VKI-RVAD-2005-BMW-Presentation

Application of aLattice-Boltzmann Code inAutomobile and MotorcycleAerodynamics.

Dr.-Ing. Norbert GrünAerodynamics Simulation

Lecture Series on Road Vehicle Aerodynamicsvon Karman Institute for Fluid Dynamics, BrusselsMay 30 – June 03, 2005

BMW GroupDr. Norbert Grün

Lecture Series onRoad VehicleAerodynamics

VKI, Brussels

May 30-June 3, 2005

Page 2

Application of a Lattice-Boltzmann Code in Road Vehicle Aerodynamics.

Outline

� Aerodynamic Development Process

� Physics Overview

� Simulation Process

� Validation Examples

� Various Applications

� Conclusion



VKI, Brussels

May 30-June 3, 2005

Page 3


CFD in the Aerodynamic Development Process

Simultaneous Usage of Experimental & Virtual Tools

Serial Development PhaseConcept Phase

Prototypes100%

Windtunnel Model

CFD-Models

A

C

D

F

CC

F

A

B

C

D

E

F

Styling-Freeze

Styling–Competition

A

C

D

F

CC

F

A

B

C

D

E

F

40%Windtunnel Models

CFD-Models

Proportion-Studies

CFD-Models

Sty

ling

Pro

cess

Aer

oA

naly

sis

Too

ls



VKI, Brussels

May 30-June 3, 2005

Page 4


Requirements on CFD as a Productive Tool

• Accuracy (∆CD <±0.005, ∆CL <±0.010), at least for trends

• Geometry input preparation minimized

• Ability to handle complex geometries (underhood & underbody)

• Deliver results in a reasonable timeframe (over night)

• Easy to use (by non-numerics specialists)



VKI, Brussels

May 30-June 3, 2005

Page 5


CFD Resources

285

222

95

48

248

253

0

50

100

150

200

250

300

1997 1998 2000 2001 2002 2004 2005

Tot

alN

umbe

rofP

roce

ssor

s

SUNSUN

SGI

2 x SGI

(95+127)

1 x SGI

(127)

2 x HP

(je 63)

SUN

1 x SGI

(160)

2 x HP

(je 63)

decicated PowerFLOW servers

Number of Processors

Speed-Up

Efficiency onParallel Computers



VKI, Brussels

May 30-June 3, 2005

Page 6

New Goal :

• Construct simplified microscopic description (mesoscopic)that still contains the essential micro-physics to achievedesired macroscopic behaviour.


Motivation for Lattice-Boltzmann Methods (LBM)

Microscopic______________

Mesoscopic______________

Macroscopic

Microscopic______________

Mesoscopic______________

Macroscopic

Kinetic Theory

Lattice Methods

Navier-Stokes

Kinetic Theory

Lattice Methods

Navier-Stokes

• Simulate fluid at microscopic level since the physics is simplerand more general than macroscopic, continuum (PDE) approach.

• However, complete reproduction of molecular dynamicsis much too expensive (today and also in the „near“ future).



VKI, Brussels

May 30-June 3, 2005

Page 7


LBM vs. Traditional CFD Methods

Real FluidFree molecules in continous space

Kinetic TheoryMicroscopic particles (Boltzmann Equation)

Real FluidFree molecules in continous space

Kinetic TheoryMicroscopic particles (Boltzmann Equation)

Traditional CFD Methods___________________________

Chapman-Enskog ExpansionStatistical Method applied to real gases

Navier-Stokes EquationsConservation of Mass, Momentum and Energy

Numerical MethodsDiscrete Approximation of

Partial Differential Equations

Traditional CFD Methods___________________________

Chapman-Enskog ExpansionStatistical Method applied to real gases

Navier-Stokes EquationsConservation of Mass, Momentum and Energy

Numerical MethodsDiscrete Approximation of

Partial Differential Equations

Lattice-Boltzmann_________________________________

Simulation of Particle Dynamics

• No integration of partial differential eqn.

• Movement & collisions conservemass, momentum and energy

• No numerical instabilities

Lattice-Boltzmann_________________________________

Simulation of Particle Dynamics

• No integration of partial differential eqn.

• Movement & collisions conservemass, momentum and energy

• No numerical instabilities

ResultsFluid dynamic quantities at discrete points in space and time

ResultsFluid dynamic quantities at discrete points in space and time



VKI, Brussels

May 30-June 3, 2005

Page 8


Basics of Kinetic Theory

Boltzmann Equation ),,(),,(),,(),,( tcxCtcxfctcxft

tcxfdt

d rrrrrrrrr =∇⋅+∂∂=

Describes the rate of change of the velocity distribution function due to nonequilibrium

Velocity Distribution Function ),,( tcxfrr

Gives the number of particles at time t per unit volume in phase space around x and c

Collision Term C satisfies the necessary conservation laws

∫ = 0)()( cdcCcrrrξ

Mass

Momentum

Energy

1)( =crξ

ccrr =)(ξ

2

2

1)( cc

rr =ξ

Describes fluid behaviour using the interactions of air molecules

∫= cdtcxftxrrrr

),,(),(ρDensity

∫= cdctcxftxutxrrrrrr

),,(),(),(ρMomentum

∫ −= cductcxftxErrrrrr 2))(,,(),(Energy



VKI, Brussels

May 30-June 3, 2005

Page 9


Basics of Lattice Methods

Replace the continuous velocitydistribution function by a discreteset of particle velocities defined ona lattice of equal shaped cubic cells

Vtxiftxintcxf ∆≡→ ),(),(),,(rrrr

},...,1;{ miicc =∈ rr

Particle dynamics is now described by the Lattice Boltzmann Equation

),(),(),( txiCtxintticxinrrr +=∆++

The collision operator C determines if a lattice systemproduces a physically meaningfull fluid behaviour

During an elementary time interval particles can only hop fromone center of a cell to one of the m near neighbouring cellsaccording to their velocity

)1(=∆txr

ticx ∆+ rr

icr



VKI, Brussels

May 30-June 3, 2005

Page 10


Macroscopic Quantities

• Macroscopic quantities, such as density, pressure, velocity, etc.are computed by statistical methods from the state vectors

DENSITY

MOMENTUM

ENERGY

• Higher order moments (Energy Flux, Stress Tensor)are also available locally (do not involve derivatives)

∑=j

j txntx ),(),(rrρ

∑=j

jj txnctxu ),(),(rrrrρ

[ ]∑ •=j

jjj txnccmtxE ),(),( 21 rrrr

0=urρ 0≠u

rρ

Vector lengthdenotes numberof particles movingin that direction

m

TkVRMS 3= ≈ 1000 m/s for oxygen at 20° C

Particle velocities can be much higherthan the resulting macroscopic velocity



VKI, Brussels

May 30-June 3, 2005

Page 11


Transport Coefficients in Lattice Methods

Kinetic Theory allows to compute viscosity and thermal conductivityfrom the velocity distribution function !

TD

Da MFPMFP

2+== λλνThe molecular viscosity depends on themean free path between collisions andthe speed of sound (temperature).

Viscosity is set by adjusting the relaxation parameter of the collision operator

{ }( )

( ) jceqjc

eqjjcj

jjjjj

nn

nntxn

txnCtxntcxn

ωωω

−+=−−=

+=++

1

),(

),(),()1,(r

rrrr

Lattice-Boltzmann Equation

Viscosity is reduced by reducing the meanfree path or equivalently the timebetween collisons

Collision frequency for2<cω 0>Lattcν

cω/1

−=

2

11

cT ων

Chapman-Enskog Expansion

−+=

2

11

2

2

c

D

T ωρλ

Viscosity Thermal Conductivity



VKI, Brussels

May 30-June 3, 2005

Page 12

Simple 2D Model with 4 directions and 3 speeds


Concept of Particle Models

• The fluid is composed of a very large number of particles(not molecules, this is a mesoscale model)

• Particles are only allowed to move in certain directions on the latticewith limits on how far they can get in a single time step (their speed)

• The state of the fluid is represented by the number njiof particles moving with speed (energy) j in direction i

1

PossibleDirections

2

3

4

Particle withspeed 1 indirection 4




A model allowing 3 speeds(0,1,2) and 4 directions re-presents the particle popu-lation by 9 state vectors nji

n0 ( = n01 = n02= n03= n04)n11 , n12 , n13 , n14n21 , n22 , n23 , n24

State vectors are integers !Particle with speed 0

Particle with speed 0

The maximum number of particles per statedepends on the number of bits for state vectors !



VKI, Brussels

May 30-June 3, 2005

Page 13

• Repetition evolves time (t -> t+1) and forms an inherently transient solver

• The process of evolving ( solving ) the update equation is inherentlyparallel (computationally efficient) and stable (computationally robust)

is the collision operator that exactly conserveslocal mass, momentum and energy

jC

• Also drives local distribution to equilibrium (entropy maximized)neq

j


Fluid – Fluid Interaction

• Dynamics in the fluid consists of two steps : MOVE & COLLIDE

• Update equation { }),(),()1,( txnCtxntcxn jjjjj

rrrr +=++

Time tTime t+1

n1

n2

n‚2

n‘1

Example : Mass Conservation

n'1 + n'2 = n1 + n2



VKI, Brussels

May 30-June 3, 2005

Page 14


Fluid – Surface Interaction

Facets

Solid Body

Voxels

Surfels

Automatic discretization

The intersection of voxels with the facetsrepresenting solid bodies creates surfelswhich define the computational surfaceresolution.

In each timestep surfels gather and scatterparticles, altering their momentum accordingto the boundary conditions

Surface forces depend on the momentumexchange between fluid and wall

VinVout

Specular Reflection

Vtin

Vnin

Vtout

Vnout

Vin Vout

Bounce Back Reflection

Slip ConditionNormal component invertedTangential component unchanged

Momentum balance →→→→ normal force only

No Slip ConditionNormal component invertedTangential component inverted

Momentum balance →→→→ normal & tangential force



VKI, Brussels

May 30-June 3, 2005

Page 15


Reynolds-Number Regimes

Regime Reynolds Number PowerFLOW__________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

Low Re < 10,000 Direct SimulationTransitional 10,000 < Re < 100,000 currently not applicableHigh Re > 100,000 Boundary Layer Simulation

approximate values,actual values problem dependent

Regime Reynolds Number PowerFLOW__________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

Low Re < 10,000 Direct SimulationTransitional 10,000 < Re < 100,000 currently not applicableHigh Re > 100,000 Boundary Layer Simulation

approximate values,actual values problem dependent

Solid Wall Solid Wall

Modeled Flow

Direct SimulationUsing a large number of voxels theboundary layer is resolved down to the wallwith zero velocity at the wall.Particles are bounced back from the wallexactly canceling their momentum.

Boundary Layer SimulationThe presence of the wall is modeled by ashear stress at the slip surface.Particles loose momentum at the slip surfaceaccording to the (modified) law of the wall.



VKI, Brussels

May 30-June 3, 2005

Page 16


Turbulent Wall Model

( ) Byu += ++ ln1

κ

Assumption: Universal velocity profile of a turbulent2D boundary layer with dp/dx=0

++ = yu

:505for ≤≤ +y

:5for ≤+y

0.5

4.0

≈≈

B

κ

τu

uu =+

υτu

yy =+

ρτ

τwu =

PowerFLOW Extension:

• include the effect of a longitudinal pressure gradient

∂∂+=→ ++++

x

pfAAyUyU 1mit)/()(

The wall model provides the wall shear stressto alter the momentum of scattered particles.

wτ



VKI, Brussels

May 30-June 3, 2005

Page 17


Approaches to Turbulence Modeling

Dissipation

dl LLength

ν/2dl UL /Time

Turbulent Scales

4/3Re/ ≈dlLRange

( ) ( ) 2/12 Re/// ≈νdlULRange

RANS = Reynolds AveragingAll scales of motion are described by statistical methods (time averaged )

LES = Large Eddy SimulationAlle Skalen werden berechnetmodeled computed via modified unsteady Navier-Stokes equations

Filter Width (Grid Size)

DNS = Direct SimulationAll scales of motion in space and time are computed

VLES = Very Large Eddy Simulation

modeled computed unsteady

Coherent anisotropic eddiesUniversal eddies



VKI, Brussels

May 30-June 3, 2005

Page 18


CFD Simulation Process

CAD/CAS ModelCATIA/ALIAS

CAD/CAS ModelCATIA/ALIAS

Clay ModelPOLYWORKS

Clay ModelPOLYWORKS

Simulation Model(Surface Facetization)

ANSA, QUICKMESH, PowerWRAP, ...

1-5 Days

Simulation Model(Surface Facetization)

ANSA, QUICKMESH, PowerWRAP, ...

1-5 Days

SimulationPowerFLOW

1 Day

SimulationPowerFLOW

1 Day

PostprocessingPowerVIZ

PostprocessingPowerVIZ

ResultResult

Shape Modificationof CAD/CAS Data

Shape Modificationof CAD/CAS Data

Morphing of theSurface Mesh

(PowerCLAY)

Morphing of theSurface Mesh

(PowerCLAY)

Turnaround

2-6 Days

Turnaround

2-6 Days



VKI, Brussels

May 30-June 3, 2005

Page 19


CFD Process: Geometry Preparation (Wrapping)

Complete STL Data(imperfect facetization)

� Gaps & holes� Overlaps & intersections� Interior details

Wrap

Wrapped Surface Facetization(ready for simulation)

� Water-tight single solid� Controlled granularity� Interior details removed

Preparation time reducedfrom days to hours !

Complete Set of CAD Data

Export or

facetize withoutcleanup or de-featuring



VKI, Brussels

May 30-June 3, 2005

Page 20


CFD Process: Geometry Morphing

Modification of the surface facetization instead of changing the CAD datawhich would require a re-facetization.



VKI, Brussels

May 30-June 3, 2005

Page 21


CFD Process: Geometry Input

The surfacefacetizationrepresents thegeometry only.

It does not setthe resolutionfor the simulation.

Depending on thelevel of detail up to2-3 million facetsare used.



VKI, Brussels

May 30-June 3, 2005

Page 22


CFD Process: Modular Assembly

The completeconfiguration maybe composed ofany number ofcomponents.

Components may be arranged in anarbitrary fashion and also intersect each other.



VKI, Brussels

May 30-June 3, 2005

Page 23


CFD Process: Automatic Discretization

Voxels(Fluid Cells)

Solid Body

Facets(G

eometry)

Surfels

(Surface

Elements)

Typical voxel countsfor external aerodynamiccases range from 20-100milion cells.

Geometry representationembedded in a lattice ofcubic cells (with differentlevels of resolution).



VKI, Brussels

May 30-June 3, 2005

Page 24


CFD Process: Simulation Timestep

� Simulations are always run in transient mode

� The physical time per timestep is determined by resolution and test conditions

[ ]epsec/timestV

xMaa

V

xVt LatticeLattice

∞∞

∆⋅⋅=∆⋅=∆

� Strictly there is no room left for the user to control the timestep

� Artificially elevating the Mach number increases the time step

� Example:

mmxepsec/timesttMaCT

smV

210515.020

/506

=∆⋅=∆⇒=⇒°=

=−

∞

∞

That means 1 secondof physical time requires 200,000 timesteps

Using Ma=0.30instead of Ma=0.15cuts the run time in half !



VKI, Brussels

May 30-June 3, 2005

Page 25


CFD Process: Transient SimulationNo explicit convergence criterion, user monitors key quantities to decide when to stop the simulation.

100,000 Timesteps

(1 Timestep = 4.7 10-6 sec.)

Averaging Window



VKI, Brussels

May 30-June 3, 2005

Page 26


Validation Models (Scale 1:2.5).

5series touring

Open Convertible

5series Limousine with/without Mirror

Calibration Motorcycle



VKI, Brussels

May 30-June 3, 2005

Page 27


Validation: Aerodynamic Forces

CZ2

0.114 0.105

CZ1

0.067 0.070

PowerFLOW 3.4: 0.252

CX

BMW Windtunnel: 0.252

CZ1

CZ2

-0.038 0.009-0.027 0.006


CX




VKI, Brussels

May 30-June 3, 2005

Page 28


Validation: Surface Pressure Distribution

Top Centerline(Geometry not to scale)

PowerFLOWExperiment

Bottom Centerline(Geometry not to scale)



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May 30-June 3, 2005

Page 29


Validation: Near Surface Flow Topology



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May 30-June 3, 2005

Page 30


Validation: Reynolds Effect



VKI, Brussels

May 30-June 3, 2005

Page 31


Validation: Motorcycles (Windshield Variations)

0,300

0,320

0,340

0,360

0,380

0,400

0,420

0,440

Serie LT Sport

Cx

*A

Windkanal(Aschheim)

PowerFLOW

Hot Wire MeasurementPowerFLOW

Serie

LT

Sport



VKI, Brussels

May 30-June 3, 2005

Page 32


Analysis of Drag Generation

-0,06

-0,04

-0,02

0,00

0,02

0,04

0,06

0,08

0,10

0,0 0,1 0,3 0,4 0,5 0,6 0,7 0,9 1,0

0,00

0,05

0,10

0,15

0,20

0,25

0,30

0,35

0,400,0

Cx(x) Verteilung

Cx(x) Integral


CX




VKI, Brussels

May 30-June 3, 2005

Page 33


Analysis of Lift Generation

-0,03

-0,02

-0,01

0,00

0,01

0,02

0,03

0,0 0,1 0,3 0,4 0,5 0,6 0,7 0,9 1,0

-0,40

-0,30

-0,20

-0,10

0,00

0,10

0,200,0

Cz(x) Verteilung

Cz(x) Integral

CZ1

CZ2

0.011 0.0130.143 0.123

PowerFLOW 3.4

BMW Windtunnel



VKI, Brussels

May 30-June 3, 2005

Page 34


Visualization : Transient Surface Pressure



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May 30-June 3, 2005

Page 35


Visualization : Near Wall Streamlines



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May 30-June 3, 2005

Page 36


Visualization : 3D Streamlines

Colors represent Near Surface Velocity Distribution



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May 30-June 3, 2005

Page 37


Visualization: Transient Isosurface V X=0

Reverse flow (Vx<0) inside the isosurface



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May 30-June 3, 2005

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Visualization : Transient Flow Field Slices



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May 30-June 3, 2005

Page 39


Visualization : Transient Isosurface C pt=0

For Cpt=0 the total pressure loss is equivalent to the dynamic free stream pressure



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May 30-June 3, 2005

Page 40


Applications: NASTRAN Interface (Structure)

Select parts per PID

Match NASTRAN parts

with the PowerFLOW model

PLOADs [N/mm2]

on the PowerFLOW model

Map area loads onto

the NASTRAN model

Forces on

individual parts



VKI, Brussels

May 30-June 3, 2005

Page 41


Applications: ABAQUS Interface (Heat Transfer)Mapping heat transfer coefficients

from a PowerFLOW simulation

onto an ABAQUS structure model



VKI, Brussels

May 30-June 3, 2005

Page 42


Applications: Detail Optimization (Mirror)



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May 30-June 3, 2005

Page 43


Applications: Underhood Flow



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May 30-June 3, 2005

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Applications: Motorcycles - Transient Flow FieldNear Surface Velocity



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May 30-June 3, 2005

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Applications: Motorcycles - Transient Flow FieldReverse Flow (V x<0)



VKI, Brussels

May 30-June 3, 2005

Page 46


Applications: Motorcycles - Transient Flow FieldDifferent Windshields

TouringTouring StandardStandard

SportSport

Helmkraft

StandardStandard

TouringTouring SportSport



VKI, Brussels

May 30-June 3, 2005

Page 47


Applications: Motorcycle Acoustics

Punkt 92

0

20

40

60

80

100

120

140

10 100 1000 10000

Hz

dB(A

)

Experiment Berechnung_grob

Punkt 101

0

20

40

60

80

100

120

140

10 100 1000 10000

Hz

dB(A

)

Experiment Berechnung_grob

Punkt 110

0

20

40

60

80

100

120

10 100 1000 10000

Hz

dB(A

)Experiment Berechnung_grob

� Small timesteps enable high sampling rates forpressure and velocity fluctuations.

� The upper frequency limit is determined by thebackground noise of the Lattice-Boltzmann method.

� The lower frequency limit depends on the physical time(number of periods) covered by the simulation.



VKI, Brussels

May 30-June 3, 2005

Page 48


Applications: Electronics Cooling

Goals: qualitatively – Heat Transfer Distribution

quantitatively – Surface Temperatures

Heat Transfer Coefficient

Velocity Magnitude



VKI, Brussels

May 30-June 3, 2005

Page 49


Applications: Windtunnel Design



VKI, Brussels

May 30-June 3, 2005

Page 50


Conclusion

+ Maturity level sufficient for external aerodynamics

+ Short preprocessing phase due to automatic meshing.

+ Capability to handle complex geometries(underhood/underbody).

+ Steep learning curve due to ease-of-use.

+ Does not require a numerics expert.

- Optimization loops still slower than the wind tunnel.

- Hardware requirements high for rapid turnaround.

- Thermal management capabilities still under development.

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