Propagation of a pulsating reaction front in solid fuel combustion

Journal Article · Wed Nov 01 04:00:00 EST 1978 · SIAM J. Appl. Math.; (United States)

DOI:https://doi.org/10.1137/0135038· OSTI ID:6020338

Matkowsky, B J; Sivashinsky, G I

We consider a system of reaction diffusion equations which describe gasless combustion of condensed systems. To analytically describe recent experimental results, we show that a solution exhibiting a periodically pulsating, propagating reaction front arises as a Hopf bifurication from a solution describing a uniformly propagating front. The bifurcation parameter is the product of a nondimensional activation energy and a factor which is a measure of the difference between the nondimensionalized temperature of unburned propellant and the combustion products. We show that the uniformly propagating plant front is stable for parameter values below the critical value. Above the critical value the plane front becomes unstable and perturbations of the system evolve to the bifurcated state, i.e., to the pulsating propagating state. In our nonlinear analysis we calculate the amplitude, frequency and velocity of the propagating pulsating front. In addition we demonstrate analytically that the mean velocity of the oscillatory front is less than the velocity of the uniformly propagating plane front.

• Research Organization: Northwestern Univ., Evanston, IL
• OSTI ID: 6020338
• Journal Information: SIAM J. Appl. Math.; (United States), Journal Name: SIAM J. Appl. Math.; (United States) Vol. 35:3; ISSN SMJMA
• Country of Publication: United States
• Language: English

Related Subjects

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY
400800* -- Combustion
Pyrolysis
& High-Temperature Chemistry
ACTIVATION ENERGY
AMPLITUDES
CALCULATION METHODS
CHEMICAL REACTIONS
COMBUSTION
DIFFERENTIAL EQUATIONS
ENERGY
EQUATIONS
FLAME PROPAGATION
FREQUENCY MEASUREMENT
FUELS
MATHEMATICAL MODELS
NUMERICAL SOLUTION
OXIDATION
PULSATIONS
SOLID FUELS
TEMPERATURE DEPENDENCE
THERMOCHEMICAL PROCESSES
VELOCITY