17-egm - Lecture 17 Eulerian-Granular Model Applied...

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Lecture 17 - Eulerian-Granular Model Applied Computational Fluid Dynamics Instructor: André Bakker http://www.bakker.org © André Bakker (2002-2006) © Fluent Inc. (2002)
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Contents Overview. Description of granular flow. Momentum equation and constitutive laws. Interphase exchange models. Granular temperature equation. Solution algorithms for multiphase flows. Examples.
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Overview The fluid phase must be assigned as the primary phase. Multiple solid phases can be used to represent size distribution. Can calculate granular temperature (solids fluctuating energy) for each solid phase. Calculates a solids pressure field for each solid phase. All phases share fluid pressure field. Solids pressure controls the solids packing limit.
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Granular flow regimes Elastic Regime Plastic Regime Viscous Regime. Stagnant Slow flow Rapid flow Stress is strain Strain rate Strain rate dependent independent dependent Elasticity Soil mechanics Kinetic theory
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Collisional Transport Collisional Transport Kinetic Transport Kinetic Transport Kinetic theory of granular flow
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Granular multiphase model: description Application of the kinetic theory of granular flow Jenkins and Savage (1983), Lun et al. (1984), Ding and Gidaspow (1990). Collisional particle interaction follows Chapman-Enskog approach for dense gases (Chapman and Cowling, 1970). Velocity fluctuation of solids is much smaller than their mean velocity. Dissipation of fluctuating energy due to inelastic deformation. Dissipation also due to friction of particles with the fluid.
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Particle velocity is decomposed into a mean local velocity and a superimposed fluctuating random velocity . A “granular” temperature is associated with the random fluctuation velocity: C C r v = 2 1 2 3 θ s u r C r Granular multiphase model: description (2)
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Gas molecules and particle differences Solid particles are a few orders of magnitude larger. Velocity fluctuations of solids are much smaller than their mean velocity. The kinetic part of solids fluctuation is anisotropic. Velocity fluctuations of solids dissipates into heat rather fast as a result of inter particle collision. Granular temperature is a byproduct of flow.
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Analogy to kinetic theory of gases Free streaming Collision Collisions are brief and momentarily. No interstitial fluid effect. Velocity distribution function Pair distribution function
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Several transport mechanisms for a quantity Ψ within the particle phase: Kinetic transport during free flight between collision Requires velocity distribution function f 1. Collisional transport during collisions Requires pair distribution function f 2. Pair distribution function is approximated by taking into account the radial distribution function into the relation between and f 1 and f 2.
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