Application of the Lambert W function for the impact of the exhaust gas turbocharger on nanoscale PM emissions from a TGDI engine

•Nano-scale PM from a TGDI engine is measured before and after the turbine.•Variations in PM across the turbine are modelled by means of the Lambert W Function.•The model predicts turbine-out PM with a coefficient of determination of 0.917.•The input variables of the model are known to the ECU or can be measured on-board.•The model could be implemented within engine performance simulation software.

A phenomenological model based on the Lambert WW Function is presented which is capable of describing the variations in nano-scale particulate matter (PM) number concentrations across the turbine stage of a turbocharged gasoline direct injected (TGDI) engine over a wide range of engine operating conditions with a coefficient of determination (CDCD) of 0.917. The model predictors are variables which are available to the engine control unit (ECU) either by means of stored maps or on-board measurements. The suitability of the proposed model for real-time usage within the ECU for vehicle calibration is discussed.