This thesis investigates mean reaction rate closures for turbulent reacting flow. The closures model the mean rate of reaction in the flow and are applied to simulations of nanoparticle formation. The simulations couple detailed chemical reaction, particle population dynamics and turbulent flow, and offer the potential to improve the understanding of a range of industrial processes. The numerical behaviour of a mean reaction rate closure based on the direct quadrature method of moments using the interaction by exchange with the mean micromixing model (DQMoM-IEM) is studied in detail. An analytic expression is presented for the source terms and a filter function introduced to address issues of boundedness and singularity. Analytic integrals are presented for special cases of specific terms. The implementation of the method in the Star-CD computational fluid dynamics code is described in detail and validated against a test problem. The numerical performance of DQMoM-IEM is systematically compared to the stochastic fields (SF) turbulent reaction model. The methods share many similarities and are presented in a common mathematical framework for the first time. They differ in their treatment of key terms that make DQMoM-IEM numerically challenging. A variance reduction technique using antithetic sampling is introduced to increase the efficiency of the SF method. However, DQMoM-IEM is shown to remain competitive for the test problem considered. A new methodology is presented to couple a detailed particle model to simulations of turbulent reacting flow. A projected fields (PF) method based on DQMoM-IEM is used to combine detailed chemistry and the method of moments with interpolative closure (MoMIC) population balance model in Star-CD. The method is applied to the example of the chloride process for the industrial synthesis of titania nanoparticles and includes full coupling between the flow, chemistry and particles undergoing simultaneous inception, coagulation and surface growth.