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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
technische universität
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
technische universität
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
technische universität
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
technische universität
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
technische universität
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
technische universität
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
technische universität
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
technische universität
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 C
Eo=97,1 Mo=0,971 1: 2 = 1: 2 = 1:100
ReSim =20,0 Regrapℎ =18,0
technische universität
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 D
Eo=97,1 Mo=1000 1: 2 = 1: 2 = 1:100
ReSim =1,50 Regrapℎ =2,03
technische universität
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)
technische universität
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
technische universität
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)
case 2: VD/Vtot = 0,04 (exp/sim)
case 3: VD/Vtot = 0,02 (exp/sim)
. .
. .
. .
case 1: VD/Vtot = 0,08 (exp/sim)
case 2: VD/Vtot = 0,04 (exp/sim)
case 3: VD/Vtot = 0,02 (exp/sim)
. .
. .
. .
Experimental results: Group of Prof. Walzel BCI/Dortmund
Effects of contact angle?
technische universität
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
technische universität
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!
technische universität
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
technische universität
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
technische universität
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