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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

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

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

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

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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/ = 21400 W = 400 mm H = 560 mm Water n Experiment of Lyn & Rodi n Square rod in water flow n Flow parameters Inlet Outlet

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Fluid Mechanics Group University of Zaragoza Modelling

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7 Turbulence modelling Case considered Modelling Equations Numerical details Domain & grid Solving BC Discretisation Int. parameters Computing Iimplementation in PHOENICS Results Conclusions Further workEquations n Governing equations n Continuity n Momentum n Filtered equations n Continuity n Momentum

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

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Fluid Mechanics Group University of Zaragoza Numerical details

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10 Turbulence modelling Case considered Modelling Equations Numerical details Domain & grid Solving BC Discretisation Int. parameters Computing Iimplementation in PHOENICS Results Conclusions Further workDomain n Dimensions H15H 14H 4.5H H 4H y z z x H = 40 mm Flow Inlet Flow Outlet y zx

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

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

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

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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 n Strouhal number f – vortex-shedding frequency n Drag & lift coefficients

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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 n Time and spatial definitions Q1 file Major PIL settings Time STEADY=T TLAST=GRND Domain GRDPWR(X,.. GROUND User Module Y CFL Condition 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 Common formulation of PHOENICS Sources added Common formulation of PHOENICS Sources added

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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 n 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 Switching Special grounds Dump data Integral parameters RG( ),IG( ),LG( )

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

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Fluid Mechanics Group University of Zaragoza Results n 2D analysis n 3D simulation

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

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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 n Vertical velocity V1 Sampling Point 2H Adam Moulton No scheme V1 (m/s) t (s)

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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 n Vertical velocity V1 Sampling Point 2H Combined effect Smagorinsky No model V1 (m/s) t (s)

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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 n Vertical velocity V1 Sampling Point 2H Combined effect All models and schemes No model V1 (m/s) t (s)

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

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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 n Mixture-fraction contours

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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 n Integral parameters Work:Label St Numerical data: Verstappen and Veldman [23]GRO0.0051.452.090.1780.133 Porquie et. al. [13] - Simulation 1UK1-0.021.012.20.140.13 - Simulation 2UK2-0.041.122.30.140.13 - Simulation 3UK3-0.051.022.230.13 Murakami et. Al. [29]NT-0.051.392.050.120.131 Wang and Vanka [4]UOI0.041.292.030.180.13 Nozawa and Tamura [10]TIT0.00931.392.620.230.131 Kawashima and Kawamura [14] - Simulation 1ST20.011.262.720.280.16 - Simulation 2ST50.0091.382.780.280.161 Experimental data: Lyn et. al. [2] [3]EXP--2.1-0.132 This workS8A0.031.42.010.220.139

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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 n Experimental and this work data Domain length H U axial (m/s)

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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 n Numerical, experimental and this work data U axial (m/s) Domain length H

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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 n Comparison between experimental and numerical streamlines ExperimentalThis work

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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 n Streamwise n Spanwise Vorticity

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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) n Streamwise ENUT

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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 n Vertical velocity V1 Sampling Point 2H U axial (m/s) LES K-epsilon t (s)

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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 n Mean axial velocity on the center plane U axial (m/s) Domain length H LES K-epsilon

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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

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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

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36 Turbulence modelling Case considered Modelling Equations Numerical details Domain & grid Solving BC Discretisation Int. parameters Computing Iimplementation in PHOENICS Results Conclusions Further workSpeedup Grid 120x102x20 24 min/dt1 processor 12 processors3 min/dt 30 sweeps/dt (implicit time) Ideal This work Processors used (n) Speedup Computing time: approx 11 hr (on 12 processors) Domain split along z direction

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

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

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Fluid Mechanics Group University of Zaragoza End of presentation Thank you

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