3d-surface engineering für werkzeug- systeme der ... · dynamics of droplet generation (b7)...

3D-Surface Engineering für Werkzeug-

systeme der Blechformteilefertigung

- Erzeugung, Modellierung, Bearbeitung -

O. Mierka, O. Ouazzi, T. Theis, S. Turek

Efficient simulation techniques for incompressible two-phase flow

4. öffentliches Kolloquium

15. November 2011

TP B7

technische universität

dortmund

Motivation

SFB 708 - TP B7

CFD simulation tool: Droplet generation and deposition

Simulation results: dispersity, droplet sizes, splash thickness/diameter (shape)

Simulation parameters: physical and geometrical parameters, operation conditions

+

-

Regions of interest

Dynamics of droplet deposition (B1) Dynamics of droplet generation (B7)

• Turbulence

• Modulation

• Solidification

• Contact angle

• Interaction

• Roughness


dortmund

Methods for B1 and B7

SFB 708 - TP B7

• Mass conservative FEM levelset approach with „exact“ interphase reconstruction.

Implicit treatment of the surface tension force term

• Fast solvers (parallel multigrid) for scalar equations and for the Pressure-Poisson

equation supporting large density jumps

• Systematic validation and benchmarking (CFX, FEMLAB, FLUENT, OpenFOAM).

• Incorporation of adaptive grid deformation techniques and/or hanging nodes


dortmund

Governing equations

SFB 708 - TP B7

The incompressible Navier Stokes with the heat equation

0,

ST

T

vv

gfvvvvv

gkt

c

pt

p

on, nnf ST

Dependency of physical quantities

vD

Interphase tension force

0

v

t

Interphase indicator

Level Set

with reinitialization

S

n

21 CPCk

v

t

Pkv

kt

k

kT

k

k

T

u

u

Turbulence model – standard/modified k – model

2kCT

2T

TkP uu

Only for the

gas phase!

unknown

interphase

location ,,vD

0,

ST

T

vv

gfvvvvv

gkt

c

pt

p

T

turbulent

effects


dortmund

Efficient flow solver - FeatFlow

SFB 708 - TP B7

Discretization:

• Navier-Stokes: FEM Q2/P1

• Level Set: DG-FEM P1

• Crank-Nicholson scheme in time

in space

Main features of the FeatFlow approach:

• Parallelization based on domain decomposition

• High order discretization schemes

• Use of unstructured meshes

• Newton-Multigrid solvers

• FCT & EO stabilization techniques

• Adaptive grid deformation

Benchmarked applications

• Laminar Newtonian flows

• Laminar non-Newtonian flows

• Turbulent flows (k-epsilon)

• Fluid-structure interaction

• Immiscible laminar two-phase flow


dortmund

Efficient interphase capturing method

SFB 708 - TP B7

Level Set Method (“smooth“ distance function)

Problems:

• It is not conservative mass loss

• Needs to be reinitialized to maintain its distance property

• Higher order discretization: possible, but necessary?

Benefits:

• Provides an accurate representation of the interphase

• Provides other auxiliary quantities (normal, curvature)

• Allows topology changes

• Treatment of viscosity, density and surface tension without

explicit representation of the interphase

• Adaptive grid advantageous, but not necessary

0

v

t


dortmund

Problems and Challenges

SFB 708 - TP B7

• Steep gradients of physical

quantities at the interphase

• Reinitialization (smoothed sign

function, artificial movement of the

interphase)

• Mass conservation (during

advection and reinitialization of

the Level Set function)

• Representation of interphacial

tension: CSF, Line Integral,

Laplace-Beltrami, Phasefield, etc.

1

SS uu

,ST xnf

2121 1,1 xxxx ee

Cellwise averaging

PDE based reinitialization

CSF smoothening with Dirac function


dortmund

Free parameters to adjust Eo and Mo:

Validation for the rising bubble problem

SFB 708 - TP B7

1) Clift R., Grace J.R., Weber M. Bubbless, Drops and Particles. 1978, Academic

Press, New York.

2) Annaland M. S., Deen N. G., Kuipers J. A. M., Numerical simulation of gas

bubbles behaviour using a three-dimensional volume of fluid method. Chem.

Eng. Sci., 2005, 60(11):2999–3011, DOI: 10.1016/j.ces.2005.01.031


dortmund

*

*Annaland M. S., Deen N. G., Kuipers J. A. M., Numerical simulation of gas

bubbles behaviour using a three-dimensional volume of fluid method.

Chem. Eng. Sci., 2005, 60(11):2999–3011, DOI: 10.1016/j.ces.2005.01.031

Rising bubble – Case B

Eo=9,71 Mo=0,100 1: 2 = 1: 2 = 1:100

ReSim =4,60 Regrapℎ =5,60


dortmund

*




Rising bubble – Case C

Eo=97,1 Mo=0,971 1: 2 = 1: 2 = 1:100



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*

Rising bubble – Case D

Eo=97,1 Mo=1000 1: 2 = 1: 2 = 1:100



dortmund

Benchmarking on experimental results

SFB 708 - TP B7

Glucose-Water mixture

1

3

64,3

972

500

minmlV

mkg

smPa

D

D

D

Continuous phase:

Silicon oil

1

3

04,99

1340

500

mlminV

mkg

smPa

C

C

C

Dispersed phase:

1034,0 mNCD

Validation parameters:

• frequency of droplet generation

• droplet size

• stream length

Experimental Set-up with AG Walzel (BCI/Dortmund)


dortmund

Benchmarking on experimental results

SFB 708 - TP B7

Separation

frequency

[Hz]

Droplet

size

[dm]

Stream

Length

[dm]

Exp 0,58 0,062 0,122

Sim 0,6 0,058 0,102

Group of Prof. Walzel

BCI/Dortmund Exp. results


dortmund

Validation for wide range of experiments

SFB 708 - TP B7

VD [ml/min]

Je

t le

ngth

[m

m]

VD [ml/min]

Dro

ple

t siz

e [

mm

]

Example 1:

VD= 1,1 ml/min

VC= 13,0 ml/min

VD/Vtot = 0,08

.

.

. .

Example 2:

VD= 1,5 ml/min

VC= 41,1 ml/min

VD/Vtot = 0,04

.

.

. .

Example 3:

VD= 2,5 ml/min

VC= 123,2 ml/min

VD/Vtot = 0,02

.

.

. .

case 1: VD/Vtot = 0,08 (exp/sim)



. .

. .

. .




. .

. .

. .

Experimental results: Group of Prof. Walzel BCI/Dortmund

Effects of contact angle?


dortmund

Influence of modulation

SFB 708 - TP B7

Resulting operation envelope:

• Size: 4.5 mm – 5.7 mm

• Volume: 0.38 cm3 – 0.77 cm3

Regulated

Flowrate: 150%

Capillary: STD

Droplet size: 5.7mm

No Regulation

Flowrate: 100%

Capillary: STD

Droplet size: 5.2mm

Regulated

Flowrate: 75%

Capillary: 50% STD

Droplet size: 4.5mm

Regulated

Flowrate: 100%

Capillary: STD

Droplet size: 5.0mm


dortmund

Droplet deposition

SFB 708 - TP B7

Pourmousa A, WIRE-ARC SPRAYING SYSTEM: Particle Production, Transport, and Deposition,

Department of Mechanical and Industrial Engineering University of Toronto, PhD Thesis, 2007.

+ Contact angle & interaction & solidification!


dortmund

Solidification

SFB 708 - TP B7

• Enthalpy method for binary alloy solidification

• The condition of zero velocity in solid regions

is accounted with:

Temperature dependent viscosity

Fictitious boundary method (FBM)

Without solidification With solidification

Influence on impinging droplets

gk

tcp v

1) Swaminathan C. R., Voller V., On the enthalpy method, Int. J.

Num. Meth. Heat Fluid Flow, 1993, 3, 233-244.

2) McDaniel D. J., Zabaras N., A Least squares front tracking FEM

analysis of phase change with natural convection, Int. J. for Num.

Meth. In Eng., 1994, 37, 2755-2777.

f


dortmund

Validation of turbulence models

SFB 708 - TP B7

395Re

duChannel flow for

625,47Re

HUBackward facing step for

• Standard k- model

• Chien‘s low Re k- model

+ Boundary conditions!

5.60.5 literature, rxReattachment length


dortmund

Conclusions and future plans

SFB 708 - TP B7

status:

Overview of the modules of the desired simulation tool

Parallelized, multi-grid based, high order, Benchmarked

Heat equation Parallelized, Solidification is tested and verified in 2D

Level Set Parallelized and equipped with reinitialization, Benchmarked

Turbulence model Sequential, tested and verified in 3D, low/high Reynolds

number extensions

module:

Dynamics of droplet generation Dynamics of droplet deposition

CFD solver

CFD solver

Level Set Heat equation

CFD solver

Level Set Turbulence model

+ Modulation

Experimental/computational reference results

+ Solidification

Proposal of benchmark problems

3d-surface engineering für werkzeug- systeme der ... · dynamics of droplet generation (b7)...

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