Quadrature-based moment methods for the simulation of turbulent polydisperse multiphase systems

This talk will present and discuss a class of approaches for the simulation of turbulent multiphase flows, called quadrature-based moment methods (QBMM). These methods are based on an Eulerian description of the multiphase system, where polydispersity is modeled through a number density function (NDF). Since only transport equations for the (pure and mixed) moments of the NDF are solved, the NDF must be reconstructed from the moments. This is done by using basis functions (such as Dirac delta functions) that result in the use of quadrature approximations for overcoming the so-called closure problem. The talk is divided in two parts. In the first part the Generalized Population Balance Equation (GPBE), that dictates the evolution of the NDF, will be presented and its relationship with similar balance equations (e.g., Boltzmann, Williams, particle dynamics and population balance equations) will be highlighted. Moreover, the derivation from the GPBE of the characteristic equations of the Eulerian-Eulerian multifluid models, widely adopted in many commercial computational fluid dynamics (CFD) codes will be analyzed and its limitations discussed. In the second part of the talk some practical cases will be presented. In particular, the use of our implementations of the quadrature method of moment (QMOM), conditional quadrature method of moments (DQMOM) and direct quadrature method of moments (DQMOM) in Ansys/Fluent, Openfoam and TransAT will be illustrated. Particular attention will be devoted to the coupling with turbulence models, both with the Reynolds-average Navier-Stokes equations (RANS) and large-eddy simulation (LES) approaches. The issues related to the implementation of QMOM, CQMOM and DQMOM in CFD codes based on the finite-volume method will also be considered. The problems of moment corruption, realizability and conservation and the relative strategies to overcome them will be presented and discussed. The potentials of QBMM will be eventually demonstrated by presenting data concerning the simulation of mixing and segregation in fluidized beds, bubble coalescence, break-up and mass transfer in bubble columns and gas-liquid stirred tanks and of turbophoresis in turbulent particle-laden flows.