15-dpm - Lecture 15 Discrete Phase Modeling Applied...

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1 Lecture 15 - Discrete Phase Modeling Applied Computational Fluid Dynamics Instructor: André Bakker http://www.bakker.org © André Bakker (2002-2006) © Fluent Inc. (2002)
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2 Discrete phase modeling Particle tracking. Steady vs. unsteady. Coupled vs. uncoupled. Advantages and limitations. Time stepping. Discretization. Particle trajectories in a spray dryer Particle trajectories in a cyclone
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3 Discrete phase model Trajectories of particles/droplets are computed in a Lagrangian frame. Exchange (couple) heat, mass, and momentum with Eulerian frame gas phase. Discrete phase volume fraction should preferably be less than 10%. Mass loading can be large (+100%). No particle-particle interaction or break up. Turbulent dispersion modeled by: Stochastic tracking. Particle cloud model. Model particle separation, spray drying, liquid fuel or coal combustion, etc. continuous phase flow field calculation particle trajectory calculation update continuous phase source terms
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4 DPM theory Trajectory is calculated by integrating the particle force balance equation: typical continuous phase control volume mass, momentum and heat exchange ( 29 p i p p i p i i D p i F g u u F dt du ρ ρ ρ ρ / / ) ( + - + - = drag force is a function of the relative velocity Additional forces: Pressure gradient Thermophoretic Rotating reference frame Brownian motion Saffman lift Other (user defined) Gravity force
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5 Coupling between phases One-way coupling: Fluid phase influences particulate phase via drag and turbulence. Particulate phase has no influence on the gas phase. Two-way coupling: Fluid phase influences particulate phase via drag and turbulence. Particulate phase influences fluid phase via source terms of mass, momentum, and energy. Examples include: Inert particle heating and cooling. Droplet evaporation. Droplet boiling. Devolatilization. Surface combustion.
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6 Particle types are inert, droplet and combusting particle. Particle types Particle Type Description Inert inert/heating or cooling Droplet (oil) heating/evaporation/boiling Combusting (coal) heating; evolution of volatiles/swelling; heterogeneous surface reaction
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7 Temperature particle time Inert heating law Vaporization law Boiling law T b T v T injection Heat and mass transfer to a droplet
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8 volatile fraction flashes to vapor Escape Reflect Trap Particle-wall interaction Particle boundary conditions at walls, inlets, and outlets: For particle reflection, a restitution coefficient e is specified: t t t n n n v v e component: Tangential v v e component: Normal , 1 , 2 , 1 , 2 = =
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9 Particle fates “Escaped” trajectories are those that terminate at a flow boundary for which the “escape” condition is set. “Incomplete” trajectories are those that were terminated when the maximum allowed number of time steps was exceeded.
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