1. In-Cylinder Investigation of Engine
Size- and Speed-Scaling Effects
Student: Doug Heim
Advisor: Jaal Ghandhi
Sponsor: Wisconsin Small Engine Consortium
Ph.D. Thesis Defense
February 18, 2011

2. Presentation Outline
February 18, 2011 2
• Motivation and Objectives
• Literature Review
• Experimental Setup
• Steady Flow Test Results
• Optical Engine Measurements and Analysis
• Summary

3. Motivation
February 18, 2011 3
• Engine development is time consuming and
complicated – adapt existing designs.
• Difficulties are magnified when engine size changes
considerably from existing designs.
• WSEC companies have limited resources.
– Kohler, Mercury Marine, Briggs & Stratton, Harley-
Davidson, Cummins Power Gen
• WSEC companies are interested in how to scale down
highly refined engines.

4. Objectives
February 18, 2011 4
• To study the fundamentals of engine size- and
speed-scaling.
• Scaling laws have been proposed in the past.
• Speed-scaling relations have been verified
experimentally.
• Size-scaling relations have not.
• Increase our understanding of turbulent in-cylinder
flows.

5. Methodology
February 18, 2011 5
• Build two precisely scaled, single-cylinder optical
engines.
• Study the mean and fluctuating velocity during
compression until TDC using particle image
velocimetry (PIV).

6. Literature Review: Principle of Similitude
February 18, 2011 6
• Similar engines have their respective parts made of
the same material and have proportional linear
dimensions.
• Similar engines should have the same turbulence at
the same piston speed, which indicates the same rate
of combustion (never been shown to date)
Purday, H.F.P.: Diesel Engine Design, D. Van Nostrand Co., New York, 1919.
Lichty, L.C.: Internal Combustion Engines, 5th
ed., McGraw-Hill, New York, 1939.

7. Literature Review: Engine Size-Scaling
February 18, 2011 7
• Three scaled single-cylinder, SI
engines.
• Main areas Taylor studied were
volumetric efficiency, mean
effective pressure, in-cylinder
pressure.
Taylor, C.F.: “Effect of Size on the Design and Performance of
Internal-Combustion Engines,” Trans ASME, July, 1950.

8. Literature Review: Engine Size-Scaling
February 18, 2011 8
Volumetric efficiency
mep: work per engine cycle
divided by cylinder volume
displaced per cycle.
Pressure at same
piston speed

9. Literature Review: Engine Size-Scaling
February 18, 2011 9
• Study shortcomings:
• Geometry of intake ports not specified or varied
to study effect of different flows into the engine.
• Study conducted at a time when modern
diagnostic methods not available to study flow
fields or make turbulence measurements.

10. Literature Review: Engine Speed-Scaling
February 18, 2011 10
•TDC turbulence intensity
versus engine speed is
linear.
•Swirl increases turbulence
intensity.
Liou, T.-M., and Santavicca, D.A.:
“Cycle Resolved Turbulence
Measurements in a Ported Engine
With and Without Swirl,” SAE paper
830419, SAE Trans, v. 92, 1983.

11. Literature Review: Engine Speed-Scaling
February 18, 2011 11
Liou, T.-M., Hall, M., Santavicca, D.A., and Bracco, F. V.: “Laser Doppler
Velocimetry Measurements in Valved and Ported Engines,” SAE paper
840375, SAE Trans, v. 93, 1984.
•Slope depends on:
•Definition of the mean
velocity
•Engine geometry/intake
•How would two similar
engines fall on this graph?

12. Literature Review: Engine Speed-Scaling
February 18, 2011 12
• Shortcomings of many studies:
• Data taken at a limited number of points in the
engine cylinder.
• Geometry of intake ports fixed.
• None have verified how the turbulence intensity
scales with engine size.

13. Small Engine Large Engine
Experimental Setup
February 18, 2011
13
Scale ratio = 1.69
(Dimensions
in mm)
Connecting
Rod Length
Crank
Radius
Connecting
Rod to
Crank
Radius Ratio
Bore, B Stroke, S
Compressi
on Ratio
TDC
clearance
Large
Engine
144.8 38.0 3.81 82.0 76.0 10.0 8.44
Small
Engine
84.0 22.5 3.73 48.6 45.0 10.0 5.00

14. Experimental Setup
February 18, 2011 14
Port Housing
Fixtures
Shim Plate Shim Plate
Intake Port
Exhaust Port
Rocker Arms
Camshaft Blocks
Flowbench Intake Horn
Aluminum Base Plate
Spring and Valve
•Intake ports are modular
(allow rotation, different
ports).
•Valves sit flush with
engine head surface.
•Engine cylinder
approximates a right
cylinder.
Small and large engine heads.

15. Experimental Setup
February 18, 2011 15
Cylinder Wall
Cylinder Axis
Exhaust Valve
Intake Valve
Intake Port
Shroud
Intake Valve
Intake Port
90°
Cylinder Wall
Cylinder Axis
Exhaust Valve
0-degree Orientation (0-deg) 90-degree Orientation (90-deg)
Performance Port (PP)
•Higher performance engines
Utility Port (UP)
•Lower manufacturing cost
Shrouded Valve (SV)
Non-shrouded Valve (NV)

16. B
H
DI
HI
L
Intake Port
Intake Horn
Swirl Adapter
Fixture
Impulse Torque
Meter
Honeycomb
D
T
Steady Flow Test Results
February 18, 2011 16
• Similar engines should have similar:
• flow coefficients
• swirl coefficients
•SuperFlow 600 flow bench
•Transducer Techniques
torque sensor
•28 inH2O pressure drop
•40 seconds
vB
f
AV
m
C
ρ

=
BVm
T
C
B
s

8
=
2
2
)(
4








=
∫
∫
IVC
IVO
IVC
IVO
dCA
dCCA
BS
R
fV
sfV
v
s
θ
θ
θ
θ
θ
θ
πη

17. Steady Flow Test Results
February 18, 2011 17
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
Cf
2402101801501209060300-30
Crank Angle Degrees
PP, 0-deg., SV
Large Head
Small Head
Large Head, Cf,avg = 0.303
Small Head, Cf,avg = 0.299
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
Cs
0.250.200.150.100.050.00
L/D
Performance Port
Utility Port
Open Symbol: Small Head
Filled Symbol: Large Head
0-degree Orientation, SV
Large Head Small Head
Valve Port Orientation Rs ± uRs Rs ± uRs
Shrouded Utility 0-degree -3.214 ± 0.032 -2.967 ± 0.065
Performance 0-degree -3.058 ± 0.030 -2.728 ± 0.058
Non-shrouded Utility 0-degree -0.251 ± 0.008 -0.265 ± 0.008
90-degree 0.128 ± 0.009 -0.065 ± 0.008
Performance 0-degree -0.234 ± 0.008 -0.054 ± 0.007
90-degree 0.121 ± 0.008 0.045 ± 0.007
•Rs of SV is 12 times
greater than NV
•Close agreement
between small and
large head Rs

18. Particle Image Velocimetry (PIV)
February 18, 2011 18
Imaging
Mirror
Bowditch
Piston
Extension
Sapphire
Piston
Window
Engine
Head
Quartz
Ring
Window
Nd:YAG LASER
•Seed intake with olive oil
droplets (~1-2μm).
•At TDC, light sheet is
nearly equidistant to piston
and engine head.
•Large engine: 300, 600,
900, 1200 rpm.
•Small engine: 600, 1200,
1800 rpm.
•Images processed with TSI
Insight3G software.

19. PIV Field-of-View (FOV)
February 18, 2011 19
Cylinder Wall
Cylinder Axis
Exhaust Valve
Intake Valve
Low-Magnification
FOV
High-Magnification
FOV
Second
High-Magnification
FOV
Cylinder
Visible
Area
•Top view of engine cylinder showing FOVs
with respect to engine cylinder for both
engines (FOVs scale between two engines)
•Low-magnification FOV: 50 cycles of data at
crank angles of -90, -45, and TDC.
•High-magnification FOV: 200 cycles of data
at TDC.
Large Engine
17.5mm x 14mmSmall Engine
10.4mm x 8.3mm

20. Low-Mag. FOV: Swirl Center Location
February 18, 2011 20
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
y/(B/2)
-0.4 0.0 0.4
x/(B/2)
TDC
90 bTDC
45 bTDC
UP, SV, 0-deg
Cylinder Axis
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
y/(B/2)
-0.4 0.0 0.4
x/(B/2)
TDC
90 bTDC
45 bTDC
UP, NV, 0-deg
Cylinder Axis
Utility Port
•Top view of engine cylinder.
•Axes made non-dimensional by cylinder radius (B/2).
•Open symbols: small engine, filled symbols: large engine.
•Swirl centers at a given crank
angle do not vary much over
the range of engine speeds.
•The swirl center precesses in
time.
•Grouped in the same location
in the cylinder at the same
crank angle time for both
engines.

21. Normalized Angular Rotation Rate
February 18, 2011 21
6
5
4
3
2
1
0
Ω/ΩEngine
-90 -45 0
Crank Angle Degrees
UP, SV, 0-deg
300 rpm
600 rpm
900 rpm
1200 rpm
1800 rpm
6
5
4
3
2
1
0
Ω/ΩEngine
-90 -45 0
Crank Angle Degrees
300 rpm
600 rpm
900 rpm
1200 rpm
1800 rpm
UP, NV, 0-deg
Utility Port
Ω: angular velocity magnitude
ΩEngine
: engine angular rotation rate
•At TDC, on average, the normalized angular velocity of the small
engine compared to the large engine is lower
28% lower
16% lower
•A decreasing trend in angular
velocity approaching TDC,
which is attributable to viscous
losses at the wall.
•The ratio of the cylinder area
to volume of the small engine
increases by the scaling factor
of 1.69 compared to the large
engine.

22. Swirl Ratio Comparison
February 18, 2011 22
•On average, Ω(TDC)/ΩEngine
compared
to Rs:
-large engine, SV: 19% higher
-small engine, SV: 4% lower
-NV: 3-7 times higher
•At very low levels of swirl, Rs largely
underpredicts the normalized angular
velocity.
5
4
3
2
1
0
AverageΩ(TDC)/ΩEngine
543210
Rs
PP, SV
PP, NV
UP, SV
UP, NV
One-to-One Line
Ports in 0-deg Orientation
Open Symbol: Small Engine
Filled Symbol: Large Engine
Average normalized angular
velocity at TDC vs. swirl ratio

23. Mean, Fluctuating Velocity Calculation
February 18, 2011 23
∑ ==
cN
i
c
iEA iyxU
N
yxU
1
, 2,1),,(
1
),(
•Ui is the instantaneous velocity
•Nc is the number of cycles
•i=1,2 refers to the components of the
velocity in the x- and y-directions
2D Instantaneous velocity field
2D wavenumber field
Low pass filter
(depends on cutoff frequency, fc)
Low pass (mean) velocity field
2D Fourier Transform
2D Inverse Fourier Transform
c
c
L
f
1
=
Ensemble Average: Spatial-Average:
.2,1),(),(),( =−= iyxUyxUyxu iii
The fluctuating velocity is defined as:

24. High-Mag. FOV: Turbulence Intensity
February 18, 2011 24
.)},(),({
1
),('
2
2
1
2
1 yxuyxu
N
yxu
cN
c
+= ∑
x [mm] [m/s]
y[mm]
5 10 15
-12
-10
-8
-6
-4
-2
3
3.5
4
4.5
x [mm] [m/s]
y[mm]
2 4 6 8 10 12 14 16
-12
-10
-8
-6
-4
-2
1.2
1.4
1.6
1.8
2
2.2
x [mm] [m/s]
y[mm]
5 10 15
-12
-10
-8
-6
-4
-2
1.2
1.4
1.6
1.8
2
2.2
Ensemble Average Method
Higher u’ since swirl center precesses.
Spatial-Average Method
Edge effects.
Throw away
edge data.

25. 5
4
3
2
1
0
<u'>EnsembleAverage[m/s]
543210
Vmps [m/s]
PP, SV, 0-deg
PP, NV, 0-deg
PP, NV, 90-deg
UP, SV, 0-deg
UP, NV, 0-deg
UP, NV, 90-deg
Open Symbols: Small Engine
Filled Symbols: Large Engine
Turbulence Intensity: E.A.
February 18, 2011 25
Liou, T.-M., Hall, M., Santavicca, D.A., and Bracco, F. V.: “Laser Doppler
Velocimetry Measurements in Valved and Ported Engines,” SAE paper 840375,
SAE Trans, v. 93, 1984.
Non-shrouded
Shrouded
1-D <u’>: our data divided by 21/2

26. Turbulence Intensity: S.A.
February 18, 2011 26
5
4
3
2
1
0
<u'>Spatial-Average[m/s]
543210
Vmps [m/s]
PP, SV, 0-deg
PP, NV, 0-deg
PP, NV, 90-deg
UP, SV, 0-deg
UP, NV, 0-deg
UP, NV, 90-deg
Open Symbols: Small Engine
Filled Symbols: Large Engine
fc*hTDC = 1.7
5
4
3
2
1
0
<u'>Spatial-Average[m/s]
543210
Vmps [m/s]
Open Symbols: Small Engine
Filled Symbols: Large Engine
PP, SV, 0-deg
PP, NV, 0-deg
PP, NV, 90-deg
UP, SV, 0-deg
UP, NV, 0-deg
UP, NV, 90-deg
fc*hTDC = 0.7
•Spatial-average <u’> depends on fc=1/Lc.
•Data collapse well with hTDC: TDC clearance:
-Small Engine: 5 mm
-Large Engine: 8.4 mm

27. Turbulence Intensity: S.A.
February 18, 2011 27
1.6
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0.0
<u'>Spatial-Average/Vmps
1.21.00.80.60.40.20.0
fc [mm
-1
]
Ensemble Average
PP, 0º, SV
PP, 0º, NV
PP, 90º, NV
UP, 0º, SV
UP, 0º, NV
UP, 90º, NV
Open Symbols: Small Engine
Filled Symbols: Large Engine
1.6
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0.0
<u'>Spatial-Average/Vmps
86420
fc*hTDC
Ensemble Average
PP, 0º, SV
PP, 0º, NV
PP, 90º, NV
UP, 0º, SV
UP, 0º, NV
UP, 90º, NV
Open Symbols: Small Engine
Filled Symbols: Large Engine
Non-shrouded Shrouded
•Linear trend slopes collapse well with hTDC.
0.1
2
3
4
5
6
7
8
9
1
<u'>Spatial-Average/<u'>EnsembleAverage
3 4 5 6 7 8
1
2 3 4 5 6 7 8
10
fc*hTDC
PP, 0º, SV
PP, 0º, NV
PP, 90º, NV
UP, 0º, SV
UP, 0º, NV
UP, 90º, NV
Open Symbols: Small Engine
Filled Symbols: Large Engine

28. Correlation Coefficient
February 18, 2011 28
)()0(
)()0(
)(
22
ruu
ruu
r
ji
ji
ij
⋅
⋅
=ρ
Distance, r
x, y
Transverse ρ22
(perpendicular to the axis):
Distance, r
)0(iu )(rui
Longitudinal ρ11
(parallel to the axis):
x, y
)(rui)0(iu
Correlation Coefficient: High Pass Velocity, κ(cutoff)=1256.6[rad/m]
x [mm] [m/s]
y[mm]
2 4 6 8 10 12 14 16
-12
-10
-8
-6
-4
-2
0
2
4
6
8
10
12
14
)0(iu)(rui
)0(iu)(rui
Single-sided
(horizontal):
Double-sided
(horizontal): )(rui

29. Integral Lengthscales
February 18, 2011 29
1.0
0.8
0.6
0.4
0.2
0.0
-0.2
ρ11
121086420
Δy [mm]
Double-sided
Single-sided
Lc = 5 mm
Lc = 10 mm
Lc = 15 mm
Open Symbol: Ensemble-averaged
Filled Symbol: Spatial-averaged,
Double-sided
1.0
0.8
0.6
0.4
0.2
0.0
-0.2
ρ22
121086420
Δy [mm]
Double-sided
Single-sided
Lc = 5 mm
Lc = 10 mm
Lc = 15 mm
Open Symbol: Ensemble-averaged
Filled Symbol: Spatial-averaged,
Double-sided
)exp(
2
1)exp(
2
1 xd
xd
cxb
xb
aR ∆⋅−




 ∆⋅
−+∆⋅−




 ∆⋅
−=
drL ∫
∞
=
0
1111 ρ drL ∫
∞
=
0
2222 ρ
•Little difference in
E.A. double- or single-
sided methods.
Best-fit curve (SAE Paper 880381) used to extend ρ11 to calculate L11:
Integral Lengthscales (measure of the larger eddies):

30. Normalized Integral Lengthscales: E.A.
February 18, 2011 30
10
8
6
4
2
0
Lii[mm]
3.53.02.52.01.51.00.5
Vmps [m/s]
L11, Vertical
L22, Vertical
L11, Horizontal
L22, Horizontal
UP, SV, 0-deg
Open Symbol: Small Engine
Filled Symbol: Large Engine
1.0
0.8
0.6
0.4
0.2
0.0
Lii/hTDC
3.53.02.52.01.51.00.5
Vmps [m/s]
L11, Vertical
L22, Vertical
L11, Horizontal
L22, Horizontal
UP, SV, 0-deg
Open Symbol: Small Engine
Filled Symbol: Large Engine
•Longitudinal and transverse integral lengthscales versus mean piston speed in
the vertical and horizontal directions using the ensemble average method.
Normalize by hTDC
•Lengthscales relatively constant with Vmps.
•Similar lengthscales between SV and NV cases.

31. Normalized Integral Lengthscales: E.A.
February 18, 2011 31
•Good agreement in vertical and
horizontal directions: indication of
isotropy in the plane.
1.0
0.8
0.6
0.4
0.2
0.0
Lii(Vertical)/hTDC
1.00.80.60.40.20.0
Lii (Horizontal) / hTDC
L11
L22
One-to-One Line
Open Symbol: Small Engine
Filled Symbol: Large Engine
•Non-dimensional integral lengthscales for all engine conditions and speeds in
the vertical versus horizontal directions using the ensemble average method.
Scatter in L11 due
to best-fit curve.
0.6
0.5
0.4
0.3
0.2
0.1
0.0
L22/hTDC
0.60.50.40.30.20.10.0
L11 / 2*hTDC
Open Symbol: Small Engine
Filled Symbol: Large Engine
PP, SV, 0-deg, UP, SV, 0-deg
PP, NV, 0-deg, UP, NV, 0-deg
PP, NV, 90-deg, UP, NV, 90-deg
One-to-One Line
•Isotropic turbulence
(L22/ L11 = 0.50).

32. Modified Integral Lengthscales: E.A.
February 18, 2011 32
•L11
*
integrated directly from correlation data (does not use best-fit curve) up to a
distance equal to the height of the FOV in both directions.
1.0
0.8
0.6
0.4
0.2
0.0
L11
*
(Vertical)/hTDC
1.00.80.60.40.20.0
L11
*
(Horizontal) / hTDC
Open Symbol: Small Engine
Filled Symbol: Large Engine
One-to-One Line
1.0
0.8
0.6
0.4
0.2
0.0
Lii(Vertical)/hTDC
1.00.80.60.40.20.0
Lii (Horizontal) / hTDC
L11
L22
One-to-One Line
Open Symbol: Small Engine
Filled Symbol: Large Engine
•There is close agreement between the lengthscales in either
direction, indicating a high level of isotropy, and the difference
between the small and large engine data appear smaller.
1.0
0.8
0.6
0.4
0.2
0.0
-0.2
ρ11
121086420
Δy [mm]
Double-sided
Single-sided
Lc = 5 mm
Lc = 10 mm
Lc = 15 mm
Open Symbol: Ensemble-averaged
Filled Symbol: Spatial-averaged,
Double-sided
Integrate to here.

33. Normalized Integral Lengthscales: S.A.
February 18, 2011 33
0.30
0.25
0.20
0.15
0.10
0.05
0.00
Lii(Horizontal)/hTDC
5 6 7 8
1
2 3 4 5 6 7 8
10
fc*hTDC
UP, NV, 0-deg
L11
L22
0.30
0.25
0.20
0.15
0.10
0.05
0.00
Lii(Vertical)/hTDC
5 6 7 8
1
2 3 4 5 6 7 8
10
fc*hTDC
UP, NV, 0-deg
L11
L22
•Very little difference with engine speed (similar to E.A. data).
•Again, close agreement between the engines when the data are made
non-dimensional by hTDC.
•L11 still calculated using best-fit equation (some waviness).
•The transverse lengthscales in both the vertical and horizontal
directions give very similar results for a given engine condition and are
quite consistent comparing all conditions.

34. x [mm] [m 2/s2]
y[mm]
2 4 6 8 10 12 14 16
-12
-10
-8
-6
-4
-2
5
10
15
20
25
30
35
40
45
50
55
Energy Spectra Analysis
February 18, 2011 34
.
2
3
)(
2
1 22
⋅+⋅= vuk
Turbulent kinetic energy
Fast Fourier Transform (FFT) of a row
Complex Conjugate of FFT of adjacent row
multiplied by
=
Energy Spectrum vs. Wavenumber Plot
Average energy spectra over all
rows and engine cycles

35. Energy Spectra Analysis
February 18, 2011 35
Iterative process that picks turbulence Reynolds number, Re£ (or £ since k measured):
ηκεκ ffCE £
3/53/2
)( −
=
Relation between Re£ and
Kolmogorov (η) lengthscale,
characteristic of the smallest
turbulent motions.
3/422/1
£
££
Re 





===
ηενν
kk
.1
)(
)(
1
2
2
1
111 κ
κ
κ
κ
κ
κ
κ
d
E
E ∫
∞








−=
κ
κ
κπ
d
E
u
L ∫
∞
=
0
2
1
11
)(
2
calculates Pope’s model (3-D) spectrum:
then calculates best-fit model (1-D) spectrum (by varying £ ):
L11 is calculated using E(κ):
Pope, S.: Turbulent Flows, Cambridge University Press, Cambridge, UK, 2000.

36. Energy Spectra Analysis: E.A.
February 18, 2011 36
Ensemble average method
Deviation from
model at small
separation distances
(~2x PIV
interrogation size).
10
5
10
6
10
7
10
8
10
9
10
10
10
11
10
12
E11(κ1)/(εν
5
)
1/4
0.001
2 4 6 8
0.01
2 4 6 8
0.1
2 4 6 8
1
κ1η
300 rpm
600 rpm
900 rpm
1200 rpm
UP, SV, 0-deg
Vertical Direction
Model, 300 rpm
Model, 1200 rpm
Slope -5/3
Large Engine
10
5
10
6
10
7
10
8
10
9
10
10
10
11
10
12
E11(κ1)/(εν
5
)
1/4
0.001
2 4 6 8
0.01
2 4 6 8
0.1
2 4 6 8
1
κ1η
600 rpm
1200 rpm
1800 rpm
UP, SV, 0-deg
Vertical Direction
Model, 600 rpm
Model, 1800 rpm
Slope -5/3
Small Engine
Large inertial
subrange at higher
RPMs.

37. Energy Spectra Analysis, L11: E.A.
February 18, 2011 37
0.6
0.5
0.4
0.3
0.2
0.1
0.0
L11/hTDC
3.53.02.52.01.51.00.5
Vmps [m/s]
UP, SV, 0-deg
Vertical
Horizontal
0.6
0.5
0.4
0.3
0.2
0.1
0.0
L11/hTDC
3.53.02.52.01.51.00.5
Vmps [m/s]
UP, NV, 0-deg
Vertical
Horizontal
Open symbols: small engine,
filled symbols: large engine.
Utility Port, SV
•Lengthscales relatively constant with Vmps.
•Similar lengthscales between SV and NV cases.
•Close agreement between small and large engines.
•Same conclusions based on spatial-average data.
Utility Port, NV

38. Energy Spectra Analysis, η: E.A.
February 18, 2011 38
40
30
20
10
0
η[μm]
3.53.02.52.01.51.00.5
Vmps [m/s]
UP, SV, 0-deg
Vertical
Horizontal
40
30
20
10
0
η[μm]
3.53.02.52.01.51.00.5
Vmps [m/s]
UP, NV, 0-deg
Vertical
Horizontal
•η decreases monotonically with engine speed.
•Ports with SV compared to NV exhibit smaller η at same Vmps.
•η between small and large engines are roughly the same at a
given Vmps.
•Same conclusions based on spatial-average data.
Open symbols: small engine,
filled symbols: large engine.
Utility Port, SV Utility Port, NV

39. Taylor-scale Reynolds number, Rλ: E.A.
February 18, 2011 39
£Re
3
20
=λR
cCD
VB
Z
avgf
mps
,
2
2
=
Inlet valve Mach index (modified Vmps):
Livengood, J.C., and Stanitz, J.B.: “The Effect of Inlet-Valve Design, Size, and
Lift on the Air Capacity and Output of a Four-Stroke Engine,” NACA Tech.
Notes, no. 915, 1943.
B: cylinder bore
D: intake valve inner seat diameter
c: speed of sound
Cf,avg: mass-average flow coefficient
Taylor-scale Reynolds number found from spectral analysis turbulence
Reynolds number:

40. Taylor-scale Reynolds number, Rλ: E.A.
February 18, 2011 40
180
160
140
120
100
80
60
40
20
Rλ
0.200.150.100.05
Z
PP, SV, 0-deg
PP, NV, 0-deg
PP, NV, 90-deg
UP, SV, 0-deg
UP, NV, 0-deg
UP, NV, 90-deg
Ensemble Average Method
Vertical Direction
180
160
140
120
100
80
60
40
20
Rλ(LargeEngine),Rλ(SmallEngine)*1.69
0.200.150.100.05
Z
PP, SV, 0-deg
PP, NV, 0-deg
PP, NV, 90-deg
UP, SV, 0-deg
UP, NV, 0-deg
UP, NV, 90-deg
Ensemble Average Method
Vertical Direction
•Open symbols: small engine, filled symbols: large engine.
•Z found from steady flow testing, if relation holds for more intake port
configurations, would be a good predictive tool.
•Reynolds number is:
Visc.Kin.
*
Re
VelocityLength
=

41. Turbulence Intensity vs. Z: E.A. & S.A.
February 18, 2011 41
•Turbulence intensity (velocity-scale) collapses with Z for all engine
conditions.
4.0
3.5
3.0
2.5
2.0
1.5
1.0
0.5
0.0
<u'>EnsembleAverage[m/s]
0.250.200.150.100.050.00
Z
PP, SV, 0-deg
PP, NV, 0-deg
PP, NV, 90-deg
UP, SV, 0-deg
UP, NV, 0-deg
UP, NV, 90-deg
Open Symbol: Small Engine
Filled Symbol: Large Engine
4.0
3.5
3.0
2.5
2.0
1.5
1.0
0.5
0.0
<u'>Spatial-Average[m/s]
0.250.200.150.100.050.00
Z
PP, SV, 0-deg
PP, NV, 0-deg
PP, NV, 90-deg
UP, SV, 0-deg
UP, NV, 0-deg
UP, NV, 90-deg
Open Symbol: Small Engine
Filled Symbol: Large Engine
fc*hTDC = 0.7
4.0
3.5
3.0
2.5
2.0
1.5
1.0
0.5
0.0
<u'>Spatial-Average[m/s]
0.250.200.150.100.050.00
Z
PP, SV, 0-deg
PP, NV, 0-deg
PP, NV, 90-deg
UP, SV, 0-deg
UP, NV, 0-deg
UP, NV, 90-deg
Open Symbol: Small Engine
Filled Symbol: Large Engine
fc*hTDC = 1.7
Ensemble average Spatial-average

42. Summary
February 18, 2011 42
•Sufficient similarity was achieved as evidenced by steady flow testing.
•Swirl center locations tracked similarly between small and large engines.
•Using either ensemble- or spatial-average method:
-<u’ > versus Vmps was similar between the engines.
-Similar lengthscales in vertical and horizontal directions: isotropic
turbulence in plane of measurement.
-L11, L22 constant versus Vmps: integral length scale is controlled by the
engine geometry.
-η is similar between engines at same Vmps: controlled by the Reynolds
number and Lii.

43. Summary
February 18, 2011 43
•Everything collapses well between the engines with hTDC:
-L11, L22 normalized by hTDC are similar between engines (correlation and
spectral analyses).
-Spatial-average comparisons made at same fc*hTDC are similar between
engines (<u’>, L11, L22).
•Velocity-scales between engines collapse well with Z.

44. Thank You
February 18, 2011 44
•Questions or comments?