L4-mphase-free_surface

8/7/2019 L4-mphase-free_surface

1/47

2006 ANSYS, Inc. All rights reserved. 1 ANSYS, Inc. Proprietary

Free Surface FlowFree Surface Flow

Dr. Alan D. Burns

Senior Software Developer

ANSYS Europe Ltd.

Dr. Alan D. Burns

Senior Software Developer

ANSYS Europe Ltd.


2/47


Free Surface Flow: OutlineFree Surface Flow: Outline

Introduction to Free Surface Flow

Homogeneous Multiphase

Implementation and Examples

Surface Tension

Advanced Topics Inhomogeneous Free Surface Flow

Validation Examples


3/47


What is Free Surface FlowWhat is Free Surface Flow

Free surface flow separated multiphase flow

fluids separated by distinct resolvable interface

examples: open channel flow, flow around ship hulls, water

jet in air (Pelton wheel), tank filling, etc.


4/47


Dimensionless Groups (1)Dimensionless Groups (1)

Froude number

L=h (water depth) for shallow water flow

L=P/2T (wavelength) for sinusoidal wave train in deep water

for flow around ship hulls, there is not a single wave velocity,but we can still define a Froude number based on the ship

geometry

Analogies with Mach number flow can be subcritical, transcritical, or supercritical

hydraulic jump is a shock

Supercritical outlet analogous to Supersonic outlet

speedwavespeedconvective!!

gLVFr


5/47


Dimensionless Groups (2)Dimensionless Groups (2)

Eotvos (Bond) number:

Affects shapes of drops and bubbles.

Weber number

Affects breakup of drops and bubbles.

Capillary number:

Marangoni number:

Marangoni effect = convection on a free surface due to surface tensiondifferences.

forcetensionsurface

forcegravity2!!

W

VgLEo

forcetensionSurface

forceInertialWe

2

!! W

V LU

forcetensionSurface

forceViscous

Re

WeCa !!!

W

QU

PCK

LT

T Q

W Ma

(

x

x!


6/47


Homogeneous MPF (1)Homogeneous MPF (1)

Homogeneous MPF model Air and water are separated by a distinct free surface interface (may be

smeared by numerics)

Only one velocity at each point in space: bulk velocity

Sufficient to solve for this bulk velocity field

iiiiUUrUU !!! E

E

EFE


7/47


Homogeneous MPF (2)Homogeneous MPF (2)

Other Applications in the limit of infinite interphase drag.

Hence also valid when: interphase drag is very large, and

body forces are neglible.

E.g. Cavitation Bubbles: Cavitation bubbles are very small

Cavitation usually occurs in high speed flow situations,

where bubble drift velocity due to gravity is negligible.

iiUU FE !


8/47


Homogeneous MPF: MomentumHomogeneous MPF: Momentum

Phasic momentum equations:

Sum over phases, and assume

Essentially a single-phase momentum equationwith mixture density and viscosity

E

E

EEEEEEEEEE

XV

VVM

x

rgr

x

pr

x

UUr

t

Urj

jii

ij

iji

x

x

x

x!

x

x

x

x )()()(

j

ji

i

ij

iji

xg

x

p

x

UU

t

U

x

x

x

x!

x

x

x

x XV

VV )()(

jiji

rr EE

EEE

E XXVV !!

EE

! ii UU


9/47


Homogeneous MPF: ContinuityHomogeneous MPF: Continuity

Phasic continuity:

If homogeneous:

Still need to solve for separate volume fraction fields.

Volume continuity:

Incompressible case implies:

Solve for (N-1) volume fractions and treat the other as aballast

0)()( !x

xx

xj

j

xUr

tr EEEEE VV

0)()(!

x

x

x

x

j

j

x

Ur

t

rEEEE

VV

0!xx

j

j

xU

1!E

Er


10/47


11/47


Free Surface Flow: DiscretisationFree Surface Flow: Discretisation

MPF Model usually homogeneous MPF model

Advection and transient terms

H

igh resolution scheme is too diffusive for free surface flow Hence use Compressive discretization

interface typically smeared over 2-3 elements

Pressure-velocity coupling (Rhie-Chow) special treatment of buoyancy force to keep flow well-behaved at

interface


12/47


Example: Transcritical BumpExample: Transcritical Bump

Laboratory photo (Forbes, 1988)

Fr=0.32 Fr = 2.5


13/47


Example: Bump (Mesh)Example: Bump (Mesh)


14/47


Example: Bump (Upwind)Example: Bump (Upwind)


15/47


Example: Bump (High Res)Example: Bump (High Res)


16/47


Example: Bump (Compressive)Example: Bump (Compressive)


17/47


Example: Maxwells ExperimentExample: Maxwells Experiment

2-D transient problem

Solved with hex and prismatic meshes

Hex mesh (~10000 nodes on plane)


18/47


Example: Maxwells ExperimentExample: Maxwells Experiment

Upwind Compressive


19/47


Free Surface Flow: Jet with AdaptionFree Surface Flow: Jet with Adaption

No adaption One step Two steps


20/47


Free Surface Flow: Gear BoxFree Surface Flow: Gear Box


21/47


Sink & Trim ProblemSink & Trim Problem


22/47


Free Surface Flow: Solution MethodFree Surface Flow: Solution Method

SVF = Segregated Volume Fractions CFX-10.0 and earlier releases.

Volume fraction coefficients frozen in continuity and gravitational

terms.

Solve 4x4 Momentum-Volume system simultaneously forU, V, W, P Solve phasic mass equations afterwards, for volume fractions, rE,

treating one as balast.

Time Step Restriction

Lagging of gravitational term implies a stability restriction on physicaltime scale.

Must be less than period of internal gravity waves.


23/47


Free Surface Flow: Solution MethodFree Surface Flow: Solution Method

CVF = Coupled Volume Fractions New option in CFX-11.0.

Volume fraction coefficients active in continuity due to Newton

linearisation of mass fluxes.

Volume fraction also active in gravitational term.

Solve (4+N)x(4+N) Momentum-V

olume system simultaneously forU

,V

,W, P, r1, r1, , rN.

Removes time step restriction on stability.

*****

*****

\\

\\**

\\**

\\**

2Mass

1Mass

Volume

mom-

mom

mom

W

V

U

2

1

r

r

P

W

V

U


24/47


Example: Wigley HullExample: Wigley Hull

Mesh

Coarse mesh: 100 000 nodes

Fine mesh: 500 000 nodes

Boundary Conditions Inlet: Velocity-specified

Top: Entrainment opening Far-field: slip walls

Outlet: hydrostatic pressureprofile

Scale information Hull length = 3 m

Speed = 1.45 m/s (Froude number=0.267)

Flow timescale (L/V) = 2 s


25/47


Wigley Hull (1) SVFWigley Hull (1) SVF

Physical Timescale 0.05 s for momentum

0.01 s for volume fraction

small relative to L/Vtimescale

Required for SVF stability

False TimestepLinearisation On

Observations Residuals do not

converge Drag never settles down

Coarse Fine


26/47


Wigley Hull (1) Coarse, CVFWigley Hull (1) Coarse, CVF

Physical Timescale 0.05 s for momentum

0.01 s for volume fraction

Same as for SVF

Observations Residuals converge slowly

Drag converges slowly


27/47


28/47


Wigley Hull (2)Wigley Hull (2)

Coarse mesh Fine mesh


29/47


30/47


Wigley Hull (3)Wigley Hull (3)

Coarse mesh Fine mesh


31/47


32/47


Surface TensionSurface Tension

An attractive force at the free surface

interface

Normal component smooths regions of high curvature

induces pressure rise within droplet: Tangential component

moves fluid along interface toward region of high W

often called Marangoni effect (Wdecreases with temperature)

L

F !F

WO!(p


33/47


Surface Tension: Wall AdhesionSurface Tension: Wall Adhesion

Non-wetting Wetting

Wall adhesion is responsible for capillary rise in

tubes

o90Uo90"U


34/47


Surface Tension: ModellingSurface Tension: Modelling

Conceptually a surface force at interface

awkward to deal with interface topology

Reformulate as a continuum force Brackbill, Kothe, Zemach 1992

Wall contact angle specifies direction of

normal at wall

WWO ss nf ! T

rrn

n

r

fF

s

sss

!

!

!

!

/

O

H

HTT


35/47


Surface Tension: Extreme angleSurface Tension: Extreme angle


36/47


Surface Tension: Colliding dropsSurface Tension: Colliding drops


37/47


Surface Tension: Colliding dropsSurface Tension: Colliding drops


38/47


Inhomogeneous Free Surface (1)Inhomogeneous Free Surface (1)

Possible to use full inhomogeneous Eulerianmultiphase for free surface problems. Computationally more expensive than homogeneous model.

Recommended for problems with unstableoverturning waves (Splashing). Homogeneous model may develop smeared interfaces over

several cells which persist in the solution.

Inhomogeneous model allows light and heavy phases toseparate due to non-zero slip velocities induced by gravity.


39/47



Extreme Example: Rayleigh-Taylor Instability. Inhomogeneous Model:

Homogeneous Model:

Heavy Fluid

Light Fluid

Light Fluid

Heavy Fluid

Heavy Fluid

Light Fluid

Homogeneous

Mixture


40/47



Suggested Implementation Set Liquid Phase Morphology = Continuous.

Set Gas Phase Morphology = Dispersed Bubbles.

Set Drag Law = Grace.

Hence, smeared region is modelled as entrained bubbles in

continuous liquid

Alternative

Set both Phases Morphologies = Continuous.

Set Drag Law = Mixture Model.


41/47


Example: Weir overflow (1)Example: Weir overflow (1)

Homogeneous

model fails when

splashing occurs


42/47


Example: Weir overflow (2)Example: Weir overflow (2)

Inhomogeneousmodel results

Air bubbles with

Grace drag law


43/47


Example: Slug Flow (1)Example: Slug Flow (1)

Experiments by Th. Lex et al,

TD, TU Munich.


44/47


Example: Slug Flow (2)Example: Slug Flow (2)


45/47


46/47


Slug Flow Simulation (2)Slug Flow Simulation (2)


47/47

Slug Flow Simulation (3)Slug Flow Simulation (3)

Date post:	08-Apr-2018
Category:	Documents
Upload:	mustafa-yegen
View:	216 times
Download:	0 times

L4-mphase-free_surface

Documents