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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.