AI Chat Paper
Note: Please note that the following content is generated by AMiner AI. SciOpen does not take any responsibility related to this content.
{{lang === 'zh_CN' ? '文章概述' : 'Summary'}}
{{lang === 'en_US' ? '中' : 'Eng'}}
Chat more with AI
Powered by AMiner. Clicking this button will take you away from SciOpen.
Home Experimental and Computational Multiphase Flow Article
PDF (2.2 MB)
Cite
EndNote(RIS) BibTeX
Collect
Submit Manuscript AI Chat Paper
Show Outline
Outline
Show full outline
Hide outline
Outline
Show full outline
Hide outline
Research Article | Open Access

Study on bubble-induced turbulence in pipes and containers with Reynolds-stress models

Yixiang Liao1, Tian Ma1,2( )
Institute of Fluid Dynamics, Helmholtz-Zentrum Dresden-Rossendorf, Bautzner Landstraße 400, 01328 Dresden, Germany
Department of Civil and Environmental Engineering, Duke University, Durham, NC 27708, USA
Show Author Information

Graphical Abstract

Abstract

Bubbly flow still represents a challenge for large-scale numerical simulation. Among many others, the understanding and modelling of bubble-induced turbulence (BIT) are far from being satisfactory even though continuous efforts have been made. In particular, the buoyancy of the bubbles generally introduces turbulence anisotropy in the flow, which cannot be captured by the standard eddy viscosity models with specific source terms representing BIT. Recently, on the basis of bubble-resolving direct numerical simulation data, a new Reynolds-stress model considering BIT was developed by Ma et al. (J Fluid Mech, 883: A9 (2020)) within the Euler-Euler framework. The objective of the present work is to assess this model and compare its performance with other standard Reynolds-stress models using a systematic test strategy. We select the experimental data in the BIT-dominated range and find that the new model leads to major improvements in the prediction of full Reynolds-stress components.

Keywords

bubble-induced turbulence (BIT)Reynolds-stress turbulence modelpipe flowEuler-Euler two-fluid model

References

 
Akbar, M., Hayashi, K., Hosokawa, S., Tomiyama, A. 2012. Bubble tracking simulation of bubble-induced pseudoturbulence. Multiphase Sci Technol, 24:197-222.
Crossref Google Scholar
 
Balachandar, S., Eaton, J. K. 2010. Turbulent dispersed multiphase flow. Annu Rev Fluid Mech, 42:111-133.
Crossref Google Scholar
 
Biesheuvel, A., van Wijngaarden, L. 1984. Two-phase flow equations for a dilute dispersion of gas bubbles in liquid. J Fluid Mech, 148:301-318.
Crossref Google Scholar
 
Bragg, A. D., Liao, Y., Fröhlich, J., Ma, T. 2021. Assessment of the validity of a log-law for wall-bounded turbulent bubbly flows. Int J Heat Fluid Flow, 91:108857.
Crossref Google Scholar
 
Burns, A. D., Frank, T., Hamill, I., Shi, J. M. 2004. The Favre averaged drag model for turbulent dispersion in Eulerian multi-phase flows. In: Proceedings of the 5th International Conference on Multiphase Flow, Yokohama, Japan, Paper No. 392.
 
Cokljat, D., Slack, M., Vasquez, S. A., Bakker, A., Montante, G. 2006. Reynolds-stress model for eulerian multiphase. Progr Comput Fluid Dynam Int J, 6:168-178.
Crossref Google Scholar
 
Colombo, M., Fairweather, M. 2015. Multiphase turbulence in bubbly flows: RANS simulations. Int J Multiphase Flow, 77:222-243.
Crossref Google Scholar
 
Colombo, M., Rzehak, R., Fairweather, M., Liao, Y., Lucas, D. 2021. Benchmarking of computational fluid dynamic models for bubbly flows. Nucl Eng Des, 375:111075.
Crossref Google Scholar
 
Deen, N. G., Solberg, T., Hjertager, B. H. 2001. Large eddy simulation of the gas-liquid flow in a square cross-sectioned bubble column. Chem Eng Sci, 56:6341-6349.
Crossref Google Scholar
 
Du Cluzeau, A., Bois, G., Toutant, A. 2019. Analysis and modelling of Reynolds stresses in turbulent bubbly up-flows from direct numerical simulations. J Fluid Mech, 866:132-168.
Crossref Google Scholar
 
Fröhlich, J., von Terzi, D. 2008. Hybrid LES/RANS methods for the simulation of turbulent flows. Prog Aerosp Sci, 44:349-377.
Crossref Google Scholar
 
George, W. K., Hussein, H. J. 1991. Locally axisymmetric turbulence. J Fluid Mech, 233:1-23.
Crossref Google Scholar
 
Hanjalic, K., Launder, B. 2011. Modelling Turbulence in Engineering and the Environment. Cambridge: Cambridge University Press.
Crossref
 
Hosokawa, S., Tomiyama, A. 2013. Bubble-induced pseudo turbulence in laminar pipe flows. Int J Heat Fluid Flow, 40:97-105.
Crossref Google Scholar
 
Hosokawa, S., Tomiyama, A., Misaki, S., Hamada, T. 2002. Lateral migration of single bubbles due to the presence of wall. In: Proceedings of the ASME 2002 Joint U.S.-European Fluids Engineering Division Conference, Quebec, Canada.
Crossref
 
Ilić, M. 2006. Statistical analysis of liquid phase turbulence based on direct numerical simulations of bubbly flows. Ph.D. Thesis. Forschungszentrum Karlsruhe, Germany.
 
Ishii, M., Hibiki, T. 2006. Thermo-Fluid Dynamics of Two-Phase Flow. Boston, MA, USA: Springer.
Crossref
 
Ishii, M., Zuber, N. 1979. Drag coefficient and relative velocity in bubbly, droplet or particulate flows. AIChE J, 25:843-855.
Crossref Google Scholar
 
Kataoka, I., Serizawa, A. 1989. Basic equations of turbulence in gas- liquid two-phase flow. Int J Multiphase Flow, 15:843-855.
Crossref Google Scholar
 
Launder, B. E., Reece, G. J., Rodi, W. 1975. Progress in the development of a Reynolds-stress turbulence closure. J Fluid Mech, 68:537-566.
Crossref Google Scholar
 
Liao, Y. 2020. Update to the MUSIG model in ANSYS CFX for reliable modelling of bubble coalescence and breakup. Appl Math Model, 81:506-521.
Crossref Google Scholar
 
Liao, Y., Lucas, D., Krepper, E. 2014. Application of new closure models for bubble coalescence and breakup to steam-water vertical pipe flow. Nucl Eng Des, 279:126-136.
Crossref Google Scholar
 
Liao, Y., Ma, T., Krepper, E., Lucas, D., Fröhlich, J. 2019. Application of a novel model for bubble-induced turbulence to bubbly flows in containers and vertical pipes. Chem Eng Sci, 202:55-69.
Crossref Google Scholar
 
Liao, Y., Ma, T., Liu, L., Ziegenhein, T., Krepper, E., Lucas, D. 2018. Eulerian modelling of turbulent bubbly flow based on a baseline closure concept. Nucl Eng Des, 337:450-459.
Crossref Google Scholar
 
Liao, Y., Rzehak, R., Lucas, D., Krepper, E. 2015. Baseline closure model for dispersed bubbly flow: Bubble coalescence and breakup. Chem Eng Sci, 122:336-349.
Crossref Google Scholar
 
Liao, Y., Upadhyay, K., Schlegel, F. 2020. Eulerian-Eulerian two-fluid model for laminar bubbly pipe flows: Validation of the baseline model. Comput Fluids, 202:104496.
Crossref Google Scholar
 
Liu, L., Keplinger, O., Ma, T., Ziegenhein, T., Shevchenko, N., Eckert, S., Yan, H., Lucas, D. 2018. Euler-Euler simulation and X-ray measurement of bubble chain in a shallow container filled with liquid metals. Chem Eng Sci, 192:288-305.
Crossref Google Scholar
 
Lohse, D. 2018. Bubble puzzles: From fundamentals to applications. Phys Rev Fluids, 3:110504.
Crossref Google Scholar
 
Lopez de Bertodano, M., Lahey, R. T., Jones, O. C. 1994. Development of a k-ε model for bubbly two-phase flow. J Fluids Eng, 116:128-134.
Crossref Google Scholar
 
Lopez de Bertodano, M., Lee, S. J., Lahey, R. T., Drew, D. A. 1990. The prediction of two-phase turbulence and phase distribution phenomena using a Reynolds stress model. J Fluids Eng, 112:107-113.
Crossref Google Scholar
 
Lu, J., Tryggvason, G. 2013. Dynamics of nearly spherical bubbles in a turbulent channel upflow. J Fluid Mech, 732:166-189.
Crossref Google Scholar
 
Lucas, D., Beyer, M., Banowski, M., Seidel, T., Krepper, E., Liao, Y., Apanasevich, P., Gauss, F., Ma, T. 2016. TOPFLOW—Experiments, model development and validation for the qualification of CFD-codes for two-phase flows. Final report. Technical Report. Helmholtz-Zentrum Dresden-Rossendorf eV., Dresden, Germany.
Google Scholar
 
Lucas, D., Krepper, E., Rzehak, R., Liao, Y., Ma, T., Ziegenhein, T. 2015. Status and challenges of CFD-modelling for poly-disperse bubbly flows. In: Proceedings of the 16th International Topical Meeting on Nuclear Reactor Thermal Hydraulics, Chicago, USA.
 
Ma, T. 2017. A contribution to turbulence modelling in bubbly flows. Ph.D. Thesis. Technische Universität Dresden, Dresden, Germany.
 
Ma, T., Lucas, D., Bragg, A. D. 2020a. Explicit algebraic relation for calculating reynolds normal stresses in flows dominated by bubble-induced turbulence. Phys Rev Fluids, 5:084305.
Crossref Google Scholar
 
Ma, T., Lucas, D., Jakirlić, S., Fröhlich, J. 2020b. Progress in the second-moment closure for bubbly flow based on direct numerical simulation data. J Fluid Mech, 883, .
Crossref Google Scholar
 
Ma, T., Lucas, D., Ziegenhein, T., Fröhlich, J., Deen, N. G. 2015a. Scale-Adaptive Simulation of a square cross-sectional bubble column. Chem Eng Sci, 131:101-108.
Crossref Google Scholar
 
Ma, T., Ott, B., Fröhlich, J., Bragg, A. D. 2021. Scale-dependent anisotropy, energy transfer and intermittency in bubble-laden turbulent flows. J Fluid Mech, 927:A16.
Crossref Google Scholar
 
Ma, T., Santarelli, C., Ziegenhein, T., Lucas, D., Fröhlich, J. 2017. Direct numerical simulation-based Reynolds-averaged closure for bubble-induced turbulence. Phys Rev Fluids, 2:034301.
Crossref Google Scholar
 
Ma, T., Ziegenhein, T., Lucas, D., Krepper, E., Fröhlich, J. 2015b. Euler-Euler large eddy simulations for dispersed turbulent bubbly flows. Int J Heat Fluid Flow, 56:51-59.
Crossref Google Scholar
 
Magolan, B., Lubchenko, N., Baglietto, E. 2019. A quantitative and generalized assessment of bubble-induced turbulence models for gas-liquid systems. Chem Eng Sci: X, 2:100009.
Crossref Google Scholar
 
Masood, R. M. A., Rauh, C., Delgado, A. 2014. CFD simulation of bubble column flows: An explicit algebraic Reynolds stress model approach. Int J Multiphase Flow, 66:11-25.
Crossref Google Scholar
 
Michaelides, E. E., Crowe, C. T., Schwarzkopf, J. D. 2016. Multiphase Flow Handbook, 2nd edn. Boca Raton, FA, USA: CRC Press.
Crossref
 
Morel, C. 1997. Turbulence modeling and first numerical simulations in turbulent two-phase flows. Technical Report. CEA/Grenoble, France.
Google Scholar
 
Ničeno, B., Dhotre, M. T., Deen, N. G. 2008. One-equation sub-grid scale (SGS) modelling for Euler-Euler large eddy simulation (EELES) of dispersed bubbly flow. Chem Eng Sci, 63:3923-3931.
Crossref Google Scholar
 
Qi, Y., Mohammad Masuk, A. U., Ni, R. 2020. Towards a model of bubble breakup in turbulence through experimental constraints. Int J Multiphase Flow, 132:103397.
Crossref Google Scholar
 
Riboux, G., Risso, F., Legendre, D. 2010. Experimental characterization of the agitation generated by bubbles rising at high Reynolds number. J Fluid Mech, 643:509-539.
Crossref Google Scholar
 
Rzehak, R., Krepper, E. 2013. Bubble-induced turbulence: Comparison of CFD models. Nucl Eng Des, 258:57-65.
Crossref Google Scholar
 
Rzehak, R., Ziegenhein, T., Kriebitzsch, S., Krepper, E., Lucas, D. 2017. Unified modeling of bubbly flows in pipes, bubble columns, and airlift columns. Chem Eng Sci, 157:147-158.
Crossref Google Scholar
 
Santarelli, C., Fröhlich, J. 2015. Direct numerical simulations of spherical bubbles in vertical turbulent channel flow. Int J Multiphase Flow, 75:174-193.
Crossref Google Scholar
 
Santarelli, C., Fröhlich, J. 2016. Direct numerical simulations of spherical bubbles in vertical turbulent channel flow. Influence of bubble size and bidispersity. Int J Multiphase Flow, 81:27-45.
Crossref Google Scholar
 
Santarelli, C., Roussel, J., Fröhlich, J. 2016. Budget analysis of the turbulent kinetic energy for bubbly flow in a vertical channel. Chem Eng Sci, 141:46-62.
Crossref Google Scholar
 
Sommerfeld, M. 2017. Numerical methods for dispersed multiphase flows. In: Particles in Flows. Advances in Mathematical Fluid Mechanics. Bodnár, T., Galdi, G., Nečasová, Š., Eds. Birkhäuser.
 
Speziale, C. G., Sarkar, S., Gatski, T. B. 1991. Modelling the pressure- strain correlation of turbulence: An invariant dynamical systems approach. J Fluid Mech, 227:245-272.
Crossref Google Scholar
 
Tomiyama, A., Tamai, H., Zun, I., Hosokawa, S. 2002. Transverse migration of single bubbles in simple shear flows. Chem Eng Sci, 57:1849-1858.
Crossref Google Scholar
 
Troshko, A. A., Hassan, Y. A. 2001. A two-equation turbulence model of turbulent bubbly flows. Int J Multiphase Flow, 27:1965-2000.
Crossref Google Scholar
 
Ullrich, M., Krumbein, B., Maduta, R., Jakirlić, S. 2021. Turbulent flow in a square cross-sectioned bubble column computed by a scale-resolving reynolds-stress model. Chem Eng Sci, 230:116201.
Crossref Google Scholar
 
Vaidheeswaran, A., Hibiki, T. 2017. Bubble-induced turbulence modeling for vertical bubbly flows. Int J Heat Mass Transf, 115:741-752.
Crossref Google Scholar
 
Wörner, M., Erdogan, S. 2013. Toward improved closure relations for the turbulent kinetic energy equation in bubble-driven flows. Chemie Ingenieur Technik, 85:1131-1136.
Crossref Google Scholar
 
Ziegenhein, T., Rzehak, R., Ma, T., Lucas, D. 2017. Towards a unified approach for modelling uniform and non-uniform bubbly flows. Can J Chem Eng, 95:170-179.
Crossref Google Scholar
Experimental and Computational Multiphase Flow
Volume 4 Issue 2,
June 2022
Pages 121-132
DOI: 10.1007/s42757-021-0128-0
Cite this article:
Liao Y, Ma T. Study on bubble-induced turbulence in pipes and containers with Reynolds-stress models. Experimental and Computational Multiphase Flow, 2022, 4(2): 121-132. https://doi.org/10.1007/s42757-021-0128-0

938

Views

31

Downloads

9

Crossref

9

Web of Science

9

Scopus

Altmetrics
Received: 20 July 2021
Revised: 19 October 2021
Accepted: 01 November 2021
Published: 04 January 2022
© The Author(s) 2021

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.

The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.

To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
Return