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Lecture 18  Eulerian Flow Modeling
Applied Computational Fluid Dynamics
Instructor: André Bakker
http://www.bakker.org
© André Bakker (20022006)
© Fluent Inc. (2002)
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Contents
•
Overview of EulerianEulerian multiphase model.
•
Spatial averaging.
•
Conservation equations and constitutive laws.
•
Interphase forces.
•
Heat and mass transfer.
•
Discretization.
•
Solver basics.
3
EulerianEulerian 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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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: EulerianGranular.
–
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: EulerianEulerian.
5
Twofluid 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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•
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
τ
=

=
=
,
,
k
k
k
k
k
J
u
t
r
r
=
⋅
∇
+
⋅
∇
+
∂
∂
0
)
)
(
(
,
1
=
⋅
+
⋅

∑
≠
=
k
ki
ki
i
k
n
i
k
i
k
J
n
n
u
u
r
r
r
Spatial averaging: basic equations
7
•
Consider an elementary control volume
d
Ω
bounded by the
surface
dS.
–
Length scales:
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This note was uploaded on 12/04/2010 for the course M MM4CFD taught by Professor N/a during the Fall '10 term at Uni. Nottingham.
 Fall '10
 N/A

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