Wall-Modelled Large-Eddy Simulation onUnstructured Grids

Timofey Mukha

21 November 2018

Wall-Modelled LES

Turbulence modelling approach• Resolved LES in the outer layer, scales∼ δ.

• Turbulence below the overlap layerunresolved.

• Special modelling to compensate forthat.

• Grid independent of “+”-units!Grid size scaling for a flat-plate TBL• Wall-resolved LES: N ∼ Re1.85

• Wall-modelled LES: N ∼ Re

Gothenburg OpenFOAM User Group Meeting 2018 21 November 2018 T. Mukha 1

Wall-Stress ModellingCompensating for the unresolved scales

For each time-step, for each wall-face• Sample LES solution from distance h.• A wall model predicts τ̄w.• τ̄w enforced at the face.• By adding additional viscosity.

What’s inside the wall model?• An equation relating τ̄w to the solution.• Example: Spalding’s law

y+ = 〈u〉++e−κB

[eκ〈u〉

+

−3∑

m=0

(κ〈u〉+)m

m!

]

Gothenburg OpenFOAM User Group Meeting 2018 21 November 2018 T. Mukha 2

Current Status in OpenFOAMlibWallModelledLES

Open-source library• Several algebraic and ODE-based wall

models.• Assign h on a per-face basis.• Control all parameters.• Convenient framework for adding new

models.New in v0.4.0• Compiles for multiple version of

OpenFOAM.• Foundation >3.0.x• OpenCFD >1606+• Will probably not pursue foam-extend,

unless I get a user :).Gothenburg OpenFOAM User Group Meeting 2018 21 November 2018 T. Mukha 3

Lessons Learned using Structured Hexas

• Isotropic cells, with density 27 000 per δ3.• h should not correspond to wall-adjacent cell.• The WALE SGS model is a good choice.• A mildly diffusive scheme (LUST) is a good choice.

How about unstructured meshes?• Can we use them?• How should we mesh?• What cell-type should we use?• Do the above guidelines hold?

Gothenburg OpenFOAM User Group Meeting 2018 21 November 2018 T. Mukha 4

Meshing StrategyPrinciples

1 The mesh should be isotropic.2 Average distance between cell-centres d as characteristic size.3 Resolution constant with respect to δ.4 Note: leads to varying h.

0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00x

25

50

75 0.1Lz/dd +

Gothenburg OpenFOAM User Group Meeting 2018 21 November 2018 T. Mukha 5

Meshing StrategyPrinciples

1 The mesh should be isotropic.2 Average distance between cell-centres d as characteristic size.3 Resolution constant with respect to δ.4 Note: leads to varying h.

0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00x

25

50

75 0.1Lz/dd +

Gothenburg OpenFOAM User Group Meeting 2018 21 November 2018 T. Mukha 5

Meshing StrategyFour-step procedure

1 Estimate δ. Known estimates or RANS precursor.2 Mesh the wall surface, with δ/d = const.3 Extrude layers for 0 to δ, with layer height ≈ d.4 Mesh the rest of the domain.

Gothenburg OpenFOAM User Group Meeting 2018 21 November 2018 T. Mukha 6

Results: Flat-Plate TBL up to Reθ ≈ 4000Mukha, T., Johansson, M., & Liefvendahl, M. (2018). In 7th European Conference on CFD.

1 δ estimated from a power law.2 Mesh the wall surface, with δ/d ≈ 15.5.3 Paved and polyhedral meshes.4 Npaved = 15.5 mil., Npoly = 12.9 mil., NWR ≈ 250 mil.

Gothenburg OpenFOAM User Group Meeting 2018 21 November 2018 T. Mukha 7

Results: Flat-Plate TBL up to Reθ ≈ 4000Mukha, T., Johansson, M., & Liefvendahl, M. (2018). In 7th European Conference on CFD.

• WALE model.• LUST scheme.• h = 1st and h = 3st.

500 1000 1500 2000 2500 3000 3500 4000Re

0.002

0.003

0.004

0.005

0.006

c f

Paved, 1stPaved, 3rdPolyhedral, 1stPolyhedral, 3rdDNSPower law

101 102 103

y +

5

10

15

20

25

30

u+

Re 1420

101 102 103

y +

Re 2000

101 102 103

y +

Re 2540

Gothenburg OpenFOAM User Group Meeting 2018 21 November 2018 T. Mukha 8

Results: Flat-Plate TBL up to Reθ ≈ 4000Mukha, T., Johansson, M., & Liefvendahl, M. (2018). In 7th European Conference on CFD.

• WALE model.• LUST scheme.• h = 1st and h = 3st.

500 1000 1500 2000 2500 3000 3500 4000Re

0.002

0.003

0.004

0.005

0.006

c f

Paved, 1stPaved, 3rdPolyhedral, 1stPolyhedral, 3rdDNSPower law

101 102 103

y +

5

10

15

20

25

30

u+

Re 1420

101 102 103

y +

Re 2000

101 102 103

y +

Re 2540

Gothenburg OpenFOAM User Group Meeting 2018 21 November 2018 T. Mukha 8

Results: Japan Bulk CarrierLiefvendahl, M. & Johansson, M. (2018). In 32nd Symposium on Naval Hydrodynamics.

• Test case of the Tokyo 2015 workshop, Re = 7.46 · 106.• Focus on the behaviour of WMLES in the hull boundary layer.• RANS, k-ω SST for comparison and δ estimate.• Polyhedral grid, h = 1st, N ≈ 137 mil. cells.

Gothenburg OpenFOAM User Group Meeting 2018 21 November 2018 T. Mukha 9

Results: Japan Bulk CarrierLiefvendahl, M. & Johansson, M. (2018). In 32nd Symposium on Naval Hydrodynamics.

Gothenburg OpenFOAM User Group Meeting 2018 21 November 2018 T. Mukha 10

Results: Japan Bulk CarrierLiefvendahl, M. & Johansson, M. (2018). In 32nd Symposium on Naval Hydrodynamics.

Gothenburg OpenFOAM User Group Meeting 2018 21 November 2018 T. Mukha 10

Results: Japan Bulk CarrierLiefvendahl, M. & Johansson, M. (2018). In 32nd Symposium on Naval Hydrodynamics.

Gothenburg OpenFOAM User Group Meeting 2018 21 November 2018 T. Mukha 10

Conclusions

• A strategy for unstructured mesh generation for WMLES weredeveloped.

• Two meshes for a flat-plate TBL were generated: paved and polyhedral.• Accurate results were obtained using guidlines developed for

hexahedral meshes.• Flow around a JBC in model scale was simulated.• Applicability of the approach to real-life cases demonstrated.• Accuracy trends similar to flat-plate cases were observed.

Future plans• Continue JBC simulations.• Master thesis project announced: systematic assessment of accuracy

on different meshes.

Gothenburg OpenFOAM User Group Meeting 2018 21 November 2018 T. Mukha 11