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

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

Aim

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

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

Modelling

Equations Governing equations Filtered equations Continuity Momentum

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

Numerical details

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

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

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

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

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)

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

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

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( )

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

Results 2D analysis 3D simulation

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

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

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

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)

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

Animation of results Mixture-fraction contours

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

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

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

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

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

3D: Turbulence viscosity (ENUT) Streamwise ENUT ENUT

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

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

Animation: mixf

Animation: spanwise vorticity

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)

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

Further work Large Eddy Simulation of Turbulent flames

End of presentation Thank you