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Effect of Turbulence on Flame Radiation

Flame radiation intensities or fluxes are often computed from mean properties (e.g., mean emissivity, mean flame temperature). However, Cox (CoxG:1977) has shown that neglecting turbulent fluctuations could cause significant error in flame radiation intensities, which is due to non-linear nature of radiation properties. Assuming a gray gas, the mean radiation intensity can be represented as:

 $${I = {{σφεT^{4}} \over {π}} \left[ {1+6 \left({{{A}\over{T^{2}}}}\right) + \left({{{B}\over{εT}}}\right) + ...} \right] ; A=T'^{2}, B=4ε' T'}$$
 $${I = {{σφεT^{4}} \over {π}} when \left({{{A}\over{T^{2}}}}\right) > 0.4 }$$

where σ is the Stefan Boltzmann constant, φ is the geometrical view factor, &eps; is the gray gas emissivity of flame, T is the flame temperature, and I is the flame intensity.

While this result suggests a strong effect of turbulence on radiation properties, the gray gas approximation is not very appropriate for turbulent flames. However, Faeth et al (FaethGM:1985) have shown that the use of mean properties, in conjunction with existing narrow band models, provide an adequate framework for estimating flame radiation in both non-luminous and luminous flames. The figure shows the comparison of the predicted spectral radiation intensities by the mean and stochastic property methods with measurements, in the 1-6 μm wavelength range, for a turbulent hydrogen/air flame. The stochastic method is based on the assumption that the turbulent flow field consists of many eddies and that the properties of each eddy are uniform and statistically independent of one another. The figure shows that for hydrogen/air flames, effects of turbulent fluctuations are large, with as much as 2:1 difference between mean and stochastic property predictions. Faeth et al (1985) have argued that this is because radiation properties of hydrogen/air diffusion flames vary rapidly near the stoichiometric condition.

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