A seven-equation diffused interface method for resolved multiphase flows
References
[1]
A.H. Lefebvre, Gas Turbine Combustion, CRC Press, 1998.
[2]
G.P. Sutton, History of Liquid Propellant Rocket Engines, AIAA, 2006.
[3]
C.M. Tarver, S.K. Chidester, A.L. Nichols, Critical conditions for impact-and shock-induced hot spots in solid explosives, J. Phys. Chem. 100 (1996) 5794–5799.
[4]
R. Vehring, Pharmaceutical particle engineering via spray drying, Pharm. Res. 25 (2008) 999–1022.
[5]
M. Gorokhovski, M. Herrmann, Modeling primary atomization, Annu. Rev. Fluid Mech. 40 (2008) 343–366.
[6]
R. Saurel, C. Pantano, Diffuse-interface capturing methods for compressible two-phase flows, Annu. Rev. Fluid Mech. 50 (2018) 105–130.
[7]
S. Balachandar, J.K. Eaton, Turbulent dispersed multiphase flow, Annu. Rev. Fluid Mech. 42 (2010) 111–133.
[8]
A. Panchal, S. Menon, A hybrid Eulerian-Eulerian/Eulerian-Lagrangian method for dense-to-dilute dispersed phase flows, J. Comput. Phys. 439 (2021).
[9]
S.H. Bryngelson, K. Schmidmayer, T. Colonius, A quantitative comparison of phase-averaged models for bubbly, cavitating flows, Int. J. Multiph. Flow 115 (2019) 137–143.
[10]
Bryngelson, S.H.; Fox, R.O.; Colonius, T. (2021): Conditional moment methods for polydisperse cavitating flows. arXiv preprint arXiv:2112.14172.
[11]
J.A. Sethian, P. Smereka, Level set methods for fluid interfaces, Annu. Rev. Fluid Mech. 35 (2003) 341–372.
[12]
M. Sussman, K.M. Smith, M.Y. Hussaini, M. Ohta, R. Zhi-Wei, A sharp interface method for incompressible two-phase flows, J. Comput. Phys. 221 (2007) 469–505.
[13]
C.W. Hirt, B.D. Nichols, Volume of fluid (VOF) method for the dynamics of free boundaries, J. Comput. Phys. 39 (1981) 201–225.
[14]
M. Sussman, E.G. Puckett, A coupled level set and volume-of-fluid method for computing 3d and axisymmetric incompressible two-phase flows, J. Comput. Phys. 162 (2000) 301–337.
[15]
J. Brackbill, D.B. Kothe, C. Zemach, A continuum method for modeling surface tension, J. Comput. Phys. 100 (1992) 335–354.
[16]
R.P. Fedkiw, T. Aslam, B. Merriman, S. Osher, A non-oscillatory Eulerian approach to interfaces in multimaterial flows (the ghost fluid method), J. Comput. Phys. 152 (1999) 457–492.
[17]
S. Elghobashi, Direct numerical simulation of turbulent flows laden with droplets or bubbles, Annu. Rev. Fluid Mech. 51 (2019) 217–244.
[18]
P. Das, H. Udaykumar, A sharp-interface method for the simulation of shock-induced vaporization of droplets, J. Comput. Phys. 405 (2020).
[19]
H. Terashima, G. Tryggvason, A front-tracking/ghost-fluid method for fluid interfaces in compressible flows, J. Comput. Phys. 228 (2009) 4012–4037.
[20]
P.T. Barton, B. Obadia, D. Drikakis, A conservative level-set based method for compressible solid/fluid problems on fixed grids, J. Comput. Phys. 230 (2011) 7867–7890.
[21]
M. Baer, J. Nunziato, A two-phase mixture theory for the deflagration-to-detonation transition (DDT) in reactive granular materials, Int. J. Multiph. Flow 12 (1986) 861–889.
[22]
X.-D. Liu, S. Osher, T. Chan, Weighted essentially non-oscillatory schemes, J. Comput. Phys. 115 (1994) 200–212.
[23]
B. Van Leer, Towards the ultimate conservative difference scheme. V. A second-order sequel to Godunov's method, J. Comput. Phys. 32 (1979) 101–136.
[24]
F. Petitpas, J. Massoni, R. Saurel, E. Lapebie, L. Munier, Diffuse interface model for high speed cavitating underwater systems, Int. J. Multiph. Flow 35 (2009) 747–759.
[25]
K. Schmidmayer, F. Petitpas, S. Le Martelot, E. Daniel, ECOGEN: an open-source tool for multiphase, compressible, multiphysics flows, Comput. Phys. Commun. 251 (2020).
[26]
R. Saurel, P. Boivin, O. Le Métayer, A general formulation for cavitating, boiling and evaporating flows, Comput. Fluids 128 (2016) 53–64.
[27]
M.G. Rodio, R. Abgrall, An innovative phase transition modeling for reproducing cavitation through a five-equation model and theoretical generalization to six and seven-equation models, Int. J. Heat Mass Transf. 89 (2015) 1386–1401.
[28]
R. Saurel, R. Abgrall, A multiphase Godunov method for compressible multifluid and multiphase flows, J. Comput. Phys. 150 (1999) 425–467.
[29]
N. Andrianov, G. Warnecke, The Riemann problem for the Baer–Nunziato two-phase flow model, J. Comput. Phys. 195 (2004) 434–464.
[30]
D.W. Schwendeman, C.W. Wahle, A.K. Kapila, The Riemann problem and a high-resolution Godunov method for a model of compressible two-phase flow, J. Comput. Phys. 212 (2006) 490–526.
[31]
H. Lochon, F. Daude, P. Galon, J.-M. Hérard, HLLC-type Riemann solver with approximated two-phase contact for the computation of the Baer–Nunziato two-fluid model, J. Comput. Phys. 326 (2016) 733–762.
[32]
R. Abgrall, R. Saurel, Discrete equations for physical and numerical compressible multiphase mixtures, J. Comput. Phys. 186 (2003) 361–396.
[33]
A. Kapila, R. Menikoff, J. Bdzil, S. Son, D.S. Stewart, Two-phase modeling of deflagration-to-detonation transition in granular materials: reduced equations, Phys. Fluids 13 (2001) 3002–3024.
[34]
G. Allaire, S. Clerc, S. Kokh, A five-equation model for the simulation of interfaces between compressible fluids, J. Comput. Phys. 181 (2002) 577–616.
[35]
J. Meng, T. Colonius, Numerical simulations of the early stages of high-speed droplet breakup, Shock Waves 25 (2015) 399–414.
[36]
N. Liu, Z. Wang, M. Sun, R. Deiterding, H. Wang, Simulation of liquid jet primary breakup in a supersonic crossflow under adaptive mesh refinement framework, Aerosp. Sci. Technol. 91 (2019) 456–473.
[37]
A. Murrone, H. Guillard, A five equation reduced model for compressible two phase flow problems, J. Comput. Phys. 202 (2005) 664–698.
[38]
F. Petitpas, E. Franquet, R. Saurel, O. Le Metayer, A relaxation-projection method for compressible flows. Part II: artificial heat exchanges for multiphase shocks, J. Comput. Phys. 225 (2007) 2214–2248.
[39]
A. Tiwari, J.B. Freund, C. Pantano, A diffuse interface model with immiscibility preservation, J. Comput. Phys. 252 (2013) 290–309.
[40]
G. Perigaud, R. Saurel, A compressible flow model with capillary effects, J. Comput. Phys. 209 (2005) 139–178.
[41]
R. Abgrall, M.G. Rodio, Discrete equation method (DEM) for the simulation of viscous, compressible, two-phase flows, Comput. Fluids 91 (2014) 164–181.
[42]
R. Saurel, F. Petipas, R. Abgrall, Modelling phase transition in metastable liquids: application to cavitating and flashing flows, J. Fluid Mech. 607 (2008) 313–350.
[43]
S.H. Bryngelson, K. Schmidmayer, V. Coralic, J.C. Meng, K. Maeda, T. Colonius, MFC: an open-source high-order multi-component, multi-phase, and multi-scale compressible flow solver, Comput. Phys. Commun. 266 (2021).
[44]
K. Schmidmayer, S.H. Bryngelson, T. Colonius, An assessment of multicomponent flow models and interface capturing schemes for spherical bubble dynamics, J. Comput. Phys. 402 (2020).
[45]
A.B. Wood, A Textbook of Sound, G. Bell and Sons Ltd., 1930.
[46]
R. Saurel, F. Petitpas, R.A. Berry, Simple and efficient relaxation methods for interfaces separating compressible fluids, cavitating flows and shocks in multiphase mixtures, J. Comput. Phys. 228 (2009) 1678–1712.
[47]
A. Zein, M. Hantke, G. Warnecke, Modeling phase transition for compressible two-phase flows applied to metastable liquids, J. Comput. Phys. 229 (2010) 2964–2998.
[48]
M. Pelanti, K.-M. Shyue, A numerical model for multiphase liquid–vapor–gas flows with interfaces and cavitation, Int. J. Multiph. Flow 113 (2019) 208–230.
[49]
A.D. Demou, N. Scapin, M. Pelanti, L. Brandt, A pressure-based diffuse interface method for low-Mach multiphase flows with mass transfer, J. Comput. Phys. 448 (2022).
[50]
M. Rodriguez, S.H. Bryngelson, S. Cao, T. Colonius, Acoustically-induced bubble growth and phase change dynamics near compliant surfaces, in: 11th International Symposium on Cavitation, 2021.
[51]
B. Dorschner, L. Biasiori-Poulanges, K. Schmidmayer, H. El-Rabii, T. Colonius, On the formation and recurrent shedding of ligaments in droplet aerobreakup, J. Fluid Mech. 904 (2020).
[52]
V. Coralic, T. Colonius, Finite-volume weno scheme for viscous compressible multicomponent flows, J. Comput. Phys. 274 (2014) 95–121.
[53]
H. Guillard, M. Labois, Numerical Modelling of Compressible Two-Phase Flows, 2006.
[54]
P. Gaillard, V. Giovangigli, L. Matuszewski, A diffuse interface lox/hydrogen transcritical flame model, Combust. Theory Model. 20 (2016) 486–520.
[55]
A. Chiapolino, P. Boivin, R. Saurel, A simple and fast phase transition relaxation solver for compressible multicomponent two-phase flows, Comput. Fluids 150 (2017) 31–45.
[56]
E. Goncalves, R.F. Patella, Numerical simulation of cavitating flows with homogeneous models, Comput. Fluids 38 (2009) 1682–1696.
[57]
S. Clerc, Numerical simulation of the homogeneous equilibrium model for two-phase flows, J. Comput. Phys. 161 (2000) 354–375.
[58]
S.V. Apte, P. Moin, Spray modeling and predictive simulations in realistic gas-turbine engines, in: Handbook of Atomization and Sprays, Springer, 2011, pp. 811–835.
[59]
F. Zhang, D. Frost, P. Thibault, S. Murray, Explosive dispersal of solid particles, Shock Waves 10 (2001) 431–443.
[60]
M. Herrmann, A dual-scale LES subgrid model for turbulent liquid/gas phase interface dynamics, in: ASME/JSME/KSME 2015 Joint Fluids Engineering Conference, American Society of Mechanical Engineers, 2015.
[61]
L. Han, X. Hu, N.A. Adams, Scale separation for multi-scale modeling of free-surface and two-phase flows with the conservative sharp interface method, J. Comput. Phys. 280 (2015) 387–403.
[62]
G. Tomar, D. Fuster, S. Zaleski, S. Popinet, Multiscale simulations of primary atomization, Comput. Fluids 39 (2010) 1864–1874.
[63]
C.-H. Chang, M.-S. Liou, A robust and accurate approach to computing compressible multiphase flow: stratified flow model and AUSM+-up scheme, J. Comput. Phys. 225 (2007) 840–873.
[64]
S. Tokareva, E.F. Toro, HLLC-type Riemann solver for the Baer-Nunziato equations of compressible two-phase flow, J. Comput. Phys. 229 (2010) 3573–3604.
[65]
N.T. Nguyen, M. Dumbser, A path-conservative finite volume scheme for compressible multi-phase flows with surface tension, Appl. Math. Comput. 271 (2015) 959–978.
[66]
R. Saurel, A. Chinnayya, Q. Carmouze, Modelling compressible dense and dilute two-phase flows, Phys. Fluids 29 (2017).
[67]
K. Schmidmayer, J. Caze, F. Petitpas, E. Daniel, N. Favrie, Modelling interactions between waves and diffused interfaces, Int. J. Numer. Methods Fluids (2021) 1–27.
[68]
D. Furfaro, R. Saurel, L. David, F. Beauchamp, Towards sodium combustion modeling with liquid water, J. Comput. Phys. 403 (2020).
[69]
D. Dyson, S. Vasu, A. Arakelyan, N. Berube, S. Briggs, J. Ramirez, E.M. Ninnemann, K. Thurmond, G. Kim, W.H. Green, et al., Detonation wave-induced breakup and combustion of RP-2 fuel droplets, in: AIAA SciTech 2022 Forum, 2022, AIAA–2022–1453.
[70]
R.K. Shukla, C. Pantano, J.B. Freund, An interface capturing method for the simulation of multi-phase compressible flows, J. Comput. Phys. 229 (2010) 7411–7439.
[71]
S.S. Jain, A. Mani, P. Moin, A conservative diffuse-interface method for compressible two-phase flows, J. Comput. Phys. 418 (2020).
[72]
M.S. Dodd, A. Ferrante, On the interaction of Taylor length scale size droplets and isotropic turbulence, J. Fluid Mech. 806 (2016) 356–412.
[73]
S. Fechter, C.-D. Munz, C. Rohde, C. Zeiler, A sharp interface method for compressible liquid–vapor flow with phase transition and surface tension, J. Comput. Phys. 336 (2017) 347–374.
[74]
K. Schmidmayer, F. Petitpas, E. Daniel, N. Favrie, S. Gavrilyuk, A model and numerical method for compressible flows with capillary effects, J. Comput. Phys. 334 (2017) 468–496.
[75]
M. Pelanti, K.-M. Shyue, A mixture-energy-consistent six-equation two-phase numerical model for fluids with interfaces, cavitation and evaporation waves, J. Comput. Phys. 259 (2014) 331–357.
[76]
S. Tanguy, T. Ménard, A. Berlemont, A level set method for vaporizing two-phase flows, J. Comput. Phys. 221 (2007) 837–853.
[77]
A. Chiapolino, R. Saurel, B. Nkonga, Sharpening diffuse interfaces with compressible fluids on unstructured meshes, J. Comput. Phys. 340 (2017) 389–417.
[78]
M. Akiki, T.P. Gallagher, S. Menon, Mechanistic approach for simulating hot-spot formations and detonation in polymer-bonded explosives, AIAA J. 55 (2017) 585–598.
[79]
M. Salvadori, P. Tudisco, D. Ranjan, S. Menon, Numerical investigation of mass flow rate effects on multiplicity of detonation waves within a H2/Air rotating detonation combustor, Int. J. Hydrog. Energy 47 (2022) 4155–4170.
[80]
R. Baurle, G. Alexopoulos, H. Hassan, Assumed joint probability density function approach for supersonic turbulent combustion, J. Propuls. Power 10 (1994) 473–484.
[81]
N. Patel, S. Menon, Simulation of spray–turbulence–flame interactions in a lean direct injection combustor, Combust. Flame 153 (2008) 228–257.
[82]
K. Balakrishnan, D. Nance, S. Menon, Simulation of impulse effects from explosive charges containing metal particles, Shock Waves 20 (2010) 217–239.
[83]
E.F. Toro, The hll and hllc Riemann solvers, in: Riemann Solvers and Numerical Methods for Fluid Dynamics, Springer, 2009, pp. 315–344.
[84]
K.-M. Shyue, F. Xiao, An Eulerian interface sharpening algorithm for compressible two-phase flow: the algebraic THINC approach, J. Comput. Phys. 268 (2014) 326–354.
[85]
L.D. Gryngarten, S. Menon, A generalized approach for sub-and super-critical flows using the local discontinuous Galerkin method, Comput. Methods Appl. Mech. Eng. 253 (2013) 169–185.
[86]
Jain, S.S.; Adler, M.C.; West, J.R.; Mani, A.; Moin, P.; Lele, S.K. (2021): Assessment of diffuse-interface methods for compressible multiphase fluid flows and elastic-plastic deformation in solids. arXiv preprint arXiv:2109.09729.
[87]
T.J. Poinsot, S.K. Lele, Boundary conditions for direct simulations of compressible viscous flows, J. Comput. Phys. 101 (1992) 104–129.
[88]
P. Sridharan, T.L. Jackson, J. Zhang, S. Balachandar, Shock interaction with one-dimensional array of particles in air, J. Appl. Phys. 117 (2015).
[89]
X. Rogue, G. Rodriguez, J. Haas, R. Saurel, Experimental and numerical investigation of the shock-induced fluidization of a particles bed, Shock Waves 8 (1998) 29–45.
[90]
J.B. Keller, M. Miksis, Bubble oscillations of large amplitude, J. Acoust. Soc. Am. 68 (1980) 628–633.
[91]
U. Ghia, K. Ghia, C. Shin, High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method, J. Comput. Phys. 48 (1982) 387–411.
[92]
F.M. White, I. Corfield, Viscous Fluid Flow, vol. 3, McGraw-Hill, New York, 2006.
[93]
D. Igra, T. Ogawa, K. Takayama, A parametric study of water column deformation resulting from shock wave loading, At. Sprays 12 (2002).
[94]
H. Chen, Two-dimensional simulation of stripping breakup of a water droplet, AIAA J. 46 (2008) 1135–1143.
[95]
C.T. Crowe, J.D. Schwarzkopf, M. Sommerfeld, Y. Tsuji, Multiphase Flows with Droplets and Particles, CRC Press, 2011.
[96]
L. Rayleigh, et al., On the capillary phenomena of jets, Proc. R. Soc. Lond. 29 (1879) 71–97.
[97]
T. Gallagher, M. Akiki, S. Menon, V. Sankaran, V. Sankaran, Development of the generalized MacCormack scheme and its extension to low Mach number flows, Int. J. Numer. Methods Fluids 85 (2017) 165–188.
[98]
N.V. Patel, Simulation of hydrodynamic fragmentation from a fundamental and an engineering perspective, Ph.D. thesis Georgia Institute of Technology, 2007.
[99]
U. Fey, M. König, H. Eckelmann, A new Strouhal–Reynolds-number relationship for the circular cylinder in the range 47< re< 2× 10 5, Phys. Fluids 10 (1998) 1547–1549.
[100]
S. Temkin, S.S. Kim, Droplet motion induced by weak shock waves, J. Fluid Mech. 96 (1980) 133–157.
[101]
M. Pilch, C. Erdman, Use of breakup time data and velocity history data to predict the maximum size of stable fragments for acceleration-induced breakup of a liquid drop, Int. J. Multiph. Flow 13 (1987) 741–757.
[102]
K.W. Thompson, Time dependent boundary conditions for hyperbolic systems, J. Comput. Phys. 68 (1987) 1–24.
[103]
M. Salvadori, A. Panchal, D. Ranjan, S. Menon, Numerical study of detonation propagation in H2-Air with kerosene droplets, in: AIAA SciTech 2022 Forum, 2022, AIAA–2022–0394.
[104]
J. Kindracki, Experimental research on rotating detonation in liquid fuel–gaseous air mixtures, Aerosp. Sci. Technol. 43 (2015) 445–453.
[105]
M. Gogulya, M. Makhov, A.Y. Dolgoborodov, M. Brazhnikov, V. Arkhipov, V. Shchetinin, Mechanical sensitivity and detonation parameters of aluminized explosives, Combust. Explos. Shock Waves 40 (2004) 445–457.
[106]
K. Kailasanath, E. Oran, J. Boris, T. Young, Determination of detonation cell size and the role of transverse waves in two-dimensional detonations, Combust. Flame 61 (1985) 199–209.
[107]
Pelanti, M. (2021): Arbitrary-rate relaxation techniques for the numerical modeling of compressible two-phase flows with heat and mass transfer. arXiv preprint arXiv:2108.00556.
Index Terms
- A seven-equation diffused interface method for resolved multiphase flows
Index terms have been assigned to the content through auto-classification.
Recommendations
Multiphase lattice Boltzmann flux solver for incompressible multiphase flows with large density ratio
A multiphase lattice Boltzmann flux solver (MLBFS) is proposed in this paper for incompressible multiphase flows with low- and large-density-ratios. In the solver, the flow variables at cell centers are given from the solution of macroscopic governing ...
A sharp interface method for incompressible two-phase flows
We present a sharp interface method for computing incompressible immiscible two-phase flows. It couples the level-set and volume-of-fluid techniques and retains their advantages while overcoming their weaknesses. It is stable and robust even for large ...
Viscous Regularization for the Non-equilibrium Seven-Equation Two-Phase Flow Model
In this paper, a viscous regularization is derived for the non-equilibrium seven-equation two-phase flow model (SEM). This regularization, based on an entropy condition, is an artificial viscosity stabilization technique that selects a weak solution ...
Comments
Please enable JavaScript to view thecomments powered by Disqus.Information & Contributors
Information
Published In
Elsevier Inc.
Publisher
Academic Press Professional, Inc.
United States
Publication History
Published: 15 February 2023
Author Tags
Qualifiers
- Research-article
Contributors
Other Metrics
Bibliometrics & Citations
Bibliometrics
Article Metrics
- 0Total Citations
- 0Total Downloads
- Downloads (Last 12 months)0
- Downloads (Last 6 weeks)0
Reflects downloads up to 25 Dec 2024