Modeling of bubble-column flows with quadrature-based moment methods
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Vikas et al. [307] implemented QMOM in a two-way coupled solver, solving incompressible Navier-Stokes equations for the liquid phase and moment transport equations for the dispersed bubble phase for a two-dimensional bubble column with different gas flow rates, observing a meandering behavior of the bubble plume.
“Vikas et al. [307] implemented the QMOM in a two-way coupled solver. The authors solved the incompressible NavierStokes equations for the liquid phase and moment transport equations for the dispersed bubble phase for the case of a two-dimensional bubble column with different gas flow rates, observing a meandering behavior of the bubble plume.”
From Modeling and Simulation of Photobioreactors with Computational Fluid Dynamics—A Comprehensive Review (2022) · cites this paper as [307]
Cites
Numerical Heat Transfer and Fluid Flow
Patankar, S. V. (2018) · CRC Press eBooks · doi:10.1201/9781482234213 · Cited by 23,406 · see citing works
Numerical Heat Transfer and Fluid Flow
Hsu, C. (1981) · Nuclear Science and Engineering · doi:10.13182/nse81-a20112 · Cited by 15,200 · see citing works
Bhatnagar, P. L., Gross, E. P., & Krook, M. (1954) · Physical Review · doi:10.1103/physrev.94.511 · Cited by 8,663 · see citing works
Molecular Gas Dynamics And The Direct Simulation Of Gas Flows
Bird, G. A. (1994) · doi:10.1093/oso/9780198561958.001.0001 · Cited by 7,269 · see citing works
Equation of State for Nonattracting Rigid Spheres
Carnahan, N. F., & Starling, K. E. (1969) · The Journal of Chemical Physics · doi:10.1063/1.1672048 · Cited by 5,250 · see citing works
Numerical study of the turbulent flow past an airfoil with trailing edge separation
Rhie, C. M., & Chow, W. L. (1983) · AIAA Journal · doi:10.2514/3.8284 · Cited by 4,484 · see citing works
The design and application of upwind schemes on unstructured meshes
Barth, T. J., & Jespersen, D. C. (1989) · AIAA Aerospace Sciences Meeting · doi:10.2514/6.1989-366 · Cited by 2,250 · see citing works
The Mathematical Theory of Dilute Gases
Cercignani, C., Illner, R., & Pulvirenti, M. (1994) · Applied mathematical sciences · doi:10.1007/978-1-4419-8524-8 · Cited by 1,451 · see citing works
A Drag Coefficient Correlation
Schiller, L. (1933) · Medical Entomology and Zoology · Cited by 1,350 · see citing works
Convergence to Steady State Solutions of the Euler Equations on Unstructured Grids with Limiters
Venkatakrishnan, V. (1995) · Journal of Computational Physics · doi:10.1006/jcph.1995.1084 · Cited by 989 · see citing works
Drag Coefficients of Single Bubbles under Normal and Micro Gravity Conditions
TOMIYAMA, A., KATAOKA, I., ZUN, I., & SAKAGUCHI, T. (1998) · JSME International Journal Series B · doi:10.1299/jsmeb.41.472 · Cited by 742 · see citing works
The force exerted on a body in inviscid unsteady non-uniform rotational flow
Auton, T. R., Hunt, J. C. R., & Prud'Homme, M. (1988) · Journal of Fluid Mechanics · doi:10.1017/s0022112088003246 · Cited by 650 · see citing works
Liquid velocity distribution in two-phase bubble flow
Yoshifusa, S. A. T. O., & SEKOGUCHI, K. (1975) · International Journal of Multiphase Flow · doi:10.1016/0301-9322(75)90030-0 · Cited by 596 · see citing works
The lift force on a spherical body in a rotational flow
Auton, T. R. (1987) · Journal of Fluid Mechanics · doi:10.1017/s002211208700260x · Cited by 544 · see citing works
A PRESSURE-BASED METHOD FOR UNSTRUCTURED MESHES
Mathur, S., & Murthy, J. Y. (1997) · Numerical Heat Transfer Part B Fundamentals · doi:10.1080/10407799708915105 · Cited by 473 · see citing works
Macroscopic Transport Equations for Rarefied Gas Flows
Struchtrup, H. (2005) · Interaction of mechanics and mathematics · doi:10.1007/3-540-32386-4 · Cited by 463 · see citing works
Demirdžić, I., & Muzaferija, S. (1995) · Computer Methods in Applied Mechanics and Engineering · doi:10.1016/0045-7825(95)00800-g · Cited by 367 · see citing works
Dynamic simulation of dispersed gas-liquid two-phase flow using a discrete bubble model
Delnoij, E., Lammers, F. A., Kuipers, J. A. M., & van Swaaij, W. P. M. (1997) · Chemical Engineering Science · doi:10.1016/s0009-2509(96)00515-5 · Cited by 314 · see citing works
Macroscopic transport equations for rarefied gas flows
Struchtrup, H. (2005) · Interaction of mechanics and mathematics · doi:10.1007/3-540-32386-4_9 · Cited by 306 · see citing works
Averaged Equations for Two‐Phase Flows
Drew, D. A., & Segel, L. A. (1971) · Studies in Applied Mathematics · doi:10.1002/sapm1971503205 · Cited by 271 · see citing works
Sokolichin, A., & Eigenberger, G. (1994) · Chemical Engineering Science · doi:10.1016/0009-2509(94)00289-4 · Cited by 239 · see citing works
Conditional quadrature method of moments for kinetic equations
Yuan, C., & Fox, R. O. (2011) · Journal of Computational Physics · doi:10.1016/j.jcp.2011.07.020 · Cited by 232 · see citing works
Self-citationExperimental characterization of the agitation generated by bubbles rising at high Reynolds number
Riboux, G., Risso, F., & Legendre, D. (2009) · Journal of Fluid Mechanics · doi:10.1017/s0022112009992084 · Cited by 210 · see citing works
A quadrature-based moment method for dilute fluid-particle flows
Desjardins, O., Fox, R. O., & Villedieu, P. (2007) · Journal of Computational Physics · doi:10.1016/j.jcp.2007.10.026 · Cited by 197 · see citing works
Self-citationSecond-Order Boltzmann Schemes for Compressible Euler Equations in One and Two Space Dimensions
Benoît Perthame, B. (1992) · SIAM Journal on Numerical Analysis · doi:10.1137/0729001 · Cited by 185 · see citing works
Numerical simulation of the dynamics of two-phase gas—liquid flows in bubble columns
Lapin, A., & Lübbert, A. (1994) · Chemical Engineering Science · doi:10.1016/0009-2509(94)e0121-6 · Cited by 181 · see citing works
A quadrature-based third-order moment method for dilute gas-particle flows
Fox, R. O. (2008) · Journal of Computational Physics · doi:10.1016/j.jcp.2008.03.014 · Cited by 149 · see citing works
Self-citationModelling of slurry reactors. A fundamental approach
Torvik, R., & Svendsen, H. F. (1990) · Chemical Engineering Science · doi:10.1016/0009-2509(90)80112-r · Cited by 135 · see citing works
A Quadtree-based adaptive Cartesian/Quad grid flow solver for Navier-Stokes equations
Wang, Z. J. (1998) · Computers & Fluids · doi:10.1016/s0045-7930(97)00070-4 · Cited by 108 · see citing works
Self-citationRealizable high-order finite-volume schemes for quadrature-based moment methods
Vikas, V., Wang, Z. J., Passalacqua, A., & Fox, R. O. (2011) · Journal of Computational Physics · doi:10.1016/j.jcp.2011.03.038 · Cited by 98 · see citing works
Self-citationChaotic flow in bubble column reactors
Devanathan, N., Duduković, M. P., Lapin, A., & Lübbert, A. (1995) · Chemical Engineering Science · doi:10.1016/0009-2509(95)00070-l · Cited by 92 · see citing works
Investigations and modelling of bubble columns
Grienberger, J., & Hofmann, H. (1992) · Chemical Engineering Science · doi:10.1016/0009-2509(92)87037-q · Cited by 87 · see citing works
Higher-order quadrature-based moment methods for kinetic equations
Fox, R. O. (2009) · Journal of Computational Physics · doi:10.1016/j.jcp.2009.07.018 · Cited by 84 · see citing works
Self-citationA fully coupled quadrature-based moment method for dilute to moderately dilute fluid–particle flows
Passalacqua, A., Fox, R. O., Garg, R., & Subramaniam, S. (2009) · Chemical Engineering Science · doi:10.1016/j.ces.2009.09.002 · Cited by 74 · see citing works
Self-citationOptimal Moment Sets for Multivariate Direct Quadrature Method of Moments
Fox, R. O. (2008) · Industrial & Engineering Chemistry Research · doi:10.1021/ie801316d · Cited by 62 · see citing works
Self-citationProperties and Averaged Equations for Flows of Bubbly Liquids
SPELT, P. D. M., & Sangani, A. S. (1998) · Fluid mechanics and its applications · doi:10.1007/978-94-011-4986-0_19 · Cited by 60 · see citing works
Solving the kinetic equation for all Knudsen numbers
Beylich, A. E. (2000) · Physics of Fluids · doi:10.1063/1.870322 · Cited by 55 · see citing works
Flow in bubble columns: some numerical experiments
Ranade, V. V. (1992) · Chemical Engineering Science · doi:10.1016/0009-2509(92)80304-u · Cited by 47 · see citing works
Quadrature-Based Moment Model for Moderately Dense Polydisperse Gas−Particle Flows
Fox, R. O., & Vedula, P. (2009) · Industrial & Engineering Chemistry Research · doi:10.1021/ie9013138 · Cited by 47 · see citing works
Self-citationDense particulate flow model on unstructured mesh
Wu, C. L., Zhan, J. M., Li, Y. S., & Lam, K. S. (2006) · Chemical Engineering Science · doi:10.1016/j.ces.2006.04.033 · Cited by 41 · see citing works
PRESSURE BOUNDARY CONDITIONS FOR INCOMPRESSIBLE FLOW USING UNSTRUCTURED MESHES
Mathur, S., & Murthy, J. Y. (1997) · Numerical Heat Transfer Part B Fundamentals · doi:10.1080/10407799708915010 · Cited by 39 · see citing works
A Discrete Particle Model for Bubble-Slug Two-Phase Flows
Trapp, J. A., & Mortensen, G. A. (1993) · Journal of Computational Physics · doi:10.1006/jcph.1993.1151 · Cited by 38 · see citing works
Tomiyama, A., Matsuoka, T., Fukuda, T., & Sakaguchi, T. (1995) · Elsevier eBooks · doi:10.1016/b978-0-444-81811-9.50026-3 · Cited by 35 · see citing works
Advanced continuum modelling of gas-particle flows beyond the hydrodynamic limit
Passalacqua, A., & Fox, R. O. (2010) · Applied Mathematical Modelling · doi:10.1016/j.apm.2010.09.038 · Cited by 35 · see citing works
Self-citationComputational fluid dynamics simulation of bioreactors
Hjertager, B. H., & Morud, K. E. (1995) · Modeling Identification and Control A Norwegian Research Bulletin · doi:10.4173/mic.1995.4.1 · Cited by 27 · see citing works
Development of High-Order Realizable Finite-Volume Schemes for Quadrature-Based Moment Method
Vikas, V., Wang, Z. J., Fox, R. O., & Passalacqua, A. (2010) · AIAA Aerospace Sciences Meeting · doi:10.2514/6.2010-1080 · Cited by 9 · see citing works
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Self-citationMultivariate Quadrature-Based Moments Methods for turbulent polydisperse gas-liquid systems
Buffo, A., Vanni, M., Marchisio, D. L., & Fox, R. O. (2013) · International Journal of Multiphase Flow · doi:10.1016/j.ijmultiphaseflow.2012.09.005 · Cited by 96 · see citing works
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Modeling and Simulation of Photobioreactors with Computational Fluid Dynamics—A Comprehensive Review
Luzi, G., & McHardy, C. (2022) · Energies · doi:10.3390/en15113966 · Cited by 44 · see citing works
Modeling of bubble coalescence and break-up in turbulent bubbly flow
Mukin, R. V. (2014) · International Journal of Multiphase Flow · doi:10.1016/j.ijmultiphaseflow.2014.02.008 · Cited by 45 · see citing works
Mazzei, L., Marchisio, D. L., & Lettieri, P. (2011) · AIChE Journal · doi:10.1002/aic.13714 · Cited by 41 · see citing works
Simulation of a reacting gas–liquid bubbly flow with CFD and PBM: Validation with experiments
Buffo, A., Vanni, M., & Marchisio, D. L. (2016) · Applied Mathematical Modelling · doi:10.1016/j.apm.2016.11.010 · Cited by 37 · see citing works
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Heylmun, J. C., Kong, B., Passalacqua, A., & Fox, R. O. (2019) · Computer Physics Communications · doi:10.1016/j.cpc.2019.06.005 · Cited by 30 · see citing works
Self-citationDürr, R., & Bück, A. (2020) · Processes · doi:10.3390/pr8040414 · Cited by 28 · see citing works
Sommerfeld, M., Muniz, M., & Reichardt, T. (2018) · JOURNAL OF CHEMICAL ENGINEERING OF JAPAN · doi:10.1252/jcej.17we277 · Cited by 25 · see citing works
An extended quadrature-based mass-velocity moment model for polydisperse bubbly flows
Yuan, C., Kong, B., Passalacqua, A., & Fox, R. O. (2014) · The Canadian Journal of Chemical Engineering · doi:10.1002/cjce.22006 · Cited by 23 · see citing works
Self-citationRaimundo, P. M., Cartellier, A. H., Beneventi, D., Forret, A., & Augier, F. (2016) · Chemical Engineering Science · doi:10.1016/j.ces.2016.08.041 · Cited by 22 · see citing works
Mishra, S., Kumar, V., Sarkar, J., & Rathore, A. S. (2022) · Chemical Engineering Science · doi:10.1016/j.ces.2022.118323 · Cited by 21 · see citing works
A second-order realizable scheme for moment advection on unstructured grids
Passalacqua, A., Laurent, F., & Fox, R. O. (2019) · Computer Physics Communications · doi:10.1016/j.cpc.2019.106993 · Cited by 16 · see citing works
Self-citationEffect of particle stress tensor in simulations of dense gas–particle flows in fluidized beds
Haghgoo, M. R., Bergstrom, D. J., & Spiteri, R. J. (2017) · Particuology · doi:10.1016/j.partic.2017.04.010 · Cited by 12 · see citing works
Zarepour, M., Bergstrom, D. J., Zhang, L., & Spiteri, R. J. (2024) · International Journal of Heat and Fluid Flow · doi:10.1016/j.ijheatfluidflow.2024.109354 · Cited by 9 · see citing works
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Fox, R. O. (2018) · Advances in chemical engineering · doi:10.1016/bs.ache.2018.01.001 · Cited by 8 · see citing works
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Turbulence in Multiphase Flows
Fox, R. O. (2016) · Springer eBooks · doi:10.1007/978-981-4585-86-6_2-1 · Cited by 3 · see citing works
Self-citationChen, X., Li, H., Liu, Y., Yang, H., Zhang, X., Qiu, X., Zhang, S., Lei, Q., & Luo, P. (2025) · Chemical Engineering Science · doi:10.1016/j.ces.2025.122708 · Cited by 1 · see citing works
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Fox, R. O. (2023) · Springer eBooks · doi:10.1007/978-981-287-092-6_2 · Cited by 1 · see citing works
Self-citationCheng, T., Zhang, Y., Hong, Q., Zhang, D., & Kong, B. (2025) · Chemical Engineering Science · doi:10.1016/j.ces.2025.122759
- Authors
- Vikas, V., Yuan, C., Wang, Z. J., & Fox, R. O.
- Affiliations
- Iowa State University (US)
- Corresponding author
- Fox, R.O.
- ORCID
- Venue
- Chemical Engineering Science
- Publisher
- Elsevier BV
- Published
- 2011-07
- Volume
- 66
- Issue
- 14
- Pages
- 3058-3070
- ISSN
- 0009-2509 (ISSN-L)
- OpenAlex
- W2005002502
- Cited by
- 23
- References
- 47
- Citations by year
- 2025: 2 · 2024: 1 · 2023: 1 · 2022: 2 · 2020: 2 · 2019: 2 · 2018: 2 · 2017: 1 · 2016: 4 · 2014: 2 · 2013: 1 · 2012: 1
- FWCI
- 1.14
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Chemical Engineering Science (publishedVersion)
- Funders
- National Science Foundation
- Topics
- Physical Sciences › Engineering › Biomedical Engineering › Fluid Dynamics and Mixing
- Physical Sciences › Engineering › Ocean Engineering › Particle Dynamics in Fluid Flows
- Physical Sciences › Engineering › Computational Mechanics › Fluid Dynamics and Heat Transfer
- Keywords
- bubble column, quadrature-based moment methods, two-way coupling, dispersed two-phase flow, incompressible Navier-Stokes equations, gas flow rate effects
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