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Flow boiling heat transfer to carbon dioxide: general prediction method
International Journal of Refrigeration 27 (2004) 294–301 www.elsevier.com/locate/ijrefrig
Flow boiling heat transfer to carbon dioxide: general prediction method John R. Thome*, Jean El Hajal Laboratory of Heat and Mass Transfer, Faculty of Engineering Science, Swiss Federal Institute of Technology Lausanne, LTCM-ISE-STI, EPFL, CH-1015 Lausanne, Switzerland Received 21 October 2002; received in revised form 30 July 2003; accepted 7 August 2003
Abstract An updated version of the Kattan–Thome–Favrat flow pattern based, flow boiling heat transfer model for horizontal tubes has been developed specifically for CO2. Because CO2 has a low critical temperature and hence high evaporating pressures compared to our previous database, it was found necessary to first correct the nucleate pool boiling correlation to better describe CO2 at high reduced pressures and secondly to include a boiling suppression factor on the nucleate boiling heat transfer coefficient to capture the trends in the flow boiling data. The new method predicts 73% of the CO2 database (404 data points) to within 20% and 86% to within 30% over the vapor quality range of 2–91%. The database covers five tube diameters from 0.79 to 10.06 mm, mass velocities from 85 to 1440 kg m2 s1, heat fluxes from 5 to 36 kW m2, saturation temperatures from 25 C to +25 C and saturation pressures from 1.7 to 6.4 MPa (reduced pressures up to 0.87). # 2003 Elsevier Ltd and IIR. All rights reserved. Keywords: Modelling; Evaporation; Carbon dioxide; Horizontal tube; Heat transfer; Mass transfer
Dioxyde de carbone: transfert de chaleur lors de l’e´bullition— me´thode de pre´vision Mots cle´s : Mode´lisation ; E´vaporation ; Dioxyde de carbone ; Tube horizontal ; Transfert de chaleur ; Transfert de masse
1. Introduction Carbon dioxide has become an important alternative refrigerant in the past few years and thus an accurate heat transfer prediction method for its evaporation inside horizontal tubes is required. CO2 is a special fluid with a low critical temperature and is thus utilized at quite high operating pressures compared to other refrigerants. Current experimental evidence shows that
* Corresponding author. E-mail address: john.thome@epfl.ch (J.R. Thome). 0140-7007/$35.00 # 2003 Elsevier Ltd and IIR. All rights reserved. doi:10.1016/j.ijrefrig.2003.08.003
CO2 flow boiling heat transfer coefficients are on the order of twice those predicted by existing methods. Hence, the objective here is first to understand why this is so and secondly to propose an updated version of the Kattan–Thome–Favrat [1] flow boiling heat transfer model specifically for CO2. It is important that the method is not only statistically accurate but that it also properly captures the trends in the data since these methods typically go into system simulation programs, such as that of Brown et al. [2]. If the heat transfer prediction method does not capture the trends correctly and accurately, then false optimisations and conclusions will result.
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Nomenclature A cp d g : m M pcrit pr psat q ri ReL ReV S Tsat x Greek nb nb,CO2 cb tp vapor wet " l dry strat
cross sectional area m2 specific heat J kg1 K1 tube internal diameter m acceleration of gravity m s2 total mass velocity of liquid and vapor kg m2 s1 molecular weight critical pressure Pa reduced pressure (psat/pcrit) saturation pressure Pa heat flux W m2 internal tube radius m liquid film Reynolds number vapor Reynolds number boiling suppression factor saturation temperature C vapor quality
nucleate boiling heat transfer coefficient W m2 K1 CO2 nucleate boiling heat transfer coefficient W m2 K1 convective boiling heat transfer coefficient W m2 K1 flow boiling heat transfer coefficient W m2 K1 vapor heat transfer coefficient W m2 K1 wet wall boiling heat transfer coefficient W m2 K1 liquid film thickness m vapor cross-sectional void fraction thermal conductivity W m1 K1 dynamic viscosity Ns m2 upper dry angle of tube rad stratified angle around top of tube rad density kg m3 surface tension N m1
Subscripts G vapor L liquid
Six well-executed experimental studies on CO2 evaporation were found to date. Høgaard Knudsen and Jensen [3] have measured local flow boiling data in a stainless steel (ST35) precision pipe of 1.12 m length and 10.06 mm internal diameter. They heated the test section by condensing R-22 on the outside. They found that their heat transfer coefficients were about 1.9 times
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those predicted by the Shah [4] correlation. Bredesen et al. [5] reported measurements for a 7 mm aluminum tube with electrical heating, obtaining heat transfer data significantly larger than four widely quoted correlations. Hihara and Tanaka [6] made measurements in a 1.0 mm stainless steel tube using DC electrical heating of their test section. Their data displayed dryout at high mass velocities at vapor qualities as low as 40%. Pettersen, Rieberer and Munkejord [7] similarly reported flow boiling data in a 0.79 mm tube using hot water as their heating source and the modified-Wilson plot technique to deduce their flow boiling heat transfer coefficients. They also observed the onset of dryout in their data. In addition, they compared their data to six prediction methods and found poor agreement with all six. Yun et al. [8] applied DC heating to a 6.0 mm diameter stainless steel tube to obtain their flow boiling data; they also measured heat transfer coefficients for R-134a as a base case in the same test section. Koyama et al. [9] reported measurements for a 316 stainless steel tube of 1.8 mm diameter, attaining heat transfer coefficients above 20,000 W m2 K1 at a mass velocity of 250 kg m2 s1 and heat flux of 31 kW m2 at a saturation pressure of 4.5 MPa, attesting to CO2’s formidable performance as a heat transfer fluid. Several previous attempts have been made to develop flow boiling heat transfer correlations specifically for CO2. For example, Hwang et al. [10] modified the Bennett and Chen [11] correlation for vertical tubes using the data of Bredesen et al. [5] for a horizontal 7.0 mm I.D. tube at one of the saturation temperatures they tested, applying six new empirical factors to make it work. As noted above, Høgaard Knudsen and Jensen [3] included a multiplier of 1.9 to the Shah [4] correlation to make it fit their data. No general methods have been proposed based on a broad, representative database to date.
2. CO2 heat transfer database and flow pattern map Five of the six independent experimental studies noted earlier from different laboratories in Japan, Korea, Norway and Denmark have been used to form the present flow boiling heat transfer database, whose range of test conditions are shown in Table 1. Hence, the database covers tube diameters from 0.79 to 10.06 mm, mass velocities from 85 to 1440 kg m2 s1, heat fluxes from 5 to 36 kW m2 and saturation temperatures from 25 C to +25 C (corresponding to saturation pressures from 1.7 to 6.4 MPa). The data were taken from tables in these publications where available or by digitising the heat transfer graphs in these publications to extract the plotted heat transfer coefficients. The updated two-phase flow pattern map for evaporating flows in horizontal tubes of Thome and
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Table 1 CO2 flow boiling heat transfer database Reference
Tube I.D. (mm)
Mass velocity (kg m2 s1)
Heat flux (kW m2)
Saturation temp. ( C)
Saturation pressure (MPa)
Data points
Koyama et al. [9] Hihara and Tanaka [6] Pettersen et al. [7] Knudsen and Jensen [3] Yun et al. [8]
1.8 1.0 0.79 10.06 6.0
100–250 360–1440 200–600 85–175 170–320
4–32 9–36 5–20 7–13 10–20
0, 10 15 0 to 25 25 to 10 5, 10
3.5, 4.5 5.1 3.5–6.4 1.7–2.6 4.0, 4.5
12 of 12 142 of 206 80 of 116 81 of 81 89 of 89
El Hajal [12] was then used to classify the data by flow pattern. Since the Kattan et al. [1] flow boiling model does not yet include a heat transfer model for mist flows, the data predicted by the flow pattern map to be in the mist flow regime have been excluded from the present heat transfer database. On the other hand, data which clearly appear to be mist flow heat transfer coefficients because of their very low values but which the map identifies as annular flows, have been left in the database. These values will tend to be significantly over predicted by the new heat transfer model. All together, 404 flow boiling heat transfer data points were thus obtained from these publications (i.e. 142 of the 206 Hihara-Tanaka points and 80 of the 116 Pettersen points were used and all of the data from the other three publications). The data of Bredesen et al. [5] for a 7.0 mm I.D. tube have been excluded because they differ significantly from comparable data for 6.0 mm and 10.06 mm tubes in two other studies and also because there is a large scatter among their data. Hwang et al. [10] also noted an anomaly in their 300 kg m2 s1 data when correlating them. Yet, since their tests were run with the same rigor as the other tests, it is not clear where these problems come from. The flow pattern map used here is the simplified version proposed by Thome and El Hajal [12] of the previous map described in Kattan et al. [13] and later modified by Zu¨rcher et al. [14]. This map is for adiabatic and evaporating flows in small diameter tubes. So far this map has been compared to flow pattern observations for nine evaporating fluids: R-134a, R-123, R-502, R-402A, R-404A, R-407C, ammonia, R-22 and R-410a. A version of this map for condensing flows in horizontal tubes has also recently been proposed by El Hajal et al. [15] together with a flow pattern based condensing heat transfer model by Thome et al. [16], and it has been successfully applied to 15 fluids in that study for tube diameters from 3.1 to 21.4 mm. In the present study, CO2 properties have been obtained from the most recent version of REFPROP of NIST. The Thome–El Hajal map is used here without modification for CO2. No flow pattern observations are apparently available in the literature for CO2 because of
the high pressures involved except for some very recent ones reported by Pettersen [17] in a 0.98 mm channel at 5.72 MPa. As an example of its application here, Fig. 1 shows the flow pattern map equations evaluated for CO2 at 0 C (3.48 MPa) for tube internal diameters of 1, 6 and 10 mm and a heat flux of 15 kW m2, plotted in an easy to read mass velocity vs. vapor quality format (flow pattern legend: S—stratified flow, SW—stratifiedwavy flow, I—intermittent flow, A—annular flow, MF—mist flow). The stratified flow regime is at the lowest range of mass velocities, and the three transition curves from stratified flow to stratified-wavy flow for the different tubes all fall on top of each other (bold curve). Above this transition is the stratified-wavy flow region, and its transition to the intermittent and annular flow regimes are indicated by the next three curves. Above these two flow regimes is the mist flow regime, whose transition threshold increases greatly as the channel diameter decreases. The vertical transition curve from intermittent flow to annular flow is only a function of fluid properties and hence gives the same vertical line for all three tube diameters. Application of the flow pattern map to channels as small as 1 mm is an extrapolation beyond its previous database but this cannot be avoided. It is also interesting to note that tube diameters of 1 mm would normally be thought of as micro-channels; however, at the high pressures associated with CO2, the
Fig. 1. Flow pattern map for CO2 for several tube diameters.
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bubbles are predicted to be very small and hence the flow most likely will still look like a macro-scale twophase flow. Comparing the map to the 30 very recent observations of Pettersen [17] mentioned above, the map correctly predicts just 15 of 29 of his observations for intermittent flow, annular flow and droplet flow. He labeled one of his observations as a dispersed flow for which it is not clear the meaning, but is apparently an annular flow with entrained droplets at very high vapor qualities approaching 100%. For this observation, it is not clear how the droplets could be seen through the annular liquid film unless it was partially dry; it is predicted to be an annular flow with partial dryout according to the Kattan–Thome–Favrat map, which the map classifies as a stratified-wavy flow since only part of the perimeter is wetted for modeling this flow’s heat transfer. On the other hand, the transitions are zones and not just lines as shown on the map and another 9 observations are within 10% vapor quality or within 5– 15 kg m2 s1 from the correct boundary, which would mean as many as 24 of his 29 observations are approximately correctly identified by the map. Also, 11 flow observations they have identified as annular flow that fall in the intermittent flow region have no effect on the heat transfer prediction since intermittent flow is treated as annular flow in the Kattan–Thome–Favrat heat transfer model. Thus, while it is always difficult to interpret the observations of others or for others to use the same criteria for classifying observations as used in the development of a particular map, this comparison is rather promising considering its extrapolation to high pressures and small tube diameters. Their observations also confirm that CO2 flow at 5.722 MPa in a 0.98 mm channel looks like it has macroscale flow regime features. Fig. 2 shows the effect of saturation temperature on the expected flow pattern transitions for a 6 mm tube at a heat flux of 15 kW m2 at saturation temperatures of
Fig. 2. Flow pattern map for CO2 at several saturation temperatures.
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25 C (1.68 MPa), 5 C (3.04 MPa) and +15 C (5.08 MPa). The effect of saturation pressure on the S!SW, SW!I and SW!A transitions is not so large but its effect on I!A and A!MF is quite noticeable.
3. Modified local flow pattern based evaporation model Kattan et al. [1,13,18] proposed a flow boiling model based on the local flow pattern that so far covers annular flows, annular flows with partial dryout, intermittent flows, stratified-wavy flows and fully stratified flows, but not yet bubbly flows nor mist flows (bubbly flows occur at very high mass velocities and are not shown on the previous maps). It is based on their two-phase flow pattern map for horizontal evaporating flows described above. Fig. 3 depicts the simplified two-phase flow structures assumed in their model for the fully-stratified, stratified-wavy and annular flow regimes. For fully stratified flow, the truncated annular liquid ring has a wetted angle equal to 2p-strat and a thickness of d, with the same cross-sectional area of the liquid AL in both cases. For annular flow, the cross-sectional area of the annulus is AL, strat is equal to 0, and the thickness is obtained assuming d/2 so that =AL/( d). In intermittent flows, heat transfer is successfully predicted assuming the annular flow structure applies while annular flows with partial dryout are classified as stratified-wavy flows in this model. The Kattan–Thome–Favrat general equation for the local flow boiling coefficient tp for evaporation in a horizontal, plain tube is: d dry vapor þ d 2 dry wet tp ¼ ð1Þ 2 d
Fig. 3. Simplified two-phase flow structure showing liquid and vapor zones, stratified and dry angles and liquid film thickness used in the flow boiling model.
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The dry angle around the top of the tube, if any, is dry, which varies from zero for annular flow up to its maximum value of ystrat for fully stratified flow. On the wetted perimeter [ri (2 dry)], the heat transfer coefficient is wet, which is determined with an asymptotic expression that combines the nucleate boiling nb and convective boiling cb contributions to heat transfer by the third power as: 1=3 ð2Þ wet ¼ 3nb þ 3cb The nucleate boiling heat transfer coefficient nb is determined with the dimensional reduced pressure correlation of Cooper [19], without its surface roughness correction term (i.e. assuming his recommended standard roughness of 1 mm) nor its 1.7 multiplier for copper surfaces: nb ¼ 55p0:12 ðlog10 pr Þ0:55 M0:5 q0:67 r
ð3Þ
In this expression nb is in W m2 K1, pr is the reduced pressure where pr=psat/pcrit, M is the liquid molecular weight and q is the heat flux at the tube wall in W m2. Notably, this correlation was developed without any CO2 nucleate pool boiling results in its database. The convective boiling heat transfer coefficient cb for annular liquid film flow is formulated as a film flow and not as a tubular flow as: : 4mð1 xÞ 0:69 cpL L 0:4 lL ð4Þ cb ¼ 0:0133 ð1 "ÞL lL where 0.0133 and 0.69 are empirical constants determined from their original database for five refrigerants and remain unchanged in successive tests, including those for ammonia data and now also for CO2. The term in the first bracket is the liquid film Reynolds number ReL while the second bracket represents the liquid Prandtl number PrL. Consequently, the mean liquid velocity in the annular film is utilized here to determine the liquid Reynolds number, which changes as a local function of the vapor quality x, annular liquid film thickness , and vapor void fraction ". The void fraction is determined with the Rouhani and Axelsson [20] drift flux model: ( x x 1x 1:18 þ "¼ þ : ð1 þ 0:12ð1 xÞÞ G G L m )1 1=4 g ðL G Þ ð1 xÞ ð5Þ
2L : where m is the total mass velocity of liquid and vapor. The vapor-phase heat transfer coefficient vapor is calculated with the Dittus–Boelter turbulent flow heat transfer correlation assuming tubular flow on the dry
perimeter of the tube using the vapor properties and the : mass velocity of the vapor, i.e. mx, so that: vapor
: 0:8 mxd cpG G 0:4 lG ¼ 0:023 "G lG d
ð6Þ
The vapor-phase heat transfer coefficient vapor is applied to the dry perimeter of the tube. The vapor Reynolds number ReG in the first bracketed term above includes the vapor void fraction " such that the mean vapor velocity in the cross-section of the tube occupied by the vapor is used in its determination. The rest of the description of the heat transfer model can be found in Kattan et al. [1]. Direct application of this heat transfer model to CO2 data tends to drastically underpredict the flow boiling data, particularly as low and intermediate vapor qualities. Secondly, CO2 at high saturation pressures gives an experimental trend of a monotonic decrease in tp vs. vapor quality in intermittent and annular flows, which is the exact opposite of the trend for other refrigerants at low pressures (below 1 MPa), i.e. a steady increase in tp vs. x before the onset of dryout. Fig. 4 illustrates these two contradictory trends obtained by Yun et al. [8] with a 6.0 mm tube for CO2 and R-134a. The Kattan– Thome–Favrat heat transfer model in its original form accurately predicts the R-134a heat transfer coefficients in Fig. 4; e.g. Fig. 5 depicts a comparison of measured to predicted values for R-134 at 5 C at a heat flux of 10 kW m2 and mass velocity of 240 kg m2 s1. Investigating the possible origins of this anomalous trend in CO2 data, the first problem was to understand why there is the monotonic decrease in tp vs. vapor quality for CO2. While some researchers have attributed this to some form of partial premature dryout, there are no observations to back this up. Furthermore, the CO2 data in Fig. 4 are in the intermittent and annular flow regimes, such that dry=0, and thus postulating that
Fig. 4. Flow boiling data of Yun et al. [8] for CO2 and R-134a.
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stratified flow could explain this trend (note: at otherwise fixed conditions, dry increases with x) is not correct either. Evaluating the model and the data it was observed that the nucleate boiling contribution was larger than the convective boiling contribution for CO2 while the opposite is true for R-134a. Hence, this suggests that boiling suppression is acting on nb to reduce its contribution with increasing vapor quality, i.e. like in the Chen [21] and Gungor and Winterton [22] correlations. It was observed that the nucleate pool boiling coefficients predicted by the Cooper correlation for CO2 are much lower than those predicted by the competing fluid-specific correlation of Gorenflo [23] for CO2. Evaluating the present flow boiling data at low vapor qualities (x<0.2) to extract the nucleate pool boiling contribution, the data were first set equal to tp in Eq. (1) and then the vapor phase heat transfer contribution (if any) and the convective boiling contribution were removed utilizing the respective Eqs. (6) and (4), yielding the nucleate boiling contribution nb from Eq. (2), deduced from the database listed in Table 1. Comparing these nucleate boiling dominated data to the Cooper correlation, Eq. (3), it was observed that this expression tends to under predict these values at low heat fluxes. Hence, Eq. (3) has been modified based on these data to become for CO2: nb;CO2 ¼ 0:71nb þ 3970
ð7Þ
Fig. 6 shows a comparison of this expression to the ‘‘nucleate boiling’’ coefficients so obtained while the diagonal dashed line is that of the Cooper correlation. It was also noted that for CO2 at low heat fluxes that the heat transfer coefficients seemed to remain unusually high, apparently because of the high nucleation capabilities of CO2; hence, this effect is the origin of the additive value of 3970 W m2 K1 in the above expression. Using nb;CO2 in place of nb in Eq. (2), the boiling
Fig. 5. Comparison of original model to R-134a flow boiling data of Yun et al. [8].
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suppression factor S was then determined from the whole database, resulting in the following expression: S¼
ð1 xÞ1=2 0:121Re0:225 L
ð8Þ
In summary, the new modified Kattan–Thome–Favrat heat transfer model for CO2 is obtained only by replacing Eq. (2) with the following expression: h i1=3 3 wet ¼ Snb;CO2 þ3cb ð9Þ and using Eqs. (7) and (8) above. No other changes are required to either the heat transfer model nor the flow pattern map. This modified model was found to predict 73% of the CO2 database to within 20% and 86% to within 30%. Considering the difficulty in accurately measuring CO2 heat transfer coefficients to within 15% with the majority of the values above 10,000 W m2 K1, and reaching values as large as 25,000 W m2 K1, this is quite a reasonable and reliable result. Fig. 7 shows the percent errors in the predictions compared to the database plotted versus vapor quality. Ignoring the values outside of 40%, the new model captures the trend as desired in tp vs. vapor quality over the wide range of mass velocities, saturation temperatures and heat fluxes represented in the database, as evidenced by the lack of systematic deviations in percent error vs. vapor quality.
4. Simulations with new model Fig. 8 shows a selection of simulations of the new modified heat transfer model for CO2 to show the trends in atp vs. vapor quality, for some of which the conditions match those in the flow pattern maps in Figs. 1 and 2. Fig. 8a illustrates the enhancing effect of smaller
Fig. 6. Comparison of modified nucleate boiling correlation to CO2.
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channel diameter on heat transfer, comparing a 1 mm channel to a 6 mm channel. The monotonic fall in tp vs. vapor quality is clearly evident due to the boiling suppression effect, similar to the trend illustrated by the CO2 data in Fig. 4. The smaller diameter tube also
reaches the onset of dryout in annular flow at an earlier vapor quality, as predicted by the model and as observed in various experimental data sets. Fig. 8b depicts the effect of mass velocity on the variation in tp vs. vapor quality. Because of the nucleate boiling dominance and the effect of mass velocity on the suppression factor S, it is seen that a higher mass velocity for CO2 does not necessarily always mean a larger flow boiling heat transfer coefficient as would be the case with low pressure refrigerants. Fig. 8c shows the positive influence of increasing saturation temperature (pressures of 3.48 and 4.50 MPa) on heat transfer. Fig. 8d depicts the effect of heat flux on the variation in tp vs. vapor quality; at the present nucleate boiling dominated conditions, the influence of heat flux is quite substantial. All these trends are also similar to those in the experimental database in the original publications.
5. Summary Fig. 7. Comparison of modified model to flow boiling CO2 database.
CO2 has become an important alternative refrigerant in the past few years and thus an accurate heat transfer
Fig. 8. Simulations of modified model to illustrate heat transfer trends.
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prediction method for its evaporation inside horizontal tubes is required, which until now has not been available. Forming an experimental database from five independent studies from tests conducted in Japan, Korea, Denmark and Norway, an updated version of the Kattan–Thome– Favrat [1] flow boiling heat transfer model has been developed for application specifically to CO2. Because CO2 has a low critical temperature and is thus utilized at quite high operating pressures compared to other refrigerants (and the previous database), it was found necessary to first correct the nucleate pool boiling correlation to better describe CO2 and secondly to add a boiling suppression factor to the nucleate boiling heat transfer coefficient, which dominates heat transfer at these conditions. The new method predicts 73% of the CO2 database (404 data points) to within 20% and 86% to within 30%, which is much more accurate than other existing methods. The database covers tube diameters from 0.79 to 10.06 mm, mass velocities from 85 to 1440 kg m2 s1, heat fluxes from 5 to 36 kW m2, saturation temperatures from 25 C to +25 C and saturation pressures from 1.7 to 6.4 MPa.
Acknowledgements Preparation of this review was sponsored in part by the Swiss National Science Foundation under contract no. 21/57210.99.
References [1] Kattan N, Thome JR, Favrat D. Flow boiling in horizontal tubes. Part 3: development of a new heat transfer model based on flow patterns. J Heat Transfer 1998;120: 156–65. [2] Brown JS, Kim Y, Domanski PA. Evaluation of carbon dioxide as R-22 substitute for residential air-conditioning. ASHRAE Trans 108(2); HI-02- 2002:3–13. [3] Høgaard Knudsen HJ, Jensen PH. Heat transfer coefficient for boiling carbon dioxide. In Workshop Proceedings—CO2 Technology in Refrigeration, Heat Pump and Air Conditioning Systems, 1997 Trondheim, Norway, p. 319–328. [4] Shah MM. A general correlation for heat transfer during film condensation inside of pipes. Int J Heat Mass Transfer 1979;22:547–56. [5] Bredesen A, Hafner A, Pettersen J, Neksa P, Aflekt K. Heat transfer and pressure drop for in-tube evaporation of CO2. In: International Conference on Heat Transfer Issues in Natural Refrigerants, 1997 November; University of Maryland. p. 1–15. [6] Hihara E, Tanaka S. Boiling heat transfer of carbon dioxide in horizontal tubes. In: Proc. of 4th IIR-Gustav Lorenzen Conference on Natural Working Fluids, 2000. Purdue University. p. 279–84.
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[7] Pettersen J, Rieberer R, Munkejord ST. Heat transfer and pressure drop characteristics of evaporating carbon dioxide in microchannel tubes. In: Proc. of 4th IIR-Gustav Lorenzen Conference on Natural Working Fluids, Purdue University, 2000. p. 107–14. [8] Yun R, Hwang JH, Kim YC, Kim MS. Evaporation heat transfer characteristics of carbon dioxide in a horizontal smooth tube. IIR Commission B1 Meeting, Paderborn, 2001. May, B2.15–21. [9] Koyama S, Kuwahara K, Shinmura E, Ikeda S. Experimental study on flow boiling of carbon dioxide in a horizontal small diameter tube. IIR Commission B1 Meeting, Paderborn, May, 2001. [10] Hwang Y, Kim BH, Radermacher R. Boiling heat transfer correlation for carbon dioxide, In International Conference on Heat Transfer Issues in Natural Refrigerants, November 1997, University of Maryland. [11] Bennett DL, Chen JC. Forced convective boiling in vertical tubes for saturated pure components and binary mixtures. AIChE J 1980;26:454–61. [12] Thome JR, El Hajal J. Two-phase flow pattern map for evaporation in horizontal tubes: latest version. In: Proc. 1st Int. Conf. on Heat Transfer, Fluid Mechanics, and Thermodynamics, HEFAT 2002, Kruger Park, South Africa, 8–10 April 2002. 1(1), p. 182–187. [13] Kattan N, Thome JR, Favrat D. Flow boiling in horizontal tubes. Part 1: development of a diabatic two-phase flow pattern map. J Heat Transfer 1998;120:140–7. [14] Zu¨rcher O, Thome JR, Favrat D. Evaporation of ammonia in a smooth horizontal tube: heat transfer measurements and predictions. J Heat Transfer 1999;121:89–101. [15] El Hajal J, Thome JR, Cavallini A. Condensation in horizontal tubes, part 1: two-phase flow Pattern map. Int J Heat Mass Transfer 2003;46:3349–63. [16] Thome JR, El Hajal J, Cavallini A. Condensation in horizontal tubes, part 2: new heat transfer model based on flow regimes. Int J Heat Mass Transfer 2003;46:3365–87. [17] Pettersen J. Flow vaporization of CO2 in microchannel tubes, part 1: experimental method and two-phase flow pattern. In: 5th IIR-Gustav Lorentzen Conference on Natural Working Fluids, Guangzhou, China, Sept. 17–20 2002. p. 76–91. [18] Kattan N, Thome JR, Favrat D. Flow boiling in horizontal tubes. Part 2: new heat transfer data for five refrigerants. J Heat Transfer 1998;120:148–55. [19] Cooper MG. Heat flow rates in saturated nucleate pool boiling—a wide-ranging examination of reduced properties. Advances in Heat Transfer 1984;16:157–239. [20] Rouhani Z, Axelsson E. Calculation of volume void fraction in the subcooled and quality region. Int J Heat Mass Transfer 1970;13:383–93. [21] Chen JC. (1963). A correlation for boiling heat transfer of saturated fluids in convective flow. In: 6th National Heat Transfer Conference, Boston, Aug. 11–14 1963 [ASME Paper 63-HT-34]. [22] Gungor KE, Winterton RHS. A general correlation for flow boiling in tubes and annuli. Int J Heat Mass Transfer 1986;29:351–8. [23] Gorenflo D. Pool boiling. VDI-Heat Atlas. Du¨sseldorf: VDI-Verlag; 1993 [English version].
Flow boiling heat transfer to carbon dioxide: general prediction method John R. Thome*, Jean El Hajal Laboratory of Heat and Mass Transfer, Faculty of Engineering Science, Swiss Federal Institute of Technology Lausanne, LTCM-ISE-STI, EPFL, CH-1015 Lausanne, Switzerland Received 21 October 2002; received in revised form 30 July 2003; accepted 7 August 2003
Abstract An updated version of the Kattan–Thome–Favrat flow pattern based, flow boiling heat transfer model for horizontal tubes has been developed specifically for CO2. Because CO2 has a low critical temperature and hence high evaporating pressures compared to our previous database, it was found necessary to first correct the nucleate pool boiling correlation to better describe CO2 at high reduced pressures and secondly to include a boiling suppression factor on the nucleate boiling heat transfer coefficient to capture the trends in the flow boiling data. The new method predicts 73% of the CO2 database (404 data points) to within 20% and 86% to within 30% over the vapor quality range of 2–91%. The database covers five tube diameters from 0.79 to 10.06 mm, mass velocities from 85 to 1440 kg m2 s1, heat fluxes from 5 to 36 kW m2, saturation temperatures from 25 C to +25 C and saturation pressures from 1.7 to 6.4 MPa (reduced pressures up to 0.87). # 2003 Elsevier Ltd and IIR. All rights reserved. Keywords: Modelling; Evaporation; Carbon dioxide; Horizontal tube; Heat transfer; Mass transfer
Dioxyde de carbone: transfert de chaleur lors de l’e´bullition— me´thode de pre´vision Mots cle´s : Mode´lisation ; E´vaporation ; Dioxyde de carbone ; Tube horizontal ; Transfert de chaleur ; Transfert de masse
1. Introduction Carbon dioxide has become an important alternative refrigerant in the past few years and thus an accurate heat transfer prediction method for its evaporation inside horizontal tubes is required. CO2 is a special fluid with a low critical temperature and is thus utilized at quite high operating pressures compared to other refrigerants. Current experimental evidence shows that
* Corresponding author. E-mail address: john.thome@epfl.ch (J.R. Thome). 0140-7007/$35.00 # 2003 Elsevier Ltd and IIR. All rights reserved. doi:10.1016/j.ijrefrig.2003.08.003
CO2 flow boiling heat transfer coefficients are on the order of twice those predicted by existing methods. Hence, the objective here is first to understand why this is so and secondly to propose an updated version of the Kattan–Thome–Favrat [1] flow boiling heat transfer model specifically for CO2. It is important that the method is not only statistically accurate but that it also properly captures the trends in the data since these methods typically go into system simulation programs, such as that of Brown et al. [2]. If the heat transfer prediction method does not capture the trends correctly and accurately, then false optimisations and conclusions will result.
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Nomenclature A cp d g : m M pcrit pr psat q ri ReL ReV S Tsat x Greek nb nb,CO2 cb tp vapor wet " l dry strat
cross sectional area m2 specific heat J kg1 K1 tube internal diameter m acceleration of gravity m s2 total mass velocity of liquid and vapor kg m2 s1 molecular weight critical pressure Pa reduced pressure (psat/pcrit) saturation pressure Pa heat flux W m2 internal tube radius m liquid film Reynolds number vapor Reynolds number boiling suppression factor saturation temperature C vapor quality
nucleate boiling heat transfer coefficient W m2 K1 CO2 nucleate boiling heat transfer coefficient W m2 K1 convective boiling heat transfer coefficient W m2 K1 flow boiling heat transfer coefficient W m2 K1 vapor heat transfer coefficient W m2 K1 wet wall boiling heat transfer coefficient W m2 K1 liquid film thickness m vapor cross-sectional void fraction thermal conductivity W m1 K1 dynamic viscosity Ns m2 upper dry angle of tube rad stratified angle around top of tube rad density kg m3 surface tension N m1
Subscripts G vapor L liquid
Six well-executed experimental studies on CO2 evaporation were found to date. Høgaard Knudsen and Jensen [3] have measured local flow boiling data in a stainless steel (ST35) precision pipe of 1.12 m length and 10.06 mm internal diameter. They heated the test section by condensing R-22 on the outside. They found that their heat transfer coefficients were about 1.9 times
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those predicted by the Shah [4] correlation. Bredesen et al. [5] reported measurements for a 7 mm aluminum tube with electrical heating, obtaining heat transfer data significantly larger than four widely quoted correlations. Hihara and Tanaka [6] made measurements in a 1.0 mm stainless steel tube using DC electrical heating of their test section. Their data displayed dryout at high mass velocities at vapor qualities as low as 40%. Pettersen, Rieberer and Munkejord [7] similarly reported flow boiling data in a 0.79 mm tube using hot water as their heating source and the modified-Wilson plot technique to deduce their flow boiling heat transfer coefficients. They also observed the onset of dryout in their data. In addition, they compared their data to six prediction methods and found poor agreement with all six. Yun et al. [8] applied DC heating to a 6.0 mm diameter stainless steel tube to obtain their flow boiling data; they also measured heat transfer coefficients for R-134a as a base case in the same test section. Koyama et al. [9] reported measurements for a 316 stainless steel tube of 1.8 mm diameter, attaining heat transfer coefficients above 20,000 W m2 K1 at a mass velocity of 250 kg m2 s1 and heat flux of 31 kW m2 at a saturation pressure of 4.5 MPa, attesting to CO2’s formidable performance as a heat transfer fluid. Several previous attempts have been made to develop flow boiling heat transfer correlations specifically for CO2. For example, Hwang et al. [10] modified the Bennett and Chen [11] correlation for vertical tubes using the data of Bredesen et al. [5] for a horizontal 7.0 mm I.D. tube at one of the saturation temperatures they tested, applying six new empirical factors to make it work. As noted above, Høgaard Knudsen and Jensen [3] included a multiplier of 1.9 to the Shah [4] correlation to make it fit their data. No general methods have been proposed based on a broad, representative database to date.
2. CO2 heat transfer database and flow pattern map Five of the six independent experimental studies noted earlier from different laboratories in Japan, Korea, Norway and Denmark have been used to form the present flow boiling heat transfer database, whose range of test conditions are shown in Table 1. Hence, the database covers tube diameters from 0.79 to 10.06 mm, mass velocities from 85 to 1440 kg m2 s1, heat fluxes from 5 to 36 kW m2 and saturation temperatures from 25 C to +25 C (corresponding to saturation pressures from 1.7 to 6.4 MPa). The data were taken from tables in these publications where available or by digitising the heat transfer graphs in these publications to extract the plotted heat transfer coefficients. The updated two-phase flow pattern map for evaporating flows in horizontal tubes of Thome and
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Table 1 CO2 flow boiling heat transfer database Reference
Tube I.D. (mm)
Mass velocity (kg m2 s1)
Heat flux (kW m2)
Saturation temp. ( C)
Saturation pressure (MPa)
Data points
Koyama et al. [9] Hihara and Tanaka [6] Pettersen et al. [7] Knudsen and Jensen [3] Yun et al. [8]
1.8 1.0 0.79 10.06 6.0
100–250 360–1440 200–600 85–175 170–320
4–32 9–36 5–20 7–13 10–20
0, 10 15 0 to 25 25 to 10 5, 10
3.5, 4.5 5.1 3.5–6.4 1.7–2.6 4.0, 4.5
12 of 12 142 of 206 80 of 116 81 of 81 89 of 89
El Hajal [12] was then used to classify the data by flow pattern. Since the Kattan et al. [1] flow boiling model does not yet include a heat transfer model for mist flows, the data predicted by the flow pattern map to be in the mist flow regime have been excluded from the present heat transfer database. On the other hand, data which clearly appear to be mist flow heat transfer coefficients because of their very low values but which the map identifies as annular flows, have been left in the database. These values will tend to be significantly over predicted by the new heat transfer model. All together, 404 flow boiling heat transfer data points were thus obtained from these publications (i.e. 142 of the 206 Hihara-Tanaka points and 80 of the 116 Pettersen points were used and all of the data from the other three publications). The data of Bredesen et al. [5] for a 7.0 mm I.D. tube have been excluded because they differ significantly from comparable data for 6.0 mm and 10.06 mm tubes in two other studies and also because there is a large scatter among their data. Hwang et al. [10] also noted an anomaly in their 300 kg m2 s1 data when correlating them. Yet, since their tests were run with the same rigor as the other tests, it is not clear where these problems come from. The flow pattern map used here is the simplified version proposed by Thome and El Hajal [12] of the previous map described in Kattan et al. [13] and later modified by Zu¨rcher et al. [14]. This map is for adiabatic and evaporating flows in small diameter tubes. So far this map has been compared to flow pattern observations for nine evaporating fluids: R-134a, R-123, R-502, R-402A, R-404A, R-407C, ammonia, R-22 and R-410a. A version of this map for condensing flows in horizontal tubes has also recently been proposed by El Hajal et al. [15] together with a flow pattern based condensing heat transfer model by Thome et al. [16], and it has been successfully applied to 15 fluids in that study for tube diameters from 3.1 to 21.4 mm. In the present study, CO2 properties have been obtained from the most recent version of REFPROP of NIST. The Thome–El Hajal map is used here without modification for CO2. No flow pattern observations are apparently available in the literature for CO2 because of
the high pressures involved except for some very recent ones reported by Pettersen [17] in a 0.98 mm channel at 5.72 MPa. As an example of its application here, Fig. 1 shows the flow pattern map equations evaluated for CO2 at 0 C (3.48 MPa) for tube internal diameters of 1, 6 and 10 mm and a heat flux of 15 kW m2, plotted in an easy to read mass velocity vs. vapor quality format (flow pattern legend: S—stratified flow, SW—stratifiedwavy flow, I—intermittent flow, A—annular flow, MF—mist flow). The stratified flow regime is at the lowest range of mass velocities, and the three transition curves from stratified flow to stratified-wavy flow for the different tubes all fall on top of each other (bold curve). Above this transition is the stratified-wavy flow region, and its transition to the intermittent and annular flow regimes are indicated by the next three curves. Above these two flow regimes is the mist flow regime, whose transition threshold increases greatly as the channel diameter decreases. The vertical transition curve from intermittent flow to annular flow is only a function of fluid properties and hence gives the same vertical line for all three tube diameters. Application of the flow pattern map to channels as small as 1 mm is an extrapolation beyond its previous database but this cannot be avoided. It is also interesting to note that tube diameters of 1 mm would normally be thought of as micro-channels; however, at the high pressures associated with CO2, the
Fig. 1. Flow pattern map for CO2 for several tube diameters.
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bubbles are predicted to be very small and hence the flow most likely will still look like a macro-scale twophase flow. Comparing the map to the 30 very recent observations of Pettersen [17] mentioned above, the map correctly predicts just 15 of 29 of his observations for intermittent flow, annular flow and droplet flow. He labeled one of his observations as a dispersed flow for which it is not clear the meaning, but is apparently an annular flow with entrained droplets at very high vapor qualities approaching 100%. For this observation, it is not clear how the droplets could be seen through the annular liquid film unless it was partially dry; it is predicted to be an annular flow with partial dryout according to the Kattan–Thome–Favrat map, which the map classifies as a stratified-wavy flow since only part of the perimeter is wetted for modeling this flow’s heat transfer. On the other hand, the transitions are zones and not just lines as shown on the map and another 9 observations are within 10% vapor quality or within 5– 15 kg m2 s1 from the correct boundary, which would mean as many as 24 of his 29 observations are approximately correctly identified by the map. Also, 11 flow observations they have identified as annular flow that fall in the intermittent flow region have no effect on the heat transfer prediction since intermittent flow is treated as annular flow in the Kattan–Thome–Favrat heat transfer model. Thus, while it is always difficult to interpret the observations of others or for others to use the same criteria for classifying observations as used in the development of a particular map, this comparison is rather promising considering its extrapolation to high pressures and small tube diameters. Their observations also confirm that CO2 flow at 5.722 MPa in a 0.98 mm channel looks like it has macroscale flow regime features. Fig. 2 shows the effect of saturation temperature on the expected flow pattern transitions for a 6 mm tube at a heat flux of 15 kW m2 at saturation temperatures of
Fig. 2. Flow pattern map for CO2 at several saturation temperatures.
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25 C (1.68 MPa), 5 C (3.04 MPa) and +15 C (5.08 MPa). The effect of saturation pressure on the S!SW, SW!I and SW!A transitions is not so large but its effect on I!A and A!MF is quite noticeable.
3. Modified local flow pattern based evaporation model Kattan et al. [1,13,18] proposed a flow boiling model based on the local flow pattern that so far covers annular flows, annular flows with partial dryout, intermittent flows, stratified-wavy flows and fully stratified flows, but not yet bubbly flows nor mist flows (bubbly flows occur at very high mass velocities and are not shown on the previous maps). It is based on their two-phase flow pattern map for horizontal evaporating flows described above. Fig. 3 depicts the simplified two-phase flow structures assumed in their model for the fully-stratified, stratified-wavy and annular flow regimes. For fully stratified flow, the truncated annular liquid ring has a wetted angle equal to 2p-strat and a thickness of d, with the same cross-sectional area of the liquid AL in both cases. For annular flow, the cross-sectional area of the annulus is AL, strat is equal to 0, and the thickness is obtained assuming d/2 so that =AL/( d). In intermittent flows, heat transfer is successfully predicted assuming the annular flow structure applies while annular flows with partial dryout are classified as stratified-wavy flows in this model. The Kattan–Thome–Favrat general equation for the local flow boiling coefficient tp for evaporation in a horizontal, plain tube is: d dry vapor þ d 2 dry wet tp ¼ ð1Þ 2 d
Fig. 3. Simplified two-phase flow structure showing liquid and vapor zones, stratified and dry angles and liquid film thickness used in the flow boiling model.
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The dry angle around the top of the tube, if any, is dry, which varies from zero for annular flow up to its maximum value of ystrat for fully stratified flow. On the wetted perimeter [ri (2 dry)], the heat transfer coefficient is wet, which is determined with an asymptotic expression that combines the nucleate boiling nb and convective boiling cb contributions to heat transfer by the third power as: 1=3 ð2Þ wet ¼ 3nb þ 3cb The nucleate boiling heat transfer coefficient nb is determined with the dimensional reduced pressure correlation of Cooper [19], without its surface roughness correction term (i.e. assuming his recommended standard roughness of 1 mm) nor its 1.7 multiplier for copper surfaces: nb ¼ 55p0:12 ðlog10 pr Þ0:55 M0:5 q0:67 r
ð3Þ
In this expression nb is in W m2 K1, pr is the reduced pressure where pr=psat/pcrit, M is the liquid molecular weight and q is the heat flux at the tube wall in W m2. Notably, this correlation was developed without any CO2 nucleate pool boiling results in its database. The convective boiling heat transfer coefficient cb for annular liquid film flow is formulated as a film flow and not as a tubular flow as: : 4mð1 xÞ 0:69 cpL L 0:4 lL ð4Þ cb ¼ 0:0133 ð1 "ÞL lL where 0.0133 and 0.69 are empirical constants determined from their original database for five refrigerants and remain unchanged in successive tests, including those for ammonia data and now also for CO2. The term in the first bracket is the liquid film Reynolds number ReL while the second bracket represents the liquid Prandtl number PrL. Consequently, the mean liquid velocity in the annular film is utilized here to determine the liquid Reynolds number, which changes as a local function of the vapor quality x, annular liquid film thickness , and vapor void fraction ". The void fraction is determined with the Rouhani and Axelsson [20] drift flux model: ( x x 1x 1:18 þ "¼ þ : ð1 þ 0:12ð1 xÞÞ G G L m )1 1=4 g ðL G Þ ð1 xÞ ð5Þ
2L : where m is the total mass velocity of liquid and vapor. The vapor-phase heat transfer coefficient vapor is calculated with the Dittus–Boelter turbulent flow heat transfer correlation assuming tubular flow on the dry
perimeter of the tube using the vapor properties and the : mass velocity of the vapor, i.e. mx, so that: vapor
: 0:8 mxd cpG G 0:4 lG ¼ 0:023 "G lG d
ð6Þ
The vapor-phase heat transfer coefficient vapor is applied to the dry perimeter of the tube. The vapor Reynolds number ReG in the first bracketed term above includes the vapor void fraction " such that the mean vapor velocity in the cross-section of the tube occupied by the vapor is used in its determination. The rest of the description of the heat transfer model can be found in Kattan et al. [1]. Direct application of this heat transfer model to CO2 data tends to drastically underpredict the flow boiling data, particularly as low and intermediate vapor qualities. Secondly, CO2 at high saturation pressures gives an experimental trend of a monotonic decrease in tp vs. vapor quality in intermittent and annular flows, which is the exact opposite of the trend for other refrigerants at low pressures (below 1 MPa), i.e. a steady increase in tp vs. x before the onset of dryout. Fig. 4 illustrates these two contradictory trends obtained by Yun et al. [8] with a 6.0 mm tube for CO2 and R-134a. The Kattan– Thome–Favrat heat transfer model in its original form accurately predicts the R-134a heat transfer coefficients in Fig. 4; e.g. Fig. 5 depicts a comparison of measured to predicted values for R-134 at 5 C at a heat flux of 10 kW m2 and mass velocity of 240 kg m2 s1. Investigating the possible origins of this anomalous trend in CO2 data, the first problem was to understand why there is the monotonic decrease in tp vs. vapor quality for CO2. While some researchers have attributed this to some form of partial premature dryout, there are no observations to back this up. Furthermore, the CO2 data in Fig. 4 are in the intermittent and annular flow regimes, such that dry=0, and thus postulating that
Fig. 4. Flow boiling data of Yun et al. [8] for CO2 and R-134a.
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stratified flow could explain this trend (note: at otherwise fixed conditions, dry increases with x) is not correct either. Evaluating the model and the data it was observed that the nucleate boiling contribution was larger than the convective boiling contribution for CO2 while the opposite is true for R-134a. Hence, this suggests that boiling suppression is acting on nb to reduce its contribution with increasing vapor quality, i.e. like in the Chen [21] and Gungor and Winterton [22] correlations. It was observed that the nucleate pool boiling coefficients predicted by the Cooper correlation for CO2 are much lower than those predicted by the competing fluid-specific correlation of Gorenflo [23] for CO2. Evaluating the present flow boiling data at low vapor qualities (x<0.2) to extract the nucleate pool boiling contribution, the data were first set equal to tp in Eq. (1) and then the vapor phase heat transfer contribution (if any) and the convective boiling contribution were removed utilizing the respective Eqs. (6) and (4), yielding the nucleate boiling contribution nb from Eq. (2), deduced from the database listed in Table 1. Comparing these nucleate boiling dominated data to the Cooper correlation, Eq. (3), it was observed that this expression tends to under predict these values at low heat fluxes. Hence, Eq. (3) has been modified based on these data to become for CO2: nb;CO2 ¼ 0:71nb þ 3970
ð7Þ
Fig. 6 shows a comparison of this expression to the ‘‘nucleate boiling’’ coefficients so obtained while the diagonal dashed line is that of the Cooper correlation. It was also noted that for CO2 at low heat fluxes that the heat transfer coefficients seemed to remain unusually high, apparently because of the high nucleation capabilities of CO2; hence, this effect is the origin of the additive value of 3970 W m2 K1 in the above expression. Using nb;CO2 in place of nb in Eq. (2), the boiling
Fig. 5. Comparison of original model to R-134a flow boiling data of Yun et al. [8].
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suppression factor S was then determined from the whole database, resulting in the following expression: S¼
ð1 xÞ1=2 0:121Re0:225 L
ð8Þ
In summary, the new modified Kattan–Thome–Favrat heat transfer model for CO2 is obtained only by replacing Eq. (2) with the following expression: h i1=3 3 wet ¼ Snb;CO2 þ3cb ð9Þ and using Eqs. (7) and (8) above. No other changes are required to either the heat transfer model nor the flow pattern map. This modified model was found to predict 73% of the CO2 database to within 20% and 86% to within 30%. Considering the difficulty in accurately measuring CO2 heat transfer coefficients to within 15% with the majority of the values above 10,000 W m2 K1, and reaching values as large as 25,000 W m2 K1, this is quite a reasonable and reliable result. Fig. 7 shows the percent errors in the predictions compared to the database plotted versus vapor quality. Ignoring the values outside of 40%, the new model captures the trend as desired in tp vs. vapor quality over the wide range of mass velocities, saturation temperatures and heat fluxes represented in the database, as evidenced by the lack of systematic deviations in percent error vs. vapor quality.
4. Simulations with new model Fig. 8 shows a selection of simulations of the new modified heat transfer model for CO2 to show the trends in atp vs. vapor quality, for some of which the conditions match those in the flow pattern maps in Figs. 1 and 2. Fig. 8a illustrates the enhancing effect of smaller
Fig. 6. Comparison of modified nucleate boiling correlation to CO2.
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channel diameter on heat transfer, comparing a 1 mm channel to a 6 mm channel. The monotonic fall in tp vs. vapor quality is clearly evident due to the boiling suppression effect, similar to the trend illustrated by the CO2 data in Fig. 4. The smaller diameter tube also
reaches the onset of dryout in annular flow at an earlier vapor quality, as predicted by the model and as observed in various experimental data sets. Fig. 8b depicts the effect of mass velocity on the variation in tp vs. vapor quality. Because of the nucleate boiling dominance and the effect of mass velocity on the suppression factor S, it is seen that a higher mass velocity for CO2 does not necessarily always mean a larger flow boiling heat transfer coefficient as would be the case with low pressure refrigerants. Fig. 8c shows the positive influence of increasing saturation temperature (pressures of 3.48 and 4.50 MPa) on heat transfer. Fig. 8d depicts the effect of heat flux on the variation in tp vs. vapor quality; at the present nucleate boiling dominated conditions, the influence of heat flux is quite substantial. All these trends are also similar to those in the experimental database in the original publications.
5. Summary Fig. 7. Comparison of modified model to flow boiling CO2 database.
CO2 has become an important alternative refrigerant in the past few years and thus an accurate heat transfer
Fig. 8. Simulations of modified model to illustrate heat transfer trends.
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prediction method for its evaporation inside horizontal tubes is required, which until now has not been available. Forming an experimental database from five independent studies from tests conducted in Japan, Korea, Denmark and Norway, an updated version of the Kattan–Thome– Favrat [1] flow boiling heat transfer model has been developed for application specifically to CO2. Because CO2 has a low critical temperature and is thus utilized at quite high operating pressures compared to other refrigerants (and the previous database), it was found necessary to first correct the nucleate pool boiling correlation to better describe CO2 and secondly to add a boiling suppression factor to the nucleate boiling heat transfer coefficient, which dominates heat transfer at these conditions. The new method predicts 73% of the CO2 database (404 data points) to within 20% and 86% to within 30%, which is much more accurate than other existing methods. The database covers tube diameters from 0.79 to 10.06 mm, mass velocities from 85 to 1440 kg m2 s1, heat fluxes from 5 to 36 kW m2, saturation temperatures from 25 C to +25 C and saturation pressures from 1.7 to 6.4 MPa.
Acknowledgements Preparation of this review was sponsored in part by the Swiss National Science Foundation under contract no. 21/57210.99.
References [1] Kattan N, Thome JR, Favrat D. Flow boiling in horizontal tubes. Part 3: development of a new heat transfer model based on flow patterns. J Heat Transfer 1998;120: 156–65. [2] Brown JS, Kim Y, Domanski PA. Evaluation of carbon dioxide as R-22 substitute for residential air-conditioning. ASHRAE Trans 108(2); HI-02- 2002:3–13. [3] Høgaard Knudsen HJ, Jensen PH. Heat transfer coefficient for boiling carbon dioxide. In Workshop Proceedings—CO2 Technology in Refrigeration, Heat Pump and Air Conditioning Systems, 1997 Trondheim, Norway, p. 319–328. [4] Shah MM. A general correlation for heat transfer during film condensation inside of pipes. Int J Heat Mass Transfer 1979;22:547–56. [5] Bredesen A, Hafner A, Pettersen J, Neksa P, Aflekt K. Heat transfer and pressure drop for in-tube evaporation of CO2. In: International Conference on Heat Transfer Issues in Natural Refrigerants, 1997 November; University of Maryland. p. 1–15. [6] Hihara E, Tanaka S. Boiling heat transfer of carbon dioxide in horizontal tubes. In: Proc. of 4th IIR-Gustav Lorenzen Conference on Natural Working Fluids, 2000. Purdue University. p. 279–84.
301
[7] Pettersen J, Rieberer R, Munkejord ST. Heat transfer and pressure drop characteristics of evaporating carbon dioxide in microchannel tubes. In: Proc. of 4th IIR-Gustav Lorenzen Conference on Natural Working Fluids, Purdue University, 2000. p. 107–14. [8] Yun R, Hwang JH, Kim YC, Kim MS. Evaporation heat transfer characteristics of carbon dioxide in a horizontal smooth tube. IIR Commission B1 Meeting, Paderborn, 2001. May, B2.15–21. [9] Koyama S, Kuwahara K, Shinmura E, Ikeda S. Experimental study on flow boiling of carbon dioxide in a horizontal small diameter tube. IIR Commission B1 Meeting, Paderborn, May, 2001. [10] Hwang Y, Kim BH, Radermacher R. Boiling heat transfer correlation for carbon dioxide, In International Conference on Heat Transfer Issues in Natural Refrigerants, November 1997, University of Maryland. [11] Bennett DL, Chen JC. Forced convective boiling in vertical tubes for saturated pure components and binary mixtures. AIChE J 1980;26:454–61. [12] Thome JR, El Hajal J. Two-phase flow pattern map for evaporation in horizontal tubes: latest version. In: Proc. 1st Int. Conf. on Heat Transfer, Fluid Mechanics, and Thermodynamics, HEFAT 2002, Kruger Park, South Africa, 8–10 April 2002. 1(1), p. 182–187. [13] Kattan N, Thome JR, Favrat D. Flow boiling in horizontal tubes. Part 1: development of a diabatic two-phase flow pattern map. J Heat Transfer 1998;120:140–7. [14] Zu¨rcher O, Thome JR, Favrat D. Evaporation of ammonia in a smooth horizontal tube: heat transfer measurements and predictions. J Heat Transfer 1999;121:89–101. [15] El Hajal J, Thome JR, Cavallini A. Condensation in horizontal tubes, part 1: two-phase flow Pattern map. Int J Heat Mass Transfer 2003;46:3349–63. [16] Thome JR, El Hajal J, Cavallini A. Condensation in horizontal tubes, part 2: new heat transfer model based on flow regimes. Int J Heat Mass Transfer 2003;46:3365–87. [17] Pettersen J. Flow vaporization of CO2 in microchannel tubes, part 1: experimental method and two-phase flow pattern. In: 5th IIR-Gustav Lorentzen Conference on Natural Working Fluids, Guangzhou, China, Sept. 17–20 2002. p. 76–91. [18] Kattan N, Thome JR, Favrat D. Flow boiling in horizontal tubes. Part 2: new heat transfer data for five refrigerants. J Heat Transfer 1998;120:148–55. [19] Cooper MG. Heat flow rates in saturated nucleate pool boiling—a wide-ranging examination of reduced properties. Advances in Heat Transfer 1984;16:157–239. [20] Rouhani Z, Axelsson E. Calculation of volume void fraction in the subcooled and quality region. Int J Heat Mass Transfer 1970;13:383–93. [21] Chen JC. (1963). A correlation for boiling heat transfer of saturated fluids in convective flow. In: 6th National Heat Transfer Conference, Boston, Aug. 11–14 1963 [ASME Paper 63-HT-34]. [22] Gungor KE, Winterton RHS. A general correlation for flow boiling in tubes and annuli. Int J Heat Mass Transfer 1986;29:351–8. [23] Gorenflo D. Pool boiling. VDI-Heat Atlas. Du¨sseldorf: VDI-Verlag; 1993 [English version].