Turbulent flows using Lattice Boltzmann Method : application on automotive configurations

Denis Ricot, Renault, Digital Mockup, CAE and PLM Division

MUSAF 16, September 27 & 29, 2016, ONERA, Toulouse

with contributions of :J-P La-Hargue, H. Touil, B. Gaston, R. Cuidard, CSE. Leveque, Lab. de Mécanique des Fluides et d’Acoustique, EC Lyon P. Sagaut, Lab. de Mécanique, Modélisation et Procédés Propres, Univ. Aix MarseilleO. Coste, Gantha

01 LBM and LaBS PRESENTATION

02 OCTREE MESH

03 IMMERSED SOLID METHOD : WALL-RESOLVED LES

04

05

CONCLUDING REMARKS

SUMMARY

IMMERSED SOLID METHOD : WALL-MODELED LES

INDUSTRIAL VALIDATIONS

06

Statistical mechanics• Boltzmann equation• Particles

– Kinetic energy– Momentum– Shocks– Mean free path

Continuum mechanics• Navier-Stokes equations• Continuous media

– Temperature– Pressure– Density– Viscosity

Lattice Boltzmann method

• Particle velocity discretization (finite discrete velocity set for particles instead of continuous particle velocity)• Space and time discretizations of the discrete velocity Boltzmann equation

Chapman-Enskog theoretical expansion Navier-Stokes equations

Chapman-Enskog theoretical expansion

Lattice Boltzmann Method

« LaBS Consortium » collaborates with partners whose scientific expertise enables building mathematical models, improving HPC

performance and workflow and establishing simulation best-practices for several application domains.

LaBS : collaborative development

Three industrial companies and two scientific laboratories, software’s co-owner and developpers, leading, supporting and validating LaBS.

LaBS Consortium

LaBS (2009-2013) & CLIMB (2014-2017) : collaborative projects with strong partnerships

With the support of competitiveness clusters :

Financial support from FUI & PIA CISN :

…

Post-processing

Parallel solverGUI

LaBS software and simulation workflow

Developed from scratch since 2009- a GUI for simulation setup- a parallel solver, including the volumetric mesher- PostLaBS : a Paraview script suite for automatic post-processing (incl. signal processing)

CADSurface mesh

Ensight

Paraview

Report

ANSA, Salome, … PostLaBS

LaBS

Others…

LaBS architecture

Simulation setup : dedicated GUI, with script capacities

Base octree generation & load balancing optimization

Computation scheduling (dataflow programming)

Mesh and data structure generation

Time-step loop

Merge result files and format conversion

Main numerical issues

txutxftxftxf eqcollision ,,,1

,1

1,

txftx ,,

txfctxutx ,,,

Macroscopic quantities

txctxp s ,, 2

t

xcs

3

1

2

2 tcs

Sub-grid turbulence model

Immersed solids

Wall law

txf ,

txftttcxf collision ,,

core LBM : « Collide and Stream »

Mesh refinement based on octree meshTurbulence modeling

Numerical stability

Porous media

Moving mesh

01 LBM and LaBS PRESENTATION

02 OCTREE MESH

03 IMMERSED SOLID METHOD : WALL-RESOLVED LES

04

05

CONCLUDING REMARKS

SUMMARY

IMMERSED SOLID METHOD : WALL-MODELED LES

INDUSTRIAL VALIDATIONS

06

Volumetric mesh

Based on efficient parallel octree mesher Interior of surface meshes are excluded, without limitation in term of shape, number of

surfaces, and overlapping regions Zero-thickness surfaces (« open shells ») are accepted : two-sided surfaces, one

boundary condition for each side Refinement regions are defined using boxes, hand-made shapes, automatic offsets,…

exclusion

exclusion

raffinement

exclusion

raffinement

Volumetric mesh

AMR-like mesh : successive refinement of the volume mesh (M. J. Berger and P. Colella, "Local adaptive mesh refinement for shock

hydrodynamics," J. Comp. Phys, 82:64-84, 1989)

In LaBS : vertex-centered formulation coarse mesh nodes are coincident with fine mesh nodes Partial mesh overlapping approach for data exchanges between refinement blocks Need for rescaling of distribution functions (O. Fillipova and D. Hänel. Grid refinement for lattice-BGK models. J. Comput. Phys., 147(1):219–

228, 1998)

Fine to coarse mesh transfer

Mesh refinement

Example of validation for an acoustic pulse propagation in a multi-resolution grid

Coarse to fine mesh transfer for coincident fine nodes Coarse to fine mesh transfer for non-

coincident fine nodes

01 LBM and LaBS PRESENTATION

02 OCTREE MESH

03 IMMERSED SOLID METHOD : WALL-RESOLVED LES

04

05

CONCLUDING REMARKS

SUMMARY

IMMERSED SOLID METHOD : WALL-MODELED LES

INDUSTRIAL VALIDATIONS

06

Full separation between the octree volumetric mesh and the surface mesh (triangles)

An immersed solid boundary algorithm must be used

Immersed boundary conditions : several available approaches in literature deduced from the original Navier-Stokes techniques (Peskin, 1977). See for example : Z.-G. Feng and E.E. Michaelides. The Immersed

Boundary-Lattice Boltzmann Method for Solving Fluid-Particles Interaction Problems. J. Comput. Phys., 195(2):602-628, 2004

In LaBS, not IBC : a kind of cut-cell method No cells inside the solids Special treatment of the fluid boundary nodes : « reconstruction method », similar to the model

described in : J.C.G. Verschaeve and B. Müller, "A curved no-slip boundary condition for the lattice Boltzmann method", J. Comput. Physics, 2010, 229(19), pp.6781-6803

Immersed solid

Distribution functions associated with velocity #7 and velocity #3 in its example can not be calculated by the collision / propagation LBM algorithm because neighbor nodes are inside the solid

Immersed solid : reconstruction method

Reconstruction of the distribution functions from the macroscopic data (pressure, velocity and velocity

gradients) :

Spatial interpolation needed using the available standard fluid nodes

Boundary node to be calculated

ij

ijijsji

ss

ijsjiji

s

iineqeqSccc

cc

cccuu

c

uctxftxftxf

2

,,24

2

,,

2

,

21,,,

(Chapman-Enskog expansion)

i

j

j

iij

x

u

x

uS

2

1iu ,

Spatial interpolationCalculation of velocity gradients by

off-centered finite difference scheme

Lattice Boltzmann is a native unsteady algorithm with very low numerical dissipation : it is well adapted to Large Eddy Simulation

Two sub-grid models are implemented in LaBS : Shear-Improved Smagorinsky Model (SISM) The Approximate Deconvolution Model (ADM)

Turbulence model

txutxftxftttcxf eq ,,,1

,1

1,

2

2 tcs

The shear-improved Smagorinsky model is a sub-grid turbulent viscosity model : E. Leveque, F. Toschi, L. Shao and J.-P. Bertoglio, Shear-Improved Smagorinsky Model for Large-Eddy Simulation of Wall-Bounded Turbulent

Flows, Journal of Fluid Mechanics 2007, vol. 570, pp. 491-502

Teff eff

“< >” is low-pass filtering based on an exponentially-weighted moving time average

Turbulence model

The Approximate Deconvolution Model (ADM) is not a turbulent viscosity model : dissipation is added through selective spatial filtering

Navier-Stokes : Stolz S, Adams NA, Kleiser L. An approximate deconvolution model for large-eddy simulation with application to incompressible wall-bounded flows. Phys Fluids 2001;13:997–1015

Validation of ADM for LES simulations have been done with Navier-Stokes solver (Bogey, C. & Bailly, C., 2006,

Computation of a high Reynolds number jet and its radiated noise using large eddy simulation based on explicit filtering, Computer & Fluids, 35(10),

1344-1358) and LBM solver (Lattice Boltzmann : O. Malaspinas and P.Sagaut, Advanced large-eddy simulation for lattice Boltzmann methods:

The approximate deconvolution model Phys. Fluids 23, 105103, 2011 )

LBM algorithm is unchanged compared to the DNS case : only an explicit filtering step is added

Small scales are damped without affecting the larges scales

In LaBS : 7 point stencil is used : D. Ricot, S. Marié, P. Sagaut, C. Bailly Lattice Boltzmann method with selective viscosity filter, Journal of

Computational Physics 228 (2009) 4478–4490

Wall-resolved LES : turbulent plane channel flow Ret=395

DNS = pseudo-spectral solver

LES-FV = Finite-volume LES solver (mesh size comparable to the LES of LaBS, SISM)

y+=5 à la paroi !

y+=20 in bulk

Mean axial velocity

3 resolution domains

SGS model: SISM

Wall-resolved LES : Cylinder at Re 47000

LES with SISM model9 refinement levels

17 millions on mesh nodes128 procs.

H Touil, D. Ricot, E; Lévêque, J. Comp. Phys. Vol 256, 1 January 2014

01 LBM and LaBS PRESENTATION

02 OCTREE MESH

03 IMMERSED SOLID METHOD : WALL-RESOLVED LES

04

05

CONCLUDING REMARKS

SUMMARY

IMMERSED SOLID METHOD : WALL-MODELED LES

INDUSTRIAL VALIDATIONS

06

Wall-modeled LES

Both Shear-Improved Smagorinsky model and Approximate deconvolution model can be associated with a wall law model

Analytical wall law is used : in-house composite model + viscous sub-layer continuousadaptation

Pressure gradient effectLocal curvature effect

Roughness effect

dx

dP

U 3

N. Afzal. Wake layer in a turbulent boundary layer with

pressure gradient: a new approach. In IUTAM Symposium

on Asymptotic Methods for Turbulent Shear flows at High

Reynolds Numbers. K., G., ed., Kluwer Academic

Publishers, 1996, 95-118

Patel & Sotiropoulos, « Longitudinal curvature

effects in turbulent boundary layer », Prog.

Aerospace Sci, Vol 33, pp1-70, 1997

59 eK

Wall law

35.1 e

0K

0

Both wall pressure gradient and wall curvature terms are active on high range of y+ : not useful for “standard” wall-adapted mesh (y+≈ 40)

On vehicle minimum mesh size around 1-2mm that leads to y+ ≈ 200 on vehicles (U0 ≈ 40 m/s) Some geometrical details are only a few millimeters (gap between panels, seals,…) : the

curvature term can « help » the flow to be sensitive to this local surface irregularity

Wall law calculation

Strategy :

Choose a « reference point » • at a fixed distance from de

wall (in the wall normal direction) Use known values in order to interpolate the velocity at this

reference point Calculate the wall pressure gradient and streamwise

curvature at this point • Calculate the friction velocity Utau with the Newton method Supposing the wall pressure gradient and curvature are the

same than at the reference point, calculate the tangential

velocity at the boundary node

Use the standard mixing length model to calculate the

turbulent viscosity at the boundary node

Similar to the implementation presented in “Wall Model for Large-Eddy

Simulation based on Lattice Boltzmann Method”, O. Malaspinas, P. Sagaut,

J. Comput. Physics, 2014, 275, pp 25-40

Boundary node to be calculated

Curvature calculation

One of the challenging task : calculation of the streamwise curvature… in the framework of complex geometry with open or closed solid surfaces, overlapping surfaces,…

The curvature vector is calculed during the pre-processing step using an adaptative algorithmthat depends on the local surface mesh size and on the local fluid cell size

tangtang UKK

High sensitive curvature sensor Medium sensitive curvature sensor

K

Example on a full vehicle : only convex curvature is taken into account

Curvature calculation

Wall law validation

Flat plate boundary layer development (2D computation, « RANS » mode development)

Fixed velocity U0=40m/s Fixed pressure

« 2D » configuration :

periodic in the transverse

direction

Wall law

Velocity profile at Re_X=600000

2

0

2

U

UC f

2.0Re059.0

x

emp

fC

Friction coefficient along the plate

y+=12

y+=56

y+=113

y+170

y+=215

5 computation, same mesh size (dx+ =226

à Re_X=600000) but varying the position

of the first mesh node layer regarding the

wall

Wall law validation

Flat plate boundary layer development (2D computation, « RANS » mode development)

Flat plate boundary layer development (2D computation, « RANS » mode development)

Wall law on vehicle

On the vehicle skin : some refinement

regions are defined near critical zones

The wall distance varies suddenly

y+≈ 400

y+≈ 200

28

Wall law validation on inclined flat plates

Flat plate,

aligned with the

mesh

Inclined flat plate,

small angle

Inclined flat plate,

intermediate

angle

29

Wall law validation on inclined flat platesU

tau

X (mm)

Intermediate angle

Aligned with mesh axis

Small angle

Uta

u

01 LBM and LaBS PRESENTATION

02 OCTREE MESH

03 IMMERSED SOLID METHOD : WALL-RESOLVED LES

04

05

CONCLUDING REMARKS

SUMMARY

IMMERSED SOLID METHOD : WALL-MODELED LES

INDUSTRIAL VALIDATIONS

06

Drag coefficient of a full-scale car

Setup:

≈ 2h engineering time

Solver:

≈ 48h/196 cores

Post-processing:

Automatic

Surface mesh:

O(2-4M) Δ

Volume mesh:

O(100M) cells

10 refinement levels

Simulated physical

time:

1s

300 000 time-steps

CAD mgt and surface

mesh

preparation lead time

depends on the CAD

CAD:

O(200) surfaces

AERODYNAMIC VALIDATION : Industrial case

RESULTS

CdA

(m²)

∆CdA ClA

(m²)

∆ClA

Tests in wind tunnel 0.677 REF 0.458 REF

LaBS 0.678 0% 0.315 -31%

Reference vehicle

Good overall topology

Flow detachment on the

rear part is well predicted

Good estimation of the

vortex came from A-pillars

Good accuracy of the

value of CdA

TESTS

AERODYNAMIC VALIDATION : Industrial case

RESULTS

CdA

(m²)

∆CdA ClA

(m²)

∆ClA

Tests in wind tunnel 0.800 REF 0.254 REF

LaBS 0.780 -3% 0.251 -1%

Scenic II

TESTS

Duster

SCx Ecart

Tests in wind tunnel 1.016

LaBS 1.010 -1%

TESTS

AERODYNAMIC VALIDATION : with porous media and rotating fan

Mégane IIIMean Velocity

(m/s) on radiator

LaBS(m/s)

V=165km/h 5.47

V=2km/h 1.51 Fan OFF

V = 165 km/h

Fan ON

V = 2 km/h

OK withExperimentalresults

Wall pressure fluctuation

Full scale vehicle simulation 10 levels of refinement, around 30 millions mesh nodes, 300 000 time-steps U0 = 44.4 m/s Wall Law LES (Approximate Deconvolution Model)

Aeroacoustic sources inside mufflers

Comparison expe/num of the power spectral density of the

acoustic pressure field at the external reference probe.

Sponge zone modeling to

avoid acoustic reflection on

fluid domain boundaries

Instantaneous velocity

physical noise coming

from internal sources

spurious source region

due to mesh size jump

(fine to coarse)

Instantaneous pressure

Tailpipe measurement test bench.

01 LBM and LaBS PRESENTATION

02 OCTREE MESH

03 IMMERSED SOLID METHOD : WALL-RESOLVED LES

04

05

CONCLUDING REMARKS

SUMMARY

IMMERSED SOLID METHOD : WALL-MODELED LES

INDUSTRIAL VALIDATIONS

06

Concluding remarks

Lattice Boltzmann method for complex geometry: Immersed solid approach is not a choice with LBM “false” LBM (Finite-Difference LBM, Finite volume LBM) that allow wall-adapted meshes

(unstructured-like,…) are not LBM : they loose of the main advantage of the LB scheme (high accuracy-cost ratio).

Wall-Modeled LES is natural choice : still many challenges In many industrial configurations : large regions of attached flow with poor mesh

refinement toward Wall-Modeled DDES or other hybrid RANS/LES approaches

“Easy-to-use” immersed solid methods need special attention : Surface result management : must be treated as a “HPC” challenge with its own data

structure (no direct direct/natural connectivity between surface and volume mesh) Independent and overlapping surfaces are not efficient to accurately calculate surface

integrated data (e.g. wetted surface) : need for some sewing algorithms