Accounting for effects of coagulation and model uncertainties in particle number concentration estimates based on measurements from sampling lines - a Bayesian inversion approach with SLIC v1.0

Abstract

The particle number (PN) emissions of both light- and heavy-duty vehicles are nowadays regulated and are typically measured from a full dilution tunnel with constant volume sampling (CVS). PN measurements for research and development purposes, though, are often taken from the raw exhaust to avoid the high setup costs of CVS. There is, however, a risk with these and any other kind of PN measurements with high number concentrations, which is that physical processes such as coagulation and diffusion losses inside sampling lines can alter, sometimes dramatically, the particle size distribution and bias its measurement. In this paper, we propose a method in the Bayesian framework for inverse problems to estimate the initial, unaltered particle size distribution based on the distorted measurements. The proposed method takes into account particle morphology and van der Waals and viscous forces in the coagulation model and allows the incorporation of prior information on the particle size distribution and, most importantly, a systematic quantification of uncertainty. We analyze raw exhaust PN measurements of a fuel-operated auxiliary heater and find that while a typical sampling line can reduce the PN by more than 50%, the initial particle size distribution can be feasibly estimated with reasonable computational demands. The proposed method should give more freedom for designing the measurement setup and also aid in the comparison of results obtained at different sampling locations, such as CVS and tailpipe.