A Theoretical Model for the Correlation of Smoke Number to Dry Particulate Concentration in Diesel Exhaust

A correlation between reflectance type smoke measurements and dry particulate concentrations in diesel exhaust is derived from first principles. The model has one free parameter; the mass-average diameter of the exhaust particulates. Data from the literature indicates that particulate diameters can vary depending upon the injection hardware, fuel properties, and combustion chamber design. Older engines typically have larger average particulate radii and run at higher smoke numbers. Using a simple linear relationship between smoke number and mass-averaged particulate diameter, a good match is obtained between the derived model and experimental data. As a further validation of the model, a technique is derived by which any correlation between smoke and particulate concentration can be validated with only a smoke meter, provided it has multiple draw capabilities. Using this novel technique, the correlation derived here is shown to be functionally correct.