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DREAM/DTAA 05 december 2008Lattice Boltzmann scheme; Methodsand Applications, CEMAGREF
Application of Lattice Boltzmann Method in automotive industry
Denis RicotResearch, Advanced Eng. and Materials Dpt.
with contributions of :Hervé Illy, Jean-Luc Adam, DREAMOlivier Bailly, Sylvain Parpais, DPC
2DREAM/DTAA 05 december 2008
Lattice Boltzmann scheme; Methodsand Applications, CEMAGREF
Introduction
In automotive industry : commercial codes « only »Only one commercial LB code : PowerFLOW (EXA Corp.)EXA Corp. created in 1991 by K. Molvig (MIT) and his PhD student (C. Teixeira)First commercial version of PowerFLOW around 1997, with support of FordFirst use at Renault in 1998 for aerodynamics and aeroacoustics benchmarks (comparisons with other commercial CFD codes)Today, at Renault
Aerodynamics simulation (drag prediction)External and internal aeroacousticsThermal management (since ~2006)
Great success in ground transport industryAutomotive : Ford, BMW, Audi, Toyota, Nissan, Hyundai, PSA, Volkswagen…Heavy/commercial vehicles : Scania, Volvo Trucks, MAN,…Rail transport industry : Alstom, SNCF, …
3DREAM/DTAA 05 december 2008
Lattice Boltzmann scheme; Methodsand Applications, CEMAGREF
Presentation outline
Specific models in PowerFLOWMultiscale meshImmersed boundary modelTurbulence modelNumerical stability management
Aerodynamic applicationsValidation on simplified carMegane CC without underhood flowScenic with underhood flow
Aeroacoustic applications : direct noise calculationsTheoretical resultsNoise generated by ventilation outletsNoise radiated by a fence-cube academic configuration
4DREAM/DTAA 05 december 2008
Lattice Boltzmann scheme; Methodsand Applications, CEMAGREF
Successive LB models in PowerFLOW
First version of PowerFLOW (…2002) : D4Q54 (thermal model)16-bits (integer) variablesMRT-like model (variable Prandtl number)
Second version of PowerFLOW (2002…2006) : D4Q34 (thermal model)
Last version of PowerFLOW (2006…) : D3Q19 (SRT-BGK model)single precision floating point variables (32 bits)convection/diffusion thermal equation solved with Lax-Wendroff FD scheme + Boussinesq
approximation
Chen, H. & al., Int. J. Modern Phys. C, 1997
US Patent 5848269, Chen, Hill, Hoch, Molvig, Teixiera, Traub, 1995
Li, Y. & al., JFM, 2004
Order 3 : theoretically not necessary
Fan, H. & al., Phys. Rev. E, 2006
5DREAM/DTAA 05 december 2008
Lattice Boltzmann scheme; Methodsand Applications, CEMAGREF
Multiscale mesh
21 2 tt ∆=∆21 2 xx ∆=∆
−+=
21~
21~
12 ττ n
Mesh region 2
Mesh region 1
Continuity of speed of sound :
Continuity of viscosity :
6DREAM/DTAA 05 december 2008
Lattice Boltzmann scheme; Methodsand Applications, CEMAGREF
Multiscale mesh : volumetric formulation
Fine Coarse : coalesce the eight fine volumetric distribution functions
Chen, H. & al. 2005, “Grid refinement in Lattice Boltzmann methods based on volumetric formulation”, Physica A, 362 (1), 2006
Coarse Fine : explode the coarse volumetric distribution functionNo rescaling of distribution functionsNo time-interpolation
( ) ( ) cc VgN ⋅•=• αα
7DREAM/DTAA 05 december 2008
Lattice Boltzmann scheme; Methodsand Applications, CEMAGREF
Immersed boundary model for complex geometry meshing
8DREAM/DTAA 05 december 2008
Lattice Boltzmann scheme; Methodsand Applications, CEMAGREF
( ) ( ) ( )∑◊=
=Γkx
kkiout
i txgxVt~
, ,~~α
αα
No-slip boundary condition
( ) ( )tt outi
ini
,, αα −Γ=Γ
Wall boundary condition with a prescribed friction force (turbulence wall model)
( ) ( ) ( ) ( ) ( )( ) ...21 ,,,, +−⋅′−Γ−=Γ −
− tgtgncVuCtt ieqieqii
itf
outi
ini ααα
ααα
θrr
Friction force : ( ) 22itf
it uCtF ρ′−=
tangential velocity in the first cell above the surface element iitu
fC′ local friction coefficient
Outward distribution function flux for surface element i
( ) ( )kiki xVVxV ~~ ∩= αα
Boundary condition on complex geometry (volumetric fomulation)
- Chen, H. & al., Int. J. Modern Phys. C, 1997- WO Patent 97/21195, Chen, Hill, Hoch, Molvig, Teixeira, Traub, 1997
αiV
9DREAM/DTAA 05 december 2008
Lattice Boltzmann scheme; Methodsand Applications, CEMAGREF
Turbulence modeling in PowerFLOW
Calculation of using a model :turbτ
ρετσµ
σµρρ −+
∂∂
+
∂∂
=∂∂
+∂∂
ijrij
ikT
T
kiii S
xk
xxku
tk
( )k
CCSk
Cxxx
ut ij
rij
iT
T
iii
2
30
3
21 ~1
~1~ ερηβηηητεε
σµ
σµερερ µεε
εε
+−
+−+
∂∂
+
∂∂
=∂∂
+∂∂
012.0 ,38.4 ,719.0 ,68.1 ,42.1 ,085.0 021 ========= βηεεεεµ TkTk σσσ σCCC
Modified (Yakhot & Orszag, not published) RNG model (Yakhot & Orszag, 1986)ε−k
« Swirl modification » : ηε
ν µ ~112
+=
kCT
−=′′= ijijTji
rij kSuu δρµρτ
322
ε−k
...~ +Ω⋅
+Ω+=u
ukCkBSkA r
rr
εεεη
turbmol τττ +→Standard approach :
10DREAM/DTAA 05 december 2008
Lattice Boltzmann scheme; Methodsand Applications, CEMAGREF
Discretization of equations
Lax-Wendroff finite difference scheme on the same mesh
Explicit time-marching scheme
Small floor cut-off values and large ceilling values of and to insure realizability of the turbulence quantities (for numerical stability)
Near the wall : empirical boundary condition
Pervaiz, M.M. & Teixeira, C.M., « Two equation turbulence modeling with the lattice Boltzmann method », 2nd Int. Symposium on Comput. Tech. For Fluid/Thermal/Chemical Systems with Industrial Applications. ASME PVP Division Conference, August 1-5 1999, Boston, MA.
ε−k
k ε
+−== +−+ +
yC
eCu
kk y 29.011 1.02* µµ
6
4
4
32
4* 10
04.11004.10033.004.0
+++++ −+−==
yyyyuενε
11DREAM/DTAA 05 december 2008
Lattice Boltzmann scheme; Methodsand Applications, CEMAGREF
Turbulence wall model
Byuut +
=
+
ξκln1
*
0.5=B 41.0=κ
∂∂
+=t
char xpLg ,1ξ 0
xp if 1
t
>∂∂
>ξ
1. Extrapolation of the tangential fluid velocity from the inner domain variables
2. Calculation of with a modified log-law
3. Definition of a local friction coefficient and friction force
22
2*
tf u
uCρρ
=′
( ) ( )tfin
i uCft ′=Γ ,α
4. Inject the incoming particle flux in order to obtain the friction force on each surface element i
2
2t
fiuCF ρ′−=
tu
*u
(adverse pressure gradient effect)
12DREAM/DTAA 05 december 2008
Lattice Boltzmann scheme; Methodsand Applications, CEMAGREF
« Base viscosity » approachImposed minimum value of the non-dimensional relaxation time
The base viscosity depends on the local mesh size
In high turbulent viscosity region
But in low turbulent viscosity region (near wall separation for example)
Numerical stability management
baseTeff ννν >≈
baseττ ~~ > ( )xbaseTeff ∆>+= ννννNormalized (dimensionless) Physical units
baseeff νν =baseT ννν <+ unphysical high level of viscosity
x∆
13DREAM/DTAA 05 december 2008
Lattice Boltzmann scheme; Methodsand Applications, CEMAGREF
Numerical stability management
Standard base viscosity “Manually” reduced base viscosity
Tbaseeff νννν +>>= near flow separationbaseTeff νννν >+=
Sunroof buffeting simulation(D. Ricot, ECL, 2002)
14DREAM/DTAA 05 december 2008
Lattice Boltzmann scheme; Methodsand Applications, CEMAGREF
Presentation outline
Specific models in PowerFLOWMultiscale meshImmersed boundary modelTurbulence modelNumerical stability management
Aerodynamic applicationsValidation on simplified carMegane CC without underhood flowScenic with underhood flow
Aeroacoustic applications : direct noise calculationsTheoretical resultsNoise generated by ventilation outletsNoise radiated by a fence-cube academic configuration
15DREAM/DTAA 05 december 2008
Lattice Boltzmann scheme; Methodsand Applications, CEMAGREF
Aerodynamic drag simulation
ObjectivesDrag and lift coefficient calculation design choice to minimize CO2 emissionShape and detail optimizations
“3D” wake (strong longitudinal vortices) High drag
“2D” wakeLow drag
S. Parpais, Renault R&D mag., 2003
16DREAM/DTAA 05 december 2008
Lattice Boltzmann scheme; Methodsand Applications, CEMAGREF
Validation of aerodynamic drag simulation
First validation on simplified carNo underhoodFlat underbody
Total pressure loss 10 mm downstream the simplified car
Measurements PowerFLOW
17DREAM/DTAA 05 december 2008
Lattice Boltzmann scheme; Methodsand Applications, CEMAGREF
Validation of aerodynamic drag simulation
Validation on Megane CCNo underhood flowFully detailed underbody
Normalized (Ux / U0) longitudinal mean velocity in the symetry plane
Measurements PowerFLOW
18DREAM/DTAA 05 december 2008
Lattice Boltzmann scheme; Methodsand Applications, CEMAGREF
Validation of aerodynamic drag simulation
Validation on Megane CCDrag and lift coefficients are well recovered within few percents
Measurements PowerFLOW
Total pressure loss in the Megane CC wake
19DREAM/DTAA 05 december 2008
Lattice Boltzmann scheme; Methodsand Applications, CEMAGREF
Underhood flow
Heat exhanger are modeled with equivalent porous mediaFan model
Fixed fanRotating fan using Multiple Reference Frame approach
Experimental validation based on PIV measurements
Measurements
PowerFLOW
Ux
PIV measurements PowerFLOW
O. Bailly et al., SIA, Lyon 2005
20DREAM/DTAA 05 december 2008
Lattice Boltzmann scheme; Methodsand Applications, CEMAGREF
Validation on ScenicFully detailed underbodyUnderhood flow
Validation of aerodynamic drag simulation with underhood
21DREAM/DTAA 05 december 2008
Lattice Boltzmann scheme; Methodsand Applications, CEMAGREF
Validation of aerodynamic drag simulation with underhood flow
Measurements PowerFLOW
Total pressure loss in the Scenic wake
22DREAM/DTAA 05 december 2008
Lattice Boltzmann scheme; Methodsand Applications, CEMAGREF
Presentation outline
Specific models in PowerFLOWMultiscale meshImmersed boundary modelTurbulence modelNumerical stability management
Aerodynamic applicationsValidation on simplified carMegane CC without underhood flowScenic with underhood flow
Aeroacoustic applications : direct noise calculationsTheoretical resultsNoise generated by ventilation outletsNoise radiated by a fence-cube academic configuration
23DREAM/DTAA 05 december 2008
Lattice Boltzmann scheme; Methodsand Applications, CEMAGREF
Aeroacoustic simulations
External aeroacousticsBoth aerodynamic (incompressible) and acoustic (compressible) pressure fluctuations contribute to interior wind noise
Internal aeroacousticsSource and propagation in duct (HVAC)Aerodynamic noise generated by flow through ventilation outlets
Lateral HVAC outlet of Twingo
24DREAM/DTAA 05 december 2008
Lattice Boltzmann scheme; Methodsand Applications, CEMAGREF
Acoustic propagation with LBM : theoretical study
Dispersion error Dissipation error
Number of points per wavelength
Von Neumann analysis of the LB modelsComparison with optimized finite difference Navier-Stokes schemes (DRP : Dispersion Preserving Relation)
Lower numerical dissipation than all aeroacoustic-optimized schemes Lower dispersion error than FD of order 2 in space and 3 in time (Runge-Kutta)Higher dispersion error than FD of order 3 in space and 4 in time (Runge-Kutta)… but much lower computational effort in term of number of floating point operations + compact scheme
Number of points per wavelength
(S. Marié et al., J. Comput. Phys., 2008)
25DREAM/DTAA 05 december 2008
Lattice Boltzmann scheme; Methodsand Applications, CEMAGREF
In-house D2Q9 modelNon-reflecting boundary conditionsSelective viscosity filter
Example of direct noise calculation with LBM
25.0=M
Ricot D., Maillard V., Bailly C., AIAA paper 2002-2532
In agreement with other CAA simulations performed with optimized finite difference Navier-Stokes codes (Gloerfelt, 2001, Rowley, 2002)
(Rossiter mode 2)
89.00 == UfLStpressure
vorticity
Direct noise computation of a flow over cavity
25.0=Mach3108Re ⋅=L
26DREAM/DTAA 05 december 2008
Lattice Boltzmann scheme; Methodsand Applications, CEMAGREF
Acoustic impedance of outlets, without mean flow
Acoustic reflection coefficient of a circular baffled open termination
Analytical expression
LBM simulation
LBM simulation
Acoustic reflection coefficient of a HVAC duct outlet
Sysnoise (BEM) simulation
LBM simulation
27DREAM/DTAA 05 december 2008
Lattice Boltzmann scheme; Methodsand Applications, CEMAGREF
Noise generated by HVAC vents
Upstream acoustic pressure Downstream acoustic pressure
m/s 180 =U
Measurements
LBM Measurements
LBM
Vorticity snapshot
(J.-L. Adam et al., Acoustics’08, Paris)
28DREAM/DTAA 05 december 2008
Lattice Boltzmann scheme; Methodsand Applications, CEMAGREF
• U0= 50 m/s• dx_mini = 1 mm• 50 millions of cells
Snapshot of the Ux velocity in the symmetry plane
Fence-cube configuration (MIMOSA Project)
Measurements in the aeroacoustic windtunnel of LMFA using a microphone array
(H. Illy et al., DLES 2008)
PowerFLOW
29DREAM/DTAA 05 december 2008
Lattice Boltzmann scheme; Methodsand Applications, CEMAGREF
Snapshot of the pressure field (101328 < P < 101334 Pa)
Fence-cube configuration (MIMOSA Project)
Pressure level map on the microphone array for the third octave
315 Hz
LBM simulation
Measurements dB scale
30DREAM/DTAA 05 december 2008
Lattice Boltzmann scheme; Methodsand Applications, CEMAGREF
Concluding remarks
Other application fieldsThermal management (underhood) : two-way coupling between PowerFLOW (forced and natural convection) and RadTherm (solid conduction, radiation)External aeroacoustics : simulation of wall pressure fluctuations (excitation of lateral windows and windshield by aerodynamic and acoustic pressure field)Sunroof buffeting, effect of wind deflectors
Too dissipative turbulence modelFrequency limitation for wall pressure fluctuation simulationBetter approach ? : sub-grid model based on LES theory (Dong et al., Phys. Fluid 2008)
Numerical stabilization management with numerical viscosityUnphysical effective viscosity in some regionsBetter approaches ? : selective viscosity filter (Ricot et al., ICMMES 2007), MRT models, regularization method…
Single precision variabletoo high background noise in high frequency
… totally closed code … licence cost