Simulation of reactive nanolaminates using reduced models: II. Normal propagation

Combustion and Flame

Volumn 157, Issue 3, 2010, Pages 436-445

  Salloum, Maher ^a   Knio, Omar M ^a  

^a Johns Hopkins University   (United States)

Author keywords

Normal propagation; Reactive multilayers; Reduced model

Indexed keywords

AXIAL PROPAGATION; BI-LAYER; CHEMICAL SOURCES; DETAILED MODELS; FLAME PROPAGATION; FRONT VELOCITY; GAP WIDTHS; IGNITION THRESHOLD; INERT MATERIALS; INTEGRATION SCHEME; LAYERED MATERIAL; MODEL REDUCTION; NANO-LAMINATES; NONUNIFORM; REACTION FRONT; REACTIVE MULTILAYERS; REACTIVE SYSTEM; REDUCED MODEL; RUNGE-KUTTA; SELF-PROPAGATING;

CHEMICAL STABILITY; EQUATIONS OF MOTION; RUNGE KUTTA METHODS;

MULTILAYERS;

ALUMINUM; NICKEL;

ARTICLE; COMBUSTION; DIFFUSION; FLOW KINETICS; MATHEMATICAL ANALYSIS; MATHEMATICAL MODEL; PRIORITY JOURNAL; THERMAL CONDUCTIVITY; VELOCITY;

EID: 73649122021     PISSN: 00102180     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.combustflame.2009.08.010     Document Type: Article

References (63)

1. Wang J., Besnoin E., Duckham A., Spey S.J., Reiss M.E., Knio O.M., Powers M., Whitener M., and Weihs T.P. Room-temperature soldering with nanostructured foils. Appl. Phys. Lett. 83 (2003) 3987-3989
2. Wang J., Besnoin E., Duckham A., Spey S.J., Reiss M.E., Knio O.M., and Weihs T.P. Joining of stainless steel specimens with nanostructured Ni/Al foils. J. Appl. Phys. 95 (2004) 248-256
3. Wang J., Besnoin E., Knio O.M., and Weihs T.P. Investigating the effect of applied pressure on reactive multilayer foil joining. Acta Mater. 18 (2004) 5265-5274
4. Duckham A., Besnoin E., Spey S., Wang J., Knio O., and Weihs T. Reactive nanostructured foil used as a heat source for joining titanium. J. Appl. Phys. 96 (2004) 2336-2342
5. A. Duckham, J. Newson, M.V. Brown, T.R. Rude, O.M. Knio, E.M. Heian, J.S. Subramanian, Method for fabricating large dimension bonds using reactive multilayer joining, US Patent 7,354,659, 2008.
6. J. Wang, E. Besnoin, O.M. Knio, T.P. Weihs, Nanostructured soldered or brazed joints made with reactive multilayer foils, US Patent 7,361,412, 2008.
7. G. Van Heerden, D. Deger, T.P. Weihs, O.M. Knio, Hermetically sealing a container with crushable material and reactive multilayer material, US Patent 7,143,568, 2006.
8. D. Van Heerden, E. Besnoin, S.J. Spey, T.R. Rude, M.V. Brown, D. Deger, E. Heian, S. Valliappan, O.M. Knio, T.P. Weihs, Methods of controlling multilayer foil ignition, US Patent Application 20050142495, 2005.
9. S.J. Spey, Ignition Properties of Multilayer Nanoscale Reactive Foils and the Properties of Metal-Ceramic Joints Made with the Same. PhD thesis, Johns Hopkins University, 2005.
10. Merzhanov A.G. Self-propagating high-temperature synthesis: twenty years of search and findings. In: Munir Z.A., and Holt J.B. (Eds). Combustion and Plasma Synthesis of High-Temperature Materials (1990), VCH Publishers, NY
11. Koizumi M., and Miyamoto Y. Recent progress in combustion synthesis of high-performance materials in japan. In: Munir Z.A., and Holt J.B. (Eds). Combustion and Plasma Synthesis of High-Temperature Materials (1990), VCH Publishers, NY
12. Clevenger L.A., Thompson C.V., and Tu K.N. Explosive silicidation in nickel amorphous-silicon multilayer thin-films. J. Appl. Phys. 67 (1990) 2894-2898
13. T.P. Weihs, Self-propagating reactions in multilayer materials, Handbook of Thin Film Process Technology, IOP Publishing, 1998 (Part B, Section F 7).
14. Barmak K., Michaelsen C., and Lucadamo G. Reactive phase formation in sputter-deposited Ni/Al multilayer thin films. J. Mater. Res. 12 (1997) 133-146
15. Reiss M.E., Esber C.M., van Heerden D., Gavens A.J., Williams M.E., and Weihs T.P. Self-propagating formation reactions in Nb/Si multilayers. Mater. Sci. Eng., A 261 (1999) 217-222
16. Gavens A.J., Van Heerden D., Mann A.B., Reiss M.E., and Weihs T.P. Effect of intermixing on self-propagating exothermic reactions in Al/Ni nanolaminate foils. J. Appl. Phys. 87 (2000) 1255-1263
17. 2 metastable phase and analysis of its formation. Acta Mater. 51 (2003) 3871-3884
18. Rogachev A.S., Grigoryan A.E., Illarionova E.V., Kanel I.G., Merzhanov A.G., Nosyrev A.N., Sachkova N.V., Khvesyuk V.I., and Tsygankov P.A. Gasless combustion of Ti-Al bimetallic multilayer nanofoils. Combust. Explos. Shock Waves 40 (2004) 166-171
19. Gachon J., Rogachev A., Grigoryan H., Illarionova E., Kuntz J., Kovalev D., Nosyrev A., Sachkova N., and Tsygankov P. On the mechanism of heterogeneous reaction and phase formation in Ti/Al multilayer nanofilms. Acta Mater. 53 (2005) 1225-1231
20. Adams D.P., Rodriguez M.A., Tigges C.P., and Kotula P.G. Self-propagating, high-temperature combustion synthesis of rhombohedral Al-Pt thin films. J. Mater. Res. 21 (2006) 3168-3179
21. D.P. Adams, M.M. Bai, M.A. Rodriguez, J.J. Moore, L.N. Brewer, J.B. Kelley, Structure and properties of Ni-Ti thin films used for brazing, in: J.J. Stephens, K.S. Weil (Eds.), Proceedings of the 3rd International Brazing and Soldering Conference, 2006.
22. Floro J.A. Propagation of explosive crystallization in thin Rh-Si multilayer films. J. Vac. Sci. Technol. A 4 (1986) 631-636
23. Ma E., Thompson C.V., Clevenger L.A., and Tu K.N. Self-propagating explosive reactions in Al/Ni multilayer thin-films. Appl. Phys. Lett. 57 (1990) 1262-1264
24. Dyer T.S., Munir Z.A., and Ruth V. The combustion synthesis of multilayer Ni/Al systems. Scr. Metall. 30 (1994) 1281-1286
25. Anselmi-Tamburini U., Spinolo G., Flor G., and Munir Z.A. Combustion synthesis of Zr-Al intermetallic compounds. J. Alloys Compd. 247 (1997) 190-194
26. Battezzati L., Pappalepore P., Durbiano F., and Gallino I. Solid state reactions in Al/Ni alternate foils induced by cold rolling and annealing. Acta Mater. 47 (1999) 1901-1914
27. Makino A. Fundamental aspects of the heterogeneous flame in the self-propagating high-temperature synthesis (shs) process. Prog. Energy. Comb. Sci. 27 (2001) 1-74
28. Sieber H., Park J.S., Weissmller J., and Perepezko J.H. Structural evolution and phase formation in cold-rolled aluminum-nickel multilayers. Acta Mater. 49 (2001) 1139-1151
29. Hebert R.J., and Perepezko J.H. Deformation-induced synthesis and structural transformations of metallic multilayers. Scr. Mater. 50 (2004) 807-812
30. Maglia F., Milanese C., Anselmi-Tamburini U., Doppiu S., Cocco G., and Munir Z.A. Combustion synthesis of mechanically activated powders in the Ta-Si system. J. Alloys Compd. 385 (2004) 269-275
31. Mossino P. Some aspects in self-propagating high-temperature synthesis. Ceram. Int. 30 (2004) 311-332
32. 3Ni in reactive Ni/Al multilayer foils. Scr. Mater. 56 (2007) 1055-1058
33. Knepper R., Snyder M.R., Fritz G., Fisher K., Knio O.M., and Weihs T.P. Effect of varying bilayer spacing distribution on reaction heat and velocity in reactive Al/Ni multilayers. J. Appl. Phys. 105 (2009) 083504
34. Knio O.M., Besnoin E., Xun Y., Lunking D., and van Heerden D. A simplified probabilistic model of self-propagating reactions in randomly layered nanolaminates. J. Comput. Theor. Nanosci. (2009) 10.1166/jctn.2009.1986
35. Qiu X., Graeter J., Kecskes L., and Wang J. Exothermic reactions in cold rolled Ni/Al reactive multilayer foils. J. Mater. Res. 23 (2008) 367-375
36. Y. Xun, D. Lunking, E. Besnoin, D. van Heerden, T.P. Weihs, O.M. Knio, Method of making reactive composite materials and resulting products, US Patent Application No. 20090178741, 2009.
37. Mann A.B., Gavens A.J., Reiss M.E., van Heerden D., Bao G., and Weihs T.P. Modeling and characterizing the propagation velocity of exothermic reactions in multilayer foils. J. Appl. Phys. 82 (1997) 1178-1188
38. S. Jayaraman, A.B. Mann, O.M. Knio, G. Bao, T.P. Weihs, Numerical modeling of self-propagating exothermic reactions in multilayer systems, in: E. Ma, M. Atzmon, P. Bellon, R. Trivedi (Eds.), MRS Symp. Proc., vol. 481, 1998.
39. Jayaraman S., Mann A.B., Weihs T.P., and Knio O.M. A numerical study of unsteady self-propagating reactions in multilayer foils. Proc. Combust. Inst. 27 (1998) 2459-2467
40. Jayaraman S., Knio O.M., Mann A.B., and Weihs T.P. Numerical predictions of oscillatory combustion in reactive multilayers. J. Appl. Phys. 86 (1999) 800-809
41. Jayaraman S., Mann A.B., Reiss M., Weihs T.P., and Knio O.M. Numerical study of the effect of heat losses on self-propagating reactions in multilayer foils. Combust. Flame 124 (2001) 178-194
42. Besnoin E., Cerutti S., Knio O.M., and Weihs T.P. Effect of reactant and product melting on self-propagating reactions in multilayer foils. J. Appl. Phys. 92 (2002) 5474-5481
43. M. Salloum, O.M. Knio, Simulation of reactive nanolaminates using reduced models i. Basic formulation, Combust. Flame, 2009. doi:10.1016/j.combustflame.2009.06.019.
44. Verwer J.G. Explicit Runge-Kutta methods for parabolic partial differential equations. Appl. Numer. Math. 22 (1996) 359-379
45. Verwer J.G., Hundsdorfer W.H., and Sommeijer B.P. Convergence properties of the Runge-Kutta-Chebyshev method. Numer. Math. 57 (1990) 157-178
46. van Der Houwen P.J., and Sommeijer B.P. On the internal stability of explicit, m-stage Runge-Kutta methods for large m-values. ZAMM 60 (1980) 479-485
47. Verwer J.G. A note on a Runge-Kutta-Chebyshev method. ZAMM 62 (1982) 561-563
48. Sommeijer B.P., Shampine L.F., and Verwer J.G. RKC: an explicit solver for parabolic pdes. J. Comp. Appl. Math. 88 (1997)
49. Van der Houwen P.J. Explicit Runge-Kutta methods with increased stability boundaries. Numer. Math. 20 (1972) 149-164
50. In: Van der Houwen P.J. (Ed). Construction of Integration Formulas for Initial Value Problems (1977), North-Holland, Amsterdam, NY
51. Verwer J.G. A class of stabilized three-step Runge-Kutta methods for the numerical integration of parabolic equations. J. Comp. Appl. Math. 3 (1977)
52. van Der Houwen P.J., and Sommeijer B.P. An implementation of a class of stabilized explicit methods for the time integration of parabolic equations. ACM Trans. Math. Soft. 6 (1980) 188-205
53. A.A. Medovikov, in: Numerical analysis and its applications, Lecture Notes in Computer Science, 1996.
54. Lebedev V.I. Explicit difference schemes for solving stiff systems of odes and pdes with complex spectrum. Russ. J. Numer. Ansi. Math. Modelling 13 (1998) 107-116
55. Medovikov A.A. High order explicit methods for parabolic equations. BIT 38 (1998) 372-390
56. Golushko M.I., and Novikov E.A. Explicit fourth-order methods for stiff systems. Russ. J. Numer Anal. Math. Modelling 14 (1999) 71-85
57. Abdulle A. On roots and error constant of optimal stability polynomials. BIT 40 (2000) 177-182
58. M. Bakker, Technical Note TN 62, 1971.
59. P.J. Van der Houwen, CWl Report NM-R9420, 1994.
60. A. Guillou, B. Lago, Recherche de formules a grand rayon de stabilite, in: ler Congr. Assoc. Fran., Calcul, AFCAL, Grenoble, 1961, pp. 43-56.
61. Verwer J.G., Blom J.G., and Hundsdorfer W. An implicit-explicit approach for atmospheric transport-chemistry problems. Appl. Numer. Math. 20 (1996) 191-209
62. Frank J., Hundsdorfer W., and Verwer J.G. On the stability of implicit-explicit linear multistep methods. Appl. Numer. Math. 25 (1997) 193-205
63. Najm H.N., and Knio O.M. Modeling low mach number reacting flow with detailed chemistry and transport. J. Sci. Comp. 25 (2005) 263-287