The simulation of soot formation in turbulent diffusion flames is carried out within a CFD code, by coupling kinetics and fluid dynamics computations with the solution of the population balance equation via the Direct Quadrature Method of Moments, a novel and efficient approach based on a quadrature approximation of the size distribution of soot particles. A turbulent non-premixed ethylene-air flame is used as the test case for validation of the model. Simplified kinetic expressions are employed for modelling nucleation, molecular growth and oxidation of particles, along with a Brownian aggregation kernel. A recently proposed approach for modelling the evolution of fractal dimension is used with a monovariate population balance to predict the morphological properties of aggregates. (c) 2005 Elsevier Ltd. All rights reserved.