In recent years the problem of studying particle formation and evolution in turbulent flames has become increasingly important, for both environmental and technological reasons. Information on particle size and morphology is often required, since these characteristics largely influence the effects of particulate matter on human health and global climate in the case of soot. A mathematical model able to describe the evolution of these particulate systems must solve the population balance equation within a Computational Fluid Dynamics (CFD) code that predicts the temperature, composition and velocity fields of the flame. In this work, the recently proposed Direct Quadrature Method of Moments (DQMOM) is applied to the study of soot formation in turbulent non-premixed flames. The model takes into account nucleation, molecular growth, oxidation and aggregation of soot particles; simplified kinetic rates are employed, while velocity and scalar fields are computed by simulations based on the solution of the Reynolds Averaged Navier Stokes (RANS) equations. Different population balance formulations are implemented and compared and results show that DQMOM is a suitable modelling tool; comparison of predictions with experimental data shows that the model accurately describes the morphological properties of soot aggregates.