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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