PhD Defense February 18 2011 Doug Heim v2

In-Cylinder Investigation of Engine Size- and Speed-Scaling Effects

Student: Doug HeimAdvisor: Jaal Ghandhi

Sponsor: Wisconsin Small Engine Consortium

Ph.D. Thesis Defense

February 18, 2011

Presentation Outline

February 18, 2011 2

• Motivation and Objectives• Literature Review• Experimental Setup• Steady Flow Test Results• Optical Engine Measurements and Analysis• Summary

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.

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.

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).

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.

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.


February 18, 2011 8

Volumetric efficiency

mep: work per engine cycle divided by cylinder volume displaced per cycle.

Pressure at same piston speed


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.

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.



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?



• 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.

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 Compression 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

Experimental Setup


Port HousingFixtures

Shim Plate Shim Plate

Intake Port

Exhaust Port

Rocker ArmsCamshaft 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.

Experimental Setup


Cylinder Wall

Cylinder Axis

Exhaust Valve

Intake Valve

Intake Port

Shroud

Intake ValveIntake 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)

B

H

DI

HI

L

Intake Port

Intake Horn

Swirl AdapterFixture

Impulse TorqueMeter

Honeycomb

D

T

Steady Flow Test Results


• Similar engines should have similar:• flow coefficients

• swirl coefficients

•SuperFlow 600 flow bench•Transducer Techniques torque sensor•28 inH2O pressure drop•40 seconds

vBf AV

mC

ρ

=

BVm

TC

Bs

8=

2

2)(

4

=

∫

∫IVC

IVO

IVC

IVO

dCA

dCCABS

R

fV

sfV

vs

θ

θ

θ

θ

θ

θπη

Steady Flow Test Results


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 = 0.303Small 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 HeadFilled Symbol: Large Head

0-degree Orientation, SV

Large Head Small HeadValve Port Orientation Rs ± uRs Rs ± uRsShrouded 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 ± 0.00890-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

Particle Image Velocimetry (PIV)


ImagingMirror

Bowditch Piston

Extension

SapphirePiston

Window

EngineHead

QuartzRing

WindowNd: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.

PIV Field-of-View (FOV)


Cylinder Wall

Cylinder Axis

Exhaust Valve

Intake Valve

Low-MagnificationFOV

High-MagnificationFOV

SecondHigh-Magnification

FOV

CylinderVisibleArea

•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 Engine17.5mm x 14mmSmall Engine

10.4mm x 8.3mm

Low-Mag. FOV: Swirl Center Location


-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.

Normalized Angular Rotation Rate


6

5

4

3

2

1

0

Ω /

Ω E

ngin

e

-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 /

Ω E

ngin

e

-90 -45 0

Crank Angle Degrees

300 rpm 600 rpm 900 rpm 1200 rpm 1800 rpm

UP, NV, 0-deg

Utility PortΩ: angular velocity magnitudeΩEngine: engine angular rotation rate

•At TDC, on average, the normalized angular velocity of the small engine compared to the large engine is lower

28% lower16% 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.

Swirl Ratio Comparison


•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

Ave

rage

Ω(T

DC

) / Ω

Eng

ine

543210Rs

PP, SV PP, NV UP, SV UP, NV One-to-One Line

Ports in 0-deg OrientationOpen Symbol: Small EngineFilled Symbol: Large Engine

Average normalized angular velocity at TDC vs. swirl ratio

Mean, Fluctuating Velocity Calculation


∑ ==cN

ic

iEA iyxUN

yxU1

, 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

cc L

f1=

Ensemble Average: Spatial-Average:

.2,1),(),(),( =−= iyxUyxUyxu iii

The fluctuating velocity is defined as:

High-Mag. FOV: Turbulence Intensity


.)},(),({1

),(' 22

1

21 yxuyxu

Nyxu

cN

c

+= ∑

x [mm] [m/s]

y [m

m]

5 10 15

-12

-10

-8

-6

-4

-2

3

3.5

4

4.5

x [mm] [m/s]

y [m

m]

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 [m

m]

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.

5

4

3

2

1

0

E

nsem

ble

Ave

rage

[m

/s]

543210Vmps [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 EngineFilled Symbols: Large Engine

Turbulence Intensity: E.A.


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

Turbulence Intensity: S.A.


5

4

3

2

1

0

S

patia

l-Ave

rage

[m

/s]

543210Vmps [m/s]



fc*hTDC = 1.7

5

4

3

2

1

0

S

patia

l-Ave

rage

[m

/s]

543210Vmps [m/s]



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

Turbulence Intensity: S.A.


1.6

1.4

1.2

1.0

0.8

0.6

0.4

0.2

0.0

S

patia

l-Ave

rage

/ V

mps

1.21.00.80.60.40.20.0fc [mm

-1]

Ensemble Average

PP, 0º, SV PP, 0º, NV PP, 90º, NV UP, 0º, SV UP, 0º, NV UP, 90º, NV


1.6

1.4

1.2

1.0

0.8

0.6

0.4

0.2

0.0

S

patia

l-Ave

rage

/ V

mps

86420fc*hTDC

Ensemble Average



Non-shrouded Shrouded

•Linear trend slopes collapse well with hTDC.

0.1

2

3

4

5

6

7

89

1

S

patia

l-Ave

rage

/ <

u' >

Ens

embl

e A

vera

ge

3 4 5 6 7 81

2 3 4 5 6 7 810

fc*hTDC



Correlation Coefficient


)()0(

)()0()(

22 ruu

ruur

ji

jiij

⋅

⋅=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 [m

m]

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

Integral Lengthscales


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-averagedFilled Symbol: Spatial-averaged, Double-sided

1.0

0.8

0.6

0.4

0.2

0.0

-0.2

ρ22

121086420

Δy [mm]



)exp(2

1)exp(2

1 xdxd

cxbxb

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):

Normalized Integral Lengthscales: E.A.


10

8

6

4

2

0

Lii

[mm

]

3.53.02.52.01.51.00.5Vmps [m/s]

L11, Vertical L22, Vertical L11, Horizontal L22, Horizontal

UP, SV, 0-degOpen Symbol: Small EngineFilled Symbol: Large Engine

1.0

0.8

0.6

0.4

0.2

0.0

Lii

/ hT

DC

3.53.02.52.01.51.00.5Vmps [m/s]

L11, Vertical L22, Vertical L11, Horizontal L22, Horizontal

UP, SV, 0-degOpen Symbol: Small EngineFilled 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.

Normalized Integral Lengthscales: E.A.


•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

L ii (

Ver

tical

) / h

TD

C

1.00.80.60.40.20.0Lii (Horizontal) / hTDC

L11

L22

One-to-One Line

Open Symbol: Small EngineFilled 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

/ h

TD

C

0.60.50.40.30.20.10.0L11 / 2*hTDC


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).

Modified Integral Lengthscales: E.A.


•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

L 11* (

Ver

tical

) / h

TD

C

1.00.80.60.40.20.0

L11* (Horizontal) / hTDC


One-to-One Line

1.0

0.8

0.6

0.4

0.2

0.0

L ii (

Ver

tical

) / h

TD

C

1.00.80.60.40.20.0Lii (Horizontal) / hTDC

L11

L22

One-to-One Line


•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]



Integrate to here.

Normalized Integral Lengthscales: S.A.


0.30

0.25

0.20

0.15

0.10

0.05

0.00

L ii (

Hor

izon

tal)

/ h T

DC

5 6 7 81

2 3 4 5 6 7 810

fc*hTDC

UP, NV, 0-deg

L11

L22

0.30

0.25

0.20

0.15

0.10

0.05

0.00

L ii (

Ver

tica

l) /

h TD

C

5 6 7 81

2 3 4 5 6 7 810

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.

x [mm] [m 2/s2]

y [m

m]

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


.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

Energy Spectra Analysis


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

21

111 κκκ

κκκ

κ

dE

E ∫∞

−=

κκκπ

dE

uL ∫

∞

=0

21

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.

Energy Spectra Analysis: E.A.


Ensemble average method

Deviation from model at small separation distances(~2x PIV interrogation size).

105

106

107

108

109

1010

1011

1012

E11

(κ1)

/(εν

5 )1/4

0.0012 4 6 8

0.012 4 6 8

0.12 4 6 8

1κ1η

300 rpm 600 rpm 900 rpm 1200 rpm

UP, SV, 0-degVertical Direction

Model, 300 rpm Model, 1200 rpm Slope -5/3

Large Engine

105

106

107

108

109

1010

1011

1012

E11

(κ1)

/(εν

5 )1/4

0.0012 4 6 8

0.012 4 6 8

0.12 4 6 8

1κ1η

600 rpm 1200 rpm 1800 rpm

UP, SV, 0-degVertical Direction

Model, 600 rpm Model, 1800 rpm Slope -5/3

Small Engine

Large inertial subrange at higher RPMs.

Energy Spectra Analysis, L11: E.A.


0.6

0.5

0.4

0.3

0.2

0.1

0.0

L 11

/ hT

DC

3.53.02.52.01.51.00.5Vmps [m/s]

UP, SV, 0-deg

Vertical Horizontal

0.6

0.5

0.4

0.3

0.2

0.1

0.0

L 11

/ hT

DC

3.53.02.52.01.51.00.5Vmps [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

Energy Spectra Analysis, η: E.A.


40

30

20

10

0

η [μ

m]

3.53.02.52.01.51.00.5Vmps [m/s]

UP, SV, 0-deg

Vertical Horizontal

40

30

20

10

0

η [μ

m]

3.53.02.52.01.51.00.5Vmps [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

Taylor-scale Reynolds number, Rλ: E.A.


£Re3

20=λR

cCD

VBZ

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 boreD: intake valve inner seat diameterc: speed of soundCf,avg: mass-average flow coefficient

Taylor-scale Reynolds number found from spectral analysis turbulence Reynolds number:

Taylor-scale Reynolds number, Rλ: E.A.


180

160

140

120

100

80

60

40

20

Rλ

0.200.150.100.05

Z


Ensemble Average MethodVertical Direction

180

160

140

120

100

80

60

40

20

Rλ(

Larg

e E

ngin

e), R

λ(S

mal

l Eng

ine)

*1.6

9

0.200.150.100.05

Z


Ensemble Average MethodVertical 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=

Turbulence Intensity vs. Z: E.A. & S.A.


•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

E

nsem

ble

Ave

rage

[m/s

]

0.250.200.150.100.050.00

Z



4.0

3.5

3.0

2.5

2.0

1.5

1.0

0.5

0.0

S

patia

l-Ave

rag

e [m

/s]

0.250.200.150.100.050.00

Z



fc*hTDC = 0.74.0

3.5

3.0

2.5

2.0

1.5

1.0

0.5

0.0

S

patia

l-Ave

rage

[m/s

]

0.250.200.150.100.050.00

Z



fc*hTDC = 1.7

Ensemble average Spatial-average

Summary


•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.

Summary


•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.

Thank You


•Questions or comments?

Documents

PhD Defense February 18 2011 Doug Heim v2