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Analysis and modelling of Reynolds stresses in turbulent bubbly up-flows from direct numerical simulations

Published online by Cambridge University Press:  05 March 2019

A. du Cluzeau Open the ORCID record for A. du Cluzeau [Opens in a new window] ,
G. Bois Open the ORCID record for G. Bois [Opens in a new window]  and
A. Toutant Open the ORCID record for A. Toutant [Opens in a new window]
A. du Cluzeau*
Affiliation:
DEN-Service de Thermo-hydraulique et de Mécanique des Fluides (STMF), CEA, Université Paris-Saclay, F-91191 Gif-sur-Yvette, France
G. Bois*
Affiliation:
DEN-Service de Thermo-hydraulique et de Mécanique des Fluides (STMF), CEA, Université Paris-Saclay, F-91191 Gif-sur-Yvette, France
A. Toutant
Affiliation:
PROMES-CNRS (UPR 8521), Université de Perpignan Via Domitia, 66100 Perpignan, France
*
†Email addresses for correspondence: [email protected], [email protected]
†Email addresses for correspondence: [email protected], [email protected]
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Abstract

Two-phase bubbly flows are found in many industrial applications. These flows involve complex local phenomena that are still poorly understood. For instance, two-phase turbulence modelling is still commonly based on single-phase flow analyses. A direct numerical simulation (DNS) database is described here to improve the understanding of two-phase turbulent channel flow at a parietal Reynolds number of 127. Based on DNS results, a physical interpretation of the Reynolds stress and momentum budgets is proposed. First, surface tension is found to be the strongest force in the direction of migration so that budgets of the momentum equations suggest a significant impact of surface tension in the migration process, whereas most modelling used in industrial application does not include it. Besides, the suitability of the design of our cases to study the interaction between bubble-induced fluctuations (BIF) and single-phase turbulence (SPT) is shown. Budgets of the Reynolds stress transport equation computed from DNS reveal an interaction between SPT and BIF, revealing weaknesses in the classical way in which pseudoturbulence and perturbations to standard single-phase turbulence are modelled. An SPT reduction is shown due to changes in the diffusion because of the presence of bubbles. An increase of the redistribution leading to a more isotropic SPT has been observed as well. BIF is comprised of a turbulent (wake-induced turbulence, WIT) and a non-turbulent (wake-induced fluctuations, WIF) part which are statistically independent. WIF is related to averaged wake and potential flow, whereas WIT appears when wakes become unstable or interact with each other for high-velocity bubbles. In the present low gravity conditions, BIF is reduced to WIF only. A thorough analysis of the transport equations of the Reynolds stresses is performed in order to propose an algebraic closure for the WIF towards an innovative two-phase turbulence model.

JFM classification

Turbulent Flows: Turbulence modelling Turbulent Flows: Turbulence simulation
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 866 , 10 May 2019 , pp. 132 - 168
Copyright
© 2019 Cambridge University Press 

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References

Alméras, E., Mathai, V., Lohse, D. & Sun, C. 2017 Experimental investigation of the turbulence induced by a bubble swarm rising within incident turbulence. J. Fluid Mech. 825, 1091–1112.10.1017/jfm.2017.410Google Scholar
Alves, S. S., Orvalho, S. P. & Vasconcelos, J. M. 2005 Effect of bubble contamination on rise velocity and mass transfer. Chem. Engng Sci. 60 (1), 1–9.Google Scholar
Amoura, Z., Besnaci, C. & Risso, F. 2017 Velocity fluctuations generated by the flow through a random array of spheres: a model of bubble-induced agitation. J. Fluid Mech. 823, 592–616.10.1017/jfm.2017.347Google Scholar
Amoura, Z., Roig, V., Risso, F. & Billet, A.-M. 2010 Attenuation of the wake of a sphere in an intense incident turbulence with large length scales. Phys. Fluids 22, 055105.Google Scholar
Antal, S. P., Lahey, R. T. & Flaherty, J. E. 1991 Analysis of phase distribution in fully developed laminar bubbly two-phase flow. Intl J. Multiphase Flow 17 (5), 635–652.Google Scholar
Bertakis, E., Großss, S., Grande, J., Fortmeier, O., Reusken, A. & Pfennig, A. 2010 Validated simulation of droplet sedimentation with finite-element and level-set methods. Chem. Engng Sci. 65 (6), 2037–2051.Google Scholar
Biesheuvel, A. & Wijngaarden, L. V. 1984 Two-phase flow equations for a dilute dispersion of gas bubbles in liquid. J. Fluid Mech. 148, 301–318.Google Scholar
Bois, G. 2017 Direct numerical simulation of a turbulent bubbly flow in a vertical channel: towards an improved second-order Reynolds stress model. Nucl. Engng Des. 321, 92–103.Google Scholar
Bois, G., du Cluzeau, A., Toutant, A. & Martinez, J.-M. 2017 DNS of turbulent bubbly flows in plane channels using the front-tracking algorithm of TrioCFD. In Proceedings of the ASME Fluid Engineering Division Summer Meeting & Multiphase Flow Technical Committee, ASME.Google Scholar
Bois, G., Fauchet, G. & Toutant, A. 2016 DNS of a turbulent steam/water bubbly flow in a vertical channel. In Proceedings of the 9th International Conference on Multiphase Flows (ICMF2016), ICMF.Google Scholar
Bouche, E., Roig, V. & Risso, F. 2012 Homogeneous swarm of high-Reynolds-number bubbles rising within a thin gap. Part 1: bubble dynamics. J. Fluid Mech. 704, 211–231.Google Scholar
Bouche, E., Roig, V. & Risso, F. 2014 Homogeneous swarm of high-Reynolds-number bubbles rising within a thin gap. Part 2: liquid dynamics. J. Fluid Mech. 758, 508–521.Google Scholar
Chahed, J., Roig, V. & Masbernat, L. 2003 Eulerian–Eulerian two-fluid model for turbulent gas liquid bubbly flows. Intl J. Multiphase Flow 29, 23–49.Google Scholar
Chandesris, M. & Jamet, D. 2006 Boundary conditions at a planar fluid-porous interface for a Poiseuille flow. Intl J. Heat Mass Transfer 49 (13–14), 2137–2150.Google Scholar
Cisse, M., Saw, E. W., Gibert, M., Bodenschatz, E. & Bec, J. 2015 Turbulence attenuation by large neutrally buoyant particles. Phys. Fluids 27 (6), 1–7.Google Scholar
Colin, C., Fabre, J. & Kamp, A. 2012 Turbulent bubbly flow in pipe under gravity and microgravity conditions. J. Fluid Mech. 711, 469–515.Google Scholar
Colombo, M. & Fairweather, M. 2015 Multiphase turbulence in bubbly flows: RANS simulations. Intl J. Multiphase Flow 77, 222–243.Google Scholar
Dabiri, S. & Bhuvankar, P. 2016 Scaling law for bubbles rising near vertical walls. Phys. Fluids 28, 062101.Google Scholar
Dupuy, D., Toutant, A. & Bataille, F. 2018 Turbulence kinetic energy exchanges in flows with highly variable fluid properties. J. Fluid Mech. 834, 5–54.Google Scholar
Ervin, E. A. & Tryggvason, G. 1997 The rise of bubbles in a vertical shear flow. Trans ASME J. Fluids Engng 119 (2), 443–449.Google Scholar
Feng, X., Yang, C., Mao, Z.-S., Lu, J. & Tryggvason, G. 2018 Bubble induced turbulence model improved by direct numerical simulation of bubbly flow. Chem. Engng J. (in press).Google Scholar
Fujiwara, A., Minato, D. & Hishida, K. 2004 Effect of bubble diameter on modification of turbulence in an upward pipe flow. Intl J. Heat Fluid Flow 25 (3), 481–488.Google Scholar
Hosokawa, S., Suzuki, T. & Tomiyama, A. 2012 Turbulence kinetic energy budget in bubbly flows in a vertical duct. Exp. Fluids 52 (3), 719–728.Google Scholar
Hosokawa, S. & Tomiyama, A. 2013 Bubble-induced pseudo turbulence in laminar pipe flows. Intl J. Heat Fluid Flow 40, 97–105.Google Scholar
Ilic, M.2006 Statistical analysis of liquid phase turbulence based on direct numerical simulations of bubbly flows. PhD thesis.Google Scholar
Jeong, J. & Hussain, F. 1995 On the identification of a vortex. J. Fluid Mech. 285, 69–94.Google Scholar
Kataoka, I. 1986 Local instant formulation of two-phase flow. Intl J. Multiphase Flow 12 (5), 745–758.Google Scholar
Kataoka, I. & Serizawa, A. 1989 Basic equations of turbulence in gas-liquid two-phase flow. Intl J. Multiphase Flow 15 (5), 843–855.Google Scholar
Kim, J., Moin, P. & Moser, R. 1987 Turbulence statistics in fully developed channel flow at low Reynolds number. J. Fluid Mech. 177, 133–166.Google Scholar
Lance, M. & Bataille, J. 1991 Turbulence in the liquid phase of a uniform bubbly air–water flow. J. Fluid Mech. 222 (1358), 95–118.Google Scholar
Lance, M., Marie, J. L. & Bataille, J. 1991 Homogeneous turbulence in bubbly flows. J. Fluids Engng 113 (2), 295–300.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.Google Scholar
Laviéville, J., Mérigoux, N., Guingo, M., Baudry, C. & Mimouni, S. 2015 A generalized turbulent dispersion model for bubbly flow numerical simulation in NEPTUNE_CFD. In NURETH-16, pp. 4167–4181.Google Scholar
Lopez de Bertodano, M. A. 1998 Two fluid model for two-phase turbulent jets. Nucl. Engng Des. 179 (1), 65–74.Google Scholar
Lu, J., Biswas, S. & Tryggvason, G. 2006 A DNS study of laminar bubbly flows in a vertical channel. Intl J. Multiphase Flow 32 (6), 643–660.Google Scholar
Lu, J. & Tryggvason, G. 2008 Effect of bubble deformability in turbulent bubbly upflow in a vertical channel. Phys. Fluids 20, 040701.Google Scholar
Lubchenko, N., Magolan, B., Sugrue, R. & Baglietto, E. 2017 A more fundamental wall lubrication force from turbulent dispersion regularization for multiphase CFD applications. Intl J. Multiphase Flow 98, 36–44.Google Scholar
Mathieu, B.2003 Etudes physique, expérimentale et numérique des mécanismes de base intervenant dans les écoulements diphasiques en micro-fluidique. PhD thesis.Google Scholar
Mazzitelli, I. M., Lohse, D. & Toschi, F. 2003 The effect of microbubbles on developed turbulence. Phys. Fluids 15, L5.Google Scholar
Morel, C. 2015 Mathematical Modeling of Two-Phase Flow. Springer.Google Scholar
Olmos, E., Gentric, C. & Midoux, N. 2003 Numerical description of flow regime transitions in bubble column reactors by a multiple gas phase model. Chem. Engng Sci. 58 (10), 2113–2121.Google Scholar
Pakhomov, M. A. & Terekhov, V. I. 2015 Modeling of turbulent structure of an upward polydisperse gas–liquid flow. Fluid Dyn. 50 (2), 229–239.Google Scholar
Pfleger, D. & Becker, S. 2001 Modelling and simulation of the dynamic flow behaviour in a bubble column. Chem. Engng Sci. 56 (4), 1737–1747.Google Scholar
Puckett, E. G., Almgren, A. S., Bell, J. B., Marcus, D. L. & Rider, W. J. 1997 A high-order projection method for tracking fluid interfaces in variable density incompressible flows. J. Comput. Phys. 130, 269–282.Google Scholar
Reeks, M. W. 1991 On a kinetic equation for the transport of particles in turbulent flows. Phys. Fluids A 3 (3), 446–456.Google Scholar
Riboux, G. & Legendre, D. 2013 A model of bubble-induced turbulence based on large-scale wake interactions. J. Fluid Mech. 719, 362–387.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.Google Scholar
Richardson, L. F. 1911 The approximate arithmetical solution by finite differences of physical problems involving differential equations, with an application to the stresses in a masonry dam. Phil. Trans. R. Soc. Lond. A 210, 459–470.Google Scholar
Risso, F. 2016 Physical interpretation of probability density functions of bubble-induced agitation. J. Fluid Mech. 809, 240–263.Google Scholar
Risso, F. 2018 Agitation, mixing, and transfers induced by bubbles. Annu. Rev. Fluid Mech. 50, 25–48.Google Scholar
Risso, F. & Ellingsen, K. 2002 Velocity fluctuations in a homogeneous dilute dispersion of high-Reynolds-number rising bubbles. J. Fluid Mech. 453, 395–410.Google Scholar
Risso, F., Roig, V., Amoura, Z., Riboux, G. & Billet, A. M. 2008 Wake attenuation in large Reynolds number dispersed two-phase flows. Phil. Trans. R. Soc. Lond. A 366, 2177–2190.Google Scholar
Rzehak, R. & Krepper, E. 2013 Bubble-induced turbulence: comparison of CFD models. Nucl. Engng Des. 258, 57–65.Google Scholar
Santarelli, C. & Fröhlich, J. 2016 Direct numerical simulations of spherical bubbles in vertical turbulent channel flow. Influence of bubble size and bidispersity. Intl J. Multiphase Flow 81, 27–45.Google Scholar
Santarelli, C., Roussel, J. & Fröhlich, J. 2016 Budget analysis of the turbulent kinetic energy for bubbly flow in a vertical channel. Chem. Engng Sci. 141, 46–62.Google Scholar
Shawkat, M. E. & Ching, C. Y. 2011 Liquid turbulence kinetic energy budget of co-current bubbly flow in a large diameter vertical pipe. J. Fluids Engng 133 (9), 091303.Google Scholar
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.Google Scholar
Tomiyama, A., Tamai, H., Zun, I. & Hosokawa, S. 2002 Transverse migration of single bubbles in simple shear flows. Chem. Engng Sci. 57 (11), 1849–1858.Google Scholar
Toutant, A., Chandesris, M., Jamet, D. & Lebaigue, O. 2009a Jump conditions for filtered quantities at an under-resolved discontinuous interface. Part 1: theoretical development. Intl J. Multiphase Flow 35 (12), 1100–1118.Google Scholar
Toutant, A., Chandesris, M., Jamet, D. & Lebaigue, O. 2009b Jump conditions for filtered quantities at an under-resolved discontinuous interface. Part 2: a priori tests. Intl J. Multiphase Flow 35 (12), 1119–1129.Google Scholar
Toutant, A., Labourasse, E., Lebaigue, O. & Simonin, O. 2008 DNS of the interaction between a deformable buoyant bubble and a spatially decaying turbulence: a priori tests for LES two-phase flow modelling. Comput. Fluids 37 (7), 877–886.Google Scholar
Toutant, A., Mathieu, B. & Lebaigue, O. 2012 Volume-conserving mesh smoothing for front-tracking methods. Comput. Fluids 67, 16–25.Google Scholar
Troshko, A. A. & Hassan, Y. A. 2001 A two-equation turbulence model of turbulent bubbly flows. Intl J. Multiphase Flow 27 (11), 1965–2000.Google Scholar
Tryggvason, G., Bunner, B., Esmaeeli, A. & Al-Rawahi, N. 2003 Computations of multiphase flows. Adv. Appl. Mech. 39 (C), 81–120.Google Scholar
Tryggvason, G., Dabiri, S., Aboulhasanzadeh, B. & Lu, J. 2013 Multiscale considerations in direct numerical simulations of multiphase flows. Phys. Fluids 25, 031302.Google Scholar
Vaidheeswaran, A. & Hibiki, T. 2017 Bubble-induced turbulence modeling for vertical bubbly flows. Intl J. Heat Mass Transfer 115, 741–752.Google Scholar
Vreman, A. W. & Kuerten, J. G. M. 2014 Comparison of direct numerical simulation databases of turbulent channel flow at Re = 180. Phys. Fluids 26 (1), 015102.Google Scholar
Wilcox, D. 1993 Turbulence modeling for CFD. DCW Industries.Google Scholar
Williamson, J. H. 1980 Low-storage Runge–Kutta schemes. J. Comput. Phys. 35 (1), 48–56.Google Scholar