EQUATION + LES Presentation_Fueyo.pptx

1. Fluid
Mechanics
Group
University of
Zaragoza
Large Eddy Simulation of the flow
past a square cylinder
J. S. Ochoa, N. Fueyo
Fluid Mechanics Group
University of Zaragoza
Spain
Norberto.Fueyo@unizar.es

2. 2
Turbulence
modelling
Case considered
Modelling
 Equations
Numerical details
 Domain & grid
 Solving
 BC
 Discretisation
 Int. parameters
 Computing
Iimplementation in
PHOENICS
Results
Conclusions
Further work
Contents
 Aim
 Turbulence Modelling
 Case considered
 Modelling
 Numerical details
 Implementation in PHOENICS
 Results
 Conclusions

3. 3
Turbulence
modelling
Case considered
Modelling
 Equations
Numerical details
 Domain & grid
 Solving
 BC
 Discretisation
 Int. parameters
 Computing
Iimplementation in
PHOENICS
Results
Conclusions
Further work
Aim

4. 4
Turbulence
modelling
Case considered
Modelling
 Equations
Numerical details
 Domain & grid
 Solving
 BC
 Discretisation
 Int. parameters
 Computing
Iimplementation in
PHOENICS
Results
Conclusions
Further work
Turbulence modelling
 Simulation of turbulent flows
 Reynolds Averaged Navier-Stokes equations
 Large Eddy Simulation
 Direct Numerical Simulation
 LES: Filtering
Simulated
Modellled
   

 '
'
'
, dx
x
u
x
x
G
u i
i

5. 5
Turbulence
modelling
Case considered
Modelling
 Equations
Numerical details
 Domain & grid
 Solving
 BC
 Discretisation
 Int. parameters
 Computing
Iimplementation in
PHOENICS
Results
Conclusions
Further work
Case considered
y
x
U
H
Square cylinder side
Inlet velocity
Reynolds number
Channel width
Channel height
Flow
H = 40 mm
U = 535 mm/s
Re = UD/n = 21400
W = 400 mm
H = 560 mm
Water
 Experiment of Lyn & Rodi
 Square rod in water flow
 Flow parameters
Inlet
Outlet

6. Fluid
Mechanics
Group
University of
Zaragoza
Modelling

7. 7
Turbulence
modelling
Case considered
Modelling
 Equations
Numerical details
 Domain & grid
 Solving
 BC
 Discretisation
 Int. parameters
 Computing
Iimplementation in
PHOENICS
Results
Conclusions
Further work
Equations
 Governing equations
 Continuity
 Momentum
  0
· 




u
t


  '
·
·
)
(











p
u
u
t
u
 Filtered equations
 Continuity
 Momentum
0



i
i
x
u

































 s
ij
i
j
j
i
j
i
j
j
i
i
x
u
x
u
x
x
p
x
u
u
t
u



 )
(
)
(

8. 8
Turbulence
modelling
Case considered
Modelling
 Equations
Numerical details
 Domain & grid
 Solving
 BC
 Discretisation
 Int. parameters
 Computing
Iimplementation in
PHOENICS
Results
Conclusions
Further work
Closure (Smagorinsky)
 Sub-grid Reynolds stresses
 Turbulent viscosity
ij
t
i
j
j
i
t
ij
s
kk
s
ij S
x
u
x
u
n
n


 2
3
1


















  S
Cs
t
2


n
 3
1
z
y
x 




Turbulence
generation
function
2
0 1













A
y
s
s e
C
C  2
1
2 ij
ij S
S
S 
n

yu
y 

YPLS
25


A Constant
Filter size
Smagorinsky
constant

9. Fluid
Mechanics
Group
University of
Zaragoza
Numerical details

10. 10
Turbulence
modelling
Case considered
Modelling
 Equations
Numerical details
 Domain & grid
 Solving
 BC
 Discretisation
 Int. parameters
 Computing
Iimplementation in
PHOENICS
Results
Conclusions
Further work
Domain
 Dimensions
H 15H
14H
4.5H
H
4H
y
z
z
x
H = 40 mm
Flow
Inlet
Flow
Outlet
y
z x

11. 11
Turbulence
modelling
Case considered
Modelling
 Equations
Numerical details
 Domain & grid
 Solving
 BC
 Discretisation
 Int. parameters
 Computing
Iimplementation in
PHOENICS
Results
Conclusions
Further work
Grid
 3D grid:120x102x20
y
z
x
z
y
z x

12. 12
Turbulence
modelling
Case considered
Modelling
 Equations
Numerical details
 Domain & grid
 Solving
 BC
 Discretisation
 Int. parameters
 Computing
Iimplementation in
PHOENICS
Results
Conclusions
Further work
Discretisation details
 Convective term
 Temporal term
 Timestep calculation using CFL limit as guidance
Van Leer scheme
 
W
P
P
e r 



 

 )
(
 
 
2
,
5
.
0
5
.
0
,
2
min
,
0
max
)
( r
r
r 


     
 
2
2
1
1
1
,
,
8
,
5
12









 n
n
n
n
n
n
n
n
t
f
t
f
t
f
t





Implicit 3rd order
Adam-Moulton scheme
   
 
2
2
1
1
1
,
,
3
2








 n
n
n
n
n
n
t
f
t
f
t




Explicit 2nd order
Adam-Bashforth scheme
CFL Condition 










 





 





 


w
z
v
y
u
x
tCFL
,
,
min

13. 13
Turbulence
modelling
Case considered
Modelling
 Equations
Numerical details
 Domain & grid
 Solving
 BC
 Discretisation
 Int. parameters
 Computing
Iimplementation in
PHOENICS
Results
Conclusions
Further work
Solving
0

f
1

f
(blue)
(red)
 Diferential equations solved
 Continuity (Pressure)
 Momentum (Velocities)
 Scalar marker f
 Auxiliary variables
 Density
 Viscosity
 Eddy-viscosity

14. 14
Turbulence
modelling
Case considered
Modelling
 Equations
Numerical details
 Domain & grid
 Solving
 BC
 Discretisation
 Int. parameters
 Computing
Iimplementation in
PHOENICS
Results
Conclusions
Further work
Boundary conditions
 Flow
 Square-cylinder walls
 No-slip condition
 Logarithmic functions for filtered velocity
Velocities
Mass flux
Outflow
(fixed
pressure)
Simmetry wall
(Free-slip)
Simmetry wall
(Free-slip)

15. 15
Turbulence
modelling
Case considered
Modelling
 Equations
Numerical details
 Domain & grid
 Solving
 BC
 Discretisation
 Int. parameters
 Computing
Iimplementation in
PHOENICS
Results
Conclusions
Further work
Calculation of integral parameters
 Strouhal number
 f – vortex-shedding frequency
 Drag & lift coefficients
U
fD
St 
2
2
1
U
F
C horizontal
D


2
2
1
U
F
C vertical
L

 ds
n
F
s

 
·

16. 16
Turbulence
modelling
Case considered
Modelling
 Equations
Numerical details
 Domain & grid
 Solving
 BC
 Discretisation
 Int. parameters
 Computing
Iimplementation in
PHOENICS
Results
Conclusions
Further work
Implementation in PHOENICS, 1
 Time and spatial definitions
Q1 file
Major PIL settings
• Time
STEADY=T
TLAST=GRND
• Domain
GRDPWR(X,..
GROUND User
Module
Y
• CFL Condition
 
H
CON
N
CON
E
CON
MASS
DT licit
1
,
1
,
1
max
1
exp 
Group
2.
Z
Groups
3,4
and 5.
• Spatial discretisation
SCHEME(VANL1,U1,V1,W1)
Group
8.
• Time discretisation
PATCH(TDIS,CELL,...
COVAL(TDIS,U1,FIXFLU,GRND)
Group
13.
V1
W1
• High order time scheme
Adam-Moulton Scheme
Adam-Bashforth Scheme
 
     
2
1
1
12
7
3
2
12
7
,









n
n
n
n
n
n
n
RHS
RHS
RHS
t
f
t



 
   
2
1
1
1
1
2
1
2
1
,










n
n
n
n
n
n
RHS
RHS
t
f
t



Common formulation
of PHOENICS
Sources
added
Common formulation
of PHOENICS
Sources
added

17. 17
Turbulence
modelling
Case considered
Modelling
 Equations
Numerical details
 Domain & grid
 Solving
 BC
 Discretisation
 Int. parameters
 Computing
Iimplementation in
PHOENICS
Results
Conclusions
Further work
Implementation in PHOENICS, 2
 Properties and LES model
Q1 file
Major PIL settings
Group
8.
• Turbulence model
ENUT=GRND
Group
9.
• Variables solved
P1,U1,V1,W1,MIXF
GROUND User
Module
• Variables stored
RHO1,CON1E,CON1N,CON1H
YPLS
GENK=T
Velocity gradients, GEN1
• Smagorinsky model
   
1
*
*
2
GEN
SQRT
DELTA
C
VIST filter
S

 
 
A
YPLS
EXP
C
C S
S /
1
*
0 

 3
1
*
* DZ
DY
DX
DELTAfilter 
Switching
Special
grounds
• Dump data
• Integral parameters
RG( ),IG( ),LG( )

18. 18
Turbulence
modelling
Case considered
Modelling
 Equations
Numerical details
 Domain & grid
 Solving
 BC
 Discretisation
 Int. parameters
 Computing
Iimplementation in
PHOENICS
Results
Conclusions
Further work
Computing
 Parallel cluster
 Boadicea: Beowulf-Oriented Architecture for Distributed,
Intensive Computing in Engineering Applications
 Installed at Fluid Mechanics Group (University of Zaragoza,
Spain)
 66 CPU’s (33 dual nodes)
 Pentium III, 550 MHz
 256 Mb memory/node
 10Gb disk space/node
 Linux
 PHOENICS V3.5

19. Fluid
Mechanics
Group
University of
Zaragoza
Results
 2D analysis
 3D simulation

20. 20
Turbulence
modelling
Case considered
Modelling
 Equations
Numerical details
 Domain & grid
 Solving
 BC
 Discretisation
 Int. parameters
 Computing
Iimplementation in
PHOENICS
Results
Conclusions
Further work
2D: Influences Van Leer scheme
 Vertical velocity V1 Sampling
Point
2H
Van Leer
No scheme
t (s)
V1
(m/s)

21. 21
Turbulence
modelling
Case considered
Modelling
 Equations
Numerical details
 Domain & grid
 Solving
 BC
 Discretisation
 Int. parameters
 Computing
Iimplementation in
PHOENICS
Results
Conclusions
Further work
2D: Influences of Adam-Moulton scheme
 Vertical velocity V1 Sampling
Point
2H
Adam Moulton
No scheme
V1
(m/s)
t (s)

22. 22
Turbulence
modelling
Case considered
Modelling
 Equations
Numerical details
 Domain & grid
 Solving
 BC
 Discretisation
 Int. parameters
 Computing
Iimplementation in
PHOENICS
Results
Conclusions
Further work
2D: Influences of Smagorisnky model
 Vertical velocity V1 Sampling
Point
2H
Combined effect
Smagorinsky
No model
V1
(m/s)
t (s)

23. 23
Turbulence
modelling
Case considered
Modelling
 Equations
Numerical details
 Domain & grid
 Solving
 BC
 Discretisation
 Int. parameters
 Computing
Iimplementation in
PHOENICS
Results
Conclusions
Further work
Smagorinsky model
2D: Combined effect
 Vertical velocity V1 Sampling
Point
2H
Combined effect
All models and schemes
No model
V1
(m/s)
t (s)

24. 24
Turbulence
modelling
Case considered
Modelling
 Equations
Numerical details
 Domain & grid
 Solving
 BC
 Discretisation
 Int. parameters
 Computing
Iimplementation in
PHOENICS
Results
Conclusions
Further work
 Mean axial velocity along the centreline
2D: Grid influence
120x84 grid
240x168 grid
360x252 grid
120x102 grid
Uaxial
(m/s)
Domain length
H
120x102
240x186
120x84
360x252

25. 25
Turbulence
modelling
Case considered
Modelling
 Equations
Numerical details
 Domain & grid
 Solving
 BC
 Discretisation
 Int. parameters
 Computing
Iimplementation in
PHOENICS
Results
Conclusions
Further work
Animation of results
 Mixture-fraction contours

26. 26
Turbulence
modelling
Case considered
Modelling
 Equations
Numerical details
 Domain & grid
 Solving
 BC
 Discretisation
 Int. parameters
 Computing
Iimplementation in
PHOENICS
Results
Conclusions
Further work
3D Results
 Integral parameters
Work: Label St
Numerical data:
Verstappen and Veldman [23] GRO 0.005 1.45 2.09 0.178 0.133
Porquie et. al. [13]
- Simulation 1 UK1 -0.02 1.01 2.2 0.14 0.13
- Simulation 2 UK2 -0.04 1.12 2.3 0.14 0.13
- Simulation 3 UK3 -0.05 1.02 2.23 0.13 0.13
Murakami et. Al. [29] NT -0.05 1.39 2.05 0.12 0.131
Wang and Vanka [4] UOI 0.04 1.29 2.03 0.18 0.13
Nozawa and Tamura [10] TIT 0.0093 1.39 2.62 0.23 0.131
Kawashima and Kawamura [14]
- Simulation 1 ST2 0.01 1.26 2.72 0.28 0.16
- Simulation 2 ST5 0.009 1.38 2.78 0.28 0.161
Experimental data: Lyn et. al. [2] [3] EXP - - 2.1 - 0.132
This work S8A 0.03 1.4 2.01 0.22 0.139
L
C
rms
L
C D
C
rms
D
C

27. 27
Turbulence
modelling
Case considered
Modelling
 Equations
Numerical details
 Domain & grid
 Solving
 BC
 Discretisation
 Int. parameters
 Computing
Iimplementation in
PHOENICS
Results
Conclusions
Further work
3D: Comparison among data, 1
 Experimental and this work data
Domain length
H
Uaxial
(m/s)

28. 28
Turbulence
modelling
Case considered
Modelling
 Equations
Numerical details
 Domain & grid
 Solving
 BC
 Discretisation
 Int. parameters
 Computing
Iimplementation in
PHOENICS
Results
Conclusions
Further work
3D: Comparison among data, 2
 Numerical, experimental and this work data
Uaxial
(m/s)
Domain length
H

29. 29
Turbulence
modelling
Case considered
Modelling
 Equations
Numerical details
 Domain & grid
 Solving
 BC
 Discretisation
 Int. parameters
 Computing
Iimplementation in
PHOENICS
Results
Conclusions
Further work
3D: Streamlines
 Comparison between experimental and numerical
streamlines
Experimental This work

30. 30
Turbulence
modelling
Case considered
Modelling
 Equations
Numerical details
 Domain & grid
 Solving
 BC
 Discretisation
 Int. parameters
 Computing
Iimplementation in
PHOENICS
Results
Conclusions
Further work
3D: Iso-vorticity contours
Vorticity
]
[ 1

s
Vorticity
]
[ 1

s
 Streamwise
 Spanwise
Vorticity
]
[ 1

s

31. 31
Turbulence
modelling
Case considered
Modelling
 Equations
Numerical details
 Domain & grid
 Solving
 BC
 Discretisation
 Int. parameters
 Computing
Iimplementation in
PHOENICS
Results
Conclusions
Further work
3D: Turbulence viscosity (ENUT)
 Streamwise
ENUT
]
[ 2
2
s
m
ENUT
]
[ 2
2
s
m

32. 32
Turbulence
modelling
Case considered
Modelling
 Equations
Numerical details
 Domain & grid
 Solving
 BC
 Discretisation
 Int. parameters
 Computing
Iimplementation in
PHOENICS
Results
Conclusions
Further work
3D: Comparison between LES & RANS, 1
 Vertical velocity V1 Sampling
Point
2H
Uaxial
(m/s)
LES
K-epsilon
t (s)

33. 33
Turbulence
modelling
Case considered
Modelling
 Equations
Numerical details
 Domain & grid
 Solving
 BC
 Discretisation
 Int. parameters
 Computing
Iimplementation in
PHOENICS
Results
Conclusions
Further work
3D: Comparison between LES & RANS, 2
 Mean axial velocity on the center plane
Uaxial
(m/s)
Domain length
H
LES
LES
K-epsilon

34. 34
Turbulence
modelling
Case considered
Modelling
 Equations
Numerical details
 Domain & grid
 Solving
 BC
 Discretisation
 Int. parameters
 Computing
Iimplementation in
PHOENICS
Results
Conclusions
Further work
Animation: mixf

35. 35
Turbulence
modelling
Case considered
Modelling
 Equations
Numerical details
 Domain & grid
 Solving
 BC
 Discretisation
 Int. parameters
 Computing
Iimplementation in
PHOENICS
Results
Conclusions
Further work
Animation: spanwise vorticity

36. 36
Turbulence
modelling
Case considered
Modelling
 Equations
Numerical details
 Domain & grid
 Solving
 BC
 Discretisation
 Int. parameters
 Computing
Iimplementation in
PHOENICS
Results
Conclusions
Further work
Speedup
Grid 120x102x20 24 min/dt
1 processor
12 processors 3 min/dt
30 sweeps/dt
(implicit time)
Ideal
This work
Processors used (n)
Speedup
]
[
1
proc
n
proc
t
t
• Computing time: approx 11 hr (on 12 processors)
Domain split along z direction

37. 37
Turbulence
modelling
Case considered
Modelling
 Equations
Numerical details
 Domain & grid
 Solving
 BC
 Discretisation
 Int. parameters
 Computing
Iimplementation in
PHOENICS
Results
Conclusions
Further work
Conclusions
 LES implemented to PHOENICS
 Agreement with both numerical and experimental data
 High order schemes increase accuracy
 Flow well predicted
 Superiority of LES over RANS
 Reasonable time using parallel PHOENICS v3.5

38. 38
Turbulence
modelling
Case considered
Modelling
 Equations
Numerical details
 Domain & grid
 Solving
 BC
 Discretisation
 Int. parameters
 Computing
Iimplementation in
PHOENICS
Results
Conclusions
Further work
Further work
 Large Eddy Simulation of
Turbulent flames

39. Fluid
Mechanics
Group
University of
Zaragoza
End of presentation
Thank you