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1 © 2015 ANSYS, Inc. July 13, 2017
Status of Turbulence Modelling at ANSYS
Florian Menter
Chief Scientist
ANSYS Germany GmbH
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2 © 2015 ANSYS, Inc. July 13, 2017
Problem Description
• 2D RANS CFD simulations of wind-turbine airfoils predict substantially too high Clmax
• Even the fairly ‘aggressive’ SST –especially tuned for separation/stall prediction of aerodynamic devices is too high on high Clmax
SST – Fully Turbulent (FT-tripped), Re=4·106
Experiment for DU-96-W-180 airfoil was carried out in the Delft University: Timmer W. A. & R. P. J. O. M. van Rooij (2003). “Summary of the Delft University Wind Turbine Dedicated Airfoils”, AIAA Paper, 2003-0352
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3 © 2015 ANSYS, Inc. July 13, 2017
Flat plate Backward-facing step
CS0 diffuser NACA-4412
Testing of SST-HL model for basic turbulent flows
• SST-HL (High Lift)– Allows reduction of a1 without
destroying basic calibration
– Maintains Flat Plate
– Produces more separation for Diffuser CS0
– More separation for NACA 4412 (good or bad?)
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4 © 2015 ANSYS, Inc. July 13, 2017
SST and SST-HL models
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Flow around an A-Airfoil
• Experiment for clean airfoil model was carried out in the F2-ONERA wind tunnel at Re=2.1·106 and M≈0.15
• Preliminary CFD results indicates that laminar-turbulent transition has a big impact on the airfoil characteristics
• Therefore current numerical investigations are carried out using transition models
– Intermittency-SST model (γ-SST)
– Intermittency-SST model with HL correction (γ-SST-HL)
• Computational domain is based on the experimental wind tunnel
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3D Simulations - Flow Structure• Wind tunnel (Lz=2.3C)
without sidewall BL account – Symmetry boundary
conditions in spanwisedirection are used for slip wall imitation
– Incompressible flow, Re = 2.1·106, α = 12o-16o
• Computational mesh is based on the 2D mesh extruded in spanwisedirection with uniform grid step (80 cells in Z direction)– Total mesh size is about
10M cells
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7 © 2015 ANSYS, Inc. July 13, 2017
Airfoil characteristics at midspan section
AoA=13o AoA=16oLift coefficient
• γ-SST model delays appearance of 3D structures which leads to an overprediction of lift coefficient
• γ-SST-HL model fits experimental data (lift and pressure coefficient) well in the 3D wind tunnel setup
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Streamwise velocity profiles at AoA=12o
X/C=0.529 X/C=0.815 X/C=0.952
• When looking at a number of airfoil cases it seems we need to re-calibrate RANS models to be more aggressive on separation
• Need to replace NACA 4412 (1979) data with (1987) data
• Would such a model be overly aggressive on shock-BL cases?
• Free parameter a1
helpful, as models need to be adjusted to flow types
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• Develop two-equation model framework with tunable coefficients– In the past – model coefficients have been exposed – however they are inter-related and
any non-expert change will lead to deterioration of basic flows (flat plate)
– We have a range of scale equations (k-w, BSL/SST, k-e, RKE, V2F)
• To allow users to select a suitable model for their application
• Very expensive as each model needs to be developed/combined with
– Y+ - insensitive wall, rough wall, transition, CC, buoyancy, DES/SBES, ….
• Wouldn’t it be better to have 1 scale equation which can be tuned over a wide range of the parameter space.
– BSL2 will have several free coefficients which do not affect basic flows
BSL2 Turbulence Models
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BSL2 model formulation
𝜕 𝜌𝜔
𝜕𝑡+ 𝜕 𝜌𝜔𝑈𝑗
𝜕𝑥𝑗= 𝐶𝜔1
𝜔
𝑘𝑃𝑘 − 𝐶𝜔2𝜌𝜔
2 +
𝜌𝐶𝜔32
𝜎𝜔𝜔
𝜕𝑘
𝜕𝑥𝑗
𝜕𝜔
𝜕𝑥𝑗+
𝜕
𝜕𝑥𝑗𝜇 +
𝜇𝑡
𝜎𝜔
𝜕𝜔
𝜕𝑥𝑗
𝜕 𝜌𝑘
𝜕𝑡+ 𝜕 𝜌𝑘𝑈𝑗
𝜕𝑥𝑗= 𝑃𝑘 − 𝐶𝜇𝜌𝑘𝜔 +
𝜕
𝜕𝑥𝑗𝜇 +
𝜇𝑡
𝜎𝑘
𝜕𝑘
𝜕𝑥𝑗
• BSL2 will have several free coefficients which do not affect basic flows:
– CSEP - allow to steer separation
– CNW - allow to calibrate near wall behavior
– CMIX - alow to calibrate free shear flows independently from wall boundary layers
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• Incompressible flow– Re = 107
• Model maintains calibration for wide range of coefficient changes
Flat Plate Boundary Layer
Cmix = 0, CNW = 0.5 Csep = 1, Cmix = 0
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• Incompressible flow– Re = 105
• Boundary conditions– Inlet
• Inlet boundary with uniform velocity and turbulence properties
– Wall• No-slip wall boundary
condition– Slip wall
• The experimentally measured location of a streamline is used as an external boundary with the free slip wall boundary condition
Diffuser Flows: CS0 Diffuser
Results
Csep=1, Cmix=0 Csep=2, CNW=0.5Cmix=0, CNW=0.5
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13 © 2015 ANSYS, Inc. July 13, 2017
CS0 Diffuser (Driver NASA): Csep=1, Cmix=0
Results
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CS0 Diffuser: Cmix=0, CNW=0.5
Results
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CS0 Diffuser: Csep=2, CNW=0.5
Results
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• Incompressible flow– Re = 2.8·104
• Boundary conditions– Inlet
• Inlet boundary with specified velocity and turbulence properties
– Wall• No-slip adiabatic wall
boundary condition (heat flux = 0)
– Heat wall• No-slip wall boundary
condition with specified heat flux, q = 270 [W/m]
Backward-Facing Step
Csep=1, Cmix=0 Csep=2, CNW=0.5Cmix=0, CNW=0.5
Csep => Length of separation Cmix => Spreading rate of mixing layer => Reattachment accelerates
SEPARATION AND REATTACHMENT AFTER EXPANSION
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Mixing LayerCsep=1, Cmix=0 Csep=2, CNW=0.5Cmix=0, CNW=0.5
FREE SHEAR
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Mixing Layers: Hump
Csep = 2, CNW=0.5
Slip wall
No-slip wall
Re = 9.36·105
Separation point
Incompressible flow
Inlet developed velocity profiles
and turbulence properties
Csep = 1, CNW=0.5
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Hump Flow: Velocity Profiles
Csep = 2, CNW=0.5
Csep = 1, CNW=0.5
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Turbulence Kinetic Energy and Eddy Viscosity Ratio
Csep = 1, Ccross=0.5 Csep = 2, Ccross=0.5
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Aerodynamic Flows: A-Airfoil - CSep
• Incompressible flow
– Re = U∞∙C/ν = 2.1∙106
– α = 0o-20o
• The size of computational domains corresponds wind tunnel parameters
• Boundary conditions
– Uniform freestream is specified at the inlet
• Tu = 0.1%, νt/ν=1
– Constant pressure is specified at the outlet boundary
– Non-slip walls are specified on the airfoil surface
– Slip walls is specified on top and bottom tunnel walls
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Zero Pressure Flat plate Boundary Layer
WALL BOUNDED FLOWS
Velocity profile at Rex = 8.774·106Skin friction coefficient
• Incompressible flow
• Re = Uref ∙L/ν = 107
– L = 5 [m] length of the flat plate
– Uref = 10 [m/s] uniform freestream velocity
Flow scheme
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Mixing Layer
FREE SHEAR FLOWS
Flow scheme
• Incompressible flow
– Uref = 6 [m/s]
– ρ = 1.185 [kg m-3]
Prediction quality is almost identical for all the measurements planes
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Backward-Facing Step
Profiles at X/H=4.8
Re = U∞ ∙H/ν = 2.8·104
H = 0.038 [m]
Uref = 11.3 [m/s]
Skin friction coefficient and Stanton number on the heat wall
Flow scheme
SEPARATION AND REATTACHMENT AFTER EXPANSION
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CS0 Axisymmetric Diffuser
Profiles at X/D=2.17
• Incompressible flow
• Re = U∞ ∙D/ν = 2.8·105
– D = 0.14 [m] – Diffuser diameter
– U∞ = 30 [m/s] Freestream uniform velocity
Pressure and skin friction coefficient on he bottom wall
DIFFUSER FLOWS
Flow scheme
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26 © 2015 ANSYS, Inc. July 13, 2017
α
• Incompressible flow
– Re = U∞∙C/ν
– α = 0o-20o
• The size of computational domains corresponds wind tunnel parameters
• Uniform freestream corresponded experimental values is specified at the inlet
Flow Around Airfoils in Wind Tunnels
AERODYNAMIC FLOWS
Flow scheme
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Flow Around Airfoils in Wind Tunnels: NACA-4412 at α=12o
AERODYNAMIC FLOWS
X/C=0.529 X/C=0.815 X/C=0.952
Streamwise Velocity Profiles
Wall Normal Velocity Profiles
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Transonic Flows
AERODYNAMIC FLOWS
• RAE-2822, Case-10
– Re = 6.2·106
– Ma = 0.75
– Pr = 0.7
– α = 3.19o – angle of attack
• Axisymmetric Transonic Bump
– Re = 2.763·106
– Ma = 0.875
– Pr = 0.7
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Flow around a NACA-4412 airfoil
BSL2
BSL2+EARSM (Ccross=0.5)
• Combination of BSL2 (R18) with EARSM gives improved separation prediction without need to adjust CSep!
• For this reason alone, a proper two-equation model should be adjustable, so that it can be used stand-alone or in combination with RSM/EARSM
CNW
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Summary - RANS
• SST Model not aggressive enough for prediction of Clmax on airfoils
• SST-HL model tuned for that purpose – slight over-separation for transonic flows
• NACA 4412 – should probably abandon Coles-Wadcock (1979) experiment
• BSL2– Model with free coefficients
– Can be tuned over a wide range of flows by the user
– Coefficient settings (CSEP=2, CMIX=0.35, CNW=0.5) can do all flows (CS0, backstep, all Airfoils, RAE 2822, B-J bump) – therefore more consistent than SST
– Can BSL2 replace existing scale-equations?
– Intermediate step to machine learning (ML)