Acta mathematica scientia, Series B >
MULTISCALE ISSUES IN DNS OF MULTIPHASE FLOWS
Received date: 2009-12-23
Online published: 2010-03-20
Direct numerical simulations (DNS) have now become a well established tool to examine complex multiphase flows. Such flows typically exhibit a large range of scales and it is generally necessary to use different descriptions of the flow depending on the scale that we are examining. Here we discuss multiphase flows from a multiscale perspective. Those include both how DNS are providing insight and understanding for modeling of scales much larger than the “dominant scale”(defined where surface tension, viscous forces or inertia are important), as well as how DNS are often limited by the need to resolve processes taking place on much smaller scales. Both problems can be cast into a language introduced for general classes of multiscale problems and reveal that while the classification may be new, the issues are not.
G. Tryggvason , S. Thomas , J. Lu , B. Aboulhasanzadeh . MULTISCALE ISSUES IN DNS OF MULTIPHASE FLOWS[J]. Acta mathematica scientia, Series B, 2010 , 30(2) : 551 -562 . DOI: 10.1016/S0252-9602(10)60062-8
[1] Lefebvre A. Atomization and Sprays. Taylor and Francis, 1989
[2] Bayvel L, Orzechowski Z. Liquid Atomization. Taylor and Francis, 1993
[3] Furusaki S, Fan L -S, Garside J. The Expanding World of Chemical Engineering. 2nd ed. Taylor and Francis, 2001
[4] Deckwer W -D. Bubble Column Reactors. Wiley, 1992
[5] Prosperetti A, Tryggvason G. Computational Methods for Multiphase Flow. Cambridge University Press, 2007
[6] Glimm J, Marchesin D, McBryan O. A numerical method for two phase ow with an unstable interface.J Comput Phys, 1981, 39: 179--200
[7] Glimm J. Tracking of interfaces in uid ow: Accurate methods for piecewise smooth problems, transonic shock and multidimensional flows//Meyer R E, ed. Advances in Scientific Computing. New York: Academic Press, 1982
[8] Glimm J, McBryan O. A computational model for interfaces. Adv Appl Math, 1985, 6: 422--435
[9] Glimm J, McBryan O, Menikoff R, Sharp D. Front tracking applied to rayleigh-taylor instability. SIAM J Comput, 1986, 7: 230--251
[10] Chern I -L, Glimm J, McBryan O, Plohr B, Yaniv S. Front tracking for gas dynamics. J Comput Phys, 1986, 62: 83--110
[11] Glimm J, Grove J, Lindquist B, McBryan O, Tryggvason G. The bifurcation of tracked scalar waves. SIAM J Sci Stat Comput, 1988, 9: 61--79
[12] Du J, Fix B, Glimm J, Jia X, Li X, Li Y, Wu L. A simple package for front tracking. J Comput Phys, 2006, 213: 613--628
[13] Brackbill J U, Kothe D B, Zemach C. A continuum method for mod-eling surface tension. J Comput Phys, 1992, 100: 335--354
[14] Osher S, Sethian J. Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations. J Comput Phys, 1988, 79: 12--49
[15] Jacqmin D.Calculation of two-phase Navier-Stokes ows using phasefeld modeling. J Comput Phys, 1999, 155: 96--127
[16] Takewaki H, Nishiguchi A, Yabe T. Cubic interpolated pseudo-particle method (CIP) for solving hyperbolic-type equations. J Comput Phys, 1985, 61: 261--268
[17] Unverdi S O, Tryggvason G. A front-tracking method for viscous. incompressible, multiuid ows. J Comput Phys, 1992, 100: 25--37
[18] Ishii M. Thermouid dynamic theory of two-phase ows. Eyrolles, 1975
[19] Tryggvason G, Scardovelli R, Zaleski S. Direct Numerical Simulations of Gas-Liquid Multiphase Flows. Cambridge University Pres, 2010
[20] E W, Enquist B. The heterogeneous multiscale methods. Comm Math Sci, 2003, 1: 87--133
[21] Launder B E, Spalding D B. Lectures in Mathematical Models of Turbulence. Academic Press, 1972
[22] Amsden A A, Harlow F. Transport of turbulence in numerical uid dynamics. J Comput Phys, 1968, 3: 94
[23] Zhang D Z, Prosperetti A. Ensemble phase-averaged equations for bubbly ows. Phys Fluids, 1994, 6: 2956--2970
[24] Drew D A, Passman S L. Theory of Multicomponent Fluids. Springer, 1999
[25] Crowe C, Sommerfeld M, Tsuji Y. Multiphase Flows with Droplets and Particles. CRC Press, 1998
[26] Lu J, Tryggvason G. Effect of bubble deformability in turbulent bubbly up ow in a vertical channel. Phys Fluids, 2008, 20: 040701
[27] Serizawa A, Kataoka I, Michiyoshi I. Turbulence structure of air-water bubbly ow{II. local properties. Int J Multiphase Flow, 1975, 2: 235--246
[28] Serizawa A, Kataoka I, Michiyoshi I. Turbulence structure of air-water bubbly ow{III. transport properties. Int J Multiphase Flow, 1975, 2: 247--259
[29] Drew D, Jr R T L. The virtual mass and lift force on a sphere in rotating and straining inviscid flow. Int J Multiphase Flows, 1987, 13: 113--121
[30] Biswas S, Esmaeeli A, Tryggvason G. Comparison of results from dns of bubbly ows with a two-fluid model for two-dimensional laminar flows. Int J Multiphase Flows, 2005, 31: 1036--1048
[31] Antal S P, Lahey R T, Flaherty J E. Analysis of phase distribution in fully developed laminar bubbly two-phase flows. Int J Multiphase
Flow, 1991, 15: 635--652
[32] Azpitarte O E, Buscaglia G C. Analytical and numerical evaluation of two-fluid model solutions for laminar fully developed bubbly two-phase
flows. Chem Eng Sci, 2003, 58: 3765--3776
[33] Lu J, Tryggvason G. Numerical study of turbulent bubbly downflows in a vertical channel. Phys Fluids, 2006, 18:103302
[34] Lu J, Tryggvason G. Effect of bubble size in turbulent bubbly downflow in a vertical channel. Chem Eng Sci, 2007, 62: 3008--3018
[35] Kunz R F, Gibeling M R M H J, Tryggvason G, Fontaine A A, Petrie H L, Ceccio S L. Validation of two-fluid eulerian cfd modeling for microbubble drag reduction across a wide range of reynolds numbers. J Fluids Eng, 2007, 129: 66--79
[36] Patel V C, Rodi W, Scheuerer G. Turbulence models for near-wall and low reynolds number flows: A review. AIAA Journal, 1984, 23: 1308--1319
[37] Biswas S, Tryggvason G. The transient buoyancy driven motion of bubbles across a two-dimensional quiescent domain. Int J Multiphase Flow, 2007, 33: 1308--1319
[38] Palacios J, Tryggvason G. The transient motion of buoyant bubbles in a vertical couette flow. AMD Contemporary Mathematics Series, 2008, 466: 135--146
[39] Liovic P, Lakehal D, Liow J G. Les of turbulent bubble formation and breakup by use of interface tracking//Geurts B, Friedrich R, M\'etais O, eds. Direct and Large-Eddy Simulation --V, ERCOFTAC Series, Vol 9. Dordrecht: Kluwer Academic Publishers, 2004
[40] Thomas S, Esmaeeli A, Tryggvason G. Multiscale computations of thin films in multiphase flows. Int J Multiphase Flow, 2010, 36: 71--77
\REF{
[41]} Yoon Y, Baldessari F, Ceniceros H, Leal L G. Coalescence of two equal-sized deformable drops in an axisymmetric flow. Phys Fluids, 2007, 19: 102102
[42] Dai B, Leal L. G. The mechanism of surfactant effects on drop coalescence. Phys Fluids, 2008, 20: 040804--1--13
[43] Baldessari F, Homsy G, Leal L. Linear stability of a draining film squeezed between two approaching droplets. J Colloid and Interface Science, 2007, 307: 188--202
[44] Lowengrub J, Goodman J, Lee H, Longmire E, Shelley M, Truskinovsky L. Topological transitions in liquid/liquid interfaces//Athanasoponlos I, et al, eds. Free Boundary Problems: Theory and Applications. Chapman & Hall/CRC, 1999: 221
/
| 〈 |
|
〉 |