A quadrature-based moment method for dilute fluid-particle flows

Desjardins, Olivier; Fox, Rodney O.; Villedieu, Philippe

doi:10.1016/j.jcp.2007.10.026

Cited by 160 publications

(216 citation statements)

References 31 publications

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“…The method of moments, presented in [5,6], consists in taking the first moments of the equation that we have to solve in order to reduce the number of variables. The system is closed by assuming that the distribution function is made of water-bags.…”

Section: Methods Of Momentsmentioning

confidence: 99%

Multi-Water-Bag Model And Method Of Moments For The Vlasov Equation

Crestetto

Helluy

2011

Finite Volumes for Complex Applications VI Problems &Amp; Perspectives

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The kinetic Vlasov-Poisson model is very expensive to solve numerically. It can be approximated by a multi-water-bag model in order to reduce the complexity. This model amounts to solve a set of Burgers equations, which can be done easily by finite volume methods. However, the solution is naturally multivalued (filamentation). The multivalued solution can be computed by a moment method. We present here several numerical experiments.

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Section: Methods Of Momentsmentioning

confidence: 99%

Multi-Water-Bag Model And Method Of Moments For The Vlasov Equation

Crestetto

Helluy

2011

Finite Volumes for Complex Applications VI Problems &Amp; Perspectives

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“…The moment spatial fluxes are closed according to their kinetic description [15,18,34]. First, the moments involved in the spatial fluxes are decomposed in two contributions:…”

Section: Closure Of Moment Spatial Fluxesmentioning

confidence: 99%

“…By definition, kinetic-based fluxes combined with a finite-volume method ensure the realizability of the transported moments and exactly reproduce particle trajectory crossing [15]. This would not be generally true if traditional interpolation methods were used to compute the moment spatial fluxes.…”

Section: Closure Of Moment Spatial Fluxesmentioning

confidence: 99%

“…This would not be generally true if traditional interpolation methods were used to compute the moment spatial fluxes. It is worth noting that the realizability condition of the transported moments is guaranteed if a firstorder interpolation scheme is employed to evaluate the cell-face values of weights and abscissas used in the computation of the fluxes [15]. However particular care has to be taken when adopting high-order interpolation schemes, since the condition of moment realizability is not automatically satisfied.…”

Section: Closure Of Moment Spatial Fluxesmentioning

confidence: 99%

“…The moment transport equations can be solved using the finite-volume method [15,17]. For sake of simplicity, we denote the set of moments M γ ijk by M, the set of weights and abscissas by N = [ρ α ,U α ], the spatial fluxes computed as a function of the weights and abscissas by Q − and Q + , and the collision terms by C. With this new notation, Eq.…”

Section: Solution Algorithm For the Moment Transport Equationsmentioning

confidence: 99%

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A Quadrature-Based Kinetic Model for Dilute Non-Isothermal Granular Flows

Passalacqua

Galvin²,

Vedula

et al. 2011

Commun. comput. phys.

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A moment method with closures based on Gaussian quadrature formulas is proposed to solve the Boltzmann kinetic equation with a hard-sphere collision kernel for mono-dispersed particles. Different orders of accuracy in terms of the moments of the velocity distribution function are considered, accounting for moments up to seventh order. Quadrature-based closures for four different models for inelastic collisionthe Bhatnagar-GrossKrook, ES-BGK, the Maxwell model for hard-sphere collisions, and the full Boltzmann hard-sphere collision integral-are derived and compared. The approach is validated studying a dilute non-isothermal granular flow of inelastic particles between two stationary Maxwellian walls. Results obtained from the kinetic models are compared with the predictions of molecular dynamics (MD) simulations of a nearly equivalent system with finite-size particles. The influence of the number of quadrature nodes used to approximate the velocity distribution function on the accuracy of the predictions is assessed. Results for constitutive quantities such as the stress tensor and the heat flux are provided, and show the capability of the quadrature-based approach to predict them in agreement with the MD simulations under dilute conditions. Abstract. A moment method with closures based on Gaussian quadrature formulas is proposed to solve the Boltzmann kinetic equation with a hard-sphere collision kernel for mono-dispersed particles. Different orders of accuracy in terms of the moments of the velocity distribution function are considered, accounting for moments up to seventh order. Quadrature-based closures for four different models for inelastic collisionthe Bhatnagar-Gross-Krook, ES-BGK, the Maxwell model for hard-sphere collisions, and the full Boltzmann hard-sphere collision integral-are derived and compared. The approach is validated studying a dilute non-isothermal granular flow of inelastic particles between two stationary Maxwellian walls. Results obtained from the kinetic models are compared with the predictions of molecular dynamics (MD) simulations of a nearly equivalent system with finite-size particles. The influence of the number of quadrature nodes used to approximate the velocity distribution function on the accuracy of the predictions is assessed. Results for constitutive quantities such as the stress tensor and the heat flux are provided, and show the capability of the quadrature-based approach to predict them in agreement with the MD simulations under dilute conditions. Disciplines Aerospace Engineering | Biological Engineering | Chemical Engineering | Mechanical Engineering Comments This article is from Communication in Computational Physics

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Modeling the thermochemical degradation of biomass inside a fast pyrolysis fluidized bed reactor

Bruchmüller

Wachem

et al. 2011

AIChE Journal

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A fast pyrolysis process in a bubbling fluidized bed has been modeled, thoroughly reproduced and scrutinized with the help of a combined Eulerian/Lagrangian simulation method. The 3-D model is compared to experimental results from a 100 g/h bubbling fluidized bed pyrolyzer including such variables as particle composition at the outlet and gas/vapor/water yields as a function of fluidization conditions, biomass moisture concentrations, and bed temperatures. Multiprocessor simulations on a high-end computer have been carried out to enable the tracking of each of the 0.8 million individual discrete sand and biomass particles, making it possible to look at accurate and detailed multiscale information (i.e., any desired particle property, trajectory, particle interaction) over the entire particle life time. The overall thermochemical degradation process of biomass is influenced by local flow and particle properties and, therefore, accurate and detailed modeling reveals unprecedented insight into such complex processes. It has been found, that the superficial fluidization velocity is important while the particle moisture content is less significant for the final bio-oil yield

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A quadrature-based moment method for dilute fluid-particle flows

Cited by 160 publications

References 31 publications

Multi-Water-Bag Model And Method Of Moments For The Vlasov Equation

Multi-Water-Bag Model And Method Of Moments For The Vlasov Equation

A Quadrature-Based Kinetic Model for Dilute Non-Isothermal Granular Flows

Modeling the thermochemical degradation of biomass inside a fast pyrolysis fluidized bed reactor

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