Instability growth rate of two-phase mixing layers from a linear eigenvalue problem and an initial-value problem

Physics of Fluids

Volumn 22, Issue 9, 2010, Pages

  Bagué, Anne ^a,b   Fuster, Daniel ^a,b   Popinet, Stéphane ^c   Scardovelli, Ruben ^d   Zaleski, Stéphane ^a,b  

^a SORBONNE UNIVERSITÉ   (France)

^b INSTITUT JEAN LE ROND D ALEMBERT   (France)

^c NATIONAL INSTITUTE OF WATER AND ATMOSPHERIC RESEARCH   (New Zealand)

^d UNIVERSITY OF BOLOGNA   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

ALUMINUM METALLURGY; EIGENVALUES AND EIGENFUNCTIONS; INITIAL VALUE PROBLEMS; MIXING; STABILITY; TWO PHASE FLOW;

ADAPTIVE MESH REFINEMENT SCHEMES; EIGENVALUE PROBLEM; INCOMPRESSIBLE NAVIER STOKES EQUATIONS; INSTABILITY GROWTH; PHYSICAL PARAMETERS; TEMPORAL INSTABILITY; TWO-PHASE MIXING LAYERS; VISCOSITY RATIOS;

NAVIER STOKES EQUATIONS;

EID: 79251571799     PISSN: 10706631     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.3483206     Document Type: Article

References (30)

1. Lasheras J.C. Hopfinger E.J. Liquid jet instability and atomization in a coaxial gas stream. Annu. Rev. Fluid Mech. 2000, 32:275. ARVFA3, 0066-4189, 10.1146/annurev.fluid.32.1.275.
2. Drazin P.G. Introduction to Hydrodynamic Stability 2002, (Cambridge University Press, Cambridge, ).
3. Yih C.S. Instability due to viscosity stratification. J. Fluid Mech. 1967, 27:337. JFLSA7, 0022-1120, 10.1017/S0022112067000357.
4. Hooper A.P. Boyd W.G. C. Shear-flow instability at the interface between two viscous fluids. J. Fluid Mech. 1983, 128:507. JFLSA7, 0022-1120, 10.1017/S0022112083000580.
5. Hinch E.J. A note on the mechanism of the instability at the interface between two shearing fluids. J. Fluid Mech. 1984, 144:463. JFLSA7, 0022-1120, 10.1017/S0022112084001695.
6. Keller F.X. Li J. Vallet A. Vandromme D. Zaleski S. Direct numerical simulation of interface breakup and atomization. Proceedings of ICLASS'94 1994, 56-62. A. J. Yule, and in edited by (Beggell, New York)
7. Li J. Calcul d'interface affine par Morceaux (piecewise linear interface calculation). C. R. Acad. Sci., Ser. IIb: Mec., Phys., Chim., Astron. 1995, 320:391. CMCAEK, 1251-8069.
8. Leboissetier A. Zaleski S. Influence des conditions amont turbulentes sur l'atomisation primaire. Combustion: Revue des Sciences et Techniques de Combustion 2002, 2:75. 1028-2599.
9. Tauber W. Unverdi S.O. Tryggvason G. The non-linear behavior of a sheared immiscible fluid interface. Phys. Fluids 2002, 14:2871. PHFLE6, 1070-6631, 10.1063/1.1485763.
10. Yecko P. Zaleski S. Fullana J.-M. Viscous modes in two-phase mixing layers. Phys. Fluids 2002, 14:4115. PHFLE6, 1070-6631, 10.1063/1.1513987.
11. Boeck T. Zaleski S. Viscous versus inviscid instability of two-phase mixing layers with continuous velocity profile. Phys. Fluids 2005, 17:032106. PHFLE6, 1070-6631, 10.1063/1.1862234.
12. Popinet S. Gerris: A tree-based adaptive solver for the incompressible Euler equations in complex geometries. J. Comput. Phys. 2003, 190:572. JCTPAH, 0021-9991, 10.1016/S0021-9991(03)00298-5.
13. Francois M.M. Cummins S.H. Dendy E.D. Kothe D.B. Sicilian J.M. Williams M.W. A balanced-force algorithm for continuous and sharp interfacial surface tension models within a volume tracking framework. J. Comput. Phys. 2006, 213:141. JCTPAH, 0021-9991, 10.1016/j.jcp.2005.08.004.
14. Popinet S. An accurate adaptive solver for surface-tension-driven interfacial flows. J. Comput. Phys. 2009, 228:5838. JCTPAH, 0021-9991, 10.1016/j.jcp.2009.04.042.
15. Fuster D. Bagué A. Boeck T. Le Moyne L. Leboissetier A. Popinet S. Ray P. Scardovelli R. Zaleski S. Simulation of primary atomization with an octree adaptive mesh refinement and VOF method. Int. J. Multiphase Flow 2009, 35:550. IJMFBP, 0301-9322, 10.1016/j.ijmultiphaseflow.2009.02.014.
16. Boeck T. Li J. López-Pagés E. Yecko P. Zaleski S. Ligament formation in sheared liquid-gas layers. Theor. Comput. Fluid Dyn. 2007, 21:59. TCFDEP, 0935-4964, 10.1007/s00162-006-0022-1.
17. Michalke A. On spatially growing disturbances in an inviscid shear layer. J. Fluid Mech. 1965, 23:521. JFLSA7, 0022-1120, 10.1017/S0022112065001520.
18. Gaster M. A note on the relation between temporally-increasing and spatially-increasing disturbances in hydrodynamic stability. J. Fluid Mech. 1962, 14:222. JFLSA7, 0022-1120, 10.1017/S0022112062001184.
19. Lock R.C. The velocity distribution in the laminar boundary layer between parallel streams. Q. J. Mech. Appl. Math. 1951, 4:42. QJMMAV, 0033-5614, 10.1093/qjmam/4.1.42.
20. Monkewitz P.A. Huerre P. Influence of the velocity ratio on the spatial instability of mixing layers. Phys. Fluids 1982, 25:1137. PHFLE6, 1070-6631, 10.1063/1.863880.
21. Boeck T. Zaleski S. Instability of two-phase mixing layers: Analysis of exact and approximate base flows from boundary layer theory. J. Non-Equilib. Thermodyn. 2005, 30:215. JNETDY, 0340-0204, 10.1515/JNETDY.2005.017.
22. Boyd J.P. Orthogonal rational functions on a semi-infinite interval. J. Comput. Phys. 1987, 70:63. JCTPAH, 0021-9991, 10.1016/0021-9991(87)90002-7.
23. Boomkamp P.A. M. Boersma B.J. Miesen R.H. M. Beijnon G.V. A Chebyshev collocation method for solving two-phase flow stability problems. J. Comput. Phys. 1997, 132:191. JCTPAH, 0021-9991, 10.1006/jcph.1996.5571.
24. Schmid P.J. Henningson D.S. Stability and Transition in Shear Flows 2001, and (Springer, New York, ).
25. Orszag S.A. Accurate solution of the Orr-Sommerfield stability equation. J. Fluid Mech. 1971, 50:689. JFLSA7, 0022-1120, 10.1017/S0022112071002842.
26. Moler C.B. Stewart G.W. Algorithm for generalized matrix eigenvalue problems. SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal. 1973, 10:241. SJNAAM, 0036-1429, 10.1137/0710024.
27. Lafaurie B. Nardone C. Scardovelli R. Zaleski S. Zanetti G. Modelling merging and fragmentation in multiphase flows with SURFER. J. Comput. Phys. 1994, 113:134. JCTPAH, 0021-9991, 10.1006/jcph.1994.1123.
28. Gueyffier D. Nadim A. Li J. Scardovelli R. Zaleski S. Volume of fluid interface tracking with smoothed surface stress methods for three-dimensional flows. J. Comput. Phys. 1999, 152:423. JCTPAH, 0021-9991, 10.1006/jcph.1998.6168.
29. Bell J. Colella P. Glaz H. A second-order projection method for the incompressible Navier-Stokes equations. J. Comput. Phys. 1989, 85:257. JCTPAH, 0021-9991, 10.1016/0021-9991(89)90151-4.
30. Brackbill J. Kothe D. Zemach C. A continuum method for modeling surface tension. J. Comput. Phys. 1992, 100:335. JCTPAH, 0021-9991, 10.1016/0021-9991(92)90240-Y.