On the Dynamics of a Combustible Atmosphere
The paper considers plane gas-dynamic waves of small amplitude that propagate through an exothermically reacting (combustible) atmosphere. The latter is spatially uniform but its temperature and pressure are both increasing with time. Any such problem needs several parameters for its description, but four have particular significance; they are the amplitude and frequency of the disturbance, a Reynolds number, based on the initial ambient frozen sound speed and the induction time for the atmosphere, and the activation energy for the chemical reaction as a multiple of the initial level of thermal energy; the inverse of this activation energy number is written as ε (≪ 1).
By identifying certain relationships between the parameters a number of physical situations can be modelled by rational approximate (parameter-perturbation) methods. In particular the following results are derived.
For simple waves of audible acoustic amplitude it is shown that the amplifying effect of the perturbed reacting atmosphere will exceed any damping due to the actions of viscosity and heat conduction; waves of low frequency will be most strongly amplified. Similar results apply to standing acoustic waves, with the fundamental mode being most strongly amplified. Combustible gas mixtures will therefore be naturally “noisy.”
When the dimensionless amplitude and frequency of a simple wave becomes comparable with ϕ, nonlinear gas-dynamic effects become significant. The motion is governed by a modified form of the Burgers equation, and a rapidly amplifying temperature peak can propagate at the local frozen sound speed relative to the gas. In the neighborhood of the consequent imminent local ignition, parameter-perturbation analysis shows that the gas-dynamic character of the process changes. Waves are created that propagate in both directions as each fluid element experiences its own ignition event in conditions that lie between the limits of combustion at constant pressure and constant volume; transport effects are negligible to a first approximation.
KeywordsShock Wave Induction Time Burger Equation Simple Wave Acoustic Disturbance
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