A two-equation turbulence model for dispersed dilute confined two-phase flows

Rizk, Magdi; Elghobashi, S.

doi:10.1016/0301-9322(89)90089-x

Cited by 162 publications

(57 citation statements)

References 18 publications

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“…Especially in turbulent flows, the closure of the dispersed phase kinetic stresses and the fluid-particle interaction terms are associated with sophisticated modelling approaches (see e.g. Rizk and Elghobashi [21], Simonin et al [22], Simonin [23]). The consideration of a particle size distribution requires the solution of a set of the conservation equations for each particle size class by accounting, if required, by exchange terms due to inter-particle collisions/coalescence and break-up.…”

Section: Multiphase Flow Modelsmentioning

confidence: 99%

State of the Art and Future Trends in CFD Simulation of Stirred Vessel Hydrodynamics

Sommerfeld¹,

Decker

2004

Chem Eng & Technol

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Computational fluid dynamics (CFD) has become a widely used tool for analysing, optimising and supporting the design of mixing processes in stirred vessels. The present contribution gives a brief summary of the methods applied for numerically treating the power input by the impeller, such as empirical methods, the multiple frame of reference approach and unsteady methods using sliding or clicking meshes. Thereafter, recent developments and trends in the numerical computation of single phase flows in stirred vessels on the basis of DNS (direct numerical simulations), LES (large eddy simulations) and RANS (Reynolds-averaged Navier-Stokes) approaches are summarised. Since many operations in stirred vessels involve at least two phases, also the methods for modelling these flows, such as the two-fluid method and the Euler/Lagrange approach are briefly described and recent applications are reviewed. Finally, also own calculations for single-phase mixing and particle dispersion in a stirred vessel using the Euler/Lagrange approach are introduced emphasising some recent developments.

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Section: Multiphase Flow Modelsmentioning

confidence: 99%

State of the Art and Future Trends in CFD Simulation of Stirred Vessel Hydrodynamics

Sommerfeld¹,

Decker

2004

Chem Eng & Technol

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“…It is possible, therefore, that such numerical methods could produce a bounded continuous solution to the problem of steady flow past a flat plate when, in fact, none should exist. Second, many two phase turbulence models (see, for example, Pourahmadi and Humphrey, 1983;Elghobashi et al, 1984;Chen and Wood, 1986;and Rizk and Elghobashi, 1989) contain diffusion terms in the particle phase mass balance. It is possible that the presence of such terms is critical to the existence of solutions in these models.…”

Section: U C =F C (Ii) V C = ({\~-I)/(li)) Y \Gmi) + Rf C (Iri))mentioning

confidence: 99%

Boundary Layer Theory for a Particulate Suspension

Chamkha

Peddieson

1994

Journal of Fluids Engineering

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IntroductionThis paper is concerned with boundary layer theory for a particulate suspension. Given the importance of boundary layers in applications, this topic has received surprisingly little attention. There is a history of work on the problem of the steady laminar boundary layer on a semi-infinite flat plate with recent contributions by Osiptsov (1980), Prabha andJain (1980), andWang andGlass (1988). References to earlier work can be found in these papers. In contrast to investigations of the flat plate and a few other specific geometries, there appears to have been little effort devoted to determining the general form of boundary layer equations. The present paper deals with this topic.A boundary layer order of magnitude analysis is carried out using a typical set of two fluid equations representative of the current literature. It is found that a variety of outcomes are possible depending on the order of magnitude assumptions selected. Three of the most interesting cases are singled out for explicit presentation. Some specific numerical results are then given for the problem of steady laminar boundary layer flow past a semi-infinite flat plate. It is shown that the boundary layer model employed greatly influences predictions.

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“…This problem is similar to the modelling of particle turbulent viscosity in the twin-fluid modelling of particle-laden turbulent flows [13,21]. Following Rizk and Elghobashi [21], this parameter can be estimated by…”

Section: Stochastic -Probabilistic Particle Dispersion Modelmentioning

confidence: 99%