1 FACE8 Multiphase flow FACE8 2006 Multiphase flow
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FACE8 2006
Multiphase flow
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Course structure
Lecture 1
Intro to multiphase flows. Characterization. Eq. of motion. Particle motion & response time
Lecture 2
Particle-fluid interaction in dilute regime
Lecture 3
Euler-Lagrange formulations. Non-spherical particles. Bubbly flows. Sprays. Granular flows.
Turbulent dispersion
Lecture 4
Turbulent dispersion
Lecture 5
Turbulence modulation
ExcersisesSingle particle modelling
MatLab/EES based
ExcersisesSingle particle modelling
Matlab/EES based
ExcersisesSingle/multiple particle
modellingFLUENT based
ExcersisesSingle/multiple particle
modelling - FLUENT based
ExcersisesSingle/multiple particle
modelling - FLUENT based
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Structure of lecture 2
· 8.15-8.30 Resume· 8.30-9.15 Continue exercises from lecture· 9.15-9.30 Break· 9.30-10.30 Equation of motion· 10.30-10.45 Break· 10.45-11.45 Exercise from lecture 2· 11.45-12.00 Plenum
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Task for lecture 1
· Formulate Stokes law· Formulate drag coefficients in Matlab/EES
▫ Evaluate validity limits▫ Discuss reasons for errors for different correlations
· Plot the motion of a particle under Stokesconditions▫ eg a settling dust particle (dp~5μm, ρ~2500kg/m3)
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Aerodynamic response time - briefly
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Thermal response time - similar
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Stokes number – time scale ratio
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Particle-fluid interaction
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The equation of motion
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Drag force
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Drag force
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Drag forces – flow regime influence
Stokes regime
Gradual build-upof wake
1,
, <<τD
pD
CC
Laminar vortex shedding
Separation of laminar boundary layer
1,
, ≤τD
pD
CC
Critical Reynolds number
Completely turbulentboundary layer
Partly turbulent boundary layerTurbulent vortex shedding
44.0..42.0
1,
,
=≈
>
cstCCC
D
D
pD
τ
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Drag force – other aspects
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Drag force – other aspects
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Drag force – effect of trotation
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Suggested drag coefficients
Modification of Stokes drag - ”departure from Stokes conditions”:
The task: to formulate f in a ”reasonable” manner
)1000(800Re,Re15.01 687.0 <+= ppfSchiller & Naumann (1933):
( ) ( ) 5116.14687.0 105.3Re,Re1025.410175.0Re15.01 ×<×+++=−−
pppfClift & Gauvin (1970):
55.0 105.3Re,Re0167.0Re167.01 ×<++= pppfBrauer (1971):
( ) gvufdtvd
p
+−=τ
ffCCp
StokesDD Re24
, ==
Often product fRep is used
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Other forces
Tab 2.1, Brennen p 40
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Lift forces
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Implementation of forces
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Exercise
· Continue programming…· This time implement the MR equation for non-
Stokes flow▫ Allow for drag+simple lift forces▫ Calculate a trajectory for a ”heavy” and a ”light” particle
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