Large Eddy Simulation of the flow past a square cylinder

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Large Eddy Simulation of the flow past a square
cylinder

• J. S. Ochoa, N. Fueyo
• Fluid Mechanics Group
• University of Zaragoza
• Spain

Norberto.Fueyo_at_unizar.es
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Contents

• Aim
• Turbulence Modelling
• Case considered
• Modelling
• Numerical details
• Implementation in PHOENICS
• Results
• Conclusions

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Aim
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Turbulence modelling

• Simulation of turbulent flows
• Reynolds Averaged Navier-Stokes equations
• Large Eddy Simulation
• Direct Numerical Simulation

• LES Filtering

Simulated
Modellled
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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
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Modelling
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Equations

• Governing equations
• Continuity
• Momentum

• Filtered equations
• Continuity
• Momentum

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Closure (Smagorinsky)

• Sub-grid Reynolds stresses
• Turbulent viscosity

Turbulence generation function
Smagorinsky constant
YPLS
Filter size
Constant
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Numerical details
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Domain

• Dimensions

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Grid

• 3D grid120x102x20

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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
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Solving

• Diferential equations solved
• Continuity (Pressure)
• Momentum (Velocities)
• Scalar marker f
• Auxiliary variables
• Density
• Viscosity
• Eddy-viscosity

(blue)
(red)
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Boundary conditions

• Flow
• Square-cylinder walls
• No-slip condition
• Logarithmic functions for filtered velocity

Simmetry wall (Free-slip)
Outflow (fixed pressure)
Velocities Mass flux
Simmetry wall (Free-slip)
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Calculation of integral parameters

• Strouhal number
• f vortex-shedding frequency
• Drag lift coefficients

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Implementation in PHOENICS, 1

• Time and spatial definitions

GROUND User Module
Q1 file
Major PIL settings

• Time

• CFL Condition

Group 2.
STEADYT TLASTGRND

• 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
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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
GENKT
Velocity gradients,
GEN1

• Turbulence model

Group 9.
ENUTGRND

• Dump data
• Integral parameters

Switching Special grounds
RG( ),IG( ),LG( )
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Computing

• Parallel cluster
• Boadicea Beowulf-Oriented Architecture for
  Distributed, Intensive Computing in Engineering
  Applications
• Installed at Fluid Mechanics Group (University of
  Zaragoza, Spain)
• 66 CPUs (33 dual nodes)
• Pentium III, 550 MHz
• 256 Mb memory/node
• 10Gb disk space/node
• Linux
• PHOENICS V3.5

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Results

• 2D analysis
• 3D simulation

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2D Influences Van Leer scheme

• Vertical velocity V1

Van Leer No scheme
V1 (m/s)
t (s)
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2D Influences of Adam-Moulton scheme

• Vertical velocity V1

Adam Moulton No scheme
V1 (m/s)
t (s)
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2D Influences of Smagorisnky model

• Vertical velocity V1

Smagorinsky No model
V1 (m/s)
Combined effect
t (s)
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2D Combined effect

• Vertical velocity V1

All models and schemes No model
V1 (m/s)
Smagorinsky model
Combined effect
t (s)
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2D Grid influence

• Mean axial velocity along the centreline

120x102
240x186
120x84
360x252
Uaxial (m/s)
120x84 grid 240x168 grid 360x252 grid 120x102 grid
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Animation of results

• Mixture-fraction contours

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3D Results

• Integral parameters

Work Label St
Numerical data Numerical data Numerical data Numerical data Numerical data Numerical data 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
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3D Comparison among data, 1

• Experimental and this work data

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3D Comparison among data, 2

• Numerical, experimental and this work data

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3D Streamlines

• Comparison between experimental and numerical
  streamlines

Experimental
This work
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3D Iso-vorticity contours

• Streamwise

• Spanwise

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3D Turbulence viscosity (ENUT)

• Streamwise

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3D Comparison between LES RANS, 1

• Vertical velocity V1

LES
K-epsilon
Uaxial (m/s)
t (s)
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3D Comparison between LES RANS, 2

• Mean axial velocity on the center plane

LES
LES
K-epsilon
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Animation mixf
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Animation spanwise vorticity
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Speedup
Ideal This work
Speedup
Processors used (n)
Domain split along z direction
Grid 120x102x20
24 min/dt
1 processor
30 sweeps/dt (implicit time)
12 processors
3 min/dt

• Computing time approx 11 hr (on 12 processors)

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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

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Further work

• Large Eddy Simulation of Turbulent flames

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End of presentationThank you