Non-linear Regression Model for Fitting Experimental Emissions Data

Abstract

Abstract The measurement and reporting of non-volatile Particulate Matter (nvPM) emissions is now integral to aircraft engine emission certification. Akin to other gaseous emissions, CAEP11 sets a new LTO based standard. So far, the question how nvPM emission can be corrected for ambient conditions has to remain open. Addressing this, combustor rig tests may be consulted, where performance parameter such as Air-to-fuel ratio, pressure and temperature can be varied independently. However, results from selected tests may be misleading as nvPM emissions may show measurement uncertainties within actual sensitivities. The paper provides a novel approach utilising experimental data to investigate the prevailing sensitivities at different operation conditions and derive applicable correction factors. This methodology makes use of the fundamental assumption that each change measured in nvPM emissions is explainable with the relative change in combustor AFR, the combustion chamber inlet pressure P3, and combustor inlet temperature T3, for a given combustor design running on the same fuel. Computing the relative changes between all measurements of the same test for all performance and emission parameters enables the fitting of a nonlinear regression model to the experimental data. The fitted function consists of the product of the relative change of the performance parameters to the power of polynomial exponents. The methodology has the potential to be applied to a wide variation of emissions data obtained from different sources as combustor rig tests as well as from engine emission tests. The paper concludes with a first application of the methodology to experimental engine emissions data and a short discussion on AFR sensitivity. In order to set-up a more broadly applicable model nvPM pathways and mechanisms and their dependencies must be better understood helping to identify relevant parameters, e.g. characteristic AFR in the nearfield of the fuel spray nozzle.