بررسی کارایی مدل تعادل جمعیت در پیش‌بینی رفتار انتقال حرارتی جریان دوغاب یخ درون لوله

نوع مقاله : مقاله پژوهشی

نویسندگان

دانشکده‌ی مهندسی مکانیک، دانشگاه شیراز، شیراز، ایران.

چکیده

در پژوهش حاضر به بررسی کارایی مدل تعادل جمعیت در شبیه‌سازی جریان دوغاب یخ پرداخته شده است. هدف، رفع نقص مطالعات پیشین بوده است، که تغییر اندازه‌ی ذرات یخ را نادیده می‌گرفتند. نتایج نشان داده است که استفاده از مدل تعادل جمعیت، خطای محاسباتی را در جریان‌های آشفته با کسر حجمی کمتر از ۱۰٪، به زیر ۵٪ کاهش می‌دهد. همچنین مشخص شده است که افزایش کسر حجمی و سرعت جریان، باعث بزرگ‌ترشدن میانگین قطر ذرات می‌شود. با بررسی مکانیزم‌های مختلف تجمیع و شکست ذرات مشخص شده است که ترکیب پیشنهادی لوو، دقیق‌ترین نتایج را در مقایسه با داده‌های تجربی به دست می‌دهد. نتایج نشان داده است که توزیع اندازه‌ی ذرات به محدوده‌ی مجاز قطر در مدل بستگی دارد. درنهایت، محدوده‌ی بهینه برای استفاده از سیستم‌های دوغاب یخ بین ۱۰ تا ۲۰ درصد حجمی یخ تعیین شده است، زیرا در خارج از محدوده‌ی ذکرشده، ضریب انتقال حرارت کاهش و افت فشار به‌شدت افزایش می‌یابد.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

Investigating the Effectiveness of the Population Balance Model for Predicting Thermal Transfer Characteristics of Ice Slurry Flow within a Pipe

نویسندگان [English]

  • Mohammad Amin Alavi Nobandegani
  • Hossein Ali Pakravan
School of Mechanical Engineering, Shiraz University, Shiraz, Iran.
چکیده [English]

In this research, we performed a detailed numerical investigation into the effectiveness of the Population Balance Model (PBM) for simulating the complex phenomena of particle aggregation and breakage. The results demonstrated a substantial improvement in prediction accuracy when the PBM is integrated into the simulation framework. Specifically, for turbulent flows with a volume fraction below 10%, the PBM was shown to reduce calculation errors to less than 5%. Our findings also reveal a direct correlation between increased volume fraction and flow velocity, and an increase in the average particle diameter within the flow. Further analysis evaluated different aggregation and breakage mechanisms. These were tested within the PBM framework. The combination proposed by Luo proved to be the most effective, yielding more reliable results than other models. This was consistent across both laminar and turbulent flow regimes and was consistently validated against experimental data. We also examined how the predefined range of allowable particle diameters within the PBM influences the results. Our investigation highlighted a strong dependency between this parameter and the distribution of the average particle diameter across the pipe's cross-section.

کلیدواژه‌ها [English]

  • Ice slurry
  • Population balance model
  • Breakage
  • Aggregation
  • Particle size distribution
1. Wang, K., Eisele, M., Hwang, Y. and Radermacher, R., 2010. Review of secondary loop refrigeration systems. International Journal of Refrigeration, 33(2), pp. 212-234. https://doi.org/10.1016/j.ijrefrig.2009.09.018
2. Han, Z., Ma, Q., Fang, Y., Hua, L., Jin, C. and Huang, J. Progress and innovations of ice slurry generation based on scraped-surface method. IOP Publishing, p. 042021. https://doi.org/10.1088/1742-6596/1550/4/042021
3. Bordet, A., Poncet, S., Poirier, M. and Galanis, N., 2018. Flow visualizations and pressure drop measurements of isothermal ice slurry pipe flows. Experimental Thermal and Fluid Science, 99, pp. 595-604. https://doi.org/10.1016/j.expthermflusci.2018.04.024
4. Hirochi, T., Maeda, Y., Yamada, S., Shirakashi, M., Hattori, M. and Saito, A., 2004. Flow patterns of ice/water slurry in horizontal pipes. J. Fluids Eng., 126(3), pp. 436-441. https://doi.org/10.1115/1.1760541
5. Guan, X., Xu, Q., Yang, N. and Nigam, K.D., 2021. Hydrodynamics in bubble columns with helically-finned tube Internals: Experiments and CFD-PBM simulation. Chemical engineering science, 240, pp. 116674. https://doi.org/10.1016/j.ces.2021.116674
6. Gong, H., Li, W., Zhang, X., Peng, Y., Yu, B. and Mou, Y., 2021. Effects of droplet dynamic characteristics on the separation performance of a demulsification and dewatering device coupling electric and centrifugal fields. Separation and Purification Technology, 257, pp. 117905. https://doi.org/10.1016/j.seppur.2020.117905
7. Song, G., Li, Y., Wang, W., Jiang, K., Shi, Z. and Yao, S., 2018. Numerical simulation of hydrate slurry flow behavior in oil-water systems based on hydrate agglomeration modelling. Journal of Petroleum Science and Engineering, 169, pp. 393-404. https://doi.org/10.1016/j.petrol.2018.05.073
8. Xu, D., Liu, Z., Cai, L., Tang, Y., Yu, Y. and Xu, A., 2018. A CFD-PBM approach for modeling ice slurry flow in horizontal pipes. Chemical engineering science, 176, pp. 546-559. https://doi.org/10.1016/j.ces.2017.11.022
9. Liangxu, Z., Fei, M., Zhaonan, M. and Peng, Z., Numerical Investigation of Flow and Heat Transfer of Ice Slurry Based on Population Balance Model. Journal of Shanghai Jiaotong University, 53(12), pp. 1459. https://doi.org/10.16183/j.cnki.jsjtu.2019.12.008
10. Cai, L., Liu, Z., Mi, S., Luo, C., Ma, K., Xu, A. et al., 2019. Investigation on flow characteristics of ice slurry in horizontal 90° elbow pipe by a CFD-PBM coupled model. Advanced Powder Technology, 30(10), pp. 2299-2310. https://doi.org/10.1016/j.apt.2019.07.010
11. Ma, K., Liu, Z., Tang, Y., Liu, X., Yang, Y. and Yang, S., 2022. Numerical investigation on ice slurry flow in horizontal elbow pipes. Thermal Science and Engineering Progress, 27, pp. 101083. https://doi.org/10.1016/j.tsep.2021.101083
12. Cai, L., Mi, S., Luo, C. and Liu, Z., 2022. Numerical investigation on heat and mass transfer characteristics of ice slurry in pulsating flow. International Journal of Heat and Mass Transfer, 189, pp. 122722. https://doi.org/10.1016/j.ijheatmasstransfer.2022.122722
13. Gao, P., Li, Z., Yan, F., Chen, K. and Cao, A., 2024. Study on flow and heat transfer characteristics of salt solution ice slurry. International Journal of Refrigeration, 159, pp. 1-16. https://doi.org/10.1016/j.ijrefrig.2023.12.007
14. Rezaei, M. and Pakravan, H.A., 2023. Thermo-fluidic characteristics of ice slurry flows in U-bend pipes for cold thermal energy storage. Journal of Energy Storage, 57, pp. 106224. https://doi.org/10.1016/j.est.2022.106224
15. Rezaei, M. and Pakravan, H.A., 2023. Numerical study of ice slurry flow and heat transfer in successive U-bends as part of tubular heat exchangers. International Journal of Thermal Sciences, 191, pp. 108357. https://doi.org/10.1016/j.ijthermalsci.2023.108357
16. Xie, F., Guo, W. and Zhu, Y., 2023. Numerical Study on Flow-Melt Characteristics of Ice Slurry in Horizontal Straight Pipe with a Local Large Heat Flux Segment. Energies, 16(1), pp. 476. https://doi.org/10.3390/en16010476
17. Mi, S., Xu, F., Cai, L. and Xu, C., 2024. Study on convective melting heat transfer of a solid-liquid phase change slurry in U-shaped curved tubes. International Communications in Heat and Mass Transfer, 154, pp. 107377. https://doi.org/10.1016/j.icheatmasstransfer.2024.107377
18. Mi, S., Geng, S., Cai, L. and Xu, C., 2024. Investigation on the flow characteristics of a phase change material slurry in horizontal and U-shaped tubes based on CFD-PBM. Chemical Engineering Research and Design, 201, pp. 409-424. https://doi.org/10.1016/j.cherd.2023.12.007
19. Faghri, A. and Zhang, Y. 2006 Transport phenomena in multiphase systems. Academic Press Elsevier.
20. Lee, W.H., 1980. A pressure iteration scheme for two-phase flow modeling. Multiphase transport fundamentals, reactor safety, applications, 1, pp. 407-431. https://doi.org/10.1142/9789814460286_0004
21. Ahmadkermaj, H., Maddahian, R. and Maerefat, M., 2021. Effect of swirl on thermal and hydraulic properties of ice slurry flow. Heat Transfer Engineering, 42(9), pp. 764-786. https://doi.org/10.1080/01457632.2020.1735796
22. Gidaspow, D., Bezburuah, R. and Ding, J. 1991 Hydrodynamics of circulating fluidized beds: kinetic theory approach. Illinois Inst. of Tech., Chicago, IL (United States). Dept. of Chemical Engineering.
23. Drew, D.A., 1983. Mathematical modeling of two-phase flow. Annual review of fluid mechanics, 15(1), pp. 261-291. https://doi.org/10.21236/ADA114535
24. Bordet, A., Poncet, S., Poirier, M. and Galanis, N., 2018. Advanced numerical modeling of turbulent ice slurry flows in a straight pipe. International Journal of Thermal Sciences, 127, pp. 294-311. https://doi.org/10.1016/j.ijthermalsci.2018.02.004
25. ANSYS, I., 2020. Ansys® FLUENT, Release 20.0. FLUENT Theory Guide; ANSYS, Inc.: Canonsburg, PA, USA),
26. Wang, J., Wang, S., Zhang, T. and Battaglia, F., 2018. Numerical and analytical investigation of ice slurry isothermal flow through horizontal bends. International journal of refrigeration, 92, pp. 37-54. https://doi.org/10.1016/j.ijrefrig.2018.05.038
27. Cai, L., Mi, S., Luo, C. and Liu, Z., 2022. Numerical investigation of hydraulic and heat transfer characteristics of two-phase ice slurry in helically coiled tubes. Energy and Buildings, 256, pp. 111773. https://doi.org/10.1016/j.enbuild.2021.111773
28. Li, D., Li, Z. and Gao, Z., 2019. Quadrature-based moment methods for the population balance equation: An algorithm review. Chinese Journal of Chemical Engineering, 27(3), pp. 483-500. https://doi.org/10.1016/j.cjche.2018.11.028
29. Yan, W.C., Luo, Z.H., Lu, Y.H. and Chen, X.D., 2012. A CFD‐PBM‐PMLM integrated model for the gas–solid flow fields in fluidized bed polymerization reactors. AIChE Journal, 58(6), pp. 1717-1732. https://doi.org/10.1002/aic.12705
30. Luo, H., 1995. Coalescence, breakup and liquid circulation in bubble column reactors. The University of Trondheim, Technical Report.
31. Liao, Y., Rzehak, R., Lucas, D. and Krepper, E., 2015. Baseline closure model for dispersed bubbly flow: Bubble coalescence and breakup. Chemical engineering science, 122, pp. 336-349. https://doi.org/10.1016/j.ces.2014.09.042
32. Lehr, F., Millies, M. and Mewes, D., 2002. Bubble‐size distributions and flow fields in bubble columns. AIChE Journal, 48(11), pp. 2426-2443. https://doi.org/10.1002/aic.690481103
33. Ghadiri, M. and Zhang, Z., 2002. Impact attrition of particulate solids. Part 1: A theoretical model of chipping. Chemical engineering science, 57(17), pp. 3659-3669. https://doi.org/10.1016/S0009-2509(02)00240-3
34. Lee, D.W., Yoon, E.S., Joo, M.C. and Sharma, A., 2006. Heat transfer characteristics of the ice slurry at melting process in a tube flow. International journal of refrigeration, 29(3), pp. 451-455. https://doi.org/10.1016/j.ijrefrig.2005.10.003
35. Niezgoda-Żelasko, B., 2006. Heat transfer of ice slurry flows in tubes. International journal of refrigeration, 29(3), pp. 437-450. https://doi.org/10.1016/j.ijrefrig.2005.09.017