated average value of (UA)_c determined from the procedure of Fig. 9 is 4.93% higher than that obtained from straight application of Eq. (20). This is a predictable result since, in this case, effects of single-phase regions are taken into account, diminishing the overall heat transfer coefficient. On the other hand, the simulated average (UA)_c from Eq. (20) is within 0.52% of the experimental (UA) from Fig. 9. A minor deviation suggesting that a higher precision can be obtained by directly applying Eq. (20) in the determination of the average value of (UA)_c.

Conclusions

The proposed simulation model for parallel flow micro-channel condensers for automobile air conditioning applications has produced physically sound results. Quantitatively, results from the model in terms of overall parameters, namely heat rejection rate, refrigerant pressure drop and overall heat transfer coefficient, compare very well with the experimental ones. Deviations are rather low, mostly in the range from 1 to 6%. Noteworthy is the fact that heat transfer and pressure drop correlations have been independently obtained from the open literature and the model does not include any adjusted parameter.

Acknowledgements

The authors gratefully acknowledge the support by Talleres Electro Auto S/A., Madrid, Spain, and the following Brazilian institutions: CNPq (Conselho Nacional de Desenvolvimento Científico e Tecnológico) and FAPESP (Fundação de Amparo à Pesquisa do Estado de São Paulo). They would also like to extend their recognition to MSc Marcelo R. Ianella and Mr. José Roberto Bogni for their kind assistance in the experimental activities of this study.

Paper accepted March, 2003

Technical Editor: Clóvis Raimundo Maliska

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Publication Dates

• Publication in this collection
  18 Mar 2004
• Date of issue
  Apr 2003

History

• Accepted
  Mar 2003