The present paper presents a comprehensive approach for modelling soot formation in turbulent flows that incorporates a recently developed conservative finite volume sectional method for the solution of the population balance equation (PBE) into the Large Eddy Simulation - Probability Density Function (LES-PDF) framework for modelling turbulent reacting flows. The approach thus predicts the particle size distribution of soot and accounts for the complete set of aerosol dynamic processes (nucleation, surface growth, oxidation, condensation and aggregation) as well as for the interaction between turbulence, chemistry and soot. We employ a combination of gas-phase chemistry, soot kinetics and aerosol dynamics recently used by the authors in the context of a laminar co-flow diffusion flame and maintain the same kinetics without adjustments in order to focus on the modelling issues in turbulent sooting flame simulations. The results show that several features such as the location of the soot forming zones and the qualitative profiles of soot volume fraction and species concentrations can be predicted reasonably well, but there is a considerable underprediction in the magnitude of soot volume fraction. The possible reasons for this underprediction are discussed in the context of the aforementioned laminar flame simulation and the previous validation of the components of our methodology. The CPU time analysis shows that the solution of the PBE by the conservative sectional method and the associated transport of the discretised number densities account for less than 25% of the total CPU time, indicating that its incorporation in LES-PDF simulations of turbulent combustion is computationally feasible.