Abstract
The evaluation of mixing effects is crucial in industrial production such as chemical and metallurgical industries. An improved Betti number method is proposed by using a gas-liquid top-blow mixing experiment and a direct contact heat exchange experiment. This method is adapted to the comprehensive evaluation of flow mixing and heat transfer performance under conditions of dispersed particles or bubbles where the target is identifiable. The comparison results and reveals that our method can not only portray the mixing effect by the critical point of the area integration curve of the Betti number time series but also the parameters (i.e., slope and intercept) obtained after the area integration of the Betti number curve by the logistic regression model can effectively characterize the mixing time and heat exchange performance. The intercept variation of the area integral of the Betti number curve was found to have a high correlation with the correlation coefficients of mixing time and heat transfer coefficient. Meanwhile, a new index for evaluating the mixing performance was obtained. The optimal working condition was obtained. This method is simple and easy to implement and can be extended to processes where the target is identifiable in a transparent reactor and where both mixing and heat transfer effects need to be quantified.
Funding source: National Natural Science Foundation of China
Award Identifier / Grant number: 52166004
-
Author contributions: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.
-
Research funding: We acknowledge the financial support from the National Natural Science Foundation of China (Project Nos.: 52166004).
-
Conflict of interest statement: The authors declare no conflicts of interest regarding this article.
References
Alexias, P., and K. C. Giannakoglou. 2020. “Optimization of a Static Mixing Device Using the Continuous Adjoint to a Two-phase Mixing Model.” Optimization and Engineering 21 (2): 631–50, https://doi.org/10.1007/s11081-019-09466-x.Search in Google Scholar
Cai, H., F. Liu, J. Huang, F. Liu, J. Huang, M. Wu, and J. Xu. 2020. “Effect of Size Distribution of Bubble Groups on Average Volumetric Heat Transfer Coefficient in the Process of Direct Contact Boiling Heat Transfer.” International Communications in Heat and Mass Transfer 117: 104709, doi:https://doi.org/10.1016/j.icheatmasstransfer.2020.104709.Search in Google Scholar
Chu, K. Y., H. H. Chen, P. H. Lai, H. C. Wu, Y. C. Liu, C. C. Lin, and M. J. Lu. 2016. “The Effects of Bottom Blowing Gas Flow Rate Distribution during the Steelmaking Converter Process on Mixing Efficiency.” Metallurgical and Materials Transactions B 47 (2): 948–62, doi:https://doi.org/10.1007/s11663-016-0593-1.Search in Google Scholar
Fei, Y., Q. Xiao, J. Xu, J. Pan, S. Wang, H. Wang, and J. Huang. 2015. “A Novel Approach for Measuring Bubbles Uniformity and Mixing Efficiency in a Direct Contact Heat Exchanger.” Energy 93: 2313–20, doi:https://doi.org/10.1016/j.energy.2015.10.126.Search in Google Scholar
Huang, J., J. Xu, X. Sang, H. Wang, and H. Wang. 2014. “Quantifying the Synergy of Bubble Swarm Patterns and Heat Transfer Performance Using Computational Homology.” International Journal of Heat and Mass Transfer 75: 497–503, doi:https://doi.org/10.1016/j.ijheatmasstransfer.2014.03.084.Search in Google Scholar
Jia, H., P. Han, K. Liu, Y. Li, K. Ba, and L. Feng. 2021. “Jet Characteristics of a Double-Structure Oxygen Lance and its Interaction with the Molten Pool in BOF Steelmaking.” AIP Advances 11 (8): 085330, doi:https://doi.org/10.1063/5.0059583.Search in Google Scholar
Khalifa, A., H. Ahmad, M. Antar, T. Laoui, and M. Khayet. 2017. “Experimental and Theoretical Investigations on Water Desalination Using Direct Contact Membrane Distillation.” Desalination 404: 22–34, doi:https://doi.org/10.1016/j.desal.2016.10.009.Search in Google Scholar
Kim, T. Y., A. Negash, and G. Cho. 2017. “Direct Contact Thermoelectric Generator (DCTEG): A Concept for Removing the Contact Resistance between Thermoelectric Modules and Heat Source.” Energy Conversion and Management 142: 20–7, https://doi.org/10.1016/j.enconman.2017.03.041.Search in Google Scholar
Lee, J. G., W. S. Kim, J. S. Choi, N. Ghaffour, and Y. D. Kim. 2018. “Dynamic Solar-Powered Multi-Stage Direct Contact Membrane Distillation System: Concept Design, Modeling and Simulation.” Desalination 435: 278–92, doi:https://doi.org/10.1016/j.desal.2017.04.008.Search in Google Scholar
Li, M., L. Li, Q. Li, and Z. Zou. 2018. “Modeling of Mixing Behavior in a Combined Blowing Steelmaking Converter with a Filter-Based Euler–Lagrange Model.” JOM 70 (10): 2051–8, doi:https://doi.org/10.1007/s11837-018-2889-x.Search in Google Scholar
Li, Z., B. Li, H. Wang, P. Yang, and J. Xu. 2021. “Effect of Gas-Liquid Two-phase Macro-Mixing on the Uniformity of Temperature Distribution in a Top-Blown Stirred Tank Using Image Analysis.” International Journal of Thermal Sciences 168: 107083, doi:https://doi.org/10.1016/j.ijthermalsci.2021.107083.Search in Google Scholar
Li, N., and K. Xu. 2017. “Simulation Study on Ultrasonic Tomography in Bubbly Gas/liquid Two-phase Flow.” In 2017 IEEE International Conference on Imaging Systems and Techniques (IST). Shaanxi: IEEE.10.1109/IST.2017.8261476Search in Google Scholar
Ling, H., and L. Zhang. 2019. “Numerical Simulation of Gas and Liquid Two-phase Flow in the RH Process.” Metallurgical and Materials Transactions B 50 (4): 2017–28, https://doi.org/10.1007/s11663-019-01583-3.Search in Google Scholar
Pranav, P., R. Van de Weygaert, G. Vegter, B. J. T. Jones, R. J. Adler, J. Feldbrugge, C. Park, T. Buchert, and M. Kerber. 2019. “Topology and Geometry of Gaussian Random Fields I: on Betti Numbers, Euler Characteristic, and Minkowski Functionals.” Monthly Notices of the Royal Astronomical Society 485 (3): 4167–208, doi:https://doi.org/10.1093/mnras/stz541.Search in Google Scholar
Sanmartino, J. A., M. Khayet, M. C. García-Payo, H. El-Bakouri, and A. Riaza. 2017. “Treatment of Reverse Osmosis Brine by Direct Contact Membrane Distillation: Chemical Pretreatment Approach.” Desalination 420: 79–90, doi:https://doi.org/10.1016/j.desal.2017.06.030.Search in Google Scholar
Shui, L., Z. Cui, X. Ma, M. Akbar Rhamdhani, A. Nguyen, and B. Zhao. 2015. “Mixing Phenomena in a Bottom Blown Copper Smelter: A Water Model Study.” Metallurgical and Materials Transactions B 46B: 1218–25.10.1007/s11663-015-0324-zSearch in Google Scholar
Sur, P., and E. J. Candès. 2019. “A Modern Maximum-Likelihood Theory for High-Dimensional Logistic Regression.” Proceedings of the National Academy of Sciences 116 (29): 14516–25, https://doi.org/10.1073/pnas.1810420116.Search in Google Scholar PubMed PubMed Central
Wei, J. H., and Y. Li. 2015. “Study on Mathematical Modeling of Combined Top and Bottom Blowing VOD Refining Process of Stainless Steel.” Steel Research International 86 (3): 189–211, https://doi.org/10.1002/srin.201400042.Search in Google Scholar
Xiao, Q., S. Wang, J. Xu, and H. Wang. 2017. “Visualized Measurement on Evolution of Bubble Patterns in a Direct-Contact Heat Exchanger.” In ASME Power Conference, 57601, V001T05A004. Kunming, Yunnan: American Society of Mechanical Engineers.10.1115/POWER-ICOPE2017-3084Search in Google Scholar
Xiao, Q., K. Yang, M. Wu, J. Pan, J. Xu, and H. Wang. 2018. “Complexity Evolution Quantification of Bubble Pattern in a Gas-Liquid Mixing System for Direct-Contact Heat Transfer.” Applied Thermal Engineering 138: 832–9, doi:https://doi.org/10.1016/j.applthermaleng.2018.04.058.Search in Google Scholar
Xiao, Q., Y. Zhang, X. Zhu, J. Xu, J. Pan, and H. Wang. 2018. “Novel 3-D Homogeneity Metrics of Multiple Components in Gas-Stirred Liquid Systems.” Powder Technology 336: 210–9, doi:https://doi.org/10.1016/j.powtec.2018.05.043.Search in Google Scholar
Xu, J., F. Liu, Q. Xiao, J. Huang, Y. Fei, Y. Yang, Y. Zhai, J. Pan, and H. Wang. 2020. “Synergistic Effect of Flow Pattern Evolution of Dispersed and Continuous Phases in Direct-Contact Heat Transfer Process.” International Journal of Refrigeration 112: 201–14, doi:https://doi.org/10.1016/j.ijrefrig.2019.11.020.Search in Google Scholar
Xu, J., H. Wang, and H. Fang. 2011. “Multiphase Mixing Quantification by Computational Homology and Imaging Analysis.” Applied Mathematical Modelling 35 (5): 2160–71, https://doi.org/10.1016/j.apm.2010.11.028.Search in Google Scholar
Xu, Z. Y., R. Z. Wang, and C. Yang. 2019. “Perspectives for Low-Temperature Waste Heat Recovery.” Energy 176: 1037–43, https://doi.org/10.1016/j.energy.2019.04.001.Search in Google Scholar
Xu, J., Q. Xiao, Y. Fei, S. Wang, and J. Huang. 2016. “Accurate Estimation of Mixing Time in a Direct Contact Boiling Heat Transfer Process Using Statistical Methods.” International Communications in Heat and Mass Transfer 75: 162–8, doi:https://doi.org/10.1016/j.icheatmasstransfer.2016.04.012.Search in Google Scholar
Yao, L., R. Zhu, K. Dong, G. Wei, F. Zhao, and Y. Tang. 2021. “Influence of the Non-uniform Bottom Blowing Gas Supply Mode on the Dynamic Conditions of Molten Pool during the Converter Steelmaking Process.” Ironmaking and Steelmaking 48 (2): 180–90, doi:https://doi.org/10.1080/03019233.2020.1758996.Search in Google Scholar
Yang, K., S. B. Wang, X. L. Zhu, J. X. Xu, and H. Wang. 2019. “Flow Pattern Visualization and Nonlinear Analysis of Gas-Liquid Mixing Process with Top-Blowing Gas Stirring.” Journal of Central South University 26 (8): 2029–40, doi:https://doi.org/10.1007/s11771-019-4151-2.Search in Google Scholar
Yin, Y., C. Zhu, R. Guo, T. Fu, and Y. Ma. 2018. “Gas-Liquid Two-phase Flow in a Square Microchannel with Chemical Mass Transfer: Flow Pattern, Void Fraction and Frictional Pressure Drop.” International Journal of Heat and Mass Transfer 127: 484–96, doi:https://doi.org/10.1016/j.ijheatmasstransfer.2018.07.113.Search in Google Scholar
Zhang, X., J. Wu, H. Zhang, W. Ding, and J. Zhang. 2021. “Visualization of Liquid Reaction in Submerged Top‐blow Agitation Process.” Fuel Cells 21 (1): 18–23, doi:https://doi.org/10.1002/fuce.202000016.Search in Google Scholar
Zhao, H., P. Yin, L. Zhang, and S. Wang. 2016. “Water Model Experiments of Multiphase Mixing in the Top-Blown Smelting Process of Copper Concentrate.” International Journal of Minerals, Metallurgy and Materials 23 (12): 1369–76, doi:https://doi.org/10.1007/s12613-016-1360-7.Search in Google Scholar
Zhao, H., T. Lu, F. Liu, P. Yin, and S. Wang. 2019. “Computational Fluid Dynamics Study on a Top-Blown Smelting Process with Lance Failure in an Isa Furnace.” JOM 71 (5): 1643–9, doi:https://doi.org/10.1007/s11837-019-03389-9.Search in Google Scholar
Zhao, W., X. Zhang, J. Huang, K. Ni, and J. Wang. 2018. “Hydrogenation of Bio-Oil via Gas-Liquid Two-phase Discharge Reaction System.” Process Safety and Environmental Protection 118: 167–77, doi:https://doi.org/10.1016/j.psep.2018.03.035.Search in Google Scholar
Supplementary Material
The online version of this article offers supplementary material (https://doi.org/10.1515/ijcre-2021-0286).
© 2022 Walter de Gruyter GmbH, Berlin/Boston