Experimental Study of Bypass Transition in a Boundary Layer. MS ...

•

NASA

Technical

a"

Memorandum

100913

Experimental Study of Bypass in a Boundary Layer _NASA-TM-100913) BYPASS Thesis

EXPERIMENTAL

TRANSITION _N&SA)

IN A _99 p

BOUNDARY

STUDY LAYER

Transition

OF

N88-23186

M.S. CSCL 20D G3/34

%

Lew/s _ch Cleveland,

Center

_

Ohio

Eli Reshotko Case Western Reserve Cleveland, Ohio

May

1988

University

Unclas 0145922

EXPERIMENTAL

STUDY

OF BYPASS

IN A BOUNDARY

Kenneth National

L. Suder

TRANSITION

LAYER

and James

E. O'Brien

Aeronautics and Space Administration Lewis Research Center Cleveland,

Ohio 44135 and

Eli Reshotko Case Dept.

Western

Reserve

University

of Mechanical and Aerospace Cleveland, Ohio 44106

Engineering

SUMMARY

A detailed process

in a low intensity

environment has

investigation

been

in which conducted

turbulence

values

rectangular-bar frequency For

longitudinal several

fluctuations region

skin

through

corresponding

initially Hereafter,

linear the

and

rms

boundary

0.3%

non-linear

Test

integral

section

length

to characterize

the

boundary velocity

transition

in an in amplitude freestream

to approximately

longitudinal

of the

layer

to that

initially

model.

turbulence,

and

5%

using

scale,

intensity,

freestream layer

surveys

of the

fluctuations

were

obtained

with

a linearized

hot-wire

constant

From

these

surveys

resulting

boundary

friction the

boundary

to each initially

transition

coefficients, layer

level

and

distribution

were

used

of freestream

non-linear process

the

initiated

transition by the

turbulence. cases linear

were growth

mean at

temperature

of the

to identify

and

turbulence.

locations

system.

inferred

are

plate

from

acquired

of freestream

velocity

anemometer

The

were

streamwise

factor,

varied

grids.

level

a flat

the

environment

disturbances

using

spectra

each

disturbance

the

were

to compare

layer

shape

velocity the

Both

transition the

identified. of Tollmien

Schlichting whereas,

(T-S)

waves

the transition

will be referred mechanism

process

turbulence

The following

the two transition flush-mounted depths

within

flush-mounted

through

the boundary hot films,

The results

layer,

layer

of approximately

correlations

transition

time

initiated,

measurements

rms of the velocity

within

traces

of a

wire located

at different

betweeen

locations

indicate

a flush-mounted

throughout

streamwise

that

fluctuations

regardless

and simultaneous

layer

reached

of the transition time

of a turbulent

traces burst

flowfield.

ii

there

within

3 to 3.5% of the freestream the boundary

the features

prevailed. and compare

between

at various

a

turbulence

to study

correlations

at various

with

mechanism

2) crosscorrelations

spectra

transition

the

distances

region.

of these

for the peak

layer

disturbances

for a freestream

were acquired

3) two---point

to transition;

was associated

1) simultaneous

wire positioned

value

bursting

The

hot film and a hot wire for the hot

the transition

illustrate

measurements

and 4) boundary

unsteadiness

the bypass

mechanisms:

hot film and a hot flowfield,

waves

however,

path

non-linear

process.

of T-S

level of 0.3%;

detailed

by finite

transition

growth

of 0.65% and higher,

to as the T-S

initiated

to as the bypass

based on linear

freestream intensity

will be referred

exists

the boundary

velocity.

Once the

this critical mechanism.

within

value,

turbulent

The two

the transition

and its effect

a critical

point

region

on the surrounding

TABLE

OF

CONTENTS

Pages i

Summary Nomenclature

vi

Chapter

I.

INTRODUCTION

Chapter

II.

RESEARCH

2.1

2.2

5

EQUIPMENT

5

Facility 2.1.1

Flow

Conditioning

2.1.2

Turbulence--Generating

2.1.3

Test

2.1.4

Probe

2.1.5

Test

Chamber Grids

Wind

6 7

Section Traversing

Mechanism

8 9

Configuration

Instrumentation 2.2.1

6

10 Tunnel

Instrumentation

°°°

in

10

2.2.2 2.3

Chapter

Data

3.1

Section

Acquisition

Instrumentation

12

15

3.1.1

Hot-Wire

Calibration

15

3.1.2

Hot-Film

Calibration

16

Tunnel

18

Set-up

DATA

IV.

ACQUISITION

Characterization

4.1

-

of Freestream

20

Turbulence

20 21

Turbulence

Intensity

4.1.2

Length

Scale

22

4.1.3

Power

Spectra

25

Boundary

4.3

Determination

of Friction

4.4

Measurement

of Turbulent

4.5

Boundary

Layer

Data

Layer

Longitudinal

5.1.2

Integral

5.1.3

Frequency

Mean

5.2.2

Skin

33

Bursting

34

&

DISCUSSION

of Freestream

5.1.1

5.2.1

31

Velocity

Spectra

Characterization

Determination

27

Analysis

PRESENTATION

V.

5.2

REDUCTION

4.1.1

4.2

5.1

15

PROCEDURE

Calibration

3.2

Chapter

10

Systems

EXPERIMENTAL

III.

Chapter

Test

Turbulence

Length

Velocity

RESULTS

36

Turbulence

36

Intensity

37 38

Scale

40

Spectra of the

OF

Transition Profiles

Region

41 41 45

Friction

iv

5.2.3 5.2.4

RMS

Profiles

Intermittency 5.2.5

5.3

Comparison

T-S

52

Factor

Documentation the

48

53

of Methods of the

Transition

Process

via

56

Path

_P

5.3.1

Description Process

5.4

Verification

5.3.3

Features

T-S 5.4.1

path

T-S

Path

of T-S of the

56

Transition

waves

T-S

57

Waves

& Comparison

58 with

the

61

to Transition

Simultaneous

Hot-Wire

/ Hot-Film

63

Traces

5.4.2

Two-Point

5.4.3

Boundary

VI.

the

Transition

Time

Chapter

via

5.3.2

Bypass

of the

SUMMARY

Correlations Layer

&

Spectra

CONCLUSIONS

65 68

76

References

82

Tables

87

Figures

96

._

V

NOMENCLATURE

A

Calibration

constant.

B

Calibration

constant.

b

Bar

Cf

Skin

CCF n

Normalized

width

of the

friction

turbulence-generating

grids.

coefficient. cross-correlation

C

Wave

propagation

E

Bridge

E1

Linearizer

output

f

Frequency

(Hz).

f'(_)

Blasius

H

Boundary

I

Intermittency

K

Calibration

L

Longitudinal

n

Exponent.

R

Correlation

output

coefficient.

speed. voltage. voltage.

similarity layer

variable shape

(f07)

=

U/Ue).

factor.

factor. constant. integral

length

scale

of the

coefficient.

Reynolds

number

based

on

x-distance.

II o

Reynolds

number

based

on

momentum

R, 6

Reynolds

number

based

on

displacement

X

freestream

vi

thickness. thickness.

turbulence.

T

Overall

time.

Te

Integral

time

Tu

Freestream

t

Instantaneous

U

Mean

U

T

scale

associated

with

the

freestream

turbulence.

turbulence. time.

velocity

Friction

in the

streamwise

direction.

in the

streamwise

direction.

velocity.

U

Local

velocity

u'(f)

Power

u+

Streamwise

V

Volts.

X

Streamwise

spectral

of the

density

mean

Y

Vertical

y+

Normalized

velocity

distance

flat-plate distance

distance

the

tunnel

wind

in wall

units

or direction

test

referenced

from

in wall

the

units

or direction test

(u +

= u / Ur)-

to the

(y+

referenced

flat-plate

test

from

the

y [Ue/(2_,x)]l/2

).

section.

fl

Normalized

¢9

Boundary

layer

thickness.

Boundary

layer

displacement

_7

Blasius

0

Boundary

similarity layer

(fl = 2r

variable momentum

Wavelength. #

Viscosity

of the

fluid

edge

(air).

vii

f).

thickness. (7/=

thickness.

surface.

= y U r / v).

Greek

frequency

leading

surface.

or direction

y distance

Spanwise

(V 2 / Hz).

centerline

of

V

Kinematic

P

Density

T

Time

delay.

Wall

shear

F

viscosity of the

of the

fluid

fluid

(air).

(air).

stress.

W

Power U)

spectral

Frequency

density,

_ = _w).

(radians/second).

Subscripts

e

Referring

to the

value

at

x

Referring

to the

x direction,

to the

value

the

edge

of the

x component,

distance. oo

Referring

in the

Superscripts

Time

averaged

Fluctuating

quantity. quantity.

viii

freestream.

boundary or based

layer. on

x

CHAPTER

I

_TRODUCTION

In a quiescent boundary (T-S)

layer waves

eventually

has

layer

levels,

been

at

low

and

finite

the

bypass

transition

process waves. path Some

and effects

the

to the Hereafter, the

T-S

the

which

stages

of this

levels

bypass

spots

of this

linear

transition these

are

without

process process

two

known

type

of boundary

Unfortunately, transition

process

transition

to describe

stability

considerations

The

at

and

bypass

to compare

in which

layer

the will

is

disturbance

is to examine

to influence

theory

the are

mechanism

Tollmien-Schlichting

mechanisms

to boundary

to the

freestream

occur.

investigation

transition

layer

and

stability

[6].

of high

traditional

leads

Linear

instabilities

path

which

boundary

term

distance

[1,3].

presence

of turbulent intent

with

the

in a laminar

as Tollmien-Schlichting

streamwise

disturbance

In the

The

with

layer

levels

instabilities

known

the initial

freestream

non-linear

formation

associated

bypass

predict

in which

initial

of turbulence

boundary

[7] introduces

process

the

to

amplified

disturbance

Morkovin

the waves,

bursts

understood.

amplification.

T-S

into

shown

well

bypassed permits

are

of a turbulent

transition

are

which

freestream very

environment

two-dimensional

[1,2],

transition

higher not

are

breakdown

development [4,5]

flow

wave

the

features

the

bypass

initial

instabilities

be referred

to as the

transition. boundary

layer

transition

2

are freestreamturbulence, acoustic disturbances, surface vibration, surface roughness,pressuregradient, and streamwise curvature. Several investigators [8,9,10,11]have tried to isolate the effects of freestream turbulence and pressuregradient on boundary layer transition.

Each of

these studies concentrated on the macroscopicparameters such as the location of the start and end of the transition region, and the distribution of the skin friction coefficient and heat transfer rates within the transition region. In the present study much effort has been taken to look at the details of the boundary layer transition by acquiring experimental data to describe the mean and disturbance freestream and boundary layer flowfields prior to and during the transition process. Boundary layer transition results from the buildup of disturbances in the boundary layer. Therefore, in order to understand the transition process,one must understand how the disturbancesare generatedand amplified in the boundary layer. Dyban, Epik, and Suprun [12] have investigated the structure of laminar boundary layers under high freestream turbulence levels ranging from 0.3 to 25%. They found a peak in oscillation magnitude within the boundary layer, believed to be caused by the penetration of the freestream turbulence. They referred to these laminar boundary layers which were buffeted by the freestream turbulence as pseudo-laminar boundary layers. Their results indicated that the depth of penetration of the external disturbancesinto the boundary layer did not depend on the freestream turbulence and increasedslightly with Reynolds number. Unfortunately, the results of this investigation by Dyban, Epik, and Suprun were limited to the distribution of disturbanceswithin laminar

boundary layers. Elder [13] conducteda study to determine the conditions required to initiate a turbulent spot within a laminar boundary layer. Elder concluded that regardlessof how disturbances are generatedin a laminar boundary layer, breakdownto turbulence occurs by the initiation of a turbulent spot when the velocity fluctuations within the boundary layer exceedsabout 2% of the freestreamvelocity over most of the boundary layer. More recent investigations to examine the details of the boundary layer transition processinclude the work of Paik and Reshotko [14] and Sohn and Reshotko [15]. Unfortunately, in these experiments the data was limited to centerline measurementsin facilities of limited capability. In the present investigation the boundary layer development is describedfor six levels of freestream turbulence intensity ranging from 0.3% to 6%. In addition, the facility used in this researchprogram provided the flexibility for off-centerline measurementsand the acquisition of two-point correlations which were obtained to examine the features of the boundary layer flow in all three dimensions. The present experiment focuseson the effect of the freestream turbulence intensity on the transition region of a smooth flat plate at zero pressure gradient and ambient test conditions. The goals of this investigation are not only to documentthe effects on the macroscopic features such as skin friction coefficient and boundary layer thicknesses within the transition region, but also to obtain detailed measurements within the transitioning region which will provide a better understanding of the mechanismsassociatedwith the transition process. This research program is aimed at identifying the fundamental similarities and differences

4

between the T-S transition processand the bypass transition process. In addition, this information will provide a useful databasewhich can be used to develop models and verify computational prediction schemes. The experiments were conducted in a closed--circuit wind tunnel located at the NASA Lewis ResearchCenter. The test surface is a smooth flat plate subjectedto zero pressuregradient at ambient test conditions. Care was taken to establish spanwiseuniformity over the flat plate and to insure that the boundary layer developedfrom the leading edge of the flat plate. Test section freestream turbulence levels were varied from 0.3% to 6% using grids. The freestream turbulence was characterized by its intensity, integral length scale, and frequency spectra. Measurementsof the mean longitudinal velocity and longitudinal velocity fluctuations through the boundary layer were used to determine the transition region for each level of freestreamturbulence. Once the transition region was identified for each freestreamturbulence level detailed measurementswithin the transitioning boundary layer were acquired to establish a better understanding of the transition process. Such detailed measurementsincluded the boundary layer spectra and two-point correlations to assessthe features within the transitioning boundary layer.

CHAPTER RESEARCH

2.1

EQUIPMENT

Facility

The Lewis

data

presented

Research

to study The

the

facility

velocity,

in this

Center's

wind

gradient,

major

components

2) flow

conditioner,

bleed

5) test

section,

cooler.

The

of 10 000

blower CFM

Chicago

Blower

120041).

A vortex

test

section

enters

the flow

contraction

convergence ratio

located

from

level. in the

accelerates

and

wind

tunnel

motor

at the

SQA

blower

is used

blower

transverse

direction)

flow to produce

with the

1 are:

9) air

the

number to adjust the

blower,

the

chamber a 3.6

the

straightens

reduces

required

test

a capacity

by

which

plenum

and

with

exiting

and

the

layer

filter,

serial

chamber)

of the

5

Fan

the

in Fig.

fan

Upon

Downstream

the

8) air

inlet

(plenum

centrifugal

within

is manufactured

to 120 ft/s.

chamber the

III

flow.

over

4) boundary

centrifugal and

designed

as depicted

heater,

diameter

was

control

temperature

nozzle,

7) air

NASA

to turbulent

provides

level,

in the

which

laminar

which

Class

20 ft/s

exiting

turbulence (no

(SISW

conditioning

irregularities

freestream nozzle

valve

inch

a 20 HP

Corporation

velocities flow

by

1/2

obtained

facility

from

3) contraction

6) diffuser,

is a 24

driven

tunnel

of the

were

research layer

turbulence

1) blower, line,

layer

of a boundary

is a closed-loop

The

investigation

boundary

transition

pressure

section.

the

II

a 2-D : 1

test

section

air

6

Reynolds numbers. Prior to entering the test section, the boundary layer and corner vortices which developedin the contraction nozzle are drawn through a bleed line by an auxiliary suction blower and returned to the main wind tunnel circuit at the inlet of the main blower. The test section flow exits into a diffuser where the air velocity is reduced prior to entering the return duct. The return duct consisting of the air heater, filter,and cooler completesthe wind tunnel circuit.

More details of specific tunnel

componentswill be discussedin the following paragraphs.

2.1.1

Flow The

part

span

blower,

Conditioning flow baffles

which

2) a series

large--scale

the

tunnel

the

flow---conditioning

section

flow

freestream

freestream

and

section

turbulence

velocity levels,

chamber

change

arrays

space

was

flow

flow

uniformity

centrifugal

to straighten to reduce

resulted

exit

plane

test

higher of the

of rectangular-bar

grids.

the

freestream

Grids turbulence

levels

within

the

test

of

of the

in a

in the

to achieve the

exit

+___2 percent

0.3 percent

at

the

at the

conditioning

In order

1)perforated

screens

to be wi.thin

allocated

for insertion

straws

of fine-mesh

The

of 100 ft/s.

exiting

of soda

measured the

following:

irregularities

3) a series level.

of the

of approximately

Turbulence--Generating To

and

Also,

intensity

consists flow

was

velocity.

turbulence-generating

2.1.2

the

turbulence

a freestream

flow--conditioning

chamber

reduce

swirls,

turbulence at

Chamber

of honeycombs

through-flow

freestream

Plenum

conditioning

the

mean

/

section,

7

various turbulence--generatinggrids may be inserted at the exit plane of the flow---conditioningchamber (Fig. 1). The turbulence grids are located upstream of the contraction nozzleso that the resulting turbulence would be more homogeneousand have a lower decay rate along the test section length. The turbulence---generating grids consist of rectangular-bar arrays with approximately 60 percent open area. Four grids were designedto produce test section turbulence levelsranging from approximately 1 to 6 percent. An additional grid configuration in which a 20-mesh screenwas placed directly in front of grid #1 was also used to generate freestream turbulence within the test section. Hereafter, this grid configuration will be referred to as the grid 0.5 configuration. Dimensions of the four rectangular bar grids are given in Fig. 2.

2.1.3

Test

Section

The

test

section

measures

6 inches

The

section

test

surface

(i.e.

employed

are

be pivoted the

test

surface, the

of the

the

tunnel

27 inches

is rectangular

in width,

and

to be removable cooled

boundary

constructed

and

wind

designed

frame

of plexiglass wall

was

heated

stainless-steel

top

in height,

to study

sidewalls

of the

surface, layer

of plexiglass,

holding

three

third

comprising

such

successive

probe

to obtain

either

a favorable

or adverse

of the

section

floor

test

The wall

the

test

section

could

floor

consists

inlet

as the

plane

gradient flat-plate

be

and of a -

two

mechanism.

pressure

serves

test

panels

traversing

is hinged

in length.

etc.)

interchangeable

section

The

top

and

a different

surface,

the

test

section.

that

process.

whereas

at

60 inches

roughened

transition

the

in shape

The and

can

within test

surface. At the entrance to the test section, a seriesof two upstream-facing scoopsare employed to bleed the boundary layer which developsin the contraction nozzle. A schematic depicting the details of this double-scoopconfiguration is presentedin Fig. 3. The larger upstream scoopentraps the boundary layer and corner vortices generatedin the contraction nozzle. The smaller downstream scoopis smoothly attached to the test surfaceand servesas the leading edge of the fiat plate. The leading edgeof the small scoop is a 4 x 1 ellipse to prevent a local separation bubble and possible tripping of the boundary layer. Both scoops dischargeinto the boundary layer bleed duct within which a slide valve is used to control the volume of flow through the scoops. Within each scoop a perforated plate is inserted to distribute the flow through the scoop uniformly in the spanwisedirection. These perforated plates are also used to control the relative distribution of flow through each of the two scoops. Rows of static taps in the spanwisedirection along the top and bottom of each of the scoopsprovide guidance in establishing the suction rate and spanwiseuniformity at the leading edge of the fiat plate.

2.1.4

Probe The

in the plate

probe

vertical, test

enabled and

Traversing

actuator

provided

traversing

mechanism

streamwise,

surface. vertical

Mechanism

An

and

L.C.

positioning assembly

streamwise

and

spanwise

Smith within

was

mounted

spanwise

permitted

precise

directions

actuator

driven

increments

relative

by

of 0.001

to a screw-driven probe

-

positioning

probe

positioning to the

a stepping inches. X-Z

within

flat

motor The

table

probe which

increments

of

0.01 inches. In order to provide maximum flexibility in positioning the probe throughout the test section with minimal flow disturbance, an epicyclic device was used which allowed probe positioning anywhere within a 19 inch diameter circle. A brief description of this device follows. The probe is inserted in the test sectionthrough a hole in a small circular plate which is eccentrically mounted within a larger circular plate (See Fig. 4). Both circular plates are supported by ball bearingsand are free to rotate in either direction, independently; thereby, permitting linear positioning of the probe via an X-Z drive mechanism. These two circular plates are located within a rectangular section which comprisesone of the three panels making-up the top wall of the test section. Also, these three panels are interchangeable, such that the sectioncontaining the traverse mechanism can be positioned at different streamwisedistancesfrom the leading edge of the flat plate. However, this probe positioning system was limited in that there were certain areas of the test section where the probe could not be positioned. The most noteworthy limitations were: 1) the probe could not be positioned within the first 5 inchesfrom the leading edge of the flat plate, and 2) due to interference with the X-Z drive mechanism the probe positioning was limited to 17 inches in the streamwise direction. In summary, the probe could be positioned anywherewithin a 17 inch diameter circle and the circle center could be located at distinct streamwise positions; thereby, permitting probing throughout the test section with only one probe insertion hole in the top wall of the test section.

2.1.5

Test For

Configuration the

present

investigation

the

facility's

aforementioned

10

control deviceswere configured to provide the following: 1) freestream velocity of approximately 100 ft/s (see Tables I - VI), 2) zero pressure gradient along the flat wall test surface, 3) ambient temperature within the test section which was held constant for a given test run --

i.e., +__2 OF

fluctuation over an 8 hour test period, and 4) freestream turbulence levels ranging from 0.3 to 6 percent within the test section. Also, the roof panel containing the probe traversing mechanism was centered along the test section centerline and at the streamwise distancesof 13 and 37 inches from the leading edgeof the flat plate test surface.

2.2 Instrumentation

2.2.1

Wind The

Tunnel wind

tunnel

temperature

sensors

conditions.

Figs.

thermocouples Initially,

which

is equipped

are

used

sensing

instrumentation

was

this

instrumentation

of each

component

within

Test

Section

The

test

devices used

wind

many the

illustrate

is used the

with

to monitor

6, respectively,

pressure

Currently,

2.2.2

circuit

5 and

and

this

InstrumentatiQn

for

within

tunnel

tunnel the the

shakedown

primarily

pressure

operation

location test

of the facility.

testing

to monitor

and

of the the

circuit.

Instrumentation

section

is instrumented

with

static

pressure

taps,

facility.

operation

11

flush-mounted hot-film sensors,thermocouples,and pitot tubes. At both the test section inlet and exit planes,a pitot tube and thermocouple are located in the freestream at the centerlineof the test section. From these measurementsof total pressureand total temperature the freestream velocity entering and exiting the test section can be determined. Also, at the test section inlet there are static pressuretaps located on the boundary layer bleed scoopsas indicated in Fig. 7. The largei" and most upstream scoopentraps the boundary layer which developsalong the nozzle, while the smaller scoop servesas the leading edgeof the flat-plate test surface. Therefore, the static taps on the larger scoopare used to monitor the rate of boundary layer bleed. The static taps on the smaller scoopare used to insure that the incoming flow has approximately a zero incidence angle to the leading edge of the flat-plate and that the flow is uniform in the spanwisedirection. Additional static pressuretaps are located along the flat-plate test surface as indicated in Fig. 8. The x---distancein Fig. 8 is measuredfrom the leading edge of the flat plate. These static taps are used to check the streamwise and spanwisepressuregradient within the test section. Also, located along the flat-plate test surface are 30 flush mounted hot-film sensors(TSI model 1237). SeeFig. 9. The signals from these sensorsare used qualitatively to determine the state of the boundary layer (i.e. laminar, transitional, or turbulent) at the location of each sensorwithin the test section. In order to characterizethe turbulence and document the boundary layer development within the test section, probes were inserted into the flow path and positioned via the probe traversing mechanism. The following types of probes were usedin this investigation: 1) a TSI model

12

1210-T1.5 single sensorstraight hot-wire probe was used to measurethe characteristics of the freestream turbulence, 2) a TSI model 1218-T1.5 single sensorboundary layer hot-wire probe was used to measure the mean and fluctuating velocities within the boundary layer, and 3) a miniature boundary layer total pressureprobe was used to measurethe mean velocity boundary layer profile (seeFig. 10).

2.3 DATA ACQUISITION SYSTEMS

The test section pressuregradient, freestream velocity, and boundary layer bleed rate, as well as the remaining pressuresand temperatures located throughout the rig were set, monitored, and recorded with the aid of the Escort Data Acquisition System. The Escort system is an interactive, real time data acquisition, display, and recording system which is used for steady state measurements. This system consistsof a remote acquisition microprocessor(RAMP), data input and output peripherals, and a minicomputer. The minicomputer coordinatesand executesall real time processing. The RAMP acquires the data from the facility instruments, sendsthe data to the minicomputer, and distributes the processeddata from the minicomputer to the display device. To determine the mean and rms of the signal voltages from the hot-film and hot-wire systemsa TSI model 1076 True RMS Voltmeter and a Racal-Dana model 5004 digital averaging multimeter were used. The hot-wire systemincludes the hot-wire probe, a TSI model 1050 constant

13

temperature anemometer,and a TSI model 1052 linearizer. The hot-film system consists of the flush mounted hot-film sensorcontrolled by a TSI model 1053B constant temperature anemometer. To acquire and analyze the analog waveform signal from the hot-film and hot-wire systemsthe following data acquisition systems were used: 1) Genrad 2500 Signal Analysis System,2) Nicolet Scientific Corporation model 660A dual channel FFT (Fast Fourier Transform) analyzer, and 3) Datalab DL6000 'Multitrap' Waveform Recorder. Each of these systemswere borrowed from other researchfacilities and therefore, were used for only a segmentof this investigation. For example, the Genrad system was used to characterize the functions), and

the

Nicolet

are The

briefly

the

spectrum

thermal

printer),

sampling

rate

channels.

and of the

Overall The

to digital

(selectable

acquisition

disk

model conversion

frequency

range

ranges 660A at from

dual a rate

based

for

10Hz

channel

data

and

acquisition

10-bit on

data

the

may

analyzer

times

100 Khz).

the

and

The

number

to 25 Khz

maximum of active

be selected.

features

selected This

to

techniques

(a CRT

storage.

by

analog

FFT

de.vice

FFT

of 2.56

10 Hz to

spectra

of 1) a

2) a 6 ps,

divided

from

layer

for analysis

of these

display

drive

is 160 Khz

used

consists

section

5) a hard

autocorrelation

paragraphs.

section,

4) a data

system

Each

System

processing

and

for boundary

was

following

functions,

frequency

Nicolet

system

Analysis

spectra

used

signals.

in the

3) a digital

power

primarily

Datalab

Signal

data

analysis

(i.e.

hot-film

2500

analog

converter,

was

described

Genrad

four-channel

analog

and

of simultaneous

systems

digital

turbulence

system

crosscorrelations,

recording

for

freestream

system

a 12-bit

frequency provides

14

a maximum of 2K words of operation 136A pen

and

1K memory

Digital plotter

was

acquisition hand

Pen

the

The

maximum

each

Datalab

stored was

downloaded

Hewlett the

to 128K

data

Packard acquisition

an

desktop

the

for

device

single

channel

A Nicolet

results.

model

Unfortunately,

available

quantitative

with

information

up

computer

process.

sample

this was

this data

recorded

by

data. (Direct system

module,

analog The

data

was

channel

ranging one

to digital

Memory which

provided Each

intervals

storage

precision

DMA

recorder

to 8 channels.

with

of digitized IEEE

waveform

and

a 12 bit

words

via

for

digitization

contained

memory

operation).

to plot

Multitrap

of 1 Mhz

A waveform

up

the

2K

channel

storage

of data

rate

(i.e.

acquisition.

D16000

recording

channel,

output

of data

sample

to 1 _.

used

Therefore,

time

simultaneous

was

only

system.

at

for dual

Plotter the

memory

stored Access) also

from

dedicated

had

a

50 ms for

converter

and

in each

channel

interface used

to

to control

an

CHAPTER

EXPERIMENTAL

3.1

PROCEDURE

Calibration

3.1.1

Hot-wire The

range

Calibration

hot

wires

of about

King's

Law

were

20 wind

calibrated

tunnel

in---situ

settings.

where

E is the

anemometer, from

the

based

output

U is the

King's

linearize

the

linearization versus

bridge

Fig.

Law.

A signal of the

is done

by

with the

the

coefficients

of this

linearizer,

output

range

a pitot

calibrations

probe, were

over

based

a

on

procedure the of the

and

linearizer

are

coefficients linearizer.

(TSI

the

were

for the

Once

the

15

is used

To

output

Therefore, calibration

the data

conditioning maximize

to the

normalized

0 -

to

This

of bridge

signal

normalized

1052)

curve

anemometer.

polynomial.

in [17].

determined

calibration

model

curve

linearizer

given

B are. constants

temperature

coefficients the

temperature

a representative

degree

into

(1)

constant

A and

approximating

linearizer

B V 1/2

of the

constant

a fourth

to determine resulting

voltage

11 depicts

output

velocity

Details

The

A +

air velocity,

calibration.

on

against

[16]. E2=

the

III

voltage next

and

step

is

to input

circuit.

the

sensitivity

10 volt

coefficients

input have

of and been

16

registered in the linearizer, the output voltage of the linearizer is related to the velocity in the following manner: U

nlax

u = --Y0where hot

u is the wire

bridge

was

3.1.2

are

given

Hot-film

in Fig.

indicate

wall

flush-mounted relationship (E)

was

shear

stress.

hot-film

gage

constant

A and

wall

B are

used

that

determining

the

calibration

calibration

is performed

wall

stress

not

only

stress

the

Plots

voltage

of

versus

average

wall

where

case

developed shear

by stress

that

a

friction. output

The voltage

_

the

(3)

calibration.

to significant

are

large

boundary

Ramaprian but

bridge

in evaluating

there

in the

to

[18] showed

B

lead

and

sensors.

sensors

skin

was

is:

from

may

hot-film

the

= A E2 +

constants

is the

and

sensors

hot-wire

to measure

(rw)

determined

hot-film

Schultz

anemometer

in flows

(such

the

and

be used

procedure

a procedure, the

output

for the

to calibrate

could

shear,

this

above

Bellhouse

constants

out

In addition,

of which

voltage.

flush-mounted

described

temperature

[19] pointed

shear

output

linearizer

for the

rw 1/3 where

and

velocity

12.

as that

between

of the

maximum,

linearizer

velocity

procedure

procedure

the

(2)

Calibration

calibration

following

E 1 is the

versus

as straightforward

The

Uma x is the

and

voltage

The not

velocity,

calibrated,

output

velocity

local

E1

also

layer and

the

Sandborn errors

skin

friction

fluctuations transition Tu

in if the in the region).

[20], to evaluate

instantaneous

wall

shear

17

stresswas attempted. Their expressionsrelating voltage output to wall shear stress are: 7w and

taking

the

time

average

7w=

where wall

is the

time-averaged

shear

stress,

E is the

determined

7 w must

be known.

to evaluate

by

instantaneous

from

the

of two

determined

E2 +

of equation

_w

minimum

r'w = (A

(4)

B) 3

(4)

A3E6+3A2B]_4+3AB2E2

constants

used

+

wall

The

time

average points,

equation

7w +

and

voltage,

values

With

fluctuation

time---averaged

moments

the

(5).

stress,

voltage,

output

of the

B3

r'w is the

output

calibration. instantaneous

shear

stress,

instantaneous

calibration

wall

shear

The

solving

+

r'w can

wall

E 2, E 4, and

values

B are

shear

stress,

E is sampled

of A and

the

A and

in

E 6.

B can

From

be

of A and

be calculated

and

B, the

from

equation

(4). The profile

The

Section. produce

wire,

wire

a turbulent

which

recorded

the with

layer

at the

layer

layer

be determined

will

placed

boundary

positioned

can

procedure

was

Boundary was

level

boundary

of this

A trip

surface.

friction

turbulent

details

Simultaneously, were

skin

of a fully

[21].

test

mean

be described

in the

Data

Reduction

leading

of the

flat

entire

length

of the

were

acquired

with

being

calibrated.

to the

of the

the

DL6000

Datalab

technique

profiles

fluctuations

velocity

plot

the

hot

output

the

the

Clauser

along

velocity

adjacent

using

from

edge

film voltage

Multitrap

of the

Waveform

plate

to

fiat-plate the

hot-film Recorder.

hot

gage

a

18

Calibration

data

are indicated

were taken

in Fig.

13.

the wall shear stress,

at 5 wind

Note

that

tunnel

the friction

the friction

proportional

flows.

calibration

procedure

wall shear

stress

equations

The

stress

straight

predictions

U r is related

to

line in Fig.

based

power

calibration

power

(3), whereas,

layer.

region

for on the

the triangles

procedure

methods

boundary

transition

is directly

13 is based

on the calibration

turbulent

layer

(6)

to the one--third

the hot films for the measurement the boundary

and the results

rw / p

by equation

Both

case of a fully

calibrate

velocity,

to the two--thirds

described

(4) and (5).

for this

within

velocity

to the wall shear

incompressible

settings

r w as follows:

vr = Therefore,

speed

yield

described

satisfactory

Results

are by

results

of attempts

to

of instantaneous

skin friction

will be discussed

in the Results

Section.

3.2

Tunnel

set-up

Prior to insure

to a test,

that

before

for about

a test

on the voltmeters,

operation

and maximum

4) the calibration

data

checks

and adjustments

are acquired.

The following

was initiated:

an hour,

performed

ft/s,

calibration

the appropriate

were performed to warm-up

several

1) all equipment

2) self-tests

3) the hot

frequency

procedures

was turned

and zero calibrations

wire was adjusted

response

are made

over

the test

of the hot wire was checked

on

were

for stable range

at several

of 0 to 120 wind

tunnel

19

speeds

against

pressure from and

gradient

the the

gradient on the

static

taps

hinged

top

boundary

3 in the

the

located wall

section

static fiat-plate

respectively.

test

of the

the

tunnel

is adjusted

equal describin_

test

test

conditions

were

was

to the outlet the facility.)

distribution

surface

on

are illustrated

test

adjusted

such

of 100

established.

fiat-plate

as this adjustment

duct

pressure

5) the section

along

to zero

bleed

and

the

is approximately

streamwise and

probe,

within

is as near

velocity Fig.

a pitot

will

The

surface until

the

allow.

that

the

test

section

boundary in Figs.

and

zero

pressures

are monitored pressure

The

inlet

damper

test

layer 14 and

valve

section

velocity.

A representative the

ft/s

(Refer

spanwise bleed 15,

scoops

to and

CHAPTER

DATA

The describing flow

over

were ft/s

purpose

of this

experiment

boundary

layer

development

a range

acquired with

development

was

subjected

the

from

data

turbulence

properties

and various

transitional, within

the

frequency

4.1

state

and

at ambient

to about

of the

transition

Characterization

region and

spatial

of the

turbulence

6%.

by

the

boundary

Freestream

is generated

2O

measurements

into

turbulent

boundary

layer

to a freestream

velocity

temperature.

Boundary

of freestream

The

following

grids,

development the

evolution

within

layer

turbulence will

2) evaluate wall

the the

shear

stress

laminar, of turbulent

and the

of 100

sections

the (i.e.

layer,

data

to 1) characterize

3) estimate

boundary

correlations

All

rectangular

4) determine of the

flow

techniques

layer, layer

detailed

laminar

values

reduction

of boundary

turbulent),

spectra

and

generated

stages

Freestream

0.3%

to acquire

levels.

for several

acquisition

freestream

in the

gradient

characterized

varying

address

a flat

pressure

REDUCTION

from

disturbance

plate

-

was

of freestream

along

zero

intensity

ACQUISITION

IV

bursts

5) evaluate

boundary

layer.

Turbulence

into

the

flow

field

by

inserting

21

rectangular

grids

upstream

on the Facility

Description

location

within

the wind

become

turbulent

decays

the test

fluctuations, frequency

4.1.1

shed

with

:

increasing

length

faster

intensity

However,

grid---generated

isotropic

downstream

= "_2

measured

).

in this

reduces

than

the larger

of the turbulence

scale of the turbulence,

turbulence or velocity

and 3) the

is defined

(Schlichting

[5]) as follows:

/ turbulence

of the grids.

indicated

that

Therefore,

to:

Assuming

is more Results

isotropic

a wind

is nearly

the longitudinal

using a single

(7)

or less homogenedus from

the turbulence

only

investigation

to the flow direction. intensity

distance

the freestream

•u _-

v_2

turbulent

Intensity

The turbulence

[22] have

The

of

of the turbulence.

Turbulence

design

downstream

downstream

dissipate

1) the intensity

and

from the grid bars

are used to characterize

2) the integral

to the section

more or less homogeneous.

fashion

section

spectrum

(Refer

the grid and at some distance

the smaller eddies

parameters

inlet.

on the grid configurations

The wakes

becomes

because

Three

throughout

tunnel.)

in a nonlinear

from the grids, eddies.

for more detail

close behind

the grid the turbulence energy

of the test section

hot

tunnel

of similar

isotropic

( u'2

velocity

fluctuations

wire oriented

turbulence,

and

= were

perpendicular

the turbulence

22

Note

that

for a linearized

instrumentation ratio the

of the signal

perform the

section, rms

of the

linearizer.

linearizer

output

Discussion

of Results

The the

In order motion the

zero to the

Uoo

anemometer turbulence

system,

to the

voltmeter

averages

of the

in order

to determine

measurements

as described

intensity

fluctuations

Racal-Dana

(8)

will

is equivalent

mean was

true

in the

rms

voltage

to output

programmed and

the

mean

of

to voltage

longitudinal

be presented

the

of

turbulence

in the

Scale length

eddy

size

the

to infinity.

at

of the with

turbulence the

longitudinal

position

velocity

measured

scale

associated

a specified

fluctuating

velocity

voltage

/

Section.

to determine at

u '2

local

of these

integral

average

wire

signal

Results

Length

hot

250

intensity.

4.1.2

=

the

The

approximately

Tu

'x',

measured position

Expressed

at

'x +

random

length

the

is the

position

terms

of this

coefficient

describes turbulence.

fluctuating or covariance

of the

for all this

that

in the

'x t to that

r' is integrated

in mathematical

motions

scales

correlation

scale

values

definition

of

fluctuating of 'r'

from

translates

following: 00

L = f0

where, and,

R(r)

=

R(r)

u 1 u2

(9)

dr

/J--_u

1

_

(10)

23

uI

u 2 = Ul(X ) 1

u2(x+r) T

= T f0 where

L is the

covariance,

r is the

represents See

integral

the

Ref.

spatial

does

that

probe

can

one

probe.

Since

section

configuration

in the

correlated

(ll.a)

correlation

coefficient

streamwise

(fluctuating

this

Taylor's

change

with

or

direction, velocity

spatial

delay

in this

states

that

the

mean

then

with

Therefore,

to measure

the

hot

wire

is performed:

with

length if the

and

in this

pass

u(t+r)

separation

representing

scale

the

u

case).

00

scale, the

an

velocity

turbulence. are

lines

do

not

If Taylor's

be the

streamwise

test

was

fluctuations

fluctuating

autocorrelation

fluctuating

and

freestream

point.

and

other

method

or vortex

/ ----_2, will

probe

mechanism

velocity eddies

upstream

to the

an alternate of the

the

hot-wire

traversing

of the

U r in the

hot-wire

that

relative

a given

autocorrelation

= u(t)

a length

positions the

two

a manner

turbulent

velocity,

that

downstream

investigation

as they

the

the

various

possible

integral

in such

with

at

the

r, R(r)

correlation

single

not

requires

section

interfere

in shape

is valid,

time

test

used

appreciably

hypothesis

not

was

hypothesis compared

the

correlation

be moved

to approximate

direction

separation

two-point

into

probe

with

R is the

being

this

be inserted

small

scale,

dt

[23].

hot-wire

used

u2(x+r't)]

length

quantity

However, probes

[Ul(X't)

velocity same

direction of the in the

u

as the [23]. signal

streamwise

from

24

u(t+r) This

= _

autocorrelation

velocity

f0T[u(x,t)

function

fluctuations

u(x,t+r)]

is normalized

in the

streamwise

dt

by

(ll.b)

the

direction

mean

square

to yield

the

of the

autocorrelation

coefficient. R(r)

Integrating Te,

the

which

= u(t)

u(t+r)

autocorrelation

is a measure

/ _

(12)

coefficient

of the

average

results

in the

persistence

integral

of turbulent

time

scale,

activity

at

a

point. o0

Te Taylor's length

= f0

hypothesis scale

can

R(r)

then

(13)

dr be applied

to estimate

the

longitudinal

integral

as follows:

L = Te Ue The

Racal-Dana

averages velocity

of the was

processor the rate

mean

used

was

Genrad _

averaging

were

2.56

voltmeter

voltage

in the

used

(14)

so that

length

scale

for obtaining

the

as follows:

times

frequency

bandwidth

integration

of the

frequency

of the

analyzer

and

then

and

accurate

The

autocorrelation

1024

4) Hanning

function

a numerical

set

Genrad

at

were was

performed

from integration

the

FFT

25 Khz

window

mean

The

averages

was

250

of the

data.

range 2)

to perform

measure

calculation.

coefficient

autocorrelation

performing

an

bandwidth,

autocorrelation

plot

programmed

1) frequency

of 25 Hz,

resulting

was

on by

Genrad (the

signal

settings -

on

sampling

taken,

3)

. The digitizing

the

signal

trapezoidal

rule

25

[24]). Data were acquired at x from the

the

leading

spanwise

Power

acquired

were

acquired

at

32.6,

45.2,

56.0

settings

for

2)

1024

was The

functions

square

56.0

the

floor

inches along

of 24 locations.

was

centerline the

and

from

obtained

at

comprising

total

Also, Y = 1,

an

number

velocity

turbulence

level

squared

of the

power

distribution

with

Only

the

thereby,

inches data

a single

resulting

power hot

of survey

the

leading were

frequency

was

within

is referred spectral

are

related

by

coefficient the

following

and

the

Fourier

to as

density

Turbulence by

of the

turbulent

kinetic

power

spectrum.

The

for

x = -7.5,

of the

flat

plate.

25 Hz),

and

Hz

power transform

pair:

20.,

range (except

4) the

spectral

data

The

1) frequency

of 15.625

the

6.0,

of for

Hanning

on. autocorrelation

each

processed

as follows:

bandwidth

bandwidth

and

and edge

fluctuation

spectrum.

wire

in a 1-D

z = centerline,

acquisition

frequency

as the

u '2 component

from

averages,3) the

of the

is defined

y = 3 inches,

and

1 in which

window

the

bringing

The

acquired

analyzer.

was

grid

4 inches

function

from

overall

density.

were

FFT

25 Khz,

of the

of frequency

spectra

Genrad

inches

45.2,

for a total

autocorrelation

to the

spectral

as a function

energy

tunnel

32.6,

Spectra

bandwidth

power

Genrad

wind

Thereby,

contribution

frequency

power

20.,

to 40.

The

the

x = 20 the

16 locations.

locations

6.0,

y = 1, 2, 3, and

of the

4 for z = +_ 5.0

additional

4.1.3

with

centerline

at x = 6 and 2, 3 and

edge

= -7.5,

density

26

R(r)

= _0_w)

cos(wr)

2 f_0 R(r)

where

R(r)

is defined

a function

of frequency,

spectral the

in Eq.

density,

PSD(f)

cos(wr)

(12)

and

(15)

dr

_w)

(16)

is the

w, in radians

per

second.

as a function

of frequency

power

spectral

The

normalized

in Hz

density

as

power

is represented

by

following: PSD(f)

The the

dw

integral mean

reference coefficient, represents Also,

of the

frequency

power

of the

to Eqs.

(12),

R(r)

over

the

in the

we evaluate

_(w)

square

the

spectral

square

value

approaches

zero

L =

(14),

of the

of the of the

integral

we find

R(r)

over As

velocity spectral the

all

by

the

turbulent

in

freestream

coefficient

density

is

autocorrelation

velocity

fluctuations,

frequencies

mentioned

of the

autocorrelation

power

2 F R(r) J0

Ue

the

_,2.

of r multiplied scale

of the

function

fluctuations,

and

integral

(17)

density

velocity

length

v(0) =

therefore,

5 '2

all values

the mean

2r

(13),

integral

evaluating

results

=

_,2. function

velocity

fluctuations. at

r = 0

Likewise

, if

as the

following:

dr

(18)

dr

= U e _o(0) _-

(19)

27

V e

L=--

PSD(0)

(20)

4_' 2

In

summary,

mean all

the

square

values

of the

density scale, mean

square

of the

integral

and

the

4.2

Boundary

value

of the

length

The be addressed

Data

scale.

over

calculated

using

for three

section:

different

1) the

laminar

velocity

profiles

are

reduced

solution

for boundary

layer

pressure

profile

transitioning

gradient

is defined

in terms

(2vx)

and

f'(_)

= u/U e.

broken

down

into

four

distinct

zone,

3) the

logarithmic

boundary

([5],

_/ Ue/

buffer

power

layer,

the

velocity

the

boundary

layer,

The

results

investigation

of boundary

boundary

zero

integral

spectrum

types

3) the

with

both

over

power

to the

In this

and

plate

the

frequency

fluctuations.

layer,

Blasius

Similarly,

the

the

integrated

is proportional

boundary

well-known

value

represents

values spectrum

Analysis

reduction

in this

were

its

zero

methods.

Layer

data

integrated

scale

autocorrelation

time at zero

velocity

at

whereas

integral

evaluated

its

evaluated

fluctuations,

in the

function

whereas

in the

function

velocity

of r results

spectral time

autocorrelation

The regions: region,

pp.

layer.

and

For

development and

similarity

turbulent 1) the

2) the the

and. compared

144-148

of the

layers

boundary viscous

4) the

wake

turbulent laminar

to the along

[1], pp.

a flat

253-273).

variables layer sublayer, region

will

77 = y can

be

2) the (See

Fig.

16).

28

The viscous layer is a very thin is dominated

by

However, (the

within

stresses

stress.

wake

the

zero

layer

at the

and

turbulent

the

not

well

very

The boundary

only

very

velocity were

following

and

measured

thickness,

of the

and

3) the

the

momentum velocity

The with

with

important

shape

wall

stress.

decay

to a value boundary

laminar

a laminar

The

layers.

shear

It

profile

stress

type

layer

profile.

This

calculations

is

increases

boundary

a turbulent

shear

the

transitioning

the

in drag

which

momentum

thickness profile.

which and

of the

fluctuating

a single-wire

boundary

layer

to satisfy

factor,

rms with

the

boundary

be displaced

a measure

associated

associated

measurements

displacement

layer

levels

layer.

layer

of boundary

between

stresses

to the

shear

stresses The

flow.

turbulent

boundary

types

somewhere

levels

and

stress

but

to

change also

is

understood.

mean

these

would

low

is not

layer

the

of boundary

higher

stress

and

type

three

shear

of laminar

to the

layer.

the

contribute

turbulent

boundary

lies

molecular

contributors

of the

where

case

turbulent

where

structure

relatively

in shear

of the

wall

fluctuations)

of the

region

understood

its

relatively

From

mixing

the

velocity

dominant

the

as in the

both

region

the

edge

least

that

the

by the

are

near

viscosity zone,

logarithmic

believed

the

buffer

is the

is the

from

the

stresses

region

near

molecular

generated

In

turbulent

the

layer

layer

parameters

indicates

within

boundary

layer

development were

the

velocity

distance

was

1)

a steady

conservation

of mass,

defect

boundary

layer

of the

displacement

is the

in the ratio

is indicative

In mathematical

of the form

the

2) momentum

shape

flow thickness,

related

of the

displacement

probe. characterized

determined: that

the

to drag, thickness

to

boundary thickness

is

29

defined as :

= f0 and

the

momentum

1 -

thickness

dy is defined

$=f0°°_

To the

gradient

the

measured

solution

for

laminar

the

data

of 7? vs f'(_/)

will

mean

velocity

profile

data

velocity

are

velocity

was

compared

distribution

U+

=

turbulent

wall

ATAN

+ LOG10

[(Y+

-

plate

at

[(2 Y+

the

units

boundary

r/and

plots

layer

the

mean

for

the

layer

16.7]

+2-

to

pressure

boundary layer

in wall

-8.15)/

10.6)9"6/(Y

zero

layer

variable

of boundary

of a turbulent

+

boundary

similarity

expression

region

5.424

of the

to compare

type

to Musker's

in the

a fiat

of the

Likewise,

to the

profile

along

in terms

be presented.

(22)

dy

flow

reduced

profile

as:

[1-_,J

compare

Blasius

(21)

[25]:

(23)

8.15Y +

+

86) 2]

3.52,

where,

U+ = u / Ur

(23.a)

and,

Y+

(23.b)

and,

The

= y Ur / v

V 7 = _/r

mean

distance

velocity was

was

normalized

w /

p

normalized by

the

(23.c)

by the ratio

of the

friction

velocity,

kinematic

Ur,

viscosity,

and

the

v, to the

y

3O

friction velocity, Ur. The data was then plotted on the universal or U+ versus y-t- coordinatesand compared to the correlation indicated by Eq. (23). The determination of the friction velocity will be discussedin the next section. The Blasius solution was also transformed to U+ vs Y+ coordinates so that the measuredvelocity profile could be compared to both a laminar and turbulent boundary layer velocity profile. If the data lie on the Blasius curve the velocity profile will be laminar; whereas, if the data fall on the turbulent curve the profile will be assumedto be fully-turbulent. However, if the data fall on neither curve, but lie somewherebetween the two curves, then the boundary layer is consideredto be in transition from laminar to turbulent flow. A brief description of this transformation from Blasius coordinates to universal coordinatesfollows. From White ([1], p. 264) we find the following relations for the Blasius solution of a flat plate at zero pressure gradient:

o = 0.664

x/

(24) 00

rw / p =

Therefore, thickness

from and

the

from

_0-

rw / p

0.4696

definition equation

0.664

= 0.22049

uU e_/U

e

/

of Reynolds (25)

__ Ue

(2

u x)

number

based

(25)

on

momentum

we obtain:

J _2

2 U e / _0

u x

(26)

(27)

31

Substituting the value for rw/p from equation (27) into equation (23.c), it is easily seenthat the Blasius solution can be representedin terms of the U+ and Y+ coordinatesas follows:

U + = uru y+

The

U + vs Y+

velocity,

= y U r-

coordinates

which

requires

It is known

the

to turbulent

region.

Therefore,

following

4.3

stress

and

stress,

skin

U r = _/r w stress near

section

/

is defined the

wall,

regimes

p,

Cf =

the

change

of the

wall

wall

shear its

the

(29)

of U r, the

shear

stress

path

stress

on

friction

dramatically

is unknown

a handle

friction

or skin

varies

determination

in the

this

of the

from transition

parameter.

The

friction

velocity.

Velocity

of the

within

be discussed. coefficient

each The

are

related

2 r w / (pU2e)

as follows:

r/__

evaluation

determination

will

(28)

U eY=

to get

coefficient

friction

f'(t})

the

and

address

the

friction

regions

and

the

of Friction

skin

development

that

will

Determination

In this

require

it is important

paragraphs

_

.4696

knowledge

coefficient. laminar

= 2.1296

of the friction to one

velocity, boundary velocity, another

= 2 U 2r / Ue.2

du r w = p i_-Iy=0. in velocity

friction

is linear

In the with

The

laminar distance

wall

shear

layer wall

shear

as follows: wall

shear

region from

very the

wall.

32

Therefore, the approximation of stress.

However,

very

thin

this

and

for

the

turbulent

it was

not

possible

For

the

approximation.

correlation zero

was

pressure

used

An

initial

page

value

of

the

layer

close case

the

wall

U r was

Y+

the

the

viscous to the

wall

shear

sublayer wall

stress.

For

correlation

to use

a flat

plate

at

of Clauser

[21]

is:

(30)

4.9

from

is

'law-of-the-wall'

shear

+

obtained

this

enough

'law---of-the-wall'

= 5.6 LOG10

to determine

the

following

correlation

([1]

518):

Cf

and

used

50 < y÷ goodness agree

in Eq

the

correlation

momentum-integral was

Schlichting

the

been

of the

used ([5],

squares

by

how

plot

above equation

to estimate p. 160),

were

data (30)

[21].

in Eq.

applicable.

for

the

within and

(30).

and

region

at

momentum

the

wall. integral

slopes

the

referred

transitioning In this

data

If the

incompressible stress

the

curve-fitted

turbulent

the

for two-dimensional,

expression

falling

is sometimes

For

value" of shear

(31)

of the

is assumed

procedure

H

is performed

slope given

layer

technique

the the

the

correlation

This

methods

0.283

in Eq.

well

boundary

estimated.

+

fit of the

given

of Clauser's

then

H

[R0)1.753

A least

fit or Clauser

neither

e -137

(LOG10

(30).

slope

of U r has

a Clauser

layers

88

of fit is determined

in agreement

layer

=

< 200 to the

with

value

is:

boundary

turbulent

0.2

are

is used

to get

to estimate

gradient

U+

Au/Ay

to as

boundary the boundary From equation

33

p However,

for a flat plate

rw p Therefore,

from

be determined

polynomial

the mean

4.4

Then

curve fit.

Measurement

recorded

with

128K of data

in a time

trace

located

level,

within

evolution fluctuation

these

to :

polynomial

equation

(33).

bursting

with

data

the boundary

0, can

the leading with

a

was differentiated

from Eq.

be determined.

The

Bursting

of the turbulent of up to eight

Waveform

approximately

on the hot-film

from

was then estimated

bursts signal,

time

For each

at a rate

as indicated

traces

were

of the eight resulting

At each freestream

and recorded

transition

downstream

of 50 Khz, thereby

2.62 seconds.

were acquired layer

hot-film

Recorder.

were acquired

of the turbulent

of x, distance

thickness,

could

records

channels,

the momentum

the value of d0/dx

the Datalab

over

reduces

of 0 vs. x was approximated

resulting

the evolution

simultaneous

profiles

as a function

The

stress

distance,

turbulence

velocity

of Turbulent

To track

this equation

/32/

(33)

this data

to x so that

of wall shear

lye)

2 d0 Ue_y_

and plotted

respect

value

at zero incidence

-

edge of the plate.

with

d_t_ iv2 o/+ **ue

-

region.

for the hot films

From

by a positive

could be observed.

Also,

these

data

voltage

the

34

crosscorrelations

of the

to estimate

the

convection films

the

coefficient

convective

the

boundary

layer

is defined

as the

percentage

an intermittency

an intermittency

factor

located

at

factor

layer

off the

amplitude

of the

Data

acquired

for grid

profiles

corresponding were

signal

acquired

the

over

bandwidth spectra For

the

frequency

were

Hz.

that

hot

flow

flow

also

used

intermittency is turbulent.

a laminar

the

test

obtained

surface

flow,

whereas,

is turbulent.

were grid

frequency

the

all

data

frequency

the

0.5 and and

three

grid

normal

within and

grid

equal

the

1, the

resolved

data

with

660A

were

the

the

velocity

a frequency

power

* 2.56)

streamwise

Nicolet

within

over

layer.

mean

configurations

acquired 500

1 at

layer

with

point

boundary

grid

boundary

wire

to the

the

a representative were

hot

corresponded

acquired

range

to get

the

0, 0.5,

where

spectra

250 times

(sampling

which

configurations

for

with

fluctuations

For

Also,

grid 0 configuration range

were

analyzer.

averaged

implies

velocity

The

10 Khz

of 12.5

of zero

were

The

the

the

crosscorrelation

factor. that

The

between

signatures

of time

to locations

obtained.

dual--channel

in the

performed

bursts.

distance

time

indicates

spectra

maximum

distances

hot-film

were

turbulent

the

peak

films

Spectra

a distance

were

dividing

intermittency

of one

Layer

Boundary

The

hot

of the

to the

to Eq.

Boundary

velocity

corresponding 12).

succeeding

by

(refer

Therefore,

4.5

between

is determined

r value

to evaluate factor

average

velocity

by

signals

power

spectrum. 500

800

Hz. lines

of

35

resolution or a frequency bandwidth of 0.625 Hz. Crosscorrelationsbetween a flush-mounted hot film and a hot wire were acquired with the Nicolet dual-channel FFT analyzer. These correlations were performed throughout the transition region for the grid 0, grid 0.5, and grid 1 configurations. All data were acquired with the Nicolet set at the 10 Khz frequency range and 200-250 averagesper correlation.

CHAPTER

PRESENTATION

5.1

longitudinal

turbulence,

and

parameters

used

turbulence. integral

the

and

from

the

Data

scale

floor

comprising

A limited

number

configuration.. and

length

grid

at the

frequency same

data

4 for

were

thereby,

locations

were

grid were

spectra

streamwise

at

were positions

acquired.

36

the

three

intensity 6.0,

tunnel

5.0 inches

studied

total

2, grid

for

acquired

at

where

the

the

4 inches a total

the

40 survey

1, grid

32.6,

function

from the

and

20.,

for

autocorrelation

these

of the

freestream

wind

bringing

acquired

scale

y = 1, 2, 3, and

of the

z = ±

configurations:

of survey The

scale

Data

with

x = 20 the

16 locations;

to 40.

the

at x = -7.5,

centerline

at x = 6 and

Y --- 1, 2, 3 and

following

edge

are

turbulence

acquired

leading

length

turbulence

longitudinal

were

spanwise

an additional

of the

inches,

the

Also,

locations

the

RESULTS

integral

to characterize

to extract

the

the

of the

investigation

from

along

at

spectrum

OF

Turbulence

intensity,

information

56.0 inches

obtained

each

frequency

used

of 24 locations.

survey

turbulence

in this

length

45.2,

and

DISCUSSION

Characterization of the Freestmam

The

was

AND

V

centerline number

points 3, and

grid

for grid

4.

0.5

y = 3 inches, turbulence

of

z = 0

intensity

37

5.1.1

Longitudinal The

distribution

turbulence Fig.

17.

The

rectangular

surface.

at

the

all of the

variations

in the

spanwise

direction

symbol that

in Fig. the

turbulence

Therefore, 3 and from

the

generated

the

bar

from

the

edge

streamwise from

width,

flat

developed

turbulence

the

for grids with

Baines

and

Peterson

18.

Baines

and

freestream

The and of the

0, 0.5,

1, and

x -

from

increasing were

2

distance. data

grids

distance

compared

to the

[26] for isotropic Peterson

turbulence grid,

in

size

However,

results

generating

presented

y--direction

within

These

the

data

paragraph.

with

Fig.

of the

previous

lie

in

of the

intensity

constant

plate.

4 is presented

turbulence

in the

that

longitudinal

edge

the

intensity

turbulence

= 1.12

that

homogeneous.

between

generating

Tu

17 note

by

See

leading

in the

position

Fig.

freestream

dimensions

of the

is relatively

of the

b, of the

Note

of turbulence

turbulence.

the

intensity

is nearly

relationship

1, 2, 3, and

mentioned

of turbulence

a decay

correlation

following

positions

turbulence

leading

the

average

intensity

4 indicate

empirical grid

the

arithmetic

Also

0, 0.5,

to Fig. 2 for the grids.

at each 17.

of the

from

generating

values

section

is measured

Refer

turbulence

test

by grids

distance

17 represents

acquired

the

generated

x -

test

Intensity

within

intensity

flat-plate

Fig.

Turbulence

and

the

established intensity,

Tu®,

distance,

l,

grid:

(l/b) -5/7

(34)

o0

Agreement 'typical' isotropic.

with for

grid In this

this

correlation,

generated investigation

Eq. (34)

turbulence the

and

implies

that

therefore,

turbulence-generating

the the

turbulence turbulence grids

were

is is nearly located

38

upstream

of the

turbulence

contraction

generating

contraction

nozzle plus

employed

to achieve

and

grid on

90 inches

the

Peterson.

nozzle. was

the

modified

turbulence

distance

from

of the

the

distance,

to account

the

the

effect

grids

by

turbulence

the

effect

An

effective

generating

agreement

with

of the

contraction

an

l, from

for

development.

a satisfactory

Therefore,

to a displacement

Therefore

additional

the

of the distance

grid

nozzle

of

was

correlation

90 inches

the

of Baines

is equivalent

ahead

of the

test

section.

5.1.2

Integral

Length

Scale

Measurements turbulence

were

fluctuations

scales

the

of the

turbulent

edge

leading

determined the

wire

surface.

and

inches,

x = 45.7

longitudinal

length

the

eddies

smaller

are

decreasing.

the

for the

in Fig.

scale

with

dissipating The distance Also

from

downstream faster

average when this

the size

in reality same

larger

figure

the

for

with

appears

intensities

we see

for the

that

plotted

grid

0

of the is due

to

increasing to be growing

of all eddy for

length

x = 36.3

increase

eddies

Fig.

centerline

increase

This

therefore

the

x location

inches

0.5.

the

of

These

scale

7.7

19 note

with

grid

spanwise

length

distance.

than eddy

each and

7.5 and

In Fig.

associated

surface.

at

vertical

integral

19, were

freestream

as a function

test

spectrum the

size

scale

flat-plate

at

of the

1, 2, 3, 4, and

length

power

respectively.

distance.

downstream

of the

scale eddy

grids

integral

values

shown

average

behind

positioned

The

not

with

from

integral

the

flow

the

configuration,

streamwise

to depict

of the

19 with test

longitudinal

distribution

from were

in Fig.

obtained

in the

19 shows distance

of the

increasing

sizes grid

39

bar

width

Peterson

(refer [26] and

length

scale

exponent. held

to Fig.

Compte-Bellot

is proportional Baines

for

several

and grid

data

shown

Eq.

(35).

The

length

scale

Recall

that

an

x-shift

effects. and

turbulence

intensity

streamwise Fig.

21.

cross At

each

an(l

indicated

that

raised

to some

grid

the

was

following

the

relationship

section survey 0.05

Figs.

20 and

21 indicate

with

previous

researchers

the

scale

to account

the

taken.

integral

arithmetically the

were

length averaged

standard

deviation

that

for

for the

0.1 for grid

that

the

length

scale

distributions

the

length

scale

values

are

grids

are

4.

nozzle 1, 2, 3,

acquired

of the

1 to about

that

longitudinal

scales and

the

and

contraction

taken

in

grid. grid

for grid

and

indicate

rectangular-bar

for the

to 0.56.

indicated

20 and

measurements

The

pla,e

of 0.53

turbulence-generating

measurements

that

were

of the

range

relationship

in Fig.

width

required

in the

to fit the

shown

bar

from

locations were

forced

to the

length

approximately

turbulence.

have

the

that

exponent

fit are

distance

from

isotropic

n is an

of the

of 90 inches

same

from

[26] showed

19 were

is correlated

the

distance

[27]

Baines

(35)

and

results

x is the

Corrsin

increases.

K

in Fig.

Additional

4 at

to the

scale

sizes:

K is a constant

The

length

and

Peterson

=

where

2) the. integral

at

plotted data

in

ranged

Comparison are

each

of

in agreement

representative

for

4O

5.1.3

Frequency For

each

data

were

test

section

from

the

and

Spectra turbulence--generating

acquired at

along

x locations

leading

edge

26 illustrate

3, and

the

freestream

the

of the

longitudinal L f / Ue; previous

where

theoretical

spectrum

Taylor's

so that

scale,

grid---generated turbulence. turbulence

22,

the

L and

I,; where _

the

power

far

downstream

Figs.

spectra

on the

frequency measured

distribution

turbulence In addition,

and

22 thru each

26 plot

spectra values

of frequencies, has

the

the

follows

the

isotropic

the

characteristics

results

homogeneous

indicate

of turbulence

for grids and

isotropic.

0.5,

in the is

to Taylor's

do not

for

as

spectrum

turbulence

grids.

is

same

isotropic

freestream

mean

L is the

[28] for one-dimensional in the

1, 2,

U e is the

wavenumber

defined The

0.5,

is the

and

dimensionless

spectrum.

25,

in dimensionless

density,

U e are

inches

grids

] _

velocity,

the

23, 24,

be compared

is expected

is nearly

56.0

it can

frequency

and

Figs.

spectrum

within

and

is presented

spectral

dimensionless

manner

generating

based

and

power

turl)ulence-generating

is U e u'(f)

and

45.7,

surface.

longitudinal

scale,

one--dimensional

Therefore, length

for

turbulence

in the

of the

the

centerline

36.2,

spectrum

power

f is frequency

in this

turbulence

is the

length

20.2,

for

power

vertical

test

spectrum

fluctuations

normalized

spikes

The

integral

6.2,

spectra

configuration

and

flat-plate

power

u'(f)

expression

isotropic

of-7.5,

dimensional

velocity,

square

spanwise

of the

4 respectively.

parameters:

the

grid

since of the any

features

unusual of

turbulence. intensity,

longitudinal

rectangular-bar associated

with

1, and

2 indicate

isotropic that

the

41

5.2

Determination

5.2.1

of the

Mean

Velocity

Profiles

Mean

velocity

profiles

determine

where

freestream

turbulence.

spanwise

layer

transition All of the

within

flat-plate

test

velocity,

while

surface the

Therefore, test

the

surface

plate

depict

the

boundary

distance for

from

either

The the

surface

along

layer

increasing

variables

and

were

a flat

in that

flow

the

rl and

compared plate

mean

with

the

Each

the

with

velocity

at

of zero

at Carpet

edge

of the

fiat

flat-plate

test

of these at

increasing flow;

thickness

layer.

velocity

layer

layer

boundary

along

the

frecstream

a value

leading

The

plots a given

streamwise whereas

a given

indicate

y -

y distance

for a distance

distance. velocity

f'(r/)

(see

to the zero

from

the

form.

from

the

the

32.

along the

boundary

of the

from

boundary

the

edge

31, and

streamwise layer

the

decreases

or turbulent

boundary

similarity

Analysis) layer

development

test

at

by

to

of

obtained

distance

scaled

development

layer

boundary with

layer

28, 29, 30,

the

a given

by

level

in dimensionless

is normalized

x distance

27,

laminar

transitioning increases

boundary

at

each

acquired

to characterize

plotted

u/U e are

of one

vs u/U e at each

typical

arc

were

were

In order

layer

vs.

for

profiles

is normalized

of y/_

layer

located

layer

y distance)

of y/_

Figs.

was

data

boundary

y distance

boundary

surface.

the

plots

See

region

test

to a value

surface.

the

boundary

(the

plots

Region

within

development

local velocity

the

the

centerline

boundary

(699).

Transition

profiles section

Blasius

pressure

were 4.2

solution gradient.

plotted

Boundary for See

in terms Layer

a laminar Figs.

of

Data boundary

33 thru

38.

42

For a laminar boundary layer the plots therefore the

profiles

flat

plate

boundary

acquired

should

layer

profiles correspond should

lie on

along

should

agree

therefore,

with

are

transitioning behavior.

with

mark

region

where

transition distance

the

edge

grid

region Fig.

35, the

and

10.0

started from

inches,

leading

edge

To determine mean

velocity

compared

to the

turbulent

boundary

of the the

profiles

to the

end

were

empirical layer.

data

another data

which

36,

flow

1 ease

begins

at

from

the 10.3

at

from

for

the

transition inches,

2) from

x = 9.0

boundary

station

Fig.

a

42 inches

between

the

therefore

region

34,

8.3 and

measuring

and

40 and

x =

the

example

transition

38,

turbulent

starts

Fig.

also

points

when

For

between

which

and

fully

laminar

37, and

of

is either

indicate

1) from

grid

first

flat

the

the

between

Figs.

Therefore,

apparently

Similarly,

edge

velocity

begins.

region

for the

3) from prior

in the

leading

the

flow

case

and

gradient

f'(T/)

process

similar

for a laminar

of one

a similar

no grid

begins

the

or is approaching

as follows:

region

to transition the

are

are

remaining

layer

from

plate.

0.5 case

and

The

transition

flat

top

of r/ versus

for the

of the

transition

lie on

solution.

somewhere

grid

pressure

solution.

should

plots

the

configurations

for the

at zero

to deviate

region

streamwise

Also,

to turbulent

these

begin

another.

of boundary

laminar

layers

from

Blasius

Blasius

boundary

other

the

f'(q)

x-distances

of one

plate

representative from

leading

top

profile

the

Therefore,

the

various

a flat

to a laminar

agree

33, the

at

of r/ versus

layer

x = 5.0

has

inches

plate.

of the plotted

transition on

the

region U+

correlation

of Musker

The

of skin

value

the

boundary

layer

versus

Y+

coordinates

(Eq.

23)

for

friction

coefficient

a fully was

and

43

determined by 4.3

of this

using

report. was

subjective

judgement

assess

the

procedure placed

friction

The

required

the

of the

was

skin

used

profile

friction

compared

the

coefficient

to the

following

Cf

and,

value

of skin

was

0.00379

from

Eq.

friction

as compared

(37).

This

test

the

well

(50

well

and

the

resulting

data

on

U+

< y+ by

the

> 200) the

of the

wire

was

value Y+

coefficient to Cf of the

applied

coordinates. facility

well.

data

compares

for

The to the

correlation.

technique

was

[29]:

_0.25

[ln2(0.06

was

of skin

very

[1] and

To

layer

in this

fit

fit

above

of Musker's

Clauser

correlations

layer.

technique

obtained

A

should

A trip

versus

of Musker slope

data

boundary

and

the

coordinates.

layer.

several

and

friction

the

fit

data

4.2

boundary

Clauser

39, the

empirical

Cf = 0.455

The

plate The

obtained

= 0.0250

how

correlation,

correlation

by how region

Y+

boundary

profiles

in Fig. fits

log-linear

fiat

to plot

indicated

U + versus

a turbulent

obtained. layer

of fit is judged

of the

the

skin

to Musker's

of the

were

coefficient

turbulent

on

refei" to sections of the

to determine

data

edge

profiles

As

data

-

value

to a fully-turbulent

leading

39.

best-fit

to be considered

boundary

goodness slope

was

tripped

Fig.

a fully

the

applied

velocity

to these

to plot

sensitivity

fit technique

resulting

in order

was at

mean

See

used

correlation

Clauser

The

coefficient

the

the

(36)

_x)] -1"0

obtained

= 0.00365 Clauser

(37)

from from

Eq.

fit technique

the

Clauser

(36)

and

gives

fit technique Cf

= 0.00379

confidence

in

44

applying the technique to the data from a post-transition turbulent boundary layer. For the grid 0 configuration, the result of tile Ciauscr fit techniqueis shown in Fig. 40. The results indicate that at the last streamwisemeasurementlocation of x --- 45.7 inches that the boundary layer is not yet fully turbulent. For the grid 0.5 configuration the first streamwiseposition that the profile appears fully turbulent is at x inches the

- see

boundary

last

Fig. layer

streamwise

profile

is very

configurations streamwise

41.

measurement close

in Figs.

investigation

Blasius order

of about

factor

and

the

also

1.6.

no grid,

grid

1, and

can

be made

shape

from

Fig.

is turbulent

at

respectively

as

transition

and

the

the

of the and

as

of displacement

shape

factor.

values

are

boundary end

region

The no

grid

layer

of the

the shape

transition for

following case

The on

of x-distance

2 configurations. the

such

ratio

turbulent

beginning

1) for

transition

parameters

as a function

46:

in this

layer

The

value

is at

region.

boundary

as

the

grid

station

be considered

is defined

factor

For

survey

at

the

42.

first

thickness.

the

grid

not

layer

is 2.59

to estimate the

observations

the

Therefore,

Fig 46 shows grid

layer

thickness

region.

0.5,

4 will

the

that

even

ttowever,

in Fig.

profile

that

boundary

factor

turbulent

5.0 inches,

Recall

displacement

shape

1.4 to

can be used

45.

and

of locating

momentum

for

5.0,

of the

1 configuration

to be. fully

layer

boundary

method

grid

as indicated

3 and

the

behavior

to the value

and

the

of x = 21 inches,

boundary

grids on

thickness

thickness

44,

therefore,

An alternate

momentum

4 the

for

al)pear

turbulent

of x = 8.2, 43,

at the

not

that

position

to being

focused

is to look

does

2, 3, and

x = 5 inches;

42 shows

profile

locations

indicated

Fig.

= 18.3

the

the

45

transition region begins at x = survey

station

region

begins

grid by

at

1 case the

survey

the

various

5.2.2

and

other

The

value

that

of a laminar

Fig.

47 shows

From

Fig.

laminar

layer.

coefficient

from

from

the

friction relation: for

the

of skin

that

transition

layer

1.05

due

laminar Cf,

section

describing

coefficient

within

grid friction

1 case

the the

A plot

is shown

coefficient

in Fig.

versus

the

flow

the at

inches.

method

used

sections

to

focus

boundary

the

was

x and Fig.

for

skin

the

from

value

leading

turbulent

of the

region. that by

corresponding

the

the

friction

determined

49 illustrates

plate.

from

fully

reduction,

the

layer. a flat

for the

transition

and

region

_x

in the

regimes,

between

of Cf varies

x 105

acquisition

x-distance

end

station

significantly

value

variations

48.

not

2 case

following

of Cf versus

of 0 versus

grid

of the

varies

to detect

transition

does

of l0

of a turbulent

to large

3) for the

region.

to Cf u 4.35

data

survey

dependence

coefficient

be used

first

x location

to turbulent

can

the

The

last

transition

and

4) for

at

this

the

11 inches

region.

the

18 inches,

the

to that

x 105

x =

and

an RxU 4 x 105,

Therefore

= 2 _]_.

at

the

at

0.5 case

before

distribution

at

coefficient,

Cf

ends

the

friction

boundary

the

begins

not, end

grid

at x =

to determine

skin

of about

boundary

and

indicate

of the

of the

47 note

the

approximately

a representative

value

friction

ends

methods

Friction

2) for

does

at x = 21 inches,

paragraphs

Skin

and

begins

region

location

inches

9 inches

region

station

above

determine

x =

transition

inches

The

inches,

transition

layer

x = 5.0

on

about

the

last

boundary

of x = 45.7

40

Recall, the

distribution

edge

skin

the curve

the

skin

of the

fit

46

fiat plate for the various grid configurations of interest. Fig. 49 show,_that the transition onset for grids 0.5 and 1 occur at approximately the same location. However, the grid 0.5 caseapproachesthe turbulent values of Cf at a much faster rate than the grid 1 case.

The

is not

value

clear

at

turbulence

this

is lower

regions

with

The

of the

value

velocity These

plots

turbulent

on

coefficient

profile

transitioning

distance. plotted

most

Tables

parameters grid

for the I, II,

coefficient discussed

with

the

IV,

V,

(also

with

Blasius

and

report)

shown

to

for

the

skin

of a laminar

preceding

are

other

boundary

streamwise

distance

with

mean 55.

in Figs.

the

the

in

downstream

VI summarize

included

the

laminar

obtained

increasing

the

distribution.

50 thru

from

profile

that arc

development

curve

laminar

note

to plot

Figs.

values

gradual

freestream

factor

used see

occurrence

coefficient

transition the

profile

streamwise

in this

50 thru

the

55,

transition

distribution

of the

layer for

each

of the

configurations. As mentioned

made

to calibrate

shear

stress.

location, speed

that

theoretical

III,

-

this

Also,

shape

then

of the

I.

friction

the

was

indicate

to a turbulent the

by

coordinates

smoothness

consistent

that

friction

Y+

skin

for

of the

to grid

the

coefficient

therefore, are

Note

region.

friction

the

by

determined

U + versus

and

friction

skin

skin

the

0.5 as compared

locations

illustrate

flow

since

as determined

the

profiles

especially

for grid

of transition

agreement

was

time,

reason

At

boundary settings.

in the the

calibration

flush-mounted

an x location layer A trip

hot-film

corresponding

profiles wire

section

was

were placed

report,

an

effort

was

sensors

to measure

the

wall

to a flush-mounted

obtained at

of this

the

at

different

leading

edge

wind of the

hot-film tunnel flat

plate

47

to insure that the boundary layer

would

wall

using

shear

correlated

stress

was

to the

bridge

anemometer the

and

The

layer

profiles

(Eq.

36)

in section

a transitioning

boundary

not

to the

simultaneous

time

transition flush-mounted wire

vary

by

fluctuations from the

a factor

47

friction

boundary

layer

turbulent

flow

hot-wire

fluctuations

laminar

flow

of about

a linear

velocity

the

friction

can

only

least

by

indicate

a factor

turbulent

distribution value in the a factor

from

4 -

the

film

shear

Note test

this

of shear

of 3.

of about

signal

Recall

boundary

and

from

the

was

layer

of the mean

hot

voltage

1.003.

Recall,

this

situation)

transitioning the

laminar

as /_ Au/Ay, shear

stress

from

the

wire

that

the

assumption

the

wall

would

it seems

represent calibration

and the

since

Therefore, should

to

to the

for

in the

surface

stress.

the

between

that

point

57 shows

if the

stress

of 3 swing

between

hot

number

to be jumping

flow.

Fig.

of about

13

subjected

calibration

the

Reynolds

in Fig.

the

as close

whereas

the

was

fluctuations

a factor

(the

a factor

inches

velocity

by

be assumed

within

located

three,

Approximating

0.007

fluctuations of at

vary

vary

to the

in a lower-than-actual that

film

regimes.

flow

was

The

that

from

empirical shown

film

region.

located

which

of approximately

should

distance

wire,

film,

for Rx u 4 x 105

skin

the

hot

realized

transition

as possible.

hot

that

it was

layer

of the

a hot

film

of the

Fig.

boundary

and hot

flow,

hot

was

temperature

obtained

was

of

and

constant

curve the

value

technique

aforementioned

calibration when

The

coefficient

to the

However,

layer

traces

region,

The

fit

hot-film

friction

compared

56.

turbulent.

Clauser

of the

of skin

are

3.1.

the

output

values

in Fig.

discussed

applicable

by

voltage

system.

boundary

correlation

obtained

be fully

is at

a of

result reasonable

a swing

in skin

section

in this

48

report that the mean voltage output of the hot film is proportional to the shear stressto the 1/6th power. Therefore to get a shear stress or skin friction coefficient variation of a factor of 4 would require that the voltage output of the hot film should vary by a factor of 1.26. As indicated in Fig. 57 the hot-film fluctuations depict only a factor of 1.003 variation in the bridge output voltage. Therefore, it was not possibleto extract the instantaneousshear stress in the transition region from the hot films which were calibrated at turbulent flow conditions. Cook [30] attributes this inability of the flush-mounted hot-film sensorto follow rapid flow changes to a thermal lag due to heat conduction in the substrate of the hot film.

5.2.3 The

RMS

rms

were

Profiles

of the

recorded

acquired.

at

These

x-component the

type

longitudinal the

of flow

associated of the

fluctuations hot

film

region.

shown Figs.

normal

fluctuations with

the

be seen in Fig.

58 thru

data

within the

stress)

can

layer.

In the

should

be much

velocity

57 where 63 show

the the

be

the sensors profiles

boundary

velocity

than

layer

intermittently increase

the

layer the

However,

boundary

will from

in the

signal

from

the

hot

are

within

the

of the

rms

of the

were

indicator

boundary

profile.

This

profiles

as an

smaller

layer

represents

used

laminar

velocity

of flow.

the

of which

also

is jumping

examining

mean

square

in a transitioning

type by

for

(the

a turbulent

fluctuations

to a turbulent can

the

boundary

of all because of flow

fluctuations

fluctuations

in the

fluctuations

type

time

of Reynolds

velocity

greatest

same

velocity

longitudinal

amplitude

velocity

of the

velocity the be the a laminar

velocity wire

and/or

transition longitudinal

49

velocity fluctuations for the various levels of this

investigation.

The

plot

for the

the

laminar

profiles

the

rms

values

from

laminar

to transition increases rise

rapidly.

to a peak

turbulence the

and

the

increases

is laminar peak

10.3,

(x =

flow

value

boundary

velocity

units.

grid

2 data.

inches

are

The

rms

layer

it has

at y+

_- 17.

were results that

2.5

Therefore,

agrees

with

normalized

by

of this the

T is approximately

data

boundary 1.7 for

the

the

layers. the

The velocity

rms

value

boundary

layer

is intermittent distance

a maximum decreases

shown

[31] that

should

trends,

friction

values From

how the

data

of the plotted

64

for the

of x greater

post-transitioning

the

and

in Fig

Fig.

peak

within

well

rms

as the

the

occur

velocity

is shown for

values

in which

streamwise

to 3 and

these

rms

peak

subsequently

been

for

fluctuations

of thc

flow

to determine

normalization plotted

rms

the

it reaches

value

begins

dissipation.

when

increasing

where

be approximately

post-transitioning

of u'/U

peak

boundary

investigation

Note

with

flow

region

of the

when

that

longitudinal

the

of the

iu

shows

the

of the

magnitude

used

of y the

turbulence

location

to a point

velocity

values

profiles

The

rapidly

behavior.

fluctuations

the

58 -

of the

marks

However,

turbulent

in this

wall

59.

The

T should

by

Fig.

As

value

curves

of the

inches).

layer

freestream

x=6.4).

12.3)

rms

turbulence,

low.

increasing

streamwise

increases

a turbulent

of u'/U

obtained

value

14.3

for

direction

-

relatively

in the

in Fig.

case

the

is balanced

and

and

approaches For

the

value

that

peak

for each (x=5

rms

(x = 8.3, value

This

is depicted

gradually

are

off to the

streamwise

fluctuations

flow

notice

production

in the

no grid

to turbulent,

drop

intensity.

turbulence

trend

Also

fr_stream

than

64, the

12

maximum

boundary

in

5O

layers and occurs at the measurementlocation nearest to the wall which is at y+ _ 20. The reason that the peak value of u'/U T was less than the expectedvalue of 2.5 to 3.0 is explained in a publication by Ligrani and Bradshaw [31]. Ligrani and Bradshaw measuredthe turbulence intensity and spectra within the viscoussublayer of a turbulent boundary layer using various hot-wire probes of different dimensions. They concluded that in order to obtain the spatial resolution to accurately measurethe turbulence properties within the viscoussublaycr of a fully turbulent boundary laycr the hot wire sensingelement must have a viscouslength of 20 or less. The viscous length, 1+, is defined as follows: l + = lwire Ur wires hot

used

in this

wires

location

of 1+ greater of the

shown

64

value

occurrence

transitioning to be

and

increasing

diminishes streamwise

In addition, were

acquired

for

located

post-transitioning

layer

with

to occur

intermittent approaches and

the

value

y+

magnitude

appears

of 1+ was

peak at

in agreement

of the

boundary

'hump'

remains

the

value

20 the

of a 'hump',

a remnant

As the

value

are

but

the

than

[31] in that

expected

this

peak

in Fig.

Bradshaw

the

investigation

y+

at y+

findings

Also

__ 95, in the layers..

behavior

during

profiles

turbulent become

the

shown

This the

flow, more

rms

and

the

results and lower

than

in Fig.

64

data

for

'hump'

the

process.

magnitude more

of

similar

distance. to check a fully

the

turbulent

validity

of the

boundary

rms

layer

measurements, and

compared

is

appears

transition the

For

but

x is slightly

_ 20.

hot

60.

of Ligrani

boundary

fully

the

approximately

Therefore,

of (u'/Ur)ma at

For

of u'/Urdecreases,

__ 17. the

/ v.

data to the

with

51

'classical' results of Klebanoff [32]. For these profiles a trip wire was placed at the leading edge of the test surface. The rms of the velocity fluctuations is plotted against the results of Klebanoff in Fig. 65. The data agree very well with Klebanoff's results. Thc differencesat least at the outer edge of the boundary layer are due to the fact that

Klebanoff's

measurementswere obtained at a lower value of freestream turbulence than the data acquired in this investigation. Also, from this figure, we can see the shapeof the longitudinal turbulence intensity within the boundary layer for a turbulent profile. Reviewing Figs. 58 thru. 63, we find the following: 1) for grid 0 (Fig. 58) transition onset beginsat about x = 40 inches and doesnot appear to approachfully turbulent behavior by the last survey station at x=44.3 inches, 2) for grid 0.5 (Fig. 59) transition onset occurs at approximately 8.3 inches and does not becomefully turbulent even by x = 20 inches, 3) for grid 1 (Fig. 60) transition onset occurs at approximately x -- 9 inchesand doesnot becomefully turbulent by x inches,

4) for grid

survey

station

rms

different distributions different

61)

at x -- 5 inches

approximately the

2 (Fig.

x = 12.2

of the than

velocity those

of the method

fluctuations

skin

transition

and

inches.

inferred

used

the

from

becomes

The

results imply

the

mean

friction

coefficient.

to determine

the

onset

begins

fully

turbulent

obtained transition velocity The

location

prior

from

the that

profiles

and

of the

to the

first

profiles

of

are

slightly

by

regions

next

= 21

section transition

discusses region.

a

52

5.2.4

Intermittenc¥ The

intermittency

boundary films

layer

located

grid

Factor

0.5,

the

and

intermittency

factor

mean

output

voltage

voltage

levels

At

to

would

each

added

and

layer

turbulent the rate

regimes

data

The time

laminar

step

and

Fig.

67.

The

grid

0 transition

0.5 transition

time

region

transition

region

from

transition

region

begins

of a hot threshold

performed

values

from

for

each

grid inches

x = 6.2 inches

before

inches

film

located

value

was

traces

2.62

seconds.

x = 4.2 inches

were

boundary

laminar

factor

and

Recall,

from

recorded

at

flush-mounted are

plotted

inches,

inches,

at

a

hot-film in

is as follows:

inches, ends

flow.

this

in the

were

to x = 50.2

and

threshold

illustrates

configuration

18.24

-

individually

time

all

All

of zero

or one

as possible.

to x = 24.2

to x --

value.

between

of intermittency,

x = 38.3

x = 4.2

on

zero 66

it distinguished

film

of the

to a turbulent

Fig.

as accurately

the

the

value

this

of either

time.

for

a value

above

hot

traces

threshold

corresponding

all

hot

time

arbitrary

voltages

the

to eight

recorded

be assigned

values

that

the

was

regions

from

would

of approximately

resulting

region

value

trace

procedure

transition

as the

trace

that

a time

to use

over

such

section,

films

-

of up

these an

all

of time

were

choosing

voltage

trace

of the

the

surface

by

assigned

averaged

traces

From

of one

the

The

time

test

whereas,

a value

was

over

above

traces

flow;

for a time

reduction

of 50 Khz

hot

threshold

region.

for each

the

this

procedure

transition

selected

from

total

of the

determined

percentage

time

1 configurations.

was

time

the

calculation

centerline

be assigned

discrete

as the

Simultaneous

grid

below

corresponding value

is defined

is turbulent. along

0, grid

factor

2) grid

grid 3) grid

x = 10.2

1 2 inches,

1)

53

and 4) grid film

at

very

x = 4.2

well

with

transition made

3 transition inches the

at

obtained

steady--state

in a wind

tunnel

of similar

acquired

68 were

freestream

Blair's

in Fig.

results

herein

the

following

section

boundary

layer and

transition the

compared

The following were

compared

from

these

classical

transition

region. theoretical

the

profile

of the

zero

pressure

will

used

The

between

were

in this

data

shown

gradient

at

levels results

and

flush-mounted

hot

films

technique.

In the

to determine

the

compared

to one

be summarized,

on empirical

in

a

Blair's

methods

based

agree thc

turbulence

of the

various

transition

1) Initially

layer

laminar

68.

hot

which

tunnel

an appropriate

to predictions

of the

methods:

traditional

use

results

located

in Fig.

freestream

the

first

measurements to the

with

was

These Blair

transfer

shown

of the

correlations.

of Methods

location

region.

[33].

Blair

agreement

indicate

region

by

the

excellent

results

inches.

plate

with

location

x = 8.2

are

region

transition

Comparison

transition

The

reported

to determine

another,

68.

the

construction

a flat

of 100 ft/s

before

heat

results

along

velocity

indicated

when

ends

from

Fig.

to the

begins

region

[22].

5.2.5

and

results

investigation

the

region

region

the

mean

to 'classical' profiles 2) The and

laminar deviated

indicated boundary

layer values

of the

value

and

from

and

the

value

the

been

velocity

laminar

turbulent

3) The

has

profiles

turbulent

beginning shape

factor

empirical laminar

the

friction

in the

end was

boundary Deviation

compared

coefficient

of flow

the

of the

location

turbulent type

by

profiles.

and

to detect skin

determined

value to the

to the

of the was

compared

to determine turbulent

54

type of flow. 4) The value of the rms of the longitudinal velocity fluctuations was used to determine where the transition region was located. 5) Finally, the intermittency factor obtained from flush-mounted hot-film sensorswas used to gauge the type of boundary layer flow. The results of each of these methods are summarized in Table VII and they are compared to predictions of the onset of the transition region (seeTable VIII) based on the empirical correlations developedby Van Driest and Blumer [8], Seyb [34], Abu---Ghannamand Shaw [10], and Dunham [35]. The agreementof the data depicted in Table VII with the empirical correlations (depicted in Table VIII) indicates that the results presentedherein are reasonable. In addition, Mack's [36] modified en method, a more theoretically based method, was used to predict the onset of transition for each grid configuration. Basedon Mack's method [36], the predicted locations for the onset of transition were as follows: 1) at x x > 20 inches

for grid

0.5,

inches

2.

modified

for grid

stability

theory;

predict grids (i.e.

the 0.5, grid

modified

The therefore,

location 1, and

0) the

for the

location

VII,

transition

region

However,

the

of the

[36]

onset

is in good

investigation note

that

at an earlier

intermittency

the

that the

case

the

bypass

1, and

with

(see

VII).

intermittency location determined

method

via

the

factor

0, 2) 4) at

locations

method

at x _ 8

on

linear

fails

to

cases

(i.e.

T-S

path

the

as predicted

agreement Table

largely

transition

of transition

of transition

was

for grid

[36] is based

for

streamwise factor

inches

for grid

it is understandable

ttowever,

in this

In Table

e n method

onset

e n method

experimentally

3) at x = 17 inches

of transition 2).

= 36

by

Mack's determined

detected

than

the

other

from

measurements

the

methods. of the

55

flush-mounted hot films which detected the unsteadinessnear the test surface, whereas, the other methodswere based on measurementsthroughout the boundary layer. Thereforeit is apparent that the mean profiles are not affected by small amounts of intermittency. The only surprising feature depicted from these results is that even though the turbulence associated with grid 0.5 was less than that of grid 1, the transition region not only started at about the same location for each of those grid configurations but also that the boundary layer flow becameturbulent for the grid 0.5 configuration before it becameturbulent for the grid 1 configuration. Recall, that grid 0.5 consistsof a 20-mesh screenlocated directly in front of grid 1. The differencesin the characteristics of the freestream turbulence for each caseis documentedin Figs. 17, 19, 22 and 23. However, the flush-mounted hot films detectedthe beginning and end of the transition regions in the anticipated order - see Fig. 67. This indicates that something is happeningthroughout the boundary layer in one of these cases to either retard (grid 1) or accelerate(grid 0.5) the boundary layer transition process. One possibleexplanation could be related to the integral length scalesassociatedwith each level of freestream turbulence. Recall from Fig. 19 that the integral length scale of the freestream turbulence for the grid 0.5 configuration was approximately 0.3 inches whereas,for the grid 1 configuration the integral length scale of the freestream turbulence was approximately 0.5 inches. Therefore, for the grid 0.5 configuration, the boundary layer would be buffeted by more freestream turbulent eddies in comparisonto the number of eddiesbuffeting the boundary layer associated with the grid 1 configuration, within a given time period.

56

The intent of this investigation is to study the bypass transition processas compared to transition via the T-S path. Thus far, for each grid configuration, the characteristics of the freestream turbulence have Ix_cn documentedand the correspondingboundary laycr transition region has Ix_en identified. However, for grids 2, 3, and 4, the transition t)roccssstarted upstream of the first measurementlocation at which boundary layer surveys were acquired. Only a portion of the transition region was therefore captured for these configurations.

Therefore, the remainder of this rcport

will focus on the transition region for the grid 0, grid 0.5, and grid 1 configurations.

5.3 Documentation of

5.3.1

Description The

plate of the

is described

leading is an

edge

Linear

number

at which T-S

streamwise

stability

waves, vortices

the

[1].

the

T-S

they

flow flow

can

waves begin

develop.

via

begin

to vary

is a stable

A periodic

T-S

Path

Path

past

White's

a smooth

flat

[1] representation

downstream. laminar

Near flow.

the

Then

there

Tollmien-Schlichting

(T-S)

to predict

Reynolds

to grow. in the

T-S

flow

develops

be used

the

the

69 depicts

two-dimensional theory

via

disturbance

Fig.

as the

plate

of unstable

Process

for low

place

fiat

Process

Transition

White

take

of the

initiation

Transition

process by

that

waves.

of the

of the

transition

steps

the

After

spanwise

streamwise

the

critical

a period direction

vorticity

of growth and

system

57

developsinto counter-rotating vortices. Shear layers develop in the boundary layer and the vortices, which have been stretched in an S-shal)c in the spanwisedirection, begin to break down. The vortices continue to break down into smaller and smaller vortices until the unsteadinessis characterizedby fully three-dimensional fluctuations. Next, turbulent bursts occur and three dimensionalturbulent spots form. These turbulent spots are believed (Schubauerand Klebanoff [37]) to be wedge shapedand are continuously being distorted due to the downstream end of the spot traveling faster than the upstream end. The turbulent spots grow and merge with other turbulent spots until the flow is fully turbulent.

5.3.2

Verification For

films

the

depict

surface. from

grid

the

the

T-S

70 were

first

distance.

At

fully theory.

until

turbulent. Fig

that the

amplification not

waveform inches

inches

of the

the

flow

flow, These

71 depicts

of T-S

wind

y -

the

by

curves

The

the

of neutral

develop

traces

the

increasing hot from for

periodic

evident.

(i.e.

to results

of

streamwise

is first

with

shown

first

of the

intermittency

test

traces the

increasing

stability

the

succeeding

flush-mounted

compared

time

amplification

increases

hot

rather

x = 30 inches

with

The

along

but

The

of turbulence

is turbulent)

were

the

inches,

axis.)

as sensed

waves

tunnel.

is recognized. illustrate

flush-mounted

excited

At

bursting

results

of the

artificially

in the

at x = 30.3

x = 38.3

in scales

time

distance

noticed

traces

simultaneously.

x = 34.3

waveform,

time

were

inherent

acquired

and

change

and

waves

of a periodic

x = 32.3,

of the

0 configuration,

disturbances

occurrence

Waves

existence

These

in Fig.

the

of T-S

(Note fraction

streamwise

films,

becomes

linear

neutral

stability

frequencies

58

of disturbance on a fiat plate at zero incidence. This figure was extracted from Schlichting ([5], p.479). The curve labeled 'measurements'was generatedfrom the results of Schubauerand Skramstad [6] and the theoretical curve was generatedfrom the works of Tollmien [4]. The area betweenthese two curves shown in Fig. 71 indicates the conditions at whi(:h the T-S waves grow in amplitude. In this investigation the initial growth of T-S wavesoccurs at x 30.3

inches

the

Therefore, on

displacement

at

a freestrcam

displacement

thickness

shown 400

in Fig. Hz.

frequency

stability

theory as T-S

configuration described

5.3.3

velocity

the

of Fig.

indicates

in section

Features

streamwise flush-mounted

and

values

agreement the

transition

Reynolds The

fir v /

of this

periodic

process

via

on

shown

T-S

base(!

fv / Ue 2 is

the

neutral

with

the

in Fig.

for

the

path,

grid which

Waves

of the of the film

was

streamwise T-S

waves,

cross-correlated

wavelength. the

To

periodic with

the

determine

signal signal

the

of a from

linear

70

5.3.1.

T-S

of

normalized

experiment

the

inches.

frequency

and

process

x =

waveform

Ue 2 = 2r

triangle,

waveforms transition

At

number

a characteristic

solid

periodic the

the

of _ . _ 1900

as the

70.

to be 0.039

1900.

frequency,

therefore

the

wavelength hot

The

in Fig.

measured

exhibits

plotted,

that

of the

Determination

inches

These

were

simulates

was

of 100 ft/s

normalized

71 .

waves

as indicated

is approximately

x = 30.3

= 45 x 10-6 plot

inches

thickness

45 x 10 -6.

stability

behave

70 for

Therefore,

approximately

= 30.3

a hot

0 was

59

wire which was positioned at different locations relative to the hot film. An example of such a crosscorrelationis shown in Fig. 72. The crosscorrelationof two periodic functions is also a periodic function and the frequency of the crosscorrelationfunction represents the streamwise frequency of the T-S waves. The crosscorrelationcoefficient was normalized by the product of the rms of the voltage fluctuations of the hot wire and hot film so that its values would range from +l to -1.

A value of +l for

this normalized crosscorrclationcoefficient, CCFn, would indicate that the signals from the hot film and hot wire arc exactly in phase with eachother. Similarly, if CCFn out

of phase.

hot

film

to the

went

out

which

signals

were

of the

back waves,

9) with

the

distance. was

furthest found

the

The For

wire

in phase Ax. hot

downstream

is positioned

and

in phase

at increasing

each

other.

traversed,

such

that

the

with

other,

each

procedure

the

positions The

was from

found

was

applied

x = 34.3

to slightly near

hot-wire relative resulting

the

film,

locations to the

hot

streamwise

signals state

and

hot-film wavelength

to hot

film

inches

to x = 38.5

with the

#16

measured

the

wavelength,

(sec

downstream

corresponding film

in

streamwise

streamwise

increase

hot

one

to the

hot-wire

the

the

distances

the

The

1800

over with

film,

returned

with

are

downstream

hot

eventually,

signals directly

are

flush-mounted

positioned

at

hot-wire

signals

positioned

locations

1.1 inches.

the

in phase

was

and

and

wire

72),

other

This

wire

hot-wire

hot

of the

each

wavelength

0.9 inches

to be

was

again

hot

hot-film

the

location with

the

in Fig.

wire

once

T-S

inches.

x

that

case

fixed

were

then when

hot

of phase

they

distance

A

is the

As the

relative

Fig.

Initially,

(this

another.

= -1,

value

value

of

to the of Ax was Ax, was

6O

averagedover the distance of x = 34.3 to x = 38.5 inches and was found to be approximately 0.98 inches. T--S wave propagation speed. propagation

speed,

and

the

the

streamwise

frequency,

f, of the

wavelengths

corresponding wave

c, is directly

wave

the

linear

for

the

stability

at

on

Fig.

velocity

value

value

Likewise,

the

400

wave

know

Fig

the

streamwise

the

measured

velocity

inches

value

Since

from

that

was

with

the

Spanwise

73 illustrates

the

curves

34.3

velocity

normalized

is in the

is indicated

estimated

Fig.

for

73 that

< c _< 33 ft/s,

those

0.75

of streamwise values

waveforms represent wavelength.

a frcestream

wavelength

shown

from in Fig.

this

number from

freestream to 0.33.

the

solid

The triangle.

be calculated.

velocity then

< Ax _< 0.99

calculated

T-S

can

For

The

70 to be approximately

Ax = c / f, and

is:

73 by

wavelength from

25 ft/s

of 0.25

in Fig.

stability

Therefore, the

to

c, as a

Reynolds

by

range

T-S

of neutral

1900.

of

compare(l

velocity,

the

is approximately

each the

thickness.

inches,

Ax,

average

then

wave

on displacement

streamwise

was

values

do indeed

was

disturbances and

The

result

of x =

For

paragraph)

calculated.

the

wave

wavelength,

This

based

the

c = Ax f.

previous

/3 = 2_r f, and

wave

0.31

was

ft/s.

thickness

wavelength

periodic

30.8

x location

of the

frequency

Hz.

in the

speed

function

streamwise

(discussed

Fig.

of the

to the as follows:

number

for amplified

measured

T-S

the

a periodic

waveform

frequency,

displacement

73, the

was

theory.

of Reynolds

investigation based

speed

disturbance

function

related

propagation

propagation

For

inches.

and

linear

the

wave stability

of 100 ft/s calculated The

we value

of

agreement

of

propagation theory

70 for x = 30.3,

indicate

32.3,

and

34.3

waves. The

spanwise

wavelength

of the

T-S

waves

61

was measuredin a similar manner to that used to measurethe streamwise wavelength. Crosscorrelationsbetween a flush-mounted hot film and a hot wire were acquired for hot film #16.

The hot wire was traversed in the

spanwisedirection in increments of 0.25 inches. At each spanwiseposition the crosscorrelation coefficientwas obtained and the phase relationship between the hot-film signal and the hot-wire signal was observed. A phase shift correspondingto one period of the waveform resulted a spanwise wavelength of approximately 2.0 inches,or about twice

5.4

Bypass

Transition

The which

bypass

domain

with

bypass

0.5 and

grid

of the

Figs.

74 and

of a laminar turbulence coalescence flow

the

boundary occur. of the

is fully

time

that

transition

trace

at

x = 4.2

inches

traces

at with

Similarly,

by time

time

turbulent.

The

These

However the

by

first

the

increasing

the

in the

linear

linear growth

of T-S

waves

region

simultaneous

traces

are

in Fig.

.x locations streamwise hot-film

for

the

time

shown

in

74 is indicative

x = 6.2 inches

75 the

layer

displaying

transition

remaining

in Fig.

boundary

is no evidence

is identified films.

to Transition

originating

without

process.

hot

spots

a laminar

there

flow.

turbulent

when

environment

layer

The

T---S Path

disturbances

a disturbance

1 configurations

The

the

formation

is to say

flush-mounted 75.

occurs

non-linear spot

In such that

traces

the

finite

is bypassed,

with

process

turbulent

growth.

associated grid

with

displays

disturbance

Comparison

transition

is perturbed

freestream

&

)_X"

bursts

of

show

the

distance time

until traces

62

show no evidenceof any periodic waveformssuch as those identified with the grid 0 configuration (see Fig. 70). In order to check for periodic waveformsbetween hot films, the hot-wire probe was located near the flat-plate test surface (within _ 0.007 inches) and traversed from the first survey station at x bursting

was

first

sited.

film

located

closest

and

the

wire

hot

flow,

the

to the

[38].

in

the

instabilities

linear

evidenced

Fig.

by

The

edge

were

bypassed

to transition

bypass

mode.

transition

results

0.3%.

indicate Consider

region

of the

took

place

flat-plate

test

surface

at

that

for the

transition

from

that

occurred

However

at

at

value

of displacement

the

bypass

that

inches)

This

waveforms

grid

0.5 and

first

of

present

in the

periodicity grid

as was

1 configurations,

indication

test

bypass

hot

of a correlation

some

the

(x = 4.2

performed.

exhibit

the

the

of transition

is

surface.

mode

as compared

to the

T-S

_ii_

the'_transition

occurs

40 inches with

9 inches

for a fr_stream

a smaller

to make

"

mode

and

required

plate

the

grid

the

turbulence

thickness

and

How

do the

earlier

path,

the

the

turbulence boundary edge

of only

0.65%.

for

momentum What

for

i.e grid

leading

occurred

to occur?

occur?

T-S

0.5,

from

transition

transition

the

much

for a freestream

x _ 8 -

bypass

between

x_

I, II,

causes

was

turbulencc

via

bypass

III,

the

for transition

Tables

What

and near

•

path

flat

periodic

for the

of turbulence

macroscopic

inches

would

Therefore, are

where

of the

any

function

72.

film

76, is representative

If there

bursts

hot

a crosscorrelation

x = 5.0

in Fig.

crosscorrelation

evidenced

leading at

shown

signals

to the

In addition,

located

crosscorrelation, random

= 5 inches

the

of

layer of the Also, bypass

note mode

thickness.

disturbance

disturbances

0, the

levels

are

propagate

!

_RICAYqAL I_:)OR

PAGE QUALITY

IS

63

into the boundary layer? In order to investigate the features of the bypass transition processand to make comparisonswith the linear growth transition processthe results of the following measurementswill be discussed:1) simultaneous time traces of a flush-mounted hot film and a hot wire with the hot wire traversedthroughout the boundary layer, 2) two-point correlations betweena hot film and hot wire in both the x--z plane and y--z plane of the test section, and 3) boundary layer spectra acquired for both the bypasstransition case and the case of transition via the T-S path.

5.4.1

Simultaneous To

determine

turbulent film the

Hot-Wire

burst

and

what

occurs,

a hot-wire

boundary

happens

were

acquired.

1 configuration

at

Fig.

77.

corresponds

The

top

Each trace

77 correspond y-axis

on

hot-wire

plot and

to the

signal.

Near

wire

is positioned

and

the

voltage further

fluctuations For

the

different

location

the

test

from

wire

of 8.2

plot the

with

each

the with

located

test the

as a

and

they for

lower figure

passing

at y positions

the

trace

are hot

plot

wire.

in Fig.

and

the

mean

probes

As

velocity

of a turbulent of 0.027

to the

hot-wire

burst.

and

the

shown

correspond

and

turbulent

with

the

of each

hot-film

surface

throughout

acquired

y-location

the

hot

locations

were

inches

in this

surface,

excursion

y -

traces

whereas,

of each

the

time

layer

of a flush-mounted

right-hand--side

signal;

associated hot

at The

on

boundary

traces

to a different

hot-film

left-hand-side

a positive

x -

y-axis

the

sense

decrease.

the

the

Traces

the

time

positioned

grid

Time

through

simultaneous probe

layer

/ Hot-Film

the

hot

increases burst 0.037

inches

in

64

the fluctuations are both positive and negative about tile mean velocity. As the hot-wire probe is positioned from a y location of 0.052 inches to the edge of the boundary layer the fluctuations associatedwith the turbulent bursting are negative. This changeof phase between the flush-mounted hot film and the hot wire can be rationalized as follows. The effect of the passingof the turbulent spot effectively makes the boundary layer flow switch instantaneouslyfrom a laminar flow to a turbulent boundary layer flow. Fig. 78 showsa typical laminar and turbulent boundary layer profile. As indicated in Fig. 78, near the wall a jump from a laminar to turbulent flow would result in a positive velocity fluctuation whereasnear the edge of the boundary layer an instantaneousswitch from laminar to turbulent flow would result in a negative velocity excursion. Also from Fig. 78, note that there exists a point where the laminar and turbulent boundary layer profiles intersect. At this crossoverpoint, the velocity excursion due to the passingof a turbulent spot would be essentially zero. Returning to Fig. 77, note that for y

= 0 to 0.027

positive.

and

At

fluctuations

y -- 0.027 occur,

which

crossover

point

of the

Fig.

Note

also

by

78. the

hot

wire,

are

that

increase

decrease

to the

freestream

the Fig.

rms 64.

profiles

(see

the

highest

point,

through

would

laminar

crossover

fluctuations

0.032

the Figs.

inches

inches

the

both

correspond and

near

the

immediately

to the

wall,

the

level.

transitioning

velocity

reach

and

60),

and

and

negative

profiles

layer explains

velocity about

point, trend was

also the

the

illustrated

fluctuations,

a minimum

same

are

bouncing

crossover

This

boundary

excursions

flow

velocity

of the

after

turbulence

58, 59,

positive

turbulent

amplitude

velocity

at

in

sensed the and

then

of the

velocity

depicted 'hump'

in in

65

The excellent correlation between the hot-film and hot-wire signals (as shown in Fig. 77) through the boundary layer indicates that disturbancesare communicated through the boundary layer. Also shown in Fig. 77 is that as the hot wire was traversed in the vertical direction above the hot film, the passageof the turbulent burst is sensedat an earlier instant in time by the hot wire. This result agreeswith findings of Schubauerand Klebanoff [37] that indicate that the turbulent spot extends vertically through the entire thicknessof the boundary layer and that the turbulent spot is convected at a higher velocity near the edge of the boundary layer than it is near the test surface within the boundary layer (seeFig. 79). Also note that for the hot wire at y locations greater than or equal to 0.052 inches,the freestreamturbulence is detected between the turbulence bursts. At y - locations lower than 0.052 the high frequencies associatedwith the freestreamturbulence is damped within the boundary layer and only bursts of turbulence can be identified. Note that at this position the theoretical edge of a laminar profile would occur at y _ 0.06 inches. All of the above observationssupport the claim that a burst occurs and is transported downstreamat speedswhich are dependent on the distance from the wall and that the passingof the turbulent spot has the same effect as an instantaneousshift from laminar flow to turbulent flow.

5.4.2

hot-wire

Two-Point

Correlations

Due

excellent

to the signal

through

the

correlation boundary

between layer

the

hot-film

as is evidenced

and in Fig.

the 77,

a

66

seriesof crosscorrelationswere performed with 8.2 inches, x = 8.2 and

y = 0 inches, inches,

0.110

y = 0.007,

inches

for

0.75,

4- 0.1, and

these

crosscorrelations

turbulent

the

the

peak

was determined

CCF n in the shows

the

fluctuations sensed

by the

boundary

hot

layer.

plots

in Fig.

burst

passing

flowfield.

spanwise

wire

77.

as the results

hot

film

as the

hot

wire

by the

passing

example,

Fig.

80 shows

time the which was

the hot

hot

hot

film

wire

represented

was

and

the

hot

at

the

region

burst

over

normalized

(see

the

the

the

at

larger

effect

film

hot

and

the

in the

which

film.

was

For

coefficient of 0.5

spanwise

As

by

direction

labeled

vertical

of a

tunnel

fl()wfiel(t

0.5).

the

surrounding

of the

contour

the from

hot

of the

in the

of approximately

direction,

5.4.1

to a value

the

fluctuations

80 shows

floor

plot

through

crosscorrelation

deteriorated

z = 0 inches

spanwise

along

of the

voltage

velocity

flush-mounted

+ 0.4 inches

a CCF n value

in the

the

spanwise

wire

traversed

Fig.

coefficient,

hot-wire

in section

(90)

contour

vertically

earlier

of a

of these

This

z = y = 0) on

traversed the

that

is moved

between

obtain

distribution

of the

_-

a passing

each

80. and

results,

at

of a turbulent

was

film located

traversed

(located

indicated

affected

the

to these

± 0.50, To

by

the

Fig.

amplitude

noted

0.095,

crosscorrelation

hot-film

wire

were

crosscorrelations

direction,

between

hot

tunnel.

x = at

0.080,

_= 0.25,

From

at

located

0.065,

showing See

located

wire

triggered

film.

plot

in the

In addition

the

was

constructed.

reduction

0.050,

normalized

the

hot

of the

hot

between

film

of z = 0.0,

acquisition

of the

hot

the

centerline

a contour

was

These

The

wire,

and

the

the

value

of phase

and

position

from data

and

0.037,

flush-mounted

y---z plane

change

0.027,

spanwise

the

over

crosscorrelations

hot

each

z = 0 inches

0.017,

1.5 inches

burst

CCFn,

and

the

'L' the

distances

the from

in Fig. hot

80

wire from

the

67

flush-mounted hot film, the correlation between the hot wire and hot film was confined to a more narrow spanwiseregion. Note that the edge of the boundary layer correspondsto a vertical distance of approximately 0.12 inches. Therefore, the turbulence bursts are propagated throughout the boundary layer but indicate no evidenceof spanwiseperiodicity in the mean. Additional crosscorrelationswere obtained to study the effect of the turbulent burst on the flowfield in the streamwise and spanwisedirections. Crosscorrelationsbetween the same hot film used in Fig. 80 and the hot wire were acquired in the x-z plane near the test surface for the grid 1 configuration. Figs. 81 and 82 depict the survey locations and the resulting contour showing the distribution of the maximum CCFn for the grid 1 configuration. Similar crosscorrelationswere obtained for the grid 0.5 configuration. Fig. 83 showsthe survey locations and Fig. 84 showsthe resulting contours for the grid 0.5 case. Figs. 82 and 84 depict the averagespanwiseand streamwisepersistenceof a turbulent spot passing over the hot film.

For example, choosingan arbitrary cut--off value of

CCFn -- 0.5, the spanwiseextent of the turbulent spot passing over the hot film would be approximately _ 0.4 inches for both the grid 1 and grid 0.5 configurations. Note that thesecrosscorrelationswere acquired within the boundary layer transition region using the hot film which exhibited an intermittency of about 50%.. Figs. 82 and 84 indicate that the passingof an event at the hot film is highly correlated in the streamwise direction as compared to the spanwisedirection. Crosscorrelationsbetweensucceedingflush-mounted hot films located throughout the boundary layer transition region were also obtained

68

in order to determine an averageconvective velocity fi)r ttle bursts of turbulence near the wall.

A rcl)resentative crosscorrelation between two

succeedinghot films is provided in Fig. 85. The crosscorrelation shown in Fig. 85 indicates that the time it took for an event passing the upstream hot film to reach the downstream hot film was approximately 2.4 ms. Since the hot films were separatedby a distance of 2 inches, the average convective velocity of the turbulent bursts is approximately 70 ft/s or 0.7 Ue. This procedurewas applied to the transition regions for the grid 0 and the grid 1 configurations and the same value (0.7 Ue) for the average convective velocity of the turbulent bursts was determined. Note that this averageconvective burst velocity is in agreementwith the measurementsof Schubauerand Klebanoff [37] --

5.4.3

Boundary

Layer

Bypass occurs

when

boundary

layer.

overall

level

of the

by

rms of the layer

these

velocity

layer

spectra

configurations

velocity

spectra

acquired the

within

various

as a function for the

the

layer.

grid

streamwise

the

Figs.

positions

0.5

the

freestream

In section

5.2.3

layer

characterized

distribution

0, grid

which

laminar

how

58 thru

of frequency

process the

boundary

(see

provide

perturb

to determine

boundary

fluctuations

fluctuations

at

disturbances

to the

disturbances

frequency

as a transition

it is important

transmitted

were

described

non-linear

Therefore

are

boundary

is usually

finite

disturbances

the

Spectra

transition large

seeFig. 79.

was 63). of the

The square

bandwidth. and

the

encompassing

grid

the

of

Boundary 1 the

69

transition region. The boundary layer spectra were acquired at the position in the boundary layer where the rms of the fluctuating velocities was a maximum so that the power spectrum would be obtained at the highest level of signal quality. The boundary layer spectra were checked at different y locations through the boundary layer and similar features resulted. The boundary layer spectrafor the grid 0 configuration are shown in Fig. 86. The spectra at x locationsof 28.9 thru 38.3 inches show an increasein the power spectral density (PSI)) at frequenciesof 350 llz to approximately 440 Hz which correspondto the frequenciesassociatedwith the T-S waves. The increasein the PSD at approximately 50 to 70 Hz is causedby a structural vibration related to a support of the wind tunnel located at x _ 29 inches. When the support was removed the floor of the tunnel vibrated; therefore the support was left intact. This figure shows the increaseof the overall energy level (note the overall energy level is directly proportional to the integral of the PSD over all frequencies)within the boundary layer with increasingstreamwisedistance. This increasein the velocity fluctuations within the boundary layer with increasing streamwise distance was also shown in Fig. 58. From the neutral stability curve shown in Fig. 71, for _

. _ 1900,

between

100 Hz

and

velocity

fluctuations

damped.

Prior

x = 36.3

and

the

behavior

500

38.3

predicted

velocity

Hz would

occurring

to the x =

the

outside

turbulent inches) by

linear

fluctuations

be expected of this

bursting the

power

stability

occurring

at

to be amplified, frequency

(turbulent spectra theory

range bursting

shown in that

whereas would began

in Fig. the

frequencies

be between

86 follow

velocity

7O

fluctuations occurring below a frequency of 100 Itz are not amplified with increasingstreamwise distance; whereas, the velocity fluctuations occurring within the frequency bandwidth of 100 to 500 Ilz are amplified with increasing streamwisedistance. The power spectra at x

= 28.9,

and

level

34.3

inches

comprised

of velocity

frequencies waves. the

below

100 Itz

frequencies

associated

of the

PSD

within

x = 40.3,

the

42.3,

decreased

monotonically

1 configurations, lowest

boundary

shown

in Fig.

be amplified, frequency

whereas

range

before

velocity

would

x = 8.3

the behavior

between

be

inches) predicted

the

to the

bursts

l)

to the

the

T-S

produced

overshadowed

at by

the

of wide-band

turbulent

bursting

was

highest

at lower

continued,

that

of a fully

frequencies

and

frequencies.

Fig.

spectra

for

87 note

that

6.3

fluctuations

power linear

the

1300

to the

spectra stability

grid

the

0.5 and

energy

From

the

level

fluctuations

Hz would

be expected

outside turbulent

shown theory

grid was

neutral

velocity

occurring

Prior

the

inches).

for _ . _ 1000, 500 Hz and

by

became

resembled

damped.

regions:

levels

spectra

= 5.0 and

71,

frequency

energy

32.3,

is largely

corresponding

the

As the

From

curve

frequencies

due

frequency

(x

main

waves

increasing

respectively.

energy

power

PSD

the

cases

at

inches T-S

the

the

88 show

two

layer.

44.3,

laminar

occurring

the

with

overall

frequencies

frequencies

for the

stability

follow

with

in that

87 and

2) the

to x = 40.3

and

flowfield

the

within

and

at all

turbulent

Figs.

that

fluctuations

x = 38.3

turbulence

(i.e

86 show

From

increase

i.e

in Fig.

30.3,

of this bursting

in Fig,

87 partially

in that

the

velocity

to

71

fluctuations occurring below a frequency of 500 llz are not amplified with increasing streamwisedistance. Ilowever, the velocity fluctuations o(:curring at frequenciesgreater than 1300IIz were not damped as predicted by linear stability theory, but rather wereamplified with increasing streamwise distance. As turbulent bursting was initiated (x the

PSD

increased

0 -

500

Hz range.

the

value

of the

energy

level

(i.e.

the

same

trends

grid

0.5

PSD

within

the

0 -

1000

increasing

with

frequency

spectra.

whole

Fig.

88 for

the

grid

The

is that higher

grid

1 configuration

frequencies. range

are

the

The is fully

1 configuration difference

The essentially

shows

between

values

the

has of the

the

of

x distance

layer

primary

the

value

within

intermittency

boundary

Hz frequency

Figs.

86, 87, and

streamwise

range,

regardless

laminar

region

turbulence

on

lowest

on linear corresponding

distance

of whether this the

increasing

no evidence the

the

frequencies

the

0.5 case.

the

same

a PSD

for

these

cases. Compare

with

the

the

once

1 configuration at

for

inches)

constant

inches). grid

even in the

over

relatively

content

-

increase

increased

as the

grid

energy

the

x = 18.3

and

higher

frequencies

With

remains

turbulent

two

at all

--- 8.3

may

stability. to the

All

PSD flow

indicate

that

three

figures

increased

over

is laminar the

distance. bursting,

bandwidth When lowest

-

the

which

turbulent

frequency

effect

remained

is consistent bursting

bandwidth

increased:

freestream

strengthens

where

relatively

occurred

frequency

In the

layer

with

for

of the

of the

for x locations

PSD

that

most

boundary

Also the

show

or tfirbulent.

buffeting

or pseudo-laminar

streamwise

frequency

the the

laminar

of turbulent

88.

there constant

predictions the

was at based

PSD From

Figs.

58

72

thru 60 recall that the rms of the velocity fluctuations increasedthrough the laminar region, increasedsignificantly during the burst of turbulence to a peak, and then dropped off as the boundary layer 1)ccamefully turl)ulcnt. Likewise, in Figs 86, 87, and 88, the value of the PSD within the lowest, frequency bandwidth increasedand decreasedin the same aforementioned manner. Therefore the low frequency portion of the power spectra is most sensitive to the changesin the rms of the velocity boundary values

of the

were for

layer. PSD

plotted the

versus

manner For

in which

unsteadiness layer,

Fig.

theory

turbulent

peak

between

to the

approximately

2-4%

can

the

be estimated

bursting

first

value

U e.

at

case

until

the

From

x _ 6 inches,

the

values

and

decreased

70,

x

59. and

Fig. from

the distance a

what

value

of

the

boundary

bursting

= 38.3

first

59 the

layer

occurred case

was

(i.e.

grid

turbulent that peak

first

From

boundary

transition

74 indicates

was

inches.

the

to initiate

in

reaches

within

bursting

Fig.

PSD

in a

streamwise

within

bypass

frequency

of the

86)

turbulent,

and

required

in which

a given

determine

turbulent the

89

of unsteadiness

velocities

for

Fig.

with

bursting

Fig.

the

59.

0 -

To

inches

where

74 and

that

degree

turbulent

of unsteadiness Figs.

for

(grid

begins.

Similarly,

88)

in Fig.

within

in Fig.

Fig.

increases

fluctuating

x locations

from

shown

layer

58.

shown

Hz increased

x = 34.3

of the

level

occurs

100

to initiate

rms

89 shows

bursting

70 and

clearly from

to transition

stability

to Figs.

87)

rms

boundary

somewhere

Fig.

Fig

the

corresponding

0.5 -

peak

is required

58 the

obtained

50, and

path

the

return

initiated

of 25,

T-S

with

case

is more

x distance.

within

accordance

this

as the

the

unsteadiness

observation

(in

frequencies

similar

level

This

fluctuations

bursts

turbulent rms

of the

73

fluctuating velocities prior to turbulent bursting is approximately 3-4% Uc. Likewise for grid 1, the peak rms value of the fluctuating velocities within the boundary layer before turbulence bursts occur is approximately 3.5% Uc. There appearsto be a critical value (0 3 to 3.5°£ Ue) of the peak rms of the velocity fluctuations within the boundary layer at which the breakdown to turbulence bursting occurs. This idea of a critical intensity of the velocity fluctuations within a boundary layer was also proposedby Elder [13]. Elder conducted an investigation to determine the conditions rcquire(t to initiate a turbulent spot within a laminar boundary layer. Elder's results indicated that regardlessof how disturbancesare generatedwithin a laminar boundary layer, turbulent spots will occur when the velocity fluctuations over most of the boundary layer thicknessexceed2°£ Ue. In this investigation not only doesturbulent bursting occur when the velocity fluctuations within the boundary layer exceed20£Ue, but when the peak value of the velocity fluctuations exceeda critical value of 3 to 3.5°£ Ue. Therefore, regardlessof the transition mechanism,once the disturbancesin the laminar boundary layer reacha critical value turbulence bursting begins. Why do we have transition via the T-S path for grid 0 whereas,for grid 0.5 and grid 1 bypasstransition occurs? The bypass transition case is usually consideredto result from large non-linear disturbances. Yet, in this investigation the bypasswas causedby relatively low disturbances (relatively low becausethey were on the same order as the disturbances associatedwith the T-S path transition case). In addition, recall that the boundary layer transition via the T-S path occurred from disturbances

74

inherent to the wind tunnel. For the T-S path to transition case, the disturbancesin the freestream occurring at certain frequencieswere received by

the

boundary

theory

until

turbulence

the

layer the the

case,

and

bypass

of the

disturbances

Although

the

grid

17)

0.65%

frequency

received

and

and

the

did

not

quite

the clear

freestream within

the

bursting

initiated.

value

of _ , was

the

curve, follow

is not

the

unsteadiness

turbulent

stability

and

case,

to transition

neutral

and

for the

and

The 0 case

frcestream

0.95%, are

for the

92.

grid

the

disturbances

these

value path

spectra

90, 91,

1 configurations

0 to 100

until

stability

reached

transition

layer

for this

frequency

Fig.

bypass

was

linear

yet

in the

linear at

bypass

stability

this

time,

the

is plausible.

in Figs.

from

the

reason

explanation

freestream

the

and

growth

shown

damps

critical

on

approximately

the

boundary

path

Freestream

(recall

the

with

unsteadiness

the

shown

following

are

For

the

in accordance

of the

range

the

theory.

level

reached

T-S

amplified

began.

buffeted

boundary In both

and

critical

bursting

disturbances

within

layer

largely

low

disturbances.

range

which

can

amplified

by

magnitude.

However,

for the

disturbances

within

the

the

The

was

whereas

0.3%,

turbulence

grid

frequency

0.5 range

region

However,

grid

of 500

intensity for

the

are

grid

to

1300

grid 0.5

0 case

the

fluctuations

within

boundary

disturbances stability

relatively 1 cases

the

was

of the

to linear

layer and

the

of velocity

viscous

1 configurations

intensity

For

be (according boundary

and

turbulence

composed

range.

0, 0.5,

freestream

respectively.

Hz frequency frequency

grid

layer within

theory)

small

in

the

freestream

Hz

(recall

this

is the

75

frequency range in the

in which

boundary

layer

approximately

two shown

disturbances

generated the

fluctuations that

grid

0.5 case the

PSD

corresponding

T-S

path

(see

Fig.

10 -6

path

and

layers

the for

path

to 0.65%

disturbances two

of the

within

orders freestream

freestream

of the

bypass

intensities

PSD

bypass

the

frequency

influence

For

only

transition range

Therefore, and the

not

a laminar tile

possibly, only

mechanism

the

linear the overall

for

via

the range

laminar

range

even

from

though

10 -3

values

stability

value

of boundary

via

of the curve

frequency

varied

distribution of the layer

to

the

for transition the

the

of the

Hz frequency

87)

0.3%

Also

values

to the

process,

of the

velocity

boundary

transition

a 500

So,

from

the

layer

for

(Fig.

for

so as to

boundary

correspondifig

range.

large

initiates.

example

layers

case

freestream

bursting

within

V 2 / Hz over

varied

the

disturbances

disturbance

observed

freestream

value

laminar

transition

for

critical

amplified

are

sufficiently

turbulence the

Hz frequency

of magnitude.

the

boundary

values

the the

1 are

case.

laminar to 10 -7

the

grid

that

level

than

and

curve)

Apparently,

within

the

be received stability

higher

and

10 -4

a 1300

turbulence

such

to transition

from

neutral

0.5 and

level than

should

0 case.

immediately

to the

range

freestream

by

T-S

V 2 / Hz over

T-S

layer

is higher

for

boundary

grid

unsteadiness

layer

86)

grid

by

boundary

the

to the

of magnitude

for the

is obtained

note

disturbances

according

orders

disturbances

overwhelm

the

transition.

the

CHAPTER

SUMMARY

A detailed process

via

the

the

disturbances

The

flat-plate

conditions levels grid

were

path

are test

for

and

Peterson

measurements

grew

law:

Baines

and

Peterson

agreed

with

Taylor's

turbulence. integral

Therefore length

scale,

rectangular-bar

turbulence.

that

turbulence

For

with

for

grids

where

each

with

_= 1.12

[26].

The

agrees

power

based and

on

the

frequency

In addition,

of freestream

measured spectra,

the

and

0.95%

4.

The

to the

following findings

spectrum

for isotropic

concluded

for grids

of

turbulence

of turbulence

the

of scale

length

freestream

values

for

correlation

experimental of the

test

intensity,

that

the

characteristics

0.5,

1 and

of

2 indicated

isotropic.

turbulence,

76

for grid

exhibited

results

0.5,

empirical

it was

conducted.

turbulence

grid

according

in which

ambient

Integral

power

turbulence

for

(_)-5/7.

spectra

[28] one-dimensional

and

4-6%

with

been

freestream

the

distance

also

is homogeneous level

agreed

transition

proccss

has

0, 0.65% 3, and

downstream which

transition

The

grid

Tu

layer

gradient

vehicle. for grid

grid---generated

isotropic the

[26]

layer

pressure

research

for all

boundary

in amplitude

zero

to be 0.3%

L _ _ (_)0.56

power

with

2, 3-5%

the

boundary

non-linear

as the

grid

intensities

Baines

to the

surface

used

CONCLUSIONS

to compare

initially

measured

1, 1.95%

turbulence

investigation T-S

was

&

VI

boundary

layer

surveys

of the

77

mean velocity and rms of the velocity fluctuations were acquired at several streamwiselocations with a linearized hot-wire constant temperature anemometersystem. From thesesurveys the resulting boundary layer shalx_ factor, inferred skin friction coefficients,and distribution of the velocity fluctuations through the boundary layer were nsed to identify the transition region correspondingto each level of freestream turl)ulence.

Also, the

intermittency factor determinedfrom time traces of flush-mounted hot films located along the centerline of the fiat plate was used to indicate the location of the transition region. The location of the transition region as determined by the flush-mounted hot-films was found to be in good agreementwith the transition regions indicated by steady state heat transfer measurements- Blair [33] -which were acquired within a similar wind tunnel operating under similar conditions as those associatedwith this investigation. Not only did the different methods in determining the transition region compare well with each other but they also were in agreement with predictions of van Driest and Blumer [8], Abu--Ghannam and Shaw [10], Seyb [34], and Dunham [35]. One discrepancy arosefrom these results depicting the location of the transition region. The boundary layer surveys indicated that for grid 0.5 the boundary layer was turbulent by x

= 18.3

turbulent from end would each

at

the for

inches,

whereas

x = 21 inches.

flush-mounted the

grid

be expected grid.

hot

for grid However, films

1 configuration based

A possible

on

1 the

explanation

the

was

an earlier indicated

freestream could

layer

intermittency

indicated than

the

boundary

that

factor transition

for the

turbulence be

was

since

level the

grid

not

fully

determined start

0.5 case,

associated length

and

scale

as

with of

78

the freestreamturbulence for the grid 1 casewas approximately twice that resulting from grid 0.5, the mean velocity profile for grid 1 could withstand a higher intermittency. Another result was that for the turbulent boundary layers the skin friction coefficients, determined by the Clauser fit technique, agreed well with empirical correlations of White [1] and Kays [29]. Attempts to calibrate the flush-mounted hot fihns for wall shear stress within the boundary layer transition region were not successfuldue to the thermal lag associatedwith the heat conduction in the substrate of the hot film [30]. In summary, the initiation of the transition region was identified for freestreamturbulence levels of 0.3%, 0.65% and 0.95%. At higher freestreamdisturbance levels the boundary layer transition was in progress at the first survey location. Simultaneoustime traces of the flush-mounted hot films revealed that for the lowest freestream turbulence level of 0.3% the initial disturbanceswere the unstable two-dimensional Tollmien Schlichting (T-S) waves.

However,

0.95%, and

the

the

were

starting

simultaneous

process

time for

bypassed

of the

via

to study

the

the (Tu

turbulence the

T-S

path

_ 0.65%).

and

compare

Once the

the

two

of a flush-mounted located

at

_ 0.3%)

different

x _- 40.3

the

T-S

detailed

transition hot

film

depths

was

finitc to

inches

to x _ 8 inches

both

and

were

transition

from

following

of 0.65%

disturbances

bypass

region (Tu

levels

initial,

of the

transition

identified

wire

and effect

were

traces hot

freestream

The

location

mechanisms

acquired

acquired

were

process

transition

transition

higher

in amplitude.

transition

bypass

the

waves

non-linear

move the

T-S

for

and

for for

bypass

measurements

mechanisms: and

a hot

within

the

1) wire

were

boundary

the

79

layer,

2) crosscorrelations

3) two-point positioned

at various

4) boundary transition these

correlations

layer

flush-mounted

between

a flush-mounted

locations

spectra

region

between

throughout

at various

were obtained.

hot films were performed, hot film and a hot wire

the flowfield

streamwise

were acquired,

distances

The following

conclusions

through

and

the

resulted

from

measurements:

The bursting

lo

of turbulence

was characteristic from laminar

layer

test o

of the boundary

turbulent

to encompass

and is convected

transition layer

flow behavior.

the entire

downstream

boundary

at a higher

layer

than

it is near

the

surface.

The convective

velocity

bursting

independent

in the streamwise

Two-point

direction

near the wall was measured

of the transition correlations

was a highly

o

explosion

to fully

appears

of the bypass

near the edge of the boundary

turbulent

o

burst

thickness

velocity

of a sudden

flow behavior

The turbulent

.

at the onset

random

that

with

the turbulent

no hint

Also, the characteristics

bursting

for both

path

to transition.

The

velocity

transition the velocity

fluctuations

occurred

the T-S

associated

at low frequencies

fluctuations

associated

path

with

bursting

of any periodicity

two---dimensionality. were similar

to be 0.7 Ue,

mechanism.

indicated process

of the

of the turbulent and

the T-S

the bypass

path

(0 - 500 Hz.); with

the bypass

to

whereas, transition

or

80

process The

.

the

occurred

low

over

frequency

end

development

contribution constant

frequency

end

flow,

increased

with

bursting

up

to the

decreased

as the

flow

became

frequency

end

layer

low

turbulent

high

range

of the

(0 -

10 Khz).

layer

spectra

depicted

in that

the

boundary

boundary

the

laminar

frequency

of the

of the from

for

a higher

50%

of the the

spectra

spectra

was

initiation

intermittency

fully

energy

of the

point,

turbulent.

and

then

In contrast,

increased

until

the

the

flow

was

turbulent. A critical

.

within

value

the

Once

boundary

the

value,

for the

peak

layer

unsteadiness

turbulent

rms

velocity

of 3 to 3.5%

in the

bursting

of the

boundary

initiated,

fluctuations

U e was layer

identified.

reached

regardless

the

of the

critical

transition

mechanism. .

The the

freestream case

via

process.

However,

the

according

frequency to linear

of magnitude.

These

results

range stability

the

for

the

freestream

disturbance

only

of the

the

influence

for

varied frequency

only the

the

0.3% the

bypass

would by

two

occur orders

distribution

overall

mechanism

value

the

importance

of the

frequency

spectra,

of of

of boundary

transition.

emphasize

for

disturbances

amplification

considerations

not

from

to 0.65%

values

which

and

disturbances

path

the

possibly,

freestream

varied

T-S

Therefore,

the

layer

intensities

of transition

transition within

turbulence

length

81

scale and rms intensity of the freestreamdisturbances in predicting the transition region. Clearly, more effort must be put forth to establish the effect of each of these parameterson the receptivity of the boundary layer.

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Bellhouse,B.J. and Schultz, D.L., "Determination of Mean and Dynamic Skin Friction, Separation and Transition in Low Speed Flow with a Thin-Film Heated Element," Joum_al of bTuid Mechanics,

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A.J.,

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Baines, W.D., and Peterson,E.G., "An Investigation of Flow through Screens," Transactions of the ASME, Vol. 73, No. 5, 1951,

27.

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M.E.,

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Klebanoff,

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Introduction

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35.

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87

TABLE I SUMMARY

x (in.)

OF

GRID

0 VELOCITY

PROFILES

0(in.)

H

R0

Cfxl06

ur(a/s)

Ue/U r

29.0

0.01484

2.629

716

571

1.647

59.18

97.5

30.3

0.01463

2.682

706

551

1.613

60.25

97.2

32.3

0.01543

2.680

740

525

1.565

61.72

96.6

34.3

0.01556

2.620

726

518

1.514

62.14

94.1

36.3

0.01628

2.550

772

524

1.552

61.78

95.9

38.3

0.01635

2.615

752

512

1.502

62.50

93.9

40.3

0.01803

2.536

835

609

1.627

57.31

93.2

42.3

0.01972

2.075

908

965

2.038

45.52

92.8

44.3

0.02179

1.783

1005

1487

2.532

36.67

92.9

45.7

0.02377

1.691

1101

1971

2.919

31.85

93.0

Ue(R/s)

88

TABLE

SUMMARY

X (in.) 5.0 6.3 8.3 10.3 12.3 14.3 16.3 18.3 20.3

O(in.)

OF

II

GRID

0.5

R0

0.006158 2.762 310 0.006946 2.735 350 0.008319 2.665 420 0.0100902.310 512 0.011941 2.079 607 0.014208 1.748 737 0.017920 1.642 934 0.020562 1.424 1079 0.0231911.408 1217

II

VELOCITY

PROFILES

Cfxl06 UT(ft/s) Uc/UT Ue(ft/s) ,233 1109 1070 1404 2143 2867 3934 4704 4569

2.504 2.370 2.333 2.680 3.315 3.929 4.627 5.093 5.023

40.26 42.25 43.21 37.76 30.56 26.42 22.54 20.62 20.90

100.8 100.6 100.8 101.2 101.3 103.8 104.3 105.0 105.0

89

TABLE

SUMMARY

x (i..) 0

(in.)

OF

III

GRID

1 VELOCITY

PROFILES

It

R0

CfxlO 6

U r (_/s)

UJU

r

Ue(ft/s)

4.92

0.006899

2.585

325

1302

2.542

39.18

99.6

5.84

0.007336

2.649

344

1198

2.433

40.85

99.4

6.34

0.007740

2.595

364

1178

2.416

41.18

99.5

7.00

0.008288

2.533

390

1129

2.368

42.10

99.7

8.00

0.008851

2.530

417

1073

2.309

43.18

99.7

9.00

0.009295

2.534

440

1172

2.423

41.27

100.0

i0.0

0.009437

2.565

444

1401

2.639

37.78

99.7

11.0

0.009876

2.470

465

1666

2.877

34.65

99.7

12.0

0.011414

2.269

538

1949

3.118

32.04

99.9

13.0

0.012120

2.156

573

2233

3.343

29.91

100.0

14.0

0.013598

2.016

643

2505

3.541

28.24

100.0

15.0

0.015370

2.094

728

2757

3.722

26.92

100.2

16.0

0.016422

2.023

777

2980

3.868

25.90

100.2

17.0

0.019010

1.895

902

3172

4.000

25.10

100.4

18.0

0.019595

1.868

929

3331

4.096

24.49

100.3

19.0

0.020797

1.826

984

3460

4.167

24.05

100.2

20.0

0.022632

1.774

1070

3565

4.227

23.68

100.1

21.0

0.024310

1.738

1152

3654

4.288

23.37

100.2

9O

TABLE SUMMARY

OF

GRID

IV

2 VELOCITY

PROFILES

x (i-.)

0(in.)

II

I 0

Cfxl06

U v (R/s)

5.0

0.00795

1.794

391

3395

4.120

24.10

99.3

6.2

O.OlOlO

1.663

498

3752

4.331

22.95

99.4

7.2

0.01349

1.553

667

3922

4.406

22.58

99.5

8.2

0.01348

1.527

668

5308

5.132

19.41

99.6

9.2

0.01604

1.499

796

5034

5.005

19.92

99.7

10.2

0.01768

1.478

878

4885

4.925

20.24

99.7

12.2

0.02167

1.468

1073

4590

4.775

20.88

99.7

14.2

0.02524

1.447

1254

4391

4.672

21.34

99.7

16.2

0.02827

1.473

1405

4248

4.601

21.69

99.8

18.2

0.03223

1.437

1605

4125

4.547

21.97

99.9

20.2

0.03589

1.421

1792

4016

4.495

22.25

lO0.O

Uc/U

r

Uc(R/s)

91

TABLE

SUMMARY

OF

V

GRID

3 VELOCITY

PROFILES

0 (in.)

H

R0

CfxlO 6

Uv(ft/s

)

UJU_.

Ue(ft/s

5.0

0.01046

1.515

531

5670

5.44

18.78

102.2

10.2

0.02079

1.444

1059

4693

4.964

20.65

102.5

20.2

0.03759

1.357

1916

4118

4.649

22.05

102.5

)

92

TABLE

SUMMARY

OF

VI

GRID

4 VELOCITY

PROFILES

X (in.)

0 (in.)

It

R0

Cfxl0 6

U T (ft/s)

Ue]U

r

Ue(ft/s)

5.0

0.01265

1.502

634

5445

5.267

19.18

101.0

10.2

0.02266

1.419

1151

4651

4.927

20.74

102.2

20.2

0.05518

1.330

2133

4124

4.692

21.97

103.1

93

TABLE VII

SUMMARY OF TRANSITION

Grid

Method

REGIONS

Onset

End

(in.)

(in.)

0

Mean

Profiles

40.3.

> 45.7

Factor

40.3

> 45.7

Skin

Friction

38.0

> 45.7

RMS

Profiles

40.0

> 45.7

38.3

50.2

Shape

Intermittency

0.5

Mean

Profiles

9.3

18.3

Shape

Factor

9.3

18.3

Skin

Friction

9.3

20.3

RMS

Profiles

8-9

> 20.3

6.2

24.2

Intermittency

2

Mean

Profiles

9-10

> 21

Shape

Factor

11

> 21

Skin

Friction

9

> 21

RMS

Profiles

9

> 21

Intermittency

4.2

_ 18

Mean

Profiles

< 5

u

Shape

Factor

< 5

u 10.2

Skin

Friction

< 5

u

RMS

Profiles

< 5

u 12.2

< 4

u 10.2

Intermittency

8.2

9.2

94

TABLE TRANSITION

VIII

ONSET

EMPIRICAL

BASED

CORRELATIONS

Onset

Method

Grid

ON

(in.)

Van

Driest

38

& Blumer
LLI a m

rr m a W N _J

< rr

0 Z

.o

I o 0_

o

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0

0

l

0

i

I

i i

0

0

i09

\

0

i 0

-

-

-

0

T--

0 A

0 00>

n

m

U.i Z _!


-

O

0

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>

o o

I

NI

N!

N[

gl_'Ol-X

O0_*_l-X

gle'_l-X

O£_*?I-X

000"$

STY°9

St_'L

St_*O

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N!

NI

NI

NI

Ni

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127

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(::)

0

C:)

=s

o \

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0

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Q o

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NI

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000"5

=X

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l c)

128

oD

\ >-

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C)

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C)

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C3

C3

C:)

C:)

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ad

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129

c.O

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= p_

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130

/

BLASIUS

/ C)

X_

X X X X X

8

(IN.)

29.0 ×

30.3

+

32.3

O

36.3

rn

98.3

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q

Fig.

33

Grid

0 -

plots

of y vs.

f'(_)

overlaid.

X_

131

p BLASIUS /

%

8 m

1 2

I 3

I q"

I 5

rl

Fig.

34

Grid

0.5 -

plots

of 7/vs.

f'(rl)

overlaid.

I 6

132

X

(IN.)

4_

7,0

X

8.0

+

9,0

A

I0.0

(D

12.0

[]

I_-.0 16.0

I l

I 2

)I(

18.0

X

20.0

I 3

I '_

I 5

n

Fig.

35

Grid

1 -plots

of r/vs.

f'(r/)

overlaid.

I b

133

I

,- BLASI US

/

g

n

Fig. 36

Grid

2 - plots

of rl vs. f'(_)

overlaid.

134

BLASIUS \ \

o

AI_

,¢

X +

X

(IN,)

g 4,

I I

I 2

5.0

X

10.2

+

20.2

I 3

] '1-

I 5

rl

Fig.

37

Grid

3 -

plots

of r/vs.

f'(r/)

overlaid.

I 5

135

BLASIUS 7 ! /

o

X +

X

g

(IN,) 5.0

,,,,',,1 X

I0.2

+

20.2

rl

Fig.

38

Grid

4 -

plots

of r] vs. f'(r])

overlaid.

X +

X +

136

BLAS IUS -,-,_

Q tn

U +

/

= y+-'_.

II

+

___-'_'-MUSKER 10..

0I

I

I

I

I

II1!

II

I0..

I

I

I

I

Itlf

I0.,

2I

[25] _ I

I

I

I

II(I

l

0,,.

Y+ = YUT/U

Fig.

39

Application velocity

of the for

Clauser

technique

a turbulent

boundary

to determine layer.

the

friction

3

137

_BLASIUS

I-,

II +

'_MUSKER [25]

mrrl

y÷ = yUT/V

Fig.

40

Grid

0 last

Clauser survey

technique station.

applied

to the

boundary

layer

at

the

138

Q_

/

_BLASIUS U+ = y+J

O

//_

II

//-

MUSKER[25 ]

+

C

o

I0--

I 0

I

I

I I1tll

l I

I0--

y+=

Fig.

41

Grid

0.5 -

Clauser

boundary

layer.

I

I

I IIIII I0-,,,

t 2

l,l

i I IIII I0--

yu.t./U

technique

applied

to post-transition

turbulent

3

139

O

....-- BLAS I US U÷ =

II +

RtJSKER

¢3

/ . 0,,,,

I 0

I

I

[251

I I I!tl

10_,,,

I I

I

I

I

I _11

10 ,.N

I 2

I

,I

I

I II_t

10.,,.

3

Y+- y /v

Fig.

42

Grid

1 last

Clauser survey

technique station.

applied

to the

boundary

layer

at

the

140

C_ LE)

C_ ,=1"-

0_-

1 0

J_

1

1 I III1 10-_

I 1

y+=

I"ig.

43

Grid

9 _ boundary

Cla, uscr layer.

techuique

I

I

I I III1 i0-

X

I 2

I

I

I I IIII 10--

yUT/V

a,pplied

to post-transition

turbulent

3

141

Om It)

u+ = y+_

BLASIUS r

I-'

¢o!

MUSKER[25]-,

II

\

÷

C

IO*N

I 0

I

I

I

I IIII lO*"

I I

y+=

Fig.

44

Grid

3 boundary

Clauser layer.

technique

I

I

I I IIII lO*m

I 2

I

I

I

I IIIl I0"*

yUT/U

applied

to post-transition

turbulent

3

142

C:3 m tt_

\_BLASIUS

..m

MUSKER

[25]

\ \ \ \

÷

0--

I 0

I

I

I

I llll I0,-

I l

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I

I

I

I fill I0--

y+ = yU.I./u

Fig.

45

Grid

4 - Clauser boundary

layer.

technique

applied

to post-transition

turbulent

3

143

o

•

_0

O

D

-

GRID

0

0

-

GRID

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-

GRID

1

-

GRID

2

+

-l-

O

O

b--

•

D

O

0

0o

166

SPANWISE VORTICITY

T/S

THREEDIMENSIONAL VORTEX BREAKDOWN

FULLY TURBULENT FLOW

WAVES\ I-I I I I

STABLE LAMINAR FLOW

U

I I I

i I I

i--_x

i

Re

0

W,EDGE

crit

CONTAMINATION

U

LAMINAR

I-_---TRANSITION

LENGTH

_:

TURBULENT Retr

Fig.

69

Transition

via

the

T-S

path

-

from

White

[1].

ueaw3/3

167

E 0 E

°_

0

j

_6

°'_'4

0

168

400 0

360

OBSERVED NATURAL OSCILLATIONS (SCHUBAUER AND SKRAMSTAD)

320

280 24O

I.D 0

MEASUREMENTS

2OO

160 r

THEORY

J

120

80

40

0

800

1600

2400

3200

R - U_61 V

Fig.

71

Neul, ra.I sl, al)ilil,y

curve

-

from

Schlichting

[5].

I I I I I

169

I I 4Z)Z)

I

o. 0

0 0

U 14,1

I--

o

0_

o

o o_

8 o

I

ID,-0_

170

.20

.4--

--

.3-/

,- Cr/Uoo

/

,2

8 U

0--

104

105

106

Uoo81 V

Fig.

73

Neutral

stability

curve

-from

Schlichting

[5].

|

I X

-i_i

_i-

1

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uEew3/3

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171

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ueaw3/3

172

r_

Q

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(WII_-lOH)

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=

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OF+POOR QUAI+tT_

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175

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176

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("NI)

177

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178

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179

A B C D E F G H I

16.2

O.lO00 0.2000 0.3000 0.4000 0.5000 0.6000 0.7000 0.8000 0.9000

14.2

0

Z < 12.2

.< a;

10.2

[..,

8.2

DISTANCE

Fig.

82

Grid

1 -

Contours

flush-mounted the

x-z

plane.

of the hot

film

(IN.)

maximum an

a hot

crosscorrelation wire

traversed

between throughout

a

A

W 0 .C 0 C m

N ]_n_nn_nnn_

]00000000000

0000000

0000000000

]00000000000

]

]

[]

[]

[]

[]

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[]

OF7[][]

[]

]0[]

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[]

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[]

180

O0

[]

I

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[]

[]

[]

O

N

N

N W 0 e0 m

X

W tO

0 0 -J 0

0 im

E

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m

0

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[]

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r_

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k-i

o

x:

,_.._

°_

I

bl

X

°_

o

181

19.2

A

0.1000

B C D E F (; H

0.2000 0.3000 0.4000 0.5000 0.6000 0.7000 0.8000

\ =_ Z

I,-,,,1

15.7

LIJ

LU k-¢J3

( \ 12.2 I

-1.5

Fig.

84

Grid

l

0.5 -

Contours

flush-mounted the

I

0 1,5 SPANWISE DISTANCE, IN.

x--z

plane.

of the hot

film

maximum

cross---correlation

and

wire

a hot

traversed

between throughout

a

,

I

v

I

if_ rr

I

t I

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182

e

I

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(L)

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186

ORIGINA OF. POOR

U

9

0

M_

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0

wN

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L r,_QUALITZ

(r) O--

-_

•

25

H.

•

50

H=

•

1 O0

H.

X

200

H.

_(

500

H.

•

1000

H.

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2000

H.

#

5000

HZ

.°

ONM

--_

ONN

--_

; / : /

/ 0

m_

--7

10--

-8

5

10

0

2

×

Fig.

89

Grid

0.5 disturbance

Streamwise amplitude

distribution at

selected

of the

boundary

frequencies.

)

layer

O

,,,,,,, I

0 W 0

r"