ISSN: 0145-7632 print / 1521-0537 online DOI: 10.1080/01457630600793947
Heat Transfer in the Evaporators
of a Double-Evaporator
Refrigerating System
CHAO-JEN LI, JIUNG-HORNG LIN, and CHIN-CHIA SU
Department of Mechanical Engineering, National Taiwan University, Taipei, TaiwanThis paper presents the heat transfer characteristics of the evaporators in a double-evaporator refrigerating system with an environment-friendly refrigerant, propane (R-290). Based on the Buckingham Pi theorem, dimensionless correlations are developed to predict the heat transfer coefficients of the refrigerant in high- and low-temperature evaporators (hHand
hL) and the ratio of the cooling capacity of the high-temperature evaporator to the total capacity (α) in the system. The
results show that hHis affected mainly by the condensing pressure, the length of the low-temperature capillary tube, and the logarithmic-mean temperature difference of the high-temperature evaporator, while hHis affected mainly by the length of the
high-temperature capillary tube and the logarithmic-mean temperature difference of the low-temperature evaporator. Note, though, that the condensing pressure and the logarithmic-mean temperature difference of the high-temperature evaporator are the main factors affecting α. Some of the correlations result in good predictions, though the required numbers of variables of these correlations are much more than those presented in this work.
A comparison of the experimental measurements of hHand hH to the values calculated by the correlations from the
literature is made. Some of the correlations result in good predictions, though the required variables of these correlations are much more than those presented in this work.
INTRODUCTION
The high ozone-depleting potential (ODP) and global warm-ing potential (GWP) has led to the restriction in the use of chlo-rofluorocarbons (CFC) and hydrochlochlo-rofluorocarbons (HCFC), such as R-12 and R-22 [1]. Propane (R-290), with zero ODP and extremely low GWP characteristics, is very attractive in this respect and has been recommended as an alternative to R-22 due to the similarities in their refrigerating properties.
The two-phase heat transfer coefficient of the refrigerant af-fects the performance of the evaporator in a refrigerating sys-tem. For the two-phase flow in the evaporator, the heat transfer involves both nucleate boiling and forced-convection. Several authors [2–5] have proposed correlations for the two-phase heat transfer coefficient in the evaporator. These correlations have been developed through an extensive database of fluids, includ-ing water, R11, R12, R13B1, R22, R113, R114, R134a, R152, R22/R124/R152a, benzene, n-pentane, n-heptane, cyclohexane,
The authors would like to acknowledge the financial support by the National Science Council of Taiwan under the contract of NSC89-2212-E-002-143.
Address correspondence to Dr. Chin-Chia Su, Department of Mechanical Engineering, National Taiwan University, No. 1, Sec. 4, Roosevelt Road, Taipei 106, Taiwan. E-mail: chinchiasu@ntu.edu.tw
methanol, ethanol, n-butanol, hydrogen, helium, neon, nitrogen, ammonia, and ethylene glycol. However, propane (R-290) is not included in this list and warrants further study.
From a thermodynamic viewpoint, a refrigerator with two evaporators in series and one capillary tube performs better than that with only one evaporator. A two-evaporator refrigerator with the zeotropic refrigerant R22/R11 proposed by Lorenz-Meutzner [6] showed a power savings of up to 20% compared to a conventional refrigerator with R-12. With two capillary tubes and two evaporators connected in series, different evaporating temperatures can be obtained by a refrigerating system with pure azeotropic or zeotropic refrigerants [7]. For such a system, the distribution of the cooling load between the evaporators may be an important characteristic.
The design of the distribution of the cooling load between the evaporators in a refrigerating system with two evaporators connected in series is an important study. Based on the present experimental results and the Buckingham Pi theorem, dimen-sionless correlations for the heat transfer coefficients of refrig-erant in the high- and low-temperature evaporators and the ratio of the cooling capacity of the high-temperature evaporator to the total capacity are developed. The experimental measurements of the heat transfer coefficients of the refrigerant are then compared
Table 1 Test conditions
Pc f dH dL Le Di,i Do,i Di,o Do,o LH LL
(kPa) (Hz) (mm) (mm) (m) (mm) (mm) (mm) (mm) (m) (m) 1764 40 1.0 1.4 2 8.7 9.525 14.85 15.875 1.6 0.3 1666 50 1.9 0.6 1568 60 2.2 0.9 1470 70 2.5 1.2 1372 80 2.8
with the results calculated by the correlations in the literature [2–5].
EXPERIMENTAL METHOD Facility
Figure 1 shows the experimental facility of a series-connected two-evaporator refrigerating system with R-290. The test
appa-Figure 1 Schematic diagram of the experimental facility.
ratus is composed of a refrigerant loop and two heat-exchange fluid loops. The states of the working fluids are monitored with T-type thermocouples and pressure gauges.
The reciprocating compressor in the refrigerant loop is con-trolled by the frequency converter. The output of the converter for stable operation can be adjusted to 40–80 Hz. The rotating speed of the fan controlled through a voltage transformer af-fects the condensing pressure of the system. The dimensions of these components are listed in Table 1. The two evaporators are double-tube with the same dimensions. Di,i and Do,i represent
the inside and outside diameter of the inner tube, respectively, while Di,o and Do,o represent the inside and outside diameter
of the outer tube, respectively. The refrigerant flows in one di-rection through the inner tube, while the heating medium flows in the opposite direction through the annular space between the inner and outer tubes. Note that the evaporators and capillary tubes are all made of copper and heat-insulated.
Both heat-exchange loops are composed of a refrigerator, a pump, a flow meter, a thermometer controller, and an electri-cally heated unit. The heating media of both evaporators are water/glycol (50/50 wt.%) mixture. The temperatures of wa-ter/glycol entering the high- and low-temperature evaporators are set at around 25◦C and−9.5◦C, respectively. The condens-ing pressure, the lengths of the capillary tubes for the high- and low-temperature evaporator, and the compressor frequency are the variables of the experiment. Table 1 lists the details of the test conditions.
Data Reduction and Dimensionless Correlation The Heat Transfer Coefficient of the Refrigerant
To calculate the heat transfer coefficient of the refrigerant in both evaporators, the heat transferred to the refrigerant should be known. For a given evaporator, the cooling capacity (Q) may be expressed as Q= (U · A) · (LMTD) (1) where (U· A) = 1 hr· Ai + R + 1 hhm· Ao −1 (2)
(LMTD)= (Thm,out− Tr,in)− (Thm,in− Tr,out) ln
(Thm,out−Tr,in)
(Thm,in−Tr,out)
(3)
Assuming that the variations in Thm,inare negligible and keeping mhmconstant, the heat transfer coefficients of the heating media
(hhm) are more or less fixed. The conduction resistances (R) are
more or less constant, while the inside and outside heat transfer areas, Ai and Ao, are fixed. With all temperatures in Eq. (3)
and the cooling capacity (Q = ˙mhm· Cphm· (Thm,in− Thm,out))
measured, the experimental values of the heat transfer coefficient of refrigerant (hr) can then be obtained through Eqs. (1–3). Dimensionless Correlations
The quality of the refrigerant in the high- and low-temperature evaporators is different, and the analyses for the heat transfer co-efficient of refrigerant in the evaporator (hr) are thus divided into
two categories: the heat transfer coefficients of refrigerant in the high- and low-temperature evaporators, hHand hL. The analytic
process used to develop the dimensionless correlations for pre-dicting hrin the system is based on the Buckingham Pi theorem.
The first step is to determine the variables that may influence
hr: both the diameters and lengths of the high-temperature (dH
and LH) and low-temperature (dL and LL) capillary tube, the
inlet conditions of the refrigerant (PcandTsc), the frequency
of compressor ( f ), the saturated properties of R-290 (liquid density ρf, liquid viscosity µf, and liquid-specific heat Cpf),
and the logarithmic-mean temperature difference of the specific evaporator (LMTDH, LMTDL). Note that the properties of
re-frigerant are obtained by using REFPROP [8]. LH and LL are
non-dimensionalized by dH and dL, respectively. However, in
order to non-dimensionalize hr, Pc,Tsc, and f , a new
repeat-ing variable ¯d, based on the definition of hydraulic diameter, is
defined as (d2H+ dL2)(dH+ dL)−1. hrcan then be expressed as hr= f1(Pc, LH, LL, dH, dL, ¯d, Tsc, ρf, Cpf, µf, f, LMTD)
(4) Similarly, the ratio of the cooling capacity of the high-temperature evaporator to the total capacity (α) can be expressed as
α= f2(Pc, LH, LL, dH, dL, ¯d, Tsc, ρf, Cpf, µf, f, LMTD)
(5) where dH, dL, ¯d, ρf, µf, and Cpfare the repeating variables.
The dimensionless correlations for hH, hL, or α can now be
expressed as
8,9,or10 = A · 1B· C2 · D3 · 4E· 5F· 6G· 7H (6)
where1,2,3,4,5,6,7,8,9, and10in Eq. (6) represent Pc, LH, LL,Tsc, f , LMTDH, LMTDL, hH, hL, and α,
respectively, as shown in Table 2. By substituting the experimen-tal values into the statistical software STATISTICA, the values of constant A and exponents of the parameters are obtained.
Table 2 Dimensionless parameters group
Pi Groups Definition Effect
1 ¯ d2·ρ f·Pc µ2 f Condensing pressure 2 (LdHH) Geometry 3 (LdLL) Geometry 4 ( ¯ d2·ρ2f·Cp f·Tsc µ2f ) Subcooling 5 ¯ d2· f ·ρ f µf Compressor frequency 6 ( ¯ d2·ρ2 f·Cp f·LMTDH µ2f ) LMTDH 7 ( ¯ d2·ρ2 f·Cp f·LMTDL µ2 f ) LMTDL 8 C phHf·µ· ¯df hH 9 ChL· ¯d p f·µf hL 10 QHQ+QH L Ratio of QH
RESULTS
The Dimensionless Correlation for hH
Note that LMTDLis not one of the main factors affecting hH.
The dimensionless correlation for hHis thus 8= 10−4.52·−0.343 1 · 0.097 2 ·−0.2093 ·−0.0454 ·−0.0215 · 0.888 6 (7) From the exponents of the parameters in Eq. (7), it is clear that hHis affected mainly by Pc, LL, and LMTDH. The effect
of Pcon hH seems more significant than that of LL. Increasing Pcwill increase the mass flow rate of refrigerant ( ˙mr) but
de-crease LMTDH. For the two-phase flow in the evaporator, the
heat transfer involves both nucleate boiling and forced convec-tion. The nucleate boiling heat transfer increases with LMTD [9], while forced-convection heat transfer increases with Reynolds number, which is in proportion to ˙mr. It seems that the effect
of LMTDHinduced by Pcon hHdominates that of ˙mr. In
addi-tion, both ˙mrand LMTDHdecreases with LL[7], which induce hH to decrease with LL. Figure 2 shows that the range of the
maximum error (β) for hHusing Eq. (7) is between –16% and
+16%. Note that β represents the maximum deviation of the experimental data from the predicted values.
The Dimensionless Correlation for hL
Again, LMTDHis not a main factor affecting hL. The
dimen-sionless correlation for hLis 9= 10−6.095·−0.038
1 ·−0.1852 ·−0.083 ·40.023·05.00002·07.688
(8)
Figure 2 Measurement of hHversus predicted hH using Eq. (7).
Equation (8) shows that LHand LMTDLare the main factors
affecting hL. hLdecreases with LHbut increases with LMTDL;
˙
mr decreases but LMTDL increases with LH [7]. It seems that hLdecreases with LH, as the effect of ˙mr on hLdominates that
of LMTDLinduced by LH. Figure 3 shows that β for hLusing
Eq. (8) is between−12% and +16%.
The Dimensionless Correlation for α
The ratio of the cooling capacity of the high-temperature evaporator to the total capacity (α) is an important characteristic of the system because the relative cooling capacities of the two evaporators in the system may vary in various applications. The analysis shows that α can be expressed as
10 = 10−1.416· −0.253
1 · −0.08152 · −0.023
· −0.0524 · −0.0275 · 1.563
6 · −0.9997 (9)
From the relative values of the exponents of parameters in Eq. (9), α is mainly affected by Pc, LMTDH, and LMTDL.
αdecreases with Pc and LMTDL but increases with LMTDH.
However, the effect of LMTDL on α is more significant than
that of Pc. Figure 4 shows that β for α using Eq. (9) is between
−10% and +10%.
Comparison of Experimental Results with Existing Correlations
For the two-phase heat transfer coefficients of a refrigerant in the two evaporators, hH and hL, some correlations may be
Figure 3 Measurement of hLversus predicted hLusing Eq. (8).
found from various sources (e.g., [2–5]). These correlations for the two-phase heat transfer coefficient cover both the nucleate boiling and forced convection regions. A comparison is thus made for these correlations with the test values measured in this work.
Figure 4 Measurement α versus predicted α using Eq. (9).
Correlation from Gungor-Winterton [2]
A large database for water, R11, R12, R22, R113, R114, and ethylene glycol was used by Gungor-Winterton [2]. The empiri-cal equation obtained for the two-phase heat transfer coefficient
Figure 5 Measurements versus predictions in hrwith correlation [2].
in evaporator is
hr = E · hf + S · hpool (10)
The expressions for hf, hpool, E, and S in Eq. (10) are hf = 0.023 · Ref0.8· Pr0f.4· kf/Di,i (11) hpool= 55 · Pr0.12· (− log10Pr)−0.55· M−0.5· q0.67 (12) E = 1 + 24000 · Bo1.16+ 1.37(1/ Xtt)0.86 (13)
Figure 6 Measurements versus predictions in hrwith correlation [3].
S = 1
1+ 1.15 · 10−6E2· Re1.17 f
(14) where Bo and Xtt in Eq. (13) are
Bo= q λ· G (15) Xtt = 1− x x 0.9ρ v ρf 0.5µ f µv 0.1 (16)
Figure 7 Measurements versus predictions in hrwith correlation [4].
Figure 5 shows that, compared with the experimental results in the present work, both hHand hLcalculated by the correlation
from [2] are over-predicted by about 0–40%.
Correlation from Kandlikar [3]
A large database for water, R11, R12, R13B1, R22, R113, R114, R-152, neon, and nitrogen was also used by Kandlikar
Figure 8 Measurements versus predictions in hrwith correlation [5].
[3]. The correlation for the two-phase heat transfer coefficient in evaporator is
hr = hf · (C1· CoC2· (25 · Frlo)C5+ C3· BoC4· Ff l) (17)
where Co is a convection number expressed as
Co= 1− x x 0.8ρ v ρf 0.5 (18)
The constants C1through C5and the fluid-dependent
param-eter Ff lare given in the literature [3]. Figure 6 shows that both hH and hL calculated by the correlation from [3] are
under-predicted by about 0–35%.
Correlation from Steiner-Taborek [4]
Again, a large database for water, R11, R12, R13B1, R22, R113, benzene, n-pentane, n-heptane, cyclohexane, methanol, ethanol, n-butanol, hydrogen, helium, nitrogen, and ammonia were used by Steiner-Taborek [4]. The correlation for the two-phase heat transfer coefficients in evaporator is
hr = ((hpool)3+ (hcb)3)1/3 (19)
where hcbis the forced convection coefficient, which is a
func-tion of µf, µv, kf, kv, ρf, ρv, G, the Fanning friction factor,
quality, and the local liquid- and gas-phase forced convection coefficients. The expression of hcbis very complex; therefore,
the details are not listed here. Figure 7 shows that β for both hH
and hLfrom the correlations of [4] is between−12% and +10%. Correlation from Wattelet et al. [5]
The database for R-12, R134a, and a mixture of R22/R-124/ R-152a were used by Wattelet et al. [5]. The correlation for the two-phase heat transfer coefficient in evaporator is
hr = ((hpool)2.5+ (hcb)2.5)0.4 (20)
where hcbcan be expressed as hcb=
1+ 1.925 · X−0.83tt
· hl· δ (21)
The reduction parameter δ in Eq. (21) is δ= 1.32 · Fr0f.2 if Frf < 0.25
δ= 1 if Frf ≥ 0.25
Figure 8 shows that β for both hHand hLfrom the
correla-tions of [5] is between−11% and +9%.
Note that β for both hHand hLfrom the correlations of [4, 5]
are smaller than those from the present correlations, Eqs. (7) and (8). However, the required numbers of variables of the cur-rent correlations are much fewer than those of the correlations from [4, 5].
CONCLUSIONS
The dimensionless correlations for analyzing the characteris-tics of the series-connected two-evaporator refrigerating system with R-290 as the refrigerant, hH, hL, and α, are developed in
this paper. In addition, a comparison of the experimental mea-surements of hHand hLto those calculated by the correlations
from literature is made. Some conclusions may thus be drawn:
1. Based on the present experimental results and the Bucking-ham Pi theorem, the dimensionless correlations for hH, hL,
and α can be developed. The accuracy of those is acceptable. 2. Pc, LL, and LMTDH are the dominant factors of hH, while LH and LMTDL are those for hL. On the other hand, the
dominant factors for α are Pc, LMTDH, and LMTDL.
3. β for both hHand hLfrom the correlations of [2, 3] are greater
than those from the current correlations, Eqs. (7) and (8), while that from the correlations of [4, 5] are smaller. 4. In this study, the dimensionless correlations for R-290 may
be applied to other refrigerants with refrigerating properties close to R-290, such as R-22.
5. For the two-phase heat transfer coefficient of a refrigerant in an evaporator, the accuracy in prediction with some correla-tions from the literature [4, 5] is good. However, the specific correlations are much more complicated than the dimension-less correlations developed in this paper.
NOMENCLATURE Bo boiling number
Cp specific heat, J· kg−1K−1 C1–C5 constants in Eq. (17)
dH diameter of the high-temperature capillary tube, mm dL diameter of the low-temperature capillary tube, mm Di,i inside diameter of the inner tube of evaporator, mm Di,o inside diameter of the outer tube of evaporator, mm Do,i outside diameter of the inner tube of evaporator, mm Do,o outside diameter of the outer tube of evaporator, mm E enhancement factor
Frlo Froude number with all flow as liquid F frequency of the compressor, s−1
G mass flux, k· gm−2s−1
hcb heat transfer coefficient of convective boiling, W ·
m−2K−1
hf heat transfer coefficient of saturated liquid, W ·
m−2K−1
hH heat transfer coefficient of refrigerant in the
high-temperature evaporator, W· m−2K−1
hL heat transfer coefficient of refrigerant in the
low-temperature evaporator, W· m−2K−1
hpool heat transfer coefficient of pool boiling, W· m−2K−1
kf thermal conductivity of saturated liquid, W· m−1K−1 LH length of the high-temperature capillary tube, m LL length of the low-temperature capillary tube, m LMTDH logarithmic-mean temperature difference of the
high-temperature evaporator, K
LMTDL logarithmic-mean temperature difference of the
low-temperature evaporator, K M molecular weight
˙
M mass flow rate, kg s−1
Pc condensing pressure, Pa
Prf Prandtl number of saturated liquid Q heat flux, W· m−2
QH cooling capacity of the high-temperature evaporator,
W
QL cooling capacity of the low-temperature evaporator,
W
Ref Reynolds number of saturated liquid S suppression factor
T Temperature, K
U overall heat transfer coefficient, W· m−2K−1
X Quality
Greek Symbols
Tsc Subcooling, K
ρf density of saturated liquid, k· gm−3
ρv density of saturated vapor, k· gm−3 µf viscosity of saturated liquid, Pas
µv viscosity of saturated vapor, Pas A ratio of cooling capacity B range of maximum error
dimensionless parameter λ latent heat (J· m−3)
REFERENCES
[1] United Nations Environment Program, Decisions of the Fourth Meeting of the Parties to the Montreal Protocol on Substances That Deplete the Ozone Layer, Copenhagen, Denmark, 28 July, 1992. [2] Gungor, K. E., and Winterton, R. H. S., A General Correlation for
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[3] Kandlikar, S. G., A General Correlation for Saturated Two-Phase Flow Boiling Heat Transfer inside Horizontal and Vertical Tubes, ASME Journal of Heat Transfer, vol. 112, pp. 219–228, 1990.
[4] Steiner, D., and Taborek, N., Flow Boiling Heat Transfer in Ver-tical Tubes Correlated by an Asymptotic Model, Heat Transfer
Engineering, vol. 13, pp. 43–69, 1992.
[5] Wattelet, J. P., Chato, J. C., Souza, A. L., and Christoffersen, B. R., Evaporative Characteristics of R-12, R-134a, and a Mixture at Low Mass Fluxes, ASHRAE Transactions, vol. 100, no. 2, pp. 603–615, 1994.
[6] Lorenz, A., and Meutzner, K., On Application of Nonazeotropic Two-Component Refrigerants in Domestic Refrigerators and Home Freezers, Proc. XIV Int. Cong. Refrig., Moscow, vol. 2, pp. 1005– 1011, Paris.
[7] Li, C. J., and Su, C. C., Experimental Study of a Series-Connected Two-Evaporator Refrigerating System with Propane (R-290) as the Refrigerant, Applied Thermal Engineering, vol. 23, pp. 1503–1514, 2003.
[8] McLinden, M. O., Lemmon, E. W., Klein, S. A., and Peskin, A. P.,
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Chao-Jen Li is a researcher at the Industrial Tech-nology Research Institute in 2005. He received his Ph.D. from the department of mechanical engineer-ing, National Taiwan University, in 2004. His main research interests are heat transfer, refrigeration and air conditioning, and numerical analysis.
Jiung-Horng Lin is a Ph.D. student in the depart-ment of mechanical engineering, National Taiwan University, Taipei, Taiwan. He is currently studying the heat transfer characteristics of some wavy chan-nels in PHEs and the application of absorption refrig-eration system on automobiles.
Chin-Chia Su is a professor of mechanical engineer-ing at National Taiwan University, Taipei, Taiwan. He received his Ph.D. in 1986 from Cambridge Univer-sity, UK. His main research interests are heat transfer, refrigeration and air-conditioning, and fuel cell tech-nology. He has published more than 70 articles in journals, books, and proceedings.
![Figure 5 Measurements versus predictions in h r with correlation [2].](https://thumb-ap.123doks.com/thumbv2/9libinfo/8782621.216564/6.918.232.733.109.454/figure-measurements-versus-predictions-h-r-correlation.webp)
![Figure 7 Measurements versus predictions in h r with correlation [4].](https://thumb-ap.123doks.com/thumbv2/9libinfo/8782621.216564/7.918.185.685.108.488/figure-measurements-versus-predictions-h-r-correlation.webp)
