NASA / TM--1998-208503

Experimental Study of Boundary Layer

Behavior in a Simulated Low Pressure Turbine

Rickey J. Shyne

Lewis Research Center, Cleveland, Ohio

National Aeronautics and

Space Administration

Lewis Research Center

October 1998

https://ntrs.nasa.gov/search.jsp?R=19990008518 2018-05-11T17:14:50+00:00Z
Acknowledgments

The author wishes to gratefully acknowledge the support of the many individuals who were helpful in this

endeavor. Special thanks is extended to Dr. Eric McFarland and Mr. Nicholas Georgidias for their help in the

computational analyses used in this dissertation. Special gratitude and thanks is extended to Dr. Ki-Hyeon Sohn

for his assistance in the experimental research portion of this dissertation. The author also wishes to thank

Dr. Robert Simoneau, Mr. Frederick Simon and Dr. John Adamc_¢zk for their advice and consultation in formulating

this research. A very special note of appreciation is extended to my advisers, Drs. Kenneth J. DeWitt and

Theo G. Keith, Jr., for their encouragement, guidance, and patience during the completion of this work.

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An Abstract of

EXPERIMENTAL STUDY OF BOUNDARY LAYER BEHAVIOR IN A

SIMULATED LOW PRESSURE TURBINE

Rickey J. Shyne

Submitted in partial fulfillment

of the requirements of the

Doctor of Philosophy Degree

The University of Toledo

An experimental investigation of boundary layer behavior on the suction surface

of a simulated low pressure turbine (LPT) blade was conducted. The Boundary Layer

Transition Tunnel at the NASA Lewis Research Center was used in the study. A large

scale experiment was developed for this facility to simulate the pressure gradients

typically found in low pressure turbines. A two-dimensional flow was established, and

passed through the test section. The upper wall of the test section was designed so that

the LPT pressure gradients would be imposed on a flat plate opposite it. The large size

and simple geometry of the experiment facilitated the detailed measurement of the

boundary layer flow. A basic understanding of the detailed flow physics is required to

consistently design high performance low pressure turbines, which have to operate over a

wide range of conditions. An inviscid, integral equation solver was used to design the

test section, and a Navier-Stokes computational fluid dynamics code was used to analyze

the design.

Detailed data including flow visualization data were acquired to help understand

the boundary layer transition process in the LPT. Measurements were made in the test

section module at Reynolds numbers experienced in a LPT at typical take-off and cruise

conditions. Reynolds numbers of 100,000 and 250,000 based upon the test section length

and exit velocity were used for this study. This was due the scaling of the test section to

tunnel blower constraints. The flow behavior at these test conditions are representative of

NASA/TM-- 1998-208503 i
thoseencountered at cruise and take-off flight conditions with separated and attached

flow occurring at the lower and higher Reynolds numbers, respectively. The effects of

freestream turbulence intensity (TI) and Reynolds number on the transition process were

investigated during this study. Flow visualization was performed using a nichrome wire

smoke generator system as well as tufts, and these methods were used to identify areas of

separation. Hot-wire probes (single and x-wire) were utilized to obtain detailed

boundary layer measurements at multiple axial locations and flush mounted hot-film

gages were used to identify the onset and location of transition and turbulent spot

development. Static pressure measurements were also made to quantify the surface

pressure distribution.

Detailed measurements revealed that a separation bubble occurs on the lower

wall at a typical take-off Reynolds number for atl freestream turbulence levels tested.

Separation was confirmed for 0.8% TI (grid 0) through the use of smoke flow

visualization and for all turbulence levels through hot-wire measurements.

The separation bubble starts just downstream of the throat (minimum flow area) and

reattaches as a turbulent boundary layer downstream. Hot-wire signals were also

analyzed to compute intermittency values all lev:As of TI and Reynolds numbers tested.

The transition process over the separated flow region was observed to behave like

a laminar free shear layer flow through the formation of a large coherent eddy structure.

It can be concluded from this study that the transition process is still bypass, but it

follows a different process. The study also reve_Jed that classical disturbances were not

discerned in the flow field generated in the upstream portion of the test section from the

boundary spectra data and it could not be concluded that the upstream disturbances affect

the downstream boundary layer behavior. Additionally, it can be concluded that for the

ranges of freestream turbulence intensity evalualed in this experiment and a Reynolds

number of 100,000, a separation bubble will occ Jr for a pressure gradient parameter, K,

below -4.0 x l0 6.

NASAfI'M-- 1998-208503 ii
TABLE OF CONTENTS

Abstract ...................................................................................................................... i

Nomenclature ............................................................................................................. v

List of Figures ............................................................................................................ ix

List of Tables ............................................................................................................. xvi

I. INTRODUCTION .................................................................................................. 1

II. BACKGROUND ................................................................................................... 6

A. Low Pressure Turbine Flow Physics .................................................................. 6

B. Boundary Layer Behavior ................................................................................... 7

C. Computational Efforts ........................................................................................ 9

III. RESEARCH FACILITY ...................................................................................... 20

A. Boundary Layer Transition Tunnel .................................................................... 20

B. Test Section ........................................................................................................ 21

C. Flow Visualization ............................................................................................. 23

D. Instrumentation .................................................................................................. 24

1. Steady-State Instrumentation ............................................................................ 24

2. Dynamic Instrumentation .................................................................................. 25

IV. DATA ACQUISITION ........................................................................................ 35

A. Steady-State Data ............................................................................................... 35

B. Unsteady Data .................................................................................................... 36

C. Calibration .......................................................................................................... 36

1. Hot-wire Calibration ......................................................................................... 37

2. Hot-film Calibration .......................................................................................... 37

V. RESULTS AND DISCUSSION ........................................................................... 39

A. Characterization of Flow .................................................................................... 39

B. Flow Visualization Data ..................................................................................... 45

C. Establishment of Test Conditions ...................................................................... 47

D. Pressure Distribution Data ................................................................................. 48

E. Hot-wire Data ..................................................................................................... 52

1. Mean Velocity Contour Plots ......................................................................... 52

2. Law of the Wall Plots .................................................................................... 58

3. Fluctuating (rms) Velocity Profiles ................................................................ 65

4. Boundary Layer Parameters ........................................................................... 75

NASA/TM-- 1998-208503 iii
5. Intermittency Profiles ..................................................................................... 90

6. Power Spectra Density Data ........................................................................... 95

7. Integral Length Scales .................................................................................... 105

8. Classification of Separation Bubble ............................................................... 105

F. Hot-film Data ...................................................................................................... 108

G. X-wire Data ........................................................................................................ 114

1. X-wire u' Velocity Profiles ............................................................................ 114

2. X-wire v' Velocity Profiles ............................................................................ 119

3. Reynolds Shear Stress Profiles ...................................................................... 125

VI. UNCERTAINTY ANALYSIS ............................................................................ 131

VII. CONCLUSIONS AND RECOMMENDATIONS ............................................. 136

VIII. REFERENCES .................................................................................................. 139

NASA/TM-- 1998-208503 iv
NOMENCLATURE

AR

F span

Aspect ratio |-

L chord

A

B

Cf

Constant in thermal response equations of hot-wire

Constant in thermal response equations of hot-wire

Cf

F

[ P_ -p= Pressure coefficient L q=

EL

f

HI2

H32

Linearized voltage, volts

Frequency, hertz

Shape factor I= -_0_-]

 pe acto [:ol

K

Wire current, amperes

Pressure Gradient Parameter v dU,,,] ---U,_ dx

dw

+

w

PSD

Length-to-diameter ratio of wire

Wire length normalized in wall units [= -_-]

Power spectral density _:.

Local static pressure, --lb! or kPa

InN AS A/TM-- 1998-208503 v
P_

lbf

Free-stream static pressure, v--v or kPa

In"

qoo

Re x

Re o

RE 6,

Dynamic pressure, I = -_p= 1 v_

lbf

, .---v or kPa

inLength Reynolds number I= -U_]

Momentum thickness Reynolds number i- -

I U "=]

Displacement thickness Reynolds number - _

V

r Radius of wire, inches or mm

T

TI

Instantaneous or Mean temperature, "F or °C

Free-stream turbulence intensity [ +w,2) U

ft m

u' Fluctuating streamwise velocity, -- or

sec _ec

U Instantaneous or mean streamwise velocity, --

ft m

or--

sec sec

ft m

U,, Magnitude of actual velocity, -- or

see see

u_ Friction velocity = , --

sec

or --

seem

U +

v

Streamwise mean velocity in wall units

Spanwise vertical velocity, --

ft m

or--

sec sec

N AS A/TM-- 1998-208503 vi
ft m

v" Instantaneous or rms vertical fluctuating velocity, -- or --

sec sec

V Bridge voltage of the hot-wire anemometer or instantaneous, volts

lb t- N

- u'v' Reynolds shear stress, ft----yor m2

X or x Streamwise distance from leading edge of test section, inches or cm

y Vertical distance from the wall, inches or cm

Yo Typical distance between wall and first measurement station, inches or cm

+

Vertical distance in wall unitsI_- -_1

Yb Contour height, inches or cm

y,, Flow path height, inches or cm

Yo Tunnel inlet height, inches or cm

Y2 Exit height, inches or cm

NASA/TM-- 1998-208503 vii
Greek

F

C

A

0

V

P

27

Temperature coefficient of resistance

Intermittency factor

Boundary layer thickness at U = 0.995 U_, inches or mm

di, , cemen [:i/, ]i c e, ormm

Integral energy thickness = 1-,_- -_- dy

Longitudinal integral length scale, inches or mm

Integral momentum thickness [= i (1 - UJ(u)dY ]

Kinematic viscosity, --

Density, Ibm kg

ft--3- or m3

Wall lb_ shear stress, -- or --

Inft 2 m 2

or

see sec

N

m 2

, inches or mm

, inches or mm

Subscripts

a

e

lam

max

w

n

0

t

tur

O0

Ambient conditions

Boundary layer edge or free-stream

free -stream

laminar

maximum

Wall or wire

Non-turbulent part of the quantities

Total quantities

Turbulent part of the quantities

Turbulent

Free-stream conditions

NASA/TM-- 1998-208503 viii
Figure

Figure 2

Figure 3

Figure 4

Figure 5

Figure 6

Figure 7

Figure 8

Figure 9

Figure 10

Figure 11

Figure 12

Figure 13

Figure 14

Figure 15

Figure 16

Figure 17

Figure 18

LIST OF FIGURES

Typical turbine blade-row velocity diagram and surface static

pressure distribution ................................................................................. 5

Boundary layer development on a turbine ............................................... 12

Viscous effects in flow around an airfoil .................................................. 12

Transition events on a turbine airfoil

(Laminar separation and reattachment) ..................................................... 13

Separated flow velocity profile, velocity gradient and velocity

curvature and pressure distributions ........................................................ 14

Generic low pressure turbine (LPT) blade ................................................ 15

Generic low pressure turbine blade (LPT) Panel code pressure

distribution ................................................................................................ 16

Panel code simulated low pressure turbine test section geometry ........... 17

Comparison of LPT blade and simulated LPT lower wall Panel code

pressure distributions, Re = 250,000 ........................................................ 18

NPARC velocity contour plot of simulated LPT test section ................. 19

Schematic diagram of unmodified boundary layer transition tunnel ....... 30

Schematic diagram of simulated low pressure turbine test section ......... 31

Photograph of boundary layer transition tunnel with simulated low

pressure turbine test section ..................................................................... 32

Photograph of simulated low pressure turbine test section from inside

and upstream of boundary layer transition tunnel .................................... 33

Schematic diagram of simulated low pressure turbine test section

lower wall ................................................................................................ 34

Sample Streamline hot-wire probe calibration curve .............................. 38

K, pressure gradient parameter, grids 0, 2 and 3, Re = 100,000 .............. 43

K, pressure gradient parameter, grids O, 2 and 3, Re = 250,000 .............. 43

NASA/TM-- 1998-2085(t3 ix
Figure

Figure

Figure

Figure

Figure 23

Figure 24

Figure 25

Figure 26

Figure 27

Figure 28

Figure 29

Figure 30

Figure 3 l

Figure 32

Figure 33

Figure

Figure

Figure

19 Edge velocity variation, grids O, 2 and 3, Re = 100,000 .......................... 44

20 Edge velocity variation, grids 0, 2 and 3, Re = 250,000 .......................... 44

21 Photograph of flow visualization without suction, grid O, Re = 50,000..46

22 Photographs of flow visualization with suction, grid 0, Re -- 50,000 ..... 47

Experimental simulated test section lower wall pressure distributions,

grids O, 2 and 3, Re - 100,000 ................................................................. 51

Experimental simulated test section lower wall pressure distributions,

grids O, 2 and 3, Re = 250,000 ................................................................ 51

Comparison of computational and experimental lower wall pressure

distributions, Re = 250,000 ...................................................................... 52

Mean velooty and streamline contour, grid 0, Re - 100,000 .................. 55

Mean velocity and streamline contour, grid 2, Re = 100,000 ................. 55

Mean velocity and streamline contour, grid 3, Re = 100,000 ................... 56

Mean velocity and streamline contour, grid O, Re =250,000 .................. 56

Mean velocity and streamline contour, grid 2, Re =250,000 ................... 57

Mean velocity and streamline contouJ, grid 3, Re =250,000 ................... 57

Upstream streamwise mean velocity profiles in wall units, grid O,

Re = 100,000 ............................................................................................. 60

Upstream streamwise mean velocity profiles in wall units, grid 2,

Re -- 100,000 .......................................................................................... 61

34 Upstream streamwise mean velocity profiles in wall units, grid 3,

Re --- 100,000 ........................................................................................... 61

35 Upstream streamwise mean velocity profiles in wall units, grid 0,

Re = 250,000 ........................................................................................... 62

36 Upstream streamwise mean velocity 1:rofiles in wall units, grid 2,

Re = 250,000 ........................................................................................... 62

NASA/TM-- 1998-208503 x
Figure

Figure

37 Upstream streamwise mean velocity profiles in wall units, grid 3,

Re = 250,000 ........................................................................................... 63

38 Downstream streamwise mean velocity profiles in wall units, grid 0,

Re = 250,000 ............................................................................................ 63

Figure 39

Figure 40

Figure 41

Figure 42

Figure 43

Figure

Figure

Figure

Downstream streamwise mean velocity profiles in wall units, grid 2,

Re = 250,000 ............................................................................................ 64

Downstream streamwise mean velocity profiles in wall units, grid 3,

Re -- 250,000 ............................................................................................ 64

Downstream rms velocity and streamline profiles, grid 0,

Re = 100,000 ............................................................................................ 66

Downstream rms velocity and streamline profiles, grid 2,

Re = 100,000 ............................................................................................ 67

Downstream rms velocity and streamline profiles, grid 3,

Re = 100,000 ............................................................................................ 67

44 Downstream rms velocity and streamline profiles, grid O,

Re = 250,000 ........................... ................................................................. 68

45 Downstream rms velocity and streamline profiles, grid 2,

Re = 250,000 ............................................................................................ 68

46 Downstream rms velocity and streamline profiles, grid 3,

Re = 250,000 ............................................................................................ 69

Figure 47

Figure 48

Figure 49

Figure 50

Figure 51

Figure 52

Figure 53

Figure 54

Upstream rms velocity profiles, grid O, Re - 100,000 ............................. 69

Upstream rms velocity profiles, grid 2, Re = 100,000 ............................. 70

Upstream rms velocity profiles, grid 3, Re = 100,000 ............................. 70

Upstream rms velocity profiles, grid 0, Re = 250,000 ............................. 71

Upstream rms velocity profiles, grid 2, Re = 250,000 ............................. 71

Upstream rms velocity profiles, grid 3, Re = 250,000 ............................. 72

Downstream rms velocity profiles, grid 0, Re = 100,000 ........................ 72

Downstream rms velocity profiles, grid 2, Re = 100,000 ........................ 73

NASA/TM-- 1998-208503 xi
Figure 55

Figure 56

Figure 57

Figure 58

Figure

Figure

Figure 61

Figure 62

Figure 63

Figure 64

Figure 65

Figure 66

Figure 67

Figure 68

Figure 69

.Figure 70

Figure 71

Figure 72

Figure 73

Figure 74

Figure 75

Downstream rms velocity profiles, grid 3, Re = 100,000 ........................ 73

Downstream rms velocity profiles, grid 0, Re = 250,000 ........................ 74

Downstream rms velocity profiles, grid 2, Re = 250,000 ........................ 74

Downstream rms velocity profiles, grid 3, Re = 250,000 ........................ 75

59 Displacement thickness profiles, grids 0, 2 and 3, Re = 100,000 ............ 78

60 Momentum thickness profiles, grids O, 2 and 3, Re = 100,000 ............... 79

Energy thickness profiles, grids O, 2 and 3, Re = 100,000 ...................... 79

Shape factor profiles, grids O, 2 and 3, Re = 100,000 .............................. 80

Energy shape factor profiles, grids O, 2 and 3, Re = 100,000 .................. 80

Displacement thickness profiles, grids O, 2 and 3, Re = 250,000 ............ 81

Momentum thickness profiles, grids (h 2 and 3, Re = 250,000 ............... 81

Energy thickness profiles, grids O, 2 _nd 3, Re - 250,000 ...................... 82

Shape factor profiles, grids O, 2 and 3, Re = 250,000 .............................. 82

Energy shape factor profiles, grids O, 2 and 3, Re - 250,000 .................. 83

Skin friction profiles, grids O, 2 and 3, Re = 250,000 ............................. 83

Indicator function determination techlique for single wire ..................... 92

Downstream mtermittency profiles, grid O, Re = 100,000 ...................... 92

Downstream mtermittency profiles, grid 2, Re = 100,000 ...................... 93

Downstream mtermittency profiles, g_id 3, Re = 100,000 ...................... 93

Downstream mtermittency profiles, grid O, Re = 250,000 ...................... 94

Downstream mtermittency profiles, grid 2, Re = 250,000 ...................... 94

Figure 76 Downstream intermittency profiles, grid 3, Re = 250,000 ...................... 95

Figure 77 Upstream boundary layer spectra, y :-- y(u'a x ), grid O, Re = 100,000 ...97

N AS A/TM-- 1998-208503 xii
Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

78 Downstream boundary layer spectra, y = y(u'_,,_ ). grid O,

Re = 100,000 ............................................................................................ 97

79 Upstream boundary layer spectra, y -- y(u'.,_ ), grid 2, Re = 100,000 ..... 98

80 Downstream boundary layer spectra, y = y(u'.,a_ ), grid 2,

Re = 100,000 ............................................................................................ 98

81 Upstream boundary layer spectra, y = y(u_,_ ), grid 3, Re = 100,000 ...... 99

82 Downstream boundary layer spectra, y = y(u'a_ ), grid 3.

Re - 100,000 ............................................................................................ 99

83 Upstream boundary layer spectra, y = y(u,',,._ ), grid O, Re = 250,000 .... 1O0

84 Downstream boundary layer spectra, y = y(u_,,_ ), grid 0,

Re = 250,000 ............................................................................................ 100

85 Upstream boundary layer spectra, y = y(U'm_ ), grid 2, Re = 250,000 ...... l O1

86 Downstream boundary layer spectra, y = y(u'_,,x ), grid 2,

Re = 250,000 ............................................................................................ 101

87 Upstream boundary layer spectra, y = y(u',_ ), grid 3. Re = 250,000 ...... 102

88 Downstream boundary layer spectra, y = y(u _ax )' grid 3.

Re = 250,000 ............................................................................................ 102

89 Boundary layer spectra, y = y(u_), grids 0, 2 and 3, Re = 100,000,

x = 2.25 inches, (5.72 cm) ........................................................................ 103

90 Boundary. layer spectra, y = y( u_ ). grids O, 2 and 3, Re = 100,000,

x - 7.25 inches, (18.42 cm) ..................................................................... 103

91 Boundary layer spectra, y = y(u_), grids 0, 2 and 3, Re = 250,000,

x - 2.25 inches, (5.72 cm) ....................................................................... 104

92 Boundary layer spectra, y = y(u_), grids 0, 2 and 3, Re = 250,000,

x = 7.25 inches, (18.42 cm) ..................................................................... 104

NASAFFM--1998-208503 xiii
Figure 93 Gaster's two parameter bubble bursti:lg criterion, grids O, 2 and 3,

Re = 100,000 ........................................................................................... 107

Figure 94 Modified Roberts' correlation, grids O, 2 and 3, Re = 100,000 ............... 107

Figure 95 Hot-film gage voltage traces, grid 0, Re - 100,000 ................................. 1 ! 1

Figure 96 Hot-film gage voltage traces, grid 2, Re - 100,000 ................................ 112

Figure 97 Hot-film gage voltage traces, grid 3, Re -- 100,000 ................................ 112

Figure 98 Hot-film gage voltage traces, grid O, Re = 250,000 ................................. 113

Figure 99 Hot-film gage voltage traces, grid 2, Re = 250,000 ................................. 113

Figure 100 Hot-film gage voltage traces, grid 3, Re = 250,000 ................................ 114

Figure 101 X-wire u' velocity profile, grid 0, Re - 100,000 .................................... 116

Figure 102 X-wire u' velocity profile, grid 2, Re = 100,000 .................................... 117

Figure 103 X-wire u' velocity profile, grid 3, Re = 100,000 ................................... 117

Figure 104 X-wire u' velocity profile, grid O, Re = 250,000 .................................... 118

Figure 105 X-wire u' velocity profile, grid 2, Re = 250,000 .................................... 118

Figure 106 X-wire u' velocity profile, grid 3, Re = 250,000 .................................... 119

Figure 107 X-wire v' velocity profile, grid O, Re = 100,000 .................................... 122

Figure 108 X-wire v' velocity profile, grid 2, Re = 100,000 .................................... 122

Figure 109 X-wire v' velocity profile, grid 3, Re = 100,000 .................................... 123

Figure 110 X-wire v' velocity profile, grid O, Re = 250,000 .................................... 123

Figure 111 X-wire v' velocity profile, grid 2, Re = 250,000 .................................... 124

Figure 112 X-wire v' velocity profile, grid 3, Re = 250,000 .................................... 124

Figure 113 Reynolds shear stress profiles, grid 0 Re = 100,000 .............................. 128

Figure 114 Reynolds shear stress profiles, grid 2 Re = 100,000 .............................. 128

NASA/TM--1998-208503 xiv
Figure 115

Figure 116

Figure 117

Figure 118

Reynoldsshearstressprofiles,grid 3, Re= 100,000.............................. 129

Reynoldsshearstressprofiles,grid 0, Re= 250,000.............................. 129

Reynoldsshearstressprofiles,grid 2, Re= 250,000.............................. 130

Reynoldsshearstressprofiles,grid 3, Re= 250,000.............................. 130

NASA/TM--1998-208503 xv
LIST OF TABLES

Table 1

Table 2

Table 3

Table 4

Table 5

Table 6

Table 7

Table 8

Table 9

Table 10

Table 11

Table 12

Table 13

Table 14

Table 15

Table 16

Table 17

Simulated Low Pressure Turbine I'est Matrix ................................... 28

Scaling Chart for Simulated Low Pressure Turbine Experiment ...... 28

Location of Off-Centerline Static Pressure Taps ............................... 29

Location of Hot-film Gages ............................................................... 30

K, Pressure Gradient Parameter, grids 0, 2 and 3, Re = 100,000 ....... 41

K, Pressure Gradient Parameter, grids 0, 2 and 3, Re = 250,000 ....... 42

Streamwise Hot-wire Measurement Locations .................................. 54

Boundary Layer Properties at Separation, Re = 100,000 .................. 84

Boundary Layer Properties, Grid 0, Re = 100,000 .............................. 84

Boundary Layer Properties, Grid 2, Re = 100,000 .............................. 85

Boundary Layer Properties, Grid 3, Re = 100,000 .............................. 86

Boundary Layer Properties, Grid 0, Re =250,000 .............................. 87

Boundary Layer Properties, Grid _., Re =250,000 .............................. 88

Boundary Layer Properties, Grid _, Re =250,000 .............................. 89

A, Longitudinal Integral Length Scale ............................................... 105

Separation Bubble Characteristics, Re = 100,000 .............................. 108

Hot-film Gage Test Matrix ................................................................ 111

NASA/TM-- 1998-208503 xvi
I. INTRODUCTION

Designing modern gas turbine engines that operate over a wide envelope of flight

conditions is a challenging task due to the many constraints that must be properly

balanced to ensure high efficiency, low specific fuel consumption and low noise.

Engines are designed for peak performance at take-off conditions with allowances made

for climb and cruise operation. The performance of an engine at take-off has been well

documented in full scale ground tests, but engine performance at cruise (altitude)

conditions, especially the behavior of engine components such as the low pressure

turbine, is less clear due to limitations of ground test facilities in simulating altitude flight

conditions. More than forty different factors influence the performance of low pressure

turbines (LPT), but factors such as end wall losses, blade loading, boundary layer

behavior and wake passing effects are thought to play major roles. Transition and/or

separation may occur along considerable regions of LPT blade surfaces in large gas

turbine engines and this effect is amplified at the low Reynolds numbers encountered

during altitude flight conditions. LPT efficiency (as much as two points) may be lost if

the assumptions made on the state of the boundary layer in the LPT design process are

inaccurate. The accurate prediction of the transition and/or separation process can lead

directly to improved engine efficiency, lower specific fuel consumption and higher thrustto-weight ratios. Detailed experimental data regarding boundary layer behavior on LPT

blades under the influence of adverse pressure gradients, altitude Reynolds numbers and

N ASA/TM-- 1998-208503 1
varying free-stream turbulence levels is desired to modify existing LPT blade designs and

to develop new correlations for use in LPT design systems. A typical turbine blade-row

velocity diagram and surface static pressure distribution from Glassman et al., (1972) is

shown in Figure 1.

Gardner (1981) and Cherry et al. (1982) performed experimental studies on the

effect of loading on LPT blades as part of the NASA funded Energy Efficient Engine

Technology Program. This experimental program, along with others, showed when

designed properly, highly loaded blades exhibit higher performance than blades designed

with a lower loading profile. As a consequence of this, modern LPT blades are now

designed to be more highly loaded and have lower aspect ratios than their predecessors.

This trend in blade design philosophy further covnplicates the transition problem by

introducing severe adverse, as well as favorable, pressure gradients into the flow field

experienced by the blades. Because of the complexity of the flow field, more systematic

and well controlled experiments are required to help improve modeling and

computational analyses of boundary layer transiti3n as it occurs in a LPT. The purpose of

this work is to develop a comprehensive set of experimental data to improve LPT blade

design and modeling systems.

Methods for predicting boundary layer gr,_wth in laminar and turbulent flows

have improved over the years, however, in the last five years more research has been

directed towards understanding the laminar-turbulent transition process, especially within

gas turbine engines. Binder et al. (1988) state thzt the prediction of the state of the

boundary layer is important and dramatic advances in modeling an computational

analyses are required to achieve this. Blair (1982) also discusses the importance of

NASA/TM-- 1998-208503
predicting the state of the boundary layer and the interaction of the free-stream turbulence

and pressure gradient in turbomachinery flows. Computational fluid dynamic methods

are increasingly being used to model flows over blading, but the transition and/or

turbulence models incorporated into these methods often do not contain adequate physics

to accurately predict the state of the boundary layer. Mayle (1993) lectured on the

importance of understanding the transition process in gas turbine engines, Walker (1993)

amplified many of the same issues presented by Mayle (1991, 1993). Mayle made

several suggestions as to how LPTs should be designed. These suggestions may be

summarized as follows:

1) High turbulence levels should be used in experiments to correctly model transition and

separation.

2) To properly calculate turbine airfoil transitional flows, models must be able to

compute forward and reverse (relaminarization) transition in addition to wake induced

transition.

3) Calculation of separated flow transition and massive separation in LPTs at low

Reynolds numbers must include the modeling of laminar, transitional and turbulent

shear layer flows near and away from the surface.

4) The variation of the pressure gradient parameter K to critical pressure gradient I_rit as

a function of Reynolds should be considered in the design process.

5) The forcing of a short, separated, flow transition by a local change in blade shape

(curvature) should be considered by designers as a method of controlling transition

in LPTs.

Halstead et al. (1995) performed an extensive experimental and computational study of

NASAFFM-- 1998-208503
boundary layer development on the suction surface of airfoils in an embedded stage of a

LPT and compressor and this study revealed tha! laminar flow can persist over anywhere

from 30 and 40 percent of the suction surface length. Since modern LPT airfoil designs

are more aggressive (higher loadings, lower aspect ratios, etc.), an airfoil with significant

laminar flow along its suction surface may suffer significant performance losses from

boundary layer separation due to adverse pressure gradients and/or wake passing effects.

Research performed by Ashworth et al. (1985); Baughn et al. (1995); Cumpsty (1995);

Gostelow and Walker (1990); Gostelow et al. (1992); Hall and Gibbings (1972); Hodson

et al. (1993); Johnsen et al, (1965); Mayle (199317; Rivir (1996) Schulte and Hodson

(1994); Sharma (1987); Simon and Ashpis (1996); Wisler (1985) also investigated wake

passing and pressure gradient effects on boundary layer behavior in compressors in

addition to high and low pressure turbines. Additionally, Dixon (1978) discusses other

important factors in designing turbomachinery c(_mponents.

Minimizing losses in the LPT over its entire operating range is the designers

ultimate challenge and having detailed knowledg _ of how the boundary layer behaves is

of paramount importance in the design process. The purpose of this experimental study

is to develop a comprehensive experimental database that can be used to improve LPT

design systems. This study will provide data on transitional as well as separated

flow fields if they occur. Additionally, this data will allow for the improvement of

transition and turbulence models for CFD applic_ tions.

NASA/TM-- 1998-208503
Stations

o V

Vx, !

s..

,-Suct_]- r

_r'ace l/

P_.

"'" _'Srain

Axial distance

Figure 1 Typical turbine blade-row velocity diagram and surface static pressure

distribution

NASA/TM-- 1998-208503
II. BACKGROUND

A. Low Pressure Turbine Flow Physics

In November 1993, a workshop on bypass transition was held at the NASA Lewis

Research Center. Attendees at this workshop included representatives from academia, the

aircraft engine industry and government agencies. The aircraft engine industry expressed

the need for shifting the research focus from studying bypass transition in turbomachinery

to the investigation of boundary layer behavior in low pressure turbines. A performance

degradation in efficiency in a low pressure turbine of approximately 2% occurs as the

aircraft accelerates from take-off to cruise flight conditions and industry is interested in

identifying the physics involved in this performa_lce loss. This performance loss is

primarily dictated by the operating Reynolds number which varies from 450,000 to

180,000 for take-off and cruise flight conditions, respectively. The Reynolds number is

based upon the LPT exit velocity and blade suction surface length. Separation, wake

passing effects and transition are three major physical mechanisms that may singularly or

collectively affect the losses in a LPT. The understanding of separation on a LPT blade

is important due to the potential presence of separation bubbles and the mechanics of the

bubble (e.g., burst, growth, etc.). Wake passing _ fleets can have a significant impact on

the boundary layer causing separation and/or transition. Lastly, the modes of transition

must be identified such as bypass, transition in separation bubbles and calmed regions,

and turbulent spot dynamics. All of the aforementioned physical mechanisms are

N A SAFFM-- 1998-208503 6
affected by Reynolds number, free-stream turbulence intensity, pressure gradient and

reduced frequency. This research is part of a collaborative NASA/Industry/Academia

Low Pressure Turbine Flow Physics Program.

B. Boundary Layer Behavior

Figure 2 shows a boundary layer on a typical turbine blade. The boundary layer

starts developing from the leading edge of the blade with a small finite thickness and

grows along the pressure and suction surfaces. Initially the boundary layer is laminar, but

soon becomes transitional due to viscous effects and free-stream disturbances

(turbulence). Also, viscous effects contribute to the change to transition as illustrated in

Figure 3. On the upper surface of the blade the flow is subjected to adverse or rising

pressure which, in turn, leads to a region of separated flow or reversed flow. Chang

(1970) describes this separation as stalling and this phenomena can be connected with

closed separation bubbles. Separation bubbles may be short or long and both affect the

flow in different ways. If the bubble is short, it usually is enclosed and points of

separation and reattachment can be identified; however, a short bubble can also break

down (burst) and this can lead to a stall condition with an attendant increase in drag and

loss of lift. If the bubble is long, the pressure distribution along the airfoil changes

slightly, but this flow breakdown does not lead to a complete separation; instead, the

separated flow passes over the body surface and reattaches further downstream. If the

flow undergoes transition, it encounters weak disturbances (Tollmien-Schlichting waves)

which are amplified and this leads to random fluctuations in the flow that have turbulent

characteristics. Figure 3 shows a separated flow region occurring in a laminar

NAS A/TM-- 1998-208503
boundary layer. Separation can also occur in a turbulent boundary layer, but a turbulent

boundary layer is more resistant to separation because it contains more energy. The flow

separates due to a decrease in free-stream velocity which translates into a static pressure

rise along the rear section of the suction surface of the turbine blade. This results in a

dP

positive pressure gradient (or adverse pressure gradient, -- > 0 ) which decelerates the

dx

flow in the boundary layer which enables a flow reversal. The flow in the boundary layer

is retarded to such an extent that very close to the wall, the flow starts to move in a

direction opposite to the mean flow. The point at which the flow starts to reverse itself is

the separation point and this phenomena is referred to as separation. At the separation

point, the velocity gradient (_.,) =0. Figure 4 is a schematic of transition events on a

v=O

turbine airfoil. This combination of flow phenomena includes a separation bubble that

can reattach itself to the surface as a turbulent bo_mdary layer as shown in Figure 4 or

may burst if the Reynolds number is low enough. Malkiel and Mayle (1995) and

Tani (1964) have also investigated the behavior of separation bubbles.

The boundary layer can be mathematically modeled by the continuity equation

and a reduced set of the Navier-Stokes equations :lerived by Prandtl and found in

Schlichting (1959), White (1974) and Anderson ( 1991 ). The boundary layer equations

for two-dimensional steady flow of an incompressible fluid are:

with boundary conditions y = 0:

0u Ov

-- + = 3

omu &_ 1 dj_ o_2u

du 1 dp

U_dx- pdx'

u =0, v=0 ; y = o: u = U(x). From an examination of

NASA/TM--1998-208503
Prandtl's boundary layer equations and considering the relationship of the pressure

gradient d___p_P to the velocity distribution u(x,y) or u_(x), it can be concluded that for

dx

steady flow, separation can only occur in the presence of an adverse pressure gradient.

Restating this in a slightly different manner, an adverse pressure gradient is a necessary,

but not sufficient condition for separation. Figure 5 shows the velocity profile, gradient

and curvature profiles for a decelerating flow which corresponds to an adverse (positive)

pressure gradient and a turbine blade pressure distribution plot which illustrates regions

of favorable (negative), as well as adverse pressure gradient.

The largest losses in a turbine can be attributed to the boundary layer that builds

up on the blade and end-wall surfaces, Glassman et al. (1972). These boundary layer

losses are comprised of friction drag from the flow of viscous fluid over the surfaces,

profile (pressure) drag that results from fluid flow past the trailing edge of the blade and

mixing of low velocity boundary layer fluid with high velocity free-stream fluid

downstream of the blade rows.

C. Computational Efforts

The LPT blade geometry used in this study is shown in Figure 6. The surface

pressure distributions along the blade pressure and suction surfaces are shown in Figure

7. An inviscid panel code developed by McFarland ( 1982, 1984) was used to compute

the blade pressure distribution which is fairly benign. The blade geometry was supplied

by the Pratt & Whitney Aircraft Engine Company. The geometry is representative of

the blade design and loadings used in modern LPT stages. This blade geometry was then

used as the basis for designing a test section for the NASA Lewis experimental test

facility, CW-7, for conducting the LPT flow physics research. The test section is twoNASA/TM-- 1998-208503
10

dimensional in nature and consists of contoured upper and flat lower walls. The

contoured upper wall was used to generate a pressure distribution along the flat lower

wall that corresponds to the pressure distribution along the suction surface of the generic

blade. This wall contour was created by matching the mass flow from the generic LPT

blade cascade through a flow channel with a contoured upper wall and flat plate lower

wall. The inviscid panel code was used initially _o compute the flow-field of the LPT

cascade geometry shown in Figure 6. The velocity and pressure distributions computed

by the panel code are a function of the area change through the channel. The suction

surface velocity distribution was then expressed as a function of suction surface length of

the generic blade. This function was used to correctly match the suction surface pressure

distribution shown in Figure 7 by utilizing the continuity equation. The following form

of the one-dimensional continuity equation was used to obtain a relation for the upper

wall contour:

pVA = constant,

(where A = yew cos a).

The width of the test section is constant and the flow angle a, is assumed to be zero.

Thus the one dimensional continuity equation ca_ be written as

PVx Ax = P_' 2A2,

PVx y, Wx = p_,2y2w2.

For Mach numbers (M << 1) the flow is assumec to be incompressible, which yields

VxY_Wx =V2._2w2,

or

Vx(Yo - Yb)=V2Y2,

NASA/TM-- 1998-208503
II

(where y, = y,, - y j, ).

Rearranging and solving for y_, yields

Yt, =Y,, -Y.

V_ V

The quantity m was computed from the -_-(s) distribution obtained from the generic Wx

LPT blade and continuity was applied to yield a new test section geometry with a

contoured upper wall and a fiat plate as shown in Figure 8. The pressure distributions

from this new test section design and the generic LPT airfoil are shown in Figure 9.

Diffusion factors (the diffusion factor is the ratio of the exit velocity to the local

velocity, Johnson and Bullock, 1965) were computed for the contoured upper wall and

showed that the flow would separate. The new test section geometry was then analyzed

using the NPARC full Navier-Stokes computational code described in the NPARC user's

guide (1994). The analysis of the test section contour was performed to validate the

effect of contoured upper wall (proper lower pressure distribution) as well as, to identify

transition and/or separated flow regions. The NPARC analysis did reveal a small

separation region just downstream of the minimum area (i.e., throat) on the contoured

upper wall (Figure 10) and a suction system was added to the upper wall to alleviate this

problem.

NASA/TM-- 1998-208503
12

r"Transition r-Tumulent

Laminar _ region ,' boundary

l_gen_ rY _ layer

_j - _,_nat,on _,_,_/,'//_ "_ r_jion

Figure 2 Boundary layer devel(pment on a turbine blade

Ll_rs

Figure 3 Viscous effects in _]ow around an airfoil

N A SA/TM-- 1998-208503
13

Transition Events on a Turbine Airfoil

Turbulent

boundary

layer

Figure 4 Transition events on a turbine airfoil (Laminar separation and reattachment)

NA SA/TM-- 1998-208503
14

Pointof

I:_-'- _.In..fil¢ilon _ _ _

////////u "/// //_

k

(L) Velocity

profile.

(b) Velocity

gradient,

(c) Velocityprofile curvature.

Figure 5 Separated flow velocity profile, velocity gradient and velocity curvature

and pressure distributions

NAS A/TM-- 1998-208503
15

Nu'clnvNqEL |m_e 41e_tew •

Y)wts (Y) vs No_*_lio_| ¢X) Cee_lL|nate

O,O O.S

N - Ob_ldlJoee_l q_,oonu_Ju_8_e CM)

i HL ill •

,u. _t_| JPointm • lb_alt IP_tn'ea I

t°O

Figure 6 Generic low pressure turbine (LPT) blade*

*Not...__ze:Drawing is not to scale.

NASA/TM-- 1998-208503
16

CP - Pressure Coefficient

2

- - _ C = :- _ =--

-2

-3

-'- Pressure

-4

-4--Suction

-5

0

.,J_

0.2 0.4 0.6 0.8 1

Cx- Axial Chord

Figure 7 Generic low pressure turbine blade tLPT ) Panel code pressure distribution

NASA/TM--1998-208503
17

@. 75 "

i,.?O --

0.65 --

m.60 --

II.55 --

O. 50 -

0.45 --

lJo40 Q,al5 -- --

O. _ill--

O. a5 --

o. I10 -- 0.£5 --

O.IO --

• 11.105

O.W--

-Ill. 10

-8.15 -

-0.20 -

-0.15 -

-t. 30 -

-O. 35 -

-0,449 -

-0.45

-,IL

I_PNtqNI_ lmlp*tt Geouetpg It 8o411

ThotA ¢V) vs Noei_l|ee&i (X) CoolNIII_Jte

u

• •

m m

,, ,,,,, , ,,

! I I ! I I I I I ! 1

_I,O-L.N-O.50 I.N 0.50 L.N t.1O I.N I.H I.N :lJ.tO 4.N 4.10

H- IPkpPIdllonal bonNILtnaq_o (X}

[ ee G414tIpOI i°'Oiettl; ° _4 lj'Ojatj l

Figure 8

Panel code simulated low pressure turbine test section geometry*

*Note: Drawing is not to scale.

NASAFFM-- 1998-208503
18

I.00

0.50

0.00

(o

a_

-0.50

-I .00

Figure 9

I

I

]

I

!

I

I

-- -- CW-7 Panel Code Design

-- P&W LPT Panel Code Analysis

/C'. -

_w% //

0.00 2.00 4.00 6.00

X, inches

F + I

8.00

Comparison of LPT blade and simulated LPT lower wall Panel code pressure

distributions, Re = 250,000

NASA/TM-- 1998-208503
19

Figure 10 NPARC velocity contour plot of simulated LPT test section

N ASA/TM-- 1998-208503
III. RESEARCH FACILITY

A. Boundary Layer Transition Tunnel

A parametric investigation of low pressure turbine boundary layer transition

was performed in the boundary layer transition tunnel, test facility CW-7, at the NASA

Lewis Research Center. The research facility is a low-speed closed loop wind tunnel that

was designed to investigate two-dimensional, incompressible, large-scale boundary

layers. The effects of flee-stream turbulence and pressure gradient on boundary layer

behavior can be investigated in this facility. A schematic of the boundary layer research

facility is shown in Figure 11. This wind tunnel consists of nine major components

which are the blower, flow conditioner with turbulence grids, two dimensional

convergent nozzle, bleed scoops, test section with variable upper wall, diffuser, air heater,

air filter and air cooler. Facility operating conditions (velocity, temperature, pressure

gradient, and free-stream turbulence) can be controlled through the adjustment of the

previously mentioned wind tunnel components. This facility has been previously used

for bypass transition studies on an unheated and t eated flat plate by Suder et al. (1988)

and Sohn et al. ( 1991 ), respectively.

A Chicago Blower Corporation, SISW Class III SQA centrifugal fan with

capacity of 10,000 cubic feet per minute (283.2 c'lbic meters per minute) is used to

provide the main flow to the tunnel. The blower :(low rate is controlled by a vortex valve

located at the blower inlet. After the air flow exits the blower, the air enters a flow

NASA/TM-- 1998-208503 20
21

conditioningplenumchamber,whichremovesflow irregularitiesgeneratedby theblower

andreducesthefree-streamturbulencelevels. Theplenumchamberconsistsof

1) perforatedplatebaffles,whichdistributesthedistortedairflow from thebloweracross

theentireplenum,2) aseriesof honeycombsandsodastrawarrays,which straightenthe

flow, and3) aseriesof fine meshscreenswhichreducethetunnelfree-streamturbulence

level.

Thetunnelfree-streamturbulencelevelscanbechangedby theuseof turbulence

generatinggridswhichcanbeinsertedat theexit of theflow conditioningsection,just

upstreamof thecontractionnozzle.Locatingtheturbulencegridsupstreamof the

contractionnozzleallowsthegeneratedturbulenceto becomemorehomogeneousand

havealowerdecayratealongthetestsectionlength(Blair et al., 1981). Theturbulence

gridsconsistof rectangularbararrayswith approximately62%openareayieldinga

squaremesh.Fourgridsweredesignedto generatetestsectionturbulencelevelsfrom

0.25to 6percent.Grids0, 2 and3 (0.8%,2%and3%free-streamturbulenceintensity,

respectively)wereusedforthisexperiment.Table 1containsthetestmatrixwith the

turbulencelevelsandReynoldsnumbersusedin thisexperiment.A moredetailed

descriptionof thewindtunnelcomponentsincludingtheturbulencegridscanbefound in

Suderet al.(1988).

B. Test Section

The test section of the Boundary Layer Research Tunnel has a rectangular cross

section that measures 27 inches (68.58 cm) wide, 12 inches (30.48 cm) long and 6 inches

( 15.24 cm) high. The test section consists of a flat lower wall, two vertical sidewalls and

NASAFFM-- 1998-208503
22

a removable upper wall. The contoured upper wall which matches the pressure gradient

generated by the suction surface of the generic LPT blade was designed and installed in

the test section to replace the existing straight upper wall. The contoured wall was used

to match the operating environment of a LPT blade and to study the effects of favorable

and adverse pressure gradients and free-stream turbulence. A porous wall bleed system

for suction was added to the contoured upper wall to prevent flow separation on the upper

surface and to induce separation on the lower wall. Interchangeable wall bleed sections

were used in the bleed system and these sections can be porous or solid. The total

number of 1/8 inch (0.3175 cm) diameter holes for these configurations were 171, 271

and 362, respectively. Flow visualization was used to verify the test section flow, suction

system effectiveness and suction flow rates.

In order to properly match the Reynolds numbers in a full scale LPT, a splitter

plate (which also functioned as the flat lower wall) was inserted in the center of the test

section (approximately 3 inches (7.62 cm) from _he floor). The test section flow

bifurcation was required due to operating limitations of the tunnel blower. Operating the

tunnel blower at low flow settings was unstable and bifurcating the test section allowed

the blower to be operated at a higher flow setting- which yielded stable flow rates that

match typical LPT cruise and take-off Reynolds aumbers based on test section length and

exit velocity ( 100,000 and 250,000, respectively_. Table 2 was used to scale the size of

the new test section. The leading edge of the sphtter plate has a 4:1 elliptical cross

section and a 1.5 inch (3.81 cm) long flap was at ached to the end of the plate to help

control the location of the stagnation point. The plate is 27 inches (68.58 cm) wide and

14 inches (35.56 cm) long. Additionally, the flap was positioned at an angle of attack

NASA/TM--1998-208503
23

which fixed the stagnation point on the top surface of the splitter plate. Figure 12 is a

schematic of the new contoured wall test section. The double bleed scoop assembly

positioned at the bottom wall of the original test section entrance was not used in the tests

reported herein. A suction system was added to the contoured upper wall to prevent

separation and is shown in Figure 12. Figures 13 and 14 are photographs of the simulated

LPT test section installed in the boundary layer transition tunnel and of the simulated LPT

test section from inside the tunnel.

A probe traversing mechanism was used to position the hot-wire probes for

making detailed boundary layer measurements in the vertical, streamwise, and spanwise

directions relative to the flow direction. This specially designed traversing system

referred to as PACS (Probe Actuation Control System) can be precisely positioned via a

computer controlled actuation system and may be positioned in increments as small as

0.00033 inches (8.382 x 10-4 cm). Streamwise and spanwise positioning of the hot-wire

probe is performed by moving the probe through streamwise and spanwise slots situated

along centerline and off centerline locations in the contoured upper wall.

C. Flow Visualization

Flow visualization was used to qualitatively analyze the flow through the

test section. Smoke traces were generated using a thin nichrome wire connected to a

power supply and a smoke wire and camera control unit. Traces were performed at

tunnel velocities between 5-10 ft/sec (1.524-3.048 m/sec) to minimize the diffusion of the

smoke and to allow visualization of the flow-field. The nichrome wire was located in the

inlet flow measurement station of the tunnel just upstream of the entrance to the test

NASA/TM--1998-208503
24

section. The nichrome wire was pulled out of the tunnel and swabbed with a thin layer of

oil (model train smoke fluid) and then placed back into the tunnel air flow. The smoke

wire and camera control unit were then used to synchronize the timing of voltage

supplied to the wire, the duration of the burn to generate smoke, as well as to control

camera and flash units if desired. The duration of the burn time for the majority of the

traces was two seconds and a voltage of 16-20 volts was used to burn the oil. The

smoke traces were visually observed using a strobe flash unit and photographed with a 35

mm camera with two fast recovery flash units. Additionally, tufts were installed on the

contoured upper wall during testing to verify that the flow on the upper wall remained

attached. Photographs of the flow visualization will be presented later in the Results and

Discussion section.

D. Instrumentation

Static pressure taps, hot-film gages and hot-wire probes (single and x-wire) were

used to make flow field measurements. Velocit3 signals from a single wire probe were

monitored on a digital oscilloscope and mean an, t fluctuating (rms) values were

measured with a personal computer (PC) based constant temperature, anemometry

system. Detailed descriptions of the test section instrumentation, hot-wire probes and

constant temperature anemometry systems are gi yen in the following sections.

1. Steady-State Instrumentation

Free-stream flow conditions at the test se :tion inlet and exit planes are measured

with a Pitot tube and thermocouple located at the center span of the test section.

NASA/TM-- 1998-208503
25

These measurements were used to determine the free-stream velocity, temperature and

mass flow. Additionally, static pressures taps are located spanwise off the center line as

well as streamwise along the bifurcated test plate to measure the spanwise and

streamwise pressure gradients impressed upon it by the contoured upper wall. A total of

36 static taps were used to instrument the test plate. Figure 15 shows the layout of the

static taps on the flat test plate and Table 3 contains the locations of the taps situated 1

inch (2.54 cm) off the centerline.

2. Dynamic Instrumentation

Three different types of hot-wire probes were used for this experimental

investigation, two single wire probes and an x-wire probe:

1) A commercially available TSI model 1218-t1.5 single sensor boundary layer probe

was used to measure the streamwise component of the mean and fluctuating (rms)

velocity. The safety leg of the single sensor probe was removed to allow surveys as close

to the wall as possible.

2) A Dantec model 55P11 straight general purpose type probe was used with a special

"probe support to make boundary layer measurements upstream of the throat. This is a

miniature wire probe made of tungsten wire with a diameter of 0.000197 inches (5 _tm),

length of 0.0492 inches (1.25 ram) and a prong length of 0.197 inches (5 mm).

3) A Dantec model 55P63 x-wire probe was used to simultaneously measure the

instantaneous streamwise and vertical velocity components. These measurements

provide data for the determination of the Reynolds shear stresses. This is also a miniature

probe made of tungsten wire with a diameter of 0.000197 inches (5 lam), length of 0.0492

NASA/TM-- 1998-208503
26

inches ( 1.25 mm), wire separation of 0.0394 inches (1 mm) and total prong length of

0.4882 inches ( 12.4 mm). This is an x-array probe, 90 °, with its sensor plane parallel to

the probe axis.

The x-wire probe was designed to have excellent spatial resolution and

measurement capabilities. This probe was designed with a small separation distance

between the wires to properly resolve small scale near wall turbulence (viscous length

scale approximately of 0.004331 inches ( 11 lam) for the worst case of a fully turbulent

boundary layer) without significant eddy averaging in the spanwise direction. To

minimize heat conduction from the support prong and vertical averaging in the shear

flow, a short sensing length must be used. These two constraints require the use of a

miniature probe with small wires.

Hot-film gages were used to identify turb dent spot patterns, while the hot-wire

and x-wire probes were used to measure the mean and rms velocities, as well as the

Reynolds shear stress throughout the boundary layer, respectively.

The hot-film gages are TSI model 1237 slandard flush mounted platinum sensors

and these sensors are suitable for one-dimensionz_l measurement of wall shear stress

without disturbing the flow. The flat plate was instrumented with these hot-film gages

along the centerline of the plate starting at 1.5 inches (3.81 cm) from the plate leading

edge with spacing of 0.5 inch ( 1.27 cm) for the fi "st 11 gages, followed by a gage spaced

1.0 inch (2.54 cm), further, followed by two gag,:s spaced 2.0 inches (5.08 cm) apart as

shown in Figure 15 and listed in Table 4. The hot-film gages were clustered in the region

where the change in adverse pressure gradient ha:; the greatest affect on the boundary

NASA/TM-- 1998-208503
27

layer and the transition process.

A Dantec Streamline constant temperature anemometer system was used to

operate the hot-film gages and hot-wire probes. The Streamline system used for this

experiment consisted of a frame and six anemometer modules with signal conditioners

incorporated. The frame can incorporate up to six anemometer modules and each module

has galvanically separated power supplies for electrical noise protection and to prevent

crosstalk between measured velocity components. Three bridge configurations are

available from the software and each anemometer has a 20:1 general purpose bridge that

includes compensation for 16.41 foot (5 m) and 65.62 foot (20 m) cables. Each bridge

has two top resistance values, 20 and 10 Ohm. The 20 Ohm top resistance can be used

with all standard probes and the 10 Ohm top resistance is used for high power

applications (the 20 Ohm top resistance value was used for this experiment). A 1:1

symmetrical bridge ensures high system bandwidth and minimum noise and is intended

for use in flows with fluctuating temperatures in conjunction with temperature

compensated probes. This bridge is also needed for test setups that include long cables,

high-impedance probes, or probes with negative temperature coefficients. The overheat

resistor, cable compensation, probe resistance measurement circuit and amplifier

parameters can be optimized by the user or set to a fully automatic mode. The signal

conditioner contained in each anemometer module allows optimal signal adaptation to the

analog/digital (A/D) converter in the 486 personal computer and had programmable input

offset and gain. The variable input offset and gain allows for the investigation of very

low turbulence levels in steady flows. High-bypass filters can be applied when analyzing

turbulence levels in unsteady flows. Additionally, the hot-wire probes were calibrated

NASA/TM-- 1998-208503
28

using a Dantec calibration module (that replaces an anemometer module in the flame) and

Flow Unit. The calibration, calibration module and Flow Unit are discussed in detail in

the calibration section of this thesis.

Table 1 Simulated Low Pressure Turbine Test Matrix

Grid Tu Re = 100,000

0 0.8% X

2 2.0% X

3 3.0% X

Re = 250,000

X

X

X

Table 2 Scaling Chart for Simulated Low Pressure Turbine Experiment

Test section

inlet height

3.0 in.

(7.62 cm)

3.0 in.

(7.62 cm)

Scale

factor

4.11

4.11

Test section

length

11.97 in.

(30.4 cm)

11.97 in.

(30.4 cm)

ReTSL Exit velocity Inlet velocity

100,000

(cruise)

250,000

(take-of_

29.13 ft/sec

(9.56 m/s)

72.81

(23.89m/s)

19.82 ft/sec

(6.50 m/s)

44.04

( 14.45 m/s)

NASA/TM-- 1998-208503
29

Table 3 Location of Off-Centerline Static Pressure Taps

Tap Number Axial Location*, inches

1 1.0 (2.54 cm)

2 1.5 (3.81 cm)

3 2.0 (5.08 cm)

4 2.5 (6.35 cm)

5 3.0 (7.62 cm)

6 3.5 (8.89 cm)

7 4.0 ( 10.46 cm)

8 4.5 (11.43 cm)

9 5.0 ( 12.70 cm)

10 5.5 (13.97 cm)

11 6.0 ( 15.24 cm)

12 6.5 (16.51 cm)

13 7.0 (17.78 cm)

14 8.0 (20.30 cm)

15 9.0 (22.86 cm)

16 10.0 (25.40 cm )

17 11.0 (27.94 cm)

18 12.0 (30.48 cm)

*Note: Distance from leading edge. Taps are offset 1 inch (2.54 cm) from

centerline in spanwise direction.

NASA/TM-- 1998-208503
3O

Table 4 Location of Hot-film Gages

Gage Number

1

Axial Location, inches*

1.0 (2.54 cm)

2 1.5 (3.81 cm)

3 2.0 (5.08 cm)

4 2.5 (6.35 cm)

5 3.0 (7.62 cm)

6 3.5 (8.89 cm)

7 4.0 ( 10.46 cm)

8 4.5 ( 11.43 cm)

9 5.0 (12.70 cm)

10 5.5 (13.97 cm)

11 6.0 ( 15.24 cm)

12 7.0 (17.78 cm)

13 9.0 (22.86 cm)

14 11.0 (27.94 cm)

*Note: Distance from leading edge. Gages located on centerline of flat plate.

Figure 11 Schematic diagram of unmodified boundary layer transition tunnel

NASA/TM-- 1998-208503
31

V

i

0.5

Suction system

lllllEIilllll

I=,._ 1 -,el II_ 1 -el

J

Hot film gage (typical)

25 °

1.5

IV

NOTE: Drawing not to scale.

All dimensions in inches unless

otherwise indicated.

X 0.00000 0.25000 [ 0.38007 0.41542 0.46054 0.52728 0.60429 0.68840 0.77711 0.86292 0.95349

y 0.00000 0.06667 [ 0.14264 0.22245 0.29850 0.39879 [ 0.49147 0.59047 [ 0.68539 0.76987 0.84932

X I 1.05089 [ 1.15307 I 1.26895 I 1.38835 [ 1.52370 I 1.66092 I 1.80703 I 1.95376 ] 2.10131 [ 2.24904 2.38700 ]

I Y [ 0.92223 0.98827 1.05117 [ 1.10709 1.16304 1.21432 1.26672 1.31734 1.36792 .4 792 .4648

x 252542 265217 2.78008 2.90179 3.02482 314910 327399 3.40641 3.53850 3.67882 ] 381840 [

y 1151018 1154955 1.58503 1.61328 1.63528 1.6490511.65517 1.65257 1.64268 1.62593 .60385

X 3.96434 4.10962 4.26152 4.41305 4.56412 [ 4.71519 4.86378 5.01266 5.15955 5.30678 5.43854 [

l yl 1.57651 I ,54566 I 1.51055 I i.47370 1 1.43624 ] 1.39897 ] 1.36362 [ 1.32954 [ 1.29786 ] 1.26775 [ 1.24083 ]

x 5.57100I 5.70549 5.84060 5.99427 6.14799 6.30642 6.46490 6.62375 6.78259 ] 6.94165 7.1(_)66

y 1.21755 I 1.20138 1.19120 1.18860 1.19005 1.18992 1.18972 1.18901 1.18806 I 1.1871 .862

X I 7.25979 I 7.41893 [ 7.57798 [ 7.73704 I 7.89596 [ 8.05485 [ 8.21366 I 8.37242 I 8.53102 I 8.68962 I 8.84809 [

y I 1.18504] 118397 ] 1.18285] 1.18178 [ 1.18070 ] 1.17971 ] 1.17880 ] 1.17797 ] 1.17723 11.1766511.17623 ]

X 9.00657 9.16492 9.32323[9.48137 9.63951 9.79757 9.95559 10.11345 10.27130 Io.4289911o.58668

y 1.17603 1.17594 1.17611 I 1.17652 1.17718 1.17814 1.17938 1.18091 1.18281 1.1852 .88')2

X 10.72472 10.86277 10.98257 11.10221 111.21172[11.32008[11.42251 11.52206 11.61734 11.70791 [11.79372]

lyl !.19166 ] 1.19356 [ 1.19298 ] 1.18719 [ 1.17512 ] 1.15518 ] 1.12690 [ 1.08968 [ 1.04315 ] 0.98798 ]".92405 ]

X 11.87337111.94682 12.01295 12.07122 12.12142 12.16240 12.19499 12.22394 12.23449[

y 0.85259 ] 0.77372 0.68869 0.59858 0.50375 0.40690 0.30690 O. 5537 0.00 49

Figure 12 Schematic diagram of simulated low pressure turbine test section with

upper wall coordinates*

*Note: 1 inch = 2.54 cm

NASA/TM--1998-208503
32

Figure 13 Photograph of boundary layer transition tunnel with simulated low pressure

turbine test section

NASA/TM-- 1998-208503
33

Figure 14 Photograph of simulated low pressure turbine test section from inside

and upstream of boundary layer transition tunnel

NASA/TM-- 1998-208503
34

2

A

A

All Dimensions

in Inches

Unless

Otherwise

Indicated.

Legend

X Pressure taps

• Hot-film gages

X X

X X

X X

X X

XXXXXXXXXXXXX X X X X

• • • • • oooooo • • •

_ 0.5

X X

-.4 _ =,- 1 -.92P,_-_2==, _

X x

4.5 _,-

X X

X X

X X

l

I

I

I

t

I

I

I

I

I

I

r

I

I

I

I

x I

i b

J

[

t

I

I

I

I

t

J

I

f

I

I

I

I

I

I

I

A

27

Y

3 _-._ 8

-,4 14 =,_ •

l_- 1 .9l Y 25 °

0.5 4 x 1 ellipse leading edg_ _" 1.5

Figure 15 Schematic diagram of simulated low pressure turbine test section lower wall*

*Note: 1 inch = 2.54 cm

NASA/TM-- 1998-208503
IV. DATA ACQUISITION

A. Steady-State Data

Steady state tunnel conditions, i.e., flee-stream velocity, pressure, temperature and

wall static pressures were monitored and recorded using a ESCORT D multichannel data

acquisition system. The ESCORT D system provides real time data acquisition, display

and control capability for the boundary layer transition tunnel. The ESCORT D system

can be used to obtain data from a variety of modular instrumentation devices and the

system is run on a facility dedicated DEC Micro-VAX computer. This system consists

of a remote acquisition microprocessor, data input and output device, 256 multiplexing

digitizer and a personal computer. The Escort D system is described in detail in Blaha

(1993).

Steady state pressures were measured using an PSI Electronic Scanning Pressure

(ESP) system which is capable of measuring pressure to + 0.5 psi (3447.5 N/m2). The

ESP system is composed of a 32 channel module, separate transducer for each module,

and is networked to the ESCORT system. Three 15 psi ( 103,425 N/m 2) modules were

used for this experiment. Additionally, individual Setra pressure transducers were used

for the inlet and exit pitot tube static and total pressure measurements. The Setra

transducers are capable of measuring a differential pressure difference as low as 7.5

inches of water (1868.25 N/m-') and 15 inches of water (3736.5 N/m 2) for the pitot static

and total pressure measurements, respectively.

NASA/TM-- 1998-208503 35
36

B. Unsteady Data

Time averaged mean and rms velocity data were acquired using a PC based

Dantec Streamline constant temperature anemometer system. The data acquisition

process and data reduction for the constant temperature anemometry were controlled

using a Gateway 2000 series 486, 60 Mhz persor;al computer with a National Instruments

AT-MIO-16E-I, 1.2 MHz, E series data acquisition (DAQ) board and SC-2040

simultaneous sample and hold accessory. This hardware setup was used to make all of the

single wire, X wire and hot-film gage measurements.

A Nicolet Scientific Corporation model 660a dual channel FFT analyzer featuring

a 1024 point, 12 bit analog-to-digital signal con'_ersion with a maximum sampling rate of

100 kHz was used to acquire spectral data. Spectral data was obtained at a sampling rate

of 12.8 kHz using an average of 100 scans.

Instantaneous velocity signals were also monitored using a Tektronix model 7603,

digital oscilloscope that was used to sense the bridge output signal. A Hewlett-Packard

Laserjet IV printer was used for data plotting as well as ESCORT screen prints.

C. Calibration

1. Hot-wire Calibration

Hot-wire calibrations are based on King's law (Perry 1982, Lomas 1986, and

Holman 1978) as given in Equation (1):

E -_= A + BU".

E

(1)

represents the bridge output voltage of the cottstant temperature anemometer, U is the

velocity of the air flowing across the wire, A ant! B are constants calculated from the
37

calibrationandn is thepowerof theselectedexponential.TheDantecStreamlinehotwire anemometrysystemwasusedto calibratebothsingleandx-wire probes.The user

canselectafourthorderpolynomialor apowerlaw curvefit optionof King's law in the

Streamwaresoftwareasdescribedin StreamlineUser'sGuide(1994). A fourthorder

polynomialfit wasusedfor all of thecalibrationsperformedduringthisexperiment.

TheStreamlinesystemhasacalibrationmoduleandFlowUnit which contains

calibratedflow nozzles,apressuretransducerandtemperaturemeasurementsensor.

TheFlow Unit wasconnectedto theStreamlineframevia thecalibrationmoduleanda

shopair supplyline wasconnected.ThenozzlesfortheFlow Unit cancalibrateflows

with velocitiesrangingfrom 1.574ft/s (0.5m/s)upto Mach 1. Calibrationof probes

wereperformedautomaticallyutilizing theStreamlinesystem,Flow Unit andsupporting

software.A typicalhot-wirecalibrationcurvegeneratedfrom Streamwareis shownin

Figure 16.

2. Hot-film Calibration

The calibration procedure for the hot-film gages was significantly more

complicated than the procedure used for the hot-wire probes. The flush mounted hotfilm gages were calibrated to indicate the wall shear stress and this was done by

measuring the skin friction as described by Bellhouse and Schultz (1966). A relationship

of the form

r I!3 = AE 2 + B

exists for a constant temperature anemometer, where % is the wall shear stress, E is the

bridge output voltage and A and B are constants determined from the calibration.

NA SAFFM-- 1998-208503
38

This calibration procedure may lead to large errors in determining the calibration

constants as well as in skin friction in flows where large wall shear stress fluctuations

occur as in the transitional boundary layer region. For this experiment the hot-film

probes were not calibrated and were used for qualitative measurements only.

U..Es a lkl/'llt :

IC4 - .

0

.O01_

Q.Om

0.0_.

Voltage : 3.460

Meas. vei.: 5.012

C.ak:.veL: 5.010

Emx (_) : -0.046

I

Figure 16 Sample Streamline hot-wire probe calibration curve

NASA/TM-- 1998-208503
V. RESULTS AND DISCUSSION

A. Characterization of Flow

The flow within the simulated LPT test section can be characterized by the pressure

gradient parameter K. The pressure gradient parameter is defined by the following

equation

v dU

KU2 dx

where v is the kinematic viscosity of the working fluid, Us is the free stream velocity and

x is the axial or streamwise distance from the leading edge of the body. The K parameter

is equal to a constant for many geometries, but for a converging-diverging geometry such

as a typical airfoil it varies with streamwise distance. Tables 5 and 6 contain summaries

of the K parameters computed for the simulated LPT test section for Reynolds numbers

of 100,000 and 250,000, respectively. Plots of this parameter are contained in Figures 17

and 18. It was determined by Mayle (1991) that the flow on the suction surface of a

typical LPT airfoil will separate for a critical K parameter less than -4x 10.6 at a critical

Reynolds number of less than 100,000 (based on axial chord). Figure 17 shows that a

region of the flow is separated for a Reynolds number equal to 100,000 for the three

turbulence intensity levels tested. Separation does not occur for a Reynolds number equal

to 250,000 at any turbulence intensity level because the K parameter and Reynolds

number values exceed the critical K and Reynolds number values as shown in Figure 18.

39
4O

Theflow within thetestsectioncanalsobecharacterizedbyexaminingthe

variationof theedgevelocity. Figure19is aplotof theedgevelocity variationfor a

Reynoldsnumberof 100,000.Thisplot showsthattheflow in thetestsection

acceleratesupto amaximumvelocity nearthethroatat anaxiallocationof

approximately4.25inches(10.80cm). Oncetheflow proceedspastthethroat,theflow

velocitythendecreasesastheflow proceedsdownstreamandit continuesto decrease

until it reachesaconstantvaluein theconstantareaportionof thetestsection.Theflow

behavioris consistentforthethreeturbulencelevelstested.Theedgevelocity variation

for aReynoldsnumberof 250,000behavesin asimilarmannerto thatof the 100,000

Reynoldsnumbercaseexceptaconstantvaluedoesnotoccurin theconstantareaportion

of thetestsection.Figure20showstheedgevelocityvariationfor aReynoldsnumberof

250,000.
41

Table 5 K, Pressure Gradient Parameter, grids 0, 2 and 3, Re = 100,000

x, inches Grid 0 (0.8% TI) Grid 2 (2% TI) Grid 3 (3% TI)

1.75 (4.45 cm)

2.25 (5.72 cm)

2.75 (6.99 cm)

3.25 (8.26 cm)

3.75 (9.53 cm)

4.25 ( 10.80 cm)

4.75 ( 12.07 cm)

5.25 ( 13.34 cm)

5.75 (14.61 cm)

6.25 ( 15.88 cm)

6.75 (17.15 cm)

7.25 ( 18.42 cm)

7.75 (19.69 cm)

8.25 (20.96 cm)

8.75 (22.23 cm)

9.25 (23.50 cm)

1.058E-05

1.240E-05

8.347E-06

1.027E-06

-8.785E-07

-2.460E-06

-4.170E-06

-2.775E-06

-1.846E-06

-4.383E-06

-6.737E-06

-2.985E-06

O.O00E+O0

2.488E-07

2.488E-07

4.944E-07

1.520E-05

1.290E-05

9.590E-06

4.730E-06

-4.570E-07

-2.240E-06

-1.960E-06

-1.870E-06

-2.770E-06

-6.120E-06

-7.680E-06

-4.130E-06

-2.310E-07

O.O00E+O0

-2.310E-07

-4.650E-07

1.510E-05

1.510E-05

1.170E-05

5.830E-06

1.340E-06

-3.770E-06

-5.420E-06

-3.020E-06

-5.010E-06

-5.570E-06

-2.160E-06

-8.750E-07

-4.430E-07

O.O00E+O0

O.O00E+O0

*Note: No data taken at this streamwise location for this condition.

NASAFFM--1998-208503
42

Table 6 K, Pressure Gradient Parameter, grids 0, 2 and 3, Re = 250,000

x, inches Grid 0 (0.8% TI) Grid 2 (2% TI) Grid 3 (3% TI)

1.75 (4.45 cm)

2.25 (5.72 cm)

2.75 (6.99 cm)

3.25 (8.26 cm)

3.75 (9.53 cm)

4.25 ( 10.80 cm)

4.75 (12.07 cm)

5.25 (13.34 cm)

5.75 (14.61 cm)

6.25 (15.88 cm)

6.75 (17.15 cm)

7.25 ( 18.42 cm)

7.75 ( 19.69 cm)

8.25 (20.96 cm)

8.75 (22.23 cm)

9.25 (23.50 cm)

5.830E-06

5.070E-06

4.290E-06

2,790E-06

1.110E-06

-1.360E-07

-6.420E-07

-6.580E-07

-7.340E-07

-9.660E-07

-8.190E-07

-9.280E-07

-1.140E-06

-1.000E-06

-1.280E-06

5.870E-06

4.160E-06

3.360E-06

2.940E-06

1.3,50E-06

-3.280E-07

-8.220E-07

-6.970E-07

-8.660E-07

-1.020E-06

-8,680E-07

-9.540E-07

-1.340E-06

-1.120E-06

-8.370E°07

5.100E-06

4.910E-06

4.240E-06

2.720E-06

1.170E-06

2.800E-08

-5.110E-07

-5.530E-07

-6.510E-07

°9.460E-07

-1.060E-06

-1.120E-06

-1.170E-06

-9.820E-07

-7,890E-07

*Note: No data taken at this streamwise location for this condition.

NASA/TM-- 1998-208503
43

2.00E -5

1.00E-5

E

r_

g.

_- 0.00E+0

l

L",

C)

E_

A

O

L .

Re : 100000

!3 G,ido

(;, Grid 2

Grtd 3

± _] L]] (-:'

z' 'AA

[_

k ]:

-1,00E-5 --

0.00 2.00 4,00 6.00 8,00 10.00

X. Axial Distance, inches

Figure 17 K, pressure gradient parameter, grids O, 2, and 3, Re = 100,000

_o

E

g.

ea

6.00E-6

4.00E-6 -

2.00E-6

i

0.00E+0 •

/:"-

'0 _

(;,

Re = 250000

_] GrldO

:_; Grbd 2

,A Grid 3

0

-2.00E-6 T [ T-- _ - _ T 7 _---

000 2.00 4.00 0.00 8.00 10.00

X, Axial Distance, inches

Figure 18 K, pressure gradient parameter, grids O, 2, and 3, Re = 250,000

NASAFFM-- 1998-208503
44

Ue,ft/sec

45.00

40,00

i

l

35.00 j

30.00

(7)

25.00

Figure 19

0.00 2.00 4.0C 6.00 8.00 10.00

×, inches

Edge velocity variation, grids 0, 2 and 3, Re = 100,000

Ue , ft/sec

100.00

I

!

I

90,00

i

!

80.00

,,,,"::?'

i

i

zo,oo - _ - _ I _ T ' l --

0.00 2.00 4.0( 6.00 8.00 10.00

<,inches

Figure 20 Edge velocity variati )n, grids 0, 2 and 3, Re = 250,000

NASA/TM-- 1998- 208503
45

B. Flow Visualization Data

Smoke wire flow visualization was conducted to capture the qualitative features

of the flow field. Photographs of smoke traces were taken and used to validate the ability

of the panel code generated contoured upper wall of the test section to mimic the flow

physics of the generic LPT blade. The flow visualization was performed with grid 0 at a

Reynolds number of 50,000 (based on an exit velocity of 15 ft/s (4.921 m/s), which is

lower than a typical cruise Reynolds number. Due to rapid dispersion of the smoke at

higher Reynolds numbers and intense mixing with higher turbulence levels, good quality

photographs could not be obtained for higher Reynolds numbers and higher turbulence

conditions.

Figure 21 is a smoke trace photograph of flow through the test section without

suction. The photograph shows a region of separated flow on the upper wall that was

previously predicted by the NPARC code. This photograph again verified the need for

suction to prevent flow separation on the upper wall. Figure 22 contains smoke trace

photographs with the upper wall suction turned on. These photographs are a time lapse

sequence that clearly show a separation bubble on the lower wall and attached flow on the

upper wall. The photographs show the absence of smoke in the region between the

separated shear layer and the test surface within the front part of the separation bubble

and this is due to infinitesimal viscous shear stresses. The flow-fields in this so-called

'dead-air' region look similar in each photograph, which indicates that the laminar region

of the separation bubble is steady. However, the flow pattern in the region downstream

of the maximum bubble height is substantially different than the one in the upstream

laminar bubble region. This is evidence that the transition and reattachment

NASA/TM-- 1998-208503
46

processesareunsteady.A largeeddystructureisclearlyseenin thephotographs

downstreamfrom themaximumbubbleheightin theshearlayer. Theseeddieseventually

becomeunstableand,throughinteractionwith eachother,finally developintoa turbulent

boundarylayer. Thistransitionprocessissimilarin behaviorto alaminarfreeshearlayer

flow, wherediscretespanwisevorticesformdueto aKelvin-Helmholtzinstabilityand

eventuallybreakdownintoafully turbulentshearlayer. A detailedflow visualization

studyperformedby Morin andPatrick(1991)alsorevealedthis eddyformationin the

shearlayer. Thepresenceof this separationbubbleonthelowerwall is akeyparameter

in thesimulationof thegenericLPT bladeandthesephotographshelpto validatethatthe

testgeometrygeneratedby thepanelcodedoesindeedmimic theflow physicsof the

genericblade. Duringtestingat Reynoldsnumbersof 100,000and250,000,tufts

revealedthattheupperwall flow stayedattachedfor all testconditionsandsuctionflow

ratestested.If theseparationbubbleshownin thephotographsstartsto burstat low

Reynoldsconditionsin arealLPT, hugelossesir_performancewill result.

Figure21 Photographof flow visualizationwithoutsuction,grid 0, Re= 50,000

NASA/TM--1998-208503
47

Figure22 Photographsof flow visualizationwith suction,grid 0, Re= 50,000

C. Establishment of Test Conditions

Results from the flow visualization study were used to determine the proper

amount of suction flow and to verify the existence of a separation bubble on the

NASA/TM-- 1998-208503
48

lower wall. Since the flow visualization studies were performed at velocities lower than

the actual test condition velocities, a methodology for determining the proper suction

flow rates at the test conditions had to be determined. This methodology consists of

setting the tunnel flow to the cruise Reynolds number flight conditions, varying the freestream turbulence levels and suction mass flow rates and using tufts as the flow

visualization technique. The procedure that was used is as follows: First, set tunnel flow

to a Reynolds number of 100,000, increase the tree-stream turbulence level, and decrease

the suction mass flow rate to match the inviscid pressure distribution on the flat plate

which defines an upper suction flow limit; second, remove the turbulence grids and

increase the suction flow rate to define a lower suction flow limit identified by the tufts

flow visualization. If too much suction is applied for a Reynolds number of 100,000 test

condition, too much diffusion occurs and the sep2tration bubble on the lower wall is

overly large. If too little suction is applied for a Reynolds number of 100,000 test

condition, the separation bubble collapses and the upper wall separates. Neither of these

conditions are desirable since both cases represel t a departure of the lower wall

pressure distribution from the desired pressure distribution.

This flow visualization data compares fax orably with data from an experiment

performed by Morin and Patrick ( 1991 ) on a flat plate with a contoured wall modeled

from a compressor blade.

D. Pressure Distribution Data

Plots of the pressure distributions measur:d along the flat test plate are shown in

Figures 23 and 24. Off-centerline static pressure tap locations are shown in figure 15 and

NAS A/TM-- 1998-208503
49

listed in Table 3.

Figure 23 is a pressure coefficient plot for a Reynolds number of 100,000 test

condition. The pressure coefficient behaves as expected in the upstream (converging)

portion of the test section, decreasing to a minimum value at the throat as the flow

accelerates. However, downstream of the throat in the diverging portion of the test

section, the pressure coefficient increases and then becomes flat for a short distance

indicating that the flow has separated from the lower wall. The behavior of the pressure

coefficient is consistent for the three turbulence intensities tested for a Reynolds number

of 100,000 except for the length of the flat region of the curve. The length of the flat

region of the curve decreases as turbulence intensity increases which implies that the

length of the separation bubble is inversely proportional to the freestream turbulence

intensity. This result is consistent with those of Gaster (1967) and Morin and Patrick

( 1991 ) in their studies of separation bubbles.

Figure 24 is a plot of the experimental pressure distribution for a Reynolds

number of 250,000 and the three levels of freestream turbulence tested. The pressure

distributions for three turbulence levels collapse into a single curve, and it can be

deduced from this data that freestream turbulence does not affect the freestream flow for

the range of turbulence intensities tested. The pressure distributions for grids 0, 2 and 3

closely resemble a typical turbine blade suction surface pressure distribution with a

decrease in pressure coefficient in the diverging region of the channel (favorable pressure

gradient region) followed by an attendant increase of pressure in the converging region of

the channel (adverse pressure gradient region). The pressure distributions for a Reynolds

number of 250,000 compare favorably with the panel code generated pressure

NASA/TM-- 1998-208503
5O

distributionsasshownin Figure25.

A comparisonof thepressuredistributionsfor thegenericLPT blade,Panelcode

simulatedtestsectiondesignandexperimentis shownin Figure25. TheReynolds

numberof 250,000correspondsto thedesignpointfor thegenericLPT blade.The

pressuredistributionscomparefavorablyin theacceleratingportionof theflow reflected

bytheclosenessof thepressurecoefficientcurvesasshownin theFigure25. However,

theminimumpressurepointdiffersfor eachcurveandthis isprimarily dueto a slight

differencein theratioof theexit velocityto critical velocity. If thesimulatedtestsection

andexperimentratiosof exit velocityto critical velocity areincreasedthecurvescollapse

ontopof theLPT bladepressuredistribution. In theadversepressuregradientregion

(convergingregionof thechannel),thedifferencein theexperimentalpressure

distributionismorepronouncedthanthebladeandtestsectionpressuredistributions

primarily becauseof viscouseffectsandtheexit velocityratiomismatch.

NASA/TM--!998-208503
51

Figure 23

Cp

10

0.5 t

0.0 t

-0,5 i

-!

-I.0 _--T_ _ --_ ..... • T--

0.0 4.0

x, in.

i -@ G.a2

_ T - I

8.0 12.0

Experimental simulated test section lower wall pressure distributions,

grids O, 2 and 3, Re = 100,000

1.0 --

0.5 --

Cp o.o

-0.5

-1

-1.0

Re = 250000

G r_d 0

G rid 2

G r_d 3

I I I l I I I I I l I i

0.0 4.0 8.0 12.0

X, in.

Figure 24 Experimental simulated test section lower wall pressure distributions,

grids O, 2 and 3, Re = 250,000

NASA/TM-- 1998-208503
52

1.00 --

0.50

"_ 0.00

0

-0,50

-I .00

I

I

Re= 250,000

I

L _ -- -- -- PaneJ CoOe Design

-- Generic LPT

II _ _ ExperlmentafData

\ "W_/

0.00

_ _ [ 1 _ t i I _ t t I t _ _ I _ I I ] _ _ = I

0.20 0.40 0.60 0.80 1.00 1.20

Surface Distance, X/L

Figure 25 Comparison of computational and experimental lower wall pressure

distributions, Re = 250,000

E. Hot-wire Data

Single sensor hot-wire data were obtained for Reynolds numbers of 100,000

and 250,000 operating conditions at free-stream turbulence levels of 0.8% (grid 0), 2%

(grid 2) and 3% (grid 3). Table 1 lists the test matrix used for this experiment and the

measurements were made at centerline axial locations shown in Table 7 (all distances are

in inches and referenced from the leading edge o_' the flat plate).

1. Mean Velocity Contour Plots

Mean velocity contour plots for Reynolds numbers of 100,000 and 250,000 and

lbr grids 0, 2 and 3 are shown in Figures 26 to 31. The velocity and streamline profiles

were computed from reduced velocity profiles obtained from single sensor hot-wire probe

digitized data.

NAS A/TM-- 1998-208503
53

Figures 26-28 are contour plots for a Reynolds number of 100,000 and freestream

turbulence intensity levels of 0.8% (grid 0), 2% (grid 2) and 3% (grid 3), respectively.

The contour plot for grid 0 is shown in Figure 26 and clearly shows a well defined

separation bubble indicated by the deflection of the streamlines with the bubble starting at

an axial position of approximately 5.25 inches (13.33 cm) and extending to

approximately 7.25 inches (18.42 cm). The maximum separation bubble height and

length of 0.040 and 2.00 inches (0.102 and 5.08 cm), respectively, occurs at this

freestream turbulence level of 0.8%. The contour plot for grid 2 is shown in Figure 27

with the starting position of the bubble remaining the same as for grid 0, but the bubble

height and length have decreased. This behavior is repeated in Figure 28 for grid 3 with

the starting point of the separation bubble again remaining fixed, but the bubble height

and length are further reduced due an increased level of freestream turbulence. It can be

deduced from this behavior that the height and length of the separation bubble varies

inversely with freestream turbulence intensity and that the separation bubble starts at the

same streamwise location for the levels of turbulence intensity tested at this Reynolds

number. A summary of the separation bubble characteristics for this Reynolds number

condition with corresponding freestream turbulence levels is contained in Table 8.

Figures 29-31 are contour plots for a Reynolds number of 250,000 and they reveal

that no separation occurs for the three turbulence levels tested. These contour plots show

that for this Reynolds number, the flow in the adverse pressure gradient region is

attached. The pressure distributions for this Reynolds number condition are

representative of the pressure distributions that would be obtained in a LPT at takeoff

conditions.

NASAM'M-- 1998-208503
54

Table 7, Streamwise Hot-wire l_,4easurement Locations

x, inches (Grid O)

1.75 (4.45 cm)

2.25 (5.72 cm)

2.75 (6.99 cm)

3.25 (8.26 cm)

3.75 (9.53 cm)

4.25 (10.80 cm)

4.75 (12.07 cm)

5.25 ( 13.34 cm)

5.75 (14.61 cm)

6.25 ( 15.88 cm)

6.75 (17.15 cm)

7.25 (18.42 cm)

7.75 (19.69 cm)

8.25 (20.96 cm)

8.75 (22.23 cm)

9.25 (23.50 cm)

x, inches (Grid 2) x, inches (Grid 3)

1.75 (4.45 cm)

2.25 (5.72 cm)

2.75 (6.99 cm)

3.25 (8.26 cm)

3.75 (9.53 cm)

4.25 ( 10.80 cm)

4.75 (12.07 cm)

5.25 ( 13.34 cm)

5.75 (14.61 cm)

6.25 (15.88 cm)

6.75 (17.15 cm)

7.25 ( 18.42 cm)

7.75 (19.69 cm)

8.25 (20.96 cm)

8.75 (22.23 cm)*

9.25 (23.50 cm)

1.75 (4.45 cm)

2.25 (5.72 cm)

2.75 (6.99 cm)

3.25 (8.26 cm)

3.75 (9.53 cm)

4.25 (10.80 cm)

4.75 (12.07 cm)

5.25 ( 13.34 cm)

5.75 (14.61 cm)

6.25 (15.88 cm)

6.75 (17.15 cm)

7.25 (18.42 cm)

7.75 (19.69 cm)

8.25 (20.96 cm)

9.25 (23.50 cm)

Not..._._e:

* No data taken at this streamwise location for Reynolds number = 250,000

** No data taken at this streamwise location for Reynolds number = 100,000 and 250,000

NA SA/TM-- 1998-208503
55

0.4

0.35

0.3

0.25

y, in. 0.2

0.15

0.1

0.05

0

4.5

Grid 0 Re = 100,000

r t i 1 , ' E

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0 J.

0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0

o/o o o o _ _ _ o

/ o _ o o o o o o

o / o o--_--___ o o o

0 0 0 0 0 0 0 0

/ o o_-_-___ o o o o o

o/ o o _ o o o

/ o o o o o _- 8- _-

_v, ¥ , II , II , II W, _

5 5.5 6 6.5 7 7.5 8 8.5 9 9.5

X, in.

Figure 26 Mean velocity and streamline contour, grid 0, Re = 100,000

Grid 2 Re = 100,000

0.4 i i , , r _ i r i

0.35

0.3

0.25

y, in. 0.2

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

o o

00_ 0 0 0

• ._'_"- 0 0 0 0

0 0

0 0 0 0 0

0.15 o

J

4.5 5 5.5 6 6.5 7 7.5 8 8.5 9

x, in.

0 0 0 0

0 0 0 0

0 0 0 0

0 0

0 0 0 0

0 0 0 0

0 0 0 ---------_9-

0 0 0 0

0 0 0 0

O O O __DO 0 0 0

0

0

0-

0

0

0 _

0

0-

0

0

Oj,

9.5

Figure 27 Mean velocity and streamline contour, grid 2, Re = 100,000

NASA/TM-- 1998-208503
56

0.4

0.35

0.3

0.25

y, in, 0.2

0'15 I

0"1 t

0.05

0"

4.5

Grid 3 Re = 100,000

i i i T i i i i i i

0 0 0 0 0 0 0 0 C

0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0

O 0 _ 0 0 0

0 0 0 0 0 (5

0 0 0 0 0 0

_ 0 0 0 0-

0 ) 0 0 0 0

0 0 0 0 C I

j, D 0 0 0

JJJ 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5

X, in.

Figure 28 Mean velocity and streamline contour, grid 3, Re = 100,000

0.4

0.35

0.3

0.25

y, in. 0.2

Grid 0 Re:: 250,000

i _ i i i i _ i i i

0 0 0 0 D 0 0 0 C

0 0 0 0 0 0 0 0 C

0 0 0 0 0 0 0 0 C

0 0 0 0 0 0 0 0 C

0 0 0 0 0 0 0 0 C

0 0 0 0 _ 0 _ 0

0 0 D _"""_D '''_ 0 0 C

0 0 0 0 O 0 0 0 O

o o °o o _ o o

D 0 0 0 0

0,15, 0°01 I ....... J.... i, ,

4.5 5 5.5 6 6.5 7 75 8 8.5 9 9.5

X, il,.

Figure 29 Mean velocity and streamline contour, grid 0, Re = 250,000

NASA/TM-- 1998-208503
5?

0.4

0.35

0.3

0.25

y, in. 0.2

0.15

Grid 2 Re = 250,000

, i , i _ i i

0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0

0 0 0 0 0 _ 0

0 _ 0 0 0

0 0 0 0 0 0 0 0

o o

© 0

0 0 0 0 0 0 0 __Q_

O"

4.5 5 5.5 6 6,5 7 7.5 8 8.5 9 9.5

X, in.

Figure 30 Mean velocity and streamline contour, grid 2, Re = 250,000

0.4

0.35

0.3

0.25

y, in. 0.2

0.1

Grid 3 Re = 250,000

i , , f i r i i i

0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0

0

0 0 0 0

0 0 0 0

0 0 _ 0 0

0 0 _.,,-""'f 0 0 0 0 0

0 0 0 0 0 0 0 _

0.05

0 _ _ _ _ _ _ _ _ f

4.5 5 5.5 6 6.5 7 7.5 8 8.5

×,in.

o o o

0

0

0

0

(5

i

9.5

Figure 31 Mean velocity and streamline contour, grid 3, Re = 250,000

NA SA/TM-- 1998-208503
58

2. Law of the Wall Plots

The onset of transition on the lower wall can be clearly visualized by normalizing

the mean velocity profiles and plotting these variables using logarithmic and semilogarithmic scale axes. The wall unit variables u* and y* are defined by the following

relations:

u e yu ÷

u +- and y+-

U r V

The quantity ue is the velocity at the edge of the boundary layer, u¢ is the friction velocity

and is defined as the square root of the wall shear stress divided by the local density,

•

i.e., _--p-, y is the vertical distance from the test surface and v is the kinematic viscosity.

A curve fit technique developed by Clauser (1956) was used to plot the mean velocity

profiles in the above coordinates and further details of this technique can be found in this

reference, as well as in Suder et al. (1988) and Sohn and Reshotko (1991). This

technique involves iterating on a skin friction coefficient value for the measured mean

velocity profile and plotting the best fit value of lhe skin friction coefficient on the u +

versus y+ curve.

The mean velocity plots of these variables are shown in Figures 32-37 for the

upstream measurements at Reynolds numbers of 100,000 and 250,000 and for

downstream measurements at a Reynolds numbe_' of 250,000. Downstream mean

velocity profiles for a Reynolds number of 100,000 could not be constructed because the

skin friction coefficient is zero for separated flow. Additionally, for comparative

purposes, reference curves for u + versus y+, Blasi is' laminar boundary layer solution and

Musker's (1979) continuous law-of-the-wall turbtJlent boundary layer solution are also

plotted. Figures 32-34 are plots of the upstream mean velocity profiles for a

NASA/TM-- 1998-208503
59

Reynolds number of 100,000 and for grids 0, 2 and 3. These plots show excellent

agreement with the u+ = y+ curve for all of the upstream axial stations plotted except at

x=4.25 inches ( 10.80 cm). This deviation from the u+ -- y+ curve at x--4.25 inches ( 10.80

cm) is present for each freestream turbulence level, but grid 0 has the largest discrepancy

from the u + -- y+ curve. The deviation at x=4.25 inches ( 10.80 cm) may be attributed to

the impending flow separation at x=5.25 ( 13.34 cm) inches for a Reynolds number of

100,000. For each grid, the u÷ value increases or, alternatively, the skin friction

coefficient decreases as the flow progresses downstream from x-- 1.75 (4.45 cm) to 4.25

inches (10.80 cm). The upstream mean velocity profiles for a Reynolds number of

250,000 are presented in Figures 35-37 and show excellent agreement with the u+ = y+

curve for all axial locations including x--4.25 inches (10.80 cm). These profiles follow

the same trend that the upstream profiles for a Reynolds number of 100,000 exhibit with

the u+ value increasing as the flow progresses downstream from x--1.75 (4.45 cm) to 4.25

inches ( 10.80 cm).

The downstream mean velocity profiles for a Reynolds number of 250,000 are

shown in Figures 38-40 for grids 0, 2 and 3, respectively. Excellent agreement is

obtained with the u+ = y+ curve for each axial location as with the Reynolds number

of 100,000 profiles. Again, these profiles exhibit a similar behavior to the Reynolds

number of 100,000 profiles with the u+ value increasing as the flow progresses

downstream until the onset of transition occurs. The u+ value then decreases or

alternatively the skin friction coefficient increases after the onset of transition. The skin

friction coefficient continues to increase until the flow becomes fully turbulent. As the

NASA/TM-- 1998-208503
6O

flow approachesafully turbulentprofile, theme_mvelocityprofilesapproachtheMusker

curveontheplot asthiscurverepresentsfully turbulentflow. Fully turbulentflow does

not occurfor anyof theaxialmeasurementstationsfor grid 0 asshownin Figure38,but

fully turbulentflow is achievedfor grids2 and3 asshownin Figures39and40.

Onsetof transitioncanalsobededucedfrom theseplotsandfor grid0 transitiononset

startsto occurat approximatelyx=7.75inches(19.68cm). Additionally,transition

onsetstartsto occurfor grid 2 at approximatelyx=6.75inches(17.15cm) andat

approximatelyx=5.75inches(14.61cm) for grid 3. Approximatetransitiononset

locationsdeterminedfrom intermittencyprofileswill bepresentedin alatersection.

Theselaw of thewall plots showsimilartrendswith thosepresentedby SimonandQiu

(1996).

50

45

40

35

30

25

20

15

10

5

O

Re : 100 _)00

p

[

Gnd 0 ,]

[] X = 1 75 inches /

,:_ X = 2.25 inches u+=y,/

0 X = 275 inches

L/ X = 325 inches ,,

+ X = 375 inches ,'

J

¢e X = 425 inches ?

/

....+._++;J .........

10 _ 10: 10 _

+

Y

Figure 32 Upstream mean velocity profile,, in wall units, grid 0, Re = 100,000

NA SA/TM-- 1998-208503
61

Figure 33

5(]

Re : 100,000

45

4O

35

30

25

2(]

15

1(]

5

0

10 _

Grid 2

[] X = 1 75 inches

E, X = 225 inches

O X= 2 75 inches

O X= 325 inches

-- X = 375 inches

X = 425 inches

u+=y

_'d _,,_++++H4+ k_* ÷----+_-H.+4 _

_ - _ Dc._

L

101 1(] 2 10 _

Y

Upstream mean velocity profiles in wall units, grid 2, Re = 100,000

u +

Figure 34

50

45

4(]

35

3(]

25

20

15

1(]

5

0

Gnd 3

7 x = 1 75 inches

E, X = 2.25 inches

O X = 2.75 inches

v X = 3,25 inches

+ X = 3.75 inches

•_: X = 4.25 inches

Re = 100,000

/

{

/"

u+=y} _

t'

/

/

,/

i i

1(] I 1(]: 10 ]

Y

Upstream mean velocity profiles in wall units, grid 3, Re = 100,000

NA SA/TM-- 1998-208503
62

u•

5O

45

:1

±

40

0

v

35

30

25

20

15

10

5

0

Grid 0

X = 1.75 inches

X = 2.25 inches

X = 2.75 inches

X = 3.25 inches

X = 3.75 inches

X = 4,25 inches

Re = 250000

u':y _

i

loU 101 10: 10:

Y

Figure 35 Upstream mean velocity profiles in wall units, Re = 250,000

Figure 36

5O

4°t

35

30

25

20

15

10

5

0

10 _

Re = 250 000

Grid 2 ,_'

X = 1.75 inches /

; X = 2,25 inches _ / I

0 X = 2,75 inches u =y

v X= 3.25 inches

X = 3.75 inches /

X = 4.25 inches "

!

,/ '

C1_+ %-

I R i

10 10:' 10:

y"

Upstream mean velocity profile_, in wall units, grid 2, Re = 250,000

NASA/TM-- 1998-208503
63

u"

°°I

45_

'°t

I

Grid 3

[] X = 1.75 inches

X = 2.25 inches

O X= 2.75 inches

</ X = 3.25 inches

Re = 250,000

u*=y *

10° 10 10: 10 _

Y

Figure 37 Upstream mean velocity profiles in wall units, grid 3, Re = 250,000

100 101 10; 10;

y*

Figure 38 Downstream mean velocity profiles in wall units, grid 0, Re = 250,000

NASA/TM-- 1998-208503
64

Figure 39

Re = 25[ 000

50 _ r

45 Grid 2

[] X = 475 inches

40 /_ X=525inches

O X = 5 75 inches

v X = 625 inches

35 + X= 675 inches

,_- X = 7.25 inches

_' X = 7.75inches

30

• X = 8 25inches

• X = 925 inches

25

15

10 .

5 l _- "

t .... , ....

10 u 10

i

y'

/

/

i

f

t

U*=y_

,,y oo== ooo 

°Z f

10:' 10 =

Downstream mean velocity profiles in wall units, grid 2, Re = 250,000

50

45

40

Re = 250 000

r _ _

Grid 3 i

1-1 X = 4.75 inches

A X =5.25inches

O X = 5.75 inches

v X = 6.25 inches

35 -- X = 6.75 inches ,r __

¢r X=725inches " •_ --

30 r- _2 X = 7.75 inches ,r Z J_"_3 .0'_"

Oi_J ----_- i ,i

10 s 10 _ 102 10 _

y_

Figure 40 Downstream mean velocity profil,_s in wall units, grid 3, Re = 250,000

NASA/TM-- 1998-208503
65

3. Fluctuating (rms) Velocity Profiles

Fluctuating (rms) velocity profiles are shown in Figures 41-46 for grids O, 2 and 3

along with the same streamline patterns plotted for the mean velocity profiles in Figures

26-31. Figures 47-58 show the upstream and downstream rms profiles in outer

coordinates. The upstream rms velocity profiles shown in Figures 47-52 are consistent

in behavior in that the rms velocity levels increases as the free-stream trubulence

increases. In the laminar boundary layer at a low freestream turbulence level (grid O,

Figure 53) and a Reynolds number of 100,000, the rms velocity profile is nearly flat with

small magnitudes for the entire flow field except for a small hump near the wall. This

small peak grows in magnitude and moves away from the wall to the shear layer as the

flow proceeds downstream from the separation location. This peak in the shear layer

grows rapidly after the maximum bubble height location and triggers a slowdown of

bubble growth due to turbulent energy dispersion. Additionally, the small peak can be

seen inside the bubble at x=6.25 inches (15.88 cm). Due to the limited number of

measurement stations within the separation bubble and the inability of the hot-wire to

correctly measure velocity profiles in the reverse flow region, the peak that developed

inside the bubble could not be studied. However, in the LDV experiment on the

diverging channel flow performed by Morin and Patrick (1991), it was observed that the

second peak which developed inside the bubble substantially outgrew the first peak and

they merged together further downstream. They also found that a third peak developed

around the edge of the boundary layer. For higher freestream turbulence levels (grids 2

and 3), the peak is much larger than that for grid 0 at the first measurement station

because the laminar boundary layer is buffeted by higher freestream turbulence. Note that

NASAFFM--1998-208503
66

thefluctuatingvelocityprofilesmeasuredatthe_astmeasurementstation(x=9.25inches,

23.50cm)aredifferentfrom thatof theequilibriumturbulentboundarylayersuggested

by Klebanoff(1955)for eachcondition,whichindicatesthateventhoughanattached

turbulentboundarylayerprofilewasmeasuredat x-9.25 inches(23.50cm), thenatureof

theboundarylayeris differentdueto theseparationbubblethatoccursupstream.

0.4

0.35

0.3

0.25

y, in. 0.2

0.15

0.1

0.05

0

4.5

Grid 0 Re = 100,000

i J T r i J i

0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0

o ojj_o o o o -G -5 _ o

o_ o o o o o

o o _ 0 o_'_"_ o o o o

o _ o o o o --5 _ --5 o

0 _ 0 0 0 0 0

o o j-'o o o _---o._ .__2o o o o

o _ o o o o o ---_ "-6 o

5 5.5 6 6.5 7 7.5 8 8.5 9 9.5

X, irl.

Figure 41 Downstream rms velocity and streamline profiles, grid 0, Re = 100,000

NASA/TM-- 1998-208503
6?

0.4

0.35

0.3

0.25

y, in. 0.2

0.15

Grid 2 Re = 100,000

F _/ T m l T

O O O O O O

o o o o o 0

O O O O O O

0 0 0 0 0 0

oj1_o o o o o

0 o _ o

o o o o

0 o o o

O0 0 n . N

0 o

0.05

0' d

4.5 5 5.5 6 6.5 7 7.5

×,in.

0 o o o

0 o 0 o

O O O O

0 O_ 0

0 0 0 0

0 0 0 0

0 0 _ 0

0 0

0 0

0 0

0 0

o o

o o

0 -- o

o o

9 9.5

Figure 42 Downstream rms velocity and streamline profiles, grid 2, Re = 100,000

0.4

0.35

0.3

0.25

y, in. 0.2

Grid 3 Re = 100,000

r q T _ T r r r r "?_

0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0

0 O_ 0 0 -- 0 0 0

0 /"0 0 0 0 0 0 0 0

0 J 0 0 0 0 0 0 0 0

--o----o- o o

0 _ 0 0 0 0 0 0 0 0

o °o o o o

0"15/0.1 o o o i

0.05 _

0 '_ '

4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5

x, in.

Figure 43 Downstream rms velocity and streamline profiles, grid 3, Re = 100,000

NASA/TM--1998-208503
6_

0.4

0.35

0.3

0.25

y, in. 0.2

Grid 0 Re = 250,000

r r 7 r r i i i _ I

o o o o o o 0 o o ],

.4

I

o 0 o 0 o o o o o

o o o o o o o o o

o o o o o 0 • o o o

o o o o o o o o o

o o o o o _ o _ o

o o o -_ 0 _"""'0 f 0 0

0 0 0 0 0 0 0 0 0

o o o °o o .-o--______--_o o

0 0 0 0

0,, i o,

o-i. i,

oii o

J J

t/1_

---:--

o 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5

X, in.

Figure 44 Downstream rms velocity and streamline profiles, grid 0, Re = 250,000

0.4

0.35

0.3

0.25

y, in. 0.2

0.15

0"1 t

0.05

0"

4.5

Grid 2 Re = 250,000

i i _ 1 q 1 i f i

0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0

0 0 0 0 0 _0o_JO o oo

o o o o _ o o

o o o o o o

C) O O O O O O O O

5 5.5 6 6.5 7 7.5 8 8.5 9 9.5

x, iq.

Figure 45 Downstream rms velocity and streamline profiles, grid 2, Re = 250,000

NASA/TM-- 1998-208503
69

0.4_

0.35

0.3

0.25

y, in. 0.2

1

o o

o o

o o

o o

o o

Grid 3 Re = 250,000

r 1 T T"

O

O

o

o

o

o

o

o

o

o

o o o o o o

o o o o o o

o o o 0 0 o

o o o o o o

o o o o o o

o o o o o ___

o o o o_ o o o

o o o o o

0 0 0 _ 0

0 0 0 --_"I_0 0 0 0

0.15 _ 0 0 0 0 0 0 0 0

0.05

O_

4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5

x, in.

Figure 46 Downstream rms velocity and streamline profiles, grid 3, Re = 250,000

Re = 100,000

0.2 - _ _ ....

u'lU

0.18

016

0.14

0.12

0.1

008

0.06

0.04

0.02

0

0

Gnd 0

_1 x= 1.75inches

5,, X = 2.25 inches

O X = 275 inches

V X = 3.25 inches

1 X = 3.75 inches

X = 4.25 inches

2 4 6 8

10 12

y/a*

Figure 47 Upstream rms velocity profiles, grid 0, Re = 100,000

NASAFFM-- 1998-208503
7O

u'IU

0.2 - • --- -

018

0.16

0.14

0.12

01

0.08

Re = 1G ).000

T

Gnd 2

E X = 1.75 inches

iL X = 2.25 inches

O X = 2.75 inches

_, X = 3,25 inches

+ X = 3.75 inches

_- X = 4.25 inches

" T

i

!

i

]

i

I

I

!

I

0.06 !

i

l

0.04 . _ ._

0

0 2 4 6 8 10 12

Figure 48 Upstream rms velocity profiles, grid 2, Re = 100,000

o.2[

!

0,18_

i

0.16_

o14P

012

U'/LJ O. 1

0.08

0.06

0.04

0.02

Re = 100.000

m • -- _ •

Grid 3

L X = 1.75 inches

A X = 2.25 inches

O X = 2,75 inches

v X = 3.25 inches

+ X = 3.75 inches

_" X = 4.25 inches

°o÷_o

i I J

2 4 6 8 10 12

yl_"

Figure 49 Upstream rms velocity profiles, grid 3, Re = 100,000

NASAfrM-- 1998-208503
71

0.2

0.18!

016

Re = 250,000

r

Grid 0

[] X = 1.75 inches

:', X = 2.25 inches

O X = 2.75 inches

v X = 3.25 inches

X = 375 inches

-;c X = 4.25 inches

uYU÷

01L

008 i

i

0.06 -

0.02

i L i t

00 2 4 8

J

8

y/F,*

Figure 50 Upstream rms velocity profiles, grid 0, Re = 250,000

U'_IJ÷

02'

0.18

0.16-

014 I

012

Re = 250.000

Grid 2

L X = 1 75 inches

X = 2.25 inches

O X = 2 75 inches

v X = 3.25 inches

+ X = 3.75 inches

X = 4.25 inches

01

0.08

0 06

0.04 _,,_

002

0 I i I

0 2 4 6 8

li0 12

Figure 51

y/_,*

Upstream rms velocity profiles, grid 2, Re = 250,000

NASA/TM-- 1998-208503
72

u'/U

0.2

Re = 250.000

018

0.1B

Q14

012

Gnd 3

FI X = 1 75 inches

X = 2.25 inches

O X = 2 75 inches

v X = &25 inches

t- X = &75 inches

X = 4.25 inches

008

006

0.04

0.02

0O 4 6 8 10 12

yl_*

Figure 52 Upstream rms velocity profiles, grid 3, Re = 250,000

0.2

Re = 100 000

u'/U

0,16

I_ ---'--,o_ _ _

006

[ + o

004/ ^ 0 _ "# '; I O=_

0'02 _ilh _ --'<>_,O ++'- _ I- <" ¢" *

O0 2 4 6

y/_,*

Grid O

[] X : 475 inches

:_ X = 525 inches

O X = 5 75 inches

v X = 625 inches

X = 6 75 inches

X = 7.25 inches

7 X = 7.75 inches

• X = 825 inches

• X = 875 inches

• X = 925 inches

@I 01 II

10 12

Figure 53 Downstream rms velocity )rofiles, grid 0, Re = 100,000

NASA/TM-- 1998-208503
73

021

Re : 100,000

uVU e

!

018;

016

014

012

01

008

006

J

0.041

i

0.02

0

0

÷

Grid 2

[] X = 4.75 inches

_', X = 5.25 inches

O X = 575 inches

_ X = 6.25 inches

+ X = 675 inches

•:_ X = 7.25 inches

-" X= 7.75 inches

• X : 8.25 inches !

• X = 8.75 inches

• X = 9.25 inches

2 4 6 8 'tO f2

y/B*

Figure 54 Downstream rms velocity profiles, grid 2, Re = 100,000

u'/IJ

02

018 l

016

i

014

0.12

0.1

0 06

0.06_

004

0o2__i 1

0 L

0

Re = 100.000

- - r - - I

I

i

Grid 3

X = 475 inches

,"_ X = 525 inches

O X = 575 inches

v X = 625 inches

+ X = 6.75 inches

X = 7.25 inches

X= 775inches

• x : 625inches ]

• X = 925 inches i

2 4 6 8 10 12

y16*

Figure 55 Downstream rms velocity profiles, grid 3, Re = lO0,OO0

NASAFFM-- 1998-208503
74

0.2

Re = 250000

u'lU

018

0.16

0.14

0.12

0.1

008

0.06

0.04

0.02

0

Grid 0

J X = 4 75 inches

_ X = 5.25 inches

O X = 575 inches

v X = 6.25 inches

t- X = 675 inches

-_ X = 7.25 inches

2 4 6 8 1'o

y/a*

12

Figure 56 Downstream rms velocity profiles, grid 0, Re = 250,000

Re = 250,000

0.2 - -- _ r - • ..... _.... _ - '

u'/U

0.18

0.16

0,14

0.12

01

OOB

0.06

004

0.02

I i

00 2 4

Grid 2

X = 4.75 inches

_, X = 525 inches

O X = 5.75 inches

v X = 625 inches

_p_ +_ X = 6.75 72 inches

_ g

+ _-

J

8 10

y/3'

i

12

Figure 57 Downstream rms velocity profiles, grid 2, Re = 250,000

NASAfFM-- 1998-208503
75

02!

018

0.16

014

0.12

u'/Up 0.1

0.08

0.06

0.04 i

0.02,

0

0

Figure 58

Re = 250,000

Grid 3

X = 4.75 inches

:_'_X = 5.25 inches

O X = 575 inches

X = 6.25 inches

X = 6.75 inches

-_- X = 7.25 inches

i t i h i

2 4 6' ,5' ?G 12

y/3*

Downstream rms velocity profiles, grid 3, Re = 250,000

4. Boundary Layer Parameters

Plots of the variation of displacement (_5"), momentum (0) and energy (e)

thicknesses determined from integrating the mean velocity profiles along the test surface

for grids 0, 2 and 3 are presented in Figures 59-68. Additionally, a skin friction

coefficient plot is presented in Figure 69 for a Reynolds number of 250,000 only, since

the skin friction coefficient is zero for separated flow (Reynolds number of 100,000).

Boundary layer parameters were also computed from a code developed by Crawford

and Keys (1987) to assist in the reducing of the pre-separation and pre-transition

experimental data.

For a Reynolds number of 100,000 and all three turbulence intensities, the

displacement thickness increases rapidly to a local maximum near transition and

decreases to a local minimum downstream from the reattachment point and then slightly

NASA/TM-- 1998-208503
76

increases again as shown in Figure 59. The maximum and minimum values of 5* are

inversely proportional to the freestream turbulence level. The momentum and energy

thicknesses increase monotonically throughout the test section. The growth rates of both

0 and e, Figures 60 and 61, are the greatest and similar to each other in the separated flow

region with both 0 and e increasing as the freestream turbulence level increases up to

transition. There is, however, no clear trend downstream from the point of reattachment.

The characteristics of the bubble are generally described by the properties at separation.

At separation the displacement thickness changes rather rapidly, but the momentum

thickness varies slowly due to negligible skin friction. Thus 0 is a much more suitable

choice than 5" to describe bubble behavior (Gaster, 1969; O'Meara and Mueller, 1986).

The variation of shape factors, Ht2 (= 5"/0) and H32 (= E]0), for each condition are

presented in Figures 62 and 63. For each condition, HI2 monotonically increases to a

local maximum around transition and sharply decreases to a local minimum downstream

from reattachment and then levels out to the values of a turbulent boundary layer. The

peak values move upstream with increasing freestream turbulence and this trend is very

similar to that observed in the 8" variation. Opposite trends are observed in the variation

of H32 for each condition. The most commonly used parameter for determining the

separation location is the shape factor H_2; howe_ er, as noted in the Figure 62, HI2 varies

rapidly at separation due to the large gradient of _* and scatters in the upstream region up

to transition for different levels of freestream turbulence. On the other hand, H32 changes

quite slowly throughout the separated flow and is nearly identical up to separation

regardless of freestream turbulence levels, so H32 is a more logical choice for determining

the separation location. The separation locations are determined in this study where H32

NASA/TM-- 1998-208503
77

is equal to 1.522 for each condition. The separation bubble characteristics for all three

grids are summarized for a Reynolds number of 100,000 and are listed in Table 8.

Reattachment models based on shape factors H_2 and H32 have proven to be useful

in previous separation bubble calculations. Horton (1968) suggested a universal

velocity profile at reattachment with values of H_2 and H32 of 3.50 and 1.51, respectively.

The reattachment locations in this study were determined to be where H32 is equal to 1.51

for each condition. The separation and reattachment locations determined from the shape

factors agree quite well with those obtained from the pressure distribution data.

The variation of the skin friction coefficient, Cf for a Reynolds number of 250,000

is shown Figure 69. Cf is defined below for laminar and turbulent flows as found

in Schlichting (1959):

0.664

__ r,_ -1/7

Cf _ and Cf =0.026 l,ietu r .

The skin friction coefficient behaves as expected for an attached laminar boundary layer,

decreasing in magnitude as the flow passes from the favorable pressure gradient region

into the adverse pressure gradient region. The skin friction coefficient decreases to a

minimum value just before the onset of transition and then begins to increase ;as transition

onset occurs. It continues to steadily increase until it reaches a fully turbulent value

before finally leveling off to a nearly constant value. This behavior is also consistent for

grids 2 and 3, but for grid 0 the skin friction coefficient does not reach the fully turbulent

value. These trends are consistent with those obtained from the mean velocity profiles

obtained from the Clauser fit technique which also show that for a Reynolds number of

250,000 and grid 0, the last measurement station (x=9.25 inches, 23.50 cm) is not fully

NASA/I'M-- 1998-208503
78

turbulent. Additionally, the trends observed in the skin friction coefficient are similar to

those presented by Mayle (1991). The boundary layer properties for each axial measuring

station are summarized in Tables 9-14 for grids 0, 2 and 3 and Reynolds numbers of

100,000 and 250,000, respectively.

01

Re = 10_,000

0.09

0.08

0,07

006

fi', in. 005

0.04

0.03

0.02

001

0

O Grid 0

'* Grid 2

+ Grid 3

0

0 •

t +

0

0

+ + • •

0

+ +

i i i i : 1 t I I

2 3 4 5 6 7 8 9

x, in

10

Figure 59 Displacement thickness profilt',s, grids 0, 2 and 3, Re = 100,000

NASA/TM--1998-208503
?9

0.05

Re = 100,000

i

0.045

0.04

0,035

0.03

0, in 0025

002

0.015

0.01

0.005

0

Grid 0

Grid 2

Grid 3

+

+ 0

0

+

+

°

0

Q

0

+

i I t I i i t I

2 3 4 5 6 7 8 9 10

x, in

Figure 60 Momentum thickness profiles, grids 0, 2 and 3, Re = 100,000

Re = 100,000

0.08 , , , , ' '

0.07

006

0.05

_', in. 0.04

0 03

0.02

0.01

Figure 61

0 Grid 0

Grid 2

+ Grid 3

Q

4-

+

4-

O

O

4-

i i i i i _ i i

2 3 4 5 6 7 8 9 10

x, in.

Energy thickness profiles, grids 0, 2 and 3, Re = 100,000

NASA/TM-- 1998-208503
80

6

5.5

5

45

4

H12 35

3

2.5

2

1.5

1

Re = 10:),000

O Grid 0

Grid 2

+ Grid 3

Q O

]-

• O

• +

+ O

O

+

I i i i I i _ J

2 3 4 5 6 7 8 9 10

x, in

Figure 62 Shape factor profiles, grids O, 2 and 3, Re = 100,000

2

19

1.8

H32 1.7

1.6

1.5

1.4

Re = 10(,000

O Grid 0

,_ Grid 2

+ Grid 3

+ 0 _ e

0 0

÷

o

+

O

L I

2 3

+

0

+ +

o _

O

0

i I I I i I

4 5 6 7 8 9

x, ii3.

10

Figure 63 Energy shape factor profiles, grids 0, 2 and 3, Re = 100,000

NASAFFM-- 1998-208503
81

0.1

0,09

0,08

0.07

0.06

8", in 0,05

0.04

003

0.02

001

0

Re = 250,000

i , i i i I _ i

O Grid 0

'_ Grid 2

+ Grid 3

e _ e e 6

I I i

2 3 4

4- +

8 •

i i i i J

5 6 7 8 9 10

x, in

Figure 64 Displacement thickness profiles, grids 0, 2 and 3, Re = 250,000

0.05

0,045

0.04

0035

0 03

,9, in. 0.025

0 02

0015

001

0005

0

Re = 250,000

, , i E , ,

O Grid 0

* Grid 2

+ Grid 3

+

+

+

0

+ + * 0

e , _ 6 6 6

I i L I k I I I

2 3 4 5 6 7 8 9

x, in

10

Figure 65 Momentum thickness profiles, grids 0, 2 and 3, Re = 250,000

NASA/TM--1998-208503
82

0.08

Re = 251.000

0.07

0.06

0 O5

t'. in 0.04

0.03

0.02

0.01

O Grid 0

_, Grid 2

+ Grid 3

i i L

2 3 4

+

+ •

+

O

+ + + m

+ ?_o °

L I I I I

5 6 7 8 9 10

x. in

Figure 66 Energy thickness profiles, grids 0, 2 and 3, Re = 250,000

6

5.5

5

4.5

4

H12 36

3

15

1

Re = 250.000

O Grid 0

"_ Grid 2

+ Grid 3

0 0

0 0

+ 0

+

+

+

+ •

+

i i I I i i J i

2 3 4 5 6 7 8 9 10

x, in

Figure 67 Shape factor profiles, gr! ds 0, 2 and 3, Re = 250,000

NASA/TM-- 1998-208503
83

2

1.9

1.8

H32 1 7

1.6

1.5

14

1

Figure 68

Re = 250.000

O Grid 0

41 Grid 2

+ Grid 3

+

4-

+

+

+ 0

+ + + _ +

o • o + o

o c

I I I I I I I I

2 3 4 5 6 7 8 9 10

x, in.

Energy sha W factor profiles, grids 0, 2 and 3, Re = 250,000

C_

Re = 250,000

10 _ --.- T • " _ _-_ ----T --

[] Grid 0

Grid 2

0 Grid3

Blasius 74

O

OTurbulent

O

e o

_5 o

O

. 0[_0 A

Y_

10 I

104 10_ 10"

Re

Figure 69 Skin friction coefficient, grids 0, 2 and 3, Re = 250,000

NASA/TM--1998-208503
84

Table 8 Boundary Layer Properties at Separation, Re = 100,000

Grid 0

Grid 2

Grid 3

_* in. •

0.04441 0.01247

0.(14646 0.01257 0.01914

0.04871 0.01337

0, in.* c, in.* Hi2 H.__,

0.01897 3.562 1.522

3.696 ! .522

0.02036 3.643 1.523

Re_ Reo

93913 223

101315 243

99615 254

*Note: 1 inch = 2.54 cm.

Table 9 Boundary Layer Properties, Grid 0, Re = 100,000

x, in.** u_, ft/s** 8', in.** 0, in.** c, in.** HI2 H3_, Rex Re0 ct

1.75 31.650 0.01357 0.00544 0.00875 2.495 1.608 29015 90

2.25 33.540 0.01400 0.00562 0.00905 2.486 1.610 40385 101

2.75 36.952 0.01436 0.00605 0.00990 2.374 1.637 53134 117

3.25 38.087 0.01762 0.00965 0.01691 1.825 1.752 65081 193

3.75 37.628 0.02140 0.01187 0.02089 1.803 1.759 76025 241

4.25 37.621 0.02207 0.00819 0.01287 2.694 1.571 83732 161

4.75 36.158 0.02960 0.01001 0.01553 2.956 1.551 89729 189

5.25 35.443 0.04441 0.01247 0.01897 3.562 1.522 93913 223

5.75 34.777 0.06703 0.01531 0.02279 4.377 1.488 100822 268

6.25 34.495 0.08432 0.01763 0.02582 4.782 1.464 108846 307

6.75 32.707 0.06855 0.02339 0.03483 2.931 1.489 111498 386

7.25 31.572 0.05353 0.03064 0.05132 1.747 1.675 115838 490

7.75 31.549 0.04758 0.03176 0.05545 1.498 1.746 124207 509

8.25 31.644 0.04756 0.03264 0.05785 1.457 1.773 132712 525

8.75 31.637 0.04803 0.03303 0.05886 1.454 1.782 140728 531

9.25 31.696 0.04921 0.03372 0.06022 1.459 1.786 149003 543

0.18271

O*

O*

O*

O*

0.20679

0.22520

0.22987

0.23037

0.23036

*Note: Separated flow at this location.

**Note: 1 inch = 2.54 cm. 1 ft/sec = 0.3048 m/see.

NASA/TM--1998-208503
85

Table 10 Boundary Layer Properties, Grid 2, Re = 100,000

x, in.** ue, ft/s** 8 _, in.** 0, in.** _, in.** Hi2 H32 Re_ Reo cr

1.75 31.329 0.01315 0.00525 0.00851 2.506 1.622 28601 86

2.25 34.334 0.01475 0.00674 0.01150 2.189 1.706 40278 121

2.75 37.356 0.01606 0.00810 0.01413 1.981 1.743 53517 158

3.25 39.669 0.01682 0.00817 0.01410 2.058 1.726 67181 169

3.75 40.423 0.01886 0.00914 0.01571 2.063 1.719 79057 193

4.25 39.423 0.02060 0.00868 0.01435 2.372 1.653 87363 178

4.75 39.006 0.03180 0.01028 0.01609 3.024 1.565 93737 203

5.25 38.209 0.04646 0.01257 0.01914 3.696 1.522 101315 243

5.75 37.884 0.06653 0.01502 0.02233 4.429 1.486 109947 287

6.25 36.585 0.06515 0.02200 0.03289 2.961 1.495 115409 406

6.75 34.639 0.05013 0.02782 0.04600 1.802 1.653 118255 487

7.25 32.946 0.04658 0.03086 0.05329 1.509 1.727 120888 515

7.75 32.812 0.04594 0.03164 0.05560 1.452 1.758 128872 526

8.25 32.825 0.04668 0.03239 0.05742 1.441 1.773 137193 539

8.75 32.753 0.04806 0.03404 0.06056 1.412 1.779 145236 565

9.25 32.740 0.05035 0.03462 0.06161 1.454 1.779 153423 574

0.15358

O*

O*

O*

0.20600

0.22311

0.22895

0.23103

0.22983

0.22924

*Note: Separated flow at this location.

**Note: 1 inch = 2.54 cm. l ft/sec = 0.3048 m/sec.

NA SA/TM-- 1998-208503
86

Table II Boundary Layer Properties, Grid 3, Re = 100,000

x, in.** u_, iVs** 5", in.** e. in.** e, in.** H_3 H32 Re_ Reo c_

1.75 30.354 0.01385 0.00566 0.00935 2.449 1.653 27935 90

2.25 33.166 0.01404 0.00579 0.00974 2.424 1.681 39187 101

2.75 37.116 0.01592 0.00787 0.01377 2.024 1.751 53527 153

3.25 39.685 0.01842 0.00999 0.01780 1.844 1.783 67598 208

3.75 40.791 0.01834 0.00930 0.01620 1.972 1.741 80129 199

4.25 40.574 0.01985 0.00937 0.01594 2.118 1.700 90241 199

4.75 38.324 0.03004 0.01055 0.01658 2.847 1.572 92291 205 0.15358

5.25 37.438 0.04871 0.01337 0.02036 3.643 1.523 99615 254 O*

5.75 36.552 0.05572 0.01701 0.02569 3.275 1.510 106414 315 O*

6.25 34.738 0.04821 0.02296 0.03671 2.!69 1.599 109963 404 0.18893

6.75 33.947 0.04223 0.02584 0.04421 1.634 1.711 116251 445 0.22246

7.25 33.661 0.04181 0.02823 0.04911 1.481 1.740 124020 483 0.22801

7.75 33.547 0.04410 0.02964 0.05220 1.488 1.761 132121 505 0.23067

8.25 33.468 0.04576 0.03145 0.05557 1.455 1.767 140312 535 0.23049

9.25 33.465 0.05074 0.03430 0.06098 1.479 1.778 157357 584 0.22901

*Note: Separated flow at this location.

**Note: 1 inch = 2.54 cm. 1 ft/sec = 0.3048 m/sec.

NASA/TM-- 1998-208503
87

Table 12 Boundary Layer Properties, Grid 0, Re = 250,000

x, in.** u_, ft/s ** 8*, in.** 0, in.** g, in.** Hi2 H32 Re_ Reo ¢f

1.75 72.569 0.00926 0.00390 0.00637 2.372 1.631 66186 148 0.00356

2.25 78.871 0.00936 0.00370 0.00597 2.529 1.614 92263 151 0.00309

2.75 85.361 0.00952 0.00358 0.00577 2.659 1.611 122527 159 0.00276

3.25 91.480 0.00981 0.00400 0.00655 2.455 1.638 155750 192 0.00257

3.75 94.777 0.01014 0.00402 0.00652 2.524 1.622 186208 199 0.00237

4.25 95.486 0.01046 0.00421 0.00682 2.485 1.619 212402 210 0.00226

4.75 94.334 0.01319 0.00501 0.00815 2.635 1.629 220673 233 0.00189

5.25 93.179 0.01434 0.00547 0.00871 2.621 1.593 240586 251 0.00171

5.75 92.024 0.01605 0.00609 0.00964 2.633 1.582 260233 276 0.00156

6.25 90.689 0.01798 0.00693 0.01093 2.593 1.576 279037 309 0.00141

6.75 88.809 0.02021 0.00755 0.01182 2.675 1.564 295825 331 0.00123

7.25 88.137 0.02287 0.00821 0.01273 2.783 1.549 315204 357 0.00108

7.75 85.948 0.02518 0.00916 0.01419 2.749 1.549 328270 388 0.00114

8.25 84.652 0.02730 0.01096 0.01701 2.491 1.560 344940 458 0.00144

9.25 81.332 0.02783 0.01599 0.02772 1.740 1.734 371495 642 0.00368

**Note: Separated flow at this location.

**Note: 1 inch = 2.54 cm. 1 ft/sec = 0.3048 m/sec.

NA SAFFM-- 1998-208503
88

Table 13 Boundary Layer Properties, Grid 2, Re = 250,000

x, in.** u¢, f't/s** 8", in.** 0, in.** _, in.** H2 H32 Re_ Re0 ci_

1.75 74.157 0.00921 0.00414 0.00677 2.223 1.635 67237 159 0.00363

2.25 80.663 0.01022 0.00493 0.00834 2.073 1.692 93929 206 0.00319

2.75 85.105 0.01116 0.00556 0.00959 2.009 1.727 120713 244 0.00288

3.25 90.512 0.01116 0.00529 0.00905 2.110 1.710 151445 247 0.00258

3.75 94.751 0.01133 0.00512 0.00863 2.215 1.686 184021 251 0.00228

4.25 95.433 0.01168 0.00509 0.00845 2.296 1.661 209893 251 0.00214

4.75 93.622 0.01525 0.00717 0.01227 2.127 1.711 220072 332 0.00199

5.25 92.464 0.01490 0.00609 0.00974 2.445 1.599 240309 279 0.00173

5.75 91.204 0.01672 0.00659 0.01056 2.538 1.603 258562 296 0.00160

6.25 89.590 0.01904 0.00752 0.01198 2.532 1.592 276256 332 0.00145

6.75 87.904 0.02141 0.00862 0.01360 2.483 1.578 292926 374 0.00145

7.25 86.880 0.02378 0.01001 0.01585 2.375 1.583 311783 431 0.00159

7.75 85.010 0.02683 0.01247 0.01990 2.152 1.596 326768 526 0.00199

8.25 83.045 0.02538 0.01463 0.02445 1.735 1.671 338786 601 0.00329

9.25 80.761 0.02753 0.01809 0.03151 1.522 1.742 370633 725 0.00445

*Note: Separated flow at this location.

**Note: 1 inch = 2.54 cm. 1 ft/sec = 0.3048 m/sc c.

NASA/TM-- 1998-208503
89

Table 14 Boundary Layer Properties, Grid 3, Re = 250,000

x. in.** u_, ft/s** 8', in.** 0, in.** c. in.** H12 H32 Re_ Reo cf

1.75 72.457 0.01024 0.00490 0.00826 2.087 1.683 65492 383

2.25 77.874 0.01048 0.00508 0.00867 2.065 1.707 90494 422

2.75 84.514 0.01133 0.00582 0.01012 1.948 1.740 120130 495

3.25 90.141 0.01238 0.00658 0.01158 1.881 1.761 151481 577

3.75 93.412 0.01286 0.00670 0.01177 1.919 1.756 181306 622

4.25 94.226 0.01303 0.00647 0.01116 2.015 1.725 207416 636

4.75 93.530 0.01751 0.00877 0.01522 1.997 1.736 221119 815

5.25 92.389 0.01730 0.00767 0.01274 2.254 1.660 241895 797

5.75 91.608 0.01782 0.00770 0.01254 2.315 1.629 261306 810

6.25 90.177 0.01981 0.00966 0.01601 2.051 1.658 280061 888

6.75 88.524 0.02119 0.00997 0.01636 2.126 1.641 296920 932

7.25 86.759 0.02433 0.01338 0.02267 1.818 1.695 312555 1049

7.75 85.085 0.02362 0.01415 0.02419 1.670 1.710 327886 999

8.25 83.360 0.02333 0.01550 0.02704 1.505 1.745 342678 969

9.25 81.316 0.02816 0.01915 0.03376 1.470 1.763 375916 1144

0.00361

0.00327

0.00293

0.00261

0.00239

0.OO221

0.00190

0.00171

0.00170

0.00194

0.00224

0.00264

0.00369

0.00472

0.00477

*Note: Separated flow at this location.

**Note: 1 inch = 2.54 cm. 1 ft/sec = 0.3048 m/sec.

NASA/TM-- 1998-208503
9O

5. Intermittency Profiles

Intermittency profiles were computed from the digitally recorded mean velocity

profile data. Intermittency, F, is defined as the fraction of time during which the flow at a

given position remains turbulent after the onset of transition. A flow is considered fully

turbulent if F= 1 and fully laminar if F= 0. The instantaneous velocity signal was

segregated into turbulent and non-turbulent parts based on the squares of the first and

second derivatives of the signals. The details of this technique can be found in papers by

Hedley and Keffer (1974) and Sohn and Reshotko (1991). An illustration of this

technique is shown in Figure 70. The intermittency profiles are shown in Figures 71-76.

Figure 71 is an intermittency profile plot for a Reynolds number of 100,000, grid

O, and it shows that transition begins between x=5.75 (14.61 cm) and x=6.25 inches

( 15.88 cm). A peak intermittency value occurs fl,r x=6.25 inches (15.88 cm) at an

approximate y/5 value of 0.5. As the flow proceeds downstream in the test section, the

peak intermittency values move towards the wall with the flow becoming fully turbulent.

Figures 72 and 73 are the intermittency profile pl 3ts for grids 2 and 3 for a Reynolds

number of 100,000. These plots exhibit similar t ends to the grid 0 intermittency plot

except the transition point moves upstream and the transition length decreases. This

transition process occurs in the shear layer which bounds the freestream flow and bubble

surface. Additionally, the fiat portions of the intermittency profiles for y/_ values < 0.2

for each condition correspond to the constant velocity region inside the separation bubble.

Shear flow transition starts at approximately x=5.75 inches (14.61 cm) for grid 2 and

before x=5.75 inches (14.61 cm) for grid 3, respeCtively. Peak intermittency values occur

for grid 2 at x=5.75 inches (14.61 cm) at a y/5 vai:ue of approximately 0.25. Fully
91

turbulentflow occursatapproximatelyx=6.75inches(17.14cm) for grid 2 andat

approximatelyx=6.25-6.75inches(15.88-17.14cm) for grid 3. Approximatetransition

onsetandfully turbulentflow locationsobtainedfrom theintermittencyprofilesagree

favorablywith thosededucedfrom thehot-film datafor eachcondition.

Figures74-76areintermittencyprofile plotsfor aReynoldsnumberof 250,000

andgrids0, 2 and3,respectively.Transitioninitiatesatapproximatelyx=7.25inches

(18.42cm)for grid 0, betweenx=6.25-6.75inches(15.88-17.14cm) for grid 2 and

betweenx=5.25-5.75inches(13.33-14.61cm) for grid 3.Thetransitionlengthincreases

for eachgrid for aReynoldsnumberof 250,000in comparisonto thetransitionlengths

for thesamegridsfor aReynoldsnumberof 100,000.Thisdifferencecanbeattributedto

thenatureandtypeof transitionthatoccursat aparticularReynoldsnumber.For the

Reynoldsnumberof 100,000,laminarshearflow transitionoccursdueto theseparated

flow region,whereasfor theReynoldsnumberof 250,000,bypasstransitionoccurs.

Becauseof theintensemixing(energy)in theshearlayerdueto turbulentdiffusionfrom

thefreestreamfor theReynoldsnumberof 100,000,thetransitionlengthisshorterasa

resultof thehigherlevelof turbulentdiffusion.

NASA/TM--1998-208503
92

u/Ue

Smooth1o.o2

0 I, I- I i

0.1

Gttd2 Xs6,75inch Y"0.0061nch

2| ' -- i i i i , ,

1

0

I I I I

I

I i _0450 I i t _

3000 3010 3020 3030 3040 3060 3070 3080

Time (ms)

f

3090 3100

Figure 70 Indicator function determination technique for single wire

1.2r Re = 100 000

r

I- 0.6

0.4

0.2

r

i

oo +4-

O (> +

000000 0

C_pQD

o o o _,

0

0 0

0

0

0 ' Klebanoff

0

0

0.5 '-

Grid 0

[] X = 5.75 inches

X = 6.25 inches

O X = 6,75 inches

v X = 725 inches

.4- X = 7.75 inches

Y/_

Figure 71 Downstream intermittency profiles, grid 0, Re = 100,000

NASA/TM--1998-208503
93

12

Re = 100,000

1

08

06

04

0.2

rD

DEE

Grid 2

X = 5.75 inches

L_ X = 6.25 inches

O X = 6.75 inches

Klebanofl

O.

k

2_

4.

7-

0.5 1

y/&

15

Figure 72 Downstream intermittency profiles, grid 2, Re = 100,000

Re : 100.000

[]

04 •[Z

02. CJ

',_ Klebanoff

Q

Grid 3

[] X = 5 75 inches

z X= 6.25 inches

O X = 6.75 inches

[] []

[]

0 05 1

,_ Or] & "-'1 5

Figure 73 Downstream intermittency profiles, grid 3, Re = 100,000

NASA/TM-- 1998-208503
94

1.2

Re = 25C 000

0.8 _

0.6 _

0.4 - • . ++ +_+

0.2

0 _OQ_OOOOOOOaO0000 0

0 0.5

y/8

Grid 0

v X = 7.25 mches

X = 7.75 inches

X = 8.25 inches

X = 9.25 inches

Klebanoff

7

-b J

15

Figure 74 Downstream intermittency profiles, grid 0, Re = 250,000

Re = 25C 000

--T

0.8

F 06

04

0.2

"9

+++++++++_--+±_+__

4+ _- ++ .

0

0 0

0 o ooo

0 +

0

0 00000000 0 + .

0

oO o o oOo°°oo° o° o o

0

Grid 2

O X = 6.75 inches

v X = 7.25 inches

+ X = 7.75 inches

X = 8.25 inches

T X = 9,25 inches

00--

Klebanoff

1

y15

Figure 75 Downstream intermittency profiles, grid 2, Re = 250,000

NASA/TM-- 1998-208503
95

1.2

Re = 250,000

I

08

06

04

02

0

0

-+-_

0 0

0 0

0

Gnd 3

[] X = 5.75 inches

X = 6.25 inches

O X = 6.75 inches

,v X = 7.25 inches

+ X = 775 inches

X = 825 inches

o

<> +_',

O ', Ktebanoff

O

o +_

'_ Z_ 0 0 '\

0 0

El 0

0

[]

0.5 1

y/8

Figure 76 Downstream intermittency profiles, grid 3, Re = 250,000

6. Power Spectra Density Data

Results of power spectra density (PSD) data for Reynolds numbers of 100,000

and 250,000 are contained Figures 77-92. PSD data were taken in order to better

understand the character and nature of the disturbances in the boundary layer and

freestream regions of the flow field. Data was taken for grids 0, 2 and 3 at vertical

distances above the plate corresponding to locations where the fluctuating velocity signal

(rms) is a maximum and in the freestream of the flow field. For a Reynolds number of

100,000 the corresponding y values are y = y(u _,a_)= 0.015 inches (0.038 cm) and

y = y(ut' _ )=0.5 inches (1.27 cm) for x=1.75 and 2.25 inches (4.45 and 5.72 cm) and

y= y(ut' )= 0.7 inches (1.78 cm) for x=7.25 and 7.75 inches (18.14 and 19.68 cm). For a

Reynolds number of 250,000 the corresponding y values are y = y( u 'm_ ) -- 0.010 inches

NASA/TM-- 1998-208503
96

(0.0254 cm) and y = y(u'f_ )= 0.5 inches (1.27 cm) for x=1.75 and 2.25 inches (4.45 and

5.72 cm) and y = y(u _,,) = 0.7 inches ( 1.78 cm) fc,r x=7.25 and 7.75 inches ( 18.14 and

19.68 cm). The Nicolet FFT spectral analyzer used to make the PSD measurements is

described in the instrumentation section. Spectral data was taken using an average of 100

scans and a sampling rate of 12.8 kHz.

Figures 77-82 are PSD plots for the maximum rms location at Reynolds numbers

of 100,000 and 250,000. Figure 77 shows the PSD plot at the maximum rms position for

grid 0 and a Reynolds number of 100,000. This data shows that almost all of the

fluctuating energy is confined in low frequencies less than 700 Hz. at x= 4.75 and 5.25

inches ( 12.07 and 13.34 cm), resembling a laminar flow-field spectra. The flow field was

contaminated by main and bleed blower noise and their sub-harmonics. A two-order of

magnitude jump in PSD occurs at x=5.75 inches (14.61 cm) for low frequencies less than

1200 Hz. followed by a larger jump in the spectra for all frequency bands measured at

x=6.25-6.75 inches (15.88-17.15 cm). This small jump around x= 5.75 inches

(14.61 cm) indicates transition onset and the spectra increases in magnitude as the flow

becomes fully turbulent as it moves downstream. This behavior agrees with the

intermittency profile for grid 0 as shown in Figur,; 71. The PSD spectra over the

separation bubble shows no broad band disturbance hump around 1500 Hz., which would

be caused by a Kelvin-Helmholtz type instability in the flow-field. Additionally, the

approximate locations of transition onset and fully turbulent flow deduced from the PSD

agree favorably with those deduced from the intel mittency profiles.

NASA/TM-- !998-208503
97

-2F

r

-3-

1

Re = 100,000, Grid 0

i

1: x = 1.75 in.

2: x= 225 in.

3: x = 2.75 in,

4: x = 3.25 in.

5: x = 3.75 in.

6:x=425in

-11_ 500 10"00 1500 2000 2500 3000 3500 40_00 4500 5000

f, HZ

Figure 77 Upstream boundary layer spectra, y = y(u',, x ), grid 0, Re = 100,000

Figure 78 Downstream boundary layer spectra, y = y(u_,,_x ). grid 0. Re = 100,000

NASA/TM-- 1998-208503
98

n

o

-2

-3-:i ̧-,

Re = 100.00C Gnd 2

;- T ...... ,

i

1: x = 1.75 in.

2: x = 2.25 in.

3: x = 275in.

4: x = 3.25 in

5: x = 375 in

6: x = 4.25 in

1000 1500 2000 2500 3000 3500 4000 4500 5000

f, HZ

Figure 79 Upstream boundary layer spectra, y = y(u _n._). grid 2, Re = 100,000

>

_9

-7_

o

t

-8

'i

I

!

-10!

• Re = I00,000, Grid 2

o2 , r ,

_._",, 1 x=4.75in

''--_,_'Sr_'5;:.::_-7 2: x = 5.25 in. 3

'_" "_,__-'__._;"-- 4. x = 6.25 n

4_- , _ 4"_-_ 5 x=675in.

..... _"-'---_'_ ",--._ 6 x = 7.25 in.

_-_'_'_"_"--- ._ .... 7: X = 7.75 in.

"110 560 1000 1500 2000 2500 3000 3500 4000 4500 5000

f, Hz

Figure 80 Downstream boundary layer spectra, y = y(u ,'.. ), grid 2, Re = 100,000

NASA/TM-- 1998-208503
99

Re = 100,000, Grid 3

-2 T---

' 1: x = 1.75 in

_ 2: x = 225 in

i'"'_,,'_ 3:X = 2 75 n

-4 h_,__,_:!i I 5: x = 375 in

i 6: X = 4.25 in.

-lo i

I

..... .L ....... J -. J

"% 500 10"001500_20_0 25'00 3o00 3600 ,0'00-4_ _0

f, Hz

Figure 81 Upstream boundary layer spectra, y = y(u '.,.x), grid 3, Re = 100,000

1: x = 4.75 in,

2: x = 5,25 in

3: x = 5.75 in

4: x : 6.25 in

5: x = 6.75 in

6: x = 7,25 in.

7: x = 775 in

-9

-10

-11g _ _ -- _ -

500 1000 1 SO0 2000 2500 3000 3500 40"00 4500 5000

u

f, HZ

Figure 82 Downstream boundary layer spectra, y = y(u'.,.,.. ), grid 3, Re = 100,000

NA SA/TM-- 1998-208503
I O0

-2

-3

-4

Re = 250,00(' Grid 0

1: x = 175 in

2: x = 2.25 in

3: x = 2.75 in

4: x = 3.25 in.

5: x = 3.75 in.

6: x = 4.25 in

i,,

N I[

I

_ -7 _

-10, 1

i

-11 _ ---- 1 ........ i__ ; ....... _t ...... a ..........

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000

f, Hz

Figure 83 Upstream boundary layer spectra, y = y(u',., ), grid 0, Re = 250,000

Re = 250,000 Grid 0

-2 i T T

1: x = 4.75 in.

-3 2: x = 5.25 in

'" 3: x = 575 in

_._-_.7 41 x = 6.25 in

" _ '"°_" 5: x=675in

', __' _"',.. 6: x = 725 in

_3 - ,, 7: x = 7.75 in.

/

"i 1

-10

!

-11 /........ , c _ ..... ;

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000

f, HZ

Figure 84 Downstream boundary layer spectra, y = y( u'., ), grid 0, Re = 250,000

NASA/TM-- 1998- 208503
IOl

Re = 250,000. Grid 2

-2 .... :

1; x = 1.75 in.

-3 -_ 2: x = 2.25 in.

'+-;+.... 3: x = 2.75 in.

, ,., 4: x = 325 in.

-4 ,_ =_,_' 5: x = 375 in.

_,_,_ _. _.6 o 6: x = 425 in.

-9-

-10,

_ !.... 5_0 I00_0_500 20'002500 3000 3_ 40_ 4sbo 5000

f, Hz

Figure 85 Upstream boundary layer spectra, y = y(u',x ), grid 2, Re = 250.000

Re = 250,000. Grid 2

-2_7_, - _ -- -_- • r .......

_',;k_ I: x = 475 in

31 _::,_ '- 2; x = 5.25 in

" ! ;_.;_';;: .;_: .:, .3 3: x : 575 in.

_", ':_1,7_'7,,,,_l"_'_.,,,, , 4: X = 6.25 in.

-4 - , 2'_;_.:_ : "_,- .... 5; x = 6.75 in.

• .+'_-.-.-,-_.,,_ ' _ . "_-_ ..... + . 6: x = 7.25 in.

o "_'4

;[ i

"110 500 1000 1500 2000 2500 30100 3500' 4000 45_00 5000

f, Hz

Figure 86 Downstream boundary layer spectra, y = y(u '.,._ ), grid 2, Re = 250.000

NASAFI'M-- 1998-208503
102

Re = 250,00(_ Gr_d 3

Figure 8g Downstream boundary layer spect_'a, Y= y(u_,._ )

, grid 3, Re = 250,000

N AS A/TM_ 199g.208503
103

-2

-3-

.-4,

i ̧ ̧,

:_ -6-

if)

o

-8-

i

-91

-10r

-110

Re = 100,000, x=225 in.

1: grid 0

2: gnd 2

3: gr_d 3

_ __ _ __L. J _ -

500 1000 1500 2000 2500 30_00 3500 4000 4500 5000

f, Hz

Figure 89 Boundary layer spectra, y = y(u'f_ ), grids 0, 2 and 3, Re = 100,000,

x=2.25 inches (5.72 cm)

Re = 100,000, x=725 in.

1: grid 0

2: grid 2

3: grid 3

_,_ ....

-10_

i =

"1101--- 560 1000 1500 2000- -- 2500 3000 35_00 " 40(}0 4500 5000

f, Hz

Figure 90 Boundary layer spectra, y = y(u'_ ), grids O, 2 and 3, Re = 100,000,

x=7.25 inches ( 18.42 cm)

NASA/TM--1998-208503
I o4

-2 .... 1

Re = 250,000 x=225 in.

r - - r • -- _-

-3

g

o

-8

1: grid 0

2: grid 2

3: grid 3

500 10-00 1500 20()O 2,500 3000 3500 4000 4500 5000

f, Hz

Figure 91 Boundary layer spectra, y = y(u _ ), grids 0, 2 and 3, Re = 250,000,

x=2.25 inches (5.72 cm)

Re = 250,000, x=725 in

-2 , - i _ .......

-4.

-5.

;>

o

-8

-9

-10

-11

1:grid0

2: grid 2

3: grid 3

5oo _ 1_ 2000 25'0C

f, Hz

J

3000 3500

[

i

4000 4500 5000

Figure 92 Boundary layer spectra, y = y(u '_), grids 0, 2 and 3, Re = 250,000,

x=7.25 inches (18.42 cm)

NASA/TM-- !998-208503
105

7. Integral Length Scales

The longitudinal integral length scales computed from the power spectral density

data is summarized in Table 15. The integral scale is a measure of the characteristic

length of the turbulent structure in the flow and it also gives a measure of the average size

of the turbulent eddies. The length scales were computed from the following equations:

Rl12d

L= JR(r) dr,

0

where u_ and u _ are axial fluctuating velocities measured at the same location, but at a

different instant in time t_ and t2 = h+t, respectively. The integral length scale increases

as the turbulence level increases and this is consistent for both Reynolds numbers tested.

Table 15 A, Longitudinal Integral Length Scale

Grid 0

Re = 100,000 0.21 in. (0.53 cm)

Re = 250,000 0.33 in. (0.84 cm)

Grid 2 Grid 3

0.62 in. (1.57 cm) 1.20 in. (3.05 cm)

0.74 in.(1.88cm) 1.34 in.(3.40cm)

8. Classification of Separation Bubble

Gaster (1969) proposed a two parameter bubble bursting criterion using a

relationship between momentum Reynolds number at separation Re0_, and pressure

parameter P = (0s-/v)(AU/Ax). The criterion was based on his two sets of airfoil data and

other researcher's experimental and calculated data. In the pressure parameter, AU is the

rise in freestream velocity that would occur over the bubble length Ax in an unseparated

NASA/TM-- 1998-208503
!06

inviscidflow sincethebubbleshapeis dependentonthepressuredistributionthatwould

occurwithout separation.Gaster'stwoparameterburstingcriterionwith pressure

parametersmeasuredin thepresentexperimentsareplottedin Figure93. Threedomains

aredefinedin thisfigure. For _ < -0.09,theflow will notseparateregardlessof

Reynoldsnumber.To theright of theburstingboundary,a shortbubblewill beformed,

andto the left+a long(bursting)bubblewill bedeveloped.It isclearthatthebubbles

formedin thepresentexperimentareall of theshortvariety. In thepresentexperiment,

theinviscidpressureandAU are estimated from the Reynolds number of 250,000 case at

which the boundary layers are attached for the entire test section.

Several empirical correlations have been developed accounting for the effects of

freestream turbulence on the separation bubble length. Roberts (1975, 1980) related the

transition length of the separation bubble to the turbulence scale factor, in which the

turbulence scale is involved. The turbulence scale is a quantity not easily obtainable in

experiments. Davis et al. (1985) modified the R_,berts' correlation to replace the

freestream turbulence factor with the local freestlmeam turbulence level, which is

.Re_ = 25000 × log_,,{coth[I 7.32 × Tu )]}. The variation of transition length Reynolds

number at separation along with Roberts' modified correlation is presented in Figure 94.

The transition region determined from the intermittency profiles for each freestream

turbulence level shows excellent agreement with this empirical correlation. Additionally,

the boundary layer properties at separation are shown in Table 16 for grids 0, 2 and 3

and a Reynolds number of 100,000.

NASA/TM--1998-208503
107

II

-0.4

-0.35

-0.3

-0.25

-0.2

-0.15

-0.1

-0.05

01

o Grld '0 ' ' /

Short Bubble

Long Bubble / +

0 )K

No Separation

160 200 360 400

1_# s

Figure 93 Gaster's two parameter bubble bursting criterion, Re = 100,000

10 s

Figure 94

10:

10 "1

1

10 0 10 _

Tu(%)

Modified Roberts' correlation, grids O, 2 and 3, Re = 100,000

NASAFFM--1998-208503
108

Table 16 Separation Bubble Characteristics, Re = 100,000

Xs (in.)* X1-(in.)* XR(in.)* LB(in.)* LT (in.)* Ht_(in.)*

Grid 0 =5.25 5.75-6.25 =6.85 ---1.60 0.5-1.10 =0.042

Grid 2 =5.25 =5.75 =6.25 ---1.00 -0.50 =0.022

Grid 3 =5.25 <5.75 =5.85 =0.60 <0.50 =0.()12

*Note: 1 inch =2.54 cm.

F. Hot-Film Data

A series of flush-mounted hot-film gages were used to identify and study the

transition process on the flat plate. Figures 95-100 show results of the traces obtained

from the flush mounted surface hot-film gages. The test matrix used for the hot-film

traces is listed in Table 17. All fourteen gages could not be operated simultaneously due

to the availability of only six constant temperatur:_ anemometer modules; therefore, four

groups of six modules were used to obtain all of the traces. Hot-film signals are shown

for the second set of gages only (7-12) which correspond to axial locations of 4.0, 4.5,

5.0, 5.5, 6.0 and 7.0 inches, (10.16, 11.43, 12.70, 13.97, 15.24 and 17.78 cm),

respectively, measured from the leading edge. H(,t-film traces for Figures 95-97 are for

a Reynolds number of 100,000 with a separation bubble present and Figures 98-100 are

for a Reynolds number of 250,000 with fully atta_hed flow.

Figure 95 represents the hot-film traces o1: tained for grid 0 (0.8% TI) at a

Reynolds number of 100,000. This figure shows he traces of the second six gages (7-12)

which start downstream (x=4.0 inches, 10.16 cm) of the test section throat (x=3.75

inches, 9.53 cm) and extends into the adverse pressure gradient region to x=7.0 inches

(17.78 cm). These hot-film traces exhibit a typical laminar behavior as shown by the

NASAFFM-- 1998-208503
109

signals for x= 4.0, 4.5, 5.0, 5.5 and 6.0 inches (10.16, 11.43, 12.70, 13.97 and 15.24 cm),

respectively. This can be attributed to the low freestream turbulence and acceleration of

the flow through the converging region which stabilizes (relaminarizes) the flow and

suppresses some of the effects of the freestream turbulence and pressure gradient.

However, as the flow progresses downstream the hot-film signal becomes highly

intermittent, indicating the presence of some type of flow instability. The instability

encountered in this case is transition as shown by the signal at x=7.0 inches (17.78 cm).

This signal shows that the flow is in the late stages of transition and close to becoming

fully turbulent. The detection of transition at this location correlates well with the

hot-wire (intermittency and velocity contour, figures 71 and 26) measurement data which

shows that the flow is almost fully turbulent at x=7.0 inches ( 17.78 cm).

This behavior is more pronounced for grids 2 and 3 (freestream turbulence levels

of 2% and 3%, respectively) as shown in Figures 96 and 97. For grid 2 the onset of

transition is initiated at approximately x=6.0 inches (15.24 cm). Turbulent spots can be

seen in the signal at times of approximately 142-145 milliseconds, 170-172 milliseconds

and 176-178 milliseconds at x-6.0 inches. The hot-film signal at x=7.0 inches (17.78

cm) is representative of a near fully turbulent flow and its highly intermittent signal.

The hot-film traces for grid 3 reveals that transition onset is detected by the hot-film gage

located at x=5.5 inches (13.97 cm). Turbulent spots are evident in the signal at times of

approximately 1355-1356 milliseconds, 1391-1396 milliseconds and 1398-1402

milliseconds, respectively. At the next hot-film location, x=6.0 inches (15.24 cm), the

turbulent spots have grown significantly and are close to completely merging and

forming a fully turbulent flow. The hot-film trace at x=7.0 inches ( 17.78 cm) is again

NASA/TM-- 1998-208503
110

representative of a fully turbulent signal and these traces for grids 2 and 3 demonstrate

the effect freestream turbulence intensity has on the transition process. The hot-film

traces for all three grids for a Reynolds number of 100,000 show that the transition

process experienced by the flow is of a shear layer type in contrast to a bypass or natural

transition process. A bypass transition type flow is characterized by the development of

turbulent spots, whereas in a shear layer transition type flow turbulent spots do not form.

Figures 98-100 show the hot-film traces for a Reynolds number of 250,000 and

grids 0, 2 and 3. As expected the transitional process begins farther upstream than the

lower Reynolds case (100,000) and intermittent turbulent spots begin to develop at x=5.5

inches ( 13.97 cm), x=5.0 inches (12.70 cm) and ×=4.0 inches (t0.16 cm) for grids 0, 2

and 3, respectively. For grid 0, turbulent spots are visible in the hot-film traces at x=5.5,

6.0 and 7.0 inches (12.70, 15.24 and 17.78 cm) at a time interval of approximately

1493-1496 milliseconds. Turbulent spots can be seen in the hot film traces for grid 2 at

x=5.5, 6.0 and 7.0 inches (13.97, 15.24 and 17.78 cm) at approximate times of 78-82

milliseconds and also at times of 117-118 millise:onds and 60-70, 98-101, 133-136

and 140-150 milliseconds at x= 7.0 inches (17.78 cm). For grid 3, numerous turbulent

spots are clearly visible at all hot-film locations at 324-326, 333-336 and 342-344

milliseconds and multiple spots appear as the flow moves downstream. The transitional

process for this Reynolds number is of the bypas,, type and is contrast to the case for a

Reynolds number of 100,000 in which transition starts earlier, but takes a longer time and

has to travel farther downstream to achieve fully :urbulent flow.

NASA/TM-- 1998-208503
111

Gages

Table 17 Hot-film Gage Test Matrix

Setl Set2 Set3 Set4

1-6 7-12 9-14 5, 7, 9, 11,12,13,14

1.02

1.02

1

I

1.02

1

Grid 0 Re = 100,000

L I i I I I i I

L _ I _ L _ I i L

i i i i i i i i i

x=4in

x = 4.5 in.

x=5in

1,02

EIEmean 1

i i i i i L i L

x : 5.5in

1 02 ...... [

1 j x=6in.

i i L i

1.02

1 _ x=7in

i i i i L I L I I

100 110 120 130 140 150 160 170 180 190 200

Time (ms)

Figure 95 Hot-film gage voltage traces, grid 0, Re = 100,000

NASA/TM-- 1998-208503
112

Grid 2 Re = 10C 0(30

1 02 , i , , T , , , ,

1 _'_

L I I L

x=4in.

1,02

t x=4.5in.

L i i J i i i k

1 02 t

E/Emean 1 t

x=5in,

x=55in

1.02

1FL --I_l I- I I I J - x:61e

1.02

100 110 120 130 140 150 160 170 180 190 200

Time (ms)

Figure 96 Hot-film gage voltage traces, grid 2, Re = 100,000

1.02

Gri03 Re=100000

x=4in

1,o:1

102

i l i _ i i

1.02 .....

EIE I _ _

mean 1_ "_/_ "_-_ x=5,5in

t i i i i i i _ i

1.02

1 02

1350 1360 1370 1380 1390 1400 410 1420 1430 1440 1450

Time (ms)

Figure 97 Hot-film gage voltage Uaces, grid 3, Re = 100,000

NASA/TM-- 1998-208503
il3

EIE

1,02

1.02

i i L i

Grid 0 Re = 250,000

x=4in

I

x = 4.5in

1.02 , ,

1 i

1.02

x=5in,

mean 1

J J L I L J i i L

1.02 i , [ i _ , f , i

1 ' ' ' ' ' ' f ' ' x=6in.

i

i i i i i i i i i ]

1.02

1 x=7in

1450 1460 1470 1480 1490 1500 1510 1520 1530 1540 1550

Time (ms)

x=55in

Figure 98 Hot-film gage voltage traces, grid 0, Re = 250,000

Grid 2 Re = 250.000

1.021 x=4in.

1.02

i L i i t i L I

1.02

I d I I _ L I I d

1.02 ......

FJEml_an 1 I _ I L I I I I J

1.02 i , i i J J r i r

1.02 q J , ,

430 435 440 445 460 465 470 475

x = 4.5in.

x=5in,

x = 5.5in,

x = 6 it'1

450 455

Time (ms)

x=7in

480

Figure 99 Hot-film gage voltage traces, grid 2, Re = 250,000

NASA/TM--1998-208503
114

Grid 3 Re = 250.300

1.02

i i r , r i i , F

1-_ x=4,n

1 02

1 02 i , r , r q i T J

1 _ x=5in

i i i i

X=451n.

1.02 .........

E/Emean 1 x = 55 in

1 02

102 [

I

310 315 320 325 330 335 340 345 350 355 360

Time (ms)

Figure 100 Hot-film gage voltage traces, grid 3, Re = 250,000

G. X-wire Data

Normalized velocity and shear stress prof:les from an x-type hot-wire probe are

presented in Figures 101-118. Profiles are presented for grids 0, 2 and 3 at Reynolds

numbers of 100,000 and 250,000. Downstream profiles only were made with the x-wire.

1. X-wire u' Velocity Profiles

The streamwise fluctuating velocity profiles for grids 0, 2 and 3 are shown in

Figures 101-106. These profiles compare favorably in magnitude and shape with those

obtained from the single wire probe. Figure 101 s the x-wire streamwise fluctuating

velocity profile for grid 0 and a Reynolds numbel of 100,000. The low rms values

obtained for profiles at x=5.25 and 5.75 inches (13.34 and 14.61 cm) for grid 0 occur

within the separated flow region and are indicati',e of values that would occur in a

NASA/TM-- 1998-208503
115

separated flow. As the flow undergoes transition the rms values increase in magnitude as

the flow progresses downstream. The behavior of this x-wire profile is similar to that of

the single wire probe profile in that the peak u' value occurs at a y/_5* value of

approximately 1.0 for all axial locations tested; however, the magnitude of the x-wire

peak rms values are slightly lower than those of the single wire. The peak rms value

increases in magnitude as the flow proceeds downstream, reaching a maximum value of

approximately 0.158 between x=6.75 and 7.25 inches (17.15 and 18.42 cm) which

corresponds to the approximate location of transition onset that was obtained from the

intermittency profiles. The peak rms value decreases in magnitude as the flow passes

through transition, finally decreasing to a value of approximately 0.1 at the last

measurement station (x=9.25 inches, 23.50 cm). Additionally, all of the u' profiles

collapse on top of each other as the flow proceeds downstream and approaches a u'/Ue

value of approximately 0.01. The behavior of the u' profiles described above is repeated

for grids 2 and 3, at a Reynolds number of 100,000 in Figures 102 and 103 with peak rms

values occurring at axial locations of x=6.25 and x=5.75 inches (15.88 and 14.61 cm) for

grids 2 and 3 respectively. These values correspond to the approximate locations of

transition onset and are also consistent with transition onset values obtained from the

intermittency profiles.

Figures 104-106 show the x-wire rms profiles for grids 0, 2 and 3 and at a

Reynolds number of 250,000. These rms profiles are also consistent with the single wire

rms profiles except that the x-wire peak rms values are again slightly lower than the

single wire values. Peak rms values occur again at a y/8* value of approximately 1 with

NASA/TM-- 1998-208503
116

a maximum occurring at approximate u'/Ue values of 0.115 at x-8.25 inches (20.96 cm)

for 0, 0.12 at x=7.75 inches ( 19.69 cm) for grid 2 and 0.11 at 6.75 inches ( 17.15 cm) for

grid 3, respectively. However, the rms profiles for this Reynolds number differs from

those for a Reynolds number of 100,000 in that these rms profiles do not collapse on top

of each other as the flow progresses downstream. Instead of collapsing to a single value

as the flow progresses downstream, the rms levels steadily increase, which can be

attributed to the merging of boundary layers from the lower (test plate) and upper wall.

The deviation is more pronounced at downstream measurement stations x=7.25-9.25

inches (18.42-23.50 cm) for all levels of turbulence intensities tested and this behavior

was also seen in the single wire data.

Re = 100.000

0,2 _ i

1

0,18 _ Gnd 0

/

X = 5.25 inch

0.16 O X = 5.75 inch

l _:_ ,%,. ÷ XX == 6.25 675 inch inch

0141 +_E- _ X = 7 25inch

°"21 u'/U 0.1

0.06 _ _

006 ,_ "++_% _,el,,

0.04 0

0.02

i

V X = 7.75 inch

• X = 8.25 inch

• X = 8.75 inch

• X= 9.25 inch

0 _ 70 _81LA

+

i k J i l

2 4 6 6 1 o

y16*

12

Figure 101 X-wire u' velocity prcfile, grid 0, Re = 100,000

NAS A/TM-- 1998-208503
117

Re = 100,000

Grid 2

X = 5 25 inch

O X = 5 75 inch

v X = 6 25 inch

•+ X = 675 inch

.t,_ X=725inch

_r X = 775 inch

• X = 8.25inch

• X = 8.75 inch

• X = 9 25 inch

0.2[ v T

i

°18 i

0.14,- O_

!

oo8- I_.. o _$

o.o_,,f "-o o* _ ==•

004 /L 0 0 t

/

0.02

I

oL

0

0

L. -.-

o o04 t •

,_,o & .

_,,,o ,9 _ O.LO _0 '_ _ _ -.

I i L .....

2 4 6 8 10 12

y/6*

Figure 102 X-wire u' velocity profile, grid 2, Re = 100,000

0.2j

Re = 100.000

u'/U

0.18

0.16

014

012

0.1

0.08

0.06

0.04

002

0

Gnd 3

,_ X = 5.25 inch

_.__A_t O X = 575 inch

C, v X = 6.25 inch

+ X = 6 75 inch

X = 725 inch

7 X = 7 75 inch

• X = 825 inch

SO 0 --&l "7

_'-_ '_.o% 0 + + _I_aw

i i i i

0 2 4 6 8 10

yl_,*

Figure 103 X-wire u' velocity profile, grid 3, Re = 100,000

12

NASATFM-- 1998-208503
118

Re = 254,,0O0

02 T r

0.18 Gnd0

L X = 5.25 inch

0.16[ 0 X = 5 75 inch

v X = 6.25 inch

X = 6.75 inch

014_ _ X = 7.25 inch

X = 775 inch

0,12_ • X = 8,25 inch

• X = 9 25 inch milk,.

0.1 Amr_A&k

u'lU

0.08 _.

,,_ ••&

•

_..%_ 7 • _, •

0.06 •

• •& • • •

0.02 _'_'_.'_._' .ff ._ ti. _ ,_, ,V L:'

ol

0 2 4i 6I 8i I IO 12

yl?,"

Figure 104 X-wire u' velocity profile, grid 0, Re = 250,000

u'/U

Re = 250.000

02

0.18

0.16

0.14

J

0.12

0,i

0o8;

006

0,04

002

0

Grid 2

.:_ X = 5.25 inch

O X = 5.75 inch

_., X = 6.25 inch

+ X = 6.75 inch

X = 7.25 inch

X = 7.75 inch

• X = 8.25 inch

• X = 9.25 inch

_:_÷ _,. • •

":.v.o--.÷ o'_%_',, • _ •• • • •

,_y^'.c,_÷ 2v= • • • • • • • • • • l

2 4 6 8 10 12

y/5'

Figure 105 X-wire u' velocity prcfile, grid 2, Re = 250,000

NASA/TM-- 1998-208503
119

u'_

0.2

0"181 -

0,12

01

0.08

0.06

0.04

0.02

Re = 250.000

Grid 3

,2. X = 5.25 inch

O X = 5 75inch

_,, X = 625 inch

--,- X = 6,75 inch

X = 7.25 inch

_' X = 7.75 inch

• X = 8.25 inch

• X = 9.25 inch

,_'-* %v'1_A

_,,o,_c,.+_,'Tml " •

::,,%_>/,_•• , . , • ,, J

2 4 6 8 10

y/8*

12

Figure 106 X-wire u' velocity profile, grid 3, Re = 250,000

2. X-wire v' Velocity Profiles

The x-wire vertical or v' velocity profiles are presented in Figures 107-112

for grids 0, 2 and 3 and Reynolds numbers of 100,000 and 250,000.

The profiles for grids 0, 2 and 3 and a Reynolds number of 100,000 are shown

in Figures 107-109 and these profiles exhibit behavior that is similar to the u' rms

velocity profiles. Figure 107 is the v' plot for grid 0 and it shows that maximum values

of v' occur closer to the wall than the u' rms velocity profiles and these values increase

and move away from the wall as the flow proceeds downstream. A maximum v' value

occurs for grid 0 at x=6.75 inches (17.15 cm) and a v'/U_ value of approximately 0.125

and a y/_5* value of approximately 1.5 and this contrasts with the maximum u'/U_ value of

approximately 0.16 occurring at x= 7.25 inches (18.42 cm) and a y/_5* value of

approximately 1.0. The location of the maximum v' value corresponds to the

NASA/TM--1998-208503
120

approximate location of transition onset for grid 0. The levels of v'/U_ for grid 0

gradually decrease after transition onset finally leveling off to a value of approximately

0.01. The v' plot for grid 2 is shown in Figure 108 and it shows that v' levels have

increased close to the wall due to the increase in freestream turbulence level. Again, the

v' levels of the upstream profiles occur near the wall and move away from the wall as the

flow moves downstream with a maximum occurring between x=6.25 and 6.75 inches

(15.88-17.14 cm, approximate location of transition onset) with a v'/Ue value of

approximately 0.12 and an approximate y/8* value of 2. The v' levels then decrease

gradually and level off to a value of approximately 0.22. The v' levels for grid 3 in

Figure 109 increase in a fashion similar to those for grid 2 with increased v' levels for the

upstream profiles due to the higher freestream turbulence level. A maximum v' occurs at

x=6.25 inches (15.88 cm) with a v'/U_ value of approximately 0.12 and an approximate

y/8* value of 1.2.

Figures 110-112 contain the v' profile plols for a Reynolds number of 250,000

and these maximum v' values tend to occur at an approximate value y/k* of 1.0 for grids

"0, 2 and 3. Maximum v' values of approximately 0.082, 0.097 and 0.090 occur at x=8.25,

x=7.75 and 6.75 inches (20.96, 19.69 and 17.15 c n) for grids 0, 2 and 3, respectively.

The behavior of u' and v' in the transition_:l boundary layer can also be an

indication of the distribution of turbulent kinetic energy in a steady shear flow (Tennekes

8,: Lumley, 1972). More energy is transferred to t_le u' velocity component than the other

components because it receives all of the kinetic energy production generated by the

mean flow. The transfer of turbulent kinetic energy to the other components is then

NASA/TM-- 1998-208503
121

performed by the nonlinear pressure-velocity interaction, p',:?u" / Ox i . In the early stages

of transition when the eddies are relatively large due to the production of turbulent kinetic

energy, the energy accumulates first in the u' velocity component with the remaining

energy being transferred to the other components. Because of this process the u'and v'

velocity components increase in energy resulting in an attendant increase in their rms

levels. As transition continues, the size and strength of the eddies decrease, resulting in

an increase in viscous dissipation until it is globally balanced with the energy production.

Some portions of the energy are redistributed to other velocity components which

decreases the energy in the u' velocity component and decreases the magnitude of the u'

rms. However, as the energy gained by v' from the u' component is being locally

balanced with viscous dissipation, the v' rms level remains close to a constant value in the

later stages of transitional flow. A similar energy level is attained by both the u'and v'

velocity components near the edge of the boundary layer, indicating that isotropy of the

turbulent fluctuations near the edge of the boundary layer is almost completed in the late

stages of transitional flow.

NASA/TM--1998-208503
122

v'lU

Re = 100 000

0.2 I

!

0.18, Grid 0

i /, X = 525 inch

0.16i- O OO O O X=575inch

v X = 625 inch

i + X = 6.75 inch

0.14.- .¢;-,× = 7 25inch

_,' X = 7.75 inch

' -_r • X = 825 inch

0.12 ! _,._. & X=875inch

0.08

f _ _o _. •

004 _ -_ _ I _ _ _ Vl_ll_l_ •

V_A +

002 ¢%o_2 _-..- - _ _, ",-_-,*_=_= _=

2 4 6 8 10 12

y/8"

Figure 107 X-wire v' velocity profile, grid O, Re = 100,000

v'/IJ

Re = 10[ ,000

018

0.12r

Grid2

,I' X = 5.25 inch

O X = 5.75 inch

._ X = 6.25 inch

X = 6.75 inch

X = 7.25 inch

_7 X = 775 inch

• X = 825 inch

• X = 8 75inch

• X = 925 inch

008 _V

oo6 _ .... _ffi_,,=..

%+ ,, ,_,,. •

002! > _*<>O_ O _- _0 7_

000000 O O, O (_.o _ ' _ ± _ &

i

00 2 4 6 8 t0 12

yh3"

Figure 108 X-wire v' velocity prc file, grid 2, Re = 100,000

NAS A/TM-- 1998-208503
123

02

Re = 100,000

v'./U

0.18

0.16

0.14

0.12

01

0.08

0.06

0.04

0.02

1

Grid 3

X = 5.25 inch

O X = 575 inch

v X = 625 inch

X = 6.75 inch

",_- X = 7.25 inch

_; X = 775 inch

• X = 8.25 fnch

_ • X = 9.25 inch

o° •

2 4 6 8 10 12

y/3*

Figure 109 X-wire v' velocity profile, grid 3, Re = 100,000

Re = 250000

0.2

v'/U

0.18

016

0.14

O12

0.1

0.08

006

ii;I

0 _

0

Grid 0

_'_ X : 525 inch

O X : 575 inch

x/ X = 6 25inch

t X = 6 75 inch

X = 7 25 inch

7 X = 775 inch

• X = 825 inch

• X = 925 inch

&&

_.v7 I_ i & • • • . • • • & • • .

Figure 110 X-wire v' velocity profile, grid 0, Re = 250,000

NASA/TM-- 1998-208503
124

v'/U

Re = 25C 000

0.2 ..... r - _ T - - T

0.18

0.16

0.14

0.12

Q1

0.08 0.06

0020.04 ...._,%

I

ol

0 2

Gdd 2

L X= 5.25 inch

O X = 5.75 inch

v X= 6.25 inch

- X = 6 75 inch

_- X = 7.25 inch

',j X = 7.75 inch

• X= 8.25 inch

• X = 9 25inch

• •A• • • • • -- • • ]/

I

4 6 8_ 1_0 12

y/_;"

Figure 111 X-wire v' velocity profile, grid 2, Re = 250,000

Re = 25(3 000

0.2 _ • -

v'tU

018

0.16

0.14

0.12

01

008

0.06

0.O4

0.02

0 L

0 2

Grid 3

X = 5.25 inch

O X = 5.75 inch

v X = 625 inch

•-'- X = 6.75 inch i

i

_- X = 7.25 inch 7

v" X = 7.75 inch I

• X = 8,25 inch

• X = 9,25 inch

i .... L • ,

4 6 8 10 12

y/_,"

Figure 112 X-wire v' velocity profile, grid 3, Re = 250,000

NASA/TM--199g-208503
125

3. Reynolds Shear Stress Profiles

Reynolds shear stress profiles for Reynolds numbers of 100,000 and 250,000

for grids 0, 2 and 3 were computed from the digitally recorded instantaneous x-wire

probe measurements and are shown in Figures 113-118. These profiles were normalized

with respect to the square of the edge velocity.

Figure 113 is the Reynolds shear stress profile for grid 0 and a Reynolds number

of 100,000. Profiles at axial locations of 5.25 and 5.75 inches (13.34 and 14.61 cm)

(which are inside the separation bubble) are zero near the wall because the production

of turbulent kinetic energy is ideally zero in the region. As transition begins to occur

around an axial station of 6.25 inches (15.88 cm), production of turbulent kinetic energy

is initiated and the Reynolds shear stress attains a peak value of approximately 0.002 at

this location. As transition proceeds more turbulent kinetic energy is produced and a

maximum value of approximately 0.0078 occurs at a y/8* value of approximately 1.0 and

an axial location of 6.75 inches ( 17.15 cm). The levels of the Reynolds shear stress then

decrease as transition is completed and turbulent flow is achieved, finally leveling off to

zero near the edge of the boundary layer. The Reynolds shear stress profiles for grids 2

and 3 behave similarly to the grid 0 profile except the profiles at x=5.25 and 5.75 inches

(13.34 and 14.61 cm) are not zero inside the boundary layer and a higher maximum value

is achieved, as shown in Figures 114 and 115. The effect of the freestream turbulence

can be clearly seen in these figures as the level of the Reynolds shear stress has increased

significantly in the near wall region for x=5.25 and 5.75 inches ( 13.34 and 14.61 cm).

The adverse pressure gradient experienced by the flow increases the rate of turbulent

NASA/TM--1998-208503
126

shear stress production in the transition region ar, d this phenomena was also seen

experimentally by Mislevy and Wang (1995). Approximate locations of transition

deduced from these shear stress distributions agree quite well with those deduced from

the intermittency data.

The Reynolds shear stress plots for a Reynolds number of 250,000 and grids 0, 2

and 3 are presented in Figures 116-118. At this higher Reynolds number and for grid 0,

the entire Reynolds shear stress distribution is approximately zero for axial locations of

x=5.25 inches (13.34 cm) to x=7.25 inches (18.42 cm). For grid 0 at this Reynolds

number, transition begins at approximately 7.25 inches (18.42 cm) according to the

intermittency profiles. It can be seen in Figure 116 that turbulent shear stress production

also begins approximately at this axial location. After transition is initiated, the grid 0

Reynolds shear stress profiles behave similar to the profiles at a Reynolds number of

100,000 except the magnitude is smaller. A maximum shear stress value of 0.0035

occurs at a y/_i* value of approximately 1.0 and an axial location of x=8.25 inches (20.96

cm). Additionally, the profiles for this Reynolds number condition do not exhibit the

same drop in magnitude as the profiles did for a l',eynolds number of 100,000 because

fully turbulent flow is not achieved. The Reynolds shear stress profile for x=9.25 inches

(23.50 cm) drops below zero and this is mostly attributed to the merging of the lower and

upper wall boundary layers near the end of the te:,t section.

Figure 117 is plot of the Reynolds shear s'.ress distribution for grid 2 and a

Reynolds number of 250,000. The behavior of tl-_e shear stress profile for grid 2 is

similar to that of grid 0 except that only the profile at x=5.25 inches ( 13.34 cm) is zero

NASAFI'M-- 1998-208503
127

for the entire profile and the profiles for the other axial locations have moved up due to

an increased level of freestream turbulence. After transition is initiated, at approximately

x=6.75 inches (17.15 cm), the grid 2 profiles move upward towards the maximum value

of 0.0035 which occurs at a y/5* value of approximately 1.0 and an axial location of

x=8.25 inches (20.96 cm). The flow is almost fully turbulent at this axial station and the

shear stress production starts to decrease from x=9.25 inches (23.50 cm) since the flow is

fully turbulent at this location. Additionally, the Reynolds shear stress profile for x=9.25

inches (23.50 cm) again drops below zero and this is due to the merging of the lower and

upper wall boundary layers near the end of the test section. The behavior of the grid 2

shear stress profile is repeated for grid 3, as shown in Figure 118, except the maximum

shear stress value of 0.0031 occurs at x=7.75 inches (19.69 cm) and a y/8* value of

approximately 1.2. After transition is initiated, at approximately x=6.25 inches (19.69

cm), the grid 2 profiles move upward towards the maximum value and then decrease as

the shear stress production starts to decrease at x=8.25 inches (20.96 cm) after fully

turbulent flow is attained.

NASA/TM-- 1998-208503
128

x 10 "3

9 _

8_

6

U ._

' 4

3

2

1

0

Re- 100 000

Gdd 0

ZI X - 525 inch

O X ,, 5.75 inch

_+_I-: 0 X - 6.25 Inch X • 6.75 inch

+

+ _ X - 725 inch

+ ÷ _' X ,' 7.75 inch

_:._r _._. • X = 8,75 inch

+ . • X•9.25iflch

+ * "**%"I"

IQBX U

"10 2 4' 6' 8' 1o 12

y/_"

Figure 113 Reynolds shear stress profiles, grid 0, Re = 100,000

-- U'V'

10.3 Re • 100 000

+

O +

O

O +

Grid 2

LI X ,, 5.25 inch

O X - 5.75 inch

@ X - 8.25 inch

+ X ,, 6.75 inch

,_ X - 7.25 bch

_7 X - 7.75 inch

• X - R.25 _.h

• X • 8.75 inch

• X - 9.25 inch

2 4 6 8 10 12

Figure 114 Reynolds shear stress profiles, grid 2, Re = 100,000

NASA/TM--1998-208503
129

-- U'V'

tJ_

x 10-3 Re = 100,000

Grid 3

A X - 5.25 inch

I

O X • 5.75 inch -1

I

O X - 6.25 Inch

+ X - 6.75 Inch

X = 7.25 inch [

V X - 7,75 inch

• X • 8.25 inch I

• X • 9.25 inch

9

8

2 • VCr

1 i i 1 1

1 2 4 6 8 10 12

Figure 115 Reynolds shear stress profiles, grid 3, Re = 100,000

-- U"V'

tJ+

10 -3

g_

8

7

6

4

3

2

Re - 250,000

i

I

Glid 0

A X • 525 Inch

O X • 5.75 Inch

X • 6.25 Inch

-+- X • 6.75 inch

•_ X - 7.25 inch

V X - 7.75 inch

• X - 825 Inch

• X = g.25 Inch

- -..',,

-,,

i L I J- J2 4 6 8 IO 12

y/8"

Figure 116 Reynolds shear stress profiles, grid 0, Re - 250,000

NASA/TM-- 1998-208503
13O

7

6

m 5

• u'v'

4

3

2

1

0

-1

c_0 _

9

8

Re - 250,000

Grld2

A X - 5.25 inch

O X - 5.75 inch

O X - 6.25 inch

+ X- 6.75 inch

_r X - 7.25 inch

V X - 7,75 Inch

• X - 8.25 Inch

• X 1 9.25 inch

2 4 e 8

I

_v_l_v o_

1J0 12

Figure 117 Reynolds shear stress profiles, grid 2, Re = 250,000

-- iJ'v'

u_

x 10.3 Re - 250,000

[

g_-

8

7

6

5

GY_d3

X. 525 inch

O X - 5.75 inch

0 X - 6.25 Inch

"k- X - 6.75 Inch

•_ X - 7.25 Inch

V X - 7.75 inch

• X - 8.25 irtch

• X - 9.25 inch

Figure 118 Reynolds shear stress p]ofiles, grid 3, Re = 250,000

NASA/TM-- 1998-208503
VI. UNCERTAINTY ANALYSIS

An uncertainty analysis was performed on the hot-wire data using the methods of

Yavuzkurt (1984). Yavuzkurt derived the following equations for computing the

uncertainty in velocities obtained from hot-wire calibration data, with the following

assumptions: a constant temperature anemometer, an isothermal flow with no velocity

fluctuations, and velocity is measured with a pitot tube probe connected to a

micromanometer. The anemometer output E (in volts) and the micromanometer reading

h (in inches of oil) are recorded. The flow velocity u can be calculated from h and will be

called u/with an uncertainty called Au/. For

(1)

2hpgRT= )1/2 u, = P_ (2)

where g and R are constants with negligible uncertainties. The uncertainties in the

quantities in Equation (2) can represented by the following relations:

h + Ah, p + @, T + ATe, Ps + APs. Utilizing methods from Kline and McClintock

(1953) and Holman (1978), the uncertainty Aul can be represented by the following

equation:

NASA/TM-- !998-208503 131
132

Rearrangingyields

A,.,=_.,LVJ,a + +v _ ) +v R_a J

(3)

Instantaneous velocity data measured with the calibration process yields an effective

velocity of u<t_ and will have an uncertainty of

=[(A.,)-' + ''2

Defining ot from equation (3), leads to

a- ,_ -2L k h J + +_.T= ) +t,-_.,.) J

Replacing Ah AP, -- with -- the relative uncertainty of the total pressure (since a pressure

h P

transducer was used instead of a manometer board) yields

,. -_=2LV. P) +k _ ) + T "

ArtI = 0(./I:0'

Au 2 = ,6u_:tt

The quantity 13can be calculated from the curve fit data as follows:

112

NASA/TM-- 1998-208503
133

Hence,

Au<t t __ lt,tt (t_ 2 + /_2) t/2 '

Using data obtained from the Dantec Streamline calibration flow unit:

n U E T P Ecorr Ucorr

volts m/s* °C* kPa * volts m/s*

1 0.49467 1.17238 28.50794 98.30303 1.19079 0.49422

2 2.29737 1.35147 28.51239 98.30578 1.37271 2.31376

3 4.11157 1.44054 28.51114 98.30578 1.46316 4.08173

4 5.84837 1.50359 28.51154 98.30303 1.52721 5.80823

5 7.85840 1.56446 28.51346 98.30578 1.58904 7.91243

6 9.53361 1.60475 28.51715 98.30303 1.62998 9.56792

7 11.30462 1.64031 28.51755 98.30028 1.66610 11.21661

8 13.01815 1.67677 28.51483 98.30028 1.70312 13.10108

9 14.87473 1.70712 28.51111 98.29753 1.73394 14.82722

10 16.59053 1.73726 28.50449 98.30028 1.76452 16.68931

11 18.39380 1.76471 28.49442 98.29753 1.79236 18.51782

12 20.14946 1.78649 28.47153 98.29203 1.81439 20.05871

13 22.29227 1.81498 28.42935 98.30303 1.84314 22.19776

14 24.00756 1.83672 28.37830 98.30028 1.86500 23.92433

15 25.44061 1.85401 28.31592 98.29753 1.88228 25.35272

16 27.47637 1.87891 28.24036 98.30303 1.90723 27.51473

17 29.46212 1.90105 28.15704 98.29753 1.92934 29.53252

18 31.73464 1.92494 28.06400 98.29753 1.95316 31.81570

19 32.75958 1.93401 27.99271 98.30303 1.96204 32.69641

20 34.53765 1.95238 27.90659 98.30028 1.98029 34.55689

*Note: 1 m/s = 3.281 ft/sec, °C = 5/9 (°F +40)-40, 1 kPa= 1.450x10 -4 psi.

Using data point 7 to calculate the density and its associated error,

P = 98.300278 kPa, AP= +0.05 kPa,

T= 28.517548 °C, AT= _+0.3 °C,

V= 11.216614 m/s (calibration free jet set point)

p= l. 13539 kg/m 3, Ap= 0.01052 kg/m _

Ps = 98.25221 kPa, APs= +0.05 kPa

NASA/TM-- 1998-208503
134

The error in computing the density is determined from the following equations,

P

pRT

p=f(e, T)

ap 1

m

aP RT

Op - P

aT RT 2 "

yielding

Substituting in for P, we, T and wr yields

Ap =_+0.01052 kg/m s.

Computing the quantity ot using P, AP, P, Ap, T_, ATe, Ps, APs. gives

= 0.01404.

Computing the quantity 13using P, AP, p, Ap, T_, ATe, Ps, APs, yields

13= 0.00492167.

Computing

''2

NASA/TM--1998-208503
135

yields

(a 2 +/32)1/2 = 0.014499 or 1.4499 %.

Therefore, the error in the mean and rms velocities from the calibration is 1.4499%.

NASA/TM-- 1998-208503
VII. CONCLUSIONS AND RECOMMENDATIONS

The parametric investigation of the flow field on a simulated LPT blade was

performed at three levels of freestream turbulence for Reynolds numbers of 100,000 and

250,000. The flow visualization data confirmed that the boundary layer was separated

and formed a bubble. Based on a two parameter bubble bursting criterion proposed by

Gaster (1969), the bubbles formed in this experiments were of the short, non-bursting

type.

Flow visualization photographs revealed that the laminar portion of the bubble is

steady, while the regions downstream from transition are unsteady. The transition

process over the separated flow region for a Reyr olds number of 100,000 is similar to a

laminar free shear layer through the formation of a large coherent eddy structure.

However, the transition path for an attached boundary layer at a Reynolds number of

250,000 is through the formation of intermittent lurbulent spots. These two distinct

transition mechanisms were confirmed by a serie_ of instantaneous hot-film signals.

The pressure distribution shows a typical feature, namely a nearly constant pressure zone

followed by a sharp pressure rise region. Intermi_tency profiles showed that shear flow

transition (Reynolds number of 100,000) is initia ed at approximately x=6.25 inches

(15.88 cm) for grid 0, at approximately x=5.75 ir_ches (14.61 cm) for grid 2 and before

x=5.75 inches (14.61 cm) for grid 3. Additionally, the intermittency profiles revealed that

fully turbulent flow occurs approximately at x=7 25-7.75 inches (18.42-19.69 cm) for

N ASA/TM--1998-208503 136
137

grid 0, at x=6.75 inches (17.15 cm) for grid 2, and between x=6.25-6.75 inches (15.88-

17.15 cm) for grid 3. For a Reynolds number of 250,000, the intermittency profiles show

that transition is initiated between x=5.75 and 6.25 inches (14.61 and 15.88 cm) for grid

0, between x=6.25 and 6.75 inches (15.88 and 17.15 cm) for grid 2 and before x=5.75

inches (14.61 cm) for grid 3. Additionally, the intermittency profiles revealed that fully

turbulent flow does not occur for grid 0, but it does occurs at between x=8.25 and 9.25

inches (20.96 and 23.50 cm) for grid 2 and between x=7.75 and 8.25 inches (19.69 and

20.96 cm) for grid 3.

The transition onset location and length are inversely proportional to the

freestream turbulence level. Additionally, the characteristics of transition deduced from

the intermittency profiles and boundary layer spectra data show excellent agreement. The

modified Roberts' transition length correlation predicts quite well the transition length of

the bubble for each condition. It was also observed that bubble length and height

decreased as freestream turbulence level increased.

Power spectral density (PSD) profiles showed that almost all of the fluctuating

energy is confined in low frequencies less than 700 Hz. This data also shows that the

flow field was contaminated by main and bleed blower noise and their sub-harmonics. A

two-order of PSD magnitude jump occurs at x=5.75 inches (14.61 cm) for low

frequencies less than 1200 Hz. followed by a larger jump in the spectra for all frequency

bands measured at x=6.25-6.75 inches (15.88-17.15 cm). Transition onset is indicated by

this small jump and the spectra increases in magnitude as the flow becomes fully

turbulent as it moves downstream. The PSD spectra over the separation bubble shows no

broad band disturbance hump around 1500 Hz., which would be caused by a KelvinNA SA/TM-- 1998-208503
13g

Helmholtz type instability in the flow field. Classical flow instabilities (Kelvin-Hemholtz

or Tollmien-Schlichting) and their propagation downstream were not identified in any of

the PSD profiles in this experimental study. Additionally, the approximate locations of

transition onset and fully turbulent flow deduced from the PSD profiles agree favorably

with those deduced from the intermittency profiles and hot-film traces.

It is recommended that future research concentrate on identifying the Reynolds

numbers at which the separation bubbles burst for various levels of freestream turbulence.

It is also recommended that steady state data be taken in experiments with stationary bars

or rods upstream of the test section to analyze the effect of wake shedding on the

separation/transition process. This data may lead to a clearer understanding of some of

the fundamental physics involved in wakes interacting with a transitional or separated

flow. Additionally, fundamental research with a moving wake will also be required to

characterize the unsteady effect of the wake on the boundary layer since an unsteady wake

occurs in a real engine environment.

N A S A/TM-- 1998-208503
VIII. REFERENCES

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Halstead, D. E., Wisler, D. C., Okishi, T. H., Walker, G. J., Hodson, H. P., Shin, H. W.,

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NASA/TM-- 1998-208503
REPORT DOCUMENTATION PAGE Fo_Approve:

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1. AGENCY USE ONLY (Leave blank) 2. REPORT DATE 3. REPORT TYPE AND DATES COVERED

October 1998 Technical Memorandum

4. TITLE AND SUBTITLE 5. FUNDING NUMBERS

Experimental Study of Boundary Layer Behavior in a Simulated

Low Pressure Turbine

6. AUTHOR(S)

Rickey J. Shync

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)

National Aeronautics and Space Administration

Lewis Research Center

Cleveland, Ohio 44135-3191

9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES)

National Aeronautics and Space Administration

Washington, DC 20546-0001

WU-523-26-33-00

:8. PERFORMING ORGANIZATION

REPORT NUMBER

E-11305

i10. SPONSORING/MONITORING

AGENCY REPORT NUMBER

NASA TM--1998-208503

11. SUPPLEMENTARY NOTES

This report was submitted as a dissertation in partial fulfillment for the degree Doctor of Philosophy to the University of

Toledo, May 1998. Responsible person, Rickey J. Shyne, organization code 5820, (216) 433-3595.

12a. DISTRIBUTIONIAVAILABILITY STATEMENT

Unclassified - Unlimited

Subject Categories: 02, 07, and 34 Distribution: Nonstandard

This publication is available from the NASA Center for AeroSpace Information. (301) 621-0390.

112b. DISTRIBUTION CODE

13. ABSTRACT (Maximum 200 wonds)

A detailed investigation of the flow physics occurring on the suction side of a simulated Low Pressure Turbine (LPT)

blade was performed. A contoured upper wall was designed to simulate the pressure distribution of an actual LPT blade

onto a flat plate. The experiments were carried out at Reynolds numbers of 100,000 and 250,000 with three levels of

freestream turbulence. Freestrcam turbulence levels ranging from 0.8% to 3%: was used in this experiment. Smoke-wire

flow visualization data was used to confirm that the boundary layer was separated and formed a bubble. Hot-wires (single

and x-wire) and surface mounted hot-film gages and static pressure taps were used to map the flowfield. The transition

process over the separated flow region is observed to be similar to a laminar free shear layer flow with the formation of a

large coherent eddy structure. For each condition, the locations defining the separation bubble were determined by

careful examination of pressure and mean velocity profile data. Transition onset location and length determined from

intermittency profiles decrease as freestream turbulence levels increase, Additionally, the length and height of the laminar

separation bubbles were observed to be inversely proportional to the levels of freestream turbulence,

14. SUBJECT TERMS

Low-pressure turbine: Boundary layer; Experiment

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143

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Suder, K. L., O'Brien, J. E. and Reshotko, E., "Experimental Study of Bypass Transition

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Testing", Journal of EngineeringJor Gas Turbines and Power, Vol. 7, April 1985, pp.

354-363.

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Engineering, Vol. 106, June 1984, pp. 181-186.

NAS A/TMm 1998-208503