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FLUSH WAIL GAUGES IN CSCILIATING LAMINAR flOW Final l€clnical Fercrte i Jun. - 31 Aug. 1986 ~Iol>ia Stat.z Univ. of Science and

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RESPONSE OF HOT ELEMENT FLUSH i-lALL GAUGES

IN OSCILLATIXG LAHINAR FLml

Timothy A. Giddings and Hilliam J. Cook

February 15, 1986

ISU··ERI-Ames-86435

Final Technical Report (Part 2 of 2 parts)¥for Grant ~CC 2-200 entitled "Study of Turbulent Boundary Layers in Oscillating F1o\lTs"

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Grant Period: June I, 1986 to August 31, 1986

j i-lilliam J. Cook, Principal Investigator

J. D. Hurphy, Grant Technical Honitor, NASA Ames Research Center, Moffett Field, CA

*"art 1: Cook, l-l. J., "Turbulent Boundary Layers in Oscillating Flmvs: An Experimental and Computational Study," ISU-ERI-Ames-86~3!;,

February, 1986.

iovvo: state university COLLEGE OF ENGINEERING) ArvlES .. Im'IAJ 50011

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ABSTRACT

An investigation of the time-dependent response characteristics 0: flush-mounted hot element gauges used as instruments to m~asure vall shear stress in unsteady periodic air flovs is reported. The study vas initiated because anomalous results have been obtained from the gauges in oscillating turbulent flovs for the phase relation of the vall shear stress variation, indicating possible gauge response problems. An experimental investigation was carried out for flat plate lal:linar oscillating flows characterized by a mean free stream velocity vith ~ superposed sim,soidal \'ariation. Laminar rather than turbulent flows vere studied, because a numerical solution for the phase angle ~. between the free stream velocity and the vall shear stress variation thaf is knovn to be correct can be obtained. Gauges vith elements of two types vere mounted flush with the surface of the flat plate and tested over a vide range of reduced frequency w = ~/U. The two element types were a thin platinum film deposited on a quartzOsubstrate and a small diameter vire buried flush vith the surface of a polystyrene substrate. The study focused on comparing $ indicated by the hot element gauges with corresponding nUlilericaI predictions for ';r' since agreement would indicate that the hot eleoent gauges faitHfully ~ollow the true wall shear stress vari~tion.

An experimental study of velocity variation in the laminar oscillating flows generated vas carried out by ~cans of hot wire anemometry to verify that the boundary layer flows behaved as predict.ed by the numerical method. Good agreeffient vas obtained. Hot ele~ent ' gauges ",ere tested with the long dimensicn of the elament perpendicular to the flov for a range of operating resistance ratio, O~~, defined as the ratio of hot clc~ent resistance during operation to its resistance at room temperature. In the range 1<ORR~1.15, mCOlsured values for G) vere found to depend on W, ORR, and the type of element. For 1.15<ORR~1.30 there vas no significant influence of ORR. COfllparisons of 4> m-easuI:ed at ORR • 1.30 "'ith the corresponding predicted ~T revealed that~for the platinum film gauges, the experimental variatlon of the wall shear stress lagged the predicted variation by values ranging from 6±: degrees at W .. 0.2 to 16±3 degrees a~ w a 2.4. (Predicted values for .~ ranged from zero at w = 0 to near 40 degrees at w = 2.4.) The flush ,lire gauges 'Jere studied for 0.145W~O.9. Similar comparisons shoved that the experimental vall shear stress lagged the predicted value by 14!4 degrees in the noted w range. Thus, the conclusion is reached that the hot element gauge~ do not faithfully fOLlov the vall shear stress variation in laminar oscillating flovs. Ther~ is a significant time lag in the variation indicated by the gauges that depends on cAi and the gauge tYIJE. The results of this study strongly suggest that time lag in gauge response viII also occur for turbulent os~illating flows.

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TABLE OF CONTENTS

NOMENCLATURE

I • INTRODUCTION

II. REVIEW OF OSCILLATING LAMINAR FLo\{

A. Lighthill's Solution to the Boundary Layer Equations

B. Numerical Solution to the Boundary Layer Equations for ~ t

C. Hill and Stanning Study of Oscillating Laminar Flow

III. FACILITY DESCRIPTION

IV. DATA AQUISITION SYSTE:! FOR VELOCITY ;!EASt,;RE~!ENTS ..

A. Steady Flow

B. Oscill.ating Flow

V. RESULTS OF THE BOUNDARY LAYER STUDY

A. Comparison of the Experimental Boundary Leyer Results With ~umerical Predictions

n. Numerical Prediction of ¢ t

VI. DATA AQUISITION SYSTEM AND GAUGES FOR ';'t ;!EASUREHENTS

VII • RESULTS FOR ~ t MEA~, UREl'IENTS • • • • • •

A. Comparisons wi:hin the Experimental Results 1. Cor.:parison 1 2. Comparison 2 3. Comparison 3

B. Comparison of Experimental Results and Numerical Predictions for ~

t

VIII. CONCLUSIONS

IX. BIBLIOGRAPHY.

X. APPEX;:nX A •

XI. APPE~;DIX B

XII APPE~mIX C

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17

• 17

19

.. 21

28

34

36

36

41

41

62

67

77

85 85 85 86

89

95

98

100

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Not1ENCLATURE

bi

rate of decrease of froestream velocity with distance from

leading edge, Equation (8)

f frequency, Hz

ORR operating resistance ratio = R/Rf

p

Rex

t

u

U

u v

x

y

~

6

* 6

11

v

~

p

t

~

M t

static pressure

Reynolds number based on x, U x/v o

time

x component of boundary layer velocity

freestream velocity

variation of the freestreanl velocity, Equation (1)

y component of boundary layer velocity

distance m~asured from the plate leading edge parallel to the flow direction

distance measured perpendicular to the plate surface

pLessure gradient parameter for laminar steady flow, Equation (10)

b~undary layer thickness

boundary layer displacement thjckness

dimensionless normal distance from the plate surface, y~ o

kinematic viscosity

dimensionless pressure gradient term, b1x/Uo ' Equation (8)

density

surface shear stress

phase angle

diff~rence between two shear stres3 phase angles

'

-;:1 . w -,'

:'~:i

l:·~~

angular frequency, rad/s

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w Strouhal number, wx/U o

Subscripts:

0 mean value

1 variation

e experimental quantity

n num"rical quantity

u velocity quantity

t shear stress quantity

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1

I. INfRODUCTION

The capability of understanding and predicting the boundary layer

behavior in response to an oscillating or pari-odic flow is important in

a number of areas of fluid mechanics. Two of these areas arc

turbo~achinery flow and flow over helicopter rotor blades. A complete

boundary layer description would inr.lude the time-dependent velocity

variation in the boundary layer and the time-dependent wall shear stress

variation as functions of position on the surface. Flows in the areas

mentioned are very complex and as a result several unsteady boundary

layer studies have been conducted that deal with inccu,pressible

oscillating flews over plane surfaces as a first step in devl!loping an

understanding of their behavior.

A typical description of the freestream flow for such studies is

expressed as

U(X,t) _= Uo(x) + U(x"t)

(1) = Uo(x) + U1(X) cos wt

where U (x) is the average velocity, U(x,t) is the fluctuating velocity, o

U1(x) is the half amplitude of the velocity variation, and w is the

angular frequency of oscillation.

The time-dependent freestream velocity generates an unsteady

pressure gradient which, at a given x, varIes sinusoidally. I/hen U and o

U1 in Equation (1) are independent of x, the press~re gradient leads the ,

freestream velocity va~iation by a phase angle of n/2 [1,2,3J. The

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phase relationship between the freestrearn velocity variation and the

unsteady pressure gradient for this case is shown in Figure 1 with the

freestream velocity variation and the pressure gradient represented by

rotating vectors. Since the unsteady pressure gradient does not

coincide with the freest ream velocity, a phase diffe~ence is created

between the freestream velocity and the slower velocity in the boundary

layer. Lighthill [3] has shown for lamir.ar boundary layers that this

pressure gradient produces a velocity phase lead relative to the

freestream velocity in the inner part of the boundary layer and a phase

lag in tho outer part of the boundary layer. The ensemble averaged

velocity (defined as the average of instantaneous velocity values at the

same point in the cycle over a specified number of cycles) in the

bou.ndary layer at 12 specified x location is given by

u(y,t) = u (y) + u1(y) cos [wt + ~ (y)] o u (2)

where y ~s the distance perpendicular to the wall, u (y) is the mean o

velocity, u1(y) is the half amplitude of the velocity variation, and

~u(y) is the velocity phase angle relative to thu freestream velocity.

A positive ¢ corresponds to a phase lead. This is illustrated in u

Figure 2 which shows at fixed values of x and y the velocity variation

in the freestream, Equation (1), and in the boundary layer, Equation

(2). The velocity variation in the boundary layer shown in Figure 2

le?ds that in the freestream, but at other values of y, the boundary

layer velocity variation may lag that in the freestream.

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3

FIGURE 1. Phase relationship between the unsteady pr'~ssure gradient and the freestream velocity variation in Equation (1) with U Bnd U1 independent of x 0

'I

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== lJO

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u(t) = Uo y U1 COS (wt + ~U]

(y < 0)

wt--'"

FIGURE 2. Description of the velocity variation in the freestream and in the boundary layer

~

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5

As noted in Equation 2, the boundary layer quantities uo ' u1' and

¢ vary with y. In turbulent flows, the behavior of u , uI

' and ¢ are u 0 U

fairly well-understood for most of the boundary layer. However, there

is uncertainty about the boundary layer behavior near the wall,

particularly with regard to the phase anele ~. While the velocity u

phase angle in the outer part of the boundary layer can be

experimentally measured, accurate measurement of the phase angle very

near the wall is quite difficult by means of conventional hot wire and

laser (LDV) systems because of physical limitations related to probe

size.

In turbulent flow, direct t.heoretical prediction of the phaso angle

i& very difficult, so numerical and other techniques must be employed.

Cousteix, et a1. [4 J have attacked this problE:M using a :;mall

perturbation development with complex notation for solving the turbulent

flow very m'ar the wall. \Hth this method, they claim to have described

the behavior of the velocity phase angle near the wall for turbulent

flow. A sketch of their results is presented in Figure 3. It is

~vident from Figure 3 that in turbulent flow the velocity phase angle

appears to exhibit a unique and interesting behavior near the wall.

One approach to obtaining more information on ~ at small values of u

Y is to measure the phase angle for the wall shear stress variation.

The wall shear stress variation is given by

t (x,t) = t (x) + t1(x) C05 [wt + ~ (x)} W 0 t

(3)

.'

~ ----- 1'£1

:,~~

t~'l .'.'~ ., .,~ ,~:

,.

~tl

,~ ;;\ ~j ,~ ~

1 .,% ~

i J ,01

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t

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tJ ... (1 .1

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6

y

o -- <P --!> U

FIGURE 3. Behavior of ~ near the wall in turbul~nt flow as calculated u by Cousteix at al. (4]

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:1

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~ i ,

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ii II F.! t.·

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~~ - .; : t:

r. l ' ., I

~ i ; . T)J'°t

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'.""1 /. }-1 ,'" '7 r

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7

where to(x) is the mean shear stress, t1(x) is the half amplitude of the

shear stress, a~d ~ (x) is the shear stress phase angle. Lighthill [~1 t

he.s stated that the wall shear stress pnase angle ~ is equal to the t

velocity phase angle at the wall (lim ¢ = ¢ ). Y-+O u t

Thus, a measurement to

obtain ~ would yield valuable information about 9 . t u

However, measurement of the wall snea~ stress and subsequent

evaluation of ¢t is by no means simple at the present tim~. Surface

shear stress measurements in steady flows can be made with a fair deg~ee

of accuracy using shear stress balances. Acharya et al. [51 provide a

discus:;ion of the present state of the art in the development of these

ixlstruments. However, due to long respon~e times such instrume::lts ar'~

&enerally not suitable for measuremr.nts in time-deFcnJf.!nt flol~s. One

instrument that has been considered for time-dependent wall :;he/a str"s:

m(laSUrem~nt is the hot element gauge. Figure 4 describes a typ.L"dl het

clement gauge. It consists of a metallic ele~cnt deposited on the

substrate surface or buried flush with th;! surface. The substrate is an

electrical insulator and ideally a thermal insulator. TIle metallic

element is heated electrically by an external cir.cuit and t:he response

of the gauge is recorded by monitoring the cx~ernal circuit. The

external circuit is a constant temperature anemometer uuic l.rhich is

generally used to operate hot w i.re probes for velocity mea~:;urem(lnts.

The substrate surface is mounted flush with the surface en t"hich the

boundary layer is dev.!loped. The operation of the gauge is based on the

concept that the heat removed from the eauge by the flowing fluid I:;

, \

... \

~

. ", \

':, \ '·~''''''~J'''~~'.'TI.''r-.-'''''''~'''' "'''''''\ "-~\ ....... ",,'~ , .,

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. ~ .,,"). ..... ·ct

;~

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8

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':J. ::{

rolated to th3 local wall shear stress. For steady flow with uni.form

··,·n shear (1. e. , a lir.ear velocit.y profile), thera is a linear relationship

between the heat trans for from the gaugo .'md the ono-third power of tho

'.

"-' ~~ j '''~

~ :4 p ~ (j

r'\i " 1 J~i

':I t:. t~

t~l :1 I ~ l ~

'~l ~~, ,: ,.' .. ;.1. ,

,,';. " . . ~;:~

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local wall shear strass. In Qq~ation form, this relationship can bo

expro5sed as

q ,.v [tw/(a:{j) 1/3 (4)

where q is the heat loss by the gauge and a is tha fluid th3rmal

diffusivity. This relationship was dotermined analytically by Kalumuck

[6) using an order of magnitudu analysis; by Ling [7] using a similarity

analysis; and by Bollhouse and Schult:! [8} '.1sing an integral analysis of

the boundary layer. Tho heG.t trans f:~rI'\1d C:.way from the Rnuga is equal

to the po~er needed to maintain the gaugo :emp~rnturo and is monitored

for shear stre~s measurements. Calibration is acco~plished by placing

the gauge in n flow .. here the shear stress is known and monitoring the

power consumption for thll gause while varying tho knotm shear strClss.

This sounds six:-ple but even for stc(,dy laminar flow calihration must be

performed under condi,tions similar to those encountered during actual

use. A study to develop a comprehensive thrall-dimensional theory of hot

film gauges in stea.dy laminc.r flow has been performed by Kalumuck [6}.

Since these gauges are small, easy to install and operate, and

appear to have adequRte response, they saem to offer 0.1\ attrBctivn

possibility for measuring wall sh::Hlr stress in ull:>t(lady flows. III fact.

hot element gauges moun~cd flush with surfaces on which unsteady

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.... '\ ,~:;;.; L:,f l ':' '(_I I :~~ p' .

. ,,~ "':.~

Electrical L~3ds +

9

Thin Film Deposited on Surface or Small-Diameter Wire Buried Flush with the Polished Surface

polished Surface

Gl ass or Polys tYl"cne _____ Substrate

FIGURE 4. Description of a hot eloment gauge

~.

,~

.1 .~ '1 ,~ .~

~ ,,. "j

t~i l:;".'

, " .,~

t·i~ ;~i :\t '1~ :-J

I,,-~

;'J1 .'.,~

t.~:~l

rJ ;;.t·

I:!, ~ .... 1

I-~~ :;~~ ct:;! '?-..

~'£~ '."'./

::~

!~~,.1 "'! .~. .".

" ~~N' ",: ~,

, ~ ;" f:t ~. ., , '!-'. ";;1 ~{ I

.. 1 .. : ~.

"·~S • .w-:':J,~' 2.~: r:"'~To

.~ .... ' ~j~: :·fJ

!/:;, : ',:.:1 :;... ~~

t!·,~ f. '~l i)1 ~;): ',J. ::~;1 .".

,~:-~::t~~.:!;~·l"":'\"'-'.;~':~'\':-- ... -'.:...-.---.

10

boundary layers were developed have been used in at least three attempts

to measure ~ in turbulent flows. One study was conducted by Kobashi t

and Hayakawa [91. They studied turbulent boundary layers generated on a

flat plate which was oscillated sinusoidally parallel to a constant-

velocity freestream flow of air. Their results for ~ measur.~ments t

using hot film gauges show that the wall shear stre3S lags ~he

freestream velocity variation for the range of frequoncies covered. The

value of ~t also decreased for an increasing reduced frcqu£ncy

-* -* parametp.r, w6 /U where 0 is the average displacement thickness. These o

results differ with experimaDtal and numerical studies for turbulent

flow reportud so far in the literatura [12,131.

In another study, Ramaprian atld Tu [101 used flush mou~ted hot fil~.1

gauges to measure the wall phase angle in periodiC turbulent pipe flow

of water. For the two frcrtUe11cies at which data I .. erc available, the

measure,l wall phase angle It.gged behind their numerical predictions and

an estir,'ation of ¢ obtained by the extrapolation of 9 to the wall by a t u

significant margin. Figure 5 shows tho nwnerical predictions end the

experimentally measured phase angles from Rareaprian and Tu. It is cleal'

that for the two case~ in Figure 5, ~t values measured by hot film

gauges differ considerably from both their numerically predicted results

and results related to extrapolation of ~ . u

The third study is one conducted by Cook and Owen (11). They

genented an oscillating turbulent boundary layer on the wall of a

constant cross sectional ~rea test section opec to the atmosphere. A

.' ...........

1\~~\~~,;'::Ml~~'~~~1:-E~ji;·::\,~~:';;:±<i~~J;,'~;;·~,::)::;:..:q~;'~i],:-:?;~~ri"'~!~~~~~i;;:!.;·~;;X::;,j,if ~;;::~~it.;~;:.~}~~':~~A~~i;~~1h~~?'~:.i~~~4~:~~~;;'$2~~'/f';;('i; i·)~f.'·:2~:;:'::\~;I~;t.~~ . . . .' ~

~ ,..., d -. ~ .-1 1: " /-j.

~ 1.0 I- ~ ( ..

"j-;

0.8

0.6

1. r 0.4

o o o o o o o

Ramaprian and Tu

o tP , Measurement u

f = 0.5 Uz

o ~. Hot fil~ measurement T

-- Prediction

O.2~ \\ ]

I~I I 1 0.0 1-1- 010 20 30

-20 -10

cflu ' degrees (a) f = 0.5 liz

FIGURE 5. Phase angle reshlts from Rilmaprian and Tu (10) (r is lhe.: radius of· the pipe)

40 50

.... ....

• y. r; '1

" "

- i

I' /

~

" ~"

.' ~.F" -" .. ~+ t1L,,{",~.~~"":"~i~" ::k·'~;'~~:~~}~,\d'J4H;;-2 ~~;:;f;, .. ~·:t: i~-':"': :,\t;-;":;j ~·~i',(,:,J~·~\i~;: .. !\~:;L::'t-~~;-L.·~Y~~; ~';'fj~~}.!&.·~Ji}f:r.~i;.:"'d f.16:c::e;;~~::e::u:::::Yt~ ... _~:;e:z:::ct-.-.-- 1 h ': 1'.::f:L it 11~- '(t' - .....-~~

r .

y. r

1.0. 0 Rarnaprian and Tu 0

0 0 ~}u ~ ~iea3urement

0.8 I- 10 f = 3.6 Hz J

0 0 ~T' Hot film measurement

-- Prediction n ,. I .,.0 r

0.4

0.2

I I , t 0.0 0 ............... -- -- "- 50 -20 -10 o

CPu' degrees

(b) f = 3.6 liz

FIGURE 5. (Continued)

... N

i 1.

/ I

I

i i

..

'.

~

::-''-.'''W'l '.;,"i.i::JI

! ' •• r ~._ ': -Ot ~:;~\ .->f'~. ~ ,,-'t- .. ,~ .. " , , .. ;.. ~

~~(. \

~", .. , I ' ,> :':J :;~~ ,<,~ .

J' ;It ':1. \.

,:1.' ~ ~"'\o.,

I I

'I

I .~ .. -~~~~, \ J :~~'i;, ~

;l-; ~ '''V "~~

:~1 ~iII, , :'7 .. ,'-"

~i: '. ' 'i"" ::~ ~.

>:~:L~ :t,~f.;· t :;:::.' I ,::?\,

r. ,:~; I t ~.~ I I"· , ~ '.':; ! ! ':. I ~'" I '-.~~ ,< , -"\.< .. -,.'"

.. ~ !~i ~

f!~ Ft~ :~<'4-' , ~,,~ '..I."':.,,' ..,t .

~ \/ ~. ~. ~. ~I,l -. ,~.

~. A

~

~: '"J''': •

\'1-'-s.~'~

"<~ •

-r},,' '

~~.~. ~:." ;,1

~~I. I .~~'~:'J ,1 .0

ld~. "j' f.~f .

• '~ ,..n..-o)

;YJ .. i:1:"_.~,

j. :~',V

t'>: ... ,

, ~r'" .. ~.. '>:1" .' i'~~~

......... (:il4

13

platinum film gauge was mounted flush with the wall of the test section

at a fixed axial position. The wall phase angle was measured relative

to the freestream and compared to numerical results produced from a

computer code developed by Murphy and Prenter [12J. A graph of som~

measured wall phase angles is given in Figure 6 along with the

corresponding predicted results. It is evident that a difference exists

between the experimental measurements and the numerical predictions.

From the previous -:!xamples. it is evident that there is a

discrepancy between ~t measured with the hot element gauges and the

numerical predictions or the estimation of ¢. obtained by extrapolati~g

~ to the wall. Hence, it appears that the hot elemen~ gauge a do not u

messure ¢ corre.::tly. However, it cun not be sai.d with certainty that t

the hot element gauges do not measure tho correct phnse angle, bec.ausE',

neither the numerically computed ¢t or the ~. obtained by extrapolation

of. to the wall are known to te correct for turbulent flows. u

Extrapolation of ¢ to the wall is particularly difficult if ~ vcries u u

near the wall in the manner suggested by Cousteix et al. [4], Fi&~re 3.

Examination of the proceSses taking place a::: the gauge responds to

variations in the flow provides additional reasoris for questioning the

dynamic response of hot element gauges. The operation of a gauge is

based on the procuss of hent transfor. As noted in Equation (4). for

steady flow the heat transfer rate is proportional to the one-third

power of the wall shear stres!:. In unsteady flows. heat transfer is

still related to shear stress but possibly not in the form of Equation

/'

, ' ,;

/ " /' ~::' /' .• '!'

W'~--.---. --.

/' :t;.~

~1~~1 :~"':.

,JI', I -1(;,

\ . .'j I

'"; ~ 1 ,~,. I ~-:, . ';i i ,.' ... :,. ! ,~ , "'''J'

' .':~ . '~~.' ; .4. " ~} I .;i" '1 :'''''1 .'.',;

~.i .• ! ,~. I :~:.

//" r-';"" ! " . ~ .. /~ ';~f~

.....

:l

,

- I .'

.,. ",:"'

f,

(:;J !

;~- I '~:. I ~-:, t

".:. ! ~:" .• :

'\"~'f I

"~,"; -,.-1:

',{.~ ~ .... '.':;"

,.;.:.-;' ~~!

'~~>. ,~~':,

.. ~I ... ;:-.\

~:, .r. ..

,1 •• , ,.

~:. [;. iC

,1t" 1;-,' ";\~, '

";.;.:

l~~;: ' :~~l' ,,"

;:'''!: ". -.'

I:'~""

~t ; .::'1-

.,\'" 'It .....

4') ,~ . . ~... l

:-;'~' Ii '.}:.

. - - t.?Ll ;-,/,

.. ~'~:}A OJ" « i.~ , I

'i;~ ,~:.;,;,C'\ ~ll

14

20 r-r ----,~---_r --r- ---,-

15

10

~tt deg.

5

o

-s

-10

FIGURE 6.

o 0 o

o

-------

o o

Cook and Owen

~ I ~leasul'ement t

~ , Num~rical Prediction t

L. .---1-. ---' o 5 10 15· 20

f t Hz

Wall phase angle measurements for d turbulent oscillating flow by Cook and Owen [11]

25

•

f

.. ------· --.- .. -.------. _.-:j j

-I .;J

. -~- ... - .- -... ~. - --

15

".

~ ] -

1 . ~ :;-1

I"j '-,;Ii -~

" .-

1 I ~ i,ll

:1 (·1 'l

,,~ -, :.J ',j

1 3

I I

1 J

t]

/11

I

"{

I ti

'/11 ;' 1 ,... t

(4). Ideally all the heat generated by the hot element should be

transferred to the fluid immediately above the elem~nt. but in actual

use the substrate surrounding the element is a thern:al conductor. If

the metallic film or wire was perfectly insulated from the sub~trate it

would respond rapidly to fluctuations in the flow since it is very thin

and conspquently has sleost no thermal storage capacity. However, the

hot element does not act independently of its surroundings. It is

affected by unsteady heat conduction in the substrate which has a much

greater thermal storago capacity than does the hot element. This large

thermal storage capacity may produce a time lag and limit the response

of the systeo. Heat ccnducticn upstream of the element caUaes II thermnl

boundary layp.r to develop before the fluid reaches the element. Heat

may also be transferred f~om the boundary layer to the substrate

downstream of the element. As a result of all these factors, the

convective heat transfer and the conductiv( heat transfer are

interrelated and can not be uncoupled. The result is a very complex

multi-dimensional heat tran~fer problEm that involves unsteady

conduction and convection.

Dewey ~nd Huber [14] prasent a review of several studies related 1=0

some of the theoretical aspects of the response of hot clement gauges in

unsteady flows. They al~o describe a theoretical model they have

developed for the hot element gauge that includes the unsteady features

of its operation, but final solutions to predict the gauge performance

are not presented. The:r discussion-al~o suggests problems with the

dynamic response of hot element gauges in unsteady flows.

. ' -" .~/ .. /

~ __ ....:....o.. ... ". ........ _ • .\..~ •• h:"·"'C'-;~'=-~· -.. .• ........ (til' .'--_. __ ._---_ .... .... --~- .. ------- _ ............. -......... -.-. -..... ~- ..... ,.,-- ... -

';:~':i, . ;.\'; • I ;~; I ': .• ':- I Jr I

:JI ~j~ i .::-1) I c'" I , .... I .;.~ I ';.! l _.<", ,

~'I

E;li ,,,,~ . ;:} \ :~'i 1 ':,~_r

~S : ~:.t ~~ ""j ':':1 ~{ , ,( .. ":J \~] . :'; ~

" •• ;>.:~ '~ ... . '-~

~~:l "j

:{?t ;-,.} ;~J

\~1 ~ ::lj > .. /' f-

~.... f'

t-\ / . t~ , . ,< \1

--1 1

>, .' 11 r ).

'.

" ., :l

,';:

\ ./,

,t-o

16

It would be useful to test the performance of hot element gauges in

an oscillating f1o~1 for which unsteady aspects are known tdth a high

degree of certainty. Laminar oscillating flow offers this feature.

Accurate means are available for predicting the behavior of lamina::

oscillating flow, including ~ vs y and the value of ~ • u t

Thorefore,

this study deals with the testing of flush Qounted hot element gauges in

oscillating laminar flow. Efforts have been focused on measuring ~t and

comparing these results to predicted values. This approach to analyzing

the performance of the shear stress gauges subjects them to a crucial

test. If the gauges do not yield the correct values for ~t in

oscillating lamular flow then it can be concluded tha~ the eaugeo fai:

to perform dynamically, Le., they fail to follow the shear ut;:cr,s

variation faithfully. Failure to parfor~ proparly in laminar

oscillating flows would cast serious doubt on the usefulness of the

gauges for measureQents of ¢ in unsteady turbulent flows. t

One study in the literature has dealt with the use of hot c!lement

gauges in unsteady laminar flow. Bellhouse and Schultz [15J calibrated

several hot film gauges in oscillatine laminar flOH for measuring

fluctuating shear stress, but their work did not involve measuring the

wall phase angle to determine if the gauge~ correctly follow the shear

stress variations.

[f ~~

~":" ~.

, i.

," ),,'

.,.:-~

.~ .

. ' "

~

~~ .v t

~"I 1\ ,. ,~

., "f -".s,

? .. ~~

~.~ ..

,~ i. ;~ pi

'" ~ .;,- ft~ .- ~ ........ ~"":

y

i' ,1 p: ~~

... ---... --.... .-

".

i .J ., r

;1 . ':)

'i'L~ I . _

17

II. REVIEW OF OSCILLATING LMIINAR FLOVI

As discussed in the Introduction, this study deals with oscillating

laminar flow. This section gives a general over view of the

fundamentals involved and some of the analytical, numerical, and

experime1ltal work done in this area.

A. Lighthill's Solution to the Boundary Layer Equations

The boundary layer equations for incompressible unsteady laminar flow

over a flat plate are

au au ~u -+u-+v-= at ax ay

~.!:! + (Iv = 0 ax (ly

a2\\ 111:.+\1 2 p ax ely

where x is measured from the leading edge.

(5)

(6)

Lighthill [.3 J undertook th~ first analytical study ,:~r this type of

unsteady boundary layer. He considered small oscillations ab()ut a

steady mean velocity and represented the velocities by the fo!lowing

equations

u = uo(x,y) + cul(x,y)

v = vo(x,y) + £vl(x,y)

iwt U = Uo(x) + &Ul(x) e

iwt e

iwt c (7)

The oscillating freestream velocity given in Equati~n (7) produces

the unsteady pressure gradient ~hich is the driving force in oscill~ting

....

".

)? ).1

1-~t '\' ..• t~1

,:1

[

'11 , .1 ,. 1, .. " "

i

1 t ~

rl Id ~

4 ~l ~ ./

1 ! 1 ~

1 '11 ,-

~1 .. ~ 1/ '., . ,

1/\

flow. Lighthill considered only this case for which the precsurc

gradient le.:ds the freest.ream velocity by 11/2. This is the case

illustrated in Figure 1. There are other cases where the unsteady

pressure gradient has different phase relationship with respect to the

fr~estream velocity.

As would be expected, the unsteady pressure gradient plays a vital

role in determining the behavior of the boundary layer. As previously

noted, Lighthill has shown that this pressure gradient produces a

velocity phase lead relative to the freestream velocity in the inner

part of the boundary layer and D. phase lag in the outer part of the

boundary layer. Lighthill states that the phase difference in the

bound.ny layer is related to the magnitudes of the inertia ond the

pressure gradient forces. In the inner part of the boundary layer, the

pressure gradient forces dominate producing a phase lead, while in th~

outer part of the boundary layer the inertia forces are largest and a

phase lag results. Lighthill's solution applies to laminar osci]latin~

flous for which U1/Uo is not large.

Lighthill's approximate method of solution to Equc.tion (5) ,:md

Equation (6) restricted considerations to the lo~ Jnd high fre~uency

limit&. For the low frequency limit, the boundary layer equacions were

simplified and then solved by e K~rman-Pohlhausen method. The phase

angle and fluctuating velocity profiles were found to depend on the

reduced rrequency paran;eter, W = wx/U where x is the a:.dal distance o

from the leading edge c f the, flat pl:.te. The reduced frequency is also

.,

\

r;\ ~

>; ~.t ~

(

. -... 'j

I

~,

[~ ~1 , i

~

J.

r

, I ", f" • I ~[;'

~. ,/'

" /-, \'

, II I

'\

b:.

19

known as the Strouha1 number end is the characteristic frequency

parameter in oscillating floYT. Lighthill's 1m. frequency solution for

~ for laminar oscillating bouncl,ary layer flotl over 11 flat plate with t .

dU /dx. = 0 is shown in Figure 7. At large frequencies, the unsteady o

boundary layer equations reduce to the equatio~ for 'shear waven'.

Thus, at large frequencies, the boundary layer behaves as if it were

subjected ~o a freest ream which oscillates about a zero mean velocity.

Lin (16) also observed this characteristic of high frequency oscillating

flow. For this high frequency limit, ~t is independent of frequency and

raaches a constant value of 45 deerees. Lighthill's high frequency

solution is also shown in Figure 7.

D. Numerical Solution to the Boundary Layer Equati.ons for (It

Several numerir.a1 computer codes have been developed to solve. t:he

ll."lsteady boundary layer equations for both laminar and turbulent flo~;s.

Murphy and Prenter (12) have developed a hybrid finite-element finitc-

difference scheme which i~ second-order accurate in "x" and "til ana

fourth-order accurate in "y". ~lurphy and Prenter compared their results

for ~t to the computational procedure of Cebeci and Carr (17) and

Lighthill's low and high frequency asymptotic solutions [3). These

results are given in Figure 7. As can be seen from Figure 7, there is

good agreement between the variou~ studies. This demonstrates that

accurate prediction of ~t is pos3ible in oscillating laminar flow. The

computer codes have the advantage over the ~ethod by Lighthill in that

they can predict ~ over the full range of reduced frequencies. t

'~

.: '" ,: . "

- h~'1P?~~~k ~Y::;~~~:;{~~'j'~i;~\'2 ~?:~~:,:~,~)~ti!,)?;<:~~~~~~:'~~~~~~~~;~~:t}'yi/; (I'~~:':~::::~~t ;; '.:;'. :·.~L'~":'1·:~-t:~~ ,.~\;:!,~:::~:,,"~~~.·~;~~·~~!~~.~t~!~:!:7:~~~~~~~;:~:~~~~~~~B5iF ~ ."J

60

so

-1-00

0

0 ~oAo A 080 1\ 0 .0i o~-i1-i1-tJ-a-ll-00 ,8

or 4> , deg.

T

40 ~

l 30

o Cebeci and Carr

j 20

o f.lurphy and Prcnter

10 / I

o o

FIGURE 7.

1 2

w

La:'J Frequency } lighth~l1ls High Frequency Appro~lmate

I SolutlOn

3

Prediction of ~ for oscillaLing laminar flow over a flat t

plate with a zero mean pr~ssurc g:cdient 1121

1

4

N o

.' 1$ t~ ~ 'f. ." r, .. . ~ . , '" J' .; ~~ /~I

:.1 { ~ I

I,.""

f'~ • i,l

I

I ~

I; j' I· j I I" I I , ,. 1 • ,

~

.~

'\1 .. .0::"" ., .. (f,~~ ,d'

:?i!' ;< i,~ I -'i' 1; " I '.. I • ';:i I ~:, : ~

"I,

;¥S "1 :7 ;,.

,1' t ,j e '. l~

!'t ~, .. ,', .. , :'-!.i

~~.

~'\ i r: '.

)~. p.' ~.~

~~~~ \l­'-

t~~ ~,' .

I .... ! .~ ... i .-:-, ;l ;,r.-." ,~ . . ",

'. , . • :> I~,

~i, 1 ~.~ : :l . I .> ~. : ; ~'¥"1 ", , ,~ I ,!: j :~ -, . 1~'i

~L ~1. \

rr'~:'l . I ~, : ~'I )~~ , }.:.I .~

ift ~ i

~:1 -':t ,J~l ~;\-';'t -...tIIIII

•

21

One aspect of solving Equation (5) and Equation (6) for laminar

oscillating flow is that the solution is independent of the magnitude of

U1/Uo as long as the amplitude is not large.

C. Hill and Stenning Study of Oscillating Laminar Flow

An experimental and analytical study of oscillating laminar

boundary layers was conducted by Hill and Stenning [lSJ for flows with

both zero and adverae pressure gradients.

A laminar boundary layer was pr~duced on the wall of the test

section in a simple open-circuit suction-type wind tunnel. A hot wire

anemometer was used for not" velocity measurements. A sliding tb:ottle

valve loceted in the downstr.cam portion of the test section created the

freestream oscillations. The governing equations for the flows

devp.loped are givp.n by Equa:ion (5) and Equation (6) with a frees~reaI:l

velocity

U = Uo(l - t) + U1 cos wt (8)

where ~ ~ b1x/Uo is the dimensionll .~ pressure gradient t~rm ~'ith ~l

equal to the rate of decrease of frcestream velocity with distance fro~

the leading edga~ Calculation of t was carried out by applying Equation

(5) in the frecstream

.!~ p ax

= au + u au at ax (9)

,.,

.' ..

"~

I • •

/

r~;~'l -_._, ----.--, >i- --_ .. --

" ,~-.

'';~ ~~,

.~.i.'

''''\'r. \-< " ., )~ ~~

;"'.

',;:

"':1 "

" ~ ,of' ~

~~.\.

-r~ ~ l' -,

:t;'_ . '}'~ ~ "~~~ . ~ -;:

r·' t t. ~

,: ~ ; ~ .',

'''':1' .. '

( ,:

-. -:.. ,

f;"~l;

t· ~. ',,:: ;.:.1.:

.!.~. ~~ [~~.:;

I,' "..

", ,'" ~,:'.,:~

,:-1:'

t?'-~ -;: ~;: ''')'r ',,~~~ ", .. ~~ ." , ~ "1

-, {) ~. , ... ~~~j

:iil . . -~ .. ;;"'~ .. i-: , ,I

;,~:;~~j ,-,-,'"

'~'.' ... ,'

~\~~.I :.~

r~~ ~

22

Two values of the dimensionless pressure gradient term were studied; ~ = o and t = 0.10. These two cases correspond to Blasius flow and Howarth

flow respectively. The Howarth flow case reprezents a flot ... that; is

close to separation, where separation occurs at ~ = 0.12. When t = 0,

Equation (8) reduces to Equation (1) given in the Introduction. The

results reviewed here from Hill and Stenning will concentrate on ~ = 0

since this type of flow is similar to the one cansidEored in tho current

study. Velocity variations, U1/Uo' of the ordp.r 0.1 were used in their

study which was performed over the reduced frequency range 0 < W < 10.

Their results show thllt the boundary layer beha\'ior can be gro'Llped into

three classes depeudin3 on w. Theso classes aro low, intermediate, and

high reduced frequencies. The rE.n:;o of w in each grou? depends \.:0 soml~

extant on the Magnitude of the steady pressure gradient. For ~ = 0, the

ll)w frequency range is 0 < w < 0.6, and in this I'lln:;e Li&hthill's low

frequency theory was used to predict the boundary layer behavior. The

high frequency range corresponds to large vulues of W. In the high

frequency range, the shear wave theory should give 11 good description

for both the phase angle and the amplitude of the boundery m;cillations.

Since tho theory existing at tho time of tlleir study did not adequataly

predict the boundary layer behavi~r in the interm~diate frequency rango,

Hill and Stenning developed a theoretical solutio~ to cover the range

between the low and high froquencies.

Examples of e"perimental rosults of Hill and Stennin!; ~or t:hree

quantitic~ related to oscillating flow, u IU , u1/U1, dnd •• are o 0 U

r i

~ ~

t'; .-" ;'

" ~;.

~ \.

',. rt

...

~ ,. ~ .~-

f' ~, q

" ",'

c;;

~ k' " tj: .; ,"

r ,~

~'

f . ~~ .'. ~

f' {! >" ..

f '1'

I;: "

!: I,

r-'. J

I '.

i

~~

I t.

t ,. , 'r

I

~~ ;1

t

I . 1 , i

'-it L----.-.. -.

23

presented in Figure 8. Figure 8(a) compares their experimental results

for u /U in oscillating flow to u/U in steady flow, both for ~ = O. a 0

The' veloc.it~· ratio for both cases are plotteu against 'l\ = y-lO I\lx. TIle a

Blasius theoretical solution is also shown for compari.son. For the

oscillating flow u /U profile, III = O. 555 t~hich was tha only w for t.hich a 0

u /U data were available in reference [18]. TIle results presented in a 0

Figure 8(a) show a small difference betl.een the two experimental

profiles at the outer edge of the boundary layer. This difference could

be caused by a favorable pressure gradient present only during steady

flow operation, unsteady effects, or experimental errot'. However, Hill

and Stcnning state that the mean velocity profile ill o~cillating flow is

unaifectlld by the velocity fluctuations. Karlsson [13J ()bsorved in his

exporimontal study of zero pressure gradient laminar oscillating £101':5

that in o$cil1ating flow the mean velocity profile was not affected by

oscillations as leng as the fluctuutine velocity was noe extremely large

compared to tho mean velocity. Hence, it 1S generally accepted that the

u /U profile remains e~sentially the same for all W [13,18]. o 0

Another in~oresting characteristic of oscillating flow involves the

fluctuating velocity in the boundary layer. In the outer part of the

boundary layer u1 has a magnitude lar.;.:lr than U1, This is called che

overshoot and is associated with all frequencies in oscillating flo~,

Figura 8(b) shows theoretical and experimental u1/U1 vs n profiles

obtainc.d by Hill and Stenning for ~ = 0 and \J = 1.47, \.:hich is in the

intbrmediate frequency range. The intermediate frequency theory

,,' .~'

~<;,;C·it-... :"'/:' ';'};'t-""!;:.- '- :').~~: .. .'.. .. \, I ".', ,i> "':::"'-:""""', ., .... , "d 0, ;r,..:<J-~7: ¥ ••• ...., -,. w:. <.:.::r.:::~-:r-:::::;:l._.w.::....;;.~_,--;:r:"~~;:;-,-,-;"';""",",;,:~ __ ~..!!..:.,,,.;c:: .\ .. ,.! 1 ",""",-t.,~. +, '" •• -1<-. ',1,;:::.t7'J~ 1

1.2

1.0

0.8

, • I' i j iii i IT", 'j i , a iii i 'i , j » iii' 'i i' i , i» iii' I

+ y~O-OTlO-O-<>-<>

+ ",0

... +0.0

u/Uo +/0 ;/ u/u

0.6

o

0.4

0.2 C J+

o "rI"". o 2 3

n

o

Blasius flow Theoretical solution

uo u- • Measurement o

cd .. 0.555

.. U' 'le~slJrement Steady flow

4 5 6 7

(a) Compari:;on of :neon velocity prof! Ius for oscUlating flo;J and steady flow

FIGUR~ S. Experimental boundary layer results from Ilill and Stcnning for oscillating laminar flo~ liftj

N ~

ft ;f

r ; .. t ~ ,-i .0

,

!,

I i

-I j

I I

!

oj '_ ,4

oJ .' . '- ..

• '0'0 ""

rus~~;;;:~~"~{1'-,.i,/~~:,; .. ~1il.t.ti""·).;-ii.;~:I"'·~"'.14''!~~~I:~~~;~r~~~ih:l..J.·,~G.~:~~L.:.ll~!~~~~.!i~,,-~~~~~~~"-J\f.:~~~~~

1.2

1.0

0.8

u1/Ul

0.6

~ I 0

O. 4 ~ /

0

i I 0.2

o O-n-n_ 0- _ ~'--

o a ~~-o_o __ _

-- Intermediate frequency

Theoretical solution

w:: 1.47

o !.II II I Neasl!rernent

1

W :: 1.47 1 o " II I. I. " ".1. " .. "I. "",,1

o 2 3 4 5 6 7 i)

(b) u1/U1

FIGURE 8. (Continlled)

-.s~ ;r;,;;,:~;,~~~~~~~' ~~~~~t~·~"J':l:>~~}f ~t

t.) IJ1

.... " "

"- ' .. '. .4 " \

• ,', ' I' \ • \ . ____

['J:;\;;,: ~L 'S·::::·;"ii:;;;;:;..:.~~',~r' < ',' '" lei";'''; '"'-·;Ul.t~".:.';'.;,;" .. "\~ .,;,1 oJ "'.-'·:;::~J;\.li;G~ ~i.S~':.:.:.~J£:l:.G.0.;tf,~i/~a "::;';·"~:·~'iM~";:::·>}:~';1,1·1d,,~;,;:,:~~~,~~"<:~~,~'4l' ~.;.6;~ ~.'';;-:~''~~;'-~:';'I.~i]

a

50 r""""·""""'·""""··""""'·""""

40

30

If, • riP'l U -

20

10

o

-10

(e) ~u

t 0

(l

\ '0 o b

\

FIGURE 8. (C~IJt.inucd)

o

e

0"z o~ ,~ o .0

2 3

n

Intermediate frequency Theoretical solution

i;j :: 1.48

~ • Heilsun;ment Ui;j :: 1.48

~T.from Figure 7 at w = 1.48 Extrapolation of experimental results

---a

j 1

" " '" ., '" ,~ 4 5 6 7

N a-

! /

~/

!?';.. ..... BXI~l~.~':~;-t\~'~:_::.':-r-;-_l:::::-~:t:' " '.~~

. [it~ " .t~~-}:

':"J.:

"'- ..... ----_._'---_: ---_ .. -- -' -'-- ~~." . ~... ~~.. --

':,:'''-~'I'g~l' r - -. ,_ t\,1 ~

,;! .,

~:J'?-" • • I ft.~

~)o. i i.,,'t, ,

.:~;;l _;0:; I tSI i~' ~~-.7 ; ':~ --:1::1 ~.-"·I '41 ., I :~;. ; !'l

-'1..l '

\,;,'! I

~~~f. ! ':"'1'!

I (!~~·'I ' " , .;~

v' t::n (.'1~· ~

,/,- -:~~ r':!~'

'!.{ -.I-".~ J

(~;

f":: ;: . ". 't~ : -;t. ,q''''

':'I~ ~~.:..-_~, z' :~~~ :: t':;}-:' "'- ~.~ "I .~

'.

I

,'''' ...

!':C;~' .~y

, .... -~ .

'-.'.~" ·f .... ,',: ... ~\.k

("IJ~'

;1~;· :"'. :)~~, ",., -, '

, I. ;-,: .. ~~

:,r~i " . "}.;·1 -.... ~.

:f '.< ..' \t I

~al' ~ ".'f

;:~'-,C'J

?~~ '{~ -.. ~ > C

:'! .. -: ;' ~l

·:-~"i~

~.:.,~

:X~]

dl

27

provides a good description of the actual boundary layer behavior for

this case. Figure BCc) illustrates the behavior of ¢ in the bounda~y u

layer fer w = 1.48. The experimental results presented in Figure SCc)

confirm the theory provided originally by Lighthill which states that

the velocity in the inner part of the boundary layer leads the

freestream velocity and the velocity in the outer part of the ~oundary

layer lags the freestream velocity.

Hill and Stenning did not measure ¢ , but it is possible to obtain r

an estimation by extrapolating the experimental 0 data to the unl1 in u

Figure 8(c). Using this method, ¢ = 42°. r

From Figure 7, the numerical

prediction of ¢r at w = 1.48 i~ approximately 41.5° and has b~~n plac~d

on Figure SCc) as the solid circular symbol . This comparison rc:slllt~ in

good agreement between th~ numerical prediction and the experiment~l

es&imaticn of. and indicates that for this case the num~rical t

predictjcn of .t from Figure 7 is correct.

The results of the Hill and Stenning study provide confidenct1 that

oscillating flow laminar boundary layers can be generated that behave

according to theory. The next three chapters describe how oscillatIng

flow laminar boundary layers were generated and measured in the present

study. Also presented is a comparison of experimental results with

numericr.l predictions.

/1

~~ .

I

\ ;.;;~~! ~.,.~~

\~I~~! \:1

(~(t '1 \:.~ ; .':

, 't;f,i , 'I~;~ : :71' "} . ,r, , \ >~,

:':'., i~~ ~;'

r~~~~~ ~ ~tr

"~,l' /~ , ,-

::J I

:;'f' .'11

;·:~i": ~.:r'lf I I

ii d' I '-,,1 I

.... J~il· 1 -i.~.' !

d.: I :i;~t " ':'1.': I ~~~ .. :' ~.~ .~ := , -, ~ I ':~ : t,-.,~ I

t"';" . I <;( I )~ I . ..,)

- ';j;, I ;c::~; I .;:.: ~" ,-:~

-.- .' -' t~:~l

~

,-~'.o:: ,' ....

~t. 1:'

:-!., .

~'::f. ~~. !.\ ':S'·, ' -.::r:' • :y.

." L~~'

...

:t~ ~r~ ~r ... ;'i't ' ~. \'-

" ,~,;,-.: .~ r- , ~

/~':!r~ , r •. {jl..._, /. ' ,';:r·,

f -".:.,:1. ,

; ~:~.~~,,: J ' .. ~ .

. -.::+ 8t~ I, l'

./

28

III. FACILITY DESCRIPTION

\ \

The unsteady boundary 1aye1.' flow facility jn the Iowa State

University Mechanical Engineering Depertrnent was utilized in this study.

A diagram of the flow facility is shown in Figure 9 and descriptive

details are given in Table 1. For more inform&t:ion cbout the fa~ility

see Cook [1,2). TIle upstream end of the square const~nt cross-sectional

area test section is attached to the round-to-square entrance section.

The entrance section is open to the atmosphere. Located at the

downstream end of the test section is the convergin:;-divergine nozzle

and an oscillating wedge that makes up the wave-gener.a~ing mecnani5m.

Downstrea:n of the no::zle is a large. VECllu::l tank. To generat:& f l~)W, a

mylar diaphragm is first placed between the noz:;le exit and the tank. .

The tank is then evacuated. Rupturing the diaphragm causes [I,tmo:::pheric

air to flot~ through the test section and the nozzle to choke. The test

flow is terminated when the nozzle disc.harge regien pressure has

increased to thc point where the nozzle unchokes. \¥"\cn the \.-edge in th

wave-generating device is fixed steady subsonic flow will be produ~ed in

the test section. Duration of steady flew is primarily determined by

tank volume and the net throat cross sectional area.

The wave-generating device is used to create the velocity

fluctuations. It consists of a scotch yoke mechanism which oscillates

the wedge along the nozzle axial centerline and produces a sinusoidal

variation in freestream velocity when the ir.put sha:t is rot~ted at a

constant speed. Hhen the wedge is in the fully dowfos-.:ream position, the

\ \

. - \ ----..... '\ " ---...- - - .

~r~~' \D

t.~ .. ~ ':., .~ .

.' \ \

\ \ . \

'. \ '\

, \"'-, '.J "

". . .... , ( ./' .,."!.-'I',~ ~Ui..1",,:.,· .J),' !b jj~ Wtl ' :"::."':· .. l'W.'~ "';:='!~L·...,· ~~".~.; ____ ~.h .. :c.:.';'30-~~~~_!~~ ~!? . jf, ry" ,g :r~ ':Zj;::j ··:;:Ut:~~ -'"t; .. {~hl

,Entrance Section Test Section Generator Section

Hot Wire Probe

1 "

FiO~ "

·rPleXI91aS Test seC:IC:lr Aluminum - Wave r /' tlot ElE;f'lcnt Gllugi! I

,--~;:-----::::-~r' ---, To Vacuum ( ~ I {~_ - L'

\ . \screens I Plate Position

Honeycomb J 0.21. I ,,,' S"",, 7.5 ~, 7.5 ~ I 0.2C7f- 't$ NOTE: /lot Drawn to Scale L£." 'I

L - 0.318 ell 0.22 I!I l

Plate Position 2 "lave Generator Section

FIGURE 9. Diagram of the oscillating flow facility nnd test section configuratiolls

N \D

/'

\

, /", , /;' '

"';''''­,'.t'. ,~

'> ~ ..

??;~1' v ";l' .' t'd)" . ~~e.: I

~y," I ' " , f ,- ~:-~"t'

'i ~I"':}! ,~.~ 'I _.:;;:; f

. J .. _. :-.:f' : /'\ :,-;~, ! ,/ ,,~ I

;;'~"l ; , '-'F. • '~<4,f

I "'~:'(~. J : I.:f;' t

t'!i ~ r:~ ! I.:,j I f:';t, 1 '."t". I "'1\' ~. v •

" - ~~. f

r,t':ti I: -:},-'..J/ i

'. 'f~/t"1 I ;,'·:.'i I I, ~, ,,:;~ I

' ,~

l"'';-I ','-'

I' ::,: · ,~ .. t! (t~i f :'i~ ! t .. :-:. : ~<;.\~,

. 1'C\'b' ,/.. '~:;-l: .. : ~ .. ~ .:

~~;J ~:r·,l

'li":1 \' t~r

.'

, I

/~{ ~ l-°li. ,1 ___ '","·

·t. ~'>',!

~~~~J

:'~;1 .",' ".",.' .'~:" '. \J

/.".]j '. ,,: ... ,-- '':1 ... ~. .

. ,/ ~\. , , , ~

I > '. .~ t. ,,'

. > ~ / '~

30

TABLE 1. Description of the facility

Plexiglas Test Section Length Width Height

Entrance Section Honeycomb Cell Depth Scre~n Solidity Ratio/Per Screen Contraction Ratio

Tank Volume

76.2 cm 7.5 em 7.5 cm

4 cm 0.3 12.4: 1

2 m3

!, ,:' /

wedge tip extends upstream of the plane of minimum cross-s~ctional area

of the nozzlp.. Changing the wedge position changes the effective souic

throat area, thereby changing the mass flow rate. Proper shaping of the

wedge produces a sinusoidal variation in the freestreom flow suparpos~d

on a constant mcan velocity when the nozzle is choked, A sinusoidal

frcestrelm velocity is obtained over a wide range of frequencies. The

frequenc~ for the present study was infinitely adjustable between

approximately 2 Hz to 30 Hz.

Two low speed flows were produced in the tcst section with

frecstream velocitics of about 11 m/s and 17 m/s. Thc two freestream

flow conditions were created by two wave generator sect.ion

configuration3 which are described in Table 2. For this study. throe

combinations of the plate positions (Figure 9) and wave generator

section configurations (Table 2) .!re used. These three combinations

, 'Ii:' / " ' ~i:1 , ~r :::,!~-- - . -------_j_- '14!,~

.', ----,------------'-- -

'j' ,:

/'

,

;i~l I

I~ff'

I ~, .. :',

\ ~f' t \ ;''1 .1

'} I " . f:~; !

."1"

.~,

:"'-~tl

::$' ~~~ '\~:'J-. ) ... J;-. ,

~-t~ 'j ~-;r ••

I:/~} .. ; .• ~ ~ , .!

,,] v,'· ."","':r'

.. ~.~

.-;~ ! 7'~1

,,-~IJ

,iL m': I

~ih

/ ~,~:~l--: ,Ii' ;l~~;~

I

• j \

{S: -if'S! . -:.:,

3 ~~ • . ,,:,;;;

~ ~\~-, "

,j~ "' ~ ";. .",...'" . ,-• t-, ~ ___ •

"" . .'\,;." , :~·t " ~{''''T

:.1/: ('R··'

'1':".; I , .~-. f

.... '~' '. -,~,

::'~'". . l"-'

~7~' " I':~: , t~.~~, !

~~~~t ; ,;: I ;t~'.·

,,.~;Yl . \ I;~~ ! '/ ____ ,~l:·l

: ':"'; ~'i J' • r';" i , . ·:~~.t

, '~~j ,,~,

I,

-{I

'~::"'~" :.,-,./ ~~~.:

:'{ .' l'~>~~~

'~~i"! :;{1 - .. ~1f.

,- )).-('.'$<' ,~·g·v , -~'l'~

" J ; ..

:31

are described in Table 3 and will be r~fcrrcd to as test configurations

TC I, TC II, and TC III. Table 4 tabulates test configurations in

relation to the experimental cases studied and will be r€:fet'rerl to in

later chapters.

TABLE 2. Description of the w:ve gencratol' section configurations

Wave. Generator Section

Nominal Choked-flow

Configuration Stroke,cm

Wedge half

Angle,dee· Run Time,sec. U ,m/s o

A B

0.6350 0.6350

SAt low frequencies.

7.0 7.0

10 15

TABLE 3. Description of the test configurations

Wave Generator Test Section Plate

Configuration Configuration Position x, m

TC I A (Table 2) 1 (Fig. 9) 0.12

TC II A (Table 2) 2 (Fig. 9) 0.22

TC III D (Table 2) 2 (Fig. 9) 0.22

aBased on U • 0

A .10" _ ....

16.7 11. 7

Re a x

1.34 :( 10

2.45 x 10

L 72 x 10

5

5

5

u /U a 1 0

0.13 0.19

II

0.10

0.10

0.16

/ I

!

!{

'" ," '~

t~~' -r " ~}'

, 'i~ }

/ ~II '" 1--

J, ,.1,' .;

, ;! 1

.-" f'" ~ .~;

'. 'Il . • --I

, ~ ,~ . :1

,Ii

t"~ "~I / ;! .n

~. ~}1

,j ~l

'~1 r fJ

,"J '-:)'lC , I '

/

':j

" ~ ,I ;'J ·~l

[_.ot,

'51 'f::~S . '- . :,j.~

J :;1 ,< "~ ?j" \j " ,!~.-

<"i ~.'

"

~~

.:',.' .... -- r'" :' 6'>,

J lii~

\

;' ./

" /

32

TABLE 4. Experimental boundary layer surveys

CASE DESIGNATION PREFIX A - Wave Generator Section Configuration A, Table 2 n - Wave generator Section Configuration D, Table 2 C - Steady Flew

TEST

CASE CONFIGURATION f,Hz -a c.J

Al TC I 10.00 0.45

A2 TC II 3.00 0.25 A3 Te.' II 5.58 0.44 A4 TC II 10.00 0.78 AS TC II 15.00 1.18 A6 TC II 20.00 1. 59

Bl TC III 3.00 0.34 B2 TC III 10.00 1.19 B3 TC III 20.00 2.38

C1 TC I C2 TC II

8i:j is based' on the rnaasund value of U (Appe~.dix A).

0

•

" ,.

j../'/

~:~

" t~ t~

i) Ii. ','" '-,. ,

... -""

" . i; (ff

I J'~ I '0

I ~l ... i;; .1 !

/ ;

:'

/"~~1 / . I ~ ,

~,

;~. !

I • i " tot: \. <

; It: - _p1,.

, ,,,," I~' r) J..-

h , 'h

I .

t ';.

,. .-:

. :~ - -..: c<~ I

't

~~ . ,

~ . f: ".' ~~ I 'i ;,

.'). "

,,' t~ ..

I ~,

/ F. / ~:

I r: • t P ..

/ ;' /, I~;'

I • i/ ' ,I

,,/i

"

.5

I

./ , ' \

33

A flat steel plate with an elliptical leading edge and a sharp

trailing edge was installed along the centerline in the upstream part of

the test section. The plate surface and leading edge was polished to an

RMS finish of 15 II inches in order to ensure laminar flow. Holes were

drilled in thB plate at distances of x = 0.12 m for plate position 1 and

x = 0.22 m for plate position 2. This permitted thE\ hot element gauges

to be installed through the bottom of the test section dnd flush with

the top surface of the plate. When a hot element gauge was not

installed in a probe location, the hole was filled with wax to mjnimizc

flOH disturbances. The hot element and hot toTire probes were placed

centrally with respect to the side walls of the test section. The hot

wire probe sho~,m in Figur~ 9 was used to measure the velocity varicticn

in the boundery layer. All measurements for the boundary layer analysis

/lnd wall phase angles I/cra made above the plate.

. "" ~-"~---'"-----

, l~ , ,~

.--'- ~ , ,;-" .~

/

:'~i' ~,'1 :'--:

::;1 ," ~:~

':~~ ~ '~;

~,~

'.<

I, ~.

,,~ ~

'1: , ! ~ t:~,~

~ .:.,~

~ ~1 ,;~ .,~

) ~ J ~ o 1 ~~ 1 ~

! ~ .~

~ 1 ~ t-

. [1 " l !, ,

i

I I }

f

34

IV. DATA AQUISITION SYSTEH FOR VELOCITY NEASURE;IE~'TS

Tt.o basic instrumentation setups were used for this study; one for

measuring fre~strea~ and boundary layer velocities by means of a hot

wire aneClometer and another for measuring th€.: tlei.! r>hese angle using the

hot element gauge. The former will be described in this section.

A diagra~ of the instrumentation used to rn~asure velocities is

given in Figure 10. Velocities in the test section ~/ere measured by a

constant temperature hot wire system. A single channel anemometer

maintained a Disa P14 hot wire probe at a constant tempp-3ture with an

operating resistance ra~io (ORR) of 1.B. The ORR is de~ ed as R/R_ r

where Rf

is the re~istance of the hot wire at the fluid temperature end

R is the operating resistance of the hot t·lir~. The term o'!",r heat rilt.io

(ORR) is often used whcr. describing the operatio:! of hot wire

anemometers, where OHR = (R - Rf}/Rf

. The ORR and the olin are ::cl:!t:cd

by the equation ORR:: OHR + 1. The signal out of the anemometer ~ras

linearized and then sent through a low pass filter set at 10 kHz to

eliminate the high frequency electrical noisp-. An AID ·Joltmeter was

then used to convert the filtered signal from analog to digital form for

computer processing. This basic procedu::c for measuring vclot;ities I:as

used for both steady and oscillating flows.

Calibration of hot wire probes ~as done outside the test section

uo;ing a TSI model 1125 air flow calibLutor and standdrd celibratjon

t(;chniques.

~:;;-~-_~_1-"""'_-_______ . ~

.. ,

:,.--- . ----~i.' .. i'L~~\t."''''cl!.40.~~ ,: ':;5;':1:: I Jh't1. .. ~.:t:s; __ ·_ ... ,_~S •• _~,"" r.-..Itr::::::;;a:;c.,-~.....-.'!.<>#,::;:;:4!X=C:a:.S4jt"4A,-,'t~*t. s::;r.....-~:';'*1t ;.:-./.+;49," Cr. 2i( .;=;t ~, 'l" t .. h! l t t .,.-. ,HC k ," J'r·.~. ""\;(1. ''t.t';1

! j

<I ,

-, ., ,'1 .j .j

" I .1 I i

DISA Type DlSA Type 55001 DISA Type 55025 A:lerr:ometer f-t-- 55010 I-P Auxiliary Main Unit Linea.'izer Unit

I (Fiiter)

External trigger, one per cycle

Hewlett Packard 3437A

~ . AID Voltmeter

J Osdlloscope

-->- j DISA P14 Single-wire probe

Flow c ~

~ Flat plate

~ =s

FIGURe: 10. Data' acquisition systc:r.l for vdocity m:!3surcments

Icorrmodore Computer

f-P System, f.1achine language Prograw.med

i I

!

J

w VI

1;<-'

" '.

' ..... ~ :~'~

:.:.~,

;"ll

.5~4:

:_~ci·~ .. ':').-

-. "-..r~ 3:­<~ ..

" ... ". ~ J. ,~:,: .' - , ~~ -,;

'I',:' ;

, .. ~ ~_l,i

~~-':~ " <t~ : ~ f,} r::)i. : ~;1

[~~. . ' . " -:', ~

. /'<;1 . I: :.,.:~ \':3

I'.:'" , "1 I'~·l

. __ .~{:'~i :~:~~~I ~ I-~.

rtf, '. y

• -~~ or I [ ., 'I f, -,J ,. ,·1 . '.~ I

'{·Jl ," ,J'j ..... ,!-;-.. J' ~

-~( ; ~ ,::.' ,:"

'::";~I ; I':':~:' ; _ ... ~.'" ~-'r I ., ~ .,... 10.

, '~l" . '.. . ..... ~'~~ •• ,,0\,_-

"

" lo'} :

t

~~:,~~} '~-:~.~. ~ ':. ·}.l

" ~-

:;,~ ,',;.'-"',

·:,:·;:J1·

L>",> ~.,,~ ,.~

~~";:J '.;'1 1

H~:c~ ~'2~

36

To traverse tho bout\dJr~' layur. a hot wire prabo positioning

.'1ec:hanism built around d micromt)tor enabled the probo distanco from the

~.~te to be ndjusted.

A. Steady Flo~~

Whon stoady flow VQlocitiEts tiare bein1t rueasurnd tho weds\) in tho

Navo genorlltor soction, Figure 9, WIlS locked at midstroka. Voloc.ities

in the boundary layor surveys woro then measured by taking 500 voltage

readings OVer a 1.5 second time interval at each y location selected .

Using this informa.tion dnd J. provio\!~ hot wire calibration, the 11\'orl1go

volocity and RHS voloci'ty \~QrQ evaluated by tho compllt::::- f .. )r Elach data

point in tho 3urvcl.

n. Oscillating Flow

Oscillt:.ting flow roquiT.Qd 'Che wedg~ to bo u~ivon at a kllC!~n and

conntaut frequoncy. A variaulo spoed electric motor and a fl>"lo1hllcl

provided tho constant sPQQd while an EPU counter in Cc..I.;unction with an

optical pickup monitoNd thl) spued. The erro:: in speed ,''us estimated to

be ± O.S porcout .

Tho sanlplins \.,·."S inltiatod by .1 oncc-per-revolut.ion t::igger sant to

tho voltmottlr (Figura 10). This sigMl WllS initi1!t~d by .!l magnetic

pickup in association with a 3tccl part conncct~d to the wave-generato::

drivo SlHlft. Buforo tho sisnal was :ient to tho '11'0 1 trn\~tcr. it \.a5

conditioned and arnplifiud to provide an appropriate trigger signal. Hot

'.

i: ~'''1' '~',~ ..... "\

;,1~

:'{~~ 'i "i !., :;~, ,

~,I" I ,~(: \ :"~,' . ';-,~ " I

"'\" : .... : I ;'':t I

':."~ , ·:d' '~

; .:t -.. .... .;t'''~ \ ',t '\ -#; I

F.,C<, I' ~f~~ • ~ ....... . :-:;. "t1 1'~~

~~, :~1 1!. , '~t;.r,;,

:~,~;,. -i ~ .. -;, . (','l.

,~~~} I",,, t.': f£ ,,,

,~-. •• .J .;

~1.~ '~Ji '.'1:":1 .... ,'~

}~

l' :;\' ;;..', ~,.

ri~"

r

t;1:':, " , ~?~ ~ ' • .1;. ~~. \~~~.

~i~ :""~

q' ,'r ~ ~i~~~ :}', ,

ri{f

~}; v,

fj' .. ~~ .. :~>

;i;1,,:~ of" ~ ... .,)"'~ ,.,.} . -:1; : I

-'l~ ... ";0

<~~i.~ I

0' 1'; " • l~}>r~'"

,f;t'.·~ . ~J ' tL,~

t:-lr~', ~~i...v...:tf'

-, ,

37

wire voltago readings I.;oru takon llt 20 I!ql~lllly spacod time inttlt'vals

over the period of each cycle of oscillation at a givnn y location •

Each of these 20 voltagos per cycle uas onsemble avoraged ovor a number

of cyclns. TIle total number (If cycles was dntcrminod by tho. run time of

the facility and tho period of oscillation. For frequencies of 7 Hz and

less, the voltages woro onsemblo aVl1raged over 10 cycles I,:hilo the

remaining frequencies l.Jore ensemblo Ilvoraged ovar 50 cycles. The 20

~nsemble averaged voltages were converted to velocities by usa of the

calibration for tho hot wire. 'fhe mls velocity vari'ltion at Qach of the

20 points was also cbtained. A cosine wavo was thon fitted to the 20

ensemblo averaged velocity valuos to yiold an ~xptos~io!l for ~he

velocity "oriction of tho form

u(t) = u + u 1 cos [wt + ¢ ] o u

Figure l1(n) ~;hows t:ypic.,l osciUoscopu rocords of hot \,d,!'~ ~igno.Js

obtained with the probo -in tho froestl-cam ..Inti in tho boundary layer. It

is evident from Fit-ure 11(n) that even in tho b(lundn=~' layer the hot

wire signals are relatively clean. The RHS volocitios varied from

approximately 0.03 mls to 0.09 m/s. This corresponds to apprQxirn~t~ly

0.4 percent of tho :neU:l velocity. Thesa oscilloscopo rucorus illustrate

that a laminar boundary layer is present in the test section. Tho

values of Ro in T..'\ble 3 also indicato that a laminur boundary loins x

present . These valuos rangQ betwcon 1.34 x lOS and 2.45 x 105•

Transition from l.l~inllr flow to turbulent flow ovur a smooth flRt plate

occurs in steady f~ow at Re = 3 x 10° [19J. x

!

...

.::~~~ ~~~~ '. i',~~' ~. ~ ;.'; .. -j ·l~· .. ,pi ~ .., :\i' '5~ . \ '~"J " I )10 _ \

· ,. 1"'':;;-

",

.\~ ~.

,~ )\

",' ~:;t · .. ~ .. . -.,. -.,~~ "" f\~~

.. f~~' ! ·H:

't" .;j

\ t·,' . h>'~ [' .,~,

.\

::.. ':.~ . · .' , ~-"I~

t:'! ,.

tt,,}, "-~'l .... '). .,:

:~~~ ... ,.~

I;~;~;: 1 ..... a

'-­".~

~' .~ . ';)

t·:~ ' .. • ;0;,

I;~r: , ~.: ~<'. ~ ~-I";

¢{:~ !"~. ,ift'"

'f±~' :r::"

:~ . . ::~: i~t~,

:~, ,. :'1 ':-{~ ,;r" , .J,

"",\, -~-::.\ ...

J. ,.~

~l€' . ~~'

~~ ~ ·,:i ~,'",

':~~ ... ~~

:t· ';... ~~.~ r ;;11 • :(.?:~t;'. ";j" ,

&Jl I'-·~\J'..;\I w,:~

.-"

.. '.-.....~-'-.-...... -.,---... --..... -.... -.. -.. ------ .. _ ... - ....

38

Figure 'l!b) display~ the rusults of d comparison between the 20

ensomblo averaged velocity values and th~ cosino wave fit for the given

y locations .in the ireestroc.m and in the boundary layer. It is evident

from the figure that in each cas~ tho ensomble averaged velocity values

lio vary close to the fitted cosine wave; honco, the ensemble averaged

velocity variatIon in the test section was ~s~antially sinusoidal. T~e

fruquency for the results in Figure 11 I>ld$ 10 H:!. These results are

typical of those obtained at all fraquoncios.

,.

11';:

", ~.

rtf: if. ,: f ,..;

;' "

/'

,.'

It,. ~it· •

~ ,

'I. f

---'- ~ m,11 ~~

',c

/'

~ I,~ .?1 '1

.~~ ~,i ,%'I

~1 t'li .~

1. II ~ :J;f,

iI'} ,;14 ,~ .

I,,' ,!

.1 i'" l

ORtG!NAL p: .... ::-:~ l~ OF POOR QUj',U-r'{

39

-...."-., i 1

TC II f = 10 Hz y = 19.736 rom (y > 0)

Te II f = 10 Hz 11 := 1. 26

(y ;;: 0.559 mrn) (y < 6)

(a) Oscilloscope records of hot wire signals in the fre~stream and in the boundary layer

"

FIGURE 11. Typical experimental results for oscillJ.ting laminal- boundary layer flows

~..... .~~ _" . ',', I '\ :.~ i --.... 6 ..... ~ ~I -•• f

, '::-'-':""" ',.",... .: •. j.T: ;. ; I . ' '. I •• --......_ .... ,.~ , '; ,r"~·. 'r :

'F4G.~1.,:~~',S:J';}.~!-'\'~~::;i,~·,.:::!i:;t"~~:,t·" '-i'i!J;·t,~;::::;0cC'2;:'B~:';£C::!}~,);"lS/;'!i '.;;'.lr,.t;S$d;,r;~;; .";i':id~i~~.8;~{t~·--~

t:. m/s

25

Te II f = 10 HZ

20

15 I

10

5

Fitted cosine wave 7f Ensemble-averaged experimental values

----t ~

u = 16.78 + 2.304 cos(wt - 0.748) (y > 0)

~t--'*-* ~~ .. u = 6.24 .,. L634 cos(wt - 0.558)

o L. (I) ,= O.75)(y = 0.333 10m)

o n/2 Tl' 3rr/2

wt

(b) Cosina wave fit to the velocity in the freestream and in the boundary layer (angles ar~ in radians)

FIGURE 11. (Continued)

2rr

::­o

'"",-

""'~~

~~~r; ; ..... '...,. Ii ",I ")

;~:~ ',) ;~I I "'1 I ." , 't""' i '.;~ ; '~{I

.' ~;I ,A; .. "[

~." . ,;~" ... ~ ~';~

!';~l' ,,~.

~,

.~~~~ ,,-j.-­

.,' t ,,I( •

.-' ~~,' ',j

'" ~ ... ~ .. :'!: :.:~~ .~-:-.

"'''',' ,':l .l

,~\

I ,~'" /I";~" .. ',.' ?~~. . I <

~. ,. .~. :'~ ';L'o\,

/ I'

.1

-\"~"

~~; '>~

".-..-t":: '~ f ..

\

' ~ . ~"~\: ,"

F • ~.!

,"" ~:.~

'1'.:; ..-' ·i·

." .. : \

::.::

"

-7":." ~~;I

\

r;;~ .

.' ~, ~ .. ;1. , t ::.:

~'~ '"

J: r·r

Ir~~:.

":,'

.

'··.t,· ~.:: .

.' '~l ,'t· ,-~ ..

'. ...... 40~ ...

:~; . ~~; ;;.">

.' ,':-, -'r:".-i /' ... ~. :~(,~

,,,,,:'-;,:: ':"'J,~' .,. t'\"'" i , .. '1

.' ~".""": : , .-:'1 ' ,::::~ /.

'f;')'" r,"1' <' , •• , ~. 1 ,:1, •

~.:'" . ';:\":F."

.' .,1~". ~ r'- .\ilI! , 'j~l..4

I

/ / ~ -"~ ..

1.1

v . R~:SULTS OF THE BOUNDARY LAYER STUDY

Generating a laminar boundary layer and predicting the behavior

required considerablo wod" and effort. Tho experimental work for this

study ~las conducted at Iowa State University snd the numerical

predictions were supplied by Dr. John Murphy of the NASA Ames Research

Center. The numerical method used tlas that of Nurphy and Prenter [12].

A major objective of the boundary layer study was to ensure that

the boundary layer behavior observed exparimentally and the

corresponding numerically predicted behavior w('re in reasonable

agreement. If such agrcBment exists then the numerically predictod ~ t

values can be compared with corresponding ¢t values oeasurnd by means of

the hot element gRuCC~. This chapter is devoted to co~pRrisou of

experimental and predictGd boundary layer behavior.

A. Comparison of the Experimental !3oundax:y ~.:lycr Results Hith :-l\;,r.ler:i.ca~

Predictions

Boundary layer behavior was studied for ho~h steady and for

o~cillating flow at various frequencies, t~o axial lOCutions, and t~o

mean frecstream velocities. The steady flow .:Ind o~cillating flew

experinlcntal and numer.ically-determineu vdocity profiles will be

presented in dimensionless terms in the fOI~ of uo/Uo and u1/U 1 vs n = y/Uo/vx. The velocity phase angle ~u' i~ also plotted against Q. The

experimental cases studied arc listed in Table 4 .

, I

/ I I '0,

f ,'1/

" .} , ' ' ,,;~,

/' ,.1 " '!

" ,~' ""'\1

'tJ

/ ."

, '; .... ~~\: ..

I ,;,~.

/ "'f I 1.~

,~ ~

~I~ .... " ;:, .-' '',."t

.-1""1.. ,~

j ,,-"- G,t~.

... -.' .... : ~:~~ ::-:;1

:~~~' "-'''l~' .' Ii;}

, .... ,:;. ," :~ -':i

·· . .0'/r::~ ./ ,.-" l';~,(

;~f

/j. "

~:;i J

.:ql i ~.;i

.. -<'j ,;,r .'~;,

. .;'.' '~~t ~ . ~ Sf ! .. '; .. , L;,

J l,:, 1- .. l ;~,

I f,"$ :' f i.! ,. ~d

! .. f''''1 I .... I;' ./ / ~;~.i ,., j "'.:, • ,~, i.

I . / ):;1. I; / ~~

., -». j

./ I ~(i!; " ',.' 'ljJ~ , .. :§

•

~:.,

';;1

'.'~'J • <

JJ "'\ "

-: ::~i

.~' I !~ I I '. / iJ~ j . '. ';

-/ ; . I • "l / -, "

":1 /' ... ·1

,/~ 'I :,

., r-~ I.'

~,

>

~J ."

,I' I'

. /" I /' , . .- . ~/.~ ;'

,/

42

The first attempts to n~merically predict the boundary layer

behavior assumed that a zero mean pressure gradient existed in the test

section for oscillating flows. Since the mMn velccity profile u /U o 0

for oscillating flows is generally accepted to be the same as the

corresponding steady flow velocity profile, tne theoretical variation in

u /U with n is the Blasius profile. Using experimental case A6 (Table o 0

4) as an example, the experimental u /U velocity profile is compared in 00 .

Figure 12 with the Blasius profile.

Before proceeding further with the comparison of the experiments]

results with the numerical predictions it is important to consider the

uncertainty in tho oeasurements. The largest source of err.or in the

velocity profile is in y, the distance of the hot wir.e from the plate.

A fixed error in y is reflected in a fixed error in n (n ; yvU /vx). It o

was found ~hat a conv~ntional hot wire probe with s~raight wire supporL

prongs inserted perpen~icular to the plate surface did not properly

measure the velocity in the boundary layer so it was necessary to use

probes with right angle bends in the wire support prongs (Disa Pl4

probes: see Figure 9). Further, it was important that the axis of the

prongs near the wire be aligned parallel with the flow direction. When

the wire support prongs touched the plate surface, the hot {"ire itsalf

was above the plate surface. This occurred because the ends of the

support prongs near the wire are tapered. As a result, accurate

measurement of the distance from the wire to the plate ~as difficult. A

means was required to determine the hot wire position. The method used

. r' . I '//

.,' ,,'

,,' ;

"'j t:~i~ " ,.,

F • f~~ '~, I .,"",,1, ;) I _ :~t\

I,. "7'"1,

I ' ~:~ I :i""} , ":, I, I ,"~ I j

t ' . ~::~l; ,: ~fl L ,'\:~ l '>" I ' ..• / ,:/1

1 : • :;i-\' ,,' ... ~/ ~~:.l

.: "I: "~,, I ' ..... ',1 "

': r:'

,,'},' I ' ~~~

[~J ~' ' I

~~,.. . :-~

.. I":' -~~ .

; ,. -;~~ -""~',.

'I'-·l • ?1."' ~

~ .... :. -',/ .. ::! ---- I ""{ ... . \' ':'~!i

x" '.\1 ~.. ""-':1 ,-/ "~::ri

... -c":'j ( :~~ ,

-" I, :<i

'~.~.

." [}j , i~1/

' ... ..-.1 l.)

'''~' , <9'"

-A, ... ~,; '~,

'~!"4 i".f. i

I -J\: ,~; "'~'1

, I ",-, 'r" , .~ ·J,'I ...-"---.J ~21 . ' .\

. /' /'@ . r!.J

• '::~~1 . ' ~'"'' J ,~~{

< •

:r;~ {\

" L ell

;:!'~j \

/" tb ->'4

',·tJ

. " I"t~~~ ,. .~.;

,,"-, Y;t ''/ ~;~!~

~:t~

'I' ! ! " - ? -'

43

involved attaching a thin block of known thickness to the plate near the

probe axial position and inserting the plate in the tes": section. The-n

by locking through the tent section wall \>/ith a low power magnifier, the

micrometer dial reading corresponding to the hot l-lire position when it

was aligned with the block surface I.as determined. The plate was then

removed from the test nection and the block removed. The plata was then

reinstalled and secured in position. This procedure result~d in some

uncertainty for the micrometer reading corresponding to y = 0 fer the

hot wire. This error is ditficult to estim~te but based on experience

with the me[!surement system the value e;f ± 0.10 mm seems the largest

possible valu~. The bars in Figure 12 indicate the range of n for casa

A6 corrcspondin& to the uncertainty in y of ± 0:10 rnm.

It is evident from Figure 12 that an error in ce~crmining the y = 0

probe position reflects in an error in thc experimental boundary l~ycr

v~locity profiles. When th~ experimental oscillating flow u /U o 0

velocity profiles and the steady flow velocity profiles were plotted

against n it Has obse),ved that the extrap:Jlat:ed pr"files did not pass

through zero. luis was interpreted to be due to an error in y.

Therefore, the profiles were adjusted to correct thls error. This

correction required a ~han8e in y of 0.075 rum to 0.10 mm. The

experimental results in Figure 12 and subsequent figures reflect thin

correction. TIle experimental data points in Figure 12 lie close to the

curve dr.awn through.tllera. The absence of l"rge scatter around the curve

lends confidence to t"c experimental velOCity profile. This is

.. ,.' .... ~ --

---- '".' .. '..... . \. . . . ""'-- ',' - -' .. : "'. <. '. -'-'. ~, • • '. ". • '-""""'" '\. _~ ... -" ,-.. .,......... --;:~_ • __ . '\ ~ ... ~~. ..... • .. ~. ~ •. ~ ... P' .... \. ~l __ • " .' '", .. ~,. '.' '\ ,-" ~, "

:--"~~~=~".·~·~:"·;,,:,,·:j;:~:jd,d::~~::·:.:"~;,,·z~;~i~~:;;.~,:~.~--:-i::o.-;~~~-;~':":~~{i;'.~~:;"",:~, ;"·~;~"'l~'>;'.''; {'';~::~;\>~;;)i)Xi·'':.· !.; "i"'--';~'\"\';:<"::"

u/Uo

1.2

1.0

0.8

0.6

0.4

t-ol

/-i ,

/ ~C-l

/ /

~ct: /

~_70~

/O~

/' /O~

o

__ ~Q Q D-

Case A6 Te II ; :: 1. 59 f = 20 Hz

u /U t Measurement o 0

1-0

Numerical Prediction for Blasius Flo\'f

0.2

o o

/ t

FIGURE 12.

Curve fitted to the e~periMental data

1 2 3 4 5 1)

Comparison of the c~:pcritr.ental oscillDting flo';-1 u /U o a results from case A6 to the Blasius flow lIumerical prediction

6

i

7

~ ~

,.

, .. I

-~ -~"

... ..... -:.::

......

--

.~

-/,/. -(,/ , ,/ ~.:= ~'~ F\.;:~ .,', ~~r~~:

" i~:l' ') . r·· .. ' -';;:1:' '\' -, . • '!';. I :~\j' : : I I,. ,

" ," ~.~~, ~ ~ ... ~ . ,'~' r~

~:~.

/I'~,t /;' g.

/. / . ii;I'~ . I ;~:

/. ~ ~j , .':. .....

'j' i'~{, ' .. ~ ;.:(

1J '-:;;' ~- -J '

I . ". "--'>

/ t;.;, k,~ "1

. ./ ';1 >/ ,~'~i e.~

-1 "

.If:'; ., .,:. I " '~'! • I :;J

J :.,.

'j ,'~'~ . ',7'-;-

~./ ~·t· /' . ,::p

,'. ;;/. l ~~t\

/ -, , .... ,. ~ " . • ,'~_;.,t::

'.

-.... :' 1['1 .' ~ ....

"I'}~ '~:r: I ,),.

,> '~~1, '.

~~,., ;

1. ~~~, ,

:;-:;' ;,.~

5~.1 , ,:~r~ ._ ~ __ ... ...:.._ • ~~ ~ • I

:;:) jl J.~ . .... ,.

• ,'-~ .. I I ... J I

I \? I ,.~4 A

A'/ :i/'.! .. ./ >", "

, '" -y':

45

I I 'r : .

consistent with an uncertainty analysjs presented in Appendix C which

indicates that uncertainties in x, y (exclusive of the removed fixed

error), and U produce tin uncertainty regioil in the experimental re,ml ts

in Figure 12 that is about tha symbol size. These characteristics are

typical of all of the the u IU data obtained in the experiments o 0

ccnducted in this study.

One noticeable fact about Figure 12 is that the experimental

boundary layer profile has larger values of velocity at a given q than

does the numericaLly predicted velocity profile. This was true for all

of the cases studied. The reason for this was traced to the favorable

pressuru gradient created by the growth of the boundary layer

displacement thickness in the constant cross-sectional arca test

section.

A method of evaluating the pressure gradient was required [or

correct numerical prediction of the boundary layer b~havior. This

involved determining the pressure gradient for steady fluw. This

pressure gradient was then assQ~ed to be the mean pressure gradient for

oscillating flows_ The Falkner-Skan equation [20) for the variation

with x of the freestream velocity in laminar steady flow with a pressure

gradient was used. This equation is

U(x) = K xn/ (2-e) (10)

where K is a constant and e repr~sents the strength .)f the pressuro!

gradient. The pressure gradient corresponding to trw velocity

expression in Equation (10) is

>"l{~'! ·.~~7·[~L. ___ ._. ____ -.--~-.-. --'- 4

/

,.~~ \",.1"\,, 1 ,~< .. ~;:;. ,. I

:;',;t, .j1 '''J' •• ",-" .

',/" ~:~:;. \ j ",',-' 'j

,,:~~ j ~"}:, 1 ;:- I

;. ~ ! ~;-(; I

i'<_~ .).

III ,'~>'::r ~, ~) " ~~~

/ ",' ~.,.

/' "\' ':" ,/, :.-1., ! • '--.!.

:"',:!;' :,-;:,

. ',;/ f t ~'~~

i J t~~:) r I .,::, .

.. i ; ~":f' . '~-'} .

, / ,::·~~t "d t",

j • ),~; r:·,~~· I {<t-" I t,. '~" I

i /'/' \><;'. ,I ''''" "1: '

F '!'I~''-~: j ! --1 :..-?" , 'f' ' ';"'" I ',I ," I

"

I-f ,"J, ' I

./ J:'- 'f":'~~ \ i i ({~' 't l' --

b< r!:,:~: ''I

I i , / ,.

",.:' "Joo" . " . ,:; ,

"i~[{~ " ~ j .::;" ~~:: I

:~, f:~r ; ~"\ I

. ~ .~:~: •• t '. ,,"

/ IjS~:, . , ·~~t f ':; .. j' ',,\',

1 ... ," )-: '(;;.

,,/ / -.}; ~ / ;1 ,,:;i.. l . ,.:' , ,~<f ~'~~:j

" I ,"'.Y'

I,;~~:~; 'j' , t.,;, ( .. ' 'J \!:..

'It~l i t2"J)

I ':;f'f ' ""''1'"

'/. ' , II

I,

. / t r,.,

l~6

I' J' I

.' II

~ dx

= -p K2 2~~ X(36-2)/(2-~) (lOa)

If B is a positive number t.hen a favoreble pressure gradient is present

and a negative 6 repre~ents an adverse pressure gradient. The ca~c of ~

= 0 corresponds to Blasius flow.

To estimate the value of 13 in the test section, the concept of li

and conservation of mass will be utilized. Since this is only an

estimation, several assumptions will be made. These assumptions a:e

listed below.

1.

2.

3 •

* The equation for 6 in Blasius flo~ can be npplied. The ...

expression for 0" is given a:; [20],

* .;~'~ 6 = 1. 721x/ 1\e x (11)

where Re x = U(O)x/v. U(O) ~as taken as 16 g/s which is the

approximate velocity at the test section inlet for wave

generator sectiori configuratio~ A, Table 2 .

The origin cf the boundary layer on the test section wall s

begins at the test section inlat and not in the entrance

region.

The flow is inccmpressible.

Based on th~se assunptions, calculations were made for steady flow in

test configuration TC II. Under these conditions, tha freestream

velocity was calculdted to be 17.2 m/s at x = 0.22 m. Thig change in

'i:

the freestream veloLity is caused by a favorable pressure graciient with

a = 0.098 as predicted by Equation (10).

. m'<l ':~";f~ "~.,-~l.~~ .:;~~-------- -,-.------ •

J '

'/

fTI1 tf~;:J

~';';~

.' .~~

." .'''~> I ' f':;:' .' I -:;

.' / ~~~

-':J. ,~~

:~~11 .'j ;{II -.-~ ,~.;! <0

'-:.1, ,.") ~~ .. ,~.,.

-,:1.

;.~f,1 r:J.;

;'~) '-'--~ / '-":,

I :i2

/' I, I ~~;.~I,

I "~~ .I ~'~\~"l

! : '

/'

• '!~ '.;',,-~

/I'J; • [ -I

1',':J ,t';l

";1' :~~

• t :~;~~l ~:'., i

""~i';; ~,EZI ';~~ ; ,~ 'C •

:-~',':: ':"')1 :~:.i l\. I ;::- i

-'!.~

l: .I' I -'f t

t~;~ 1 "I"',

~f!~, i _~''''' L

~~~ : ~i

'. ~;;.;: , ~~,l

. :t~ "I

/ ~:;.j ':: ";~"1

,:p ,

t':}': ". . .. -,-~ , .. :J~J;

,!~

":p

'.' ~--::~,' ' ... .J.'

:~''1~ ,.-" L?,

"-':"f' s ... '" I ;" ',j }J~ -:~r,1 .• "0;1

;f~~i I, ,',"

, t~~-

\ ) ,~,--. .. :~/

l 'J'--

.' - ' I ~.

47

It has been shown in the previous paragraph that a favorable steady

pressure gradient should exist in the test section and the Falkner-Skan

equation is a method of estimating it. The task now is to determine the

value of ~ for the flew in each of the three test configurations. The

mean pressure gradient for oscilloting flows altels the shape of the

mean velocity profile (it also affects tha u1/UI end ~u profiles) 50

determining the correct G was accomplished by matching the experimental

and numerical u IU velocity profiles. This simply means that a tJ3S o 0

varied in the numerical predictions until tha predicted u IU profile o 0

provided a sood representation for the experimental results. Extremely

precise evaluation of B is not necessary since a small error in ~ uilll I

not drastically alter results predicted by the nu~erical corle. 'fhis I

matching procedure is shown in Figure 13(0), (b) and (e) for the thrme l

test configurations TC I, TC II, .'lnd TC III, respectively. For TC I

(Figure 13(a» and TC II (Figurn 13(b), the value of a which best

represects the expp.rimental results is a = 0.10. The value of a which

best rep~esents the experimental results for TC III (Figure 13(c» i~

0.16. Interpolation was required for TC I rmd TC III since a limil:ed

number of numerical solutions were available. The values of a used to

describe the mean pressure gradient for the three test configurations

are tabulated in Table 3.

Now that values to describe the coan pressure gradient have been

determined. the experimental r~sults for the boundary layer survey cases

given in -L'able 4 can be comparp.ci to the numerical pro:~dictions. The

:: '. ,.,~ , . \.-~ .--

.- ",

fi;;:,~~~;0~:~~~~::::.j'~;"~':;::~~";i~';t~;-:" ~ :;~·~i.~~:;-:~"::~::~::~i~;;'~·;~;'·;;'·>J:,·':~~~lf~~',~;.~:o"~-~~;:";_C::2S'S~~;::,:~;d2 ~-:'~\~~l;;.i_'G}~':; ,.~,.-." , ... ',. "', .• , €!:;S~. t·,,,,,,,, -'r,.,,;;.;, .":'. '.~. .. __ ..... ~.~:.:.: . r: v·· .•. "."".,,,,~ .. -,,~~,,-.. ,' .• --=,' ,.' .. ~'~~---~-~_'.~

i~

u/Uo

(a)

1.2

1.0

0.8

0.6

O. 4

0.2

o

~ __ 9~O~ _o-~--//~~ ----0--

/:,V / "V//

r1/-I/; /, a

Case Al TC I u = 0.45 f = 10 Hz

uo/Uo' Measurement

~ = 0

1- /~

V/~

r~~O. , , , , , , , , , , , , , , , , , -- : : : ~:: 1 I • I I I t I I , • , ..L.A..L...l'" '" f" I • ".I' ...&..J...' , , J , , , ,

l t:umeri ca 1 J Pradictions

"" I

0 1 2 3 4 c: 6 ~

'I

TC I

FIGURE 13. lIeterMination of the vailles of 6 uhich best represents the meau prcs$urc gradients .... -~~ -- ..... --

7'

t­O:)

,,. " . ., ~ "j I'

~ ~, .~ . . t> ~ t ~ , i

I I , I

":"

"'-

t! L g S ~ .E 2 [ " i • , i ,. , iii' iii iii i I Ii' i I I--

-0-----

2H OZ = J 65' [ = !l

II J1 9'1 as:?J

I , , t • ~ •• , • i , i , ' i i as. iii I • T'r r..., Ii' iii i ..-rT-

---'-

o

, I."""" "~~a. r,,' r', r"." It" ,

o

II J.L (q)

o

2·0

g·o

8 ·0

o or

2 ° r

!

I I

I, I I I

I, r

. . ~;M~i:'~:,:~D::~ : ;~ t;7~~}~i~~~,~~;;f;;,":';"~ i l~ ~",r'-'~;;-J'\!':':~1~~'1t ~~;I ~\r:~: V·~:!~~;·;,'~:\·;;;'~~2.:~.F1j ~':::_:"{<;'\ ~ ~, ,~~~_"" . .'~ "~~j.~,: i,.",~\:,:;. ':1~"'~'~'" ~~ ,;.:t'~~·.;~ ~;,~.~~\~~~;;~·~ii~~~.

.' ; -----

. '. /

9

r

5

7U or ::: J 61-1 ::: !2

II! J1 za aS~J

. -----

o

r

I lJ~.L (:l)

o o

·Z"o

9 '0

a ·t

I •••••••• ' •••••••••• ' ••••••• ,.' ' •••••••••••••••••• 1 •• , ...... 1 •• , ••••• ,j G ·t

t . --.. ; .

/. .j -.- --I

;' / " : .

r "

f '" 'i • . ,

" . . ~ ~. t '.::t.

2 :' ~ , ;

~ • i· t ,~~ ,0

'" '.;' . .., ", r..

'" !.

r 'ht-

'" <: ~

r -.- 'i

~ .j!

Il , . • ~

r ~. ".

if' ~I . -\ r-ri. ~\

. -'-'-.. , r~; ~.,

~ f ~ ~ .. p ...

··1 ~ f__ ~

..

'. \:'

\:

/

~" \

51

o~perim~ntal results u /U , u1/U1, and 0 vs n for thu cases are given o 0 U

in Figure 1:~(1l) through Figure 14(i) dnd are tdbulated iII Appendix A.

Also plotted in these figures (with two exceptions) are the numerical

solutions for the value of 6 which best r~prusQnts the boundary layor

bohavior. The first exception is for case Al (Fisure 14(.:1». ThQ

numad.:al prodictions for a = 0.12 hnvo been plotted sin·~o aumerical

results for this case were not available for e :: 0.10. The second

e~ception is fer cases Bl. B2. and B3 (Figuro 1:'(8), (h), and (i».

~umoric3l solutions for a = 0.16 wore not nvailablo so tho numerical

solution with the nearest available value of a (B = 0.10 or p = 0.1S)

\-Ierc plotted for comparison. Even though tho l\umoric:~l :=csult~ in

Figure 14(a), (8), (h), and (i) are not for thu correct vnlue of B, they

give a good Q$timation of the predicted boundc::y layer beh:r:ior .

Mea~urcd values for the freestream ~ean volo~itv U and the • 0

freestrca:" half-amplitude of ~elocity oscillations U1 are list:~'d in

Appendix A for each case. The ratio U1/Uc ranged bot~Qun 0.134 and

0.220.

Comparison of the experimental u /U volo~ity profilu5 with thQ o 0

corresponding numeric31 nolutions at appropriRtn ~alues of B, shows that

n good match for tho complet.e profilo was obt:lilwd for ,\11 :he C~$o'!S .

studied. As prnviously noted, one characteristic of oscillating flow.

as described by previous studies [13,181. is that tho mQdn vt.>lccity

profile in oscillating flow matches tho stoad:;.· flo\~ pr()til~. Upo~

comparing the oxperimputal oscillating flow results with the

" ~ 1, .",,,, ~

\,

/: "' ... \ \

-. • ~.

, .. ~: " I '. ' / . '

, -1?):0i5.i';1I~A;;"<'f§0':{'P !!y;t'i'.;;,'{"1;j;i':'''~'i;'r:~;'';'';<'';;f''A;';'': ~7 ,e~;; :/:, ;c;i;;'ii.;:,",p~:-:;r1;A:F,';·:,J>.";i.?,,';;;;C~o:;~'::~;;~;:,.::!JI';Hj/>\~~'!jl?:~ t..~ .. ' ----•. ---- " .' .'if· '4..;;l' _ •. -_._._ ..... -- . .... .." -' ••.•. ~'. ""

..

, j

I .~ I i.;, ~ ~ , ! I I

50 ~. I • Ii •••• ! i • I I I I • I I. i •• I ••••• , ••• I ' •••••• I • I •••••••• .......... ~

tf • " " " "_+ B -...-6 u 0- CI

o ~ Cases Al. 40 _____ Te I

u O·f- U = 0.45 . ,/ f=lOlIz

·"..0 rement "0 t' ,. /U • Heasu - 0 0 "0 0

/ " "1/U1, +

/0 0

/ +

~u' deg

Steady F10'.". Measurement

20 Measurement

~u' Measurement

10

1.:.' g",,- 0-/

0,.......... -0- <> 1 v -o--~-{)

/ .... ~~I/a ............... . '/ I··.·i····li····"~····"! 'I I , , , •••• ! • r ....... ! • -10

flumerical P:-edfctjoil" ~ = 0.12

o

o 1 2 3 4 5 r,

(a) Cnse~ AI, Ci (* Required B = 0.)0. P = 0.12 nuccrical prediction is Lhc »cnrosL available)

FIGUHE )4. RC5Ult~ of the boundary layer surveys

5 7

1.2

1.0

0.8

L: /U o 0

0.6 u/U1

tit N

0.4

0.2

o

~ -": - ~"'" "- -"', .... J ... ..: . . ' ...... '~.j" .. ;'-

"',

p I~TsJ);t~7V,;".~j\~.r~'rc"15'!~~"'j,.,~;~.i""'I'-""·~4'~":b;".···~"'J""Ml":;L~.:;i;.D~:li'11~~J~1..0:~"'2:~:;::';:'-;:"': i':i.;,;;~;:£:."'.£:;;i=,i:/i'2:r~..:.:.;:·;} , ,·.;;~.;:~it:::;:':;;~£~;;.-', "",;.:~~;.; i~~;. !i'~4.Lj;'f<'ht~'* ;,,'~;,MiJ

~

...

\

)

t,

Q

50 """"" I ' " " , , , , I " , , , "~ , I " , , , , . , , I ' , , " " , , I " , , , " " .. " , " , , 11. 2

40 r ~ ~li. ] . -. +_-o-+--it-+-O- 1.0 (V"+.----a- Cases A2, C2 I

/' Te II i /

+ U = 0.25 I .f? f '= 3 IJz ~; O. 8

o u /U , Measurement

/ " U~/UOl' fieasurement O. 6 0+ J

" 7 v ~u' Heasureme:lt ~ 10 I':-"'Y; I -{- Steady Flow, Me~ surement . O. 4 o +

~ /0............. tlumer1cal Prediction 0____ ~ = O.}(I rId 0-0 A 0 0 0-

30

~u' deg

20

o 0.2

-10 "L .... ,., .... ""., ... , ..... , ......... I ••••••••• , ••••••••• , ••••••••• ,J 0 o 1 2 3 4 567

II

(b) Cases A2, C2

Figure 14. (Contjn~ed)

u /U o 0

u1iU1 \JJ W

....

~.,,~'I. ........ ~ .... :....... ... .. ". 1- . ' ..... ' ..... ~ ...... , ~ . ,

P'<.3~~::":i..:..-:..~~~~~ .... :~~-,-~~:..:..:.....:..;:.;.;..:..~ ,; ~.;::;:.,;,.:' .::.,-~;.". .. ;-.<;.,.~.:-!~.,.r", .. ~.~·;,;~th;7~"~;Ei;,.:..?"'i;'::;:>"~'~-:"""""$";''''·''.'>.r'':'''~;'';:';;''li'''~,J,."'1'!.",,,:;;i'/­\.

\ '. -'.

"~

, i

'. I

I I ! I j

\

50 r"""""""·'·"""" I- 'I"" Ii" i

" I> """""'''''''''''''''''''i ~ 1.2

, ___ o_+_~=+-A 1 40

30 ..

..,.r5" Cases ;'3' C2 0+ -1 1 0 [)"+ TC II • •

/ til = 0.44

Yu' deg

20

10

~ ..

o I))

/

+ f - 5 5 0/ - . 8 Hz

o uo/Uo' Measurement

+/ A

o +

u1/U1, Measurement

~ , Measurement t.:

Steady Flow, Measurement

Numerical Prediction 11 = 0.10

}~

'1 ,,' V '-L.I....t-I.J-'-L • • • i I • I I , tt I , • I

-10 I II

0---0 0 0 0--o

o 1 2 3 4 5 6 7 r)

(e) Ca~c~ A3. C2

FIGURE 14. (Continued)

0.8

0.6

o. 4

0.2

o

u /U o 0

u1/U1 I.n .po

, '.

\

I' \ \ ~ '--:-':'::-" . \ 0-. ,\ \ .. ---..... ............ • I 'i ". ' . .~.r ..

~i;~%1fi(;j~~:(~~;;~IM;i~~~~:~,J;~';;7\""" '~:i'i';~",t ':'i:':':""';;~';{'~"~:!f,,z;;~~~i~=;.:t:·;i. =c'~;~:~~",~,;<\';::':~!0:~~1};,i1 ,-

.,

50

40

30

~u' deg

20

~ t

10 f t

~ 0

+ 0/

+/ 0 1

A ~

/0

A

------~~----~--+---...----rt Ca ses A4, C2 0+ Te 1I

~ W = 0.78 /+ f = 10 Hz

o

tJ.

o

u IU • Measurement o 0

u1/U1, Measurement

Q , Measurement u

+ Steady Flow, Measurement

Numerical' Predfction ~ = 0.10

-----0 0 0

1.2

-. 1. 0

0.8

0.6

] O. 4

0.2

-)0 ~~~~~~~LL~~~~~~LL~~~'~~' I... :1 o o 1 2 3 4 5 6 7 r)

(d) Gases A4. C2

FIGURE 14. (Continued)

U /U o 0

U/U1 1.11 1.11

\

.....

~ '\' ". " - ........... -

, -- ~ , . ", ", . i _______ '._

h:722f};-~.~~!;·;\.,.'i.;'h;-i;;.;:;...:;.:./ j; ',i ... '.,.' .' "'r ':';'\:·;':.L";,~":"::':"""':"~~~';:-':i;;;::::;;=::-'::~:.-:-.:[~·,, :~-.-"..:.~ ... £:~:4";' .... "':-A.:'.,; .•. ,''''<'';'./.";:.;,,,.'1'> ~ .. :::':.,}"" ""1-\i':'::~::~,""~';;f,;~:,~i;,!'4<;.i';i';;;~~ I '

-.:.:.'

...

50

40

r:.

30

~u. deg

, .. I ~' .. , '~ , . I ' .. , , .. , , I ' , ...... , I ' .. , .. , .. I ' , .... , '11

• 2

r:. ~r:. 1 ----A --+_0 .tJ Q {·--s.a--i 1. 0 .... _0-- Cases AS, C2 0""""" Tt II

+' i:: = 1.18 0/ f = 15 liz -. 0.8

+/

0/ o u /U , Measurement o 0

20 t / ~ +

r:. U1/U i , Measurement 0.6

~ 0 Q ¢u' Measurement -,-

u IU o 0

u1/U1 V1 0-

, • I 10 E- + Steady Flow. Measureme;,t - O. 4

Nuoe<ical P<ediction 1

.. -;--

",

"

: I .:! :'i '. I , ! !

o fi = 0.10 1 1/ 0 0--0

-(j VI 0 0 0

-1 0 ~.!,! I , ,. ,~, I .!""!.,',. "" "!,,!""!! ,I,.!,.! •• ! I,!!,!!!!! I 0 o 1 2 3 4 567

o

il

(e) Guses AS. C2

FIGllRE 14. (Cont inuerl)

\,

........

"

·-'\ ..;. .... --.".... \ \

_ ~J;:;d./'\'!j"" --.- \1 ..

\.

'. ....

,~

i· I I I .'\ I '; ,-',,"-:,.

'--, .,

~-, \

...,

....... ,..... ...~ _,.; ..... ~ I \ \ - ...... _'~ -r--._ '-. ' , , .' . \'........1- \ \ ", ' _.__ • \. ' ..... • • • J ..... .... ,

• -!....... \''':.. --:--_ • . ,'-.i" '. " .... \.. --. -. - ;.,-......:.-. ", -.~ .. I . .' .' \ \' -.........,. ' .. '. - ~ .. ~----- . ..... .... -.. :.\ \~- ~\

.'

;~ .... ' ,i ",. I ' .. ;,."';"~ t':" 7 " " ~~>...,;~~Lu.o::-. M:; ''b~t"I0,~.;.!;."t~ .• ,}~ ... __ .t....~ •• , .. ;",.l, :'"';, ~~·.I·'¢.~~~'-::"-~("~·"'~~'~'~;j~·:.!:~1!"'''·\ '-!;.X'_'Y"'~'~'''l'"; ! ... i"~\.-i::- tJf !.1r'Jr"~t'\~ • .,J'/-<.1'i1o·~ • .t*~j.,t!~~ '~~t~:""':"'.o."l"-f\::-~W"':'_~"""Pfrr.f~tt~ilJ

50

1.2

~

30

~ • de9 ~ u

20 f ~ E

IO

~ /

6 ~-----A~---~---+---o-... ____ 0 +- Cases AG. C2

A 0'" TC II

/. / w = 1.59.

p/ f = 20 Hz tl +'"

0/

+/

40

0 uo/Uo• Measurement

A u1/Ul • Measurement

0 'u. Measurement

.,} Steady Flow. Heasurement

\,

1.0 \ "

0.8

u IU o 0

0.6 --u1/Ul

\.II

0.4 "

! -- Numerfcal Prediction Ii = 0.10

o ~ 0 0 0 0 0 0-1 o. 2

O v ..... , ......... ,P ..••.• ~., ••.••.• ~ -1 o o 1 234 5 6 7

n

(f) Cases A6. C2

FiGUR~: 14. (Continued)

" ...

....

\. -, "

---,

:'

".

'. • • \- \ ---~~'-- •. ' "'-c~ - _ ::"':' • ____ ••

'. . " .. , \ \. '. . ···-':'::;>'"m:'i·r '. , . . .. ·:r:;:: :,. i;:: , .• - " '.. ",,, , "h , • '. , . '. ;1'1:" . 'eO' , .... , ' . .c.. ' . 2 : '." ;.:is;;-:;';; ,..... , .•

, ,.

50

40

30

¢u' deg

20

10

0

-10

Ii"" I"'" i •• '1 "', ••••• I'" i ••••• I"""'" I'" .,. I

~-•• ,......-.-. 'n' .r-T.-.-, '"1' ':r' .•• -. - • , A---." -A_ _

~ 0-~ ()-

o

*

0---~ Case Bl

o ic III - - 0 34 w - • f = 3 Hz

o uo/Uo' Measurement

6 u1/U1, Measurement

o fu' M2asureme~t

O/~ -- Numerical Pr~dictfon ~ O~ ~=O.10

0------0 0 0 0 ---\

1 2 3 4 5 6

11

7

(g) Case ill ( Required p ::: 0.16. ti::: Ij.l0 1Il1lll!!ricel prediction- is the nearest available)

FIGURE 14. (Continued)

1. 2

1.0

0.8

u/Uo 0.6

u1'U1 VI

0.4 en

o

~

....... -',.. ,', ." -'\ '~ , , '- ;- .-.~ " .- . \" . '.,' "l'" . -~ .\,:' """" "''""___:. _. 0, ... .. . \,. ~.. -'.... . \". " '. '., .......... , '. '. \ - '.' ~ . ' \ .' .. .,," - : -"'. \ ..... ,

\ ....... \"0"10 • ~ '" • ..... \ '''- • 1.' \ '. " " - . , . . - . \ " --- ' '" '-- . .\ '.

.·f3:i-;:,;.;·."..;·"',\,.'.· . .'7\: .... ;),: ........ ~.';.-::.;.,·:!·"',' •.•. f., ....... ".:: ..• , . ...,.! .. !~ .1· ... ·7-... " ..... c.,:), .. "H."'~·;': ....... ". i ... " .-'" , .' • \, •. '.~. ir":.;':";.~~~<l-j'-" ,,~''''<I:::- '~:'A''':-'''',-; ;,.J':-;':';'!':i •• 'o;·.1.U.;".' ';':!.)'.':,",!"'~·"'J.~l","-:(~'-;;\"'~ ~;~ ':':-;'~I';~:j ,\":;~ ·'··.z' •. ~ .. ' ... ;l ... ;~ .. ·<;" ;;,;}.:. •. ~.~~;;;:~~, .. ~.~,\ .... ;lt ~.>.,,::;.: .• ~.~:,~ .~:! ;.; ~.~ ":;;~;.~;;:: 1:'- ·:1! .. 'c'~··{-~;··:'; ':,;1GiJ r·· ..... -.-----~----- ............ - .. ---~-.----..... ----.--... --~-.. --".:.--- ------~} ..... ;." .., .

-~ ..

co.

, , . .... 1

, ':'1 'i . , , ,

. .

50

1.2 A A

~ 40 ~ ",,--0-- 0 - 8·==----0 0- -f 1. 0

30

~u' deg ~\ ~

20 ~ 0

~ A/iO

10 F- 0

Ii o d! 0

~// o

-10 ~"". o ... 1 •••

1 2

of:

o

A

(j

Case BZ Te III Lj = 1.19 f = 10 Hz

uo/Uo' Measurement

u1/U1• Measurement

9\u. Measurement

" Numerical Prediction ~ = 0.18

o '----o ------0 0 0-

{;

3 4 5 6 Il

(hl Case B2 ( ReCJuired 6 = 0.16. a = 0.18 numerical pr<ldiction is the nearest .wai lable)

FIGURE 14. (Continued)

7

0.8

ua'Uo 0.6

ut/U1

0.4

0.2

o

\I! 'D

-...

"

---

-- ~. ,I '~,,:,'). \ .... ., , -: \ ,-.

, f,t.;:::, =;=~~\\ c>,; .• :V:~;:)}! ii;;;:'~':'f;; f"j~';:';~::";"-;;' ?~~;{::.: ;;i.~~"t~~;: ~~2~:'~~~:;~i=:~;"<';;;"~: c:,~.;,,;; ;.Cj E:':f"!;,"-", ~ib~?;i8i

:-

....

4 ,I 'l

1 ,I

t I I

, i i

50 ~ . " . """'T"T' OJ i J. 2

40

'.

Al:.;. ~ ___ '

a f\== -8-0-- -1 1. 0 0..----/' Case 83

o Te III 30

w = 2.38 1 0.8 f = 20 Hz @u' deg

i " /U 0 u /U , Measurement 0 0

0, ° 0.6 A u,/U1, Measurement

• ~ "j/Uj 0 ~u' Measurement V. o. 4 Numerical Predfction

fl'= 0.10

20

10

o ° ° 0 0- 0.2 o

_ 1 0 if, '" , I, '" ,~; l.c. ,0, L' , • • , " , • , , , , , • , • I o ) 2 3 o

4 5 Ii

(i) Case B3 t Rcqairctl p = 0.16. fl = 0.10 nlllr.cricai prediction is the nearest Bvai,lable)

FIGURE 14. (Continued)

6 7

0-0

'.,t-:.

!

i /

..

'j

...

•

i~l;~" : .. :.J,.\'

.... ~,. ;

;~'r ~I .;;' ..

:t~ \ I r.~'~: . . "J .. ~.

,::' ! '~:r ~

"';"~ .\~ . .. '~~ "t,

\~. .''<. :'>~~ . . ' j •• '

:;,~~.~ ".'!;/ .l.~ -"to) [:,~~

.~t

I,,~'J:. ,.j'f."

,,·~ti:,~

<;~i' '~r ~ ~ rj .. :r~

: "'V" • L'.·'\.

'3 , .~

".:;.; ~.­

, " \.t. " ""~ ..

!: :;~,

IV;" ,~ ;,. k'.f .' l: ~t: ',,"" ". E~'~~' r·,',,' "':!~ .. ~'\ ':

.... 1·"':' ;-<1 ~."!,.. •

~~~ ., ~:~

;:~ .. :1" 'k

,f "i~\

';" " ,":i:' ~ '~~j. ..

:ff·: 'I~~',$

,'i' '~;~ r~~;~ , ... , ~ ..~ :_'1 '

",:,~ l' "~~~~·-I '1:-,,' ' 1--" .".I' .~i:: ,.

t·:::" , '.,'h.:.:.'!

::~., ,4 -~ ,,:',~: I j

Irf '):" ,:}'" !

J t:' ::!.~.~ ~ ~ I f/~'" . /~~~~

l ::It&·~'· ~ lW:.~7

61

experimental steady flow re.sults in Figure 14(0.) through Figure 14(f) •

this characteristic was confirmed for the ccses studied. Thus, the

uo/Uo profile is unaffected by the fluctuating velocity.

When the u/U1 oxpcrimantal pt'ofiles are compared to the Ilumel'ical

solutions a small difference is noted [or most of the cases. For a

given n. the er.pericental results or.hibit larger values of u1/U1 than do

the numerical solutions but the profile sllapes are similar.

At low values of w (cases AI, A2, A3, Bl), there is good agree~ent

between the experimental and numerical results for ~ over the entire u

boundary layer. At higher values of w, the expcri~ental results show

that a larger velocity phase lag is presen~ in the boundary layer than

the nUQerical II!lJthod predicts. Th~re ;'s some tmcertainty in the ¢ n

measurements; it is esticated to be ± 1 degr.ce. !biro uncertainty is

slightly large~ then symbol size in Figu~e 14.

The majcr question concerning the experiment" 1. ¢u data if. rcJ ,.t;cd

to tho wall phase anglo. since tho objective for ~cdeling the boundary

layer behavior was to ensure within reasonable bound3 that the predicted

~ was the sarna as the ~ actually present in the flmi5. Usinr; the tact: t t

that the limit of .u us y approaches zero is equal to ~t' thu nu~erical

predictions of rflt

in Figure 14(3) through Figure 14(i) an~ simply ~\: .1t

11 = o. An estimation of ~ for the experimp.ntal results can be obtai~Gd t

by extrapolating the experimental 0 data to the wall. Although there u

is some uncertainty in the values obtained, it is evident that for each

case such an extrapol~tion yields a value of ~ clos~ to the numerically t

• ' .... r '.: J' •• ~ •• ~"

.' ;'

/ /

./ «

'-

, .'

~rF-. ,",~$fr. ~'";lf~j

· -~~i.1 ::1!1 ;':"'t ... ",t;, ".~ , "(3· i:''''r ':];. " , :~:, ; ·/I"~··: ''''I ~~1 ·''11 ~!,it

-"~

~i l ~~r.~ i "',,],t

~:~,l >Ii'j '-:'1 \~

'.l{ I r ~~~

JJ'j -;;l~: ',;,; I

~:':~f"l :'.-:'"

;~<! ;\;1

'Li:~ll ,.,. ", ('f.-,

,~ ";

'N";ll ,..".10

r,

;:~~1 : ·'·~·~f(

" ..

L/j' :~t / ;~i'l ! . :::~;

~~t; ;~ :

:~Ji· j :~, ! ,~ j .:-;\! ).·e··· ,,," ... ~. I

',''''t I I:~; :1 ~{'.:

}t ,.,;,.'"

" ,;;~ : ~1. '"! .1.,,-' ,,:::- I

~~~~ ~!.,. : .,( .. , ..::.~;:.'t

:>1 '~;J.i

·· ....... l:,;';li . r·").'j ,~'~'I ::;:1 " ~J.j

~;'~ .:~~

'1~"4-

)

62

predicted value. Thus, the conclusion is reached that the numerically

predicted values for ~t are reasonably accurate representations of 0t

actually present in the flows.

D. Numerictd, Pr~dlction of ~t

The purpose of this section is to dctcroinlJ. the nUr.1erir.al

prediction of 0t VB ; for the two value5 of a corre&ponding to the three

test configurations in Table 3. These results can :hen be used for

comparison with the experimental rneasurl!mcm;..; for ¢ in a later chapter. t

As prcviou:;ly mcntioned, during the p::-occ!Os of rr.atching the

experimental and num(ldcal u IU velocity profilE;s, a series e;f o 0

nU:ll<!rical ~olut ions <It various valu!2s of e and u wcr(~ obt(!.:'I".~~d for the

experimental Cilses studieci in TablE; 4. Inc r!\tio U1/Uo for ... he

numerical computations for each case W85 determined f=om the

experimental value~ of U1 and Uo listed in Appendix A. Values for ¢t

from the seri~~ of numerical solutions are listed in Table 5. These

results in the form of ~t \TS ~ at constant ware plot1'ed in Figure 15.

Curves dralOn through the data points in Figure 15 allow the prcdlction

of 0 V5 ~ for any value of R covered by the data. Curves of ~ vs ~ t t

for the three tcst configurations can now be obtained. The curve of a =

o will also be obtained for compari~on. For tha pres~ure gradient of 8

= 0 and a = 0.10, the values of ¢ can be obtained from Figure 15 or t .

taken directly fran the Table 5, but [or ~ = 0.16 the values of ¢ must t

be obtained from the curves ill Figure 15. These resu~.ts have been

( .. : '".'" .~.

..

~';, ~,!,

~

f "'! .1 ·,1·

j

"I : ... ~. . .;;: ,~ . :--1 '~1 ;,~\~~ >' '~ .~

~·l .} ... ~'l! ':.;-::t AI '~j ;t ,;~ 1~

':~~ :, ~~-: ";",j :',:.i

.,:: J

''--t:''; .. ' )~ .,.~.;

'It,~ : ::, . . ~:::i

f 1,.1,/'" ., ~.

~;~. r· .. -.' J ., , r. :i. i" ,

_~~I ~"\

fl "'1' " f· i LI }. ~ .. ' ....

7i ~ Lt I . :'.~~;,.:

--:-.," 1':

" I "', ·f ~'i •

'I'fl I~ i!~ -f:

- '$-] :'~~J :~"i .... ;Ii(. ,oil {!I

'-~t~

63

plotted in Figure 16. It is evident from Figure 15 and Figure 16 that a

favorable me en pressure gradient decreases the wall phase angle for a

given; over the range of a covered.

Now that the numerical predictions of ~ hava been obtained, the t

remaining chaptars will concentrate on measuring ~ with hot element t . .

gauges and comparing the experimental results to the n~~eri~al

predictions.

~ ......

, 'I.

"\ l:~~:J;·,f , _",-r..l.& '

. ~:.)~' ~ • -, \ - .,' I

.... ~ ~ .. ( .~ ~,~ , • -- _', 1'_ t; ~ J

,,', :::':'~ I :, ) I

_,_~. ,ret , , .. ~ 1·< .. )

. ,." .>, '1,:·,3 • 'i, ~ .: ,;:.~

' .. -..;; . ,~ .... ; ~ ... --.. ..... __ ::- ... )-'t" '

- £:,,& ,~ ~- ~- :~~~;

,- ~ "'~-.:;. ,

". .\-[>1 ,,' ~,_::;.~ I

'J;

\ i:/#:'; ... ---. ·,~·l .~, ," -,-. ~.~'~"l>i

• 'I' I : .......... , .• :":"{ i '. :':.;~ I

_ '?_;'i~1 '. f"'.'l

" j I t:. ,:r ....... . (i··c,';'; ___ \ r:' .;:t 1 , ,~ .. ....:.... t,)r 'f I

." " I ... \ l--:;',-s.l ~;\ t/:~\'~ \ " .~ ..

j.!i~ l :: }.' ; >.,~'J I \·t(.

'-~; ::,~,~: ~

~- /~i::{,i ':,:~l "iN ~f .t

1' ,> ,

'. .. \ :·'~~i

~~:i~"lj \ \ '

:j';~1 ;-;1

"- '. (7 .... ' l,'J ~~

-', .. .1.;:';,

::~.,.

L< ~}i-!~ ~ .' f":,.,

, "

,--.

\ '

64

TABLE. 5. Numol.·ic~l predictions of 0 in degrees fIJr various values of ~ t

EXPERUIENTAL CASE TEST ~lODELED CONFIG.

Al TCl

A2 Ten A3 'feU A4 TeI! A5 Ten A6 Tell

B1 rolrr B2 TC HI B3 're UI

-.1 /oj

0.45

O.:!4 0.44 0.('9 1.19 1.58

0.S4 1.13 2.26

1).0

32.5

22.7 31.3 40.0 41.0 43.1

28.4 40.3 45.8

6

0.06 0.10 0.12 0.18

24.1 19.1 15.8

14.8 12.5 11.7 9.9 24.1 20.2 32.9 29.2 37.0 34.6 39.1 37.0 36.2 33.4

19.5 16.1 33.6 28.9 39.8

~eso valuos of n are based en noci~al velocl~y values listed in Tablu ='.. Thus, tho i;i vallles differ slif;htly from the cor~osponding values list~d in T~blu 4.

....... ~ .. [~:.;;. "".. \t, _. ___ ._

-- I:; .. ~~-.~--.----.-- .... --'·- .... li~. ' ,

'. ..... .... , ---.. ! .\

"

, ...

.. ~

. '

"l: • I'~"', -, ,~ ,.,

:~~~ ~ :~ ""C'

\ lA,' •• ",!:J ~

'1~ " ',;~ . F1

::'~ ... -,":. ,"1' . :-1 ~ i

. ~l' ~:l ," '

;1f. J~'I

~-r?'i -. t.~f 1

--'-, H) ; • r,\,;}. ,

," ~ ... ~"~",~ : ~.~ 'I ;',r I :d ..... /i·l

~:". utI r, f~j

:?rl

\

?;~I :,~I "''-1 ·~2:.> , I,~

L;~1 ~

- .... :; 't'?: ----~.~,:;~.

1'­'\"--" t '.: o[ ,'I' ...

"<~: __ . ,f: ',' r<-~

- '-<'/' .... - z;~

" \ ~;' ... ~-.... 4~

" - - ''\.~'. :7.' .. --:.\ j:,1

\ ,',;, , ,t~

'" - - ~ :;1'1'; , -, ..... "!

'.. ,'7Jt I •. ~ ...... \ ,~~

<lj~~ II ;:( "

.~~. '.!!~ :,.

" "~' . • " :1

.... tif "'. -:~~

/,

50 r'1- -

45

40

35

30

¢T' deg. 25

20

15

10

5

o

Syn100l

o o o A ~ o t::I o o

-().05

65

o

0"" " ft~o"" " ~:~;'o __ o

o "'A~o ~ ~"":,o~o o~

C ........ C

;,~perin'ental hst '----Cas~ ~lodeled ;;; Confisur:atfon ~

A1 0.45 TC I A2 0.24 TC [I AJ 0.~4 TC II A4 0.79 TC II AS 1.19 TC II

.-

1

AS 1. 58 TC II ' . B1 0.34 TC III J

o

82 1.13 TC III B3 2.26 TC III I _

0.05 0.10

S

0.15 0.20 0.25 0.30

FIG~RE 15. Numerical results of Qt vs e

t .... - :~: It-- '":.7", -~ ..

'-.....\,. " ...... : ---- .. ' " l..

" I . / /. .,':'.. t" .4 ,/?~ ~, ... / ... ,,-

( t- /- ! '\ / I . I 1 ". ,

, I' ':, i -1 / - .' " " /

"(W!1,'.J'h'$",~~"~,,'i::W"""""'iI.::~ ..... ,,:,,,-,.".'!:J~':.':j.',r.'":~/I''';--f,!;;r·.·""-",,:~r.<~';9;,;\l,,,::;':"'r.'~-:::;:;::-''-~V-S~.g;:;::-::;;T,-;:;:;~:r:'~";;'':fi?'~k\,;r.;<''';;,;',.''k;':, ~"P~1:,:"p",,·~.,:;::":~0':;::':7'~~#11''t'~''''&::!''.:)~~ri'~

«

T-

"

..... -

,-

~

-

, J

·1 '. I

'1 : '/ -.'i "' .1

,I i

50 r-r-i

4~ ~

40

35

30

41

, deg·25

20

15

10

5

0 0 0.2 o.~ 0.6

,.

-------------- ----- ---------- -,,/"--

" ----/ /"

o.a 1.0 L2 1.4 1.6

'J

~umerlc.l Predictions for f~

II .. 0

II = 0.10, TC J, TC II

~ .. 0.16, iC III

I.B 2.0 2.2 2.4

FIGURE 16. NUiOlcI"iccl results of ~_ Vl> i:i for test configurations TC I, , TC II, and Tl; III

~ j

0\ c.h

..J

I

, f · '/

':' ..... '

lSI ... :;t'f ";~t]

, J' :.', ,~ ':.,~!t!ij \. 'c" · L _ ~j

~; .. "r:~~ ". ,.11 · . ..~

" t:::1 { ';'ill ~\ ~~~'~

,', I '

\-'~;5"

,~ :-1 " , l,'·'-;--.,

. I,~ . ~"''''' f'·-"-. --:----- ~(~

, I r

• i

.":;" :-t

<1"

~~} ':' -~ .. ~;'.~ ,t

/' { ...... t I t~

.y,;~

\~ :}!'.~

'" !, t;.:·; :~~ .. , .:~.:;

'.~.'; ,{:i'.l

.~~r. _ ':

~ .... ;~ ,: ·1 '2~ :~ " J

~::~'ll . ,

" I"""' ~ ;, "-I'~ ,~.J

,../;:)1

" --: {:~1 ',v, ,,~ ,,','1 :~?-' ~':.T~ '-'J: '~'~: . ~.

:"~.~ !,~1

<{ it

~jg "';.~ X{l ,\f,.,

'.. _. J,Tl .- ~ -~:~

~.

;}.~ '!

.,~~

'.}

~~ :':J ,':,)

'" 1'~ ;J 0'",'

'\ .:.:

;'

\. .,/ .~~'n ::.,,-- > '\ .. \ '-,' ~:: \ ,'\ ",~, , \.. \ \ ' ','l;b "", \\

67

VI. DATA AQUISITION SYSTE~I AKD GAUGES FOR ~ HEASURE}IE~TS t

This section describes the .htu aquisition system and gauges used

to measure <;;1Ie wall shoar stress pha::;o angle ~t' Considerable time, and

effort was expended in determining a reliable method for measnring this

quantity. Figure 17 describes the datil acquisition system used. A Disa

P14 hot l-lire probe in tho frees~rf'am served as a :-eference. Tho

freestream reference hot wire and hot element gauges were powar~d by a

Disa single channel anemometer unit. the output signal of which was

amplified and fil tored by a Tektronix ~!odel 3A10 transducer ampHfior.

The signal was then converted from analog to di3ital form by tho AID

voltmeter and sent to the computer for process ins.

Two type:; cf flush mounted hot elen'cnt: gaur-os I.ere u!,;cd in tide

study and are described iq Table 6. Each substrate elenent was

contained in a 3.173 m~ diameter stainless steel tube. One trpe cf

gauge lJsed was the TSI model 1237 AU hot fil;n gllu~;e. This type is

commercially available and consist:s of a thin platinum film deposited on

a quartz nubstrate. The other type of gause used Has 'Juilt br thl)

InstrUt':lents Branch of the NASA Ames R'.!search Center. This gauge

contained a 10 urn wire buried flush with the surface of a polystyrene

substrate. Buried wire gauges are described by ~hlrthy and Rose [21).

Four gauges, two of each type. were used.

Mounting tho hot element gauges was accomplishc<d by passing them

through th~ bottom of the test section ,.md a hole in the flat plate. A

flush fit with the top surface of the plate was ohtai~ad by visu~l

f

'v' • r : •• ~: .. " .. - ...... , . ... _ ...... ~

-_.--- " ','

, ~'

. - \

-. \ _,.. . I --,', -,' '\.j .. .. . . \ -.. \ ._" '\." " • 0' '\.

- ! ' 1 - ~ . . .' '. ~F];0"<;;'; ,;" "" ''', ','\;.~ ",'; ';ld,,~;;;s', .,""";.~.::;;" ;,;;, )'~;';'ln;'::'?-;''':'~:£~~i,;;;:;..G::j;'''i:~, ~;;.<;;\,r;:,'~ [;}, tU,;".j":{E." ,:,;;,);;;:,;;;;" , ..

...::-

.1

I ! ,

i

....

, i

,1

.'·1 -'. :,)

I I

, j

I \

Signal from hot \'Ii re probe or ilut c i eillent gauge

---~

FloH

---l!-

J --t:o-'

IUewlett Packard 6296A DC PO~Jer Supply

i l

OISA Type 55001 Anemometer 11ain Unit

Tektronix 3f\lO Transducer Amplifier

Probe positioning mechanism

/ Test section

, wall ./

I

External trigger, one per cycle

Hewlett Packard 3437A AID Voltmeter

.~

Osci lloscope I

DISA P14 Single-wire probe

~ ~Flat plate

~-----uot element gauge C; --11 s

FIGURf: 17 < Duta aquisiticn system for mea:;urfng ~ 1

Ccm.odo r;-J Computer- , System. Hachine Language P rog ra:ril1ed

0-CR

;

, "

'\

.-" '~"" ~'Y~

~;:~' ,,::;~ j

, . :~-:;I .. _ ..... \~::I

'J't' ,:.~I

<~;j

~~,~: I··~~r

:;.~~ ~ ,.\~ I

,',~I

" 'I .. <~ ":\;'1 "'':;1 ,", ~lt

,Ij.,' . .'C;,

"'1 _:.:. < ! 1',::

! .. :t ~;~ l·'~'

.. ,>,.- t>f " . 1r:;'~

.: :. '::~ ,~:f

f'" , .. ;~

tl;·~l "'·-1 .. '

;,tf (i

1'~J

"i1 '::'1 ,"'

I~~!

. .;t,J /' f)

-71/ ~,~~ .,' /' /~ , .. t' .-)

/ ;/~. , ;:t

./ <l ./. . ',(i

:'i~1 '.

.. '1 I: ;.,

'j ' .. , ..... ' t':

..=: .., '7.:."-- ':~

'~

,~l t t. tI.[r:;:;~ o

69

TABLE 6. Hot element gauges tested (see Figure 4)

Element Substrate Designation Type Manufacture L x W (Illlll) Substrate Diameter. rr.m

PFI Platinum TSI 1237 AU 1. 000 x 0.152 Quartz 2.685 Filnl

PF2 P1atinwil TSI 1237 AU 1.000 x 0.152 Quart~ 2.686 Film

FW1 nush Wire NASA ARCa 1. 753 x 0.010 Polystyrene 2.362 FW2 Flush Wire NASA ARC 1. 753 x 0.010 Polystyrene 2.362

alnstrument Branch of NASA Ames Research Center.

inspection using a low power magnifying glass. lbe orientation of the

hot element was such that the longest dimension was perp~ndicular to the

flew. See Figure 4 .

A hot element gauge produces a signal with a large DC component on

which is superposed a small oscillating component. Due to t~e small

oscilla-=ing component it was necessary to use a virtually noise-free DC

power supply to oper&tc the constant temperature ane~o~eter uhiclt

powered both the hot element and hot wire probes. Since the DC

component of the signal was not needed to determine the phase anglo for

eithcr the freestream reference or the wall measurement, the Tektronix

3AID transducer amplifier waf. AC coupled. This eliminated the DC

component and resultad in c signal oscillating about a zcr~ m, an

voltage. It was also necessary to amplify the oscillating signal to

obtain an accurate measurement.

t l.~

• '" : .a, ,~. ' .. , ..... . ,<

I '1. , .

~ t~ 1'~4J."'~: !~'4. ! :",\i I ~~f.'! ·-....."";i \~r"

''?I}~JI ~ f." ... i .' ~~·~;t

":!'>f!l ~<;" ~ "'.~ ;t."',

t··;:.1 .", '~'I ~' .:."}

:~}I

\~,I ... J" "~I ,"

,- i:":~ '~-~l

'~;:~:?' :,':('-; YJ. --:-1

;;~~ .; i ", I~

,.",,;1 '·:'.1

" l:·.!l " '! ':'d /~ .. ' ~1[~. /1 '~::~

:~11 =.,..:" ,~:.:

~~, :.. 'r.;~

~~;-I

~'! ":'J:J ., r W

':"1 I ,,'l'""-l

.. ~

':~91 ''',-I

t";~'i \ ....... I

\ ~.::.~~ i ,',~ ... ;,,\ :';.:;1

.. - --'.;i', :'·~l

....

l

~ r'':'1

;1t:ji i1 '::j1 ~"

,tff. :, Ii

.'1-:::'; ~~t :;.

" I?: '~"::~~ .. , ~.,t.

.'

",

~:~~~1 :-.1 J.::11-"" '.- ~::

.. "

70

The same procedure for obtaining 20 ensemble averaged voltage

readings per cycle as previously described for hot wiro velocity

measurements was used, but for this part of tho study the 20 points

contained both positive and negative voltages. A requirement of the

fourier analysis was that all the voltaGes be positivo, so a constant

fictitious voltage was added to t.he 20 voltage values. The sum of the

gauge voltage and the fictitious voltage will be referred to clS the

relative gauge output rath~r then voltngp-. Fitting a cosine wnv~ to the

20 ensemble averaged relative eauge output values and an appropriate

uccounting of the freestream phase angle refCI'l!DCe result:; in an

equation of the same form as Equation (3). However, the values for t o

and tl are meaninsless and only it has significance.

Now that a brief description has been giv~n of hew ~t wan maasured,

the remaining part of this chapter will be devoted to deDcribing some of

the problems encountered and the :;teps taken to ensure that the errors

in measuring ¢t yere minimized. One of these problems lIas to dctl>rwine

if the fourier analysis produced the correct value of \ for given input

information since the anemometer output signal was n~t linear with

respect to the input signal. The freestream velOCity present in t!1e

test section is sinusoidal, but the hot element or hot wire signal out

of the anemometer main unit Bnd Tektronix 3A10 trcnsduccr amplifier is

not. This is due to the nonlinear relationchip.between the input and

output signal which governs the. operation of the Ilnem(·:neter. A

linearizer was not used in conjunction with the small signals from the

. I " ~ . f" '

--~.--- ... ---........ -.----.. - .. -...,--. ..--.-.---~.------" .. -----_ .... -/

/ ,

, , I

''"- I

7 ' ! Ir

J ~.' ~ j _ ::;'l

, ...... j ~~:;:j ~~--I- ~ .

. r / .. ' ,., ::'~ /. . ?:

,: / \~] . .. '\ < "/ ...... '" .. ,' ,". .,

,: ..,'. I,~~'

. ~ "," ;

~l-,' ; ',-, '

-1 I

.:.-

',>, ~;I ( I ,~'

/ ~~~1 .;' :'~ 1(;'1

'~] :4' 'F

"j . , .~ .,

~'1~~ " "1 '~'/l , 1

;"3 ';

!I',,~.{ .:~ "'~ :'; ~',~ .t

::1 \~

:'"j ," J.

.-,--J : ~:l /1

\ ,y

'\ ;' .. " I' ~ \,', .'

II'''' ,.,,1', ~ I -:;-, , ,

/, ! ~

, :

·1 \

I' .'.

.. \ '

").' ~ "I' /' It ,,' r I'~

:~~r::7 .. "

71

hot element gauges because of electrical noise inherent to the

instrument. Figure 18(a) shows an oscilloscope record of the nonlinear

sienal produced by a TSI gauge. Figure 16(b) ShOH!; the 20 ensemble

averaged relativA gauge output values and the cosine tvave fit to the

signal in Figure 18(a). Figul:u lS(b) illustrates the fact 'chat the 20

ensemble averaeed relative gauge output values do not directly fallon

the cosine wave fit, but they do sYll':netrically fit it. It is because of

this symmetry that the corr£~ct phase angle is mea:mred. To

experimentally prove that the correct phas~ angle is measured using a

nonlinear signal, a comparison was made between ehe phase angles

measured using 11 linear llnd nonlinear signal from a hot wire in the

freestresm. The nonlinear sigul.'.1 was obtained by using the

instrumentiition described in Figure 17 while the linear signal Has

obtained by using the same instl'urnentation but adding a Disa type 55D10

linearizcr in series bettJ.:!en the anemOr.1etcr and the T.!ktronix 3A10

transducer amplifier. Th::ee run!; were teken using each instrumentation

arrangement and ~he average of the three reSUlting phase angles was

calculated. The diff&~ence between the average ph~se angles for the

linear and nonlinear signals wa~ less than one degree,

To eliminate the error caused by a phase shift within the d.!ta

aquisition system, exactly the same experimentdl setup was used to

process both the hot wire freestream reference and hot element gauge

signals. Thus, any phase shift within the instrumem:at ion system would

not affect the value ()f ¢ • This statement is true onl .... if changes in t .

4 0"

/

I / " .. {

. : \ \,

,; /!J 'I ,~:~~".~, .~

" ,'r~ I .... fJi; .. / "

,,;.,:.::'::-.-

.. ' -'

;. :/ .; "

"'I( ..... " • .5 •

• ' ."> .-..... or.

j ~i ~. m.'····, I • r;,Ji .

.. /~l: '.:)bi!J

t';~·

/ I " ~t ./ tWi p;r

/'

, ~~

'.;1 f. t:l\

"t/'{ ~j1. "J' 1~

,~i /'tl'~ / .~

j /';;'A:

,/ 11 f" ,~ / ~;i

//

,~!~

, ~:~.~.-

~i )~

~.~~.rM ~ I

72

PFl iC II ORR::: 1.18 f = 20 Hz

ORIGINAL PP,GE IS Of. POOR QUALITY

(a) Oscilloscope record of 8 hoc element signal

FIGURE 18. Description of a hot element signal

l;· .' .': _ <t+A;·i.~,:q.i~·";,~<",~,,,;,~~''''·<l-···'''''·''''·--'-''- -' .------..-.-~~~--~ ... '~~--~.-~ .... -"'-,.-'".->- ,", •• __ .,..,..,..' ............ - .... "',=>·,>::r:~!·*~·rzi~~.iP·;~.:<" .. \," .. :!.o;-..:;::~

/./ ,.// / f f , ,

i' __ , '

'; / i 1-'

.:..,. -",

. ~.::~,~":,~,;:=-"=~~~-~; ::;,:,~::;,~~,-,';-",:'::::;, .. ~~:-:~,~,::o>:~~::"".<:;,j,~''-';~'~'4~'~~~';''~'~=~'~:? ,:",~ --.. r'i;j" • ' . •.

", ";,,, \ '"

, ~l

•

"

---.~

, ""

- -- , , ! j I ) ! . 1 I I 1 I

i j

I

i I

" . i ',1

j ~ "' .~.)

. i

5

I PFl * Ensemble-averaged experimental values Te II k f=20HZ ------- Fitted cosine wave

4 ORR = 1.18

.... * * ::l C\. .... ::l

0 3 (l)

C'> ::l r:l l!)

(l)

I ;>

2 .... ta .-4J

c::::

~ 1 lL .,.

*

0 .L--l

0 n/2 iT

wt

(b) Cosine wavc fit to the 20 cnsc~b)e averaged relative gauge oUlput valuc~

FIGURE 18. (Continuccl)

*

317/2

1 .... I..,)

J

I 217

,-

/

, I )':

~ J~'~":;~"J' [",.r.

. I .:'- ~

:' Q,11 . ';'1 ,;,tJ

"'f ' , ~: )~-t

:j~1 ·';.l

;';, : ,;

:,~/f

'''" . ,r; :~~

/~:.;'~

'<~~ -~ :.~

" J '_"

: ·i "~,

<r..¥ .~"J

• 1~~

",,~ •••• J\ ., :, '~!..:;

;~~~i ,1_,":

f A' •

, " r ;.~

/ t'·<~ . ',.~-;

i ': :~l ~, ...

, f':"~ .', . "i'~"j' ;' .\ r';; ~ '~;f ::.:;. '~~ i

,!.,~ ~'.::' ':J-

. '~j

!' '" ,,'~

, :'''1

: I,lt~ ? .

~ .t·

"

~,~

. , '~i

1 I I I , ~ I 1

"

"'f I, ' ',~J 1 ~,'" j

;, ~,

~~:', ",:';

...

'''' .. ,/, :,

t

:: .~ i.

'. ; ....

<,

74

die'll settings when stlitching from the freestreac reference hot wire

probe to the hot clew-ent gauge has no effect. There were several dial

settings changed when switching between the freestream hot wire and the

hot element gauges took place. Consequently. the effect of these

chanses on the phase tingle measured needed to be investigated. The

sattings changed on the anemometer main unit were the capacitance and

inductanco settings required to stabilize the bridge and provi~e optimum

frequency respcnse. Only the amplification setting was alte=ed on the

Tektronix lAID amplifier. Gain settings of approximately 10 and SO were

required for the hot wire and hot element gauges respectively. Various

gain setting5 ~re::te ne€'ded dne to the difference in magnitude of the

signal produced by the hot element and hot "lire prob~s. Testine; was

done by changing dial settings Olle at a tirr.o, t .. ithill reasonable limit:>.

and obser"ing t:1e effect on thp. phase angle measur-ed. Both the hot wire

referen~o and the hot clemen~ Gtuges wore used for th2se tests. Since

the eff,~ct of ORR of tho hot element gau.~es t.las ono of the quantities to

be 'Jarieu in the hot element gauee respo'1se study, ORR was not changed

during these tests. Upon completion of these tests, i.:: was determined

that these dial settings have no affect on the phase angle ~easured.

The effect of the ORR on the hot element gauges will be addressed

in the next chapter. For this study, the ORR for the hot ele~ent gauges

were varied over the ::ange 1. 02 S ORR S 1. 33. The ORR is d measure of

the tempurature at wl:ich the: gaug'! operates at, !.rith a higher ORR

cor.responding to .i higher operating tC'11perature. The upper limit was

:.;;.~~ ';'1--:; '~-/ ;:.~ .. ~---.--. 'f ." i ' , I

.I ,

,

.. ... . ./

j /' • ;'

I ;

.!

iW

~ r. iI· ?

~ ~,;' ,;~

't '{

• I 'l~ I r

• i

, t~ ~r i'~

\'i i: • '" '1 if ,I :'U

/11 I ~'{ .

. j ,'-".,1,

~ ". ,,. f

l " , ",-_ '_ll~: . ~ ~ t,

~r: ~ .....

,'I' /' ',';,

,/ ;. .. . l~

,

~ ~ ~

0

r -}

~'

~

! ~"

, , ~

~ A

I ' ~ ~ ~ J.

1

t ~ ~

I'

'''t ~~

·t' ;~

"-',::' ,\J

" -, . ..

~~: ""<:;1'" r:r .?~.~'" ;. ...

75

estimated frer:. information supplied t-lith the TSI gauges. This range for

the ORR was also applied to the flush wire gauges. However, values near

the upper limit resulted in premature failure of the flush wire gauges.

No problems were observed with the TSI gauges.

The Tektronix SAID amplifier has a lew pa.:::s filtel: which IJas set at

100 Hz. Even though the filter setting Has not changed when switching

gauges, it: was desired to det3rmine if this setting eliminated any

frequencies required for an accurate measurement of ~. For this t

comparison, two fil~er settings were ehosen 100 Hz and 10 kHz. When the

~t measurCQent for each setting was compared, the difference was

negligible •

Tests nhowed that the protrusion or recession of th2 hot elemc~:

gaur,ps relative to thu plate surface will alter tha ph~se anele

measured. Determinine the change in the measured phase angle for 3

given chanz~ in gauge height: is difficult L'nd was not attempted 1:1 'Chis

study, but a T:lI gauge t.'as intentionally placed slightly above and bul!':'!>!

thu plate surface to det!::rmine the influence of surface mismatch. This

resulted in a change in ~\ of several degrees. Consequently; extl:E:I':1c

care was taken to mount :he gauges flush with the top surface of the

flat plate.

Several runs to measure 0 were made using a platinum film gauge T

with the longest dimension of the het clement oriented parallel to eh~

flow (90 degrees to that: 5ho!.;n in Figure 4). The average of eha results

fo~ 9 from these runs was B degr~es smaller than for the perpendicular r

- ---.------..... _---_.-• , ,

....... " h"',

\ ,

'~'r>:!l <.)~

:,~f~; . ';fl'l ;}" I :f"'(-,:'j: ~,

.1~ I ~~ll '-'~'l ~~~ d.: ',;,1

..... ::" i

~r j . )i- !

"';.'1 .f( t

."il'. f ""., l

{t I : ~.~, . ::?:~ !

;?-' I ,"')'1.." J

51;,\ . ~}l r:JI .... ": ~~6. ... !t.,

/ J~.(;~ I. ,; '.'" ,. r :;.~.

~ ~~:.1 ':'.J .I ~~~t;l

ti~ {:..1 \ ~:',:~:

t}~.:: .;

.~~l:·:t '·J:t·

t' j

\

., ' ~. ',.-

~~"j :~ . .. ~ , ,. ,,\-~'

·~·s :1{:

J~~.! ~{i1 ~,.r!2

• ,.--:j \ :'If

'. ";:: . , ··;1 ,.-'," -.. ':~1

... '·;.1

'.,i~l fiL._ .. ~~.

'.:

76

orientation. This indicated a rather pronounc~d sensitivity to hot

element orientat~on. As a result, caution was exercised to ensure that

the hot element orientation was SO degrees to th~ flow direction each

time a gauge was installed for testing .

To ensure that changes in the room temperature and pressure had as

little effect as possible on moas~ring ¢ , thn f=ecst"c3m ref~rence t

phase angle was obtained the same day as the corresponding wall

measurements. Each freestrcam refere,.:':e angle \o:as taken as the average

of 3 runs •

._-------_. ~ , ,

_ .. _--... ----_..-, .. _--'- ...... . . "

.. -....... --.--~,-. ...,

,J".; \ , \h,U;

\ , w~,' t .. " : '

{ , II I

/ ,j' I /

'/

\"

, ,

" /~ ,

" .....

,j,

'.

\~ <' ',J'A" -~i "', .~- .

',;" I ~ ....... 1' . i'd'

',~"I , .' r : i :J '\ It~ . :' l \ ,-' ,I

", -- \1 :\ ,i

,\. r~ (' ' f'l \ '\ '", '1 ,/ \:, ~ d /' , '"~1''''' .1)1 , I

I; ,/ , 111 .I'L.

~. , . ' ", ,I •• ' , .

' ..

'. " : '\ '., , " ..

77

VII. ~ESULTS FJR I/o t !1EASURE~IESTS

Results of ~he e~F~rimentally measured wall shear stress pha!~

angle will be presented in this section. In addition, the c~peri~ental

re~ults will ~e compared to the numerical predictions.

As previously mentioned, tl:O types of gaugec; were used to measure

~t' TI1CSEs are the :lot HIm gauges producel by TSI and the buried wire

:auges supplied by NASA Ar.les Re~.:arch Centol. Tl40 tauges were llsed frot

each type for .:l t(ltal of four which enabled cc. =.'arison bp.t~een si-j

gat.~cs and also betto:een the two different types. Thern were no

distinguishing felltures bett.ean the burip.d wire gl1u:;es but there was

am"n~ the hot fil:.l S8,U~CS. PPl (see gallge d:!signation j,n Table 6) did

not have the prote.ctivo alur!lins covering oller the p16t.inwn film tha'.: PF2

had. The ",bsencG of this covering !li11 be dis~ussed loner in t:lis

chapt(!r.

Preli~inery :ests =eve&led that the ORR affects :he si8~al quality

imd arupli tude of tho va 1 tage produced by t:w ~dugas. Inc::cas ing the ORR

causes Iln increase In voltage ,. .... ri the sign,ll quality is ul~o ie. rO'Jeri up

to an ORR of apprcxirnatcly 1.08. To illu~f t'ate the c~ .. lnge in qU;Jlity

and amplitude of the signal, os~illosccpe records at three values of ORR

l.u2, 1.06, ':>1".1 1.12 nre shewn in Figure j,9. These pict:ure.s alH ty?ical

of t~e response of all four gauges at all frequencies tested .

A list of the CilS,!S that were st:Jdied and it sumrna::y of the results

is given in Table 7. ryetailed results for the cases are tabulated in

Appendix B,

r, . "I __ , . t. I

c

Each case contains the resul:s for ¢t vs O~U fer 3 given

",', J

, ,

. , , i

I I j: r I I 1/ (J: /

.. :.: .

i I'

/1 I j ~

:' 1'/ 'I

. ,

/ 1/ f / ! J I

'I

d) to.

" \

, 1 ,

I

~ J

,: ,."

r,/ 1 ~ f t

,;t:: r'

,..~~ H ~~.:

".1 r'" " u.. (.;, t.~ 0_1· .',

'I) ~)

I, .e ;.J

V <1

,..¥'l

"J ~--; tlA;

.,,~

''/1

;.J ;:; r::,; .., ::s 0

;.J r: 'Ii f~ -;;

,·,'f ';/'

.9 l>

,.(.~

<'<5

~ I)

11J '':J I., () (,) t\1 !..

(,-:. C. ,~ 0....; () () .,'" :/1 0 0

.. ~·4 Vl ..... <I! ... ;:.1 (; p., (/j <j

0 ~.

t:/'> ~.

III ~ ;..J Cl H ~.

) I

I J.

~ ~ ~.

" ~, , i"

ii' . .;t

...

-~" ,-~-.-~, <i

-.:.~ ..... :<~ " '"

:.:: -~ ,,' f l: , , ' -t·

-- : '1~ ;;::

, " " f~·t· ..--: 1-" ':f:t · " )

.• -" .' ,"1 · -. ~

, "I:i -,._\ 'i: , .. ~ ~~.

" ~. [1 • ''.'-.J 1

~~. r~~ ,\ 1, ·"t'i .' -

\ -:-~'4' .' :J:

'~\'::; ,{ · .\- h . .~ .. f1

t ..';

", ~,,,

:i

~,' f't ....... ' ,,' ·i .. -~ !.... ' ~-~ '-.' -..i "' .. ~ Lt : ,'~' f~ ::-<:.' r'~ ~~-- r1 .-" '. £.1

.H , ' -\. ~~

..... " -\ -.' II i- J I~ .-.-._ .1

1 ,~

'., \

", , \

....... :

,~~ ... :, l I . ~

,::--.,

,I ~. \ .............. ."- • .1- :,_.:. \ '.F. .'

79

8ilU&Q~ frequel\c~', and tr:st configuration. i~hel\ calculating cr, only t~o

valu:ls of U wore used. These corresponded to the two ~ilve gel\el:ator o

section configurations (Tablu ~),nnd ware 16.7 ro/s for wav~ gcnu~ntor

sectio~ configuration A and 11.7 m/s for wave generator sec~ion

configurlltion B. This was required since the ~xact Uo \;a5 not measure'd

thQ da}' c,lch case wus obtained, but 1:he error introduced 'is not Qxpected

to b~ large sinc~ U~ romains rel~tivoly cons:ant •

Thu results for tho casp.s in Table 7 as tabulated in Appcndix B llro

plott~d iu Figure 20(n) through Figure 20(d). Each data point in thesQ

figures represents a single run. The uncertainty in tho mellsurements

was c~tirnetcd to bo ± 1 clc~!ec. It is evident from thoso,fiZuros that

thtj ORR affects the- pha.~e sngle r.:Ioasure.d by both types of hot tlbment

&I1U305. For Illast of tha casas, ~ •. increases with ORR until the ORR l

r08.cht')s about 1. 15 • .ltter \.1hich -:. tends to remain const<1nt. /l.S QRR t

incroMus. There are evid~nt exceptions to this plltt~rn. 3Q~.:luSC th(~

wall ph~se angle c~~surod b! tho gauges t!nds to bccomu indepundent of

ORR {or high valUQS, on avoragQ ~t for high ORR CIlY be dc.turmined. This

was accomplished by drawing curves through the experimentlll resul t;~ •

Onco tho curves wore established, 0 for ea~h case was daterr.1ind~ from T

thu f11t portion of the curve where the measured phase anele is

independent of ORR. If the curve was not flat tho tT was obt~ined at

ORR:: 1.30. Using cho above method, tht) values of ->t at hibh ORR for.

all c~sos hava boen t'lbuluted in Table 7 •

d .... : ,.: .. '~

'--~ t. I I

"

"

"',." {@ ". 'i .... <t :..;

• ,":.. , <~, · .:..:, ~.,

'- •.• :1

~ ... ~ .. "'::

~ ·1' . - .... z :,,< ~c '" :..:; ....

r'f';:'

'f: ~ ~ -\ · .......... ,~

;1 , .; .'\

80

TABLE 7. Experimental ~t casus studied

, TEST

• I .I. .,~ ~ --.- .. - ....

~i ,~;. .. ... ~,

,,( ,.. '!",

'~~ CASE CONFIGURATION ftH~ W ~t·de3

11 (~tn - ~\'Q)

b

f'\~ , -~~: t~

t~i~

"

.. ~;; - ~"

-. ,-·:t,'ji ~"~'. ", , (or

t';i

f1

" ' J ~_J:t ',"'--' '\ n

:1,- U \ L:

l : '\ .: f ~1 '" 't':]~ , ,,-,:~,

\, ~', ",,',

\ "'t ~ , ' .. - \ P " <:) .. , 'l'" i

"'. \::.~d '" '1'-1

'l' j , -' " ,,",:/'j ... , ,~ f~:';i

,', . "" \ '.

>Z '::/: l~~l :. ,~r'i ; .' "I: j}. I " .' " .; '.'';1 ':' "\ 'f .:'j ,,~' .. ' "':,/~

" '\~ ... '":":.:.'- .. ·t·,~,~"

PFl A PFl B

PF2 l~ PF2 B PF2 C PF2 0 PF2 E Pr2 F P~'2 G

PF2 l! PF2 I PF2 J PF2 K PF2. L PF2 M PF2 N PF2 a

PF2 P PH Q PF2 R

FW1A FWl B FWl \:

FW2A FW2B FW2 C FW2D

TC I TC II

TC I TC I T" ... ... J.

TC r TC I TC I TC I

Tell TeII 1'C II TeII TeII TC II TC II TC II

TC III TC III TC III

Tel TeI TC I

TC I TC I TC I TC I

10.00 20.00

3.00 5.00 5.00 7.00

10.00 10.00 ~o.oo

3.00 5.45 5.45 7.00

10.00 10.90 20.00 20.QO

3.00 10.00 20.00

5.00 10.00 20.00

3.00 5.00 7.00

10.00

0.4.5 15.3 L66 25.8

O.ll, -O.S 0.23 3.6 0.23 4.6 0.32 10.S 0.45 13.3 0.45 16.2-0.90 1S.2

0.25 4.4 0.45 12.4 0 ... 5 12.4 0.58 15.3 0.33 18.9 0.90 22.0 1.60 :'4.9 1.66 21 •. 9

0.35 7.0 1.18 17 .9 2.36 22.0

0.23 "5.5 0.:'5 9.5 0.90 17.3

0.14 -3.2 0.23 -2.5 0.32 4.3 0.[,5 10.4

a~ was obtaitll'd £::-0::1 the curVQS in Figura ~O 't

nt ORR = 1.30. \ 'It :~"~' \~ '\"'" :" --\ '~:~

· ,. .. if

-. ',' '!~<~ bThQ difference between the nu~erical curves and ~he

exporimuntnl data points in Figure ~l.

~ ~"~"

: ,-:::;~ '" t".~ ..... _'. r,-:,~"",

''. "'f:" \ .. ~~ , , . ", ~

, .. \/:~ ;j . --.--- ---'--'\ S [:\::L "." '" ---- , I.. I

- "\ ~ \ \ \!, ~ =~l~: .. _:_ t,." .... ., ,

., .. of'.: :,. ........

" \ I, -:- .... ,"

5.2 11.6

8.1 8.:' i.2 4.9 7.2 4.3

13.0

8.4 8.1 8.1 9.1

11.1 9.2

12.5 1~.5

6.3 11.7 16.5

17.5 11.0 13.9

10.5 1:'.3 11.4 10.1

, .. _ ....... -'~~"""'·l

.. '"

" .. ~ ... ,_..lJ .. ,

. - \''' .... -...

~:~' -', ,~' ..... --.... -'\

"" ,':It .. "" :';t, .. ;~~ :''1 [1 ,,"

.; f,-1 .. k 1 ':',1' t~~1

, , :,J · ',. . ;..,~t

\. ;,). ';.1

\ ~" \ ,,' I ,

.... '\ . .'~ :"\0] \ \) J

, \ \: ·::t , /j

. 'l ....... i,~

'\'" ,'-, ;1 .,- "?! .' "~ .. :- --,~, . ~"".. "-, ( ,., ":\'

"-'" ' :;~ • T .. J • I' '"', ~Il-

,:, t \ 'I~~: \ \") \ .,. i' ~.'" , ,. " ' .. ~

\ " ,I • •• 1 , "q

... "~lI: \ ~';'f

, :, 'p2' ," tij f' ", . ,[, "j' "' ...... ' , • \ j"

'\' • -.~ .... i~ 'r', 'H , .. ~" -:"'I~i \ \ ' ", ::! 'l \." . ":,I,~ " , • '4 · ~. <~;

.,,\ tl~

!:=", ,.,j ~:~

'J ~,"" . ..!. ~-, . ~. , .. "),, ':~f

.., . :;:1 --~7-: :" <-1 ',\ "I .:~ '- .':., .' I . ';

• \' l ;~~ ," :',/" ... ":~ • -<,.I , :i -:-/} _.< ;:jJ

/ ':'.:~ . " ..... ,,',., I •

.': -: ~~- f ;j, L ! (- •

, .' ': 'r' ~,,'! d ,.'~ : ' t~J . I ~.

"<0 '·,l , II ,;\

: :'" \ q \. L .1~ ~ '::'\11 \..... "'i · ~

,I \, ., ~. d ,', . ~~ .... , ,

~r'-'f' .~ ........... : " .... -11 ,'\ ....... j~ ~... : ,,-

"

¢t' deg.

30

25

20

15

10

\ .--"" .. - ...

81

r-r-r' i r r=. i "'I"-r-

~Y~ ~ -!L TC I 0 PFl A 0.45 0 PF2 A 0.14 0 PF2 B 0.23 Q1 PF2 C 0.23 ~ PF2 0 0.32 0 PF2 E 0.45 () PF2 F 0.45 6 PF2 G 0.90

_-_4-_,------ A-A----~ '~---m-() -- CD---u: \V / -='0-

t:::. --~/.O ___ 0- - ---0--0

if.Q~~=~--t. ---. c.: t>.-e,. 'It::::.

~ I t' /t:;: r ~--CI.1-' 5 I-~ 0 en ~ m-______ --0---0-

t- ..9_~:::-::-~ --0- - - - -Q

r -0 _____ 1 i -I o · 0_0- 0 --"""0-

if ~-O---O--~ ..

-5 ,-.

~ -10" t L • .....L....L I -' L-L-J..-.L-J -L 1-'--l....J.J

1 1. 1 1.2 1.3 OM

(a) Results for PFl and PF2 gauges ter TC I

FIGURE ~O. Experimental results for ¢t vs ORR

, • ." -r ... " .... '.- .• '._"""""'''-, '. I

-\.'.' ." •• _ t ~ I , .. :, J , \' \ '~ ..... ".: "

\ .

,- -"/ " '

0:

·~U ,\:.:'1 ~: ~~ ;':?

':¥

.' 't".' • \I~

. \ · '., ~J::l; /~-i'( ., . :: :..... ..' ;:~ · ,. .,,'

,..... "'l ~ -'J

, ,il · -; .:' fi~ \ \ " ;'ij \\ . ... .~:t · \)' I '<j' ;.. .... . .. ~ ' •• / t .... ,

J " . · t '." < " ,/.<, I c:l' <', "1 ". I~<\('I -, . . '.... . -~ • • , ,,!t-•• >]

· " .. ~ -~ '1 .) )' j '\. ." ',~ · -'f' . ["; . ~..,; . _0- ~

;' '~1' . t" , .' .; \_;., .. r._ ;~

/ . ).-1. ,.. f ... ~' .. ~~

4 A)~"~' ::1

--<'" ··t " \ ' ;v , . , roo

.... ;:..:.:.:~ "'!.: . ' ,{,

t, t ~ ,I . t' . ,}

<-' \. l~ " ,: 'ft!,' · \ : .. " ,.,

"":: -:~: :~ -,. , ;,'

·w£. ._. ,!.t ........ i'w

.,.! ~~ -~J

~ >}--!'

, "~'~ • \" -':!j .. ' ~ ~:. " 4-

........... ,.,:, f ';)

, ' ~;.~: ~: i"

• ~ !,

:~,,_ i~

""I-',,' . ~i. \ :

, '\; \, <P •..• " ~ 1~

\. I "" !~ .•

~;"'_". 1'1:= __ ~ .......... '~~~~ _. ___ ~ H ~

,; /'. .: '

QT' (kg.

30

2S

20

15

10

5

o 1

82

Symbol ~ ;:;Iic 'II' r-r-rr-r-r-, ''''''-'r-r-r <.) Ptl B 1.66 o i'Fl H 0.25 o PFZ 1 0.45 ~ PF2 J 0.45 ~ prj! t:. o.sa g PF2 l 0.83 <> <> A PF2 11 0.90 ____ 0-- --

PF2/1 1.66 & _6.__ & A 0 4 PFZ 0 1.66/,:: _--0.; , - '-~-'-o:..-t::.-6.

~,' 4' 0/

/~ 0-~t,,~

°----° __ 0 __ 0

jf 1/ ,,-0 -- -0--.- - --0- 0 0 . '~,o' ~ --- ----.-- ---'--0

t I

~I ,.-t:::.-_ o "'" ..... I /~ . ~- _

I ~ - -,,- - - ~ - -~ , / ~ . ~ o I

c.,' ~

J'A/.....--8---& "ft. 0

q. o_~e'_Q

r &, I I

tf . I ~

o - -<) ~ 0

a.. 0-("-0--0 -0---_0 __ I . Q-(> o

1.

>-.' '-'-~ !--J...-I-L.......i-~

./ , i ~l I ' . ...J-.J, I -, I

Ll 1.2 1.3 ORR

(b) Results for PFl ad ?F2 gauges for TG II •

FIGGRE 20. (Continued)

~ -.. ' ",;,.:'.-,--. .._- -- - ..... . ., -::-'-,",'! ,,~, . ...J ~ ~"'------'"

\ . - , r,-:---l ~::.. ... -..~ .. _.',~-~--- •• ~ .. ,;-:--... - .. ~ .. - .. -- ------.-7-.-.-.-\---· ... ---;---.... -·--0-:'·, .,~

[i'!I 7:il

t~:i1 .-~~

ct' F:',,'

:'1 i,,'" ~ • ~ . I;~

" ~ ----f,r . <,1 .. ~,

,---- .'1'::1' :. i' . ~, .-

II.

o. ~

· ' '-: ~ · \ ::.:J \ .. t';·fl , •. j . ~,

. 1"1;\1:~' · '. ~ -.. ' </ .'J • ,,'II

. I ... ~ .' '. ~

. t,::·!

r:::{l. '~ :!

, .. ' I,;;} ,:' ,r'~~ "J

"'" :"J • /' _ .. ~~ '-:/.t " " , 'jj

~l' '"d l .... ' "'I I· .' .• , , ,I,.i

. f .- .~.~

I \ "1 I. ! .I, I ,;;:! I! i "tl

. 'I 'I

i "'::~~1' 1 • \ ~~;

· \ ::~ ~ • ;.1.

< ~ •• ;

"{

~':~ , .. ....... :,..{ :.~

-r ;~

,.' ';'.1 .. -/.." .,;~ . " . - .'~. ~ .: ~"~ji.

'.,

'. f~1 ,.;" .,

-;, ti ., :t

'I;::~ . ::~

I t}:;~ ~' '~J

'. .~. , • ~ <

:'::- ~

83

30 ~ .... T T r·~·r--r-'-.-.,..-,--r-(r"T".,....,...,...,.....,.....,......,

25

20

¢,' deg •. 15

10

5 1-

o 1

Symbol Case PF2 P PF2 0 PF2 n

w TC III o o L.\.

0.35 1.18 2.36

/6~--"'--- 6 ~ 6-6

/ 'I --0 __

! ..... o_~ -6 --0-0

R

O/O ...... O-~---O o

-0-_____ 0 ___ 1\

v "'"'-0

I A

..... I-~.t-..t-.I-l........-'-~ '-~~ •

1. 1 1.2 1.3 ORR

(e) Results for PF2 gauge for TC III

FIGURE 20. (Continued)

{j . I I i

.'

1

j

- '~fl ..... -.. '. ~:;'-5 / t~\~· .. .':-;:, .. ;.-;-........... -.,. _.-\.A¥3 __ ............. ~~...wr..'~~oCLn1l._ .. ,"*'*"''1'tr-\It.r_~ __ ..... \1.1 ........ _____ ..... &'.-r_ .... ___ .. ~lQOl.~ • .....,.....-.._ .... :;Ml~",.., .... __ ~ .. ___ .. _ ... _

\ I " .,', • , " .'

" p" .. ' .,·rS;··~"1

r~t!{· ~: :)1,-. -' ~~t .. >:.,;.\.,

/ ';\;', .'

, ~::J" "11

~/ -~,' j/ _" ; ... :.~, t

• I· :~;; ~ ! '_ :"""'"1'" I __ ;'I:f-

;./·~~<l .. ' t .-,:

\1· ?}'.

" ~; ~

/;1' 'll;l '.''':"4 'T

, . ~~~t. / {f /~l

7 :'~ ~,,!"

,'~f~ l t. ~t;

:.~~

~: :~ '."'f. r'~".

·:::i , ~~-·,t' ...

.. . -.' ,~;J.~ .. :.~~~

I -1°1 I I'-~~ .

,I :,~r· .~r-.' t·1,'!

~. ./ ~~:' .. r .~:~ •. ...

:".frP. , .~

. ~~. ~J'

,1->:_:;"\

i~t{' ".j~.

I

! , . --.-

" ..

~

! ~.,,' ,-" o:j-.

~:;'-' . !;--

;~~ ":t~ ~-:,!;.

I ~ __ =~ .... .... ;.- " i

;.::~: ""j' ~:;f :. ,

30

25

20

15

10

~t' deg.

5

o

84

r-r-r-~

Symbol Case w TC ! -, 0 FHl A 0.23 0 FWl B 0.45 A FWlC 0.90 ¢ FH2 A 0.14 m FW2 B -0.23 ~ FW2C 0.32 <D FW2 0 0.45

~

/1:> I:> ~&' /6

Ii

/1 ~

! ..-0-::::.-;:::::.>(1)---- -$ -- - (J)

O -.,-. ---/., ___ .. -0

0/ 0 -0-

l::..;'a/ o /

I ~~ ~_&_-.----&----~ J::(" '"

I I I , I _ ---0 ..... ID

-5 [jl_ <D rn/!lI;-&--Ill':-"'::'= _1'rt1 - -- [;~-:-~O ,O_D - \£loI- -~ -0 \) . /.0/0 O---=-- ---- -----. Or 0----·· 0 ill 0

o· -10 ! I ! . t I I • , 1 ! III !~ I 1 -'-~'-l . 1 1 2 ~.l.-J.-I-l-.L I I , , • I

(d) Results for FWI and "FW2 gauges fer TC I

FIGURE 20. (Cont:inucd)

1.3 ORR

,.;""':(. ! '1":;;" ··i :c:f.lf'...... -' ],"",

:::,'i. - ! <-';'.~~

~'':l''P->i!. - .-.. .... -.- . _____ , ____ ~ ________ ~ '.~~ ,

'f~:O - 4 ....... : .. ,~ '\'. . .' •• .. ~ ~~~~tm.f,:~~~_~"":lJIC ... ~~~IC~·.u..~~I£::~,_.. ......... ~J:,..Jt;.H.~ ... 'T'L::;.L~~------- .... · ....

?:\!;oli" ~"~"'i\.~ , ~·"'tlt~ . ,1"·fb.' ,:.1. ' ,"';' ; .'~'~ I ::.;~~ j " ..

", .,1, ~"~ ,

'}L \ . ':"J'

:' Iq~ I y..h .. I ;:3J- ~ F;:' ;

-0>" _ ,

':1:'1 :,.:-. t

,'l " ';; .. :,~ I :,-,-:" .1

I('~'j'i I i t,_:~ I ':,:"j'l !¢~ ,

',.,1 "

;4"1 ~·~v;

" ":r, ;::i~: '1

:-:"} 11' •• , tf,;..t1

.. . ,t'

)"V\ '.'~ );,,;: ~

t~':;~, , ,<' J

I <!2 'j . ~: t: / .;;.~,

I I ~(:~ '/ ::-:: , . . ::'.,

I ,':-..... 1.

. : ::'.! (.

'/ \ '~f'( \ ht,-r:-t •

\ T~~! , t'~:;~'

I

/ '"

;,';;' /(, " t~:

\'f~'

l .' "K ' .... ~f'. _. 1

,f:,... t

,~ t".

1f::, ':J .• :~~ .... :~-;'i .'\1'"

~t~ \i:> -: .. !<;:.~ t

,:~~j

,~,4t' "t,. :':~~ .... '.J:.'~

:-'1 j t":-';·~t -t<;li:.t :~:l: ':1 :I~ I ,,~, ~, ,-~

!1I'i:~1\ ·~..Ii~

85

A. Co:nparisons within the Experime.ntal Results

There are several comparisons that can be made between results for

the various gauges. A lis r. of tt.e cocpa= ison3 performed is givcn below,

1. Tho repeatability of measuring ~t ~ith the sume gauge for

different gauge installations.

2. Comparison between ~he same type of gauee.

3, Comparison between the two different types of gauges.

1. Comparison 1

The first co:nparison involves using the same gauge to check the

repeatability of a:easuring ~t bett.sen various instailations of tho

gaugo. Inntallation refers to in~erting th~ gause in position for ~ t

! I I

IIlcasurements. Four comparison3 were run nsing the PFZ gauge. A li5tin~

of these comparisons and the results are givsn in Tabla 8. Tho \Oesults I

show that there is some val."iation in measuring ~ for different t

installations of the gauge. This variation ranges from I\bout 0 to :3

degrees.

~. Comparison 2

A ccmpariscn was made between gauges of the same typa. In other

\ .

words, the PFI gauge was cotnpatOed to the PF2 gauge and the sam(~ W.lS done

for the flush wire gauges. Table 9 list~: the cases where a compdrisoll

is valii. For these cases, there wes good dgreement for similar typC5

of gauges, with a runge of about 1 ~o 3 deerees. This variation is

within the differer,':I~ obtainad from Comparison i for repeatability.

f;~i.r.io' '·i... , ~WDlI. M'CT~",~~~s.:o.f2.'iI:".:.:\:~:t:..G~"1".c:G~~ect" • .c;~w."ll\.O...~t'jl~~~~~T...r;~~":;c:~.;.r~..\:."'"';: f':~.:"~t:t7'~~""

~ \:-;

/

7'

.,r 'rr

"i J] .,' rd 86

,.( / 4

'l /t~J :1

~l

~:l

;1 ;;!' ,,"

I~;~

! ~t :'I~J /' ,)

. i ;"~ .,1

/' ,,!

:"i' J "/' ':'1 I' ',J

4

"

. '::1 , :. I , p\~ . r:·J

t: ~1 hi . t ....

'. },.J \ --j " .'

. ;:1

d .'. J • "J

/} ::-1

;~ ... j

r:l 11

I ~, " ~,,' .'t,.' _-"Ii'

TABLE S. Comparison 1 - Checking for repeatability

TEST

CASE CONFIGURATION f,Hz W ~t,de8 11 . b

Mt,deg

PF2 B TC I 5.00 0.23 3.6 1.2 Pr2 C 'l'e I 5.00 0.23 4.8

PF2 E TC I 10.00 0.45 13.3 2.9 PF2 F TC I 10.00 0.l)5 16.2

PF2 I TC II 5.45 0.45 12.4 0 PF2 J TC II 5.[.5 0.45 12.4

PF2 H TC II 20.00 1.66 24.9 0 PF2 U TC II lO.OO 1.66 24.9

nAt ORR == 1.30.

bA~t is the difference bctueen ¢t for the case.s

being compared.

Thus, it can be! assumed that gauges of the same type meesure essent.ially

the sllIlle ~t'

As previously noted, the PFI Zauga did not have the ?::otect!vc

alur.tina cOdting over the film of platinum. The results &iven in T;}l>le 9

indicate that the coating does not affect the pllasc angle measured.

This result: probably could have been .1.ssumed since the gauges were not

0pcl·a.ting in a. hostile envir.onment and the co~ting is ver:y t!lin.

~.. Comp.!!.!'i50n ~

Now that the compari~ons have been mnde between gauges of tho 5a~e

type, attention will be turned toward cCMparing the two different type

~ b~ !)~~~$ c -- ... -.-.. - --. ~ '. -',,~<-. ' -.. ----.. ---- -- ~ .. ------.~.-.--~~.re1'~":I1::.."r..~,~.::;fJ .. :'\!:zj;7"!' .. :",.;.'.:"~~!'r.::::.~);j:..::..."'n-l::!."':'~"".:.<zI'~~",'fk.i~!!:4"d<.~~'l:.':..";:.-:£;;;'r.J'.J:::~_&"~€1'3'll:~~.,ll~!Z~7-lm'zr"":'I::S&'.tia.x;

.t. .... t.. I

! .. / I I~~"f ! '-'-,;.~.~. t · ,~.~\ , • 'v'"~"'~' ",

j / "'''.of-0:."_. I :~'''''''''',

: ~ "",: , '/ . ;; t·, I }.' i~2';,' '. ' • · ~~ , I .;:-.

I ,I :i;~~ ,

~" ,~~:.J /,1 _ .~' " r .' ,./ ~-J

I· r;:J7:' , · 1';I}'.'l

f

tXt;, ~ \ : ,:;. 1 ::-\:'''.'

~~ :~:~',~ ~'''"lL'

I (.~~ ··~~tG t·t· I ),_i~. " '-"tt.

,.>'

L'·f r

,~ ~.

.. :':!:

r' .7"

... \~ ,/ I./~~:

~r"'''' --. " : . . ~ .:;y """'!j

f""" , JoJ;'l;' '/ ~"'-. ' r ,-

, f'::~' " .. '~f"}~

/ I, :"i' L·:,. -I;,:,. ~ ':l!. i<.}. ~, '., f'~~·' I ::\,

"

I I,

,,': } \~,

"~\~~;'~ .; ~':

?f', :'J. "'1.-,

:~~.: ,,~~~f. ~~?

-1"':J~"'i ". ~ r .;..

?:~,. i

~"'l"'._: , ;1 ' /!1- : ,,,,,/ j

_","t'1

hi:"':" -', ,-' :~,J -

87

TABLE 9. Comparison 2 - Comparison between similar gaugo~ under th2 same test conditions

TEST CASE CONFIGURATION f,Hz iJ ~t,deg A~t·do8

PFI A TC I 10.00 0.45 15.3 2.0 PF: E TC I 10.00 0.45 13.3

PF1 A TC I 10.00 0.45 15.3 0.9 PF2 F TC r 10.00 0.1.5 16.2

PFl B TC II 20.00 1.66 25.6 0.9 PF2 N TC II 20.00 1.66 24.9

PFl B TC II 20.00 1.66 25.8 0.9 PF2 0 TeII 20.00 1.66 24.9

Th'lA TC r 5.00 0.23 -5.5 3.0 F\i2 n rc r 5.00 0.23 -2.5

F1tl1 [) TC I 10.00 O. !.s 9.5 0.9 F'vl2 n TC I 10.00 t),4S 10.4

of gaueo~. Both types of gauges operato on tho principle of he~~

tran~far but differ in tho kind of heating element r~d subsLra~a used.

The cases which r.Hly be compared arc summarized in Table 10. It is

evid~nt from Table 10 and tho results from the previous two comparisons

that thero is a larger variation in ~ measured by the two differDn~ t

types of gauGes than among similar typos, Th'l '.'uriaticn between the

flush wire gauges and the platinum film gauges r~ng~d between

approximately 1 to S degrees. Another noticeable l~pect about the

results in Table 10 is that for a given w the flus!·, wiro gauges measure

I ;,\;~ "'«'f~ -"'~"i/ F~~"-------"-"-'-' ,,_.' ~ ....... - -,.";,.:",-,,' . ' . '," [~zrr ... m~~~iJ~!1.i1."":~"''''.(.J)T~!.'""1.."'fJ~·::U~~~:.i..Y~!].tt1.:~~...n~!!>~:t~~.Ptdf'~~:!:;.a:n\Jut1~~z;J~f·"'Ir;?:i!~~.,poj.1~·~'"b..~:':-Gt~~~~t~~

.' \' . I " l

I / I I : .~},j..( ......

. / . i~\ ;"; f~ ,!

,.,./

-.

i~j' ,"' .,.~

if ,~" .;~:'

-r-....

~ :?i, .+.

f

· :':1.

/: ::.~

J' ' .. ~ ~l'

t'~;;

.:' ft~~ , .>.; I -'[.

:r. ~1

.~ p::.z: , ~.

~'"t

'::} '-:t .r:i

,).~ ,,' ..... • 'fI'~

f"~ ,i~ ., . . ~

~'.(~ "::~

. "f:'! I :; , ~;.-i I~~ I " ..,

'f~. 'I \~

I I:r ~~

J~ '1:

vi

• I

,f:1'

. I

I ' : )"

\

~~

~ ~1 I _. ',~~

,.;~<A ':~ ~

88

~ consistently lower than the platinum film gauges. The angles arc t

lower by approximately 1 to 8 degrees.

TABLE 10. Comparison 3 - Comparison between the t~o different typu of gnuges

TEST

CASE CONFIGURATION f,Hz

PF2 A TC I 3.00 . FW2A TC I 3.00

PF2 B TC I 5.00 PF2 C TC I 5.00 FW1A 'fCI 5.00 Fw2B TC I 5.00

PF2 D TC I 7.00 FW2C TC I 7.00

PF2 E TC I 10.00 PF2 F TC I 10.00 PFI A TC I 10.00 FWl B TC I 10.00 FW2D TC I 10.00

:-F2 G Tel 20.00 FWl C TC I 20.00

U

0.14 O.l!.

0.23 0.23 0.23 0.23

0,32 0.32

0.45 0.45 0.45 0.45 0.4:

0.9G 0.90

¢ ,deg t

-O.S -3.2

3.6 4.8

-5.5 -2.5

n l:.~ ,deg

t

2.4

&.2

10.8 6.5 [ •• 3

13.3 16.2 15.3 S.l) 9.5

10.4

le.2 0.9 17.3

s"ihen more than one cas£: ha~ uoen rl!t1 for the sarna i:ypc, of gauge and run conditions the avurqge of these cases is used to calculate A~ .

t

Comparisons will now be r.Iilde bet~e(!n the experil~ent.:;.l res~lts for

~t and the numerical pr.edictions.

.,.:j ;{"';."!W!? .. ".-' -'- . -_._-- .-. --- ---. < . ./'" :_... . . ~-- - _ .. ri. .. .,.~. __ ._~~.~~W ....... ~ ...... ~ ... ~'T>_=_T .. ",.".,..,....-, .. " ......... ...,._ .• ;,."' ... "",""t-..r .. '::';'-~~-",-,.-.": .... "~."..,...~.~,.",,..,..,,Y.;':"".rn";"~"'"''''''''''''' __ "'-~'J i-.......... ~~~A .. "_,-"............., ~ "'.""-M_." ...... .vao..or_~~"'.,.,~_, ......... _. __ ... '"' ...... __ "'-...:, .................. ~ ~ .... ~ •. ~~~"""

: . \ \ ... I '. . \ . . '. / I

,.'

r&:if ~ ....

I"~ ... \­"', .~! ;J ! .

ft. -0,

j. :£ " ...

> ~

n . __ . t'i , '_E-f ! 4 i '/! . ..;.~

I;:~

l " 'J "

'll . ·ftt ._ 0_ ..... \ ~

r1 ~ ,',/ !t~! -. ,

,:~

,'~ '.' , i

l'''!1 I, "\

Ji j!h

I' ~ q L-l

/ 1;1 t ~,,~

I ·1 ) , I,.~ ~'4 r; r~ ~,~ . , f"·~

.. l : ~ '...... ~':i I ' Ll I' H

'~

:i 1

/ /1 / ::::'j

.. ~ l""j' .\ ' t ~ I . \ t:f:

-- ,-'[,:1 " R· '\, < f) ,', '.+

y ': 1:'\ !. "

'~',A~

89

D. Cocparison of ExperL~ental Results and Numerical Predictions for ~~

The expe::imental results for 9't listed in Table 7 for high ORR have

been plottac in Figura 21(a) through Figure 21(c) for test

configurations TC I, TC II, and Te III, ~espoctively. Also plottcJ in

Figure. 21 are the numerical results from Figu4c 16. It is clear from

Figure 21 that tha experil:lental rcsult$ for .,It at a given i;j fall hi!lt1W

the numerical prediction::;. This is true for all four gauges /lnd all

values of w at which data were taken. Figure 21(a) illustrates that ~t

measured by the buried wire gauges are less than the ~t measurer:lGr.ts of

tho platinUt:l film S,"ugcs (as prev;.ollS ly nhown in Cooparison 3).

To iurthnr illustrate the fnet th~t all the experimental results

for ¢t are sQnller than tha num~rical precic~ion5, t~e diff~rence

uetwccn the e~parimental vdu-u::o ~ ~nd \:he numerical pNdictions ~ i.n te !n

Figura 11 hes been li~~ed in Table 7 and are plotted in Figure 22.

Figure 22 ccmt:ains t.he result!.. [or ell thrl!c test configuIations end. all

fouL' gauges. 'nle buried wiro S<luges have .. phase difference' in tht1

runge of 10 to 18 dec3rees while th,.! platinum film g,;!uges have tl phase

difference in ~h", refl~e of 4 to 17 c!egn:es .

Ther& is .ome uncertainty in the phase difference (0 - 0 ): !n te

This cor.:e!; from t,,'o sources. The first sourco is the uncer.tainty in the

measurement of ~ . As previollsly noted, thi:; was e$tim:lted to be ± 1 te

degree. The second sourt.e is the uncertcinty in detcr::lining the value

of P fot' the r.umerical prediction of ~'!:. Eas,!ri on experience with the

profile ::latching procedure used it was estimated that the uncer~ainty in

j I:,j

.J~~.~"" -.--. .. -.. ---- .. --- .. -_ .... ----.' tr'~ •

f.~ ~~~a"~~1J.'~'J~!:.J·}:ri'l!,!:·~i;,.~f.L"1::,&-.;T.:Il:.zEJ:.rz[.3::;,.;rz~:i;1tK3~1&;!'i:~":';~~~.t:~~.~.,~"3~;U:l~~!l~;;!l~!l~~~~~::~~~'~"';--'~Z;:i..'.!~-'"'-.t:=f)-i '. ~ ~ \ ~ . ., -'''1 . ",' 1 \ .••. \ \. ~ '\ . ~ \ I

"./~.: .-....... i ,. ,:, '. .. ", . / " . " . ,/ .." , ',/ \ .. . , "

" '~, \ "'",,-

. ,', . \ ,\1 ' ,', ': \_

ti;tr~~~li '.', ,,;,-:-, '" ;;,LS~:L; ~~n,~·'·:;'· ':-, " !::';':,. ,~" ';~1;':';":"'";' -'!:~~?::-:~i:~';.:. ' . ;.::,;,:'~./~if~:..:...r;;;;C:;:~""tc.~·"'\!;.';~;': -':'1.~' £.,,·A<,:;.;,.c,. ... ,.:'h,iC, )2~':r:1: \' .. :;.'!~;;;)..<I·,?, .• -i~~~:.,j"Ji~1

"

v ~ f., t\ ~ I!

~ I>'

~ . , ~

l~

). , '~

~ ::" ..... ....

;;t eJ Iii . ~

• I:"~

\.,.~ ,/ ~f;

~: ~ !~ ~ •• ,K ~ fi

~ -t~ 'I

/ L'} I .,j

, .~ .[1 ,~ ,',

I'J ~.

~' 1

'::

~~~'J <' .J .I

,>, J ... ~~ " ~t . f~ \ t!

50

45 -

40

35

30

25

~t' dcg. 20

15

10

o

8 a .

o fA D

A -

15 1--10 L.-J 1 1--1

o O.C 0.4

(a) TC I

.-r-r-I 'T

--2

o ~

TC I

E.perl~ental r.sult~ f,lr'

t at. eRR ~ 1.30

(Tdble 7)

~y~ GIUl! .1 Fell

El ruz b. PH

0 P,Z

-- Hl#1erlcal Pr/!dlcUon

.-L--''--'--.l'_L-l-L-L • I L-l-L....1 ' I

t..O O.C l.u 1.( 1.4 1.5 I.e 2.0 Z.2 2.4

...

FIGURE 2]. Comparison of the experimental !e~llt5 for. with tho t

IIl1merical prcdictio'l:':

1 -I oa

o

--

~.: ..:c/'

---' ,< ::'2.:.7~~-<2::;"; ~,~~"<" ,~ ---<: / -< -:.:--. '\ \ . .

:.:-~~.;~ . \." "-,' . . \. -;'::::::~ . ~i. ~ ; I. " : ; .... -_~ • __ .,/.: :-

·' .. ! ... " .... "'(~'"!"''''.~t.,'''...., ••... ;.'''"''-. ... ".L"". , .. t--..,....,." ... +"""1,~,,~ .... , ... :~~~~:,-:;:-"'"\j~, ~"'" .:f."l:l.: ,~.~~ ",,:;:t.,~ t'.(~ ~ -.. -< 1".""'*1:':\1 t ."" .,,,.~., ;.: .. e.":>.L ... .z.S!('--..::~,; ... ""'~,~,J;"" ''::;.I'i!'''t':;~''''~.J "~)'f" j!. ~ •• i! .. _T) ,~,' i,.,,,. ... t .. ~p,'y~l.-;.r;~! 1"" .:q ... ;;'~ __ --

\-:::" : .....

" £;"~~=

I t"-J ' ....

-'~ .

'.~1

~i~ .j x· ~J 'j Ie'!,

~i r ru f.'~ .... ,-1 &G 0l

r~ ~j

" ·y1 ~fl

~-. '1 • • .4 ,,", "1) i'" ,~

1\ ~, e it:; ~,

W ):

-.~ {,; .

. ' t~; i"'; ',~

~ .' ro' .'

~ ~.l

r/1 ~'l J1

,~ Kl

E~~ ·'1 • J

i\l fI" ,,!,!

1.,1 i1 .~ a: IP t' .~

t~ ~

50

45

40

35

::0

~" ileg. 2S

TC II ElperlDent~l results for 't .1 OR~ • 1.30 (T.bl. 7)

Syr.bc.l

~

o

~!'~

lin fF2

______ Humerlc.l Prediction

, /-----/: O( ~

~ )

(

~ @ 0 '

_1-1--1 I.-l.--l.-l.--I ' I I " ! 0.2 o,~ 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4

w

(b) TC II

FIGURJ:: 21. (Collt inllcdj

__ • __ v ____ ._~._-: - -_.-

\l)

~

-;.

":

(palllli 1 11°3)

I1I:>.L (:»

.r,

~'Z Z'Z O'Z 9't 9'1 n Z't O'{ g'O g'O ~'O Z'O 0

~ 71 0

r6 / l ~ 0 .'

j 4 O[ "'...) i

is! "

~ .-

./ N C7> oz

0 SZ '6ilP 11t .-

I

or

5£

(l ~lqrl) ot-Z~d 0 0('( = !llIO If I • .ADI

sllns~J l'lu3~I.Jadr3 ~5nt!) loqwhs 1!1 J1 5t-

~

I

" / , , t {

, of \ .,r ••

". , ,.~: ,

.' "

J"

':~ ;'~~~~~4.&.:~~.1~~,. .~~~,,;...':..u~ ..... ..;!~-:w~ ';';:J:~..i,,:~~~-;Ci':r:~;~:::-~~~~,~..:},-n':';W¥':t<~~~~~~i'l"l.. ~~;~~j\~~JL~~~::,=:'7 dO;'';' ;~~~~~!2::_J ~! ;·;L~' ,::,~'; :/., ,; f;; ,t .. ::':j;;';':,c:, d'S: I~' ,C·; ~,.::;:;;,;.Z~ ;:-1; .::'&-, :!~~ '~ . . u.. . . ' . '. .

•

""~

'. r' I.

:." .. !

22

20

18

16

14

ou -0" 12 .-

-&-f. 10

a

6

¢

A

A A ~ T

fA I ~

O~l ~ o 1-o

~

() o

~

1 o i

I 1

o

~

0 Test Syw.bol Gauae Configur~tion -I --~) fWl Te I ~ fW2 Te I 0 PH Te I 0 Pf2 Te I 0 PH Te II ~ PF2 Te II 0 Pf2 Te III :t 1 0

o [, I , , I I , " '-.' o 0.5 1.0 1.5 2.0 l.S

w

FIGURE 22. Difference between numerical predictions and experiMental results for ~ t

\D w

.... :.>. -:.-;

~~ '.-' .'':'

!/

':

',' . ['.-" / ..

-\ ~:'

:}

':>~ ", ": .

fi'?j' ~. ~~

:\~ "-':-1

f'l ·c ~ ...

-;~:11 , ~ , •• t

':~ ~1

J':] l>t

;~ ;:;1 ," j \:-'1 ~i

, .'"j

<:~'f : .<

"':j . ~~ -.;\

.~ii

'~;'l~ '.~;

.': .... -,'

.. r,~ ;.,

~/

'-.

, 1": ,~, /',' .~"

'., -;: ... '!..:

'>. " < 4,.

'"

;~i: : ~: i.i: ... ~

\~;~':.i:1.V" ''oJ>,

94

o con~ributed an additional ± 2 degrees to ~he uncertainty in ¢ - ¢ . tn te

Error bands of ± 3 degrees have been placed on several data points in

Figuro22 •

An important observation from Figure 22 is that the results for tho

platinum film gauges exhibit a trend tOHc.rd larger values of ¢ ~ 9 tn ta

with increasing U. There ara not enough experimental data for the flush

wire gauges to determine a trend. Figure 22 contains results for the

platinum film gauges for two values of a. There is no appnren~

influence of e on. - ¢ for t~!se gauges. tn te

~ -.,.' ~'. ~:":'~,-:

.-';..'

;'

~

, " -'-

~J ~'" J

---~ ~

i ~ J M ~{ ~ '~

~ j . ~ " 1 "1 -~ ~ .} ~ "i ~

[J '.': , .

~.~ _. " .,

to d ~ -1 .! 't,

1 ;t-

;~ !

',r { -. t .!, I~\_ ..

f~

~.r

-t :,-.;:. 1!

'I:~!' 1-';.1

" ~, -,

. I:' .~.: . I:, {', ., ~~~

~rt: '"

"t: 1/ ~l..

'-'-'T'S' ,.., jr' ~:'~~

95

VIII. CONCLUSIONS

This study focused on an experimental investigation of th~ dynamic

response of hot element gauges, because the ability of the gauges to

correctly follow the wall shear stress fluctuations in a time dependent

flow tillS under question. To test the gauge5, the wall shear stress

phase angle was measured in an oscillating laminar flow and then

compared to numerical predict:~ns. Before testing of the hot element

gauges could be undertaken a study of the boundary layer was performed

to verify that a laminar boundary layer was generated and that it wa5

correctly mcdeled by the unsteady boundary layer computer code.

Two types of hot element gauges t,rere tested. One had a thin

platinum film deposited on a quartz substrate and the second type had a

small diameter wire buri~d flush uit:h a polystyrene substrate. Testing

was done on a flat plate in a constant: cross-sectional area test

section. Two axial lengths along the plate and tHO mean freestream

velocities were utilized alo:lg with a range of frequencies in order to

produce a range of values for w. The results show that the repeatability of the hot ele(;1ent gauges

is good. Several tests were repeated for different installations of the

gauges. The variation was in the range of 3 degrees. This range is

fairly small so it is concluded that the gauges will yield essentially

the same ~ for similar runs. t

A co~parison was made between gauges of the same type and under the

same run conditions.

~

The variat.i.on in IjJ measured for diffe::ent gauges t

.-, .....

~

~'r; :: f!.j

~~,~~~ ;:tJl ",'.I , .. 11

~;~~ '-~ ~;. I

~'i:~11 ~; ); :~~r . ,:~ ·~il , , .. I ;,;;l:,: :![

i:ir'i ~ .,;' ..... I .(,,11 .' ~J I :'"~~"

/"'l It,_

'::~~"i ::'SJ ':~ ;,..'t,. ~-, It.

,-~, .. ;.4 .".;:1 . ~~. r-' ' .. i:,' ".J_ ..

I' ...

I"}] ,- ·1 ~ <~;,:~

!t:~,~!: , ~>!

;J~~ · ~ ':~ ... 1'·:1 · ,':,~'

:..~ ... ~

".~~ :J;"~ ; -'J,' . \ . / ...... '

J! · '~" •• ' .... I

T:~' I "';\1 ~ .t" ~

"~r! '~;I~

~ l;!:~ :, ..... ' ~-;:.tt i .";"t I

~. ~ " .. ~:~~~

• "':l J :;¢~l :;J~ '~." 'I: :~)~1 ,:' .:,} <1' t, ;.,,:

96

but of the same type was approxi~dtely 3 degrees. Since the range for

the first comparison for repeatnbility ~as also 3 degrees it was

concluded that gauges of the same type measure the same value for ~t

within experimental error.

Comparison of the experimental results for ¢t to the numerical

predictions show that both type of gauges measure P. value for ~ lower t

than the Ilumerical predictions. The phase angle difference (¢ - 9 ) tn te

for the two type of gauges are also different. The buried t.ire gauges

have a phase difference in the range of 10 to 13 degrees while the thin

film gauges have a phase difference in the range of 4 to 17 degrees .

~ - ~ for the platinuo film gauges tends to increase "lith w. It is tn te

not known why the tt.o different typ~s of gau&e~ measure different \'It"

Apparently, the substrate naterial and hClltinl; aiement affect the t;ause

response.

Sinc3 experimental and numerical results for <1> for the hot element t

do not agree, it is concluded that the gauges do not faithfully follo:.

the shear stress fluctuations in oscillati.ng laminar flO\.. This

seriously limit~ the usefulness of these geuges to measur~ surfaca shear

stress in time dependent laminar air flows. This also strongly suggests

that the gauges will not perfOrM properly in unsteadj· turbulent air

flows.

The area of unsteady Imll shear stress measurements is very

important, while at the same time very difficult. Based on the

understanding of the subject gained in this study. it ap~ears that a

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:" ~~'

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;)J , :1~i ;-j~. :;'f:.~~

\E ,,,,,", ;:/ .,-­ft' -.): .

~~Jt' " , ... \" ;'l

<~{~ ,,~: d~~~

: ''',: " .

-,':l: ","; ,''',~,'' I

; ,~::

,rr:! t' .. J, rO:&t: :~{I ::~"J ..... ..... "'1..' ,;:.:1

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r1.' >'£1 ;:r.~ :.>::~

97

considerable amount of research possibly involving new measurement

techniques will be required before an accurate and reliable means of

measuring both the amplitude and phase relations for wall shear stress

is developed.

~ ~':

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98

IX. BIBLIOGRAPHY

1. Cook, Willia~l J. !! Facility for Producing Periodic Subsonic Flows. Iowa State University Engineering Research Institute Technical Report ISU-ERI-Ames-81117, 1980.

2. Cook, liilliam J. and Yamaguchi, Yutaka !! Facili;y for Studying Turbulent Boundary Layers in Oscillating Flows. Iowa State University Engineering Research Institute Technical Report ISU-ERI-Ames-82186, 1982.

3. Lighthill, M. J. "The Response of Laminar Skin Friction and Heat Transfer to Fluctuations in the Stream Velocity." Proceedings of the ~ Society, Series A, 224 (June 1954), 1-23.

4. Cousteix J. t Houdeville, R. and Javelle, J. "Response of a Turbulent Boundary Layer to a Pulsation of the External Flow With and Without Adverse Pressure Gradient." Un5tc~ Turbulent Shear Flows. International Union of TheorE:tical and Applied Mechanics, Symposium, Toulouse, Fre.nce, ~IIlY

5-8, 1981. New York: Springer-Verlag, 1981.

5. Acharya, H., Bornstein, M. P. and Vokurka, V. "Development of a Floating Element for the Measurement of Surface Shear Stress." AIAA Journal, 23, no. 3 (1984), 410-415.

6. Kalumuck, Kenneth M. "A Theot'y fOl" the Performance of Hot-Film Shear Serees Probes." Ph.D. Dissertation, Hassachusetts Institute of Technology, 1983.

7. Ling, S. C. "Hl'at Trans fer From a Small Isothermal SpamYise Strip on an Insulated Boundary." Journal of Heat Transfer, 85 (1963), 230-236. - -- -

8. Bellhouse, n. J. and Schultz, D. L. "Determination of ~ean and Dynamic Skin Friction, Separation, and Transition in Low­Speed Flow With a Thin-Film Heated Element." Journal of Fluid Mechanics, 24 (1966), 379-400. -

9. Koba5hi, Y. and Hayakawa, H. "Structure of Turbulent Bo\.ndary Layer on an Oscillating Flat Plate." Unsteady Turbulent Shear Flows. International Union of Theoretical and Applied Mechanics, Sympos ium, Toulouse, France, ~Iay 5 -8, 1981. New York: Springer-Verlag, 1981.

10. Ramaprian, B. R. and Tu, Shuen-Wei. "Study of Periodic Turbulent Pipe Flows." Iowa Institute of Hydraulic Research Report No. 238, 1982.

d :".:'~,--. .'

-i~""

':~y~ r ;:.~

.;;1-J .,. "_~,

';~

-Ht <I '?'!

c:~1

"~' ,:'"

.. t~. If' -.,. ~ :t,

:.% ->.

of::" ;.-",.(

,J~,

,;J7 ;~ :,~

"' . . ~J, ~. :j;. .. ,i' '\'.

'~~.

~1v, i::to' ....

:~:~

t~~ .!}-.

• r

a

I~ ; lj ~ ~ . "

_0 ~

~ N

1

1 '.'

~ ... ,~ ~.;

"J.'

, !

:1' .:g. ~1::' ".

J, ,"\,.-;1.:,.

,\,~,

··Ji' . /~' " '.,'

':'r .'; .. ~~

f' "- 14:_

'ft ,~

~

" ~:'

.. "J] J-'''', ,!~.

" ';:-' ':. ~ , '~ '~

;" c-'

'1:, !-.;.. :-~ ,

99

11. Personal communicatio~ with William J. Cook, Iowa State Univer~ity regarding a study by Cook and F. K. Owen, Complere, Inc., Palo Alto, Califcrni~, 1983.

12. Hurphy, J. D. and Prcnter, P. M. "A Hybrid Computing Scheme for Unsteady Turbulent Boundary Layers." Third Symposium 2!! Turbulent Shear Flows, University of California, DaVis, September 1981.

13. Karlsson, S. K. F. "An Unsteady Turbulent Boundary Layer." Journal of Fluid Mechanics, 5 (1959), 622~636.

14. Dewey, C. F. Jr. and Huber, P. \/. "Heasurement Hethods for Fluid Shear Stress." Fluid Hechc,nics Laboratory Publications. Department of Mechanical Engineering, ~Iassachusctts Institute of Technology, 1982 .

15. Bellhouse, B. J. and Schultz, D. L. liThe Heasurer.1ent of Fluctuating Skin Friction in Air with Heated Thin-Film Gauge:>. II J;)urnal of Fluid MeC'.hanics, 32, Part 4 (1968), 675-680. - --

16. Lin, C. C. "Motion in the Boundary Lay~r With a Rapidly Oscillating External Flow." Ninth Internationa~ CongrC!ss of Apolied Nechanics, University of Brussels, Belgium, September, 1956.

17. Ceheci, T. and Carr, L. W. "A Computer Program for Calculating Laminar and Turb'.llcnt Boundc.r.y Layers for Two"Dimensional Time Dependent F lct~s ." NASA TIl -7 84 7 O. Harch 1978.

18. Hill, P. G. and Stenning, A. H. "Laminar Boundary Layers in Oscillating Flows." Journal of Basic Engin8~_ ~ing, 82 (September 1960), 593-608.

19. White, Frank H. Fluid rIechanics.. New York: HcGraw-Hill, 1979.

20. Hhit!!, Frank 11. Viscous Flui.d Flow. New York: Hc.Graw-Hill, 1974 .

21. Murthy, V. S. and Rose. \1. C. "Uuried Wire Gage for \vall Shear Stress Measurements." b.IAA 10th AerodynAmic Iesting Conference, San Diego, California, Ap~i1 19-21, 1978.

22. Kline. S. J. and McClintock, F. "Describing lJnce!~ainties in Single-Sample Expuriments." Mechanical )::ngi:1eering. 75, no. 1, (Jan. 1953), 3-8.

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:<~~:~ .o~ ", c}; .;<t-."':(:,----.------..... , . ~~ ~

100 '

101

X APPENDIX A

TABLE 11. Tabulated resl\lts for CD.se C1

U = 16.35 mIs, TC I 0

y,in 1'\ u IU o 0

0.0056 0.423 0.196 0.0114 0.869 0.389 0.0210 1.613 0.648 0.0278 2.133 0.787 0.0434 3.322 0.909 0.0472 3.619 0.964 0.0628 4.809 0.994 0.0744 5.701 0.996

TABLE 12. Tabulated results for case C2

U :: 16.49 mIs, r: II o

y,in

0.0060 0.0130 0.0226 0.0326 0.0424 1).052,2 0.0670 0.0866 ).1062

TI

0.465 0.751 1.322 1.893 2.464 3.035 3.891 5.033 6.175

u IV o 0

0.230 0.36t • 0.555 0.745 0.B57 0.931 0.984 1.COO 1.000

-' ,': ' ..... ~:-. ~::~::} .1:

-:-I,.~ - ~ _. -. - -.. ,..-----------.. -._- .. _ . , - ____ 0_. ___ ._---_· ___ . ____ _

)I

~'. "~l ",,',t

~-. ~ \

1;t{1 ~~:;';~:. I

c,}.

'::~) '\ .

[<~~, . ..... ""l';-.. ,\.~ t

~:.~~~ :,/-1

~~' ':,) , ~.;:; .

,.: ,'t,

::'~r I·,~_"': : •

~,:.:.V \:~

:<";:::'

'l::g~ ;,":;~ -

,:':2 J>:"';"~ . ".-

:::.~;

't';"';" , ;. ~~: ;,.~ I " , ~. ' ..... t,,:;; !. ". , -,

f '~

',,: ,: ... '. ,~',\.

l'~:~~~' ....... ". . . . ~ ": : "','/ .:/ . (:{

t';"';' 'I:~~~ , ~: ~

~f::;~' ,~ (.

':':\'1' -. ,~~

'.;:;~'! At:l

" ' -"I-!I - '\. ,. I'.~ . ..':};

~~ .. Ij .. ','"

~::~<~ ;: I <,,~

!.I

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~:,~~; . . )"~ . . ",

102

TABLE 13. Tabulated result~ for case Al

f = 10 Hz, w = 0.45, TC I Uo = 16.58 mis, U1 '" 2.295 r.nh'

y.in 11 u IU o 0 u1/U1 ~ ,dag u

0.0056 0.430 0.194 0.3135 16.14 0.0114 0.1379 0.391 0.688 9.00 0.0192 1.479 0.612 0.937 1 •• 47 0.0260 2.0~!" 0.760 1.067 1.64 0.0308 2.379 0.839 1.109 0.18 0.0366 2.829 0.905 1.124 0.21 0.0444 3.428 0.964 1.096 -0.15 0.0522 4.028 0.987 1.058 -0.32 0.0648 5.002 0.997 1.018 -0.71 0.0794 6.127 1.002 1.013 -0.22

TABLE 14. Tabulated results for case A2

f = 3 Hz, W ~ 0.25, TC II U o = 15.68 mis, U1 ~ 2.203 m/s

y,in 11 u /U o 0 u/U1 r1J ,cieg u

0.0076 o ./~31 0.211 0.401 7.029 0.0144 0.819 0.1.08 0.663 5.317 0.0212 1.207 0.562 0.847 3.368 0.0340 1. 929 0.767 1.056 1.331 0.0486 2.761 0.913 1.122 0.670 0.0634 3.593 0.976 1.084 -1.103 0.0780 4.1+26 0.997 1.037 -0.164 0.0976 5.535 0.995 1.0C4 0.028 0.1172 6.645 0.993 0.996 -0.031

-.-- 4' .... ~ • Il.{~

':Z)L· ... ._.,._, l;~ --.- -- --.----~i-' __ . ____ .k._ ... - -- - - .-----_._-----

"t ~,.

~ .. ~ .. , ( .~:..,

~. ; , ,

~.

c j

·~~~I .~~

· . '

~

1

f31

~~i

~~ · ~ ,,-< ~ .~

~ ~

· " 7-:" ~ ..

,.::i'~·'i ~ ". :"\ .. ::;.

/A ~ " f~'+!

~:_:~J1

I·~ :', :::;,:j

f .·1 .'

I:'r: ){.':]1 ,'." --:; , . ~ '-,:::j

\:1' ..... '·t

~~~ · , .~

:'~';'l-., -\.~

i41 \"J1 '-'1 ':~ . ....

" I:;~ ... -',':II

,t~

;i~ >~.i

· :hl'~ :." ,',-" , :~~ ~

"-~1 ~'-il ;':;J ',' ,:,.. ~:

~:'-1 ~,,~

~~~-: ... ~- ... -----

103

TABLE 15. Tabulated results for case AS

f = 5.58 Hz, w = 0.44, TC II Uo ; 16.77 m/s, U1 = 2.241 m/s

y,in T} u /U o c u1/U1 ~ ,deg u

0.0080 0.474 0.236 0.464 12.09 0.0130 0.759 0.369 0.651 8.n 0.0198 1.158 0.528 0.842 6.46 0.0296 1. 729 0.704 1.025 2.71 0.0380 2.242 0.818 1.103 1.07 0.0456 2.698 0.884 1.108 0.05 0.0616 3.610 0.968 1.080 -0.27 0.0762 4.465 0.993 1.030 0.22 0.0908 5.321 0.999 1.007 0.55 0.1.03l~ 6.060 1.003 1. 004 -0.56

TABLE 16. Tabulated results fo~ case A4

f = 10 Hz, ~ = 0.78, TC II U = 16.85 mIs, U1 ~ 2.305 m/s

o '

y,in l\ u 'u u1/U1 ¢. ,deg 0' 0 u

0.0080 0.476 0.233 0.509 16.67 0.0130 0.762 0.370 0.709 10.93 0.0198 1.163 0.526 0.095 6.65 0.0276 1.620 0.669 1.035 3.01 0.0372 2.192 0.798 1.123 -0.09 0.0490 2.879 0.903 1.127 -1.18 0.0656 3.851 0.971 1.066 -C.95 0.0810 1 •• 766 0.990 1.017 -').35 0.0976 5.739 0.993 O.9~S -C.O!

• . ------------~.--.--.----.. --- --- _ .. -------- ------_.--,.

~_;;:,;"o,-:"I

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~:I -, : .. , - ....... . ,,:")~ ~ ,

.~!'"

';;l' .~'; .

• ~,~~"t,. :~~~~t : :.~« ~~&j

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!;::~ .; ~ .~.:: >~,i~

!:'~'t r~:.'

I!r~,};; ':.'.<~ .~ ,~:i;.

'~5~ ,::/~ .. :~~:.;; ·,·t • i~~:.~~ ." ,.1',:;-,

~\ .l' ••

:;.1;.':;'

· I~t~. ';'1 ,:.s;. ;)~. :~ ..

,. (·;·t} ~,~ ;f}~.·-l ;>(>

.. r~··J~ ..,. .. ~:~-~ .,:'!;) .. ~ >1 ,f ';!_ ..... ,;;~ -~.,:P

if· <;.:;./~ ;:;:!!.!;·~11'<)1

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TABLE , -..

y,in

0.0082 0.0032 0.0130 0.Q150 0.0210 0.0278 0.0356 0.0456 0.0572 0.0720 0.086ll 0.1014 0.1114

104

Tabulated results for case ~s

f = 15 Hz, iJ = 1.18, TC II Uo = 16.73 mis, U1 = 2.'69 m/s

Tl u /U o 0 u/U1

0.480 0.237 0.579 0.479 0.257 0.575 0.766 0.377 0.786 0.882 0.421 0.842 1.227 0.552 0.988 1.630 0.673 1.095 2.090 0.782 1.151 2.665 0.882 1.152 3.355 0.953 1.102 4.217 0.993 1~039 5.080 1.002 1.005 5.942 1.000 0.998 6.517 0.998 0.986

.. ·11.: .. ··':";·-• _________ ~ __ .._. __ ... _ ... _ ... __ ._ .. _ • .60 __ • __

¢ ,deg u

15.83 15.91 9.48 i.77 3.30

-0.52 -2.86 -4.22 -3.39 -1.61 -0.11 -0.19 -0.16

~l . .

J

"1 . fl

J [j J

i ~'1

~ r {J ~ Ii .~ ~

~ ri rl

l) 'I

• '4

1.

tj ~ ':i

~ .~ .'j

105

TABLE 18. Tabulated results for case A6

f = 20 Hz, W = 1.59, TC II Uo ~ 16.60 mIs, U1 ~ 2.698 m/s

y,in TI u IU o 0 u 1/U1

0.0078 0.457 0.231 0.552 0.0'126 0.739 0.369 0.744 0.0194 1.134 0.527 C.921 0.2823 1.642 0.682 1.055 0.0368 2.150 0.801 1.108 0.0484 2.827 0.~10 1.106 0.0640 3.730 0.977 1.054 0.0804 4.689 0.997 1.014 0.0968 5.64!J 1.000 1.002 0.1142 6.664 1.000 1.000

TABLE 19. Tabulated results for case H1

y,in

f = 3 Hz, w = 0.34, TC III Uo = 11.69 mIs, U1 = 2.227 m/s

1\ u /U o 0 u1/U 1

'" ,deg u

16.47 7.77 0.09

-5.52 -8.18 -7.50 -4.00 -1.27 0.12 0.27

~ ,deg u

----------------------------------.-----------------0.0066 0.0134 0.0232 0.0330 0.0448 0.0586 0.0732 0.0918 0.1114 0.1310

0.327 0.663 1.142 1.622 2.197 2.868 3.587 4.498 5.457 6.416

0.175 0.351 0.551 0.700 0.830 0.924 0.972 0.995 1.003 0.999

0.341 0.605 0.837 0.984 1.070 1.099 1.062 1.026 1.011 1. 000

12.46 8.80 4.34 2.51 0.57 0.33

-0.77 -1.11 0.73 0.40

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(

..,. .~.': '\ ' ,

, r~';"i~~" ---------.------~ -.--- ...

",

'1: ~.[., ,."t "'J ":' i :,;;j , '-:"~i ~, f i

,- ::I~-~ ft-· ., ~, .

'. _ f~;:"!" ". L: ,.',

[:>'! r:' ~

'~

.~ ~i}~

,', "'j '~;;;l < • ',::/: ( :.ot

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f" ') ..... :;<J . , ",

>'J { ,:,cl'

t

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t,~" 'I

iIfl ,: ,'I.

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r(~:\i :;/1' ~::~ :

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l~:~' .. , . .:.:.~ ..;,

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'----.'5 ... ~ ~ .. ~~:r:~

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~.;; ":,-;

106

TABLE 20. Tlloullltud ra:;ults for case B2

f = 10 H:, ii c 1.19, 'rc III Uo = 11.08 m/s, Ul = 2.191 m/s

y,in 11 u IU o 0 u1/U1

.00661 0.315 0.174 0.473 0.0126 0.599 0.319 0.723 0.0184 0.878 0.450 0.1378 0.0262 1.253 0.589 1.014 0.0370 1. 768 0.735 1.120 0.0478 2.28'+ 0.842 1.143 0.0626 2.987 0.933 1.119 0.0i74 3.689 0.975 1.0~0 0.0970 4.627 0.993 LOn 0.1168 5.564 0.993 1. 001 0.1364 6.501 1.001 1.000

,..

¢ ,deg u

20.86 13.30 7.96 3.27

-1.19 -2.62 -3.50 -2.71 -0.65 0.03 0.01

-

..

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,~. 11 ;~~5"~1 :'--:~~ r-,,:,.t

;'?~l

~.?'i~O: ~ '",-

:;:-"·""'4

(, .. ,.. i '} (1 .~~t;

· "'$'1 ,ti:! · . ~~! :'}t, l:. ~~. , ,,-11

--,., ..... · ., "I ,~/'rJ

: :$.

'II .. ~ 'j ~-1.

'11 l'!

f:~:l ;~':~ .. ...., ' .-.... ,

l-,";~;;

. 'R t;'.:·.;'!

'~fl ~ -, ':!: · '.

'\'gi , t,' . ~ ~

':':-"'1 ':""~'~I

":.'~;:;~ '''''''"1 ::~~~.: ~ J:,J\ ,

t~~: • ,1 ~~ • . ",,'. J/~;. 'Y'{', :·'-.t· ., \~

",.1

::~i\ l.,,. • , .,

:t;(: , ,51

107

TABLE:!1. Tabulated results for case B3

y,in

0.0064-0.0132 0.0210 0.0286 0.0374 0.0490 0.0616 0.0810 0.1004 0.1196 0.1:342

f c 20 Hz, w = 2.38, TC III Uo = 11.11 mIs, U1 = 2.442 m/s

TI u IU o 0 u1/ U1

0.30B 0.176 0.576 0.631 0.341 0.809 1.001 0.500 0.927 1. 370 0.629 1.011 1. 7B6 0.745 1.044 2.340 0.857 1.035 2.940 0.929 1.020 3.863 0.982 1.007 4.787 1.001 0.995 5.710 0.993 1. OOI~ 6.403 0.999 0.991

'J:! . ;~~.J

" f 'r~~ ,,' ~:." ,. ,:~ .... ...' , .. ':: .; .;::;~:

J~~H

I;};~ ,.0."

, -,,-""' ;; ..... , :~, ::~1

!,;;11 ;·;.,r, , .~.

<~I) ;;-:: 4 t~'t.t.

. .

41 ,dog U

24.49 11.92 3.17

-3.00 ·7.21. -0.29 -6.43 -2.38 0.34 0.:5 1.02

"

'\~)~:, /.~·~,r I •

s~';';J' '" '~t,

,:'~",i!. . ':.~ I' t )'::) I

.A' I >'f. I ... :" ! ,;,~ . '. "[,;"

\it , r,'\ '; .... f

',".t' I ~:}' ! ,~:~f; ';1:

I :,:~

;','~ I .<:;;­';.}\, I

r:.:p., r 'i)~ I'

'!:lj"'1 .,. ':"; . ",: t~~

"" I

f\'·~ I ';"'~'! ' .' -?:-

'r":'·:; I 'q

"' . -,.J, ,

.:':,' i

f" ''", I " ~... .

"t ;

'1 :~~ :~': ;

I~j} ; . ,-,-, . .. ~ ~"'; . Jr~~' "!.:".

;, ... -~ ,.~ ;,,"' . .. ";1

.:,./, :j':

~:.~;; .... 1, 'd

;:~~. I

'''''\-' I ~~ . \: ',,-,

~" I ; ...... I

~:~~::. : .> I

~~:~ i .'~' "","

." ;i. , .\' ~'~!"

~r~ I

'~:,~r! ~: ~ ~

':,,~ .:. >;" • ...;..

i.~1 ~. ;~.j '~j"!' l

t!/\~ J;{ . .}~~ L..:.ii.. .. ~~

108

XI APPE~Drx II

Tf.BLE 22. Tabulated rC5ult5 for casc PF1 A

ORR ~t·dcg.

1.041 11.2 1.082 14.6 1.125 15.2

TABL.:: 23. T~bulatcd .csult3 for casu rFl J

------. ~-----

ORR rf't,dcg.

1.02 3.6 1.04 17.7 1.06 20.9 1.08 2:3.3 1.12 24.9 1.18 25.9 1.25 26,4 1.30 25.7 1.33 25.6

, /

I ~ i.~~' .,iJ

~1~

J ~J /:.

~ :~ ,~

~ ..,.:~

" . ,; ~

'. i,'

"" :'~ ~;.::,:~ t"l, '~,- ~

~§ '"

r'-;:f , ,"'r~

I: ;: 'l ~~. , ,,~

\ ~1; "\ "1' ~~ .l~~

: -~ j. . ::~.,

) -" ,~

:~~. ;...-. '.:':

.' .... 1'. /'.>~'

ttl

',0

I\l _.:.l.',

,,," " ~-',; '"

~.,; ~, > :,-':i . : i ~ .. ~. ,-~

, , ~ :';, ~J~

t ',:; ":.1 -:1 -"J "I

~:~l "

... " '1 :',

\1 ~:I ' :0 ... . \, L: ..

"::, ~,

, . ':~:-~ ;, .... ,

109

TABLE 24. Tabulated results for case PF2 A

ORR ~t·dl3g.

1.02 -2.1 1.04 -0.1 1.06 0.2 1.08 0.2 1.12 0.8 1.18 -0.7 1. 25 -1.5 1.30 -0.7 1. 33 -0.7

TABLE 25. Tabulated result5 for case ?F2 B

ORR <fit ,deg.

1.02 1+.0 1.04 3.3 1.06 5.2 1.00 11.0 1.12 3.4 1. 20 2.9 1. 30 3.8 1. 33 3.6

'"'1'

:1 q n ":1 ,~ ,-

":, ', . • I i.'

. ;~,

rl , '.j

q , '1 : :1

r:,l

1_] . '·l · ,- 'f .' "

C·i f';'j

L:) r'<~ ;:" j !,:-~

, r":c'l '. j

,J , ':'j " ,: .' · ~~

q .' ··i '.~ . ~,:; :.'';t

;: ~< ~

• · ,

;;,'f, • r ~ ~

r;';'i

:r~j 'to, '.] ~ '~'::"'J •

" 'r'l ' >'u ':';:'tj'

I";·t ;,:;';jj

~;<4 :~~ .~~~ ;~~

,"

110

TABLE 26. Tabulated results for case PF2 C

ORR ¢t,dcg.

1.04 3.7 1.08 4.f. 1.18 4.6 1.25 5.0 1.30 4.8

TABLE 27. Tabulated results for case PF2 D

---------------, ORR 41 ,dcg.

t

1.0i: 5.1 1. 04 9.8 1.06 10.7 1.08 ll.s 1.12 12.1 1.18 10.8 1.25 10.7 1.30 10.8 1.33 10.5

.,

t~'. 11'\" .,~,."~~.l.

;;.~;~: • ; " \ I ~ ~~:,~t. ~ ~ :~; ?,';-I. " ,~- ~.

~; I~J~: .I

)\" ,./

111

';:j . :: .:,~ TABLE 28. Tabulated results for case PF2 E

~

: .,. ".;;:

t:'/f

\~'J - ... '

~-- {: \ , ",,\.

' ..... ,'t .' ';-.").

., '"" .

\

:::£1 ,;~.~

~~,~-~ '.;:}. ~ , ....... ~! ?', ?J,

·'{!f-. . I

:':~ 1 ',,';' I

~ ~ ~ ! r,:~t " TABLj~ 29.

:~ : f;, ' \" ,,,

')'~:l .! ~.: ',- I ,,,,, t· I

~.:;"::.' \ r- ';"," I

tl:;l: ", .1 /. , '-,:::; .

/~l~ ~l:r : . :''''1. t

~:~r· ; '>~l: 1

l~'':;' :

.~~~~.~ , l"",

:",-i.--:'

:'--~:: ",<: f ;~:.~~ I· ,: •. {

&. . ~",;l {

J:::~{ ',,:';""1 ';~i

ll'\;l " ~ ,'. ~{li (",\ ":',.''''"'' ,-.;

:~~ ,: .'~ a;,.;u· , ..... .-.....~..-,-... --.-.--.--- .

ORR ¢It,dQg.

----1.02 5.0 1.01. 11.7 1.06 12.3 l.08 13.2 1.12 13.6 1.20 13.7 1. 30 13.0 1.33 13.0

Tabulated results for casr~ Pf2 F

ORR ¢",doe.

1.04 13.5 1.08 16.1 1.18 16.3 1.25 16.2 1.33 15.8

//'

/'

.'

., .... ~1f,

"~:2J:l

~~'~.~ ;~;t' ! ~-',J .

" I' - .I :~ ~.; ~ , .. -~ , ,< I~\, ll!

, " '~'.J :({ :;({.l 1'" .~'" I

·Y.~'1 .• :; 'J; ,~, '}

I' ,{: : ~ .. ;.~ I

'J,t. .. I .. r '

·-f·l , , . \_~~ ... I

/' J~,1; ! /// . ':~'~-;.!

.F 4;- .1

::.';;' I . ,~" j

"

'~:,~\i : .. ;; ! k:~t I I.:,::: i

f·-,:, .~~ ; (,::.; i

, f~~' ~,§.~ ; "ii' ::~:~ -j • ,to-. ~ .,:~

.; ,:." ~:~{' ,"!'. ,

;';;~ I:

k<:~ I ... , ... ' ,'"'S- ,1 ~: <.~ I

I 1\ :;'r: ~ ) )":-::,1 . ~ ~~{;' ;

t..

:.~T:;;~ ! '.1 .... 1

. ~ ~ I :\i- : '''r-:;-t I ~' ... l ! ::;_). I ,¥ •

~xti ·i ... -.I ::,~:tl :f",-~~

,-;1f :~~;'li 'L'{l

" ,~

...

ciii' . \:. ;::~' ;

t;tL,-------·~ --... ----

-'

ll2

TABLE 30. Tabulated results for case PF2 G

ORR ~t,deg.

1.02 5.6 1.04 12.0 1.06 15.0 1.08 16.3 1.08 16.3 1.12 17.3 1.20 1E.4 1.30 18.1 1.33 18.1

TABLE :n. Tabulated result:s for case pr2 H

ORR ¢.,deg.

1.02 ~.8

1.04 5.4 1.06 .5.5 1.08 5.2 1.12 5.0 1.18 S.O 1.25 4.9 1.30 4.1 1. 33 4.2

~

•

i,~ :,;:~}~Il '. , ~.';"~ ": 1 ;,' I

I (~fi , :: :~l -',~

,. I"<~~'I -::"':,,! ,,:1'

:;-"tl ' ~'} , ; I ... ~ :':t.'j

-, ." .

If /; .:_:'to ~

"1 "-~

:",~, " , -.:-'" "'., ":

~- <

\ 1<:::';'1 , ':",j

/t:~ L.:~ f' --1

fl{J "'j :',:;.1 ,:," t ,",tl

!" ~ ~ ~

";--~ '>~j ,~~,,_~~

.~'il ·j1i

" ; :;1 ~.~'. -

" ~~>: t~_'

: ~-

l' ::,

/;, / . :.:.

f~' '.-3 ;~ ~ -,i

"

.:; <:: t" -',

1

1)1 /.: I. >_

/' . i . ,.',

,...- ~?;J ____ ., __ . ___ ._ ~

113

TABLE 32. Tabulated results for case PF2 I

ORR ¢t,deg.

1.02 8.5 1.04 11.9 1.06 .11.7 1.08 12.8 1.12 12.3 1.18 12.1 1.25 12.7 1. 30 12.6 1.33 11.7

TABLE 33. Tabulated results for case PF2 J

----------------------------------------ORR ~ ,dcg.

t

1.02 10.4 1.04 11.7 1.06 .11.7 1.08 12.4 1.12 12.6 1.18 13.1 1.24 12.4 1.28 11.9 1. 30 12.5 1.33 12.3

" .//

';"' .. ·;~"Q,·~:'~/)\'": '''": l~:"~'··":''\\'::.'\'-:-'· ' ....... ~ "", - ., , r··~f.~~~ -.- ..... - . .:.,.... ... ~ .. ~~.:--~ ~ ............ __ . - ... -~. - .. -.-- ......... ~----.-- ..... ---.----,';1

'1

:~?l .-,~;?

" f ~l· ,;l

i-,j{:- ·

\~ "

~"I f, .". ~ ,!

:,:1 '·1 '~:j "1 '1 :' ;1

'~~1:! ,',

:.'

"\1 I ·':~ ':, '-1

. ,/ 1;~"::ll // f>'

" ~;:

",~ :1

': ,,~j , ,-:::; il , ~

;,.....-' . . '.< ,/ I::" -.:,; .,';: :j ., ~

/ ' « , :','::j , f :", / ':;:

'l . .,,' , ~~ ... ;

--. _--- V",i:, '!~

" u" l/:,'

": ~

'.".::'

h:',,~ . , ~

~. - !

;: I ,,',';1

, It;',~,~ . . ;;:J~ ,

~', '( :/;, '. 6"";~" ... ,r

"i·:, ~ ~

114

TABLE 34. Tabulated results for case ?F2 K

ORR ~t ,deg.

1.02 8.7 1.04 13.3 1.06 Il~. 8 1.08 15.4 1.12 16.4 1.18 15.7 1.25 14.9 1.30 15.2 1. 30 IS .4 1.33 15.3

Ti\BLE 35. Tabulated results for case PF:? L

----ORR <>t,deg.

---1.02 10.2 1.03 13.9 1.04 15.9 1.06 17.7 1.08 18.5 1.12 19.0 1.18 18.9 1.22 19.1 1.28 19.1 1.33 18.5

..

.. (;~ . "-';'"

,:~~.j

<j r .... ~ ~ ~;

"~ , " ".".;

;<. : :3

, ..... ~ , ",f. _

,'-:

:~'~~~: ~, ~

.,:::~ ,.,.1J >~ -·;t .'. ,~J

_ '::"~ ~ ,-~'~

~:>~~ ,.',~~

~:::1 > ,

;,j ' ...... - [" ,1

:/: ~l ", , ~

I.· ;-)1 r' .. ~/!'~U

-,~ 1""1 ' (!:\~'ll " ,

~. ,~

[, ,;:~ l" ;" .

..----~- f~:;l - ," j

':::~~ . :"''fl

l.~~'~6~'

·~)1 , "'~1 ,,' ~i {._'i;r (I:t

~7 :':'J r' t ~~

~ ',>'~ ;:'~~J' >::1 ~ 't' .,~

l':::! f.' f:-,?i

';':'1 ,A" ,

,.,'

, ~\j ,I,;."j

:"'~ ,' .... " : "iJ

• f ;':t1

1~~LI !I r~. ~~", ___ -,, ___ R __ '

115

TABLE 36. Tabulated results for case PF2 M

ORR C;t,deg.

1.02 13.0 1.04 19.1 1.06 21.1 1.08 22.0 1.12 22.2 1.18 22.7 1.25 22.0 1.30 21.7 1.33 21.8

TABI,s 37 • Tnbul .. tcd r'lsults fer ci'lS'e PF2 N

ORR ~t·dee.

----1.02 6.0 1.04 17.1. 1.06 21.3 1.08 22.7 1.12 24.4 1.18 25.1 1. 25 24.9 1.30 24.9 1.33 24.9

.s ... - .': "'''' ..........

.'

;:~~;~:'I ~

:[;:1 ~l' '~:,:tt: ":"';\}' , .. ". I .i; ~ .

~. -h > ~,

:-'";~'I :: ,'~- ! ', .. ~

.. ; 7'~ f :>~- . r

-'" ':$' !

d'i ~r~~~". ; <;i' ! ,.'\ ,

'-,,' '~t'~ I :: it;'

~.~~~; ":.:~~~

't':: ~ :~~~"" -'1;~ -.;~: ~

(,~;

t:;<~r t: ' ,~ f;",:,'" t . .'. i-;' f "~, l:

lr> ~.~ ~. ~ ,~,-= ~

I _. ;; •.

'<!,~:r : ,:>} i

t:':~\ . :

.~ ',,/ I

:~'~'w~ i

l.

::'{' ! :. ,"" I "{ I

"

f~t'l .. ~A:'l " I, t: I

' t:·~r'"!<. , ',' .. ~~ t

,.

~. t>-.~~r:

,.

>".d, : ::,:';:: ! -~. c.; I

ft\ .... .: ! -. ;;~. ~ . '. ·",.-1 :'""f-.'i.l ,,/:', '

:1-:-"'1 ' ~~';J!' ~t ::·~~~:~r, ;:':l'-i ~~'1 '

~}j'\:~ -:~~~~~~

116

TABLE 38. Tabulated results for case PF2 0

ORR "r,deg.

1.02 5.2 1.03 12.7 1.04 16.3 1.06 20.3 1.08 22.3 1.12 24.1 1.16 24.7 1.22 25.1 1.28 24.8 1.33 24.2

TABLE 39. Tabulatc~ results for case PF2 P

ORR ct, ,deg. t

1.02 6.9 1.04 7.B 1.06 8.4 l.08 8.5 1.08 8.3 1.12 8.9 1.18 8.6 1.25 7.6 1.30 6.9 1.33 6.3

~ .............

~.b\.~...s:.J_"":.,";."""'-~\.....~')"-" . • ~ ..... ..... r.<;r~~q " - ----'-- _.0 ..

',..!' ",.

1- r,

-~:~~:..., ,ViA --:';1~ , ,,°"1

i'~\~~~~ ~ "

' .. :1 :,;~

~: J .. ' : "'~I ~<;~

t~':·~~:

.~;:: . " . ~~

:' , :2~ t " ; ......

• ~ • ,I

.-: ;'~ j",

/:~ :J

~ , -

"'\'l .... , .. .. ' ~

!

::t)

!~J r. ,-1 !'.,:,

r"A

\"

\1 L"1 [ :'1 f' ;.:'

_II;,::~

~:i ;.~

"

"j ':,1

" "';',j

\ ' ::J .t, r~] 't~~ , --\r) "~.'l'Jl ; - '. "

. I {

\

i I" , " /~~ :.

, , : ;;j.

. ~,:, :;' .

. ,:; '~7!~ i.~

117

TABL~ 40. Tnbulated results for case PF2 Q

ORR ~T·d3g.

1.02 1.9 1.0'+ 14.9 1.06 17.1. 1.08 18.2 1.12 18.5 1.18 18.2 1.25 li.6 1.30 17.7 1.33 18.0

'fABLE 4,1. Tabulateu rcsul ts for case PF2 R

ORR ~t,der;.

1.02 3.6 1.04 14.5 1.06 18.1 1.08 19.6 1.12 21.0 1.18 21.7 1.25 22.3 1.30 21.6 1.33 22.1

. I,

"

/ /

4

..

, ,/

/ '4

I ~:::~~::' , 'j'/!,

-. 'u.

~:)~'I" ", .. ,--;-'" "._.r". I

'" r t "':"1 . ~:',~ j • :-'!\" .;; --;~ . , "::~"~f- 1 ".'.L! ~ ~:.t-'~ ~.1' t .. ;, ! ttl '.<1 , I '~ f i ~:;, "'1 ~ ,,;,"i .. ~ 'f..' I

.",~ 1 /~~. : '; :.: ! ' " ;;,~. I ';:'~:I' ',~~- ,i-'-'~ ., ::\'t ':;,": ... ,.",-:~

':'"t, '1-"""" I . - . , '~'l {;.): I

1

10, '.-: t -.~. ,~: . /\~ t '),tr i , - , ";.i!

> ... ,

-'.:,:(,\ \

.J .... 4 :

; '~7'~ r , '

.;~ : "'i'l ~ i .. " ~ ,

\fl '~ .. ,-, r

i,~1 '; '?t:I' ,I ••

'-/~

'?J~J ,·:.<li

...... , '- ~

,f :3',' "'~.I' ' ... :-~ • .#

~~:-j~t • A· f ~0i '~ -'~ J~~) -J .. ,:-:.,!~

::;"::[1' ~:!.l ,,:,~.

"J"\~ X~:~·; ."",:1 I)";;:' t-~tor.r

118

TABLE l~2 . Tabulated results for case FWl A

ORR ~ ,c!eg. t

1.02 ~9.l

LOt. -6.0 1.06 -5.8 1.03 -4.8 1.12 -5.0 1.20 -5.9 1.30 -6.0 1..33 -4.8

TI\ELE 43. Tabulated result:5 for case Fwl B

ORR 9t·d~g.

1.02 3.8 1.04 " • 3 1.06 B.6 1.03 ~.1 1.12 9.7 1.20 5.9 1.30 9.1 1.33 10.0

Ii

~'

,~:'i' 00

':: ',.'

~,~ ,,:~ ,. ~~

;:".

.::,

... J.~

~

:.... ~ .

. ::.: /0"-'

,i

'r" 'r ,I

~.~ "f :"J

, /;:J

j ,­

" ",

"

" ~'., .:~~ ~i

f1 l':J

'\ ':'j

~l F:I d I. ; ~

:'!

A ,1 ;,' ri '.. '[';1

J '1

" 1';,1 '.

'. '.

'. I

J ,J ~j

:1 .7

"

.~ il~1

~

· ,

.. ;1 __________ ._. ,:"."'<t-~

119

TABLE 44. Tabulated results far case FWl C

ORR ~t·deg.

1.02 6.3 1.04 10.5 1.06 12.8 LOB 14.2 1.12 16.5 1.20 16.8 1.30 17.2 1.33 1B.O 1. 33 18.7

TABLE 45. Tabulated resnl ts fOJ: ca:oc Fil2 A

ORR C;\,dcg.

1.02 ~7 .l~

1.04 -4.8 1.06 -4.B 1.08 -I •. i.

1.12 -3.3 loW -4.0 1.25 -4.1 1.30 -3.1 1.33 -2.4

f _ ' __ . __ "::'~~_"" __ "' __ "" __ A--__ -

/. -'

*

,

!:~.'gi ----.--.-,,;.:;(

~~. ~~t. . ,-" .; ,'. '7"

.,', ft~·t.}

.-~ , ,~ .. '~~: {"

'~,::'? .'';

; .. ~~~{~ 1,""·'

"

· .\'.'

;;::~t " . : \ f: ; ....

, ~ ~ ,";',~ ...,... ,"':':;~

'~:'~. -:;~: ;; ,;./: ~'~~ ~~f :(~~,~~'1~ :::~~'3~

t'! .\ · ',i ,"-!

.. ;-""(.' :;,~:~~ ~ {' j~'

L<\: .''' .~ t

~.~~~.~ }~ rr ..

".;-.' ~~

'T~ ~~',

.~~ , ~

.. , " ~

p"::~ ~ ~,: ~ ~

,. ~,.c.:.

I: :;; .~ , -" · ':: '. ,'~ " ..

flY'; : ~ ~,~(~ ,~,';.-.~'

f' ,". ,z" r >\,.~

· ..,! ,~'..

'~\~J \ t, h:'{~

: ~:~~, ... ~. ;~' . ~ " ,:;~ · ~:~,

'} j:'<;.'.'

,~:l:1 ';'~

.~.;~' ~.! ;~ ......

:;:.:~\}

It;~lr • .• ;v

, '~":)

',"""

r::\~: !_~~F· It}: ~l~,~

120

i I

/.. •...

TABT..E 46. Tabulated results for case Fl/2 B

ORR ~t,deg.

1.02 -8.3 1.04 -5.1 1.06 -4.0 1.08 -4.5 1.12 -4.1 LIS -4.1 1.25 -4.0 1.30 -2.5 1.33 -1.2

TABLE 1:,.7. Tabulatcci. resul~s fer case FH2 C

--_.-ORR ~t,dcg.

1.02 -4 9 1.04 0.1 1.06 1.1 1.08 1.7 1.12 3.1 1.18 3.8 1.18 3.6 1.25 2.9 1.30 4.4 1.30 4.0 1.33 4.9

•

0

N

~ Cl VI <Il 0

s.. t¢ 0 () 0 .... 0 CO ~ "t:l

VI 'D C1\ 00 ... .... ....

+J '& .... .... ::1

'" ,~ ..... Cl s..

"t:l :>: ~ "'00

<:.I ~ ° .... "'M +J 0 .... ........ .... (OJ ...... ::1 .a '" f-o

CO -!

"1 ... IX: , ~

·1

IT r ;"' ~~ . . ~ . ~ ...... ~ ,. : ~~

rt

... -.' '" , ~~/,1 .\. :,';; .. ':.:1; . ~f "L).

') r,.',,: Ai_~

i;!. :')

,f.;

rt ',r . ~" :;. ,"P. '~:~

'j.,

F2: ~ . ":. ~ -('(.. r: " '::'/

1 ~~} .~t-l~~7 r'; rr \

;( ! :.' ~.

t '; , , , \ , ' ~

Fi ;1 "~~

"'i! r~ • ,j

r·: t ~'i L'i ~', ~ , '1 "

/1 ~ . .: ,~

1:_: k,~ ",;1

/f::J ,S • "'.

',f~ ",'. ! ')

"1 OJ (1

:J J d~

::·1 ;v1 ~ '1 "

<j t;l ;;\,1 :'1 ~~ . k;'l .' , (,g~~

122

XII APPE~DIX C

This section estimateli tho uncertainr.y in the T\ (11 ::: :flU Ivx) o

measurements using the method of Kline and ~!cClintoc.k [22}. Tho

uncertainty interval loR' in the results i~ givon by

\ _ f,(aR \ )2 . CaR, )2 • AR - [a~lhl ~ a~2A2 '

(aR ~ 2J 1/2 il" n)

:l

(12)

where R is .the result of a single-sample experiment, ~ is an independent

variahle, n is the total number of independent variables, and Ai is the

uncertainty interval for each variable. Since the uncertainty interval

for each variablo is gener-ally not statistically knQwn, it is necessary

to estimate it to specified oddz. The values of Ai to be presented have

been esticoted based on 10 to 1 odds. SiOCB v is a function of pressure

Ilnd te~pcrature an uncer'Cainty analysis was c:lrried out for v. Th\~

uncertainty interval for v uas very small so it was excluded frc~ ~he

follotJing calculutions for \\' The results in Table 49 are for a y

location close to the plate surface.

From the calculation in Table 49 A ~ 0.069. The value of n n

computed' using the valuc5 in Table 49 is 0.691. Thus, for a typical run

for a y location ne3r the plate surface

n = 0.691 ± 0.069

..

m';'·SI

~ ;,:,'~: 't . ~ .. ": 'i -: ',,"i)

;..' "'";':, r.,· .. '['.,'<i,;

~ , , I

'~ ~', ... ; I

',~ \1 · .~

.' .," "'\

, 0 · ";.t :., I ,~ ,

l' ," ') ~ , i'-" , . ~, ,

;1' -:;:

[,::' ',;:: '. ,.,

I; '-Ji: I: '1~' '

;~' ;':'~

[ .'~ i

! '>':'f-J!

. /' !:~ ";~"i oil. :: ~,! .... ' '" I , . ',,-

/ - "."'" .' ' "t .,'; ,"~1

::'i ,"

l"" .'01

L :,:.:1 t ,,;; l "::~

'

I." ,'i ;H

t : :'; ~. ~~: I, ,:i i ' !

_," " : 1

. 'f.] I .. ' 01

t\:' ~";r

: ~! ,'- ~. ; · \. ~

, ',',:,,/

't' :' ;" i ",c\I

~i . ," '" ,',.

,',,:,:;J f" ·1 t' S Ii

I <,:, I j 'k .,;\

r ~ ,; \ ~:;: d

t;' '{! i -, t·~t

,) .... -: t;,:. I ~,.,j

~'.oJ , ~" 1 -.. f ~~ .:. ~:

t"'< :j

- ',.1 •

." 1":~)1 c, '"I' , :,'': , , -, ' ~ ,

.' -- .. ~-. ~,:, ::jl. :,' .... , .. '- ~ .

TABLE 49.

Variable

-_ .. , x

U 0

Y

. , I

I

123 lend

Uncertainty analysis for 11

Nominal Value l. an/a"i J.

0.21 1,1 ± 0.25 C:l -1..671

16.7 ril/'2- ± 0.25 ril/s 0.021

0.03 cm ± 0.003 em 23.025

~ 11 = ± (4.816 x 10-3)1/2

). == + 0.069 11 -

(A.an/03\}.)2 1. 1.

-4 1. 71~5 ~t 10

-5 2.759 Yo 10

4.771 x 10-3

-3 4.816 x lC

:/'1 ' . .::..~,:;:Z;j~ $' .. 1.oI:J .. 'Q. ..... !' ... \~ ... ..---,-~ .. ------~ .1

:_ .. __ ""_._,_. __ "'_ ... ~w_ ... __ ._. ____ '· ___ _

End of Document