INVESTIGATION OF TURBULENT FLOW IN A RECIPROCATING ENGINE USING PARTICLE IlMAGE

V33LOCIMETRY

A thesis submitted in confodty with the requirements

for the degree of Master of Applied Science

Graduate Department of Mechanical and Industrial Engineering

University of Toronto

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Investigation of turbulent flow in a reciprocating engine using particle image ve-

locimetry

Master of Applied Science, 1999

Jeffrey Adam Davis

Department of Mechanical and Industrial E n g i n e e ~ g

University of Toronto

A fully optical water analog engine has been designed and constructed for mod-

eling engine flow. A study of the velocity fields, in the latter part of the intake

stroke, near the piston surface shows the flow to be turbulent and three-dimensional

in the mean. For the first t h e in an engine study, terms from both the Reynolds

and kinetic energy equations have been extracted and compared. A study of the

Reynolds equation shows that a greater percentage of the convection and Reynolds

stress transport terms have magnitudes which are larger than the diffusion terms.

Results from the mean and turbulent kinetic energy equations show that a greater

percentage of the production and Reynolds stress transport terms have magnitudes

which are larger than the dissipation and viscous stress transport terms.

ACKNOWLEDGMENT

The author would Iike to express his gratitude to Profesçors P- Sullivan and J. Keffer

for their patience and guidance provided during this investigation. The author also

wishes to express thanks to Michael Marxen and Marc B d e for many stimdating

conversations. Special thanks is given to L- Roosman who constructed the optical

engine and M. Kalovsky who designeci and constructed electricd components used

in the expriment. Financial assistance through a NSERC PGS-A scholarship is

gratefuily acknowledged.

CONTENTS

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ACKNOWEDGMENT iii

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . LIST OF TABLES vii

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . LIST OF FIGURES ix

... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . LIST OF -WPENDICES xm

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Nomenclature xv

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . htroduction 1

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Background 1

. . . . . . . . . . . . . . . . . . . . . . . 1.2 Turbulence in Engine Flows 4

. . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 The Present Study 7

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4 Objectives 7

. . . . . . . . . . . . . . . . . . . . . . . . . . . 1.5 Significance of Work 7

. . . . . . . . . . . . . . . . . . . . . . . . . 2 . Optical Water Analog Engine 8

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Overview 8

. . . . . . . . . . . . . . . . . . 2 -2 Dimensional Andysis and Similitude 8

. . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Optical Properties 11

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4 Piston Chamber 13

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5 Inlet 14

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6 Piston Assembly 16

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.7 End Section 20

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.8 Crank Wheel 21

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.9 Water Tanks 21

. . . . . . . . . . . . . . . . . . . . . . 2.10 Structural Stabüity of System 25

. . . . . . . . . . . . . . . . . . . . . . 3 . Experimental Set-up and Procedure 27

. . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Experimental Set-up 27 . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.1 Particle Seeding 27 . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.2 Data Acquisition 29

. . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Experîrnental Procedure 33 . . . . . . . . . . . . . . . . . . . . . . 3.2.1 Coordinate System .. 33

. . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.2 Engine Cycles 34 . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.3 Location of Data 34

. . . . . . . . . . . . . . . 3.2.4 Mapification Factor Measurement 35

4 . Data Reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

. . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 Equations of Motion 37

. . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 hstantaneous Velocity 40

. . . . . . . . . . . . . . . . . 4.3 Velocity Validation and Extrapolation 43

. . . . . . . . . . . . . . . . . . . . 4.4 Turbulence Averaging Techniques 44

. . . . . . . . . . . . . . . . . . 4.5 Convergence of Velocity Components 45

. . . . . . . . . . . . . . . . . . . . . . . . . . . 4.6 'Iiirbulence Intensity 46

. . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.7 Velociw Gradients 46

. . . . . . . . . . . . . . . . . . . . . . 4.8 Piston Velocity Measurement 47

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.9 Error Analysis 48

. . . . . . . . . . . . . . . . . . 4.9.1 Crank Angle positioning Error 48 . . . . . . . . . . . . . . . . . . . . . . . . 4.9.2 Displacement Error 49 . . . . . . . . . . . . . . . . . . . . . . . . 49.3 Time Interval Error 50

. . . . . . . . . . . . . . . . . . . . 4.9.4 Magnification Factor Error 51 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.9.5 Summary 51

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 . Results 54 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1 Images 54

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 Piston Velocity 55

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3 Velocity Fields 56 . . . . . . . . . . . . . . . . . . . . . . . 5.3.1 Interrogation Region 56

. . . . . . . . . . . . . . . . . . . . . 5.3.2 Instantaneous Velocities 58 . . . . . . . . . . . . . . . . . . . . . . . 5.3.3 Mean Velocity Fields 61

. . . . . . . . . . . . . . . . . 5.3.4 Convergence of Mean Velocities 76 . . . . . . . . . . . 5.3.5 Mean Velocity Gradients in the Y direction 77

. . . . . . . . . . . . . . . . . . . . . . . . . 5.3.6 Flow Turbulence 78 . . . . . . . . . . . . . . . . . . . . . . 5.3.7 Thrbulence Intensities 79

. . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4 Reynolds Equation 82 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4.1 Diffusion 82

. . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4.2 Convection 85 5.4.3 Reynolds Stress transport . . . . . . . . . . . . . . . . . . . . 86

. . . . . . . . . . . . . . . . 5.4.4 Time Rate of Change of Velocity 88

. . . . . . . . . . . . . . . . . . . . . 5.5 Mean Kinetic Energy Equation 90 . . . . . . . . . . . . . . . . . 5.5.1 Mean Viscous Stress Tkansport 90

. . . . . . . . . . . . . . . . 5.5.2 Mean Reynolds Stress Transport 91 . . . . . . . . . . . . . . . . . . . . . . . . . 5.5.3 Mean Dissipation 93

. . . . . . . . . . . . . . . . . . . . . . 5.5.4 Turbulence Production 95

. . . . . . . . . . . . . . . . . . . 5.6 Turbulent Kinetic Energy Equation 97

. . . . . . . . . . . . . . . 5.6.1 Turbulent Viscous Stress Transport 97

. . . . . . . . . . . . . . 5.6.2 Turbulent Reynolds Stress Transport 98 . . . . . . . . . . . . . . . . . . . . . . . 5.6.3 Turbulent Dissipation 100

. . . . . . . . . . . . . . . . . . . . . . . 6 . Discussion and Recommendations 103

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1 Discussion 103 . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1.1 Engine Study 103 . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1.2 Velociw Field 103

. . . . . . . . . . . . . . . . . . . . . . . . 6.1.3 Reynolds Equation 104

. . . . . . . . . . . . . . . . . . . . 6.1.4 Kinetic Energy Equations 105

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 Recommendations 109

. . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.1 Engine Design 109

. . . . . . . . . . . . . . . . . . . . . . . . . 6.2.2 Engine Similitude 110

. . . . . . . . . . . . . . . . . . . . . . . . 6.2.3 Reduction of Errors 110

. . . . . . . . . . . . . . . 6.2.4 Decomposition of an Unsteady flow 111 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.5 Future Wurk 111

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References -137

LIST OF TABLES

Theoretical and Measured Piston positions for CAD O" . 180" . . . . . 20

RS-170 Video Format. from (Ranel. 1998) . . . . . . . . . . . . . . . . . 33

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Error Estimates 53

Mean Particle Densities for DifTerent Interrogation Regions . . . . . . . 57

Percentage of total flow pattern mes in flow . . . . . . . . . . . . . . 60

Standard Deviation for D i h i o n [mm/s2] . . . . . . . . . . . . . . . . . 83

Comparison of Dinusion Terms [% of flow] . . . . . . . . . . . . . . . . 84

Standard Deviation for Convection [mm/s2] . . . . . . . . . . . . . . . . 86

Cornparison of Convection Terms [% of flow] . . . . . . . . . . . . . . . 86

Standard Deviation for RST [mm/s2] . . . . . . . . . . . . . . . . . . . 87

Cornparison of RST Terms [% of flow] . . . . . . . . . . . . . . . . . . . 88

Standard Deviation for MVST [mm2/s3] . . . . . . . . . . . . . . . . . . 91

Cornparison of MVST Terms [% of flow] . . . . . . . . . . . . . . . . . . 91

Standard Deviation for MRST (104) [mm2/s3] . . . . . . . . . . . . . . 92

Cornparison of MRST Terms [% of flow] . . . . . . . . . . . . . . . . . . 93

Standard Deviation for Mean Dissipation [mrn2/s3] . . . . . . . . . . 94

Comparison of Mean Dissipation Terms [% of flow] . . . . . . . . . . . . 95

Standard Deviation for Production (104) [mm2/s3] . . . . . . . . . . . . 96

Cornparison of Turbulent Production Terms [% of flow] . . . . . . . . . 96

Standard Deviation for TVST [mm2/s3] . . . . . . . . . . . . . . . . . . 98

Cornparison of TVST Terms [% of flow] . . . . . . . . . . . . . . . . . . 98

Standard Deviation for TRST (104) [mm2/s3] . . . . . . . . . . . . . . . 99

Cornparison of TRST Terms 1% of flow] . . . . . . . . . . . . . . 100

Standard Deviation for Turbulent Dissipation [mm2/s3] . . . . . . . . . 101

vii

. . . . . . . . . 5.22 Cornparison of Turbulent Dissipation Terms [% of flow] 102

. . . . . . . . . . . . . 6.1 Total Percentages for Reynolds Equation Terms 105

. . . . . . . . . 6.2 Total Percentages for the Mean Energy Equation Tenns 105

. . . . . . . . . 6.3 Total Percentages for Turbulent Energy Equation Terms 107

. . . . . . . . . . . . 6.4 Percentage cornparison between dissipatioo terms 108

. . . . . . . . . . . . 6.5 Results of Cornparison between Energy equations 109

LIST OF FIGURES

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Flow Cell

Engine Assembly . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Variables for Engine Similitude, see equation 2.1 for variable definitions

Refraction of Light . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Influence of Engine Geometry . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Glas Section

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . End Plates

End Section Inlet Addition . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Inlet

Piston Head . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Connecting Rod (A) . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Connecting Rod (B) . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Theoretical non-dirnensionalized Piston Velocity . . . . . . . . . . . . .

Piston Displacement fkom x=O . . . . . . . . . . . . . . . . . . . . . . .

Piston Displacement betmeen CAD . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . End Section (Piston Side) 22

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Piston Support 23

Crankmeel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

. . . . . . . . . . . . . . . . . . . . . Crank ,4n gle Measurement Device 24

Structural Support . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

Experimentd Water Level Setup . . . . . . . . . . . . . . . . . . . . . . 28

Double exposed image of the flow . . . . . . . . . . . . . . . . . . . . . 29

Triggering Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Data .Acquisition 31

Signal Timing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

Coordinate System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

Description of Crank Angle . . . . . . . . . . . . . . . . . . . . . . . . . 35

Location of Data Capture Planes . . . . . . . . . . . . . . . . . . . . . . 36

. . . . . . . . . . . . . . . . . . . . Plot of Autocorrelation Coefficients 41

Plane View of Autocorrelation Peaks . . . . . . . . . . . . . . . . . . . 42

Determination of Piston Velocity . . . . . . . . . . . . . . . . . . . . . . 48

Error produced &om different measurement intervals and magni6ication factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

. . . . . . . . . . . . . . . . . . . Negative image of Flow with Seeding 54

Piston Velocity Profile . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

Piston Velocity Profile CAD 120" . 180" . . . . . . . . . . . . . . . . . 56

Typical Histogram plot for MIAU(y)/4t/dr . . . . . . . . . . . . . . . . 58

. . . . . . . Instantaneous Velocity Plots (Before and After Valida~ion) 59

Categorization of flow field patterns . . . . . . . . . . . . . . . . . . . . 60

Instantaneous Plots at CAD 160" . . . . . . . . . . . . . . . . . . . . . 62

Histogram plot of Instantaneous Veloci@ during CAD 130" . . . . . . . 63

Histogram of Instantaneous Velocity durîng C.4.D 180° (T) . . . . . . . 64

Mean Velocity Field for CAD 120" (T) . . . . . . . . . . . . . . . . . . 66

Mean Velocity Field for CAD 120" (B) . . . . . . . . . . . . . . . . . . 66

Mean Velocity Field for CAD 130" (T) . . . . . . . . . . . . . . . . . . 67

Mean Velocity Field for CAD 130" (B) . . . . . . . . . . . . . . . . . . 67

Mean Velocity Field for CAD 140" (T) . . . . . . . . . . . . . . . . . . 68

Mean Velocity Field for CAD 140" (B) . . . . . . . . . . . . . . . . . . 68

Mean VelociQ Field for CAD 150" (T) . . . . . . . . . . . . . . . . . . 69

Meao Velocity Field for CAD 150" (B) . . . . . . . . . . . . . . . . . . 69

Mean Velocity Field for CAD 160" (T) . . . . . . . . . . . . . . . . . . 70

Mean Velocity Field for CAD 160" (B) . . . . . . . . . . . . . . . . . . 70

. . . . . . . . . . . . . . . . . . Mean Velocity Field for CAD 170" (T) 71

. . . . . . . . . . . . . . . . . . Mean Velocity Field for CAD 170" (B) 71

. . . . . . . . . . . . . . . . . . Mean V e l o c i ~ Field for CAD 180" (T) 72

. . . . . . . . . . . . . . . . . . Mean Velocity Field for CAD 180" (B) 72

Mean U Velociw Component . . . . . . . . . . .. . . . . . . . . . . . . 73 . . . . . . . . . . . . . . . . . . . . . . . Mean W Velocity Component 74

. . . . . . . . . . . . . . . . . . . . . Mean (U-Vp) Velocity Component 75

. . . . . . . . . . . . . . . . . . . . . . . . . . . . Convergence of U [%] 76

. . . . . . . . . . . . . . . . . . . . . . . . . . . Plot of in B [l/s] 77

Fluctuating Vorticity for CAD 180' (T) . . . . . . . . . . . . . . . . . . 78

Turbulence Intensity in T (u component) [%] . . . . . . . . . . . . . . . 79

. . . . . . . . . . . . . . . Turbulence Lntensity in B (u component) [%] 80

. . . . . . . . . . . . . . Mean Turbulence Intensity (w component)[%] 81

Spatially Averaged Turbulence Intensity [u:. RhfS/ (Vp)] . . . . . . . . . . 82

. . . . . . . . . . . . . . . . . . . . . . . . vw Dinusion (B)[-/S*] 83

. . . . . . . . . . . . . . . . . . . . . . . . Histogram of DiEusion Terms 84

. . . . . . . . . . . . . . . . . . . . . . Kistogram of Convection Terms 85

. . . . . . . . . . . . . . Histogam of Reynolds Stress Transport Terms 87

. . . . . . . . . . . . . . . . . . . . . . . . . . Estimate of Mean 89

. . . . . . . . . . . . . . . . . . . . . . . . . Histogram of MVST Terms 90

. . . . . . . . . . . . . . . . . . . . . . . . . Histogram of MRST Terms 92

Histogram of Mean dissipation Terms . . . . . . . . . . . . . . . . . . . 94

Histogram of Turbulent Production Terms . . . . . . . . . . . . . . . . 95

Histogram of TVST Terms . . . . . . . . . . . . . . . . . . . . . . . . . 97

. . . . . . . . . . . . . . . . . . . . . . . . . 5.44 Histogram of TRST Terms 99

. . . . . . . . . . . . . . . . 5.45 Kistogram of Turbulent Dissipation Terms 101

. . . . . . . . . . . . . . . . . 6.1 Cornparison of Reynolds Equation Terms 104

. . . . . . . . . . . . . . . 6.2 Cornparison of Mean Energy Equation Terms 106

. . . . . . . . . . . . 6.3 Cornparison of ïhrbulent Energy Equation Terms 107

. . . . . . . . . . . . . . . . . . . . . 6.4 Cornparison of Dissipation Terms 108

. . . . . . . . . . . . . . . . . . . . . . . . . . A.1 Piston-Crank wheel setup 112

A . Theoretical Velocity of the Piston . . . . . . . . . . . . . . . . . . . . . . . . . 112 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B . Error Analysis 114

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C . Seeding Calculations .. 132

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D Case Definitions 133

. . . . . . E . Triple Decomposition in an Unsteady Incompessible Engine Flow 135

Nomenclature

a Center point length of connecting rod B

B Width of piston chamber; Bottom Position of data capture plane

b Radius £rom the center of the craak wheel to the connection to connecting

rod B

C m Crank Angle Degree

CL Clearance

c& Particle displacement for component i

dI Interrogationregionwidth

do Diameter of the Inlet

i Matrix or vector component

I ( X ) Greyscale image at the coordinate X

I(X + s) Greyscale image at the coordinate X + s

k Engine cycle number

M Magnification factor

MI Measurement i n t e d

m Number of samples (2 5 rn N)

N Total number of samples

refkactive index for medium i

Number of pixels; Mean pressure

Pressure distribution in the piston chamber

Instantaneous pressure

Fluctuating pressure

Reynolds number

Correlation corresponding to the convolution of the mean intensiv

RD+ (s) Displacement peak with a positive s

RD-(s) Displacement peak with a negative s

RF (s) Correlation comesponding to the fluctuating noise

Rp (s) Self correlation peak

-4utocorrelation coefficient

S troke

Mean strain component

Fluctuating st rain component

Displacement vector

Signal to noise ratio

Strouhd number

Temporal component

At T h e interval

T Top Position of data capture plane

TL Turbulence Intensity

Ui; U(8, k)i; U(B)i Mean velocity component

Uc(8, k)i Mean cyclic velocity component

U, v, w velocity components

Ci; ü (6, k) Instantaneous velocity component

4; d ( 0 , k) Fluctuating velocity component

uiVMs Root mean square velocity component

Au, Spatidchangeinvelocity

V, Velocity of fluid in the piston chamber

V, Velocity of the piston

- Velocity of fluid at the inlet

AX; A x Distance between the velocity measurements

Xi; X Spatial coordinate

x, y, z Cartesian coordinate components

(Ç) Ensemble average of the function C

EC Error in function Ç

8 Crank angle

Change in crank angle

Dynamic viscosity of the fluid

Kinematic viscosity of the fluid

Density of the fluid

Uncertainty in the function C

Independent variable

Angle of incidence; angle between connecting rod A and connecting rod B

Angular rotation of the crank wheel

CHAPTER 1

htroduction

1.1 Background

Within engine research, the goal is to maximize power produced from the

combustion of iùels while minimizing pollutants and regdateci compounds. The

difficulty is that many variables affect these processes, e.g. the piston chamber

geometry, piston speed, inlet and exhaust port design, fluid dynamics, fuel composi-

tion, and ignition devices used. The focus of this thesis is on the flow fields produced

within a piston chamber of a rnodeled engine.

In a spark ignition engine, the spark plug ignïtes the fuel resulting in a flame

front propagating through the fluid mixture. Turbulent flow ahead of the fiame &ont

has been s h o w to increase the burn rate and propagation of the flame (Heywood,

1988) mhich indirectly reduces fuel consumption by dlowing use of a lower fuel/air

mixture (Choi, 1995). Heywood (1988) &O noted that by increasing turbulence

Ievels ahead of the flame, the engine is less susceptible to cycle-to-cycle variations

because the increase in bum rate improves mixture composition and temperature,

which increases the combustion efficiency.

There have been a number of experiments (both quantitative and qualitative)

to detennine the features of flow fields nithin reciprocating engines. Of these, the

measurement techniques have m d d y included Hot-wire Anemometry (HWA), Laser

Doppler Anemometry (LDA) and Particle Image Velocimetry (PIV). HWA is an in-

trusive technique, thus it is limiteci in engine research due to the presence of the

moving piston. W A also cannot yield information in reversing flows or in flows

with high fiequencies. LDA, on the other hand, is capable of obtaining information

at single points at higher fiequencies than HWA. PIV is a newer technique capable

of obtnining instantaneous velocity information over spatial areas. This is important

in engine research as the combustion proces is dependent on the spatial structure

of the flow and its idluence on the fiame front.

Significant use of PLV techniques in piston chamber flows has been empIo_ved

for the last decade. Nino et al. (1992) compared measurements made wïth a two

color PIV and a LDV technique in a cylindrical piston chamber. Using a cylindrical

coordinate system, the results indicated that the tangentid Ensemble mean veloc-

ities (Ensemble means are descnbed in Section 4.4) were in good agreement (error

of approximately 10%) for the crank angle degrees (CAD) 0" and 20°, however,

at CAD 340° larger discrepancies between the two rnethods were found (error of

approximately 30%). No indication of why the discrepancies occurred was given.

Reuss et al. (1990) used PIV in a two-stroke combustion engine to show that PIV

was able to map fiow fields within a millimeter of the propagating flame. The ex-

periment failed to measure velocities within the flame and b m e d gas regions due to

low particle densities and random particle displacements. Driscoll et al. (1994) were

able to determine the complete flow fields including the flame. The outcome of the

experiment served to show the interactions of a 0ame in a field of a toroidal vortex.

Tabata et al. (1995) used PIV with a planar laser induced fluorescence technique,

which measures the fluorescence of the fluid, to compare a fuel injection system to

a conventional premixed fuel/air mixture in a 4 valve spark ignition engine. Con-

clusions show that the optimization of the mixture distribution was very effective

in increasing combustion stability under lean (low hie1 to air ratio) operating con-

ditions. Trigui et al. (1996) used 3-D Particle Tracking Velocimetry (PTV) in a 4

valve pent roof engine with water as a working fluîd. The results indicated that the

cycle-to-cycle variations decreased with more stable and hi& intensity dominant

flow structures such as swirl (fluid rotation about cylinder &) and tumble (fluid

rotation normal to the cylinder axk).

Use of water-analog engines has been of much interest over the past 20 years.

With water as a working fluid, Ekchian and Hoult (1979) investigated streaklines a t

different crank angles and different speeds in a cylindrical, phiglass piston cham-

ber seeded with neutrally buoyant particles. A centrally located valve was used

for the entry and exit of fluid. The results indicated that when toroidal vortices

were present the flow was highly repeatable. Arcoumanis et al. (1987) did a sirni-

lar experiment with an optical plexiglas cylindrical engine. The crank wheel was

driven at a constant speed of 200 RPM and injection of fluid was simulated at the

center of the valve. The findings concluded the injected Buid had a d e h i t e effect

on the flow field as compared to a one without injected fluid. Khalighi and Huebler

(1988) captured streaklines using a 2-W- argon laser with a cylindrical dual-intake

valve water analog engine seeded with neutrd density, spherical Piolite particles

of 150 - 200 pm in diameter. Later Khalighi (1990) using the same experimental

se t-up but wit h different valve configurations, found t hat in-cylinder flow structures

were strongly affecteci by changes in the inlet configurations. Both quantitative and

qualitative measurements were performed by Durst et al. (1989) in a cylindrical

glas piston chamber with a centrally located orifice. A mixture of dibatylphalate

and diesel oil was used as the fluid to eliminate refkaction effects by index matching

the fluid with the cylindrical glas piston chamber. By va,ying the piston speed and

clearance they were able to detennine a number of effects. First the transition to

turbulent flow occurred for a Reynolds number (based on the piston velocity and

the diameter of the chamber) as low as 125. The flow was initially lamina until

the primary vortex came in contact with the piston surface. Second, the flow field

was strongly dependent on the clearance but only weakly dependent on the piston

velocity. Using a similar experimental setup Durst et al- (1992) investigated cycle-

to-cycle variations at a point in the flow. At low piston velocities (4 = 7mm/s) the

velocify was found to have little variation for Merent piston stroke and clearance

settings, however at higher piston velocities (V, = 15mm/s), the flow was found to

have cycle-to-cycle variations and was dependent on the stroke and clearance. Stier

and M c o (1995) used a quantitative laser induced photochexnicd anemometry in

an optical quartz water analog engine with a centrdy iocated valve. They con-

sidered the changes in the flow field by changing the engine speed and valve lift,

where engine speeds were below 10 RPM. Denlinger et al. (1998) used 5-D PTV in

a cylindrical water analog engine with a 4valve pent-roof inlet. Two inlet valves

were used with the second normalized to 10% of the valves lift. An inlet port

divider was angled towards the k t valve, to induce swirl. The hdings indicated

that during the intake stroke, flow fields were highly three dimensionai and it was

seen that the primary vortex did not emerge untii the latter part of the intake stroke-

1.2 Turbulence in Engine Flows

In attempt to understand better the physics of engine ftows, the extraction

of turbulence from instantaneous velocity measurements is of great importance.

Traditionally researchers have viewed the instantaneous velocity, 738, k)i, of a fluid

in an engine as random fluctuating, u'(9, k)i , (or turbulent) velocities superimposed

on a mean, U(9, k)*, (or bulk Bow) field (Dent & Salama, 1975). For a point in an

engine, the flow is dependent on both the crank angle (6) and the engine cycle (k).

Therefore the turbulent velocity component can be written as,

Experimentdy the instantaneous velocity can be determined. However, the diffi-

culty lies in calculating the mean (or turbulent) velocity. A common approach has

been to assume that the mean is independent of the engine cycle, reducing equation

1.1 to,

Taking N samples of the instantaneous velocity for a crank angle the mean velocity

can be detennined using an Ensemble average where,

Equation 1.3 neglects variations from the mean in each cycle and, from equation 1.2,

int erprets the cyclic variations as turbulence. Lancaster (1976) suggested t hat the

mean velociv durîng each cycle could be found by assuming that it was composed

of a cycle independent component U(8)i and a crank angle independent cornponent

Here, U(B)i was found using equation 1.3 and U(k) i was determined by integrating

over a presumably short segment of the cycle (AB),

In another approach to determine U(8, k) iy Hall et al. (1986) took the Fourier Trans-

form of the instantaneous velocity profile for an engine cycle and asswned that by

setting all the fiequencies above a certain cut-off fkquency to zero, leaving only the

low frequency components, and then taking the inverse of the transform the result

would be the mean velociw component. The difJicul~ with this approach is deter-

mining the cut-off frequency for each cycle. Newer methods in engine research have

used Wavelet Transforms to decompose the flow into mean and turbulent quantities

(see Wiktorson et al. (1996) and Ancimer et al. (1998)). Wavelets are unique as

compared to Fourier Tkansforms as they resolve both crank angle and fÎequency in-

formation in the flow. For ail methods (with exception to the Ensemble average) the

mean U(6, k)* velocity component required single point measurements for a number

of crank angles, typicaily obtained from LDV or HWA. With two-dimensional Pm

data Reuss et al. (1989) used a fiequency cut-off to determine the mean velocity

component. In an example using twcxiimensional PIV data measured fkom flow in

a pipe, Zubair (1993) used a Wavelet Transform to analyze the vorticity field. The

result of this suggests that Wavelets can be v e l useful with PIV data in an engine

flow.

1.3 The Present Study

Focusing on interests wit hin reciprocating flows, a fully optical water-analog

engine model has been designed and constmcted for use with PIV as weU as con-

struction of a timing systern to resolve individual crank angles wïthin an engine

cycle. Two-dimensional flow field measurements have been taken w i t h the model.

Veiociw data was coilected following the piston surface for crank angles from 120"

CAD (near the middle of the intake stroke) to 180' CAD (end of intake/ begin-

ning of the exhaust stroke). During this portion of the cycle, the piston velociw

decelerates and changes occur to the fiow.

1.4 Objectives

The main objectives are as follows:

a Design and Construction of a fully optical reciprocating engine

a Setup of the PIV systern to capture images at specific crank angles

O Investigate the flow field near the piston surface with Particle Image Velocime-

trY

1.5 Significance of Work

The main contribution of this work are as follows:

O Quantitative study of velocity fields in a square geometry

O Investigation of flow fields near a piston surface

a Extraction of terms from the equations of motion for a fluid

CHAPTER 2

Optical Water Analog Engine

2.1 Overview

Before the optical water analog engine is discussed in detail, it is necesary to

give the reader an overall picture of the assembly and define terrns. Figure 2.1 shows

an overd set-up of the flow cell. Figure 2.2 shows a sketch of the engine assembly

with each part labeled.

2.2 Dimensional Analysis and Similitude

The flow ceil is used to simulate the working conditions in the piston chamber

of an engine. However, since typicd automobile engines operate at rates of the order

103 revolutions per minute (resulting in high low velocities) coupled with the high

Figure 2.2: Engine Assembly

cost of building equipment to measure these large velocities (see (Jackson et al.,

l995)), it was decided to replace the working fluid of an engine (air) with one that

would allow lower velocities while maintainhg similitude within the constmcted en-

@ne.

Nine parameters are used in deterrnining the velocity in the piston chamber

( ) These are: velocity of the piston (V,), velocity of the inlet jet (V,), the

stroke (S), the width of the piston chamber (B), the clearance of the piston (CL),

the orifice diameter (d,), the density of the fluid (p) , the dynamic viscosity of the

Buid ( p ) , and the pressure distribution in the piston chamber (P,), see figure 2.3.

Using Buckingham's Pi Theorem (Potter & Wiggert, 1991) the following functional

relation is defined.

Figure 2.3: Variables for Engine Similitude, see equation 2.1 for variable definitions

From equation 2.1, complete similitude requires that the engine mode1 match the

six dimensionless numbers. These are a Euler number (&), four Reynolds numbers V B v s (F, +, Y , and F) and an inverse of a Strouhal number (2). The Strouhal

number, defined as the ratio of an oscillation to a velocity scale. It is noted that

the piston velocity is a function of the angular rotation (w) of the crank wheel (See

Appendix -4 for derivation),

where a is the center point length of connecting rod B, b is the radius from the

center of the crank wheel to the connection of connecting rod B, and 8 is the crank

angle. Thus the Strouhal number is,

-- O + f sin 8 cos O (1 - (! sin O) *) '1 is the Length ~ a l e and u is the

fiequency. In previous attempts at maintaining dynamic similitude in engine mod-

eis (Ekchian and Hoult (lgïg), Choi (1995)) only the Reynolds number based on

the mean piston velocity and the diameter of the piston chamber has been used.

Thus, in order to generate lower velocities w i t b the engine a t a 1 : 1 scale only the

dynamic viscosity should be lowered. With a viscosity 17 times lower than air, water

was a good choice as a working fluid. Use of water prevented a true çimiuiation of

engines flows by the inability (under normal conditions) to cornpress water during

the exhaust stroke. However the intake stroke of a real engine flow can be assumed

incompressible (Khalighi & Huebler, 1988).

Important considerations are giveo to the optical properties of the flow and to

the piston chamber. PIV is used to track images of illuminated particles in a flow

to determine velocity fields. This requires that the piston chamber be built such

that it is transparent in the location required for a laser sheet to enter the chamber

and the location where a camera can obtain images. To obtain a tme undistorted

image of the flow, light scattered from the particles must travel in paths paraiiel to

one another. This is important in order to obtain the exact image of the object in

the flow as captured in the camera. However, when light travels through different

media the light's path is refkacted, obeyhg Snell's Law,

where nl and nz are the index of refiactions for the two media the light passes

through and the and & are the angles between the light's path and normal to the

12

boundary between the difïerent media (see figure 2.4). Within the piston chamber,

Figure 2.4: Refkaction of Light

the light scattered from the particles travels through three media, the fluid within

the piston chamber, the piston chamber wali, and the surrounding environment. If

it is assumed that the index of refraction for each medium is different and noting

that a typicai piston chamber is cylindrical in geometry then, using Snell's Law, it

can be seen that the light rays traveling through the piston wall are not parallel.

Thus when the image of the flow is captured it wili be distorted (see figure 2.5).

To overcome the problem of optical distortion two possibilities exist. First, it

is possible to make the c m t u r e of the piston chamber wall infinite (e-g. square

geometry), therefore there is no distortion. The second solution is to match the in-

dex of refraction between the media with curved interfaces. Stier and Falco (1994)

used a glas cylindrical chamber where the fluid used inside the piston chamber was

index-matched with the glass. A rectangdar glass box placed around the cylinder

Figure 2.5: Influence of Engine Geometry

and fikd with the same fluïd aiiowed light to pass through the curved surface with-

out any difhaction.

2.4 Piston Chamber

For the purpose of this study it was decided to use a square, glass section for the

piston chamber, see figure 2.6. The square geometry (sides with infinite curvature)

prevented any distortion caused by refkaction of the Light. However, this geometry

raises concems about similitude with respect to a real engine (cylindrical geometry).

The four rectangular glass sections were fastened with an adhesive silicone epoxy for

a 50 mm x 50 mm inside cross sectional area. For a passenger car engine, a typical

stroke (Iongest distance the piston travels in one direction) to bore (diameter of

piston chamber) ratio is between 0.9 - 1.1 (Heywood, 1988). Using a cross sectional

-- . ----

Figure 2.6: Glass Section

Iength of 50mm in the mode1 engine, a typical stroke is between 45 and 55mm.

The length of the piston chamber was chosen to be 155 mm to provide additional

space for a variable stroke length. Figure 2.7 shows the end plates which the piston

chamber is set into and fastened with epoxy. The end plates allow pieces to be easily

added or removed with minimal stress.

2.5 Inlet

To control the flow of water into the piston chamber an end section and an

inlet tube were added to the piston chamber, figures 2.8 and 2.9 . Figure 2.8 shows

the end section with a centrally located orifice. This piece is connected to the end

plate of the piston chamber with porous rubber placed between the two plates. This

seals and aligns the two sections when a force is applied to clamp the two sections

together. Next the inlet tube (see figure 2.9) is fastened into the orifice using epoxy.

It was expected that, due to the sudden expansion into the piston chamber and the

motion of the piston, pressures would be relatively low in the inlet. If there is too

Figure 2-7: End Plates

Figure 2.8: End Section Met Addition

Figure 2.9: Inlet

small an inlet or too great a piston velocity, the pressures would drop below the

vapor pressure causing cavitation, structural damage, or aUow air to be drawn into

the piston chamber. Thus the diameter of the inlet was chosen to be 25.4 mm. A

hose from the water tank was connected to the end of the inlet tube with a metal

clasp. A s m d hole was added to the inlet tube for a bail valve to be placed to

adding seeding to the flow, see figure 2.1. A plastic barrier was added to the valve

to prevent large amounts of water fiom escaping when the valve was open. Seeding

was added to the flow by puncturing the plastic with a syringe. Some water was

lost when the M n g e was withdrawn but it was found that the hole would quickly

expand and close preventing water hom escaping. The valve was then closed.

2.6 Piston Assembly

The piston consisted of three sections: the piston head, connecting rod A, and

connecting rod B. These are shown in figures 2.10,2.11, and 2.12 respectively. Figure

2.10 is a sketch of the piston head. The piston head consists of four plexiglass sections

and six teflon sections. To prevent Ieakage of water through the space between the

piston and the piston chamber walls, teflon Iayers were added. Connecting rod A

was then screwed into the piston head and connected with a metal pin to connecting

Figure 2.10: Piston Head

Figure 2.11: Connecting Rod (A)

:.r&iE?IaL 57EEL

Figure 2.12: Connecting Rod (B)

rod B, allowing connecting rod B to move fkeely about the (2, z) axis. It should be

noted that the Iength of connecting rod B has an effect on the piston velocity profile.

The theoretical piston velocity (see Appendix A) can be non-dimensionalized with

the angular velocity of the crank wheel as foLlows,

Figure 2.13 shows this equation plotted for = 0.27 (present set-up) and 3 -t O. It

can be seen that (for a fixed b) as a approaches infinity the non-dimensional velocity

profile becomes symmetric with a maximum at CAD 90". It can also be seen that for

the c u v e with = 0.27, from CAD 120"-180" the velocity can be weil approlrimated

with a linear profile. Once the piston was assembled, it was then mounted on the

crank wheel and motor. The total stroke (CL + S) was then measured as a function

Figure 2.13: Theoretical non-dimensionalized Piston Velocity

of the crank angle and is tabulated in table 2.1 and plotted in figure 2.14. By

comparing the theoretical and measured displacements a difference is found. The

magnitude of the difference is seen to increase from CAD O" - BO0 and then it is

found to decrease again from CAD 90" - 180". The piston displacement between each

GAD was determined and plotted in figure 2.15. Here, between CAD O" - 80°, the

measured piston displacement is greater than the theoretical displacement. However,

eom CAD 90" - 180" the reverse occurs and the theoretical displacement is greater

than the measured displacement. It was found that when the motor was runnïng

the crank wheel had a very srnail oscillation which codd explain the discrepancies.

It is also suggested that the extra spacing between the joints in the piston assembly

caused some of the discrepancy.

Table 2.1: Theoretical and Measured Piston positions for CAD O" - 180"

2.7 End Section

An additional endplate was placed on the side opposite the inlet. Porous

rubber mas placed between the piston chamber end plate and the end section (figure

2.16) to seal the two sections. Four 10 mm diameter holes have been placed in the

end section and short metai tubes were then epoxied within each hole and sealed.

Plastic tubing was connected to each metal tube which provided a sealed connection

with the secondary water ta&. Finally a metal support, shown in figure 2.17, is

mowted on the end section which guides the piston dong a specified path. Within

the piston support are two plastic O-rings. When the 6rst connecting rod is placed

in the piston support, a seal is made.

Figure 2.14: Piston Displacement fkom x=O

Crank Wheel

The crank wheel (figure 2.18) is mounted onto a rotary motor thai; drives the

piston. Four holes were placed on the crank wheel where the comecting rod could be

attached to produce strokes of either 47.6 , 54.0 , 60.4 , or 63.4 mm. Lines were also

engraved into the crank wheel at one degree intervals. A circular plate (see figure

2.19) was then placed around the crank wheel and held with screws. With a mark

placed on this plate, a dinerential angle could be determined. A metal obstruction

was mounted on the plate for image acquisition.

2.9 Water Tanks

Two water tanks are connected to the piston chamber to supply water. First a

5 7 cm diameter cylindrical water tank wit h a height of 120 cm supplied water to the

... . .- - -

Figure 2.15: Piston Displacement between CAD

Figure 2.16: End Section (Piston Side)

Figure 2.17: Piston Support

M A T E R I A L : STEEL

Figure 2.18: Crank Wheel

Figure 2.19: Crank Angle Measutement Device

working section through a 3.6 m long pIastic tubing with an inside diameter of 3 cm.

The second tank (36cm high by 25 cm in diameter) supplied water to the opposite

side of the piston, submerging the working section. During the intake stroke low

pressures in the piston chamber mere thought to cause water to be drawn into the

working section through the side of the piston. By measuring the amount of mater

displaced from the secondary water tank and the t h e it took to displace the water,

it was found that the water was being drawn fiom the tank at a rate of 14.?cm3/s.

With the crank wheel moving (on average) a t a angular rotation of 27 RPM and

assurning that ail the water from the leak is drawn in during the intake stroke,

approximately 33 cm3 of water is a result of the leak. This accounts for 18% of the

fluid volume in the piston chamber. By hcreasing the number of teflon layers, to

produce a stronger barrier, the motion of the motor became unsteady due to the

increased fiction. -4 gravity head given to the side opposite the working section

was to reduce the leakage of water during the exhaust stroke. Changing the gravity

head on the secondary water tank seemed to have little effect on the Ieakage during

the intake stroke. With the present set-up this problem could not be solved.

2.10 Structural Stability of System

Due to the motion of the piston, care was taken to assure that minimal bending

and shear moments were present in the g l a s joints and the joints between the end

sections and the gIass section. Four brackets (figure 2-20) were mounted on the flow

cell and then to a metal base plate to minimize shearing. Four threaded rods were

then added to align the piston support, ensuring a parallel surface for the piston.

The rods prevented the two end sections fkom moving independently. It was found

that when the piston was in motion a large shearing force was produced in the upper

part of the flow cell resulting in a horizontal motion dependent on the piston stroke.

Four braces were then added to prevent the upper portion from moving.

Figure 2.20: Structural Support

CHAPTER 3

Experimental Set-up and Procedure

3.1 Experimental Set-up

The flow fields within the optical water analog engine were captured with PIV.

-4 clearance of 19.2mm was used in the present experiment and the piston stroke

was set to 54.0 mm. A 1/4 horsepower direct curent motor was connected to the

piston assembly to drive the fiow. The controller for the motor was kept a t a con-

stant setting throughout the experiment, giving the piston a mean speed of 49 -/S.

Using the mean piston velocity and the wïdth of the piston chamber, the Reynolds

number achieved in this experiment was 2430. Durst et al. (1989) suggested that

transition Çom a laminar to a turbulent flow occurs at a Reynolds number of 125

(based on the piston velocity), thus the flow was turbulent once V, > 2.5mm/s.

The main water tank was placed 0.99 m above the centerline of the inlet and was

filled until the water level was 1.10 m above the centerline of the inlet (see figure

3.1). The second water tank was placed 0.69 m above the centerline of the inlet.

Reverse osmosis (RO) water was used for the experiments to ensure that there were

no large particles in the water before the addition of seeding particies with the PIV

measurements. -A cover was placed on both tanks to minimize dust accumulation.

3.1.1 Part icle Seeding

The seeding used is spherical, silver coated particles +th a hollow g l a s core

and a relative density of 1.65. The particle seeding has a mean diameter of 15 pm

with the diameters ranging from 10 - 30 pm (Potters Industries Inc., 1999). With

Figure 3.1: Experimental Water Level Setup

approximately 41L of RO water used in the experimental set-up, 6.4g of particles

was required to seed the flow (see Appendiv C for calculation). This produced a

measured value of sixteen particles in a 32 x 32 pixel area. When the piston was in

motion, particle densities reduced fÎom 16 to 4 particles in a 32 x 32 pixel area. This

was thought to be caused by the influx of water through the teflon se& during the

intake stroke which allowed the passage of water but trapped the particle seeding.

It was seen that the plastic tubing, providing the water fiom the main tank, also

trapped seeding. To increase particle densities in the chamber for the duration of

an experimental nui, an additional 10 grarns was added to both tanks and 5 grams

of seeding mas directly injected into the piston chamber, with little effect. As a

solution to this problem larger areas were used to increase the particle densities in

each area. Final seeding densities are found in table 5.1

3.1.2 Data Acquisition

To determine the velocity- fie& within the engine chamber an autocorreIation

method is used (see Section 4.2 for details). This method uses double exposed

images of the flow and determines the mean particle velocities within a smaller area

of the image. Figure 3.2 shows a section of a double exposed image of the flow,

exposed at times tl and t2. By determining the particle displacements in the known

time interval the velocity field can be detennined. To obtain Ensemble statistics for

I

Figure 3.2: Double exposed image of the flow

specific crank angles the PIV system, used for temporal measurements, was altered.

First, a triggering device was required to signal the set-up at the speciiied crank

angle. This was done with a metd obstruction on the crank wheel and mounting

an interrupter type optical sensor in the path of the metal obstruction, figure 3.3.

Once the metal obstruction blocks the light, the opticd sensor outputs an electric

signal. This signal tnggers the camera to start a new hune with an asyncronous

reset, tnggers the two lasers to puise during the t h e the camera's shutter is open,

and trïggers the barnegrabber to capture the incoming camera frame. The timing

Figure 3.3: Triggering Setup

required to initiate the fiamegrabber is longer than the tirne needed to pulse and

capture the double exposed image, t herefore the signal from the optical sensor was

split into two paths. The first was a direct connection to the fiamegrabber, the

second was connecteci to the Miro delay circuit, which provides the time delay.

From the Miro delay circuit the signal is split into two simultaneous puises. The

first pulse was a W, 12Op negatively going T'TL signal which was sent to the CCD

camera. This signal triggers the asynchronous reset and resets the camera to the

beginning of the b e . The second pulse was a 1.5q 120p positively going TTL

signal which mas sent to the delay generator. The input pulse triggered the delay

generator to send four output pulses to the laser. For each laser beam two signals

are required. First, the lasers flashlamp is triggered. Once triggered, the flashlamp

provides the laser rod with energy required for the laser beam. The second signal

t n g g e ~ the lasers quality switch (or Q-switch) and acts to increase the laser peak

power. A dual laser cavity was used in this experiment, and four triggers were

required. The first output pulse was delayed 0.0166s and was sent to the laser A's

flashlamp. This delay was required to set-up the laser to pulse during the camera

frame. The second output was deIayed 0.016752s and went to laser A9s Q-switch.

This delay was composed of the first delay of 0.0166s and an additional 1 5 2 p which

was required to obtain the beam. To obtain a time separation of 609p between the

fmt and second beam, the third output, delayed 0.017209~~ was sent to laser B's

flashlamp. This delay was composed of the nrst 0.016752s plus an additional 5 3 8 ~ .

Finally the fourth output was sent to laser B's Q-switch and was delayed 0.017361s.

This delay was composed of the first 0.016752s plus the third output 5 3 8 ~ plus

the b a l 152p required to power the laser. A diagram of the data acquisition

process is shown in figure 3.4. Figure 3.5 shows the individual signals used and the

relative time mhere they occur, once the trigger is signaleci. The figure also shows

the laser pulses and the anaiog output of the image from the camera. The camera

out shows the synchronous stripped signal that was used for timing, at the end is a

representation of the analog signal.

Figure 3.4: Data Acquisition

The laser used is a CONTINUUM MINILITE dual cavity Neodyymium-Yttrium

Figure 3.5: Signal Timing

.Muminurn Gamet (Nd:YAG) laser which produces a verticaily polarized green light

of 532 nm wavelength. The beam size is approxbately 3 mm in diameter and emits

a beam of 4.0 MW peak intensity for 5 f 2 ns duration (Continuum, 1999). To ob-

tain tmo-dimensional particle displacements it is necessary to create a iight sheet of

s m d thickness in the flow to ensure that only the particles in the path of the light

sheet are illuminated (see figure 3.6). -4 cylindncal lem of -25.4 mm focal length is

placed in the path of the laser beam to diverge the beam, a spherical lens of 250 mm

focal Iength is placed below the cylindrical lens, and in the path of the laser beam,

to illuminate a region a t the center of the piston chamber. The sphencal lens con-

verges the beam to create a point of minimum thickness located a t the center of the

piston chamber, At this point the camera was focused to capture the images of the

flow. This lem set-up produces a sheet of light 25 mm in width and 1 mm thick in

the working section. To produce the laser sheet in the x-z plane a mirror is used to

reflect the beam 90". A Stanford Research Mode1 DG535 digitaI/pdse generator is

used to trigger the laser pulses at appropriate tirne steps and a PULNIX TM-9701

series CCD camera was used to capture the images horn the flow. A RAPTOR

Series framegrabber fkom BITFLOW used in W170 format to obtain images (see

Figure 3.6: Experimental Setup

table 3.1) therefore the camera was set to interlace mode. The digital camera &O

had an asynchronous reset that d o m the camera to be reset by an extemal trigger

for uniform timing with the engine crank angle.

RS- 170 monochrome video standard format 0 640 pixels x480 lines 0 ,4nalog, interiaced

525 lines per fiame, 485 active lines per frame 0 Line scan frequency 15.734 kHz 0 29.97 frames/s

Table 3.1: RS-170 Video Format, fkom ( M e l , 1998)

3.2 Experimental Procedure

3-2.1 Coordinate System

A rectangular Cartesian coordinate system was used for this study (figure 3.7).

The origin of the spatial coordinates centered at the entrance to the flow cell with the

(x, y, z ) components as the stream*, spanwise and vertical directions respectively.

Figure 3.7: Coordinate System

The coordinate system for the corresponding velocity components (u, v, w) are also

shown in the figure 3.7.

3.2.2 Engine Cycles

The temporal evolution in engines is described by cycles. In a tmo stroke

engine one complete cycle consists of two dinerent strokes, inlet and exhaust. This

is also equivalent to one complete revolution of a crank wheel. Starting when the

piston is at top dead center (nearest to the inlet) and moving the crank wheel in a

clockwise direction the change in angle is a Crank Angle Degree (CAD). Figure 3.8

show the piston position a t C.AD O", 90°, 180°, 270°, and 360".

3.2.3 Location of Data

Changing the location of the metal obstruction on the crank wheel, the crank

angle at which frame capture occurs is changed. The experiments were limited to the

50 DEGREES

- - - - - - - - - - - - -

Figure 3.8: Description of Crank Angle

intake stroke of the water analog engine due to the compressibility effects during the

exhaust stroke. Seven crank angles were chosen for this study CAD 120°, 130°, 140°,

150°, 160°, 170°, and 180". These positions capture the flow in the latter part of the

intake stroke. At each crank angle the center plane y = O was selected to obtain the

(u, w) velocity fields. Two regions were chosen from the flow field and are shown in

figure 3.9, T (top position) and B (bottom position). These positions were chosen

to capture the flow field resulting £rom the impinging jet on the piston surface. IR

addition, using the piston surface and the top of the connecting rod, these positions

were obtained with accuracy and ease. Focused on B or T, the camera was then

positioned normal to the x-axis and parallel to the y-& to minimize the refraction

effects from the glas chamber.

3 -2.4 Magnacation Factor Measurement

Each time the camera was moved it was re-focus to ensure that a clear image

of the flow was captured. Since PIV converts the number of pixels to a distance

Figure 3.9: Location of Data Capture Planes

measurement, calibration is required. The camera is focused on a scde and the

camera moved (without refocusing it) so that the scale is in focus. A series of

frames were then recorded of the scale at al1 measurement positions. By counting

the number of pixels (P) in a measurement interval (MI) the rnagnifcation factor

(hl) between pixels and actual displacement was found using,

CHAPTER 4

Data Reduction

4.1 Equations of Motion

The motion of an incompressible fluid can be found through seven govern-

h g equations, consisting of the Consenration of Mass, Momentum, and Energy.

With velocity being the o d y quantity measured, oniy the Conservation of Mass and

Conservation of Momentum equations (see Kundu (1990) for derivations) will be

considered here. First the Conservation of Mass is defined by,

where the ûi represents the instantaneous velocity and xi is the z* spatial coordinate.

The Conservation of Momentum for the case of a Newtonian fluid (the Navier-Stokes

equations) neglecting body force effects is,

where fi is the instantaneous pressure, t is time. The instantaneous quantities can

be decomposed into a mean and Buctuating quantity (Reynolds decomposition),

where Ui and P are the mean velocity and pressure components and the u: and p'i

terms are the fluctuating velocie and pressure components respectively. Next, if

the instantaneous quantities in equations 4.1 and 4.2 are Reynolds decomposed and

Ensemble averaged, they reduce to (see Kundu (1 990) for derivations) :

1 II III IV

Equation 4.5 is the Reynolds equation. On the leh hand side of the equation, 1 and

II represent the unsteady and the mean advection of the fluid. Next III, IV, and V

represent the transport of moment- by pressure, viscous stresses, and turbulent

fluctuating velocities. Terms IV and V are also known as diffusion and Reynolds

stress transport respectively. Using equation 4.1 and Reynolds decomposing the

instantaneous velocity it can be found by inserting equation 4.4 that,

Two additional equations of importance are the equations for the mean and

turbulent kinetic energy. First, the equation for the mean kinetic energy can be

found by multiplying equation 4.5 by Ui- The turbulent kinetic energy equation c m

be found by subtracting equation 4.2 by equation 4.5, multiplying the result by u:

and averaging. The equations for the mean and turbulent kinetic energy (Kundu,

1990) are,

Mean Kinetic Energy equation,

Turbulent Kinetic Energy equation,

1 II III IV

au, -2v(s! -) - (u!u'-) - t3 83 a azj

where Sij is the mean strain defined by,

and s; is the fluctuation strain defhed by,

In equations 4.7 and 4.8, 1 represents the rate of change of kinetic energy. On the

right hand side, the tenns II, III, and IV represent energy transport fkom the pres-

sure, viscous and Reynolds stresses respectively, while V represents the dissipation

of energy. Next, term VI hom the mean kùietic energy equation (equation 4.7),

represents a loss of energy to the turbulent motion, while in the turbulence kinetic

energy equation (equation 4.8) VI represents a production (or gain) of energy fiom

the mean motion (Kundu, 1990).

It can be seen fiom equations 4.1 to 4.8 that by measuring the instantaneous

velocity within an engine a significant amount of idormation can be gained about

the flow-

4.2 Inst antaneous Velocity

In order to transform the double exposed flow images to particle displacements,

I N S I G H F M nom TSI was used with an autocorrelation algorithm. First, the

captured frames were broken down into smaller, interrogation regions. It is desired

to maximize the number of interrogation regions, as o d y one vector is determined

for each interrogation area. However, a Iower limit exists because the accuracy of

the displacement measurement is directly related to the number of particle pairs in

the interrogation region. Keane and Adrian (1990) suggested that the optimization

of a PIV system can be found by applying certain criteria. First, the number of

particles per interrogation region should exceed 10 - 20 to ensure at least 5 particle

pairs. Second, the magnitude of the displacement vectors are required to be l e s than

one-quarter the interrogation region size. This Lunits the loss of particle pairs due

to in-plane motion. Third, out-of-plane particle l o s is minimized by ensuring that

the velocity, perpendicular to the light sheet, is less than one-quarter the thickness

of the Light sheet divided by the time interval. Fourth, MIAulAt/dr < 0.05 assures

s m d velocity gradients by putting a iimit on the size of the interrogation region.

Fifth, the mean particle diameter should be approximately 1.5 pixels. Once the

optimal interrogation region was found, an autocorrelation algorithm is applied and

the result is a spatial autocorrelation coefficient R(s), for each interrogation region,

defined as follows,

where I ( X ) is the greyscale image at the coordinate X, I (X + s) is the greyscale

image at the coordinate X + s, and s is the vector which d e h the separation.

Adrian(1988) suggested that the correlation coefficient was composed of several

components, see figure 4.1.

Figure 4.1: Plot of Autocorrelation Coefficients

The first component Rp(s) is the self correlation peak defining the correlation be-

tween each particle with itself. Both Ro+(s) and RD-(s) define the particle dis-

placement peak, but in an opposite direction. Physically, \ RD (s) 1 represents the

mean particle displacement. The displacement is determined by giving the flow an

assumed direction. Next, &(s) is the convolution of the mean intensity field. Fi-

nally, &(s) is the fiuctuating noise correlation which is causeci from noise in the

image. By ignoring the self correlation peak, the displacement is determined by

finding the next highest peak (see figure 4.2). As a pixel is the smdest resolv-

Particle Displacement in X Di-on (pixel]

Figure 4.2: Plane View of Autocorrelation Peaks

able resohtion, the correlation peaks can only be determined to pixel accuracy.

Therefore a parabolic peak-finding algorithm was used to find the correlation peaks

to sub-pixel accuracy. If there is a great deal of noise wïthin the image, there is a

probability that the wrong displacement peak will be extracted. I N S 1 G H P M uses

a number of checks to reduce the probability of choosing the wrong peak. For this

procedure three signal to noise ratio (SNR) parameters SNR1, SNR2, and SNR3

are used. The first, SNR1, is the ratio of the paxticle dispIacement peak RD to the

zero peak intensity &. SNR.2 is the ratio of the displacement peak RD and the

first noise peak and SNR3 is the ratio of the displacement peak RD and the average

intensity. These values were set to values of 0.05, 1.5 and 0.1 for SNRI, SNR2,

and SNR3 respectively (TSI Inc., 1996). If any of these checks were judged invalid

(SNR< t hreshold) t hen the mean displacement for the interrogation region was left

undefined. Once the particle displacements (4) were det ermined, the instant aneous

velocity was found using the following relation,

The time interval At used for the experiment was 609ps and M was found through

the pixel-displacement calibration discussed in section 3.2.4.

4.3 Velocity Validation and Extrapolation

Once the instantaneous velocity fields are calculated it is necessary to discard

any spurious velocity vectors. M e 1 et ai. (1998) suggested that a spurious vec-

tor has a magnitude and/or direction that differ signincantly fiom its surroundhg

neighbors. This is an ambiguous definition which suggests only that the velociiy field

be smooth. -4 better technique to determine spurious vectors is to check continuity

at each point. This however requires that ali components of velocity be measured.

In the present study it was found that the direction of the velocity vectors changed

significantly over small distances, thus only the magnitude of the velocity vector

was used to locate spurious vectors. It was determineci, that if the magnitude of a

velocity vector was greater than 1.5 times the global median then the vector was

an outlier and discardeci. This scheme was chosen over the local median scheme

as described by Westemeel (1994) because it was found that when a number of

spurious vectors were close together, the local median scheme would fail to recog-

nize the vectors as spurious. The global median, however, successfully extracted

these vectors fiom the velocity field. Since a number of spurious vectors (with large

magnitude) were expected, the median would be biased towards a larger value. It

was thus difficult to determine a lower threshold for the validation scheme- For this

reason no attempt was made to validate lom magnitude vectors. FinalIy, through

trial and error, the threshold of 1.5 produces optimal results with the current set-

up. It should be noted that this validation technique may fail in experiments with

reversing flows where the global mean and median would tend towards zero.

After validation of the vectors, the velociw field is extrapolat ed by searching

for points where velocity vectors with zero magnitude are found and then averaging

the eight surrounding values to interpolate a velocity. A minimum of three sur-

rounding values was considered s e c i e n t to determine an interpolated vector. Once

al1 the extrapolated velocity vectars were determined they were added to the origi-

nal fieid- It is expected that the extrapolation will have an effect of srnoothing the

inst antaneous velociq field.

4.4 Turbulence Averaging Techniques

-4s discussed in Section 1.2 there are two main averaging techniques used to

extract fluctuating quantities in engine research: Ensemble and Cyclic methods.

DifEerent extraction methods arise fkom the difficulties in different iating mean ve-

locities in an unstationary, turbulent engine flow. It is usual practice in engine

research to collect velocity samples during specific CAD within each cycle. To ob-

tain a mean value one can use an Ensemble average which assumes that the samples

are independent of the engine cycle. However, due to variations of inlet and bound-

ary condit ions, the samples are dependent on the cycle suggesting the averaging

method should be used within each cycle. For the present study an Ensemble aver-

age approach is taken, as PIV gives results at a particular CAD not over an entire

cycle. The Ensemble average of a velocity is defined as,

The fluctuating velocity (d (8, k)i) is then determineci by Reynolds decomposition,

Problems resulting from the use of the Ensemble averaging technique nrill be the

smoothing of data and when used with the Reynolds decomposition, will resdt in

over-estimating the turbulent energy (Sullivan et al., 1999).

4.5 Convergence of Velocity Components

In order to determine whether a s a c i e n t number of samples have been col-

lected the convergence of the mean U and W components of velociq were calculated,

where m is a subset of N and has a value 2 5 m 5 N . If the set of instantaneous

velocity vectors a t a point have a Gaussian distribution then as the number of

samples increase, the mean velociw d l converge to a single value, or the difference

between the mean velocity with m samples and that of m- 1 samples will be zero. By

normalking this difFerence with the total number of samples used and converting

this into a percentage, convergence of the mean velocity was achieved when this

quanti@ is less than 10%.

4.6 Tbrbulence Intensity

To detennine the relative magnitude of the fluctuating velocities to the mean

velocities a t each point, first an estimate to the average magnitude of the fluctuating

motion ( Z L ~ , ~ ~ ) is,

The turbulence intensity was then defined as,

-4s compared with Catania and Mittica (1987) and Choi and Guezennec (1999),

where ukRMS W ~ S normalized with the mean piston speed, here the turbulence in-

tensity was determined by normalizing uiRMS with the mean velocity component

at each point. This was done in order to predict the 'local' turbulence intensity.

4.7 Velocity Gradients

Velocity gradients, important for equations 4.4 to 4.8 were determined using

a difference scheme. If the velocity gradient was determined dong a boundary then

either a forward or backward difference scheme was used,

where 4 X is the distance between the u!, CI{-', and u!+' samples. Any velocity

gradients away fiom the boundary of the image were determined using a central

difference scheme,

The second order velocity

and central ciifference schemes,

gradients were also calculateci using forward, backward,

4.8 Piston Velocity Measurement

The piston velocity was determined by the method shown in figure 4.3. First a

white particle was painted on connecting rod B and its image was captured (topleft

of figure). Three points were chosen fkom the particle and measured (bottom-le&

of figure). The piston was then set into motion and pictures of the particle were

captured (top-right). The images of the rnoving piston resulted in an elongated

particle image due to the camera's 30 Hz shutter speed. Next, by locating the

representative points on the elongated particle, the tme particle displacement can

be found (bottom-right of figure). By dividing the displacement by the shutter speed

and the magnification factor, the velocity of the piston was found.

Figure 4.3: Determination of Piston Velocity

Error Analysis

The experimental set-up was used to obtain instantaneous velocity fields at

specific crank angles, using equation 4.13. For determining the accuracy of the

instantaneous velocity estimate, four e m r categories are defined: errors in the crank

angle, errors in the particle displacement, errors in the time interval, and errors from

the magnification factor. Each are defmed in the following sections and an estimate

of each is given. These estimates are then used to determine errors from calculating

different quantities (Appendix B).

4.9.1 Crank Angle positioning Error

The angles etched on to the crank wheel had an accuracy of f O.s0, or from

equation A.4 produced an accuracy (worst case scenario) in the engine chamber of

~ t 0 . 2 mm- Fkom the images, it was found that the piston surface changed locations

between samples for a particular crank angle. By measuring the ciifferences in the

piston surface position it was determined that the crank angle position bas an ac-

curacy of =t10 pixels or 3~0.14 mm. An estimate to the total accuracy of the crank

angle measurement is f 0.34 mm. This error will not influence the instantaneous ve-

locity accuracy, however it wiU effect the results when quantities at different crank

angles are compared.

4.9.2 Displacernent Error

Images were captured fkom the flow and stored for processing using PIV. Two

major sources of error exist in determining the particle displacements. The k t

source of error is fkom the autocorrelation met hod which determines the particle

displacements. A limitation of this method is that it can not resolve the sign of

the directional component. It is thus necessary to give the displacement algonthm

a preferred direction. Another diüiculty is that the camera can only obtain images

to &0.5 pixel accuracy, since a pixel is the smallest unit of measurement. To re-

duce this enor, subpixel peak finding methods are used. Huang et al. (1997) used

experimental data wïth particles of 2.8 pixel in diameter and seeding densities of

0.05 particies/pixeP. They found that the mean-bias error, dehed as the ciiffer-

ence between the actual and mean particle displacements, was 0.2 pixels. The RMS

error, d e h e as the deviation of the particle displacement from the sample mean,

was determined to be 0.1 pixel. These results were found using a cross correlation

algorithm and an autocorrelation scheme will give a higher error, since cross corre-

lation methods do not require direction to be deked, while autocorrelation does.

For this reason the s u m of the mean-bias and FUIS error was increased from 0.3

to 0.4 pixels. Other factors, not present in the previously reported experiments,

that atfect the correlation algorithm, are fkom in-plane particle losses, out-of-plane

motion, and large gradients in the flow. M e 1 et al. (1998) estimated the RMS error

fÎom different velocity gradients using simulateci data. Particle diameters used were

2.0 pixels and seeding densities were given 20 partides/pixe12. The results show that

the RMS error increased for increasing gradients and interrogation regions. For a

gradient of 0.05 pixeIs/pixel (estimated threshold for optimizing experimental data,

see (Keane & .4drian, 1990)) the RMS error for a 64 x 64 interrogation area was

reported to be 0.3 pixeIs. Rom similar experiments Raffel et al. (1998) deterrnined

that the in-plane l o s bias error for a 64 x 64 interrogation region was -0.01 pixels.

Another source of error is a result of deviations of the images captured to that of the

real flow which are introduced fiom the experimentd equipment. Using a particle

field with no velocity, Huang et al. (1997) estimated the error introduced from the

equipment was 0.0135 pixel.

In order to estimate the displacernent error, it was determined that this value

should be the summation of the factors Muencing the experimental data. The

summation of the experimental noise (0.0135 pixels), the correlation met hod used

(approximately 0.4 pixels), the error due to in-plane losses (0.01 pixels), and error

from high gradients (0.3 pixels) was 0.72 pixels.

4.9.3 Time Interval Error

Particles in the flow are iliuminated by triggering the laser. The time inter-

val is thus the time between laser pulses. Since the trigger is produced from the

delay generat'or, this is a source of error. The Stanford Research Model DG535

digital/pulse generator has a delay accuracy of approximately i l . 5 ns (Stanford

Research Systems, 1994).

4.9.4 Magnification Factor Error

the

E.w1

Using equation 3.1 the magnification factor could be determined. Since both

pixel measurement (P) and the measurement interval (MI) have errors c p and

respect ively, the magnificat ion error (eM) c m be det ermined as foilows,

Re-arranging this equation and noting that P = M x MI, the magdication factor

error is determined by,

M x ~ I I ~ E ~ E M = - M (4.26)

MI * €MI The scale used had an accuracy (eMr) of 0.05 mm, half the smailest scale rneasure-

ment. The accuracy of the camera ( e p ) was restricted to I O 5 pixels. By using

equation 4.26, error curves were developed for different int ervals of measurement

and difFerent magnification factors (see figure 4.4). This figure shows that as the

measurement interval increases the error is reduced. For this study, a measurement

of 8 mm was used which gave a magnification factor error of approximately f 0.5

pi.xels/mm.

4.9.5 S i i m m a r y

The error associated with the four categories was estimated as f 0.34 mm,

f 0.72 pixel, f 1.5 ns, and 3~0.5 pixel/mm for the positioning, displacement, time

interval, and mapification error respectively. Next , assuming that the probabüity

that all the data is within these error estimates is 0.99 and assiiming ail errors have

a Gaussian distribution then the standard deviation for the particle displacement,

the time interval, and the magnification factor are Q. = 0.3 pixels, gbr = 6.4 x

10-~ s, and QM = 0.2 pixels/mm respectively. Using equation B.l and noting

Figure 4.4: Error produced fkom different measurement intervals and magnification factors

that the magnification factor and the time interval are constant, the error for the

instantaneous velocity (neglecting the displacement error) was found to be f 6.6

mm/s. From the methods descnbed in Appendix B, a summary of the mean error

associated with the quantities calculated from the instantaneous velocities is show

in table 4.1. Finally, a sample calculation for the average uncertainty associated

with the *ion tenn can be found in Section B.6.l.

1 Ensemble Mean Velocity

I ~ l u c t uating velocity

Turbulence Int ensity

Reynolds Stress Transport (& (-uiu;))

Mean Viscous Stress Transport & (2vUiSij)

Mean Dissipation -2vSvSI,

f f a u Turbulence Production ( u p j )

1 Turbulent Viscous Stress Transport & (2u(u:s:,))

Turbulent Reynolds Stress nansport $ (- ) ( (ui) *u;))

Turbulent Dissipation -2v(s;,s$) I

Table 4.1: Error Estimates

CHAPTER 5

Results

5.1 Images

Figure 5.1 shows an inverted greyscale Mage of the fiow. The particle displace-

ments can be easily identified visually within this image, which is a good indication

that timing of the equipment is working properly. It is also noted that the piston

Figure 5.1: Negative image of Flow with Seeding

surface (shown as the dark, vertical line) is iiluminated by the laser. Due to a large

scattering of light, it is impossible to determine the displacement of the piston fiorn

the pictures. Using the method explained in section 3.2.4, the pixel displacement

factor was found to be 74 f 0.5 pixels/mm . With a frsme size of 640 x 480 pixels,

the size of the pictures obtained in the experiment were 8.6 mm x 6.5 mm.

5.2 Piston Velocity

The piston velocity profile was found for al1 crank angles, figure 5.2. Cornparuig

Figure 5.2: Piston Velocity Profile

the piston velociw during C-AD O" - 180" to the theoretical piston velocity found

from the % = 0.27 curve in figure 2.13, it can be seen that the two c w e s differ. This

suggests that the angular velocity is not constant but is a function of the crank an-

gle. Also, the piston velocity is found to be zero kom CAD O" - 10°, 160" - 200°, and

350" - 360°, due to mechanical constraints placed on the engine. Figure 5.2 shows

that fiom CAD 10" - 35", the piston accelerates. The acceleration then changes

and the velocity of the piston increases, until C-4D 130" where the piston velocity

is maximum at 72.6 -/S. The piston then decelerates and stops at CAD 160'.

At CAD 200" the piston reverses direction and begins to decelerate until CAD 220"

where the piston accelerates. At CAD 280" the piston begins to decelerate and fi-

nally at CAD 325" the piston accelerates until CAD 350" where the piston velocity is

zero. A closer look at the velocities for the crank angles obsenred in the experiment

is seen in figure 5.3. From the data shown in figure 5.3 an equation was fit to the

720 130 140 150 1 60 170 180 Crank Angle

Figure 5.3: Piston Velocity Profile CAD 120" - 180"

data for the piston velocity (mm/s),

5.3 Velocity Fields

5.3.1 Interrogation Region

-4s stated in section 4.2, the optimal parameters for PIV codd be determined

using four criteria. For the determination of the optimal interrogation region pixel

areas of 32 x 32, 64 x 64, 80 x 80, and 96 x 96 were used. Particle densities within

each image were detennined and are summarized in table 5.1. The results of the

Table 5.1: Mean Particle Densities for Different Interrogation

1

particle densities in the 32 x 32 and 64 x 64 interrogation region sizes were found

to be insficient (much less than 10 to 20 particles per region), thus only 80 x 80

and 96 x 96 interrogation regions have a suf£icient mean particle density of 13 and

18 respectively. The next criteria suggested the magnitude of the displacement

vector be less than one-quarter of the interrogation size. For a maximum particle

displacement of 18 pixels both the 80 x 80 and 96 x 96 areas were satisfactory- Since

the ü velocities could not be measured the out of plane displacements were assumed

to be less than one-quarter the light sheet thickness. If the ü velocities are assumed

to be of the order of the G velocities, then this criteria is satisfied. Finally, the

velocity gradient MAtlAuil/dr for the 80 x 80 and 96 x 96 interrogation regions

must be less than 0.05. This was cdculated and checked for all crank angles under

observation using the 80 x 80 interrogation region. A typicd plot of the results

is shown in figure 5.4. Here a histogram plot shows a highly skewed distribution

with a s m d percentage of the distribution greater than the threshold of 0.05. For

interrogation Size 32 x 32 1 64 x 64 1 80 x 80 1 96 x 96

Figure 5.4: Typical Histogram plot for MlAU(y) lAt/dr

al1 observed crank angles, CAD 180" was shown to have the highest percentage of

data, 3.3%, with values being greater than 0.05. Since this is a low percentage of

al1 data (< 10%): the last critena was satisfied. Thus: to maximïze the resolution

and accuracy of the velocity field, the 80 x 80 pixel interrogation area was chosen,

producing a grid of 8 x 6 equally spaced velocity vectors.

5.3.2 Instantaneous Velocit ies

Figure 5.5 is an instantaneous plot before and after the validation of the vector

field is applied. The missing vectors in these plots are caused by low seeding densi-

ties (3.8 particles per 32 x 32 pixel interrogation region) which result in the use of

a larger interrogation region size (80 x 80), which in turn, increases the noise in the

images. Lt is also suggested that the los of vectors is attnbuted to a clifference in

intensities of the lasers. The left plot shows the instantaneous velocity field before

- - - ---

Figure 5.5: Instantaneous Velocity Plots (Before and M e r Validation)

the validation scheme is applied. A spurîous vector is seen on the left hand side of

the plot, which was successfully taken out of the validateci plot shown on the right

plot. In order to determine if the P N technique was extracting the correct particle

velocities, the particle displacements were approximated by directly measuring the

displacements from a sample image and checked against calculated values. Rom

this it was concluded that the PIV technique was working satisfactorily.

Velocity patterns horn the instantaneous flow fields, for each crank angle, were

found by breaking each position into four (2 mm x 3 mm) axeas. Next the mean W

velocity component, within each area, was determined and checked to see whether

the mean velocity was positive or negative. With four areas and the possibility

of either a positive or negative W velocity components in each area, there are 16

possible 0ow fields types, shown in figure 5.6. The U component is always positive

due to the use of the autocorrelation scheme and thus limits the number of pattern

types to a value of 16. The experimental data for each crank angle was categorized

and their relative percentages calculated. The results are shown in table 5.2.

TYPE 4

L

T Y P E 15

Figure 5.6: Categorization of flow field patterns

Table 5.2: Percentage of total flow pattern types in flow

1

Crank Angle Pattern Type 1 1 2 1 3 1 4 1 5 16 1 7 1 8 1 9 ~ 1 0 ~ 1 1 ~ 1 2 ~ 1 3 ~ 1 4 ~ 1 5 ~ 1 6

For the top measurement region (T), table 5.2 shows that the majority of the

flow pattern present during each crank angle was either type 1 or type 9. This

was true for all crank angles except CAD 150" and CAD 180°, where one pattern

type still occurred most frequently, but there was a larger spread in the number of

patterns present. korn CAD 120" - 150" type 1 occurred most fiequent at 72%,

72%, 62%, and 38% respectively. The fiequency of occurrence for type 1 is seen

to decrease as GAD 160" is approached suggesting that the main flow pattern is

changing. At CAD 160" a mean flow type is found, type 9. The frequency of oc-

currence for this pattern is comparatively low (53%) but increases in occurrence

with advancing crank angle- -4t CAD 180°, however, the frequency of occurrence

for type 9 decreases (22%) but is still the dominant pattern present. This suggests

that the main flow pattern is, again, changing. For the lower measurement region

(B), CAD 170" had one pattern m e dominate the flow, where the rest were seen to

have many flow types occurring. For all CAD measured (in both position B and T)

different flow type patterns were found, suggesting that cyclic variation is present

during CAD 120" - 180".

Two instantaneous velocity fields observed during CAD 160" (T) and CAD

180" were noted and for CAD 160" is shown in figure 5.7. In this plot, very large

$$ gradients, between x = 69 and 71 mm, are seen. Because of the directional

ambiguity present with the use of the autocorrelation method the vectors shown

could be interpreted to have been given a wrong direction. No attempt was made

to correct the plots since it could be possible that these are the correct fields.

5.3.3 Mean Velocity Fields

Mean velocity plots for each crank angle were determined using the Ensemble

average, equation 4.14 and are shown in figures 5.10 to 5.23. Histograms of the

Figure 5.7: Instantaneous Plots at CAD 160"

instantaneous velocity profiles at each point were determined and results found that

for the ü instantaneous velocity component, all velocity distributions were uni-modal

(see figure 5.8). This suggests that the mean velocity, (U), found using the Ensem-

ble averaging technique, represents the most kequently occurring velocity. For the

G velocity component the velocity distributions were also uni-modal for al1 CAD in

both B and T, with the exception of CAD 180" (T), where the velocity distributions

between x = 66 and x = 71mm were found to be bi-modal. Figure 5.9 shows a

typical bi-modal velocity distribution found during CAD 180" (T). Here it can be

seen that the peaks are opposite in sign. For (W), the mean velocity represents an

average between the two most fiequently occurring velocities.

The velocity fields for CAD 120" are seen in figures 5.10 and 5.11. It can

Figure 5.8: Histogram plot of Instantaneous Velocity during CAD 130"

be seen that, for both the top and bottom positions, the U velocity component is

positive and decreases near the piston surface. The W component is high in the

top position of velocity but is seen to decrease, fairly u n i f o d y until it becomes

negative at approximately z = 2.5 mm. The velocity plots for CAD 130°, (figures

5.12 and 5.13) are seen to have similar trends except that the W velocity cornpo-

nent becomes negative at approximately r = 2.0 mm. For GAD 140" (figures 5.14

and 5.15) a similar II velocity component is found and for the W velocity plot, the

velocity is seen to be negative at approxîmately z = 3.5 mm. The velocity plots for

CAD 150" (figures 5.16 and 5.17) show the same U velociw behavior but it can be

seen that the W velocity component becomes negative a t z = 3.5 mm. There is a

large change in velocity near the piston surface which is more prominent than any

of the other velocity plots. This is due to an error with the positioning of the Cam-

Figure 5.9: Histogram of Instantaneous Velocity during CAD 180" (T)

era which resulted in the velocity measurements being closer to the piston. This,

however, shows that the effects of the piston boundary does not strongly effect the

fiuid until it is a t least 0.5 I0 .4mm away fkom the piston surface (distance fiom

piston plus positioning error). For C-4D 160" (figures 5.18 and 5.19) the U velocity

component in figure 5.18 does not show a uniformly decreasing profile as the piston

is approached but is seen to both increase and decrease. The U velocity component

in B, as shomn in figure 5.19 is larger than in T with maximum values of 232 mm/s

at x = 70 mm, z = 4.5 mm. The W velocity component is mninly negative for

both the upper and bottom position. At CAD 170' (figures 5.20 and 5.21) the U

velocity in T increases as the piston surface is approached and in B the velocity is

faidy constant at 170 mm/s which is also seen to be larger than T. The W velocity

components in both T and B are negative and decrease as the piston is approached.

Figures 5.22 and 5.23 show the velocity plots for C.4D 180". Figure 5.22 shows

that the U velocity component decreases as the piston is approached but in figure

5.23 the U component is seen to increase and then decrease again- The W velocity

component is seen to decrease as the piston is approached in both T and B. Figure

5.22 shows the W velocity component changes from 50 mm/s to - 100 mm/s while

in figure 5.23 the velocity has a smder change, ranging fiom 50 mm/s to -50 -/S.

-

67 66 65 64 63 62 61 60 59 Dirtence Fmm Inkt [mm] - 125nmh

Figure 5.12: Mean Velocity Field for CAD 130" (T)

65 ô4 63 62 Distance From Iniet [[mm]

Figure 5.13: Mean Velocity Field for CAD 130" (B)

Figure 5.14: Mean Velocity Field for CAD 140" (T)

71 70 69 68 67 66 65 64 63 ûïstanœ Fmm Inlet [mm] - 125nmis

Figure 5.15: Mean Velocity Field for CAD 140" (B)

Figure 5.16: Mean Velocity Field for CAD 150" (T)

Figure 5.17: Mean Velocity Field for CAD 150" (B)

6

5

.-.

Es- - R N

g3 IL

E s2 O

1

0

73 72 71 70 69 68 ô ï 66 ô5 64 Dùtance F m lnbt [mm]

125n8nh

-

I

-

-

I 1 1 T I I

-Piam-

-- - - h % -<m. --- k

- I V

- A

-

1 I

/ <-,----- - - - / &-y---&-

4'- / / - w -Y-

I 1 I

Figure 5.18: Mean Velocity Field for CAD 160" (T)

1 . 1 1

73 72 71 70 69 68 07 66 D i From lnbt [mm]

Figure 5.19: Mean Velocity Field for CAD 160' (B)

74 73 72 71 70 69 W oI 66 o i i œ F m inlet [mm]

Figure 5.20: Mean Velocity Field for CAD 170" (T)

75 74 73 72 71 70 69 6û 6ï 66 Distance From Inkt [mm]

Figure 5.21: Mean Velocity Field for CAD 170" (B)

Figure 5.22: Mean Velocity Field for CAD 180" (T)

Figure 5.23: Mean Velocity Field for CAD 180" (B)

The spatial mean values for both the U and W components were calculateci for

each position at ail crank angles and are plotted in figures 5.24 and 5.25 respectively.

Figure 5.24 shows the mean U velocity component and it is seen that for both posi-

tion T and B the overd trend is the decrease of velocity between CAD 120" - 180". It can also be seen that for aii CAD, position B has a mean velocity greater than

Figure 5.24: Mean U Velocity Component

position T. The spatiaily averaged U profile for position T shows relatively larger

changes in the velocity with increasing crank angle at CAD 130°, 160°, and 180".

From figure 5.12, low magnitude U component vectors were found close to the pis-

ton surface in CAD 130" (T) which, when spatially averaged, resulted in a lower

mean value. It is suggested that the mean value at this point should be larger since

noise introduced by the reflection of light on the piston surface may have caused the

lower velocities. At CAD 160" (T) and 180" (T) type 14 flow patterns were found

to have a high W magnitude and a Iow U magnitude (as seen in figure 5.7) which,

when spatialiy averaged, also resulted in a lower mean value. However, fkom table

5.2 the type 14 flow pattern was found to be relatively iow (5%) in CAD 170" (T).

From this it is suggested that as the piston cornes to rest the incoming jet begins

to oscillate- The mean W velocity component plotted in figure 5.25 shows an inter-

esting trend. Here the c w e s , for both position T and B, have a roughly sinusoida1

r I I I l I I

-

-

- I I I r 1 I r r

1 20 130 140 1 SO 166 1 70 180 Crank Angle

Figure 5.25: Mean W Velocity Component

shape with the magnitude of the mean W velocity component in position T being

greater than that for position B. Comparing the mean W velocity component in

T with the piston velocity profile (figure 5.3), when the piston velocity is non-zero

the mean W component is positive, but becomes negative when the piston is a t rest.

Using the piston velocity calculated fkom equation 5.1, the piston velocity a t

each crank angle was subtracted fiom the mean Ensemble averaged velocity. This

results in a mean velocity field with a reference frame moving with the piston. One

could &O view this as the velocity difference between the fluid and the piston. Fig-

ure 5.26 shows the results of the (r - V, mean velocity a t different crank angles.

As the piston accelerates, during CAD 120" - 130°, the fluid is unable to match

Figure 5.26: Mean (U-Vp) Velocity Component

this acceleration and a decrease in U - Vp is seen. As the piston decelerates the

velocity dinerence between the fluid and the piston increases, shown during CAD

130" - I4Oa, but becomes relatively constant during CAD 140" - 150". The difference

increases in CAD 160" (B) , however, CAD 160" (T) shows a drop in U - Vp. For B,

during CAD 160" - 180" the difference decreases. In T, during CAD 160" - 170" an increase in Li - V, is seen, followed by a decrease during CAD 170° - 180'.

5.3.4 Convergence of Mean Velocities

The convergence of the mean data was calculated and a sample of the results

shown in figure 5.27. Here it can be seen that as the number of samples increases

Figure 5.27: Convergence of U [%]

the mean converges within 1% of the final mean value. It was found that the U

velocity component converged within 1% of the final mean value. The W velocity

component, however, did not converge as well as the U component and it was found

that a few points did not converge at d. It was decided that every instantaneous

velocity that did not converge to within 20% of the final mean velocity would be

discarded. This threshold mas chosen because it gave an adequate convergence,

while at the same time prevented a significant amount of data points from being

discarded. This is the reason for the spaces found in the mean velocity vector plots.

Eliminating these points, the W vetocity component converged to an average value

of 9% for B and 4% for TI

5.3.5 Mean Velocity Gradients in the Y direction

Using equation 4.4, the quantity 9 has been estimated and the results of B

shown in figure 5.28. Looking through the results for both T and B it was found

CAO 129 CAD 130 CAC) 140

CAD 160 CAD 170 CAD 180

* z=3.2m

- z d 3 m * z=6.4m

72 70 68 72 70 68 72 70 60 x [mm1 x mm1 x mm1

Figure 5.28: Plot of in B [lis]

that is present in all CAD and ranges from -95 to +105 B . This is important

since the presence of 9 suggests that (V) is non-zero.

5.3.6 Flow Turbulence

For a fiow in a cylindncai engine with a sudden expansion inlet condition,

Durst et al. (1989) found that the transition betnreen a laminar and turbulent flow

occurred at a Reynolds number (based on the piston velocity and engine chamber

diameter) of 125. For the present experiment, a Reynolds number of 2430 was

achieved. To assure that the flow was turbulent, a check was made. -4s an indicator

for a turbulent flow Bradshaw (1997) suggested that a flow is turbuient when the

fluctuating vorticity is non-zero. A plot of the fluctuating vortici@ for CAD 180"

is s h o m in figure 5.29. For al1 CAD it was found that there existed non-zero

fluctuating vorticity, thus the flow is turbulent-

CAD 180 1 1 1 1 1 1 I

Figure 5.29: Fluctuating Vorticity for CAD 180" (T)

5.3.7 Turbulence Intensities

Turbulence intensities were calcdated using equation 4.18 and the results are

shown in figures 5.30 to 5.32. The u component turbulence intensities (figures 5.30

and 5.31) are seen to range from 22% to 107%. From CAD 120" - 150°, the tur-

CAD 160 CAD 170 CAD 180

z=G.lmm a z=?2mm * z4.3mrn

z=9.3rnm - z=10.4m * 2-1 1 Sm

Figure 5.30: Turbulence Intensity in T (u component) [%]

bulence intensity near the piston (48%) is found to be greater, on average, than the

rest of the flow (34%) and is shown to increase from 48% to 69% with increasing

CAD. From CAD 160" - 170°, the turbulence intensity is found to decrease as the

piston is approached (from 67% to 41%) and, near the piston, is found to decrease

from 41% to 29% with increasing CAD. Finaliy at CAD 180° the turbulence inten-

sity near the piston surface increases to 46% in T and 72% in B.

In section 5.3.4 it was found that the w component of velocity did not con-

1 CAD 12û CAO 130 CAD 140 CID150 1

Figure 5.31: Turbulence Intensity in B (u component)[%]

verge as well as the u component. It was also determined that when calculating the

turbulence intensity for the w component, points with convergence greater than 5%

were found to give unredistic results (ie. turbulence intensities ranging from 1000%

to 14000% ) . Thus in order to give a realistic estimate of the turbulence intensity, alI

points with a convergence greater than 5% were discardeci. Figure 5.32 shows a plot

of the mean turbulence intensities for the w component. Here, it is seen that the

turbulence intensities for B are greater than T for al1 CAD. The mean values range

between 87% - 203% for T, while for B the mean values range fkom 169% - 553%.

In order to make a cornparison between the turbuience intensities found in

the present study and those determined hom previous studies, uiYRMS was further

normalized with the mean piston speed. Figure 5.33 shows the results of the spatially

600 1 ï I 1 1

c.

ces00 -

O - 1 1 1 1 1

120 130 140 150 166 170 180 cm

C

Figure 5.32: Mean Turbulence Intensity (w component)[%]

averaged u and w component turbulence intensity normalized with the mean piston

speed for CAD 120" - 180". Here, the w component was found to have a larger

magnitude than the u component in both position B and T. &O, the w component

mas found to range between 1.66-2.94, while the u component ranged between 1.18-

2.04. From single point measurements Morse et al. (1979) estimated U ' ~ ~ / ( V , )

to range between 2.5 to 3.5 at CAD 144" approxhately 8 mm from the piston

surface. The merences between these reported values and those found in the present

experiment may be explaùied fkom the ciifferences in experimental conditions (piston

speed, geomet ry, clearance, inlet diameter).

- - -

3 1 1 r

28 -

26 -

-

1.2 - a L

1 f 1 t 1 1

1 20 130 140 150 160 170 180 CAD

Figure 5.33: Spatidy Averaged Turbulence Intensity [u&,/(V,)]

5.4 Reynolds Equation

5.4.1 DZhsion

An example of the vw, m s i o n term for the bottom position is shown in

figure 5.34. Here, the diffusion t e m is shown to fluctuate both spatially and with

difTerent CAD. Plots and additional information for spatial data c m be found in

Davis et al. (1999).

The histogram of the diffusion terms is shown in figure 5.35. The mean and

standard deviation for this distribution was found to be -7 and 29 mm/s2 respec-

tively for 2688 sarnples. Table 5.3 show the standard deviation for each difhsion

term from CAD 120" - 180" over the entire plane.

GAD 120 CAO 130 CAD 150

ô4 62 60 58 66 ô4 62 6 8 6 6 6 4 70 65 x [mm1 x [mm1 x [mm1 x mm1

CAD 160 CAD 170

Figure 5.34: v,sp Diniision (~)[mm/s~]

Table 5.3: Standard Deviation for Difnision [mm/s2]

Component

vw uw

Comparing the values in the table with the standard deviation of the distnbu-

tion shown in figure 5.35 it can be seen that the clifferences between each tems is, on

average, l e s than 20%. This suggests that the distribution is a good representation

of each d i h i o n term. Next, a cornparison between the magnitude of each term

(table 5.4) was found. Each case in table 5.4 represents a cornparison between two

a2 CJ terms and is defined in Appenâix C. First, clifferences between the and v'#

120"

30

26

130"

27

27 --- vw

vw

140" 150" 160" 170" 180"

30 25 22 21 23

33

29

19

22

30

31

31

42

38

30

28

25

20

29

26

Figure 5.35: Histogram of Diffusion Terms

--

Table 5.4: Cornparison of Dinusion Terms [% of flow]

diffusion terms show that for each position the rnajority of the flow (87%) consists of

a* u a= Ci diffusion where Iu&li > I v - ~ ~ and Iv?s,I > I v ? ~ , I with the latter occurring

more frequently, on average, (50%) than the former (37%). The Merences between a* w a2 w a2 w aZ w u.#' and v-* shows that each position has d i h i o n where 1 v&k 1 > lu* 1

a2 w for 48% of the position, and d i h i o n where Iv,#.I > I V ? ~ ~ for 40% of each

position.

Case

1 2

120" 140" 170"

29 63

130"

27 60

150"

23 69

54 35

48 44

29 58

180" B T B T B T B T B T B T B T

40 44

160"

48 40

52 38

31 50

31 56

29 60

44 44

38 40

5.4.2 Convection

The histogram of the convection terms (figure 5.36) shows a distribution with

a mean of -479 rnm/s2 and a standard deviation of 2669 mm/s2. The standard de-

viation for the convection tems (table 5.5) shows both the (w) and (w) have a standard deviation which difber by l e s than 10% and is comparatively l e s

than the (?Y)% and (u)= which have standard deviations that m e r by l es

than 12%. The distribution shown in figure 5.36 can be argued to consist of two

main parts. First the sharp peak is caused from the (w)% and (w)F terms,

a0 while the broad base is caused from the contribution of the (U) and (U) a

terms.

Table 5.5: Standard Deviation for Convection [mm/s2]

Component

(u)% (w)% (u)% (w)%

Cornparhg the (u)% and (w)% convection te- (table 5.6) at each

Table 5.6: Cornparison of Convection Terms [% of flow]

point in the flow, it was determined that during ail CAD, in both B and T,

1 (U) 1 > I ( w ) ~ [ for 75% of each position. It was also detelmined that

1 (U) ( was on average, 7.5 times larger than 1 (w) FI- Coxnparing the (u) a w and (W)V convection te- it was f'ound that ( (~ }= l > I(w}*I for, on

average, 79% of each position. It was also noted that 1 (U) 91 was on average 6.5

times larger than 1 {w) 91.

5.4.3 Reynolds Stress transport

The histogram of the Reynolds stress transport (RST) terms (figure 5.37)

shows a distribution with a mean of 77 mm/s2 and a standard deviation of 1899 mm/s2.

Comparing the standard deviations for each Reynolds stress transport term (table

140"

4405

1488

4273

1069

150"

3300

1131

5483

1349

120"

4253

1226

2915

663

130"

3279

1070

3493

771

160"

2096

883

2728

812

170"

1698

1063

2422

943

180"

1953

999

2271

1371

4.5 O 0.5 Reynoid Stress Trampon [md/s]

Figure 5.37: Histogram of Reynolds Stress Transport Terms

5.7): it was found that the standard deviations for the $ ( - w J d ) are, on average, 2.2

times larger than the remaining three terms. It can also be seen that the standard

Table 5.7: Standard Deviation for RST [mm/s2]

deviations between the remaining three terms cliffer kom each by l e s than 12%.

From this it can be said that the distribution shown in figure 5.37 is composed of

the peak section (terms &(-du'), &(-u'd) and &(-w'u')) and the broad base

(term (-w'w') ) .

1 &(-w'w') 1 2315 1 1812 1 3641 1 3429 1 3419 1 2228 1 2774 1

150"

1885

1350

1518

160"

1698

1559

1790

Component

L ( - d u ' ) a~

a z ( - u ' ~ ' )

a a;(-~'~')

170"

1166

892

791

120"

1479

1175

1063

180"

1297

1620

1325

130"

1028

956

1077

140"

1542

1428

1696

Comparing the terms &(-du') and &(-u'w') (table 5.8) shows that an av-

erage of 53% of the flow was RST where I&(-u'u') ( > Ig(-dw'$ and 38% was

RST where 1 & (-u'w') 1 > 1 & (-du') 1. Comparing the Reynolds stress transport

Table 5.8: Cornparison of RST Terms [% of flow]

terms & (-w'd) and (-w'w') , the results show that the majority of each position

is composed of RST where 1 (-wrw') 1 > 1 ( - w u f ) 1 (70%). It was found that

a(-w'w') az was on average 2.5 times iarger than &{-wruf) .

5.4.4 Time Rate of Change of Velocity

It was not possible to accurately calculate the , term in equation 4.5, since

measurements were taken which respect to 9 and not t. However, an estimate can

be made. First, it is noted that,

here can be found using a dinerence scheme, however $ must be assumed. It

mas found that it took an average of 1.07s for the piston to travel between CAD

0" - 180°, which gives a constant value for of 168.22"/s. It was determineci kom

section 5.2 that $ is not constant, however for the present analysis is only indenteci

to give an estimate to the order of magnitude of W. Figure 5.38 shows the r d t s

of the mean spatial I F ( for all CAD. During CAD 125" - 14a0, the average 191

WJi) Figure 5.38: Estimate of Mean 1 1

1800-

1600

1400

1200 N-

and 191, for both B and T, have a s m d spread of values (200 mm/s2), whereas,

during C.4D 155O - 175O the values have a greater spread in the data (between 451

and 1215 mm/s2). Ako, during CAD 155" - 175O it was found that the mean 191 was greater than [Tl for each position. Using the constant the range of values

for (FI was found to be 191 to 1692 mm/s2

I 1 1 I I b 1 I I

14 - / \ - - TOP [ul I \ - Bottom [u] I \ / -

r \ - I Boltom [w] \

I \

\ - /

I \

2 g1000-

6- 3 a- C f

600-

O 1 1 1 1 1 1 I 1

I& 135 lu1 145 150 155 160 165 170 175 CAD

5.5 Mean Kinetic Energy Equation

5.5.1 Mean Viscous Stress Transport

Figure 5.39 shows the histogram for the mean viscous stress transport (MVST)

terms. The mean and standard deviation for this distribution was found to be

-619 mm2/s3 and 2838 mm2/s3 respectively. Comparing the standard deviations

Figure 5.39: Histogram of MYST Terms

400-

350-

3QO-

r I 0200-

B = 1 5 0 -

100

50

O -2

between the mean viscous stress transport terms (table 5.9) it was found that, on

average, the & (2u(W)S,) and (2v(W) S,,) te- had comparably smailer stan-

dard deviations which dinered by 23%. The $ (2v(U)S,) and & (2v(U)S,,) te-

had comparably larger standard deviations, however differed by 43%.

- ---

1 1 1 I 1 1 r

-

-

- -

- -

- I n t - I I

-1.5 -1 -0.5 O O 5 1 1.5 2

Comparing the te- & (2u(U)S,) and $ (2u(U)S,,), table 5.10 shows that

on average I& (PV(U)S,)~ > 1s (2v(U)Sz,)I for 53% of the flow, while for 39% of

~ ~ s r [mm3r~2~ x 10.

Table 5.9: Standard Deviation for MVST [mm2/s3]

the flow 1% (~Y(u)s,) 1 > 1 & (~v(u)s,) 1. Comparing the MVST te- 3 (Zu(W)S,)

and (2v(W) S,,) , 1 ( S V ( W ) s,,) ( > 1 & ( ~ v ( w ) s,) 1 for an average of 54% of each

position, whereas 37% of each position ($ ( 2 4 ~ ) s,,) 1 > 1 & (su(w)s,,) 1.

-

Component

3 a;t. (2v(U)S,)

"(2v(U)S,,) a2

~ ( 2 v ( W ) S , ) az

" ( ~ U ( W ) S ~ J 62

Table 5.10: Cornparison of MVST Terms [% of flow]

120"

5640

2440

650

964

Case

1 2

5.5.2 Mean Reynolds Stress Tkansport

For the mean Reynolds stress transport (MRST) distribution (figure 5.40) the

mean and standard deviation were found to be 8323 rnm2/s3 and 2.7 x 105 mm2/s3

respectively. Comparing the standard deviations for each mean Reynolds stress

transport term (table 5.11) it can be seen that the & (-(wlul) (W)) has, on aver-

age, the smaliest standard deviation (8.1 x 104mm2/s3) and m e r s from the other

terms by at least 20%. Next, the standard deviations for the & (-(u'wl)(U)) and

& (-(w'w') (W)) terms differ, on average by 10% (25mm2/s3 and 27.6mm2/s3). Fi-

130"

4029

3037

1071

1061

120"

140"

5148

3845

1548

1660

130"

150"

3573

3042

4013

1958

140" 150" B T B T B T B T B T B T B T 58 35

160"

2435

1837

1068

1278

160"

58 33

63 31

48 50

56 33

170"

2555

1909

989

1592

170"

48 38

52 40

63 29

180"

1910

2131

1705

1952

180"

46 40

44 50

54 42

63 27

31 50

52 42

Figure 5.40: Histogram of MRST Ter-

a00

350-

300-

-250- 3 5 V)

z m - 5 E

100-

50

O -25

1 1 a I r 1 1 1 8

-

-

4

d

- -

1 I 1 I

-2 -1.5 -1 -0.5 O 0.5 1 1 .S 2 25

Table 5.11: Standard Deviation for MRST (IO*) [mm2/s3]

MRST [~ITI%~] x 10'

Component

a(-(u'uf)(U)) az

(-(utw')(U)) a~

a 82 (-(zu'uf)(W))

nally the & (-(u'u') (U)) has the largest standard deviation, on average, of 35.2mm2/s3.

Looking back at figure 5.40 it can be determined that & (-(w'u') (W)) (lowest stan-

dard deviation) is responsible for the peak, whereas the rernaining terms are respon-

sible for broadening the base.

A cornparison of the terms (-(ut ut) (U) ) and $ (- (u'w') (U) ) (table 5.12)

1 & ( - ( ) ( ) ) 1 17.6 1 14.8 1 30.0 1 37.4 1 34.7 1 18.5 1 31.1 1

120"

41.8

26.1

6.8

130"

23.6

19.6

5.2

140"

37.8

31.4

7.2

150"

47.2

26.6

11.5

160"

37.6

27.2

7.9

170"

22.8

14.2

6.0

180"

27.8

25.8

10.2

shows that I& (-(ulu') (U)) 1 > I$ ( - { u f d ) ( ~ ) ) l for an average of 58% of each posi-

tion, whereas I$ (-(dw') (U)) 1 > 1 & (-(ulut) (U)) 1 for 34% of the flow. Comparing

the terms 2 (-(wlul)(W)) and & (-(wlw')(W)), each position was found to be

dominated by MRST where 1% (- (dd) (w)) 1 > 1 $ (- (dd) (w)) 1 for an average

of 80% of the flow. It was also noted that on average I & (-(utfwl)(~))I was 3 times

greater than 1 & (-(w'u') (W)) 1.

Table 5.12: Cornparison of MRST Terms [% of flow]

5.5 .3 Mean Dissipation

The histogram of the mean dissipation results is shown in figure 5.41. It c m be

seen that the mean dissipation is always negative and that the distribution is skewed

towards zero. To be consistent with the analysis a mean and standard deviation

were found for this distribution, which are -583 mm2/s3 and 1065 mm2/s3 respec-

t ively. Comparing the standard deviations between the mean dissipation t erms

(table 5.13) it can be shown that the terms have less than a 25% difference. This

suggests that the distribution shown in figure 5.41 is a good representation for each

term.

Table 5.14 shows a cornparison between - ~ V S = ~ S ~ and -~vS,,S,,. Here it

was found that on average -2uS,S, > -~vS,,S,, and -2uSZf SZz > -2~S,s,

Mean Dissipation [mm3/s2]

Figure 5.41: Histogram of Mean dissipation Terms

Table 5.13: Standard Deviation for Mean Dissipation [ d / s 3 ]

Component

-2~s,,S,,

-~VS,,S~~

-~VS~,S,,

have a comparable percentage of occurrence within each position being 47% and 40%

respectively. Next comparing the mean dissipation terms -2uS,,S,, and -2~Sz,Sz,

it was found that, on average, -2vS,,S,, > -2vS,,S,, for 51% of each posi-

tion, while 37% of each position was composed of dissipation where -2uS,,S, >

-2uszzszz.

120"

1323

359

586

130"

1187

897

600

- 140"

1143

1049

1147

170"

585

335

1145

180"

626

596

1151 -

150" ! 160"

1992

1857

1638

733

536

833

Table 5.14: Cornparison of Mean Dissipation Terms 1% of flow]

5.5.4 Turbulence Production

Case

1 2

From the distribution of the turbulence production (figure 5.42) the mean and

standard deviation were found to be -2467 mm2/s3 and 1.8 x 105 mm2/s3 respec-

- 120"

71 65 17 25

tively. Comparing the standard deviations fiom each turbulence production term

130"

O t 1 1 I 1 I -2 -1 -5 -1 -0.5 O 0.5 1 1 5 2

turbulent Proaicoon [ d / s 2 ] x IO"

69 25

Figure 5.42: Histogram of Turbulent Production Terms

67 19

(table 5.15) it is seen that the terms diner by at least 50%. First, the ( u ' w ' ) ~ has

140" ' 150" 160"

42 29

B T B T B T B T T B T B T 44 42

42 48

54 35

33 54

19 67

170"

42 42

180"

48 38

38 52

19 63

- -- - --

Table 5.15: Standard Deviation for Production (IO4) [ m d / s 3 ]

r r 6 ( C F ) the smdest standard deviation of I.o-~/s~. Next the (wrur) 9 and (u u } are found to have standard deviations of 6.0mm2/s3 and 13.0mm2/s3 respectively.

Finally (wtwt) is found to have a standard deviation of 29.1mm2/s3. With the

comparably large standard deviation, this term can be thought to be responsible for

the broad base in figure 5.42-

Comparing the (utut) BBf and (utwt) 9 turbulence production terms (table

5.16) it can be seen that each position is dominated by turbulence production where

1 (ut ut) % 1 > 1 (u'wt ) 1 for an average of 83% of the flow. Also 1 (ut ut) &ll was on

140"

18.4

4.7

4.9

Component

' ' &

( u t w ' ) F ' '

(W g t

Table 5.16: Cornparison of Wbulent Production Terms [% of flow]

150"

16.3

5.0

12.5

average 12.5 times larger than 1 (dwt ) 1. Cornparhg (w ' u ' ) 39 and (ut t w t ) 6(W)

160"

12.8

4.1

4.4

170"

6.7

1.8

2.4

120"

13.4

4.2

2.3

it was found that on average 90% of the position consisted of turbulence produc-

a l ~ a t t a w ) tion where 1 ( d w ) 1 > 1 (w u ) , 1. Here, 1 (w'w') 9 1 was on average 10 tirnes

r I 6 (W) larger than I (wu) , 1 -

180"

8.9

4.3

5.2

130"

10.3

3.2

3.8

5.6 Turbulent Kinet ic Energy Equation

5.6.1 Turbulent Viscous Stress 'Ikansport

Figure 5.43 shows the distribution fiom the turbulent viscous stress transport

(TVST) resuits, which also show a mean and standard deviation of 2030 mm2/s3 and

5053 m d / s 3 respectively. Comparing the standard deviations from the each turbu-

-

Figure 5.43: Histogram of TVST Terms

lent viscous stress transport tenn (table 5.17), the $ ( 2v (dsL ) ) and $ (2u(urs',.))

terms were found to have a s m d dinerence (1%) and a relatively low standard

a deviation (2653 mm2/s3 and 2277 mm2/s3) as cornpared to the & (2v(wJs:,)) and

(2v (wf s:,) ) terms which had standard deviations, on average, of 4684 mm2/s3 and

2 3 7275 mm /s respectively.

Table 5.17: Standard Deviation for TVST [mm2/s3]

a Cornparhg , (2v(u's',)) and $ (2v(urs',)) it can be found hom table 5.18

that for each position 1 & (2v(uts',)) 1 > 1 (2v(uts:,)) 1 for on average 50% of the

points, wMe (& (2v(ds',))l > l& (2u(uts&))I for 41% of the points. Next, cornpar-

* Component

"(2u(utd-!)) a~

"(2u(ut&)) at

Table 5.18: Cornparison of TVST Terms [% of flow]

150"

3260

2517

of TVST where 1 (2v(uts:,)) 1 > 1 $ (2v(wts:,)) 1, while on average 27% is TVST

a 8~ (2v(wts:,))

120"

2707

1630

5.6.2 Turbulent Reynolds Stress Tkansport

Results of the turbulent Reynolds stress transport (TRST) terms are show in

figure 5.44. The mean and standard deviation of this distribution are 17368 mmz/s3

and 2.9 x 105 mm2/s3 respectively. Comparing the standard deviations between

160"

2453

3809

5542

130"

1910

1355

140"

3913

2471

170"

1898

1687

2345

180°

1655

1419

4497 1 4728 4019 1656 7477

TRST [mn3/s2] x los

the turbulent Reynolds stress transport terrns (table 5-19), it c m be shown that

the distribution (figure 5.44) is composed of two main sections, the peak and the

broad base. The peak is made up of the 3 & ( -~((u')2w')) , and

Table 5.19: Standard Deviation for TRST (IO4) [rnm2/s3]

Component

( -$ ( (u ' )~ ) ) ax

( - ( ( U ) ~ ' ) ) a~ 1 2 1

"(-$((tu) a~ u))

(-+((w')~)) a2

2- a~ (-~((wt)*d)) terms, where the standard deviations and have dinerences of at

most 22% and are relatively srnall(15.7 - 19.1 mm2 /s3) compared to the base which

is made up of the (-+((W')~)) tenn where the standard deviation is found to be

160"

22.1

26.4

120°

15.6

9.2

13.8

52.0

170"

18.1

11.8

180"

18.0

18.4

130" -

12.0

8.0

10.0

23.9

140'

24.7

12.9

23.3

54.5

150"

20.7

15.5

21.6

52.1

21.4

72.6

13.9

31.6

16.8

37.8

Cornparing the TRST terrns & (-3((u~)~)) and & (-$ ((d)*wr)) table 5.12

shows, on average 59% of each position consists of TRST where 1s (-)((u')~)) 1 >

1 $ (-~((u')~w')) 1, while only 33% has TRST where 1 & (-i ( ( ~ ' ) ~ d ) ) 1 > 1 & (-)((u')~)) 1. ' 2 r Next, cornparing the terms $ (- 4 ((w ) u )) and & (-4 ( ( w ' ) ~ ) ) i t was found that

Table 5.20: Cornparison of TRST Terms [% of flow]

1 ( - ( ( w ' ) ~ ) ) 1 > 1 & (-)((w')~u')) 1 for on average 70% of each position, while

' 2 r 23% is TRST where 1 & (-$ ((w ) u )) 1 > I$ (-6 ((w')~)) 1.

5.6.3 Turbulent Dissipation

The results of the turbulent dissipation (figure 5.45) show that the distribu-

tion is highly skewed with a mean and standard deviation of -4865 mm2/s3 and

6221 mm2/s3 respectively. Cornparing the standard deviations for the turbulent dis-

sipation terms (table 5.21), there is on average, l e s than a 2% difference between

the - 2 ~ ( s ~ s ~ ~ ) , -2u ( S ~ ~ S ~ , ) , and - 2 v ( s ~ , s ~ , } terms which have a standard devia-

tion of 3400 mm2/s3, 3347 md/s3 , and 3347 mm2/s3 respectively. The -2v(s:,s:,)

term was found to have a standard deviation of 8622 mm2/s3 which dinered trom the

other t e m s by 150%. From this it can be determined that the turbulent dissipation

distribution shown in figure 5.45 is composed of a peak (-2v(sizs!!), -2v(s',,s',),

Figure 5.45: Histogram of Turbulent Dissipation Terms

1 Component 1 120" 1 130° 1 140° 1 150° 1 160" 1 170° 1 180a 1

Table 5.21 : Standard Deviation for Turbulent Dissipation [ d / s 3 ]

and - Iv(s:,~:~)) and broad base (-2v(s:,s:,)).

Comparing the differences between - 2 ~ ( s ~ ~ s ~ ) and - ~ V ( S ~ ~ S ~ , ) , table 5.22

shows that 54% of each position consists of turbulent dissipation where -2v(s&sL) >

- 2v (s:. s:,), while 29% has turbulent dissipation where - 2v(s~.:,s~.) > -2u (s&s!!).

Comparing the dinerences between -2v(s',s:,) and -2v(s:,9',,) it was found that

each position was dominated (93%) with turbulent dissipation where -2v(s~,s~,) >

- - -- pp - - - - - - - - - -- . . - - -

Table 5.22: Cornparison of Turbulent Dissipation Terms [% of flow]

-2v(s',s:,). It was also found that - 2 v ( s ~ , ~ , ) was on average 5 times larger than

- 2v (S;~S;J -

CHAPTER 6

Discussion and Recommendations

6.1 Discussion

6.1.1 Engine Study

Within the fully optical water anaiog engine a quantitative study of the velocity

fields has been performed using particle image velocimetry. For the first time terms

have been estirnatecl fkom both the Reynolds and kinetic energy equations for a

cyclic flow near the piston surface.

6.1.2 Velocity Field

Results £kom the (u,w) flow fields obtained during CAD 120' - 180" show

the velocity field to be both turbuient and three dimensional in the mean. Use of

an Ensemble average to determine the mean flow field resulted in determining the

most frequently occurring velocity, except during the crank angle of 180" in the

top position where a histogram of the instantaneous velocities on the right of the

position had a bi-modal distribution. The result of using an Ensemble average a t

180°, found an average between the two most frequently occurring veIocities. The

results of the mean velocity field show that as the piston decelerated and comes

to rest the (Cr) velocity component also decreases. It is also seen that the mean

(U) is a t least 100 mm/s greater than the piston velocity for all CAD. For the W

component in the top position, (W) is found to have a positive mean when the

piston velocim is non-zero but changes direction and becomes negative when the

piston is a t rest. The mean W component in the bottom position was found to be

lower than in the top position an the W component was found to become negative

during CAD 140°, before the piston is a t rest.

6-1.3 Reynolds Equation

The individual distributions fiom the Reynolds equation terms, found in Chap

ter 5, have been plotted (figure 6.1). Rom this figure, both the convection and

- - - - - - - - -

Figure 6.1: Cornparison of Reynolds Equation Teims

Reynolds stress transport terms are seen to have a s m d percentage of terms of the

order of the dîfhsion terms. This is quantitatively shown in table 6.1 where, for the

range -64 to 50 mm/s2, the percentage of convection and Reynolds stress transport

terms are 6% and 4% respectively while 95% of the dinusion terms lie within this

range. Comparing the convection and Reynolds stress transport terms, table 6.1

shows that in the range -3721 to 3876 mm/s2 the convection and Reynolds stress

transport terms have 87% and 95% respectively.

Terra Convection

I RST I 95% I -3721 to 3876 I

RST Convection

Table 6.1: Total Percentages for Reynolds Equation Terms

Percentage of Term 6%

The r e d t s of the Reynolds equation terms show that the effect of the (indi-

vidual) diffusion terms are small compared to that of the convection and Reyno~ds

stress transport terrns. Both the convection and Reynolds stress transport terms

were found to be comparable. Finaliy, £rom the results the magnitude of the con-

vection terms measured in the x-direction were found to be, on average, seven times

the magnitude of the convection tems in the direction.

Range [mm/s2] -64 to 50

4% 87%

6.1.4 Kinetic Energy Equations

For a cornparison of the terms fkom the mean kinetic energy equation the his-

tograms of the individual terms are shown in figure 6.2. From here it can be seen that

both the turbulent viscous stress transport and turbulent dissipation terms have a

small range of values compared to the turbulent Reynolds stress transport and tur-

bulent production terms. Table 6.2 shows the total percentage of each terrn, within

a specfied range. From here it is seen that in the range of -2713 to 1548 mm2/s3,

-64 to 50 -3721 to 3876

I MRST I 2% I -2713 to 1548 I

Term MVST

Percentage of Term 72%

Mean Dissipation Turbulent Production

2 3 Range [mm 1s ] -2713 to 1548

MRST Turbulent Production

97% 11%

-2713 to 1548 -2713 to 1548

Table 6.2: Total Percentages for the Mean Energy Equation Terms

86% 96%

-3.7 to 3.6 (los) -3.7 to 3.6 (105)

Figure 6.2: Cornparison of Mean Energy Equation Terms

97% and 72% of the mean dissipation and mean viscous stress transport terms are

within this range, whüe only 11% and 2% of the turbulent production and mean

Re-ynolds stress transport t erms are found. Comparing the mean Reynolds stress

transport and turbulent production term it is found that in the range -3.7 x los to

3.6 x 105 mm2/s3, 96% of the turbulent production is found, while only 86% of the

mean Reynolds stress transport t erm is found.

Comparing the terrns from the turbulent energy equation, figure 6.3 shows sim-

ilar trends as the terms nom the mean energy equation. Ftom table 6.3 it is found

that in the range -8081 to 12141mm2/s3, 96% and 84% of the turbulent viscous

stress transport and turbulent dissipation terms are within this range, while only

27% and 7% of the turbulent production and turbulent Reynolds stress transport

terms is found. Comparing the turbulent Reynolds stress transport and turbulent

800-

MO-

600-

a 1"- - i-- 2

300-

Figure 6.3: Cornparison of Tuibulent Energy Equation Terms

I 1 - -

1

TRST 1 7% 1 -8081 to 12141 1 Term TVST

Percentage of Term 96%

Turbulent Dissipation Thbulent Production

Table 6.3: Total Percentages for Turbulent Energy Equation Terms

Range [mm2/s3] -8081 to 12141

TRST Turbulent Production

dissipation te-, in the range -3.7 x 105 to 3.6 x 105 mm2/s3, 96% of the turbulent

production is present, while for the turbulent Reynolds stress transport term 88%

is found.

84% p- 27%

The mean and turbulent dissipation terms were also compared (figure 6.4).

From table 6.4, 96% of the mean dissipation term is found in the range -2713 to

-8081 to 12141 -8081 to 12141

88% 96%

-3.7 to 3.6 (los) -3.7 to 3.6 (los)

Figure 6.4: Cornparison of Dissipation Terms

O mm2/s3, while only 46% of the turbulent dissipation term is found.

1 ï'ùrbdent Dissipation 1 46% 1 -2713 to O 1

Term Mean Disbation

Table 6.4: Percentage comparison between dissipation terms

Results from the comparison of the individual t ems from the mean and tur-

bulent Energy equations show that the magnitude of the dissipation and the viscous

stress transport terms are small compared to the turbulent production and the

Reynolds stress transport terms. It was also noted that the magnitude of the tur-

bulent production and the Reynolds stress transport tenns were comparable. F'rom

the comparison of the individual terms from the energy equations, table 6.5 shows

relations for the mean Reynolds stress transport, turbulent production, and turbu-

Percentage of Term 96%

Range [mm2/s3] -2713 to O

lent dissipation terms. FinaUy, comparing the mean and turbulent dissipation, show

that there is more energy Iost from turbulent dissipation than mean dissipation.

1 Term T - - -

Relation 1 Mean Reynolds Stress Tkansport

f Turbulent Production

1 Turbulent Dissipation 1 - 2 4 s k L ) z 5 ( - 2 4 & L ~ 1

1 6 (- (wfwf) (W)) 1 = 3 1 & (- {wrur} (W) ) 1 I(duf)el 12.5 I(dd)vl

Turbulent Production

-. -- ~- ~ -

Table 6.5: Resuits of Cornparison between Energy equations

l ( w f w 3 v / zs 10 I ( w r d ) 9 I

6.2 Recornniendat ions

6.2.1 Engine Design

Although the present engine design was sufficient to obtain P N images, the

leakage of water through the piston caused lower seeding densities within the engine

which in tuni decreased the quality of the P N images. Two solutions to solve this

problem would be to increase the number of teflon layers to the piston and to add

an inlet and exhaust valve to the engine. WWe the additional teflon layers reduce

the leakage of water through the piston, the valves act to ensure a given particle

density at the beginning of each engine cycle, as weli as to provide a more reôlistic

engine design. However, with the present set-up, concems about the strength of the

g l a s chamber prevented the use of these solution- It is recommended that the en-

gine chamber be made from a high strength material, such as a metal. Four smaller

g las windows can be positioned in the engine to allow optical access for the laser

and the camera. h o t h e r concern with the present set-up was the piston velocity

profile. To compare results with other researchers it is essential to have comparable

expenmental parameters. A typical parameter used is a sinusoidal piston velocity.

t

To achieve this with the present set-up, the connecting rod is required to be length-

e n d to achieve a symrnetnc velocity profile. It is &O thought that with the present

set-up the piston velocity profiIe can become more sinusoidal by increasing the speed

of the motor. An easier solution to this problem (however more costly) would be

to replace the direct current motor with a stepper motor. With a controller, the

velocity of the stepper motor can be programmed to produce the desired velociw

profile.

6.2.2 Engine Similitude

A relation for complete similitude was deterrnined using eight parameters re-

sulting in six dimensionless parameters: four Reynolds numbers, a Euler number,

and an inverse of a Strouhal number. Modehg of engine flows, in the past, have

neglected both the effects of the Strouhal and the Euler numbers. Further study

should look at the effects of these numbers in engine flows. Another concem with

similitude was from the use of a square engine geometry as opposed to a typical

cyhdrical geometry. Experirnental and/or computational studies should focus on

the differences between flow fields in a square and cyiindrical geometry.

The most significant contribution to the errors was from the use of the autocor-

relation scheme and from the use of the k t order ciifFerence schemes in determining

velocity derivatives. The autocorrelation scheme should be replaced with a cross-

correlation scheme which will elimînate the directional ambiguity caused by the

autocorrelation scheme and will dso result in a lower displacement error. Ne*, by

decreasing the interrogation area size a higher order Merence scheme can be used

to determine the velocity gradients, which will reduce the truncation error. Also, in-

creased error from the use of a forward or backward difference scheme can be found

dong the boundaries of the image. To eliminate these areas, PIV image positions

should be overlapped as to eliminate the areas where the forward and backftrard

clifFerence schemes are usecl.

6.2.4 Decomposition of an Unsteady flow

The use of the Reynolds decomposition m this study prevented aay information

on the cyclic variations from being found. Comparing the Reynolds equation to a

similar equation (equation E. 7) det ermined using a triple decornposition (equat ion

E.3) the Reynolds stress transport term is changed. Further study of the importance

of the different decomposition methods on the terms in the equations governing a

fluid motion is necessary.

6.2.5 Future Work

In this study, the effect of individual components from the Reynolds and ki-

netic energy equations were compared. With each term in the Reynolds and kinetic

energy equations being second order tensors the next step is to obtain ail velocity

components to determine the complete tensor. With the complete tensors for the

terms in the Reynolds and kinetic energy equations, the effects of each term c m be

compared. This is important because it may be found that even though the indi-

vidual components have large magnitudes, the effect of the complete term may be

small and therefore can be discarded for computational purposes. &O, to complete

the equations, the pressure term and the time rate of change component should be

measured. Finally, different areas within an engine should be examined and com-

pared.

APPENDIX A

Theoretical Velocity of the Piston

Figure A.1: Piston-Crank wheel setup

Using figure A.1 the piston velocity in term of the crank angle and angular

rotation of the crank wheel can be derived as follows (from (Heywood, 1988)).

1

cos 4 = (1 - sin2 (4)) '

Taking the derivative of Equation A.4 with respect to B and defining the angu-

lar velocity as = wb, the piston velocity îs found through the foliowing relation:

APPENDPX B

Error Analysis

B. 1 Methodology

The uncertainty in the measurements (e) of C = f (Y l , T2, Ys,. . - , YN) can

be approxiutated using the method as describeci in (Bevington, 1969) where,

This method assumes that the covariance between the variables Ti and Tj is smail

and t herefore is neglected.

B -2 Instantaneous Velocity Error

The instantaneous velocity of a particle, &, is,

where di the particle displacement in pixels, M is the magnification factor of the

CCD camera in pixels/mm, and 4 t is the time interval in seconds.

From equation B.1, the uncertainty in the instantaneous velocity data is,

where oz is the variance in the particle displacement measurement, gM is the vari-

ance in the m a ~ c a t i o n factor, and 01, is the variance in the time interval.

Noting that,

Inserting B.4, B.5, and B.6 into equation B.3,

Using M = 74 pixel/mm, DM = 0.2 pkel/mm, At = 609 x 1 0 - ~ s, = 6.4 x

s, 04 = 0.3 pixel, and noting that di = G M 4 t equation B.7 becomes,

For the instantaneous velocity range of 50 - 200 mm/s it can be found fkom B.8 that

the change in variance is 0.02 rnm/s. Recognizing that the first term will have the

greatest influence on uncertainty, a constant uncertainty wiU be taken,

B.3 Mean Velocity Error

The mean velocity (U') is dehed as,

where the subscript k represents the sample number,

The mriance in the mean velocity, qui) , is found by summing the individual M a n -

taneous variances O, (see (Bevington, 1969)) ,

Using an average sample size of N = '75, and using B-9,

B.4 Fluctuating Velocity Error

The fluctuating velocity u: defineci as,

And the fluctuating variance a,!,

fkom B.9 and B.12,

which reduces to,

(B. 12)

(B. 14)

(B. 16)

B.5 Turbulence Intensity Error

The turbulence intensity T. ISi defined as,

where u ~ ~ ~ ~ , ~ is defined as,

The standard deviation OT.~ , can be estimated by,

Before this equation can be estimated, o ~ ; ~ ~ , ~ mwt be estimated using,

1 Ou&Ms,i

=- flU"'

Using a sample size N = 75 and a+

~ 'Ls , i = O . ~ I ~ I ~ / S

Findy QT.& can be estimated using B.12 and B.24,

(B. 18)

B -6 Velocity Derivat ive Error

In order to determine the derivative of an arbitrary function, Ç, the central,

forward, and backward schemes were used- The error produced in these schemes

is caused by the accuracy of the velocity measurements and the truncation error

resulting fiom the different scherne used.

The central merence scheme for the first order derivative is written as,

The forward clifference scheme for the first order derivative is wrïtten as,

The backward difference scheme for the first order derivative is w-ritten as,

The O (Axn) represents the truncation error. For each scheme the truncation error

is found as (see (Hohann & Chiang, l993)),

Using Ax = 1.08 mm and assuming that all derivatives are approxhately equal,

then the truncation errors can be wrïtten as,

K i O (Ax) x 0.75- axj

Without apriori knodedge of hïgher order velocity derivatives, this assumption is

only given as a rough estimate of the error associated with the tucation error.

Derivat ive calcdations neglect the truncation errors, thus equations B -26, B .27,

and B. 28 reduce respect ively to,

(B. 34)

The variance O& (neglecting the truncation error) can be calculated for each scheme-

using equation B.1, which for the central clifference scheme, reduces to (assuming a

spatiaiiy constant oFi)

The variance for the forward and backward scheme can be reduced to,

Next, if the truncation error is assumed to have a gauçsian distribution then the

variance for this error can be written as,

for the central (B.%), forwaxd and baclwrd schemes (B.39) respectively. Finaily

the complete estimate for the variance in the derivative calculation is found by

siimming the first derivative estimate with the tmcat ion estimate and noting Ax =

1.08 mm. For the central difference scheme this is written as,

and for the formard and backward schemes,

The variance for the mean velocity derivatives can now be determineci by

inserting equation B.12 into the error from each scheme. For the central difference

scheme,

And for the forward and backward difference scheme,

Next the second order derivatives of a function can be found using the central,

forward, and backward dinerence schemes and are determineci using the foilowing

equations,

The central ciifference,

The forward difference,

(Cdk+* - 2 (Ci),,, + (Ci), + * k Ax2

The backward clifference,

Using 4 x = 1.08mm and the same O(Ax) and O(Ax)l estimates, the variance

(neglecting the truncation error) is found to be,

Next the complete estimate is found by surnming the variances of the k t derivative

estimate +th the truncation error for each scheme. For the central ciifference scheme

the variance is written as,

and for the forward and backward scheme,

a2 U- The variance in the mean velocity derivative -4. is found by replacing C aith (Ui) * j

and inserting B. 12 into equations B-48 and B.49, which for the central, forward and

backward schemes reduce respectively to,

B.6.1 Sample Calcdation of Velocity Derivative Error

The average uncertainty in the second order velocity derivative was estimateci

as foilows. First, £rom equation B.50 the variance (o&~)) for each point is found

by*

a2 cli Next, using a subset of the second order velocity derivative terms ( - - ) to estimate

the uncert ainty,

the uncertainty is found to be (inserting B.53 into equation B.52),

Normalizing B.54 with the absolute value of B.53 and multiplying by 100%, the

percentage ratio of the uncertainty as compared with the second order velocity

derivative is found,

-4veraging B.55 the average uncertainty (for a subset of the sample set) is found to

be 24% of the second order velocity derivative.

B.? Mean Convection Error

The variance, oc, in the mean convection term (Ui) is found as,

B .8 Reynolds Stress Derivat ive Error

The derivative of the Reynolds stress is defined using the relation,

The variance in the quantity 02, can be found using B.40 and replacing C with

(u:u;), however it k necessary to fint £ind the variance in the quantity (u:ui),

where,

the variance in u:u> is determined by,

The quantity is determined by, ' 3

B.9 Turbulence Production Error

The uncertainty, u ~ p , h m the production term ( u : u $ ) y in equations 4.7

and 4.8 can be estimated using,

where a&cu,.) is dehed in B.62 and O& is found in 8-42. t 3

B. 10 Dissipation Error

Rom equations 4.7 and 4.8 two dissipation terms are found: the mean and

turbulent dissipation. First, the uncertainty, O M D , of the mean dissipation can be

found as foiiows. First the mean dissipation is defineci as,

Mean Dissipation E ~ u S ~ ~ S ~

125

where v is the kinematic viscosity of the Buid and S . is the mean strain denned as,

(B -66)

The uncertainty in the mean strain calculations, abfs, is found as,

Finally is estimated from,

Next the variance, UTD, from the turbulent dissipation estimate is detennined. The

turbulent dissipation is defined as,

Turbulent Dissipation = ~ U ( S ~ , S ~ ~ )

where s; is the fluctuating strain and is defined as,

(B. 72)

and (sijs;,) is defined by,

First the uncertainty, OFS, of the fluctuating strain is found using,

Noting that,

Equation B-74 becomes,

Next the variance ofs! .s;ji j) can be estimated by, 'J

126

(B. 73)

(B. 74)

(B.75)

(B. 76)

(B. 77)

(B. 78)

Findy the uncertainty in the turbulent dissipation, au is found by,

B.ll Mean Kinematic Energy Transport Errors

B. 11.1 Viscous Stress Transport Error

The uncertain@, OMVST, fiom the viscous stress transport term, 2u& ((Ui)Sij),

in equation 4.7 can be estimated using the following relation,

Before the quantity c m be found it is necessary to estimate the uncertainty,

qui)Sij 9

Inserting B.12 and B.69,

2 Next Q ~ ( ~ ~ ) ~ , can be estimated by replacing C in B.40 with (Ui)Sij,

Finally,

B. 11.2 Reynolds Stress Transport Error

The variance 9,- can be estimated from the Reynolds stress transport term,

a azj ((u~) (ului)) , in equation 4.7 can be estimat ed using the following relation,

2 - 2 OMRST - D ~ ( ~ i ) ( ~ i ~ ; )

First the variance, o&~)(,:,;), is estimated fkom,

Finally oh, is estimated by replacing the hinction, C, in B.40 with (fi)(u~u>),

B.12 Turbulent Kinematic Energy Tkansport Error

8.12.1 Viscous Stress Transport Error

The vanance, a&,, from the viscous stress transport tem, 2v$ ( (u{s i j ) ) ,

in equation 4.8 is estimated by,

Ficst the Mnance &. is estimated by, ' 'J

inserting B.16 and B.79,

Next O$, + ) is estimated as foilows, 8 v

130

Next o$( , ;~ :~ ) can be estimated by replacing the function C in B.40 with ( ~ : 4 ~ ) ,

(B. 103)

B. 12.2 Reynolds Stress Transport Error

The variance, O$-, nom the Reynolds stress transport te-, 3 & ((u:u~u>)),

from equation 4.8 c a n be estimated as foilows,

2 - 2 OTRST - u ~ { u ; u ~ u ; )

First, the variance a$,cut. can be estimated by, ' J

(B.106)

(B. 107)

(B.108)

&u!u. X J = (u:+~) p (y) ' + (y ) '1 Next the variance o&,,,,.) can be estirnateci as foilows,

S ' J

Next the variance is found by replacing the lunction C in B.40 with ( ~ { u ~ u ~ ) , 1 1 1

APPENDIX C

Seeding Caledation

1. Goal of 10 particles per 32 x 32 pixel interrogation area.

10 particles/(32 x 32 pixels) * (15 x 20 pixe1/480 x 640 pixel)

2. Require 3000 particles per 480 x 640 pixel area

3000 particles/(480 x 640 pixel) * (74 pkel/mm)* area

3. Require 54 particles per 1 mm2 area

4. Require 54 particles per 1 mm3 area assuming laser is 1 mm width with a volume

of water required in the order of 41000000 mm3 or 41 L

5. Require 2 x 109 particles. If the density of the particles is 1.65 grams/cc and the

mean diameter of the spherical particles is 15pm then

6. Require 6.4 grams

APPENDUC D

Case Definitions

1 CASE 1 MRST 1 Mean Dissipation 1

1 CASE 1

2

3

4

5

6

CASE 1

2

3

4

5

6

Diffusion

Reynolds Stress Transport

u& {U

4 k 2 2

T

Convection

MVST

(u)%

(Wg

$(-u'wl) - u f w l )

8 ( - w f )

q - u l u l ) a2

a ( - U U )

a ( - U U )

& (Sv(U)S,)

g (2v(U) Sm)

g (2v(U)Sm)

<

> < =

? > u W az uy

, 5 2

u

>

<

ywl=ywl

> < =

1 $ ( - w w , > , &(-wlwo [

, ( U } ~ , = ~ ( W ) ~ ; ~ ) ,

$ (2u (U)S,)

-g (2u(U) SZZ)

g (2u (U)Srr)

a &w1u1) a - ( -wu1) a~

~ [& (24WSZZ), > ,% (24w-)szz) 1

(w)V <w>=

a;= W ) U u w

a w v*

(W"1

( U ) ~ ~ L

( L T ) ~

az(w d'

& ( ~ Y ( W ) S , , )

2 a~ (2u(W)SZZ)

'

a w y - & 2 a wr .*

<

>

< < =

&(-wlwl) a

( W W )

< r=

( W a y (W)V.~

= ' ( w ) F

& (2v(W)Szz)

& (2u(W)Sz,)

Turbulence Production I TVST 1

1 CASE I TRST Turbulent Dissi~ation

5

6

a a ; ( - f ( ( ~ ' ) 3 ) ) ~ a (-((w)))

a 1 2 r a; (-$((w) U ) ) a 1 2 r ( - ( ( w ) a))

-2u(s'r+s:,) < -2~(s>Z,s',,)

- ~ V ( S : ~ S ; ~ ) ~ - ~ V ( S : ~ S : ~ ) .

< =

APPENDIIC E

Triple Decomposition in an Unsteady Incompressible

Engine Flow

Starting with a Newtonian, incompressible fluid the Conservation of Mass and Con-

servation of Momentum (also known as the Navier-Stokes equation) are,

From (Lancaster, 1976) a triple decomposition can be performed to decompose the

flow into a stationary mean, a cyclic mean fluctuation, and a turbulent Buctuating

velocity,

with N samples, U(0) can be determined from the Ensemble average,

subtracting equation E.4 from equation E.3 and EnsembIe averaging,

From the Conservation of mass (equation E.l) the three terms of the triple decom-

position can be combined and Ensemble averaged, reducing the equation to,

Using the triple decomposition in the Conservation of Momentum and then Ensem-

ble averaging, reduces equation E.2 to,

Comparing this equation to the Reynolds equation it can be seen that oniy the last

term has been modified. Also it c m be seen that if Uc(0)j is zero, equation E.7

reduces to the Reynolds equation. Expanding the last term,

III IV

where 1 represents the transport of momentum by the cyclic mean fluctuations.

Next, both II and III represent transport of momenturn by interactions of the mean

cyclic and turbulent fluctuations. Finally, IV represents the transport of momentum

by the turbulent fluctuations.

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