Latest Development of Generalized Mechanistic Heat Transfer Models for Flow Boiling of Carbon Dioxide in Macroscale and Microscale Tubes at a Wide Range of Reduced Pressures
Applications of carbon dioxide in various thermal and energy systems with macroscale and microscale tube evaporators can improve the energy efficiency and environment safe (Cheng et al., 2021). For instance, carbon dioxide may be used in geothermal energy utilization, hybrid power and heat systems, solar energy utilization and recovery of industrial waste heat, electronic cooling, two-phase thermosyphon loop and evaporative carbon dioxide cooling systems (Cheng, 2013; Cheng and Mewes, 2006; Cheng and Xia, 2017, 2023b,c; Cheng et al., 2023). As the effects of good thermophysical properties of carbon dioxide, favorably flow boiling heat transfer and two-phase flow characteristics of carbon dioxide can be achieved (Cheng and Thome, 2009; Cheng and Xia, 2023d; Cheng et al., 2022). However, flow boiling at low reduced pressures occurs in the carbon dioxide refrigeration systems and displays quite different heat transfer behaviors and mechanisms from those at high reduced pressures (Cheng and Chen, 2000; Cheng and Xia, 2023d; Cheng et al., 2022). Flow pattern based mechanistic flow boiling heat transfer models are promising prediction methods. Such models intrinsically relate flow patterns to flow heat transfer mechanisms (Cheng and Xia, 2023a; Cheng et al., 2008b). They do not only predict the heat transfer coefficients but also capture the heat transfer trends such as dry-out occurrence and completion. In order to design carbon dioxide evaporators for high efficiency thermal systems, it is essential to develop generalized mechanistic flow boiling heat transfer models based on flow patterns for macroscale and microscale tubes.
Cheng et al. (2006, 2008a) proposed general flow pattern map for flow boiling of carbon dioxide developed flow pattern based heat transfer models based on various flow patterns. The models favorably predict the experimental data. However, due to the limitation of flow boiling database, their models do not work for flow boiling heat transfer at low reduced pressures according to their recent evaluation of the models with new database covering a wide range of reduced pressures over the past 20 years (Cheng et al., 2021; Cheng and Xia, 2023d). Therefore, the models have been updated based on the new database of more than 6000 flow boiling heat transfer data for better prediction of flow boiling of carbon dioxide in our latest development of the models.
The updated models are based on our previous mechanistic heat transfer models for flow boiling based on flow patterns (Cheng et al., 2006, 2008a,c). The updated flow boiling heat transfer models are applicable to a wide range of the reduced pressures from 0.1332 to 0.9082 (the corresponding saturation temperature from –40.6 to 26.77°C), the channel diameter from 0.529 to 9.52 mm, the heat flux from 2 to 72 kW/m^{2} and the mass flux from 100 to 1500 kg/m^{2}s. A comprehensive diabatic flow pattern map has been developed by considering flow boiling heat transfer mechanisms for various flow patterns at first. Based on the new database, new criteria for dry-out and mist flow regimes have been proposed as follows:
\[x_{di}=0.58e^{\left[0.52-0.209\text{We}_v^{0.17}\text{Fr}_{v,\text{Mori}}^{0.06}(\rho_v/\rho_l)^{0.25}(q/q_\text{crit})^{0.27}\right]}\] | (1) |
where \(x_{di}\) is vapor quality for dry-out inception, We\(_v\) is vapor phase Weber number, Fr\(_{v,\text{Mori}}\) is Fround number defined by Mori, \(\rho_v\) is vapor phase density, \(\rho_l\) is liquid phase density, \(q\) is heat flux, and \(q_\text{crit}\) is critical heat flux. The details of these parameters may be referred to our previous study (Cheng et al., 2006, 2008a,c).
\[x_{de}=0.61e^{\left[0.57-0.148\text{We}_v^{0.16}\text{Fr}_{v,\text{Mori}}^{0.12}(\rho_v/\rho_l)^{0.25}(q/q_\text{crit})^{0.27}\right]}\] | (2) |
where \(x_{de}\) is vapor quality for dry-out completion.
The flow boiling heat transfer mechanisms are incorporated in the flow pattern map by considering the effect of reduced pressures and channel sizes. Then, generalized flow boiling heat transfer models have been proposed based on various flow patterns. A new nucleate boiling heat transfer correlation has been developed carbon dioxide at the wide range of reduced pressures. It predicts 90% of the nucleate boiling heat transfer data.
\[h_{nb}=129p_{r}^{-0.037}\left(-\log_{10}p_{r}\right)^{-0.55}M^{-0.5}q^{0.58}\] | (3) |
where \(h_{nb}\) is nucleate boiling, \(p_r\) is the reduced pressure, \(M\) is the molecular weight, and \(q\) is heat flux.
The new flow boiling heat transfer models favorably predict the extensive experimental database collected from the literature. Figure 1(a) shows the flow pattern map at the indicated condition in a macroscale tube of 4.57 mm, and Fig. 1(a) show the comparative results of the predicted heat transfer coefficients to the experimental data in the macroscale tube at the indicated conditions. Figure 2 shows the comparative results of the predicted heat transfer coefficients to the experimental data in the microscale tube at the indicated conditions. Overall, the latest developed models favorably predict 83% the experimental database without the dry-out and mist flow regime data. However, the prediction methods in dry-out and mist flow regimes need to be improved.
(a)
(b)
Figure 1. (a) Flow pattern map at the indicated condition: I – intermittent flow, A – annular flow, D – dry-out region, M – mist flow, SW – stratified-wave flow, Slug – slug flow, and S – stratified flow. (b) Comparison of the predicted and experimental data of heat transfer coefficient of carbon dioxide in macroscale channels.
Figure 2. Comparison of the predicted and experimental data of heat transfer coefficient of carbon dioxide in microscale channels
The models are applicable to the design of carbon dioxide evaporators for various thermal and energy systems. The initial research results are promising. Further refinement of the models is still in progress, such as new nucleate boiling suppression factor is still yet to develop, flow map pattern map is still adjusted to fit the high nucleate boiling heat transfer of carbon dioxide. Initial research results are reported in this focus. Complete flow pattern map and heat transfer models together with flow boiling heat transfer mechanisms at high and low reduced pressures will be published in a journal soon.
REFERENCES
Cheng, L. (2013) Fundamental issues of critical heat flux phenomena during flow boiling in microscale-channels and nucleate pool boiling in confined spaces, Heat Transf. Eng., vol. 34, no. 13, pp. 1011–1043.
Cheng L. and Chen, T. (2000) Comparison of six typical correlations for upward flow boiling heat transfer with kerosene in a vertical smooth tube, Heat Transf. Eng., vol. 21, no. 5, pp. 27–34.
Cheng, L. and Mewes, D. (2006) Review of two-phase flow and flow boiling of mixtures in small and mini channels, Int. J. Multiphase Flow, vol. 32, no. 2, pp. 183–207.
Cheng L. and Thome, J.R. (2009) Cooling of microprocessors using flow boiling of CO_{2} in micro-evaporators: Preliminary analysis and performance comparison, Appl. Therm. Eng., vol. 29, nos. 11–12, pp. 2426–2432.
Cheng, L. and Xia, G. (2017) Fundamental issues, mechanisms and models of flow boiling heat transfer in microscale channels, Int. J. Heat Mass Transf., vol. 108 (Part A), pp. 97–127.
Cheng, L. and Xia, G. (2023a) Flow patterns and flow pattern maps for adiabatic and diabatic gas liquid two phase flow in microchannels: Fundamentals, mechanisms and applications, Exp. Therm. Fluid Sci., vol. 148, p. 110988.
Cheng, L. and Xia, G. (2023b) High heat flux cooling technologies using microchannel evaporators: fundamentals and challenges, Heat Transf. Eng., vol. 44, nos. 16-18.
Cheng, L. and Xia, G. (2023c) Progress and Prospects for Research and Technology Development of Supercritical CO_{2} Thermal Systems for Energy Conversion, Energy Storage and Waste Heat Recovery, Heat Transf. Eng. (published online).
Cheng, L. and Xia, G. (2023d) Study of the effect of the reduced pressure on a mechanistic heat transfer model for flow boiling of CO_{2} in macroscale and microscale tubes, Heat Transf. Eng., vol. 4, nos. 16-18, pp. 1657–1670.
Cheng, L., Guo, Z., and Xia, G. (2023) A Review on Research and Technology Development of Green Hydrogen Energy Systems with Thermal Management and Heat Recovery, Heat Transf. Eng. (published online).
Cheng, L., Ribatski, G., Wojtan, L., and Thome, J.R. (2006) New flow boiling heat transfer model and flow pattern map for carbon dioxide evaporating inside horizontal tubes, Int. J. Heat Mass Transf., vol. 49, nos. 21-22, pp. 4082–4094.
Cheng, L., Ribatski, G., Moreno Quibén, J., and Thome, J.R. (2008a) New prediction methods for CO_{2} evaporation inside tubes: Part I – A general two-phase flow pattern map and development of a phenomenological model of two-phase flow frictional pressure drop, Int. J. Heat Mass Transf., vol. 51, nos. 1-2, pp. 111–124.
Cheng, L., Ribatski, G., and Thome, J.R. (2008b) Gas-liquid two-phase flow patterns and flow pattern maps: Fundamentals and applications, ASME Appl. Mech. Rev., vol. 61, no. 5, p. 050802.
Cheng, L., Ribatski, G., and Thome, J.R. (2008c) New prediction methods for CO_{2} evaporation inside tubes: Part II – A general flow boiling heat transfer model based on flow patterns, Int. J. Heat Mass Transf., vol. 51, nos. 1-2, pp. 125–135. DOI:10.1016/j.ijheatmasstransfer.2007.04.001
Cheng, L., Xia, G., and Thome, J.R. (2021) Flow boiling heat transfer and two-phase flow phenomena of CO_{2} in macro- and micro-channel evaporators: Fundamentals, applications and engineering design, Appl. Therm. Eng., vol. 195, p. 170770.
Cheng, L., Xia, G., and Li, Q. (2022) CO_{2} evaporation process modelling: Fundamentals and engineering applications, Heat Transf. Eng., vol. 43, nos. 8–10, pp. 1–28.
References
- Cheng, L. (2013) Fundamental issues of critical heat flux phenomena during flow boiling in microscale-channels and nucleate pool boiling in confined spaces, Heat Transf. Eng., vol. 34, no. 13, pp. 1011–1043.
- Cheng L. and Chen, T. (2000) Comparison of six typical correlations for upward flow boiling heat transfer with kerosene in a vertical smooth tube, Heat Transf. Eng., vol. 21, no. 5, pp. 27–34.
- Cheng, L. and Mewes, D. (2006) Review of two-phase flow and flow boiling of mixtures in small and mini channels, Int. J. Multiphase Flow, vol. 32, no. 2, pp. 183–207.
- Cheng L. and Thome, J.R. (2009) Cooling of microprocessors using flow boiling of CO_{2} in micro-evaporators: Preliminary analysis and performance comparison, Appl. Therm. Eng., vol. 29, nos. 11–12, pp. 2426–2432.
- Cheng, L. and Xia, G. (2017) Fundamental issues, mechanisms and models of flow boiling heat transfer in microscale channels, Int. J. Heat Mass Transf., vol. 108 (Part A), pp. 97–127.
- Cheng, L. and Xia, G. (2023a) Flow patterns and flow pattern maps for adiabatic and diabatic gas liquid two phase flow in microchannels: Fundamentals, mechanisms and applications, Exp. Therm. Fluid Sci., vol. 148, p. 110988.
- Cheng, L. and Xia, G. (2023b) High heat flux cooling technologies using microchannel evaporators: fundamentals and challenges, Heat Transf. Eng., vol. 44, nos. 16-18.
- Cheng, L. and Xia, G. (2023c) Progress and Prospects for Research and Technology Development of Supercritical CO_{2} Thermal Systems for Energy Conversion, Energy Storage and Waste Heat Recovery, Heat Transf. Eng. (published online).
- Cheng, L. and Xia, G. (2023d) Study of the effect of the reduced pressure on a mechanistic heat transfer model for flow boiling of CO_{2} in macroscale and microscale tubes, Heat Transf. Eng., vol. 4, nos. 16-18, pp. 1657–1670.
- Cheng, L., Guo, Z., and Xia, G. (2023) A Review on Research and Technology Development of Green Hydrogen Energy Systems with Thermal Management and Heat Recovery, Heat Transf. Eng. (published online).
- Cheng, L., Ribatski, G., Wojtan, L., and Thome, J.R. (2006) New flow boiling heat transfer model and flow pattern map for carbon dioxide evaporating inside horizontal tubes, Int. J. Heat Mass Transf., vol. 49, nos. 21-22, pp. 4082–4094.
- Cheng, L., Ribatski, G., Moreno Quibén, J., and Thome, J.R. (2008a) New prediction methods for CO_{2} evaporation inside tubes: Part I – A general two-phase flow pattern map and development of a phenomenological model of two-phase flow frictional pressure drop, Int. J. Heat Mass Transf., vol. 51, nos. 1-2, pp. 111–124.
- Cheng, L., Ribatski, G., and Thome, J.R. (2008b) Gas-liquid two-phase flow patterns and flow pattern maps: Fundamentals and applications, ASME Appl. Mech. Rev., vol. 61, no. 5, p. 050802.
- Cheng, L., Ribatski, G., and Thome, J.R. (2008c) New prediction methods for CO_{2} evaporation inside tubes: Part II – A general flow boiling heat transfer model based on flow patterns, Int. J. Heat Mass Transf., vol. 51, nos. 1-2, pp. 125–135. DOI:10.1016/j.ijheatmasstransfer.2007.04.001
- Cheng, L., Xia, G., and Thome, J.R. (2021) Flow boiling heat transfer and two-phase flow phenomena of CO_{2} in macro- and micro-channel evaporators: Fundamentals, applications and engineering design, Appl. Therm. Eng., vol. 195, p. 170770.
- Cheng, L., Xia, G., and Li, Q. (2022) CO_{2} evaporation process modelling: Fundamentals and engineering applications, Heat Transf. Eng., vol. 43, nos. 8–10, pp. 1–28.