Florian Menter, Chief Scientist Rob Winstanley, Engineering ManagerDomenico Caridi, Senior Regional Product ManagerKrishna Zore, Software Developer IITushar Jadhav, Senior Application Engineer

1st Automotive CFD Prediction Workshop

2

GEKO - New & Flexible RANS Turbulence Model

Motivation

• Two-equation models are the work-horse in industrial CFD

• The have typically 5 coefficients which can be calibrated to match physics

• They are calibrated for‐ Flat plate boundary layers (log-layer)

‐ Selected free shear flows (plane mixing layer, plane jet)

‐ Decaying turbulence in freestream

• Coefficients are linked and cannot be changed easily by user

Central Question: Can we do such a simulation with one set of global constants?

Probably not …

GEKO Model: Introducing Free Coefficients

( ) ( )

+

+−=

+

jk

t

j

k

j

j

x

k

xkCP

x

kU

t

k

( ) ( )

+

+

+−=

+

j

t

j

jj

k

j

j

xx

xx

kFFCP

kFC

x

U

t

23

2

2211

( ),

,max Real

tCS

k

=

• CSEP – changes separation behavior

• CMIX – changes spreading rates of free shear flows

• CNW – changes near-wall behavior

• CJET – Optimizes free jet flows

• CCORNER – Affects corner flows

• CCURVE – Curvature Correction

The functions F1, F2, and F3 contain 6 free coefficients:

All coefficients (except CJET) are UDF functions and can be changed locally

𝑢𝑖′𝑢𝑗

′

→ 𝑢𝑖′𝑢𝑗

′ −𝐶𝐶𝑜𝑟𝑛𝑒𝑟1.2 𝑡

𝑀𝐴𝑋 0.3𝜔, (𝑆2 + 2)/2𝑆𝑖𝑘𝑘𝑗 − 𝑖𝑘𝑆𝑘𝑗

Wall Treatment - Comparison

• The formulation of a turbulence model when integrated through the viscous sublayer is a key aspect of turbulence modelling‐ Defines robustness

‐ Defines accuracy

‐ Can cause undesired pseudo-transition

Makes or Breaks a Turbulence Model

Backstep Simulation

• 4x the same k-e model with different near wall treatment– ML – Menter-Lechner low-Re model

– EWT – Enhanced wall treatment built on 2-Layer formulation

– GEKO-1 exact transformation of k-e to k- with k- wall treatment

– V2F - k-e model with V2F ‘elliptic blending’ wall treatment

• Results are vastly different

• GEKO is closest

Wall Shear Stress Wall Heat Transfer

GEKO Model - Switching

• CSEP - active everywhere

• CNW - active everywhere (but only relevant near wall)

• CMIX – activated by blending function

• CJET – sub-model of CMIX( )...1 BlendJETMIXMIX FFCF −=

Wall-Distance Free Variant option available

1=BlendF

• Incompressible flow‐ Re = 107

• Variation of CSEP and CNW

• Model maintains calibration for wide range of coefficient changes

• CMIX and CJET do not affect boundary layer

Flat Plate Boundary Layer

All 4 coefficients can be tuned by user without loss of accuracy for flat plate

Velocity Profiles for CS0 Diffuser: Cmix=0

Variation of main free coefficients

• CNW – affects only near wall – no effect on Cp

• CSEP – affects separation strength

• CMIX – no effect

• Main parameter - CSEP

CNW=0.5

CSEP=1.0

Separated Flow Around a NACA-4412 Airfoil

Flow scheme Incompressible flow Re = U∞ ∙C/ν = 1.64·106

C - airfoil chord

U∞ - freestream uniform velocity

α = 12o – angle of attack

Triangular Cylinder – Variation of CMIX – Fixed FGEKO

Streamwise velocity contours at the midsection

SST

GEKO-2GEKO-1

Ahmed Body

SEPARATION AND REATTACHMENT AFTER EXPANSION

MidsectionSlant

Incompressible flow

• All the models fail to predict both separation and reattachment on the slant

• Results of GEKO-1 and GEKO-2 are close to the results of their analog

✓ GEKO-1 is similar to k−ε

✓ GEKO-2 is similar to SST

• Results of GEKO-1 and k-e models fit experimental data better than other models

k-ε Std

Best Practice Document - GEKO

https://www.ansys.com/-/media/ansys/corporate/resourcelibrary/technical-paper/geko-tp.pdf

Use 2nd order turbulence when feasible

Summary - GEKO

• A new Generalized k- (GEKO) model has been developed

• It allows optimization of free coefficients over a wide range of applications

• Instead of switching between different models, users can now adjust a single model to their application

• Good chance of consolidation of two-equation models into one optimal format

• Further free coefficients will be added

• Strong defaults

• Coefficients can be changed locally via UDF

• Already successfully used in industrial applications

• Implementation in Fluent (planned for CFX R20)

25

Tuning the GEKO Turbulence Model for Case 2a & 2b

Tuning the GEKO turbulence model using Design of Experiment

• Goal is tuning the GEKO‐ To improve the prediction of drag and lift on two and

eventually on more car models

‐ Using main driving parameters and zonal approach

• Car Models used‐ DrivAer Fastback and DrivAer Estate – Corse Ansa Mesh

• Solver Set up‐ Coupled solver, 2nd order Upwind, LSQ, Pseudo Transient

• Parameters used for this study‐ Csep global

‐ Csep local in the wheel MRF zone

‐ Cmix global

26

Design of Experiment and Optimization using Workbench DX

• DOE main set up‐ Optimal Space Filling Design

‐ 20 samples

‐ Csep range: [1-2]

‐ Cmix range: [0.3-4]

• Input parameters‐ Csep global, Cmix global,

Csep local (wheel MRF)

• Output parameters‐ dCD, dCL for Fastback and Estate, dCD Fastback-Estate, Mean Square Error

• Total time for one model DOE (20 sim) about 6000 CPU hours‐ Comparable with one scale resolved simulation

• Neural Network Response Surface

27

Results

29

• Multi Objective Genetic Algorithm‐ Seek for 0 delta for Drag, Lift on both models

‐ Higher priority for Drag

‐ Minimize Mean Square error

‐ Keep same drag trend between two models

Very good trade off improvement!

Case 2a Coarse – GEKO Csep 1.75 Vs Optimised

Csep 1.75 Optimised

Contours of X Velocity at Plane Y = 0

0 5 15 2010

Case 2a Coarse – GEKO Csep 1.75 Vs Optimised

Csep 1.75 Optimised

Contours of X Velocity at Plane Z = 0

0 5 15 2010

Case 2a Coarse – GEKO Csep 1.75 Vs Optimised

Contours of Pressure Coefficent

-0.9 0.90

Csep 1.75 Optimised

-1.00E+00

-5.00E-01

0.00E+00

5.00E-01

1.00E+00

1.50E+00

2.00E+00

-2.00E+00

-1.50E+00

-1.00E+00

-5.00E-01

0.00E+00

5.00E-01

1.00E+00

-1.00E+00 -5.00E-01 0.00E+00 5.00E-01 1.00E+00 1.50E+00 2.00E+00 2.50E+00 3.00E+00 3.50E+00 4.00E+00

Optimised-pressure-coefficient Csep 1.75-pressure-coefficient z-coordinate

Case 2a Coarse – GEKO Csep 1.75 Vs Optimised

Case 2b Coarse – GEKO Csep 1.75 Vs Optimised

Csep 1.75 Optimised

Contours of X Velocity at Plane Y = 0

0 5 15 2010

Case 2b Coarse – GEKO Csep 1.75 Vs Optimised

Csep 1.75 Optimised

Contours of X Velocity at Plane Z = 0

0 5 15 2010

-1.00E+00

-5.00E-01

0.00E+00

5.00E-01

1.00E+00

1.50E+00

2.00E+00

-2.00E+00

-1.50E+00

-1.00E+00

-5.00E-01

0.00E+00

5.00E-01

1.00E+00

-1.00E+00 -5.00E-01 0.00E+00 5.00E-01 1.00E+00 1.50E+00 2.00E+00 2.50E+00 3.00E+00 3.50E+00 4.00E+00

Optimised-pressure-coefficient Csep 1.75-pressure-coefficient z-coordinate

Case 2b Coarse – GEKO Csep 1.75 Vs Optimised

39

MosaicTM Meshing – Case 2a

Mosaic (Poly-Hexcore) Meshing

Hex Core• High quality• Fast solve time

New: MosaicTM Technology• Unique technology to

conformally connect poly prisms to hex

• High quality transition, with significantly fewer cells than tet transition

• Patent pending

Poly Prism• High quality• Significantly fewer

cells than tri prisms

Mosaic (Poly-Hexcore) Meshing Parallel – F1 Car

• If Fluent Meshing is opened in parallel Distributed Parallel Meshing will auto-enable

• Particular benefit for large meshes or number of prism layers

• Up to 8.1 Million cells/min with 64-way parallel

• Typical memory requirement: <3 GB / Million cells

Mosaic Remeshing of Medium 2a Committee Grid

• All wall tri-surfaces unchanged• Quads on MFR Internal Surfaces

triangulated and Remeshed

• BOI regions and sizing replicated

• Prism Layers‐ Car - 22 Layers, 1.8e-5m first height,

variable growth rate to Last Ratio 40%

‐ Road - 22 Layers, first aspect ratio 100, 1.17 growth rate

Mosaic Remeshing of Medium 2a Committee Grid

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0 50 100 150 200 250 300 350 400 450

CL

Iteration

ANSA (CL mean = 0.0782)

Mosaic (CL mean = 0.0697)

0.2

0.22

0.24

0.26

0.28

0.3

0.32

0.34

0.36

0.38

0.4

0 50 100 150 200 250 300 350 400 450

CD

Iteration

ANSA (CD mean = 0.2394)

Mosaic (CD mean = 0.2380)

Mosaic Vs ANSA Medium – GEKO Csep 1.75

• Mosaic creates similar spatial resolution mesh 86M vs 165M cells‐ Parallel meshing on 32 cores completes the

volume meshing in 19 minutes

• HPC Comparison‐ Mosaic➢ 280 cores (14 nodes with 2x Xeon E5-2660 v3 2.6GHZ)

➢ 618.5 CPU.Hours

‐ ANSA➢ 224 cores (8 nodes with 2x Xeon E5-2690 v4 2.6GHZ)

➢ 1422.4 CPU.Hours

• Similar accuracy 2x speed up‐ Similar results with ANSYS Hexcore meshes

Mosaic Vs ANSA Medium – GEKO Csep 1.75

Mosaic ANSA

Contours of X Velocity at Plane Y = 0

0 5 15 2010

Mosaic Vs ANSA Medium – GEKO Csep 1.75

Mosaic ANSA

Contours of X Velocity at Plane X = 0

0 5 15 2010

Mosaic Vs ANSA Medium – GEKO Csep 1.75

Mosaic ANSA

Contours of Pressure Coefficent

-0.9 0.90

-1.00E+00

-5.00E-01

0.00E+00

5.00E-01

1.00E+00

1.50E+00

2.00E+00

-2.00E+00

-1.50E+00

-1.00E+00

-5.00E-01

0.00E+00

5.00E-01

1.00E+00

-1.00E+00 -5.00E-01 0.00E+00 5.00E-01 1.00E+00 1.50E+00 2.00E+00 2.50E+00 3.00E+00 3.50E+00 4.00E+00

ANSA-pressure-coefficient Mosaic-pressure-coefficient z-coordinate

Mosaic Vs ANSA Medium – GEKO Csep 1.75

Summary

• Tuning GEKO allows a RANS model to get much closer to experimental results ‐ Running a DoE for two vehicle configurations takes similar CPU resource to a single scale

resolving simulation

• Mosaic Parallel Meshing creates a mesh with similar spatial resolution to traditional Prism-Tet-Hexcore meshes with 40% – 50% less cells‐ This results in a 2x speed up in solution time with not loss of accuracy

• Mosaic Parallel Meshing generates 86 Million cells in 19 Minutes.

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58

Thank You and Questions