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18-eulmp

# 18-eulmp - Lecture 18 Eulerian Flow Modeling Applied...

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1 Lecture 18 - Eulerian Flow Modeling Applied Computational Fluid Dynamics Instructor: André Bakker http://www.bakker.org © André Bakker (2002-2006) © Fluent Inc. (2002)

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2 Contents Overview of Eulerian-Eulerian multiphase model. Spatial averaging. Conservation equations and constitutive laws. Interphase forces. Heat and mass transfer. Discretization. Solver basics.
3 Eulerian-Eulerian multiphase - overview Used to model droplets or bubbles of secondary phase(s) dispersed in continuous fluid phase (primary phase). Allows for mixing and separation of phases. Solves momentum, enthalpy, and continuity equations for each phase and tracks volume fractions. Uses a single pressure field for all phases. Uses interphase drag coefficient. Allows for virtual mass effect and lift forces. Multiple species and homogeneous reactions in each phase. Allows for heat and mass transfer between phases. Can solve turbulence equations for each phase.

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4 Methodology A general multiphase system consists of interacting phases dispersed randomly in space and time. Interpenetrating continua. Methods: Use of continuum theory and thermodynamical principles to formulate the constitutive equations (ASMM). Use of microstructural model in which macroscopic behavior is inferred from particle interaction: Eulerian-Granular. Use of averaging techniques and closure assumptions to model the unknown quantities: Space averaging with no time averaging. Time averaging with no space averaging. Ensemble averaging with no space averaging. space/time or ensemble/space averaging: Eulerian-Eulerian.
5 Two-fluid model (interpenetrating continua) Deductive approach: Assume equations for each pure phase. Average (homogenize) these equations. Model the closure terms. Inductive approach: Assume equations for interacting phases. Model the closure terms.

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6 Application of the general transport theorem to a property Ψ k gives the general balance law and its jump condition: Continuity equation: Momentum equation: 0 , 0 , = = = k k k k J ϕ ρ ψ & r k k k k k k k k k F I P J u r & r ρ ϕ τ ρ ψ = - = = , , k k k k k J u t ϕ ψ ψ & r r = + + 0 ) ) ( ( , 1 = + - = k ki ki i k n i k i k J n n u u r r r ψ Spatial averaging: basic equations
7 Consider an elementary control volume d bounded by the surface dS.

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