Re-examination of the emissivity of diesel flames

Abstract

In the Hottel and Broughton equation, the spectral emissivity of soot in flames in the visible wavelength range is characterized by an index α = 1.39, which represents the effect of wavelength on extinction (Hottel and Broughton, 1932). In this study, the spectral specific extinction for diesel soot is examined first by focusing on soot layers sampled on a quartz window from the engine cylinder, and α = 1.38 is obtained. To examine the physics governing the value of α = 1.38, a calculation of spectral extinction is performed using the Rayleigh–Debye–Gans (RDG) theory of soot aggregate scattering with an assumption of constant refractive index. The calculated spectral extinction provides α = 1.31 close to α = 1.38, suggesting that scattering, as well as absorption, contributes largely to the spectral extinction of diesel soot. The attenuation of line-of-sight beam intensity due to out-scattering and the augmentation of the beam intensity as a result of scattering of incoming radiation from other regions are investigated using soot aggregate scattering theory. Based on this approach, a new formula of apparent spectral emissivity ε_a is proposed, allowing a theoretical explanation of the physical meaning of the KL factor defined in the Hottel and Broughton equation, which has remained vague for many years. Finally the two-colour flame temperature and the KL factor in a production engine are calculated using the new emissivity formula and are compared with those obtained using the conventional emissivity formula. The result shows that the two-colour method using the conventional emissivity formula remains quite useful, and provides values of temperature and KL factor within 1–2 per cent of those obtained with the new emissivity formula.