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Radiation and Velocity Fields Induced by Localized Temperature Fluctuations.

Radiation and Velocity Fields Induced by Localized
Temperature Fluctuations.
(259 K)

Baum, H. R.; Mell, W. E.

Combustion Institute, Symposium (International) on
Combustion, 28th. Proceedings. Volume 1. July
20-August 4, 2000, Edinburgh, Scotland, Combustion
Institute, Pittsburgh, PA, Candel, S.; Driscoll, J. F.;
Burgess, A. R.; Gore, J. P., Editor(s), 473-479 pp, 2000
AND Combustion Institute, 1st Joint Meeting of the U.S.
Sections: Western States, Central States, Eastern
States. Proceedings. 709-712 pp, March 14-17, 1999,
2000.

### Keywords:

combustion; fluid mechanics; fluctuations; radiation;
temperature; mathematical models

### Abstract:

*
A theory describing the coupling between radiative
transport, thermal conduction, and velocity fluctuations
in post-combustion gases is described. The emission and
absorption of radiant energy are taken to be dominated
by soot, distributed uniformly in space. The theory is
local in the sense that the gas is assumed to be
unbounded. However, the temperature, velocity, and
radiation fields can be both three-dimensional and time
dependent. Moreover, the model can be thought of as
describing any post-combustion scenario where the
absorption coefficient is spatially uniform. Within the
framework of the low Mach number combustion equations,
an exact representation of the velocity and rediation
fields instantaneously induced by fluctuations of any
magnitude in the temperature is presented. This result
is used to derive a single scalar integro-differential
equation for the temperature that incorporates the
conservation of mass, energy, and radiation. Some
consequences of the theory are illustrated by studying
the response generated by a spherically burning fuel
mass. More general fluctuations are discussed briefly by
calculating the velocity and rediation fields induced by
prescribed multi-dimensional temperature fluctuations.
*