Nonlinear hydrodynamic stability and spinning deflagration of liquid propellants

John K. Bechtold; Stephen B. Margolis

doi:https://doi.org/10.1137/0151068

Nonlinear hydrodynamic stability and spinning deflagration of liquid propellants

John K. Bechtold, Stephen B. Margolis

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

6 Scopus citations

Abstract

Considered is a dynamic model of liquid propellant combustion that generalizes the classical model due to Landau. In appropriate parameter regimes, this model exhibits the well-known phenomenon of hydrodynamic (Landau) instability, in which steady planar deflagration is unstable to steady, but nonplanar (cellular), modes of combustion. In a cylindrical geometry, there exist special values of the radius such that the basic solution simultaneously loses stability to two cellular modes at critical values of a parameter that determines the sensitivity of the reaction rate to the local pressure field. A nonlinear stability analysis in the neighborhood of certain members of this sequence of double eigenvalues then leads to the prediction, by either one or the other of two methods, of secondary and tertiary branching of orbitally stable, spinning deflagration waves.

Original language	American English
Pages (from-to)	1356-1379
Number of pages	24
Journal	SIAM Journal on Applied Mathematics
Volume	51
Issue number	5
DOIs	https://doi.org/10.1137/0151068
State	Published - Jan 1 1991
Externally published	Yes

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Applied Mathematics

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abstract = "Considered is a dynamic model of liquid propellant combustion that generalizes the classical model due to Landau. In appropriate parameter regimes, this model exhibits the well-known phenomenon of hydrodynamic (Landau) instability, in which steady planar deflagration is unstable to steady, but nonplanar (cellular), modes of combustion. In a cylindrical geometry, there exist special values of the radius such that the basic solution simultaneously loses stability to two cellular modes at critical values of a parameter that determines the sensitivity of the reaction rate to the local pressure field. A nonlinear stability analysis in the neighborhood of certain members of this sequence of double eigenvalues then leads to the prediction, by either one or the other of two methods, of secondary and tertiary branching of orbitally stable, spinning deflagration waves.",

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AB - Considered is a dynamic model of liquid propellant combustion that generalizes the classical model due to Landau. In appropriate parameter regimes, this model exhibits the well-known phenomenon of hydrodynamic (Landau) instability, in which steady planar deflagration is unstable to steady, but nonplanar (cellular), modes of combustion. In a cylindrical geometry, there exist special values of the radius such that the basic solution simultaneously loses stability to two cellular modes at critical values of a parameter that determines the sensitivity of the reaction rate to the local pressure field. A nonlinear stability analysis in the neighborhood of certain members of this sequence of double eigenvalues then leads to the prediction, by either one or the other of two methods, of secondary and tertiary branching of orbitally stable, spinning deflagration waves.

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Nonlinear hydrodynamic stability and spinning deflagration of liquid propellants

Abstract

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