1. BMW Group
Norbert Grün
A. Schönberger
Martin Schulz (s+c)
From Soiling to Stone Chipping.
Outline
Aerodynamic
Process
Simulation
Process
Validation
Examples
Application
Examples
Conclusion
EfficientDynamics
From Soiling to Stone Chipping.
Simulation of Particle Trajectories and Impact in Time
Averaged and Transient Flow Fields around Vehicles.
BMW Group
Dr. Norbert Grün, BMW Group
Andreas Schönberger, BMW Group
Dr. Martin Schulz, science+computing ag

2. BMW Group
Norbert Grün
A. Schönberger
Martin Schulz (s+c)
From Soiling to Stone Chipping.
 Flow Field around Cars
 Particle Motion
 Soiling in Time Averaged and Transient Flow Fields
 Stone Chipping
 Conclusion
Outline.
Outline
Flow Field
Particle Motion
Soiling
Stone Chipping
Conclusion

3. BMW Group
Norbert Grün
A. Schönberger
Martin Schulz (s+c)
From Soiling to Stone Chipping.
Properties of Flow Fields around Cars.
Outline
Flow Field
Particle Motion
Soiling
Stone Chipping
Conclusion
• high Reynolds numbers
even at moderate speeds
7Re
10Re O
Lv f
The flow field around cars is characterized by
• and is therefore completely turbulent
• producing massive regions of separation / recirculation
• and a highly transient behaviour
Including the motion of particles constitutes a two-phase flow.
However, since the fraction of solids is so low:
• their movement is simulated in a given flow field as postprocessing
• without feedback of particles on the flow itself
• disregarding inter-particle collisions

4. BMW Group
Norbert Grün
A. Schönberger
Martin Schulz (s+c)
From Soiling to Stone Chipping.
Transient Flow Fields (Snapshots in Time).
Outline
Flow Field
Particle Motion
Soiling
Stone Chipping
Conclusion

5. BMW Group
Norbert Grün
A. Schönberger
Martin Schulz (s+c)
From Soiling to Stone Chipping.
Particle Properties – Diameter and Mass.
Outline
Flow Field
Particle Motion
Soiling
Stone Chipping
Conclusion
• Real particles have an arbitrary shape and the air flow
imposes forces and moments in all three directions.
Water
Dry
Sand
Stone
• It is not feasible to simulate the aerodynamics of real particles.
 Assumption: Particles have spherical shape.
Particles considered here
vary in diameter from
Ø < 0.1 mm for dry dust
Ø < 1.0 mm for water/spray
Ø < 10.0 mm for stones
Although even a stone with a
diameter of 4 mm has a mass
of only 0.08 g, its trajectory will
differ significantly from stream-
lines.

6. BMW Group
Norbert Grün
A. Schönberger
Martin Schulz (s+c)
From Soiling to Stone Chipping.
Particle Properties – Aerodynamic Drag.
Outline
Flow Field
Particle Motion
Soiling
Stone Chipping
Conclusion
For spherical particles drag, i.e. the component in the direction of the onset flow,
is the only effective aerodynamic force.
222
8
2/1 v
F
DAv
F
C DD
D
From experiments the drag coefficient
of spheres
is known as a function of Reynolds-
number (symbols below).
16.1
687.0
Re425001
42.0
Re15.01
Re
24
DC
The approximation of Cliff & Gauvin
is valid up to the critical Reynolds-
number of 3 105 which will not be
exceeded in the scope of this
application (see below).

7. BMW Group
Norbert Grün
A. Schönberger
Martin Schulz (s+c)
From Soiling to Stone Chipping.
Equation of Motion.
Outline
Flow Field
Particle Motion
Soiling
Stone Chipping
Conclusion
Only gravity and aerodynamic drag determine the trajectory of a spherical particle
r
r
rAirD
P
v
v
vDCgm
dt
vd
m



22
2
1
4
rv
In a vehicle fixed frame of reference
the effective oncoming flow vector
which produces drag, results from the
local flow field velocity and the
particle‘s own motion
Airv

Pv

PAirr vvv

Pv

Airv

rv

Pv

g

r
r
r
P
AirDP
v
v
v
D
C
g
dt
vd



2
4
3Inserting the particle‘s mass yields
the acceleration to be integrated as:
aAero
For very small and light particles the acceleration aAero imposed by aerodynamic
drag can reach 10³g or more which leads to extremely small timesteps for a stable
numerical integration of the trajectory.

8. BMW Group
Norbert Grün
A. Schönberger
Martin Schulz (s+c)
From Soiling to Stone Chipping.
Dry Soiling (Time averaged vs. Transient Flow).
Outline
Flow Field
Particle Motion
Soiling
Stone Chipping
Conclusion
using a transient flow fieldusing a time averaged flow field
Road Test
Particle Density = 2700 kg/m³
Particle Diameter = 1 … 30 m

9. BMW Group
Norbert Grün
A. Schönberger
Martin Schulz (s+c)
From Soiling to Stone Chipping.
Wet Soiling.
Initial
Conditions
Experiment (Road Test) Simulation using a transient flow field
Outline
Flow Field
Particle Motion
Soiling
Stone Chipping
Conclusion
= 1000 kg/m³
= 0.1 … 1 mm

10. BMW Group
Norbert Grün
A. Schönberger
Martin Schulz (s+c)
From Soiling to Stone Chipping.
Water.
Drop impingement after
2 seconds of spraying
(stationary wipers)
Outline
Flow Field
Particle Motion
Soiling
Stone Chipping
Conclusion

11. BMW Group
Norbert Grün
A. Schönberger
Martin Schulz (s+c)
From Soiling to Stone Chipping.
Snow.
Outline
Flow Field
Particle Motion
Soiling
Stone Chipping
Conclusion
Snow accretion can not yet be simulated.
= 50 … 500 kg/m³
= 1 … 5 mm
m 0.005 g !

12. BMW Group
Norbert Grün
A. Schönberger
Martin Schulz (s+c)
From Soiling to Stone Chipping.
Vn,in
Vt,in
Particle Reflection.
Outline
Flow Field
Particle Motion
Soiling
Stone Chipping
Conclusion
Vsrf
Vt,out
Coefficient of Restitution (CoR)
applied to the normal component
inn
outn
v
v
,
,
= 1 : perfectly elastic collision
= 0 : perfectly inelastic collision
Coefficient of Kinetic Friction (CoF)
applied to the tangential component
intsrf
intoutt
vv
vv
,
,,
= 0 : slip condition (no friction)
= 1 : no-slip condition (maximum friction)
Vn,out
Vout
out
Vin
in
)tan(
1/1)(
)tan(
,,,
,
,
,
in
intsrfintsrfint
inn
outt
outn
out
vvvvv
v
v
v
a

13. BMW Group
Norbert Grün
A. Schönberger
Martin Schulz (s+c)
From Soiling to Stone Chipping.
Wind
= 2500 kg/m³ D = 5 mm
D = 1 mm
D = 0,5 mm
D = 0,3 mm
D = 0,15 mm
Balance of Gravity and Aerodynamics.
D = 50mm
= 2500 kg/m³ = 1500 kg/m³
= 1000 kg/m³
= 500 kg/m³
WindOutline
Flow Field
Particle Motion
Soiling
Stone Chipping
Conclusion

14. BMW Group
Norbert Grün
A. Schönberger
Martin Schulz (s+c)
From Soiling to Stone Chipping.
Effect of Random Scattering.
Static trajectories from a wheel
at steering angle without any
stochastical scattering.
 no impingement on the car
Hitpoints after simulating
500,000 particles including
random scatter on
• intial velocity
• initial direction
• diameter
• density
• reflection angle
Outline
Flow Field
Particle Motion
Soiling
Stone Chipping
Conclusion

15. BMW Group
Norbert Grün
A. Schönberger
Martin Schulz (s+c)
From Soiling to Stone Chipping.
Experimental Investigation of Initial Conditions.
Crash test facility with high speed camera (1000 frames per second)
Automated analysis of particle trajectories and velocities
Outline
Flow Field
Particle Motion
Soiling
Stone Chipping
Conclusion

16. BMW Group
Norbert Grün
A. Schönberger
Martin Schulz (s+c)
From Soiling to Stone Chipping.
Experimental Investigation of Initial Conditions.
Video with 1000 frames/sec of stone trajectories in a ground fixed frame of reference.
Outline
Flow Field
Particle Motion
Soiling
Stone Chipping
Conclusion

17. BMW Group
Norbert Grün
A. Schönberger
Martin Schulz (s+c)
From Soiling to Stone Chipping.
Mechanisms of Stone Pinching.
Stones entrained
per adhesion
Stones entrained
by tread grooves
Stones pinched
in tread grooves
Lateral pinching
Outline
Flow Field
Particle Motion
Soiling
Stone Chipping
Conclusion

18. BMW Group
Norbert Grün
A. Schönberger
Martin Schulz (s+c)
From Soiling to Stone Chipping.
Sectors of Stone Emission.
Outline
Flow Field
Particle Motion
Soiling
Stone Chipping
Conclusion
α
α
)
No-slip rolling wheel Blocked sliding wheel
entrained by adhesion
entrained by tread pinching
Sector angles depending on speed and tread pattern

19. BMW Group
Norbert Grün
A. Schönberger
Martin Schulz (s+c)
From Soiling to Stone Chipping.
Damage Probability.
low high
Surface normal momentum of stones at impact
Influence of different
rocker panel contours
Outline
Flow Field
Particle Motion
Soiling
Stone Chipping
Conclusion

20. BMW Group
Norbert Grün
A. Schönberger
Martin Schulz (s+c)
From Soiling to Stone Chipping.
Identification of Corrosion-prone Regions.
low high
Surface normal momentum of stones at impact
Outline
Flow Field
Particle Motion
Soiling
Stone Chipping
Conclusion

21. BMW Group
Norbert Grün
A. Schönberger
Martin Schulz (s+c)
From Soiling to Stone Chipping.
Comparison with Corrosion Tests.
Regions of high normal momentum impact Regions of high corrosion risk
on an experimental vehicle with a
special coating to accelerate corrosion
Outline
Flow Field
Particle Motion
Soiling
Stone Chipping
Conclusion

22. BMW Group
Norbert Grün
A. Schönberger
Martin Schulz (s+c)
From Soiling to Stone Chipping.
Conclusion.
Outline
Flow Field
Particle Motion
Soiling
Stone Chipping
Conclusion
• Soiling and stone chipping are simulated as a postprocessing step
using time averaged or transient flow fields around vehicles.
• For stone chipping a reflection model has been added.
• Dry and wet soiling requires to use the transient flow fields for realistic
results which leads to a computational effort that is impractical on desktop
workstations.
• Comparison with road tests show a good agreement concerning the
localization of corrosion-prone regions.
• Initial conditions and information about stochastical scatter have been
gathered by elaborate experiments.
• The simulation of water management, i.e. the formation, propagation and
breakup of waterfims and runlets on the surface, is still under development.
• The accretion of snow can not yet be simulated.
• Stone-chipping simulation can be used productively to identify
problems early enough in the development process to avoid later
cost-intensive remedy.

23. Thank You for Your Attention
From Soiling to Stone Chipping.
Simulation of Particle Trajectories and Impact in Time
Averaged and Transient Flow Fields around Vehicles.
EfficientDynamics
BMW Group
Dr. Norbert Grün, BMW Group
Andreas Schönberger, BMW Group
Dr. Martin Schulz, science+computing ag