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O'Rourke P.J.,CFD dOR Software and Consulting LLC | Snider D.M.,Cpfd Software, Llc
Chemical Engineering Science | Year: 2010

This paper describes several improvements to a numerical model introduced by O'Rourke et al. (2009) for collisional exchange and damping in dense particle flows. O'Rourke et al. (2009) use a Bhatnagar, Gross, and Krook (BGK) approximation to the collision terms in a particle distribution function transport equation to model the effects of particle collisions on damping fluctuating particle velocities and, in gas/liquid/solid beds, fluctuating temperatures and compositions of liquid films on particle surfaces. In this paper we focus on particle flows in which the particles have no liquid films and report on an improved expression we have developed for the collision damping time of particle velocity fluctuations used in the BGK approximation. The improved expression includes the effects on the collision damping time of the particle material coefficient of restitution and of non-equilibrium particle velocity distributions. The collision model improvements are incorporated into the general-purpose computational-particle fluid dynamics (CPFD) numerical methodology for dense particle flows. Three computational examples show the benefits of using the new collision time in calculations of particle separation in polydisperse dense particle flows and calculations of colliding particle jets. © 2010 Elsevier Ltd.


O'Rourke P.J.,CFD dOR Software and Consulting LLC | Snider D.M.,Cpfd Software, Llc
Powder Technology | Year: 2014

We use the Multi-Phase Particle-in-Cell (MP-PIC) numerical method to simulate binary fluidized beds and find that experimentally measured separation of the two particle types in such beds can be explained by including a new contact force model in MP-PIC that accounts for the inhibition of relative motion between particles of differing sizes or densities. Without the new contact force model, we find that there is poor agreement between experimentally measured and MP-PIC calculated particle separation. In the new contact force model, individual particle accelerations are a blend between the particle acceleration of the original MP-PIC method, appropriate for rapid granular flows, and an average particle acceleration that applies to closely packed granular flows, and we call the new model the "blended acceleration" model. In this paper, we develop the equations of the blended acceleration model, detail its numerical implementation, verify correct implementation by comparing with an analytic solution for one-dimensional binary beds, and compare MP-PIC calculation results with three sets of measurements of particle separation in binary beds. © 2014 Elsevier B.V.


Snider D.M.,Cpfd Software, Llc | Clark S.M.,Cpfd Software, Llc | O'Rourke P.J.,CFD dOR Software and Consulting LLC
Chemical Engineering Science | Year: 2011

Energy transport and chemistry are modeled in an extension of the Eulerian-Lagrangian computational particle fluid dynamics (CPFD) methodology. The CPFD methodology is based on the MP-PIC method, which uses a stochastic particle method for the particle phase and an Eulerian method for the fluid phase, to solve equations for dense particle flow. In our extension of CPFD, an enthalpy equation describes energy transport for fluid, and provides for transfer of sensible and chemical energy between phases and within the fluid mixture. Homogenous and heterogeneous chemistry are described by reduced-chemistry, and the reaction rates are implicitly solved numerically on the Eulerian grid. Inter-phase momentum and energy transfer are also implicitly calculated, giving a robust numerical solution from the dilute flow to close-pack limits. A three-dimensional example of a hot fluidized bed coal gasifier is presented with homogeneous and heterogeneous chemistry. The inter-dependencies of fluidization, thermal, and chemistry behaviors in this complex three-dimensional calculation are described. © 2010 Elsevier Ltd.


O'Rourke P.J.,CFD dOR Software and Consulting LLC | Snider D.M.,Cpfd Software, Llc
Chemical Engineering Science | Year: 2012

We document a new method for including collisional return-to-isotropy in particle velocity distributions calculated by the MP-PIC method for numerical simulation of particle/fluid flows. Mathematically, we include the new method by adding to the transport equation for the particle distribution function (PDF), a Bhatnager, Gross, and Krook (BGK) collision term that causes velocity distributions to relax to isotropic Gaussian distributions. The numerical implementation is by a splitting technique in which we randomly sample from velocity distributions obtained as solutions to the PDF transport equation with just the return-to-isotropy source. Thus, collisions cause numerical particles to scatter in MP-PIC calculations, just as physical particles do in particle/fluid flows. The method is implemented in the Barracuda © code, and two computational examples verify proper implementation of the method and show that more realistic results are obtained in calculations of impinging particle jets. In an appendix, we derive the particle continuum-flow (PCF) equations implied by the MP-PIC method in the collision dominated limit, and we obtain the collisional relaxation time for return-to-isotropy by matching the shear viscosity of the MP-PIC PCF equations, and the kinetic part of the shear viscosity used in PCF equations in the literature. © 2012 Elsevier Ltd.

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