Appendices include the basic equations involved in coupling the population balance equation (PBE) with fluid flow, heat and mass transfer (Appendix A), the implementation of the conservative finite volume discretisation method (Appendix B), the derivation of the probability density function (PDF) transport equation (Appendix C) and the derivation of the stochastic field equation (Appendix D).

Appendices include the basic equations involved in coupling the population balance equation (PBE) with fluid flow, heat and mass transfer (Appendix A), the implementation of the conservative finite volume discretisation method (Appendix B), the derivation of the probability density function (PDF) transport equation (Appendix C) and the derivation of the stochastic field equation (Appendix D).

Appendices include the basic equations involved in coupling the population balance equation (PBE) with fluid flow, heat and mass transfer (Appendix A), the implementation of the conservative finite volume discretisation method (Appendix B), the derivation of the probability density function (PDF) transport equation (Appendix C) and the derivation of the stochastic field equation (Appendix D).

Appendices include the basic equations involved in coupling the population balance equation (PBE) with fluid flow, heat and mass transfer (Appendix A), the implementation of the conservative finite volume discretisation method (Appendix B), the derivation of the probability density function (PDF) transport equation (Appendix C) and the derivation of the stochastic field equation (Appendix D).

The interaction of turbulent flow with the population balance is treated in this chapter. Approaches are described for integrating the population balance equation (PBE) within turbulent flow simulations based on Reynolds-Averaged Navier-Stokes (RANS), large eddy simulation (LES) and direct numerical simulation (DNS). The focus is on kinetic processes in non-inertial particles. The closure problem and the various unclosed terms that appear in the PBE in turbulent flow are discussed. Subsequently, the fundamental concepts and formulations of presumed and transported probability density function (PDF) methods for addressing the turbulence-PBE interaction are presented and explained. Stochastic numerical methods for solution of the PBE-PDF equation are also discussed.