Alberto Passalacqua

Realizable high-order finite-volume schemes for quadrature-based moment methods

Dilute gas-particle flows can be described by a kinetic equation containing terms for spatial transport, gravity, fluid drag and particle-particle collisions. However, direct numerical solution of kinetic equations is often infeasible because of the large number of independent variables. An alternative is to reformulate the problem in terms of the moments of the velocity distribution. Recently, a quadrature-based moment method was derived for approximating solutions to kinetic equations. The success of the new method is based on a moment-inversion algorithm that is used to calculate non-negative weights and abscissas from the moments. The moment-inversion algorithm does not work if the moments are non-realizable, which might lead to negative weights. It has been recently shown [14] that realizability is guaranteed only with the 1st-order finite-volume scheme that has an inherent problem of excessive numerical diffusion. The use of high-order finite-volume schemes may lead to non-realizable moments. In the present work, realizability of the finite-volume schemes in both space and time is discussed for the 1st time. A generalized idea for developing realizable high-order finite-volume schemes for quadrature-based moment methods is presented. These finite-volume schemes give remarkable improvement in the solutions for a certain class of problems. It is also shown that the standard Runge-Kutta time-integration schemes do not guarantee realizability. However, realizability can be guaranteed if strong stability-preserving (SSP) Runge-Kutta schemes are used. Numerical results are presented on both Cartesian and triangular meshes.

Characterizing Effects of the Shape of Screw Conveyors in Gas–Solid Fluidized Beds Using Advanced Numerical Models

A numerical study of the effects of the shape of an enclosed screw conveyor on the mixing and heat transfer in a horizontal gas–solid fluidized bed was conducted using computational fluid dynamics (CFD). A two-fluid model (TFM) was employed to model the gas and solid phases as continua through mass, momentum, and energy conservations. The motion of the screw conveyor was simulated by using a rotating reference frame (RRF) such that the computational mesh was free from dynamic reconstruction. The diameters of the screw flight and shaft, the pitch, and the blade thickness were varied in the parametric study. Under the operating conditions studied, it was found that the increase in the diameter of the screw flight results in the enhancement of the solid mixing and conveyance. The increase in the diameters of the screw shaft and the screw blade thickness lead to the enhanced solid mixing but reduced conveyance. The variation in the screw pitch gives rise to rather complex behaviors in the solid mixing and conveyance. As the screw pitch is decreased, the solid mixing increases initially but then decreases before it increases eventually. The solid conveyance capability was found to first increase and then decrease. Explanations to the effects of the shape of the screw conveyor were discussed in this work.

Development of High-Order Realizable Finite-Volume Schemes for Quadrature-Based Moment Method

Kinetic equations containing terms for spatial transport, gravity, fluid drag and particleparticle collisions can be used to model dilute gas-particle flows. However, the enormity of independent variables makes direct numerical simulation of these equations almost impossible for practical problems. A viable alternative is to reformulate the problem in terms of moments of velocity distribution. Recently, a quadrature-based moment method was derived by Fox for approximating solutions to kinetic equation for arbitrary Knudsen number. Fox also described 1 st - and 2 nd -order finite-volume schemes for solving the equations. The success of the new method is based on a moment-inversion algorithm that is used to calculate non-negative weights and abscissas from moments. The moment-inversion algorithm does not work if the moments are non-realizable, meaning they do not correspond to a distribution function. Not all the finite-volume schemes lead to realizable moments. Desjardins et al. showed that realizability is guaranteed with the 1 st -order finite-volume scheme, but at the expense of excess numerical diffusion. In the present work, the nonrealizability of the standard 2 nd -order finite-volume scheme is demonstrated and a generalized idea for the development of high-order realizable finite-volume schemes for quadrature-based moment methods is presented. This marks a significant improvement in the accuracy of solutions using the quadrature-based moment method as the use of 1 st -order scheme to guarantee realizability is no longer a limitation.

An Explicit Method for the Packing Limit Management in Dense Gas-Solid Flow CFD Simulations on Both Structured and Unstructured Grids

An explicit method for limiting the volume fraction of the dispersed phase in the CFD simulations of dense gas-solid flows is described and validated both on structured and unstructured computational grids. The procedure is based on the excess solids volume correction method proposed by Lettieri et al. (2003), which has been extended in this work to non-uniform grids made of cells having different shape and size. The method has been implemented in OpenFOAM and validated through the simulation of a fluidised bed in which the superficial gas velocity has been reduced to a value close to zero.

Application of the Fokker-Planck molecular mixing model to turbulent scalar mixing using moment methods

An extended quadrature method of moments using the β kernel density function (β-EQMOM) is used to approximate solutions to the evolution equation for univariate and bivariate composition probability distribution functions (PDFs) of a passive scalar for binary and ternary mixing. The key element of interest is the molecular mixing term, which is described using the Fokker–Planck (FP) molecular mixing model. The direct numerical simulations (DNSs) of Eswaran and Pope [“Direct numerical simulations of the turbulent mixing of a passive scalar,” Phys. Fluids 31, 506 (1988)] and the amplitude mapping closure (AMC) of Pope [“Mapping closures for turbulent mixing and reaction,” Theor. Comput. Fluid Dyn. 2, 255 (1991)] are taken as reference solutions to establish the accuracy of the FP model in the case of binary mixing. The DNSs of Juneja and Pope [“A DNS study of turbulent mixing of two passive scalars,” Phys. Fluids 8, 2161 (1996)] are used to validate the results obtained for ternary mixing. Simulations are p...

CFD Modelling of Bubbly Flow in Adiabatic Upward Pipe Using a Solver Based on OpenFOAM® With the Quadrature Method of Moments

An Eulerian-Eulerian approach was used to model adiabatic bubbly flow with CFD techniques. The OpenFOAM® solver twoPhaseEulerFoam was modified to predict upward bubbly flow in vertical pipes. Interfacial force and bubble induced turbulence models are studied and implemented. The population balance equation included in the two-fluid model is solved to simulate a polydisperse flow with the quadrature method of moments approximation. Two-phase flow experiments with different superficial velocities of gas and water at different temperatures are used to validate the solver. Radial distributions of void fraction, air and water velocities, Sauter mean diameter and turbulence intensity are compared with the computational results. The computational results agree well with the experiments showing the capability of the solver to predict two-phase flow characteristics.Copyright