Flow Boiling Heat Transfer of Co2 at Low Temperatures - a Critical Review

FLOW BOILING HEAT TRANSFER OF CO2 AT LOW TEMPERATURES - A CRITICAL REVIEW

P. K. Bansal# and X. Zhao Department of Mechanical Engineering, The University of Auckland Private Bag 92019, Auckland, New Zealand # Email: [email protected]

ABSTRACT

This paper presents the special thermal properties and their effects on the boiling heat transfer of CO2 at low temperatures down to -50°C. The paper reviews the current research and compares the available empirical correlations using software package Engineering Equation Solver (EES). It is noted that boiling heat transfer of CO2 at low temperatures shows different characteristics than at high temperatures due to the change of thermal properties. However, literature search revealed that no experimental data is available below -30°C, and hence further research is needed for the boiling heat transfer of CO2 at such low temperatures.

Key Words: Boiling, CO2, Heat Transfer.

1. INT RODUCTION

Due to the environmental problems of CFC’s and HCFC’s, Carbon Dioxide (CO2) has received increasing interest as an alternative refrigerant in automobile/residential air-conditioners, hot water heat pumps and food preservation systems. Carbon dioxide is a natural and environmentally favorable refrigerant, and is nonflammable, odorless and non-toxic.

Since carbon dioxide refrigerant has low critical temperature and high pressure, research on carbon dioxide is focused on the development of near critical or trans-critical cycle for refrigeration systems. Thus, CO2 evaporates with a much higher reduced pressure (the ratio of the evaporating pressure to the critical pressure) than other refrigerants. The boiling heat transfer of CO2 in the evaporation temperatures ranging from 0 to 25℃, shows different characteristics, where htp tends to decrease with refrigerant vapour quality. This is contrary to the other refrigerants, such as R134a and R717. The reason for this discrepancy is the dominance of the nucleate boiling at low/moderate vapour quality prior to dryout (Pettersen (2004), Yun et al. (2005) and Hihara and Tanaka (2000)). Pettersen (2003) found that the effect of the saturation temperature of CO2 on htp is noticeable. At high saturation temperatures, the nucleate boiling is more pronounced and plays an important role at low vapour quality. However, at lower saturation temperatures, the effect of the nucleate boiling is reduced. Yun et al. (2003) observed that the heat transfer coefficient decreases at low vapor quality with the decreasing saturation temperature, while at high vapour quality, it increases with the decreasing saturation temperature.

Lately the cascade refrigeration technology has extended the operating refrigeration temperatures lower than -40℃ by using CO2 as the low stage refrigerant. This is a very interesting application to the food industry where such temperatures are very useful. At these low evaporation temperatures, the reduced

7th IIR Gustav Lorentzen Conference on Natural Working Fluids, Trondheim, Norway, May 28-31, 2006 pressure is much lower than that at high saturation temperatures and the thermal properties change with temperature. Thus, the understanding of the two-phase heat transfer characteristics of CO2 at low temperature is essential for developing a compact heat exchanger, appropriate for cascade refrigeration systems. However, very limited information is available in the open literature on the boiling heat transfer of CO2 at low temperatures. Bredensen et al. (1997) performed the boiling heat transfer experiments with CO2 at lower temperatures of -10°C and -25°C. The experimental results show that with the decrease in the saturation temperature, htp decreases at low vapor quality. At saturation temperatures of -10°C and -25°C, htp increases with vapor quality until dryout, which is opposite to the trend at 0°C. The mass flux and heat flux all have effect on the boiling heat transfer of CO2 at low temperatures. In the research of Knudsen and Jensen (1997), the flow boiling heat transfer of CO2 was measured in the horizontal tube at saturation temperature of -28°C and -30°C. The boiling heat transfer coefficient is much smaller than that at 0°C and dryout occurred at larger vapour qualities. The overall trend differed significantly from the experimental data of Bredensen et al. (1997), where htp decreased 2 with vapour quality and htp had surprisingly very low values of the order of only 2100W/m .K at vapour quality of 0.3. These data differed considerably from other observations and reinforces the fact that more in depth research is required on the boiling heat transfer of CO2 at low saturation temperatures.

This study, therefore, aims to provide the boiling heat transfer characteristics of CO2 at low saturation temperatures down to -50°C. Thermal properties and their effect on the boiling heat transfer process are discussed. A comparison of the predictions of boiling heat transfer by currently available classical empirical correlations with experimental data at low saturation temperatures is also presented.

2. THERMAL PROPERTIES OF CO2 AT LOW TEMPERATURES

The boiling heat transfer characteristics of CO2 are related tightly with its thermal properties, which are quite different from the other refrigerants. At a given temperature, the surface tension, the liquid viscosity and the density ratio of liquid to vapor of CO2 are the smallest among other refrigerants, such as R717, R22 and R134a. For example, at 0°C, the surface tension of carbon dioxide is only 17%, 39.3% and 38.6% to that of the refrigerant R717, R22 and R134a, respectively, while at -50°C, it increases to 37.8%, 74.7% and 72.7%, respectively. The variation of surface tension and density ratio of liquid to vapour are shown in Figures 1 and 2, respectively.

0.04 1600

0.035 1400 R717 R717 0.03 1200 R22

0.025 R134a 1000 CO 2 800 0.02 R134a 600 0.015 R22 400

Surface tension(N/m) 0.01 200 0.005 CO Density ratio of liquid to vapour to liquid of ratio Density 2 0 -50 -40 -30 -20 -10 0 10 -50 -40 -30 -20 -10 0 10 o Temperature (oC) Temperature ( C) Figure1. Surface tension vs. evaporation Figure 2. Density ratio of liquid to vapour vs. temperature evaporation temperature

7th IIR Gustav Lorentzen Conference on Natural Working Fluids, Trondheim, Norway, May 28-31, 2006 At lower reduced pressure, the surface tension, latent heat, liquid density and liquid viscosity values of CO2 are larger at lower temperatures (-50°C) than at 0°C. The surface tension of CO2 at -50°C is 14.3 mN/m2, which is almost 3.3 times to that at 0°C. Because the surface tension plays an important role in the bubble formation and detachment from the liquid surface, the nucleate boiling will decrease at low saturation temperatures, resulting in lower boiling heat transfer at low vapour quality.

In addition, the density ratio of the liquid and vapor at -50°C is 6.8 times to that at 0°C (shown in Figure 3). The liquid viscosity is increased from 99.4×10−6 Pa.s at 0°C to 232.1×10−6 Pa.s at -50°C. Due to the higher density ratio of liquid to vapour at -50°C at a given vapour quality, CO2 has a larger void fraction during the boiling process, especially at low vapor quality. The variation of void fraction, calculated by Rouhani and Axelsson (1970), is shown in Figure 3 as a function of vapour quality. Thus, together with high density of CO2 liquid at -50℃, and at vapor quality less than 0.2, the two-phase Reynolds number and the velocity is small. In this region, flow is either stratified or stratified-wavy, and the boiling heat transfer coefficient is smaller than at high saturation temperature. But for the vapour quality larger than 0.2, the two-phase Reynolds number is larger, and the two-phase velocity is also larger. Therefore, flow will transform easily to intermittent and then to annular, and the liquid film will be thinner, enhancing the convective boiling at higher vapour quality before dryout.

0.9

0.8 ε

ion 0.7 t ac r 0.6

Void f 0.5

0.4 o 2 2 T= -50 C, G=200kg/m .s, q=6kW/m , di=7.0mm o 2 2 0.3 T= 0 C, G=200kg/m .s, q=6kW/m , di=7.0mm

0.2 0 0.2 0.4 0.6 0.8 1 Vapour quality x Figure 3. Void fraction of carbon dioxide vs. vapour quality at temperatures of -50°C and 0°C

3. BOILING HEAT TRANSFER OF CO2 AT LOW TEMPERATURES

During the in-tube flow boiling process, the contributions of the nucleate and convective boiling heat transfer change with vapour quality. The nucleate boiling dominates at low vapour quality while the convective boiling pronounces at high vapour quality up to dryout.

In this research, different correlations were chosen from the literature to simulate the boiling heat transfer of CO2 using EES software and compare their predictions with the experimental data from 2 2 Bredesen et al. (1997). Their base experimental conditions included- q= 6 kW/m , G= 200 kg/m .s, di= 7.0 mm for saturation temperatures of 0°C and -50°C

7th IIR Gustav Lorentzen Conference on Natural Working Fluids, Trondheim, Norway, May 28-31, 2006 The nucleate boiling is related tightly with the reduced pressure and heat flux. Cooper (1984) correlation (Equation (2) in Table 1) showed that the nucleate boiling heat transfer coefficient hnb decreases by about 56.4% when the saturation temperature decreases from 0°C to -50°C. This is due to the increasing surface tension at low saturation temperatures.

Kattan et al. (1998) correlation (Equation (21) in Table 1) was chosen to analyze the change of the convective boiling heat transfer with saturation temperature. The simulation results shown in Figure 4 indicate that the convective boiling heat transfer coefficient increases with the vapour quality before dryout at all saturation temperatures. This is due to the formation of the annular flow at high vapour quality. Simultaneously, hcb at -50°C is much higher than at high temperature of 0°C. This is due to the higher density ratio of liquid to vapor, thermal conductivity and viscosity, resulting in the earlier formation of the annular flow and thinner film thickness at high vapour quality. The difference of hcb among different saturation temperatures increases with the increasing vapor quality before dryout. This trend was also observed in the experimental results of Yun et al. (2003).

Thus, at low temperature of -50°C, due to the lower nucleate boiling heat transfer coefficient hnb and higher convective boiling hcb, htp is low at low vapour quality but high at higher vapour quality.

.k) 11000 2 2 2 10000 CO2, q=6kW/m , G=200kg/m .s, di=7.0mm 9000 Kattan et al. (1998)

8000 o Tsat= - 50 C 7000 o Tsat= - 25 C 6000 o Tsat= 0 C 5000

4000

3000

2000

1000 0 0.2 0.4 0.6 0.8 1 Convectiveboiling heat transfer (W/m Vapour Quality x Figure 4. The convective boiling heat transfer vs. vapour quality

For better understanding of the boiling heat transfer of CO2 at low evaporation temperatures, several available classical empirical correlations were chosen from the literature (listed in Table1) to predict the boiling heat transfer coefficients for the experimental conditions of Bredesen et al.(1997) and Knudsen and Jensen (1997). The simulation results (using EES ) are presented in Figures 5, 6 and 7 for saturation temperatures of -10°C, -25°C and -28°C respectively. The mean deviation, which is the absolute deviation between the predicted and the experimental value, is calculated using Equation (1), and is shown in Table 1 for all correlations.

1 ⎛ N h − h ⎞ Mean _ devivation = ⎜ tp, predicted tp,exp eriment ⎟ ×100% (1) ⎜∑ ⎟ N ⎝ i=1 htp,exp eriment ⎠

It may be noted that there is a great deviation in the prediction of the htp from these correlations.

7th IIR Gustav Lorentzen Conference on Natural Working Fluids, Trondheim, Norway, May 28-31, 2006 12000 2 2 CO2 T=-10℃, G=200kg/m .s, q=6kW/m , di=7mm 2 2 10000 CO2 T=-25℃, G=200kg/m .s, q=6kW/m , di=7mm [1] Bredesen et al. experimental data [2] Thome and Hajal [1] Bredesen et al. experimental data [2] [3] Gungor and Winterton Thome and Hajal 10000 [3] Gungor and Winterton [4] Jung et al. [4] Jung et al. [2] [5] Kandlikar

.k) [5] Kandlikar 2 .k) 8000

[6] Cooper 2 [6] Cooper [7] Liu and Winterton [2] [7] Liu and Winterton 8000 [1] [1] [4] 6000 6000 [3] [3] [4] [5] [5] [6] 4000 4000 Heat Transfer Coefficient (W/m Coefficient Transfer Heat

Heat Transfer Coefficient (W/m Coefficient Heat Transfer [6] [7]

[7] 2000 2000

0 0 00.20.40.60.81 0 0.2 0.4 0.6 0.8 1 Vapor Quality Vapor Quality

Figure 5. The heat transfer coefficient vs. vapour Figure 6. The heat transfer coefficient vs. vapour quality at temperature of -10°C quality at temperature of -25°C

For the experimental data of Bredesen et al. (1997) at saturation temperatures of -10°C and -25°C, htp is low at low vapour quality, and increases with vapour quality until dryout. The maximum htp occurs just before dryout. This is contrary to the trend at high saturation temperatures around 0°C. When the saturation temperature drops from -10°C to -25°C, the decrease of htp can be observed from the experimental data and the prediction from the correlations. The large mean deviations at low saturation temperatures can also be observed from Table 1. Thome and Hajal (2004) correlation seems to be the best fit for the experimental data with mean deviations of 21.8% and 2.6% at saturation temperatures of -10°C and -25°C, respectively.

For the experimental data of Knudsen and Jensen (1997) at saturation temperature of -28°C, the overall htp is lower and decreases with vapour quality, which is similar to the overall trend at high saturation temperatures around 0°C. Cooper (1984) correlation is the best fit for this experimental data with mean deviation of 5.2 %.

Due to different experimental conditions, the comparison of the experimental data of Bredesen et al. (1997) and Knudsen and Jensen (1997) could not be made. However, we can observe that while some correlations fit well with one experimental data, they tend to have larger deviations with the other data, e.g. Cooper (1984) and Thome and Hajal (2004) correlation. No correlation seems to agree well with the two experimental data sets. This suggests the need for further experimental research and the development of suitable correlations for the boiling heat transfer of CO2 at low temperatures.

Since no experimental data is available in the open literature on CO2 at lower saturation temperature (say -50°C), the prediction of htp from available correlations in the literature, however, is shown in Figure 8 for low saturation temperature of -50°C. The overall trend of htp is similar to that at saturation temperatures of –25°C. Most correlations predict that htp is small at low vapour quality but increases

7th IIR Gustav Lorentzen Conference on Natural Working Fluids, Trondheim, Norway, May 28-31, 2006 with vapour quality until dryout. The maximum htp occurs just before dryout. At the same time, the predicted htp is consistently smaller than at saturation temperature of -25°C.

Table 1. Empirical correlations for the prediction of boiling heat transfer of CO2 and their mean deviations (before dryout) Mean deviation Reference Correlations Application Rang Tsat -10°C -25°C -28°C Cooper Nucleate boiling 53.7% 54% 5.2% h = 55Pr 0.12 q 2 / 3 (− log p )−0.55 M −0.5 (2) (1984) nb 10 r

hTP = E ⋅hl + S ⋅hnb (3)

0.745 0.581 k ⎛ q ⋅ b ⎞ ⎛ ρ ⎞ (4) f ⎜ d ⎟ ⎜ V ⎟ 0.533 hnb = 207⋅ ⎜ ⎟ ⎜ ⎟ PrL Pure fluids and mixture 55% 42.3% 36.1% bd ⎝ kf Tsat ⎠ ⎝ ρL ⎠ 0.5 ⎛ 2σ ⎞ (5) b 0.0146 35 ⎜ ⎟ Jung et al. d = × ×⎜ ⎟ ⎝ g()ρ L − ρ V ⎠ (1989) 0.85 ⎛ 1 ⎞ (6) E = 2.37 ⋅⎜0.29 + ⎟ ⎝ Xtt ⎠ 1.22 1 .13 (7) WhenX tt < 1, S = 4048 ⋅ ()X tt ( Bo )

-0.28 -0.33 (8) When 1 < X tt < 5, S = 2.0 − 0.1 ⋅ ()X tt (Bo ) 40.1% 26.5% 7.0% hTP = E ⋅hl + S ⋅hnb (9) vertical or horizontal tube Gungor and 0.86 ⎛ 1 ⎞ (10) E = 1+ 2.4×104 ⋅ Bo1.16 +1.37⎜ ⎟ Winterton ⎜ X ⎟ ⎝ tt ⎠ 3.05mm ≤ d ≤ 32.0mm (1986) 1 (11) S = −6 0.69 1.17 1+1.15×10 E Rel h = ()Fh 2 + (Sh )2 (12) 59.0% 54.5% 19.2% Liu and TP l nb 5 0.35 568.9 ≤ Rel ≤ 8.75×10 ⎡ ⎛ ρ ⎞⎤ (13) ⎜ 1 ⎟ 2.95mm ≤ d ≤ 32.0mm Winterton F = ⎢1 + x Pr1 ⎜ − 1⎟⎥ ⎣ ⎝ ρ v ⎠⎦ (1991) 0.83 ≤ Prl ≤9.1 0.1 0.16 −1 S = ()1+ 0.055F ReL (14) −0.9 0.7 For vertical or horizontal 56.8% 42.9% 51.8% hCBD = (1.1360Co + 667.2Bo Ffl ) ⋅ hl (15) Kandlikar tube with Frl<0.04 h = (0.6683Co −0.2 +1058Bo0.7 F )⋅h (16) (1990) NBD fl l No Ffl for CO2 htp is the larger of hNBD and hCBD Here, Ffl=1.0 dθdry ×hvapor + d(2π −θdry )×hwet (17) 21.8% 2.6% 48.3% htp = 2πd Special for CO2 3 3 1/ 3 (18) -25oC ≤ T ≤25oC Thome and hwet = ()hnbco2 + hcb ] sat 0.79mm ≤ d ≤ 10.06mm Hajal hnbco2 = 0.71hnb + 3970 (19) 0.8 0.4 (2004) ⎛ mxd ⎞ ⎛ C pG μG ⎞ λ (20) ⎜ ⎟ ⎜ ⎟ G hvapor = 0.023⎜ ⎟ ⎜ ⎟ ⎝ εμG ⎠ ⎝ λG ⎠ d

0.69 0.4 ⎛ 4G(1 − x)δ ⎞ ⎛ Cp μ ⎞ λ (21) ⎜ ⎟ ⎜ L L ⎟ L hcb = 0.0133⎜ ⎟ ⎜ ⎟ ⎝ ()1 − ε μ L ⎠ ⎝ λL ⎠ δ

7th IIR Gustav Lorentzen Conference on Natural Working Fluids, Trondheim, Norway, May 28-31, 2006 8000 2 2 2 2 CO2 T= - 50℃, G=200kg/m .s, q=6kW/m , di=7mm CO2 T= - 28℃ G=80 kg/m .s, q=8 kW/m , di=10.08 mm 11000 [1] [1] Thome and Hajal .k) 7000 Knudsen and Jensen's experimental data 2 [2] Gungor and Winterton [2] Thome and Hajal .k) 2 [3] Jung et al. [3] Gungor et al. 6000 [4] Kandlikar [4] Jung et al. 9000 [5] Cooper [5] Kandlikar [6] Liu and Winterton [1] [3] 5000 [6] Liu and Winterton [7] Cooper [3] 7000 4000 [1] [7] [2]

3000 [6] [4 5000 [4]

2000 [5

[6] Heat transfer coefficient (W/m coefficient Heat transfer 1000 [2]

Heat Transfer Coefficient (W/m Coefficient Transfer Heat 3000

0 [5] 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1000 Vapour quality x 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Vapor Quality x Figure 7. The heat transfer coefficient vs. vapour Figure 8. Predictions of heat transfer coefficient quality at saturation temperature of -28°C vs. vapour quality at temperature of -50°C

4. CONCLUSIONS

In this study, the physical thermal properties and their effects on the boiling heat transfer of CO2 at low saturation temperatures are presented. The nucleate boiling heat transfer decreases due to the larger surface tension at low saturation temperatures, on the contrary, the convective boiling heat transfer is strengthened because of the higher density ratio of liquid to vapour and thermal conductivity.

The experimental boiling heat transfer data at low saturation temperatures of -10°C, -25°C and -28°C are compared with the currently available empirical correlations using EES software. Most of the correlations present the similar trend with the experimental data, but with larger mean deviations. There is a need for more experimental research and the development of new empirical boiling heat transfer correlations for CO2 at low temperatures.

NOMENCLATURE

Bd Bond number, q Heat flux, W.m-2 Bo Boiling number Re Reynolds number Cp Specific heat, J.kg-1.K-1 S Suppression factor di Inner diameter, m T Temperature E Enhancement factor x Vapour quality F Convective enhancement factor X Martinelli parameter f Friction factor g Gravitational acceleration, m.s-2 Greeks -2 -1 G Mass flux, kg.m .s θdry Dry angle h Heat transfer coefficient, W m-2.K-1 ρ Density, kg.m-3 k Thermal conductivity, W.m-2.K-1 σ Surface tension, N.m-1 M Molecular weight, kg.kmol-1 δ Film thickness, m P Pressure, Pa ε Void fraction -2 Pr Reduced pressure μ Dynamic viscosity, N.s.m Pr Prandtl number

7th IIR Gustav Lorentzen Conference on Natural Working Fluids, Trondheim, Norway, May 28-31, 2006 Subscripts nb Nucleate boiling cb Convective boiling sat Saturation v Vapour state tp Two-phase l Liquid state

REFERENCES

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7th IIR Gustav Lorentzen Conference on Natural Working Fluids, Trondheim, Norway, May 28-31, 2006