Physical Models

Physical Models#

This section will describe the various physical models available to use in TrioCFD.

References

[ABM16]

M. Abkar, H. J. Bae, and P. Moin. Minimum-dissipation scalar transport model for large-eddy simulation of turbulent flows. Physical Review Fluids, 1(4):041701, 2016.

[Almeras14]

Elise Alméras. Etude des propriétés de transport et de mélange dans les écoulements à bulles. phdthesis, Université de Toulouse, 12 2014. URL: https://oatao.univ-toulouse.fr/13925/.

[AL19]

P.-E. Angeli and N. Leterrier. Implémentation et validation du modèle de turbulence k-epsilon réalisable dans TrioCFD. Technical Report DEN/DANS/DM2S/STMF/LMSF/NT/2018-64015/A, CEA, 2019.

[ALF91]

S.P. Antal, R.T. Lahey, and J.E. Flaherty. Analysis of phase distribution in fully developed laminar bubbly two-phase flow. International Journal of Multiphase Flow, 17(5):635–652, 1991. URL: https://www.sciencedirect.com/science/article/pii/0301932291900293, doi:10.1016/0301-9322(91)90029-3.

[BH09]

A. Majid Bahari and Kourosh Hejazi. Investigation of buoyant parameters of $k$-ε turbulence model in gravity stratified flows. International Journal of Physical and Mathematical Sciences, 3(7):494–501, 2009. URL: https://publications.waset.org/vol/31.

[BFR80]

J. Bardina, J. Ferziger, and W. C. Reynolds. Improved subgrid-scale models for large-eddy simulation. In 13th Fluid and PlasmaDynamics Conference, 1357. 1980.

[BW84]

A. Biesheuvel and L. Van Wijngaarden. Two-phase flow equations for a dilute dispersion of gas bubbles in liquid. Journal of Fluid Mechanics, 148:301–318, 1984. doi:10.1017/S0022112084002366.

[BFHS04]

A. D. Burns, T. Frank, I. Hamill, and J.-M. Shi. The favre averaged drag model for turbulent dispersion in eulerian multi-phase flows. In 5th International Conference on Multiphase Flow. 2004.

[CM47]

Tchen Chan-Mou. Mean Value and Correlation Problems connected with the Motion of Small Particles suspended in a turbulent fluid. Springer - Science + Business Media, 1947.

[CYT08]

Sherman C. P. Cheung, G. H. Yeoh, and J. Y. Tu. Population balance modeling of bubbly flows considering the hydrodynamics and thermomechanical processes. AIChE Journal, 54(7):1689–1710, 2008. URL: https://aiche.onlinelibrary.wiley.com/doi/abs/10.1002/aic.11503, doi:10.1002/aic.11503.

[Chi82]

Kuei-Yuan Chien. Predictions of channel and boundary-layer flows with a low-reynolds-number turbulence model. AIAA Journal, 20(1):33–38, 1982. URL: https://doi.org/10.2514/3.51043, doi:10.2514/3.51043.

[CRF+21]

Marco Colombo, Roland Rzehak, Michael Fairweather, Yixiang Liao, and Dirk Lucas. Benchmarking of computational fluid dynamic models for bubbly flows. Nuclear Engineering and Design, 375:111075, 4 2021. URL: https://doi.org/10.1016/j.nucengdes.2021.111075, doi:10.1016/j.nucengdes.2021.111075.

[DD10]

A. K. Das and P. K. Das. Modelling bubbly flow and its transitions in vertical annuli using population balance technique. International Journal of Heat and Fluid Flow, 31(1):101–114, 2010. URL: https://doi.org/10.1016/j.ijheatfluidflow.2009.11.006, doi:10.1016/j.ijheatfluidflow.2009.11.006.

[Dav16]

Akshay J Dave. Interfacial Area Transport Equation Models and Validation against High Resolution Experimental Data for Small and Large Diameter Vertical Pipes by. PhD thesis, University of Michigan, 2016.

[dBLJ94]

M. Lopez de Bertodano, R.T. Lahey, and O.C. Jones. Phase distribution in bubbly two-phase flow in vertical ducts. International Journal of Multiphase Flow, 20(5):805–818, 1994. URL: https://www.sciencedirect.com/science/article/pii/0301932294900957, doi:10.1016/0301-9322(94)90095-7.

[dB98]

Martin A Lopez de Bertodano. Two fluid model for two-phase turbulent jets. Nuclear Engineering and Design, 179(1):65–74, 1998. URL: https://www.sciencedirect.com/science/article/pii/S0029549397002446, doi:10.1016/S0029-5493(97)00244-6.

[Dea70]

J. W. Deardorff. A numerical study of three-dimensional turbulent channel flow at large reynolds numbers. Journal of Fluid Mechanics, 41(2):453–480, 1970.

[dC19]

A. du Cluzeau. Modélisation physique de la dynamique des écoulements à bulles par remontée d'échelle à partir de simulations fines. phdthesis, Université de Perpignan Via Domitia, 10 2019.

[DTB16]

D. Dupuy, A. Toutant, and F. Bataille. Study of the sub-grid terms of the large-eddy simulation of a low Mach strongly anisothermal channel flow. In Eurotherm Seminar 106, Paris, France. 2016.

[DTB17]

D. Dupuy, A. Toutant, and F. Bataille. Étude de l'équation d'énergie pour le développement de modèles sous-mailles adaptés aux écoulements fortement anisothermes. In Congrès SFT, Marseille, France. 2017.

[DTB18]

D. Dupuy, A. Toutant, and F. Bataille. Study of the large-eddy simulation subgrid terms of a low mach number anisothermal channel flow. International Journal of Thermal Sciences, 135:221–234, 2018.

[FLB93]

Sixin Fan, Budugur Lakshminarayana, and Mark Barnett. Low-reynolds-number k-epsilon model for unsteady turbulent boundary-layer flows. AIAA Journal, 31(10):1777–1784, 1993. URL: https://doi.org/10.2514/3.11849, doi:10.2514/3.11849.

[FSCH22]

Foad Faraji, Christiano Santim, Perk Lin Chong, and Faik Hamad. Two-phase flow pressure drop modelling in horizontal pipes with different diameters. Nuclear Engineering and Design, 395:111863, 2022. URL: https://www.sciencedirect.com/science/article/pii/S0029549322002175, doi:10.1016/j.nucengdes.2022.111863.

[Fri79]

Lutz Friedel. Improved friction pressure drop correlations for horizontal and vertical two-phase pipe flow. In European two-phase group meeting, Ispra, Italy. 1979.

[FI02]

X. Y. Fu and M. Ishii. Two-group interfacial area transport in vertical air-water flow i. mechanistic model. Nuclear Engineering and Design, 219:143–168, 2002.

[GLMarie02]

C Garnier, M Lance, and J.L Marié. Measurement of local flow characteristics in buoyancy-driven bubbly flow at high void fraction. Experimental Thermal and Fluid Science, 26(6):811–815, 2002. URL: https://www.sciencedirect.com/science/article/pii/S089417770200198X, doi:10.1016/S0894-1777(02)00198-X.

[GPMC91]

M. Germano, U. Piomelli, P. Moin, and W. H. Cabot. A dynamic subgrid-scale eddy viscosity model. Physics of Fluids A: Fluid Dynamics, 3(7):1760–1765, 1991.

[GF14]

N. S. Ghaisas and S. H. Frankel. A priori evaluation of large eddy simulation subgrid-scale scalar flux models in isotropic passive-scalar and anisotropic buoyancy-driven homogeneous turbulence. J. Turbulence, 15(2):88–121, 2014.

[GF16]

N. S. Ghaisas and S. H. Frankel. Dynamic gradient models for the sub-grid scale stress tensor and scalar flux vector in large eddy simulation. Journal of Turbulence, 17(1):30–50, 2016.

[HI02]

Takashi Hibiki and Mamoru Ishii. Distribution parameter and drift velocity of drift-flux model in bubbly flow. International Journal of Heat and Mass Transfer, 45(4):707–721, 2002.

[Ish77]

Mamoru Ishii. One-dimensional drift-flux model and constitutive equations for relative motion between phases in various two-phase flow regimes. Technical Report, Argonne National Lab., Ill.(USA), 1977.

[IZ79]

Mamoru Ishii and Novak Zuber. Drag coefficient and relative velocity in bubbly, droplet or particulate flows. AIChE Journal, 25(5):843–855, 1979. URL: https://aiche.onlinelibrary.wiley.com/doi/abs/10.1002/aic.690250513, arXiv:https://aiche.onlinelibrary.wiley.com/doi/pdf/10.1002/aic.690250513, doi:10.1002/aic.690250513.

[JL72]

W.P Jones and B.E Launder. The prediction of laminarization with a two-equation model of turbulence. International Journal of Heat and Mass Transfer, 15(2):301–314, 1972. URL: http://www.sciencedirect.com/science/article/pii/0017931072900762, doi:10.1016/0017-9310(72)90076-2.

[KYN+12]

Isao Kataoka, Kenji Yoshida, Masanori Naitoh, Hidetoshi Okada, and Tadashi Morii. Modeling of turbulent transport term of interfacial area concentration in gas liquid two-phase flow. Nuclear Engineering and Design, 253:322–330, 12 2012. doi:10.1016/j.nucengdes.2011.08.062.

[Kob05]

H. Kobayashi. The subgrid-scale models based on coherent structures for rotating homogeneous turbulence and turbulent channel flow. Physics of Fluids, 17(4):045104, 2005.

[KHR94]

G. Kocamustafaogullari, W. D. Huang, and J. Razi. Measurement and modeling of average void fraction, bubble size and interfacial area. Nuclear Engineering and Design, 148(2-3):437–453, 1994. doi:10.1016/0029-5493(94)90124-4.

[KI94]

G. Kocamustafaogullari and M. Ishii. Foundation of the interfacial area transport equation and its closure relations. Int. J. Heat Mass Transfer 38, pages 481–493, 1994. doi:10.1016/0017-9310(94)00183-v.

[Kok99]

J.C. Kok. Resolving the dependence on free-stream values for the k-omega turbulence model. Technical Report NLR-TP-99295, National Aerospace Laboratory NLR, 1999.

[Kom20]

Ravikishore Kommajosyula. Development and assessment of a physics-based model forsubcooled flow boiling with application to CFD. PhD thesis, MIT, 2020.

[KR11]

Eckhard Krepper and Roland Rzehak. Cfd for subcooled flow boiling: simulation of debora experiments. Nuclear Engineering and Design, 241(9):3851–3866, 2011. Seventh European Commission conference on Euratom research and training in reactor systems (Fission Safety 2009). URL: https://www.sciencedirect.com/science/article/pii/S0029549311005401, doi:10.1016/j.nucengdes.2011.07.003.

[KW88]

J.T. Kuo and G.B. Wallis. Flow of bubbles through nozzles. International Journal of Multiphase Flow, 14(5):547–564, 1988. URL: https://www.sciencedirect.com/science/article/pii/0301932288900572, doi:10.1016/0301-9322(88)90057-2.

[Kur91]

N Kurul. On the modeling of multidimensional effects in boiling channels. ANS. Proc. National Heat Transfer Con. Minneapolis, Minnesota, USA, 1991, 1991.

[LB81]

C.K.G. Lam and K. Bremhorst. A Modified Form of the $k$-ε Model for Predicting Wall Turbulence. Journal of Fluids Engineering, 103(3):456–460, 09 1981. URL: https://doi.org/10.1115/1.3240815, doi:10.1115/1.3240815.

[LS74a]

B.E. Launder and B.I. Sharma. Application of the energy-dissipation model of turbulence to the calculation of flow near a spinning disc. Letters in Heat and Mass Transfer, 1(2):131–137, 1974. URL: http://www.sciencedirect.com/science/article/pii/0094454874901507, doi:10.1016/0094-4548(74)90150-7.

[LS74b]

B.E. Launder and D.B. Spalding. The numerical computation of turbulent flows. Computer Methods in Applied Mechanics and Engineering, 3(2):269–289, 1974. URL: http://www.sciencedirect.com/science/article/pii/0045782574900292, doi:10.1016/0045-7825(74)90029-2.

[Leo74]

A. Leonard. Energy cascade in large eddy simulations of turbulent fluid flows. Advances in Geophysics, 18A:237–248, 1974.

[LLKS11]

Yixiang Liao, Dirk Lucas, Eckhard Krepper, and Martin Schmidtke. Development of a generalized coalescence and breakup closure for the inhomogeneous musig model. Nuclear Engineering and Design, 241(4):1024–1033, 2011. URL: https://doi.org/10.1016/j.nucengdes.2010.04.025, doi:10.1016/j.nucengdes.2010.04.025.

[Lil92]

D. K. Lilly. A proposed modification of the germano subgrid-scale closure method. Physics of Fluids A: Fluid Dynamics, 4(3):633–635, 1992.

[LF56]

PA Lottes and WS Flinn. A method of analysis of natural circulation boiling systems. Nuclear Science and Engineering, 1(6):461–476, 1956.

[LMSB18]

Nazar Lubchenko, Ben Magolan, Rosie Sugrue, and Emilio Baglietto. A more fundamental wall lubrication force from turbulent dispersion regularization for multiphase cfd applications. International Journal of Multiphase Flow, 98:36–44, 1 2018. doi:10.1016/j.ijmultiphaseflow.2017.09.003.

[MGLavieville+16]

O. Marfaing, M. Guingo, J. Laviéville, G. Bois, N. Méchitoua, N. Mérigoux, and S. Mimouni. An analytical relation for the void fraction distribution in a fully developed bubbly flow in a vertical pipe. Chemical Engineering Science, 152:579–585, 2016. URL: https://www.sciencedirect.com/science/article/pii/S0009250916303372, doi:10.1016/j.ces.2016.06.041.

[MKL03]

F. R. Menter, M. Kuntz, and R. Langtry. Ten years of industrial experience with the sst turbulence model. In Turbulence, Heat and Mass Transfer 4. 2003.

[Men93]

Florian R. Menter. Zonal two equation k-cl, turbulence models for aerodynamic flows. In American Institute of Aeronautics and Astronautics 24th Fluid Dynamics Conference. American Institute of Aeronautics and Astronautics, 1993. AlAA 93-2906.

[MDN+99]

R.C. Morgans, B.B. Dally, G.J. Nathan, P.V. Lanspeary, and D.F. Fletcher. Application of the revised wilcox (1998) $k$-ω turbulence model to a jet in co-flow. In Second International Conference on CFD in the Minerals and Process Industries CSIRO, Melbourne, Australia, 6-8 December. 1999.

[MullerSH86]

H Müller-Steinhagen and K Heck. A simple friction pressure drop correlation for two-phase flow in pipes. Chemical Engineering and Processing: Process Intensification, 20(6):297–308, 1986. URL: https://www.sciencedirect.com/science/article/pii/0255270186800083, doi:10.1016/0255-2701(86)80008-3.

[ND99]

F. Nicoud and F. Ducros. Subgrid-scale stress modelling based on the square of the velocity gradient tensor. Flow, Turbulence and Combustion, 62(3):183–200, Sep 1999. URL: https://doi.org/10.1023/A:1009995426001, doi:10.1023/A:1009995426001.

[NBayaTodaC+11]

F. Nicoud, H. Baya Toda, O. Cabrit, S. Bose, and J. Lee. Using singular values to build a subgrid-scale model for large eddy simulations. Physics of Fluids, 23(8):085106, 2011.

[Pao82]

S. Paolucci. Filtering of sound from the Navier-Stokes equations. NASA STI/Recon Technical Report N, 1982.

[Pap19]

Miltiadis Papalexandris. On the applicability of stokes' hypothesis to low-mach-number flows. Continuum Mechanics and Thermodynamics, 05 2019. doi:10.1007/s00161-019-00785-z.

[PLLC06]

N. Park, S. Lee, J. Lee, and H. Choi. A dynamic subgrid-scale eddy viscosity model with a global model coefficient. Physics of Fluids, 18(12):125109, 2006.

[RH23]

Somboon Rassame and Takashi Hibiki. Modeling of turbulent diffusion terms for one-dimensional interfacial area transport equation in vertical round channels. Progress in Nuclear Energy, 157:104568, 3 2023. doi:10.1016/j.pnucene.2023.104568.

[Ris18]

Frédéric Risso. Agitation, mixing, and transfers induced by bubbles. Annual Review of Fluid Mechanics, 50(1):25–48, 1 2018. URL: https://doi.org/10.1146/annurev-fluid-122316-045003, doi:10.1146/annurev-fluid-122316-045003.

[RBMV15]

W. Rozema, H.J. Bae, P. Moin, and R. Verstappen. Minimum-dissipation models for large-eddy simulation. Physics of Fluids, 27(8):085107, 2015.

[RI00]

Henrik Rusche and Raad Issa. The effect of voidage on the drag force on particles in dispersed two-phase flow. Japanese European Two-Phase Flow Meeting, 12 2000.

[RI14]

S. Ryu and G. Iaccarino. A subgrid-scale eddy-viscosity model based on the volumetric strain-stretching. Physics of Fluids, 26(6):065107, 2014.

[RK13a]

Roland Rzehak and Eckhard Krepper. Closure models for turbulent bubbly flows: a cfd study. Nuclear Engineering and Design, 265:701–711, 12 2013. URL: http://dx.doi.org/10.1016/j.nucengdes.2013.09.003, doi:10.1016/j.nucengdes.2013.09.003.

[RK13b]

Roland Rzehak and Eckhard Krepper. CFD modeling of bubble-induced turbulence. International Journal of Multiphase Flow, 55:138–155, 2013. URL: https://www.sciencedirect.com/science/article/pii/S0301932213000633 (visited on 2024-02-23), doi:10.1016/j.ijmultiphaseflow.2013.04.007.

[RK15]

Roland Rzehak and Sebastian Kriebitzsch. Multiphase CFD-simulation of bubbly pipe flow: a code comparison. International Journal of Multiphase Flow, 68:135–152, 1 2015. URL: https://doi.org/10.1016/j.ijmultiphaseflow.2014.09.005, doi:10.1016/j.ijmultiphaseflow.2014.09.005.

[SSS81]

Y. Sato, M. Sadatomi, and K. Sekoguchi. Momentum and heat transfer in two-phase bubble flow—i. theory. International Journal of Multiphase Flow, 7(2):167–177, 4 1981. URL: https://doi.org/10.1016/0301-9322(81)90003-3, doi:10.1016/0301-9322(81)90003-3.

[Sch08]

Roland Schiestel. Modeling and Simulation of Turbulent Flows. Wiley, 1 2008. ISBN 9780470610848. URL: https://doi.org/10.1002/9780470610848, doi:10.1002/9780470610848.

[SHI15]

J.P. Schlegel, T. Hibiki, and M. Ishii. Two-group modeling of interfacial area transport in large diameter channels. Nuclear Engineering and Design 293, pages 75–86, 2015. doi:10.1016/j.nucengdes.2015.07.011.

[SLS+95]

Tsan-Hsing Shih, William W. Liou, Aamir Shabbir, Zhigang Yang, and Jiang Zhu. A new $k$-ε eddy viscosity model for high reynolds number turbulent flows. Computers & Fluids, 24(3):227–238, 1995. doi:10.1016/0045-7930(94)00032-T.

[SGOM07]

M. Simonnet, C. Gentric, E. Olmos, and N. Midoux. Experimental determination of the drag coefficient in a swarm of bubbles. Chemical Engineering Science, 62(3):858–866, 2007. URL: https://www.sciencedirect.com/science/article/pii/S0009250906006622, doi:10.1016/j.ces.2006.10.012.

[Sma63]

J. Smagorinsky. General circulation experiments with the primitive equations: i. the basic experiment. Monthly weather review, 91(3):99–164, 1963.

[SSHI12]

T.R. Smith, J.P. Schlegel, T. Hibiki, and M. Ishii. Mechanistic modeling of interfacial area transport in large diameter pipes. International Journal of Multiphase Flow, 47:1–16, 2012. doi:10.1016/j.ijmultiphaseflow.2012.06.009.

[SB97]

P.D.M. Spelt and A. Biesheuvel. Dispersion of gas bubbles in large-scale homogeneous isotropic turbulence. Applied Scientific Research, 58(1):463–482, 1997. doi:10.1023/A:1000820810732.

[SSCV21]

L. B. Streher, M. H. Silvis, P. Cifani, and R. W. C. P. Verstappen. Mixed modeling for large-eddy simulation: The single-layer and two-layer minimum-dissipation-Bardina models. AIP Advances, 11(1):015002, 2021.

[Sug17]

Rosemary Sugrue. A Robust Momentum Closure Approach for Multiphase Computational Fluid Dynamics Applications. PhD thesis, MIT, 2017.

[SKIB04]

X. Sun, S. Kim, M. Ishii, and S.G. Beus. Modeling of bubble coalescence and disintegration in confined upward two-phase flow. Nuclear Engineering and Design, 230(1):3–26, 2004. 11th International Conference on Nuclear Energy. doi:10.1016/j.nucengdes.2003.10.008.

[Sut93]

William Sutherland. The viscosity of gases and molecular force. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 36(223):507–531, 1893.

[TKZS98]

Akio Tomiyama, Isao Kataoka, Iztok Zun, and Tadashi Sakaguchi. Drag coefficients of single bubbles under normal and micro gravity conditions. JSME International Journal Series B Fluids and Thermal Engineering, 1998.

[TTZH02]

Akio Tomiyama, Hidesada Tamai, Iztok Zun, and Shigeo Hosokawa. Transverse migration of single bubbles in simple and shear flows. Chemical Engineering Science, 57:1849–1858, 2002.

[TGS+17]

F. X. Trias, A. Gorobets, M. H. Silvis, R. W. C. P Verstappen, and A. Oliva. A new subgrid characteristic length for turbulence simulations on anisotropic grids. Physics of Fluids, 29(11):115109, 2017.

[Vre04]

A. W. Vreman. An eddy-viscosity subgrid-scale model for turbulent shear flow: algebraic theory and applications. Physics of fluids, 16(10):3670–3681, 2004.

[Wal70]

G. B. Wallis. Annular two-phase flow-part 1: a simple theory. Journal of Basic Engineering, 92(1):59–72, 3 1970. URL: https://doi.org/10.1115/1.3424950, arXiv:https://asmedigitalcollection.asme.org/fluidsengineering/article-pdf/92/1/59/5621709/59\_1.pdf, doi:10.1115/1.3424950.

[WWJ05]

Tiefeng Wang, Jinfu Wang, and Yong Jin. Theoretical prediction of flow regime transition in bubble columns by the population balance model. Chemical Engineering Science, 60(22):6199–6209, 2005. doi:10.1016/j.ces.2005.04.027.

[WTSS10]

M. Weickert, G. Teike, O. Schmidt, and M. Sommerfeld. Investigation of the LES WALE turbulence model within the lattice boltzmann framework. Computers & Mathematics with Applications, 59(7):2200–2214, 2010. Mesoscopic Methods in Engineering and Science. URL: http://www.sciencedirect.com/science/article/pii/S089812210900652X, doi:10.1016/j.camwa.2009.08.060.

[YM04]

Wei Yao and Christophe Morel. Volumetric interfacial area prediction in upward bubbly two-phase flow. International Journal of Heat and Mass Transfer, 47(2):307–328, 2004. URL: https://www.sciencedirect.com/science/article/pii/S0017931003004320, doi:10.1016/j.ijheatmasstransfer.2003.06.004.

[Yos86]

A. Yoshizawa. Statistical theory for compressible turbulent shear flows, with the application to subgrid modeling. Physics of Fluids, 29(7):2152–2164, 1986.

[ZKS01]

R. Zenit, D.L. Koch, and A.S Sangani. Measurements of the average proprieties of a suspension of bubbles rising in a vertical channel. Journal of Fluid Mechanics, 429:307–342, 2001. doi:10.1017/S0022112000002743.

[ZHG+21]

Pei Zhou, Shiyang Hua, Cai Gao, Dongfang Sun, and Ronghua Huang. A mechanistic model for wall heat flux partitioning based on bubble dynamics during subcooled flow boiling. International Journal of Heat and Mass Transfer, 174:121–295, 2021. URL: https://www.sciencedirect.com/science/article/pii/S0017931021003987, doi:10.1016/j.ijheatmasstransfer.2021.121295.

[Zub64]

N. Zuber. On the dispersed two-phase flow in the laminar flow regime. Chemical Engineering Science, 19(11):897–917, 1964. URL: https://www.sciencedirect.com/science/article/pii/0009250964850673, doi:10.1016/0009-2509(64)85067-3.