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

2. Contents Aim Turbulence Modelling Case considered Modelling
Numerical details
Implementation in PHOENICS
Results
Conclusions

3. Aim

4. Turbulence modelling Simulation of turbulent flows LES: Filtering
Reynolds Averaged Navier-Stokes equations
Large Eddy Simulation
Direct Numerical Simulation
LES: Filtering
Simulated
Modellled

5. Case considered Experiment of Lyn & Rodi Square rod in water flow
Inlet U y
Outlet H x
Flow parameters
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

6. Modelling

7. Equations Governing equations Filtered equations Continuity Momentum

8. Closure (Smagorinsky)
Sub-grid Reynolds stresses
Turbulent viscosity
Turbulence generation function
Smagorinsky constant
YPLS
Filter size
Constant

9. Numerical details

10. Domain Dimensions H = 40 mm Flow Inlet Outlet H 15H 14H 4.5H 4H y z x

11. Grid
3D grid:120x102x20 y z x x z y z

12. Discretisation details
Convective term
Temporal term
Timestep calculation using CFL limit as guidance
Van Leer scheme
Implicit 3rd order
Adam-Moulton scheme
Explicit 2nd order
Adam-Bashforth scheme
CFL Condition

13. Solving Diferential equations solved Auxiliary variables
Continuity (Pressure)
Momentum (Velocities)
Scalar marker f
Auxiliary variables
Density
Viscosity
Eddy-viscosity
(blue)
(red)

14. Boundary conditions Flow Square-cylinder walls Simmetry wall
No-slip condition
Logarithmic functions for filtered velocity
Simmetry wall
(Free-slip)
Outflow (fixed pressure)
Velocities
Mass flux
Simmetry wall
(Free-slip)

15. Calculation of integral parameters
Strouhal number
f – vortex-shedding frequency
Drag & lift coefficients

16. Implementation in PHOENICS, 1
Time and spatial definitions
GROUND User Module
Q1 file
Major PIL settings
Time
CFL Condition
Group 2.
STEADY=T
TLAST=GRND
Domain
Groups
3,4
and 5.
GRDPWR(X,.. Y
High order time scheme Z
Adam-Moulton Scheme
Common formulation of PHOENICS
Spatial discretisation
Group 8.
SCHEME(VANL1,U1,V1,W1)
Sources
added
Adam-Bashforth Scheme
Time discretisation
Group
13.
Common formulation of PHOENICS
PATCH(TDIS,CELL,...
COVAL(TDIS,U1,FIXFLU,GRND) V1
Sources
added W1

17. Implementation in PHOENICS, 2
Properties and LES model
GROUND User Module
Q1 file
Major PIL settings
Variables solved
P1,U1,V1,W1,MIXF
Group 8.
Smagorinsky model
Variables stored
RHO1,CON1E,CON1N,CON1H
YPLS
GENK=T
Velocity gradients,
GEN1
Turbulence model
Group 9.
ENUT=GRND
Dump data
Integral parameters
Switching
Special
grounds
RG( ),IG( ),LG( )

18. 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. Results
2D analysis
3D simulation

20. 2D: Influences Van Leer scheme
Sampling
Point 2H
Vertical velocity V1
Van Leer
No scheme V1
(m/s)
t (s)

21. 2D: Influences of Adam-Moulton scheme
Sampling
Point 2H
Vertical velocity V1
Adam Moulton
No scheme V1
(m/s)
t (s)

22. 2D: Influences of Smagorisnky model
Sampling
Point 2H
Vertical velocity V1
Smagorinsky
No model V1
(m/s)
Combined effect
t (s)

23. 2D: Combined effect Vertical velocity V1 Smagorinsky model
Sampling
Point 2H
Vertical velocity V1
All models and schemes
No model V1
(m/s)
Smagorinsky model
Combined effect
t (s)

24. 2D: Grid influence Mean axial velocity along the centreline 120x102
Uaxial
(m/s)
120x84 grid
240x168 grid
360x252 grid
120x102 grid
Domain length H

25. Animation of results
Mixture-fraction contours

26. 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
- Simulation 3
UK3
-0.05
1.02
2.23
Murakami et. Al. [29] NT
1.39
2.05
0.12
0.131
Wang and Vanka [4]
UOI
0.04
1.29
2.03
0.18
Nozawa and Tamura [10]
TIT
0.0093
2.62
0.23
Kawashima and Kawamura [14]
ST2
0.01
1.26
2.72
0.28
0.16
ST5
0.009
1.38
2.78
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

27. 3D: Comparison among data, 1
Experimental and this work data
Uaxial
(m/s)
Domain length H

28. 3D: Comparison among data, 2
Numerical, experimental and this work data
Uaxial
(m/s)
Domain length H

29. 3D: Streamlines
Comparison between experimental and numerical streamlines
Experimental
This work

30. 3D: Iso-vorticity contours
Streamwise
Vorticity
Vorticity
Spanwise
Vorticity

31. 3D: Turbulence viscosity (ENUT)
Streamwise
ENUT
ENUT

32. 3D: Comparison between LES & RANS, 1
Sampling
Point 2H
Vertical velocity V1
LES
K-epsilon
Uaxial
(m/s)
t (s)

33. 3D: Comparison between LES & RANS, 2
Mean axial velocity on the center plane
Uaxial
(m/s)
Domain length H
LES
LES
K-epsilon

34. Animation: mixf

35. Animation: spanwise vorticity

36. Speedup Domain split along z direction Grid 120x102x20 1 processor
Ideal
This work
Speedup
Processors used (n)
Domain split along z direction
Grid 120x102x20
1 processor
24 min/dt
30 sweeps/dt
(implicit time)
12 processors
3 min/dt
Computing time: approx 11 hr (on 12 processors)

37. 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. Further work
Large Eddy Simulation of Turbulent flames

39. End of presentation Thank you