Stability of uniformly propagating SHS waves in porous solids with melting and flow of reactants

C. S. Raymond; V. A. Volpert

doi:10.1016/0009-2509(96)00290-4

Stability of uniformly propagating SHS waves in porous solids with melting and flow of reactants

C. S. Raymond^*, V. A. Volpert

^*Corresponding author for this work

Engineering Sciences and Applied Mathematics

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

We formulate a two-dimensional model describing the combustion of porous condensed phase materials in which a reactant melts and spreads through the void space of a porous solid. The melt may completely fill the pores, or some gas may remain in the pores. In each case, the volume fraction of melt is prescribed. In the limit of large activation energy, we analytically find a one-dimensional basic state consisting of a uniformly propagating combustion wave with a planar reaction front and a planar melting front. We find that the uniformly propagating solution with planar fronts is linearly unstable to traveling waves transverse to the propagation direction of the basic state above some critical Zeldovich number. The critical wave number associated with this critical Zeldovich number is generally unique and nonzero. However, the critical wave number can be zero for certain parameter values. For other special parameter values, the neutral stability curve may have two minima, so that two wave numbers lose stability at the same Zeldovich number.

Original language	English (US)
Pages (from-to)	4443-4462
Number of pages	20
Journal	Chemical Engineering Science
Volume	51
Issue number	19
DOIs	https://doi.org/10.1016/0009-2509(96)00290-4
State	Published - Oct 1996

Funding

Combustion in gasless systems is generally accompanied by melting of one or more of the components of either the initial mixture or the intermediate or final products. This is due to the large exothermicities and the resulting high combustion temperatures for most such mixtures. Melting with subsequent spreading of the melt increases the surface-to-surface contact of the reactants which significantly promotes the reaction. Gasless systems in which melting does not occur typically cannot sustain a combustion wave because of * Supported by a NASA Graduate Student Research Fellowship. * Supported in part by NSF Grant 9308708 and NASA Grant NAG3-1608.

Keywords

Gasless combustion
SHS
melting
porous medium combustion
stability

ASJC Scopus subject areas

General Chemistry
General Chemical Engineering
Industrial and Manufacturing Engineering

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10.1016/0009-2509(96)00290-4

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title = "Stability of uniformly propagating SHS waves in porous solids with melting and flow of reactants",

abstract = "We formulate a two-dimensional model describing the combustion of porous condensed phase materials in which a reactant melts and spreads through the void space of a porous solid. The melt may completely fill the pores, or some gas may remain in the pores. In each case, the volume fraction of melt is prescribed. In the limit of large activation energy, we analytically find a one-dimensional basic state consisting of a uniformly propagating combustion wave with a planar reaction front and a planar melting front. We find that the uniformly propagating solution with planar fronts is linearly unstable to traveling waves transverse to the propagation direction of the basic state above some critical Zeldovich number. The critical wave number associated with this critical Zeldovich number is generally unique and nonzero. However, the critical wave number can be zero for certain parameter values. For other special parameter values, the neutral stability curve may have two minima, so that two wave numbers lose stability at the same Zeldovich number.",

keywords = "Gasless combustion, SHS, melting, porous medium combustion, stability",

author = "Raymond, {C. S.} and Volpert, {V. A.}",

note = "Funding Information: Combustion in gasless systems is generally accompanied by melting of one or more of the components of either the initial mixture or the intermediate or final products. This is due to the large exothermicities and the resulting high combustion temperatures for most such mixtures. Melting with subsequent spreading of the melt increases the surface-to-surface contact of the reactants which significantly promotes the reaction. Gasless systems in which melting does not occur typically cannot sustain a combustion wave because of * Supported by a NASA Graduate Student Research Fellowship. * Supported in part by NSF Grant 9308708 and NASA Grant NAG3-1608.",

year = "1996",

month = oct,

doi = "10.1016/0009-2509(96)00290-4",

language = "English (US)",

volume = "51",

pages = "4443--4462",

journal = "Chemical Engineering Science",

issn = "0009-2509",

publisher = "Elsevier B.V.",

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T1 - Stability of uniformly propagating SHS waves in porous solids with melting and flow of reactants

AU - Raymond, C. S.

AU - Volpert, V. A.

N1 - Funding Information: Combustion in gasless systems is generally accompanied by melting of one or more of the components of either the initial mixture or the intermediate or final products. This is due to the large exothermicities and the resulting high combustion temperatures for most such mixtures. Melting with subsequent spreading of the melt increases the surface-to-surface contact of the reactants which significantly promotes the reaction. Gasless systems in which melting does not occur typically cannot sustain a combustion wave because of * Supported by a NASA Graduate Student Research Fellowship. * Supported in part by NSF Grant 9308708 and NASA Grant NAG3-1608.

PY - 1996/10

Y1 - 1996/10

N2 - We formulate a two-dimensional model describing the combustion of porous condensed phase materials in which a reactant melts and spreads through the void space of a porous solid. The melt may completely fill the pores, or some gas may remain in the pores. In each case, the volume fraction of melt is prescribed. In the limit of large activation energy, we analytically find a one-dimensional basic state consisting of a uniformly propagating combustion wave with a planar reaction front and a planar melting front. We find that the uniformly propagating solution with planar fronts is linearly unstable to traveling waves transverse to the propagation direction of the basic state above some critical Zeldovich number. The critical wave number associated with this critical Zeldovich number is generally unique and nonzero. However, the critical wave number can be zero for certain parameter values. For other special parameter values, the neutral stability curve may have two minima, so that two wave numbers lose stability at the same Zeldovich number.

AB - We formulate a two-dimensional model describing the combustion of porous condensed phase materials in which a reactant melts and spreads through the void space of a porous solid. The melt may completely fill the pores, or some gas may remain in the pores. In each case, the volume fraction of melt is prescribed. In the limit of large activation energy, we analytically find a one-dimensional basic state consisting of a uniformly propagating combustion wave with a planar reaction front and a planar melting front. We find that the uniformly propagating solution with planar fronts is linearly unstable to traveling waves transverse to the propagation direction of the basic state above some critical Zeldovich number. The critical wave number associated with this critical Zeldovich number is generally unique and nonzero. However, the critical wave number can be zero for certain parameter values. For other special parameter values, the neutral stability curve may have two minima, so that two wave numbers lose stability at the same Zeldovich number.

KW - Gasless combustion

KW - SHS

KW - melting

KW - porous medium combustion

KW - stability

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JO - Chemical Engineering Science

JF - Chemical Engineering Science

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ER -

Stability of uniformly propagating SHS waves in porous solids with melting and flow of reactants

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