ENHRNCED VISCOUS FLOW DRRG REDUCTION USING 

-. __ - __ . . . .. . . . . - . . . RCOUSTIC EXCITRTION 

NASA Research Grant NAG-1-654 

Final Remrt to 

NRSG Lanq ley Research Center 

Ham ot on, V i r IJ i ri i a 

J 

.- 2’3665 - 5325 

QTTENpQN : 

Mr. Jclhn E. finders. Jr. MRIL STGF1 163 

Dr. R.T. Nagel 

Mechanical R Rerospace Engineering 

North Car-olir~a State University 

Carnous EUH 73iC3 

Raleigh, Ncwtn Carcllina 27695-731121 

( 3 13) 737-2355 

(NASA-CR-182734) ENHANCED VISCOUS PLOU DBAG N88-22295 

REDUCTION USING ACOUSTIC EXCITATION Final 

Report [North Carolina State Univ.) 114 p 

CSCL 20B Unclas 

G3/34 0137319 
.._. 

LIST 3F FI~URES vi 

2.3 Detzrmination of thi Skin Friction Coefficient,c+ ... 21 

2.4 Verification of th2 Basic Flow Configuration........23 

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

4. 

5. 

5. 

3.2 Spreading Effect.................oe.......o..~e.~o..47 

3.2.2 Explanation of the Spresding Effect.. ........ .53 

3.3 Optimization of thi Existing Confisuration........ ..59 

3.4 Measurements with an Optimized Configuration ........ 65 

:3i5-Nit-Dcas Rs~uction.t.8.t............................70 

3.5 Skin Friction Measurements of Various LESU 

Configurations.......~.~......~~~...........~.~~~~71 

3.5.1 Preliminary Largi Eddy Brsak-Up Devices.......71 

3.5.2 Pr2liminary Acoustic excitation...............?^ 

3.2.1 Spanwisi Mappins Downstream of th2 LEBU.. .... .47 

3.7 Acouztic Excitation at Unit Reynolds Number of 

10 m-'. ......................................... ..79 

CONCLUSIONS AND REZOMMENDATION3.......................,.89 

4.1 Concluding Remarks......................~.~......~.~33 

4.2 Recomnsndations for Further Investigation... ........ 91 

4PPENDICES.............~................ ................ 95 

5.1 Fluctuatins Pressure at the LEBU's Trailing Edge .... 95 

5.2 Prediction of Turbulent Boundary Layer..............gg 

5.2.1 Input Data for Head's Method..................gg 

6.2.2 Velocity Profile of a Turbulent Boundary 

L~yer..................o.o~...........~m~ee~99 

6.2.3 Boundary Layer Velocity Profile for a LEBU 

Confi~uration....... ...................... .l~I 

6.2.4 Determination of cf from Velocity Profile....lO2 

6.3 Pressure Pulse Controling Device...................135 

PRECEDmG PAGE BLANK NOT FILMED 

E3 
V 

LIST: OF TABLES 

versus axis1 6 "1' 1. Measured shape p rameter 

23. Curve fittins parsmeters for ths acousticslly 

-. 8 distancs, x . (-f =O. 7x10 m- ) .................. .24 

optimized LEBU 55 confiqurqtion ................ 63 

2b. -Axial variation of the skin friction 

coefficient,cf , for the optimizsd 

configurstion...... ............................ 5~ 

2c. Axial variation of the total drag coefficient, 

for the optimized configuration..... ....... 59 

3. Ceonetry of preliminary single LZBU'S.............~~ 

cD, 

4. Curve fitting paraaeters for various flow 

- -. - ... -- - ---___ ...... - r-zcorrf-i-~urzrtian-s ;( =:waS---asured to a distanco 

of 623 from LEBU). .. ...... ... . . ... . . .74 

5. Curvi fitting psramsters and percint dr92 

rsduction for LEBU #4 configuration ............77 

- -- 6.----Experimintal -parmeters -for optimized LEBU t5 - 

and LEBU #S configurations.....,.....~~~~~.~~..79 
VI 

LIST OF FISURES 

.I. Typical flat plate boundary layer 

(flow visualization with smoke). .................. 3 

2. Largo eddy brak2-up process ........................ 3 

3. Geniral- view of the NCSU Boundary Layer Wind 

Tunnel.........................................ll . 

... . -4. Wind tunnsl-test surface....... ................... 12 

5. Schiinstic representation of the acoustic 

oxcitation m~chanism...........................l3 

5. Time delayed processor responsi to incident 

flow.........................*.................l5 

7. Axial distribution of turbulenca..intensity..... ... 17 

8. Nsrrow band acoustic signal of the pressure 

pulsi at LEBU's height ......................... 20 

. ._ __ - - __ - ___ - -9 * - -P rid ic te d -and -me a sur e d momentum t hi c kne s s ,8, 

snd skin friction coefficient,cf, for the 

plain flow.....................................24 

two axial locations.....................*......27 

13. Spanwise variation of momentum thickness,& at 

11. Predicted and measured mean velocity profils 

for the plain flow.............................29 

across the boundary layer ...................... 30 

U' 12. Measurements of the strzamwisi velocity,-, 

"0 

13. Prsdicted and measured mesn velocity profile 

14. Momentum thickness ,e, versus axial distance 

for LEBU #2 confisuration ...................... 32 

,X, for the excited and unexcited plain 

flows....... ................................... 34 

,x, for various flow configurations.. ......... .36 

15. Momentum thicknass,O, versus axial distance 

16. Vsriation of the skin friction coefficient 

,cf, for each configuration .................... 35 
.. 

VI1 

17. Schenatic for velocity cross correlation 

measurenents across thi LEBU...................40 

IS. Maximum space-time velocity cross correlation 

13. Relative variation of the low friquency RMS 

. in the boundary layer .......................... 41 

turbulence close to the LEBU trailing edgs.....43 

- - 23. Boundary layer- flow visualization for the 

_. . acoustically-excited LEBU configuration.. ..... .45 (A) plain case (B) LEBU manipulated and (C) ._ ___ __ 

21. Spanwis? mapping of the peak cross correlation 

downstream of the LEBU (solid symbols indicate 

less than 1.0)...................*.*...........43 

22. Spsnwise variation of momentum thicknsss ,6, .. -- -- for ths-excit2d-and unexcited LEBU at 

three axial 13catims..........................50 

23. Relative turbulence intensity of the excited 

bound3ry lay2r across the 1t~2dge11 of acoustic 

influ~nc2......................................5~ 

24. Model of (a) coherent structures and (b) 

acoustic pulse flow fizld......................55 

25. Top view of suggested acoustic spreading 

mechanism............................*.........56 

26. Relative peak correlation,r,, and numbir of 

acoustic pulses per second, versus riforence 

voltager ..................................... 59 v 

"a 

27. Variation of the relative peak correlation, 

rC, with time delay, t.... ..................... 62 

at LEBU's height ............................... 64 

28. Variation of the relative peak correlation, 

rc, with time averaged SPL of pressure pulse 

29. Momentum thicknass,B, versus axial distance, 

x, for various flow configurations (optimized acoustic excitation). .......................... 67 

30. Momentua thickness,B, versus axial distancs, 

x, for various preliminary configurations ...... 73 
psse 

x, for preliminary acoustic excitation .........7 5 

x, for various flow configurations at unit 

Fie= 13 m ..................................... 91 

31. Nomenturn thicknsss,e, versus axial distance, 

-- - 32. .Mornenturn thickness,e, versus axis1 distant?, - 

6 -1 

33. Variation of the skin friction coefficient -, __ 

,cf, for each configuration at unit 3ie=13 m ... 92 

._ -:I--- -------34. Time space velocity-cgosp corrslation across 

LEBU 3t unit Re=13 m- ......................... 94 

for t&e rxcited and unexcitid LEBU at unit 

35. Spanwise variation of moaentua thicknass ,8, 

__ - --- !+=lo m- ....... .*............................. ~5 

_- . -I---. ~ . =-;=..: :3SL-EIectronic diagram of -acoustic puls? triggering 

device (Courtesy of Mr. Lance Mangun) ......... I05 
IX 

a 

B 

b 

CCF 

C 

CD 

C f 

DP 

dB 

NONENCLATURE 

curve fitting parametar 

logarithmic law constant 

curve fitting paramiter 

cross correlation function 

chord length 

total drag coefficient 

local skin friction co2fficient 

fluctuating pressure 

decibsl 

___-___I .___ du max -m3ximum-velocity defect-.. at wskz' s axis of .._ .. 

duw 

e 

f 

H 

h 

k 

L 

LA 

L5 

L5A 

P 

PL 

Re 

2 

r 

sy mmz cry 

velocity defect caused by LEBU's wak? 

flow parameter 

frequency 

shape parameter 

haight above floor 

logarithmic law constsnt 

LEBU configuration 

acousticslly excitzd LEBU canfiguration 

LEBU configuration nuibir 5 

acousticslly excitsd LEBU nurnbsr 5 

nondimensional pr2ssut-e 

plain flow configuration 

Reynolds Numbsr 

correlation cosfficient 
e . Y 

T r 

SPL 

S 

w , 

X 

Y 

Y+ 

Y 

2 

ratio of measured peak values of crosscarrelstion functions 

ratio of msssured rzlative turbulence intensiti3s 

ratio of msasured momentum thicknesses 

'sound pressure level 

distanci from upstr2as prob? ta LESU's 

edge trailing 

rglative turbulence intensity 

time delay 

convection velocity 

. froe stream velocity 

axial valocity 

velocity of 9 LEBU manipulated boundary layer 

vslocity for a plain flow 

wsll friction velocity 

hot film sensor voltag2 output 

reference voltage 

longitundinal vzlocity component 

spanwise velocity component 

wake function 

axial distance moasurod from the leading edga of 

the test section 

longitundinsl distance measured from the test 

section floor 

wall units 

longitundinsl distance from wake's axis of 

symmitry 

spanwise distance messured from the centerline of 

the plate test surface 
XI 

F 

s 

v 

4 

TI 

R 

P 

wake semi-width 

boundary lay2.r thicknass 

fa constant 

aorriontum thickness=]o$l- -)dy U 

- - UO 

9 v2 r a ge roughness he i ght 

flow par 3ma t2 r 

kinsmatic viscosity 

proba separation distance 

wake psr3nneter 

Pi 

density 

-pufv' Reynolds striss 

- 

signifies average 

* signifies fluctuating quantity 
4 

1 . INTRODUCTION 

1.1. STATEMENT OF THE PROBLEM 

-. - - -T-he flow- of fluid abouka solid-body can be separated 

into two regimes: a thin layer of fluid adjacent to the body 

surface where friction is the dominant phenomenon,and the 

region outside the thin layer where the fluid can be treated 

as inviscid. The thin layer adjacent to the body surface is 

called the velocity boundary layer. The thickness of the 

boundary layer ,6 3 -- increases along the body in a downstream 

- -_- -- -- direction.- Inside the boundary layer -the flow is retarded 

because of friction with the solid surface and it forms a 

velocity profile that varies smoothly from zero at the wall 

- to-the undisturbed free sTream velocity Vi. The reduction of 

skin friction drag between a solid surface and a moving fluid 

can greatly improve the performance of many vehicles or fluid 

machinery. 

Boundary layer development over a flat plate can be 

separated into three regions. A laminar region starts from 

the flat plate leading edge and forms a Blassius velocity 

profile where the velocity fluctuations are negligible. 

Further downstream the flow undergoes transition to turbulent 

flow [I] where the velocity inside the boundary layer 

exhibits irregular velocity fluctuations. The value of the 

Reynolds number,Re,, can provide an estimate of the laminar, 

transition and turbulent regions. The skin friction 
2 

coefficient for the laminar region of a boundary layer is 

smaller than that for the turbulent region. The most popular 

approach in wall friction drag reduction therefore has been 

__ _____ - to. _attempt to- delay- --the transition-frm- laminar to turbulent 

flow [2] and maintain the laminar skin friction coefficient 

for as long as possible. Most practical flows are, however, 

turbulent and at large Reynolds numbers all flows will 

eventually undergo transition to turbulence. The main object 

of the following investigation is to reduce the skin friction 

~ - - - - I - - drag of a turbulent boundary layer by altering its structure 

r31. 

Visual investigation of turbulent boundary layers have 

shown them to contain at least three distinct types of eddy 

- -- structure (figure 1 ) : 

i. Large eddies which dominate the outer region of the 

boundary layer and have an average length of 

approximately 1.65[4] 

ii. Typical eddies having a typical length of 200 wall 

units,y+ , are encountered throughout the turbulent 

boundary layer [5]. 

iii. Well organized motions in the laminar sublayer can 

form low speed streaks [6]. 

The large scale eddies have an average axial length 

of about 1.68 [4] and cause a peak velocity fluctuation of 

the order of 0.2U0 where U, is the external velocity. The 

large scale structures are convected downstream with an 
. 

__ ........... .- -. ....... - - ....... 

................ 

- . - ...... 

.. 

3 
. 

average velocity UC=0.93U, [?I, and appear semi-periodically 

181 with an average frequency of appearance f=- UO 

2.56 

These large scale structures have a limited life span. They 

decay -after travel-ing- a -distance 03- about 108and lose their 

coherence after about 4&[9]. Large eddies are associated 

with the production of turbulent energy and the production of 

~- __ - __ . - - . - - 

__ Reynolds stress -putvt,although the exact mechanism linking 

them to the sublayer skin friction producing phenomena is 

still unclear [4,6,9]. The reason for this is the lack of 

comprehensive experimental data in - the laminar sublayer. 

layer 

structure could lead to reduced skin friction as described in 

the following sections. 

- - Consequently, - -manipulation - -of the turbulent boundary . - - __ - - 

1.2. HISTORICAL REVIEW 

Early boundary layer manipulation [IO] was performed by 

positioning mesh screens of height approximately equal to 8 

inside the boundary layer. This resulted in the destruction 

of the large eddies and a skin friction drag reduction of 50 

percent extending a distance of 1006 to 1506 downstream of 

the mesh screens. The drag of the device itself was 

excessive. Pursuing the same goal of eliminating the large 

eddies, Hefner et a1 [I13 mounted horizontal and vertical 

plates of various shapes and sizes inside the boundary layer. 

These plates or elements interacted with and modified the 

large eddies, interrupting the turbulence production. The 
reduction of the wall skin friction was attributed partially 

5 

to the alteration of the outer turbulence scale. An av2ragi 

of 24 percent drag reduction for a distance of 45 device 

- __ ----:--~heights_- was measure-d but-no -net :drag reduction was obssrved. 

A study utilizing four parallel plate manipulators ernbzddsd 

inside the boundary layer was performed by Corke et a1 [12]. 

This sethod was effictive in removing the largs scale 

structures and a 39 percent skin friction drag reduction was 

documented at a distance of downstream. Flow 

visualization recorded the breaking up of the large eddies by 

- -thz paral-le1 plates which Tesultid in *thinner manipulatad 

boundary layer. The streamwisi tgrbulsnce intensity closi to 

the wall of the msnipulated boundary layer was found to be 

reduced. No nit drag reduction was measured. In ord2r to 

improvs upon the net drag, reduction Corks et a1 [13] mounted 

a pair of tanden flat plates within the boundary layer. They 

measured a 20 percant net drag reduction at same locations. 

The local skin friction drag coefficient did not relax ta 

that of the undisturbed flow until a distancs of 698. 

also identified the possible mechanisns lesding to such 

results as the supprPssion of the normal vslocity conp9nent 

of the large eddies by the manipulators and ths 

rsdistribution of the turbulent kinstic energy by the blade 

wake. Bertelrud et a1 [14] used thin trsnsverse ribbons in 

tandem for various flow configurations. A 40 percent skin 

friction drag reduction was measured and this phznoienon 

-- ~ - 

-- 

Thsy 
persisted for about 80 downstream of the manipulator. The 

net drag reduction was moderate. 

These experiments adopted similar boundary layer 

manipulating -sche-mes,---but -the specific dimensions of chord 

length, height and tandem spacing varied considerably. In a 

review paper Hefner et a1 [I51 presented the parameters for 

- __ - - - 

-- -.I- en optimum plate .manipulation of a turbulent boundary layer. 

They stated that the flat elements should be thin and mounted 

as tension members. They estimated that the element chord 

length should be approximately equal to the boundary layer 

thickness,S, and the outer element should not exceed a 

height of 0.86above the wall surface. It was also noted that 

the .number of horizontal elements should not exceed two and 

that the plates operate most effectively in the range of 

momentum thickness Reynolds number from 3,000 to 6,000. In 

recent investigations [16], 10 to 30 percent net drag 

reduction was achieved with optimized flat plate manipulators 

in tandem under zero, mildly adverse and favorable pressure 

gradient flows. Most of the net drag reduction occurred 

within 50 boundary layer thicknesses from the manipulator. 

Airfoil shaped [I71 large eddy break-up devices (LEBLJ's) 

were tested in a range of momentum thickness Reynolds numbers 

at the manipulator near '7,400. The results indicated that 

only symmetric airfoils in tandem were effective in 

manipulating the turbulence boundary layer and a 7 percent 

net drag reduction was recorded. Finally it should be 
7 

mentioned that the repeatability of net drag reduction 

experiments was not found satisfactory [Is] and the 

microgeometry of the plate manipulators is critical with 

--respect- to their effectiveness [18]. __ _---- 

1.3. OBJECTIVE OF STUDY 

_. --Large eddy break up devices (LEBUJs) constitute a new, 

promising method of obtaining drag reduction in a turbulent 

boundary layer. The destruction of the large scale eddies and 

the associated reduction in momentum transfer to the wall can 

result in lower skin friction drag. One of the suggested 

mechanisms, based upon the work of Liss and Usol'tsev 

[13,19,20l9 leading to large eddy elimination is 

schematically represented in figure 2. Large eddies 

(discrete vortices) impinging upon a LEBU plate generate 

unsteady lift forces upon it due to the effective angle of 

attack variation. Because of the unsteady circulation around 

the device, vortices are shed from its trailing edge. The 

oncoming large eddies in the boundary layer interact with the 

shed vorticity and are partially canceled. The focus of this 

dissertation is to enhance the LEBU effectiveness by exciting 

its trailing edge with acoustic waves phase locked to the 

large scale structure and thus influence the momentum 

transfer to the wall. 

An initial estimate of the required sound pressure level 

for an effective acoustic pulse was obtained by considering 
__ . .. 

- 31 

W 

K 

0 

c \ 

A- 

' \ 

\ 

0- 

0. 

1 

I 

cv 

Y 

a 

L 

P 

x 

a 

TJ 

6, 

. 

N 

aJ 

t 

7 

bD 

L 

d 
9 

the magnitude of the pressure perturbations at the near wake 

of a thin plate in inviscid flow. A sound wave of 

approxiaately 100 dB (Appendix 1) pressure level, arriving 

.- - - a-t -the LE-BU-traiZing edge- together-with the large eddies was 

considered adequate to influence the already manipulated 

boundary layer. 

- __ - - - - 

Detailed skin friction measurements were obtained in the 

flow region downstream of a LEBU excited with acoustic waves. 

The data are compared with skin friction measurements of a 

simply manipulated flow, without acoustic excitation and with 

a plain flow configuration. The properties and the scales of 

motion in the flow regime downstream of the acoustically 

excited LEBU are studied. A parametric study based upon the 

- characteristics of the acoustic input was pursued in addition 

to careful mapping of the drag reduction phenomenon within 

the acoustically manipulated boundary layer. This study of 

boundary layer manipulation has lead to improved skin 

friction drag reduction and further understanding of the 

turbulent boundary layers. 

.. - 
10 

2. EXPERIMENTAL PROCEDURE 

2.1. BASIC EXPERIMENTAL APPARATUS 

___ -- - --The experimental =study-wasxonducted in the recently 

constructed NCSU Boundary Layer Wind Tunnel [21]. A general 

view of the wind tunnel is shown in figure 3. This facility 

features: a long test section (-7.0 m) to achieve high 

Reynolds numbers with low speeds, a velocity range of 4 to 

33 m/s and extremely uniform mean flow with turbulence 

intensities of less than-0.25 percent; A single LEBU plate 

._ - ._ L -_. -- --- z--:=---as 1 carefully fabricated from -stainless steel shinstock and 

mounted at a distance of 2.0 m from the leading edge of the 

test section, in the boundary layer (figure 4). A mounting 

- -- - sys tem for the LEBU-was designed and-built. The mount has 

accurate control over the LEBU's height above the test 

surface, the LEBU's angle of attack and tension. The LEBU 

extends through openings in the wind tunnel side walls across 

the full span of the test section. Each side of the LEBU 

mount is independently adjustable to assure precise alignment 

and eliminate possible vibrations of the stretched plate. 

The experimental arrangement to acoustically excite the 

LEBU trailing edge is shown in figure 5. A hot film probe is 

positioned upstream of the LEBU at the LEBU height. The 

signal from the sensor is obtained from an anemometer and fed 

into a specially designed processor whose electronic diagram 

is drawn in Appendix 3. The processor responds only to large 
a 

c 

a 

c 

3 

0 

m 

3 

m 

u 

z 
/ 

4 

- 

-. . _. . - .. 

/ 

c 

w 

Q 

\ 

€ 

0 a 

. 

al 

0 

a 

4 

. 

cu 

t 

3 

en 

a 

d 
13 

-- 

I 

-- ._ I-- 

3 0 T 

A 

- 

co .- -v) 

3 

W 

J 

m: 

-. 

(u 

I: 

U 

\ 

\ 
-- 

excursions of the hot film signal. The threshold voltage 

level,V, , to which the processor responds is adjustable. This 

adjustment allows selection of a lower limit of large scale 

Teddies --t~--- which the- processor -will -Pespond. Eddies with 

velocity fluctuations above this threshold level (reference 

voltage) are ignored while eddies with associated velocity 

excursions below the threshold level produce a response from 

the processor. The response is a signal with character and 

duration similar to the anemometer's large fluctuations as 

shown on the dual trace oscilloscope display of figure 6. The 

response of - the processor must also be- time delayed and 

amplified. The time delay,t, is set equal to the large eddy 

convection time [7] between the upstream hot film sensor and 

the LEBU trailing edge.- The delayed processor response is 

then amplified to produce an acoustic input capable of 

influencing the LEBU wake. 

__ __ --- - 

-_ 

The processor response is then used to drive acoustic 

waves from a location on the floor of the wind tunnel below 

the trailing edge of the LESU. The acoustic waves can 

therefore be made to arrive at the LEBU trailing edge 

together with the incident large eddies. In this manner the 

vorticity shed from the LEBU, which apparently influences the 

eddy cancellation, can be modified. The pressure pulse device 

consists of an 8 inch woofer speaker which is seal mounted on 

the wide side of a conical channel. The speaker apparatus is 

housed in a lined box to restrain noise signals from entering 
5 rnsec.1 I 

Fizur? 5. Ilia? delsyed procsssor r?sponse to Fnsidint 

flow. 
the test surface by s?urious paths. 

2.2. OPERATINS CONDITIONS 

Z-Ths-wind tunnel--is adjusted to-produce a zero prossure 

gradient flow along its length. Th? variation of the frsz 

stream turbulence intensity in ths test section is show.rl in 

figure 7.-For thz operating vslocity rang2 3 0.25 percsnt 

turbulence intensity was measured. The boundary layer is 

forcad turbulent by a coarse sandpaper trip mounted 3 C'II 

downstraam of thi test surface leading edge. The length of 

-----the --boundary layer trip -is 21 7=m which quickly establishis a 

fully developed turbulent boundary layer with a conpleti 

rang? of length scales as can ba s22n fram the photosraph in 

. - - - - - - - - - - - - - - ___ - -__ 

__ 

"O was s2t '-7' figure 1. The wind tunnel -unit'-Reynolds number 

at 0.7~10 m. The corresponding typical mssn flow velocity w3s 

spproxinstely 11 .O m/s and the Reynold's numbir based upon 

the momentum thickness,@ , at the LEBU location was about 

3,100. The boundary layer thickness,6, at LEBU location was 

estimated as 4.1 cm. This was determined using the definition 

of the boundary leyer thickness as the heisht at which 

-=.995, where u is the local velocity and Uo is thz 

velocity of the external flow. The LEBU chord lensth was 

=0.90&, its height above the test surface was '0.808and its 

thickness was 0.0058 according to the recommendations of 

reference [ 151. 

6 -1 

- 

U - 

uo 

This LEBU configuration is sn improvsd version of 
17 

. 

x 

c, 

d 

v) 

C 

U 

C 

d 

a) 

Q, 

0 

c 

al 

.. 

3 

D 

L 

3 

c, 

cr 

0 

C 

0 
several manipulators that were tested. It is described in 

detail because a major portion of this study was spent upon 

it. This plate configuration was the fifth tested (LEBU #5) 

- and-uas the -most successful. The -configurations previously 

tested also used a wind tunnel unit Reynolds number of 0.7~ 

10 m”, were located at a distance of 2.0 m from the test 

section leading edge and-are described in section 3.6. 

- _. - - - - - 

6 

The upstream eddy detector hot film probe was positioned 

at the midspan of the test surface at a height of 0.853 and 

at a distance, s, of 2.456upstream the LEBU trailing edge as 

showrr- -in-figure 5. This probe, used to detect the incident 

large eddies, was positioned as close as possible to the LEBU 

trailing edge because the large eddies lose their coherence 

after a distance of about 46[4]. The location of the large 

eddy detector probe must be, however, far enough upstream in 

order to prevent a feed back from the acoustic pulses. The 

axis of the probe was inclined at 45 degrees with respect to 

the test section vertical plane of symmetry (figure 4) in 

order to avoid probe interference with the downstream flow 

- -- - _-- __ 

s 

field. The processor delay time was set at t= ;a 0.93 Uo 

typical value of t was 10 msec. 

The pressure pulse mechanism was mounted under the test 

surface at midspan below the LEBU device trailing edge. The 

acoustic input was directed to the LEBU trailing edge through 

a circular opening (3/8 inch diameter) covered with fine 

screen flush mounted to the test surface. 
A first approximation of the required sound pressure 

level of the acoustic waves was obtained by considering the 

boundary layer pressure perturbations near the trailing edge 

- . -. --- .. - - -----:of a-flat plate .-According-to-detailed calculations (Appendix 

1) a typical value of about 100 decibel (dB) pressure 

perturbation was predicted at the LEBU trailing edge. This is 

not the pressure fluctuation generated at the flat plate 

trailing edge when it encounters an oncoming average large 

eddy, but rather the typical pressure fluctuation in that 

location for a flat plate in inviscid free stream flow. It 

-was- assumed that sound pressure levels of this magnitude 

would be necessary to have some effect upon the trailing edge 

flow. A power amplifier was utilized to deliver the required 

power to the pulse mechanism. 

I . - ._ - - -- - 

The pressure pulse mechanism was bench tested with the 

wind tunnel operating at a unit Reynolds number of 0.7xlO 6 m -1 

using the output of the upstream hot film probe. The speaker 

mechanism was mounted outside of the wind tunnel under a 

wooden baffle plate with an acoustic wave port identical to 

that in the wind tunnel test section. The time averaged Root 

Mean Square (RMS) power spectra of the acoustic output at the 

LEBU's height was measured in a hard wall room under zero 

flow conditions. Figure 8 shows the RMS broadband spectra 

from 0 Hertz to 2,000 Hertz of the acoustic pulse emanating 

from the floor pressure port. The acoustic power is 

concentrated over a narrow region from 60 Hertz to 200 Hertz 
0 

5 I 

Q) a 

a 

al 

L 

3 

hn 

d 

kl 
21 

approxinately at a level of 109 decibzls. Ths sound pr5ssure 

level at the LEBU's heizht integrated from 0 Hertz to 2,033 

Hertz was 95.4 decibils. The large eddy passing frequency was 

- --zxp_lc-te3. to--be-approx-imately-lZQ-Hertz, hencz the bulk of thz . 

amustic power occurrzd at the expected frzquencies. The 

remaining part of the spectra consists of the hsrrnmics of 

the acoustic pulses, the background noise, l1%round dip" 

phznornenon and the harrnmics of the wind tunnel fan blad? 

passing tone. A 1/2 inch Bruel and Kjaer condens2r 

microphone was utilized for thise neasurements. 

2.3. DETERMINATI3N OF THE SKIN FRICTION COEFFICIENT,c, 

Measurements of the boundary layer profile downstream of 

the manipulator plate were obtained -using a small boundary 

layer Pitot probe with an outside diarneter of 0.5rnin. A 

ramotely controlled traversing mechanisn was used to assist 

with th2 precision probe positioning. The traversing device 

providss probe movernent over tha Y-2 plane in the wind tunnil 

tpst section (figure 4) with a positionins accuracy of 23.1 

ma. The pressures from ths boundary layer probe were measured 

with a Validyne differzntial prissure transducer. The static 

pressure was obtained from static taps in the test surface. 

Approximately 200 sanples were obtained and averaged at each 

point and the velocity profile was determinid by 40 such 

points distributed ovic the thicknass of ths boundary layer. 

A Digital 15 bit resolution data acquition system in 
22 

conjunction with a Digital Computir wire utilized in ord2r to 

process the measured data and monitDr tho wind tunnel's 

operation. Variations in mean velocity of more than 1 percent 

and - mean- flow tempirature of ..more than ,2 percsnt 

automatically stopped the acquisition process, so that ths 

exact conditions could be reset. 

Thi mornenturn thickn2ss,8 , is calculated from its 

definition (list of symbols) by numerically integrating th2 

velocity profile ov2r the boundary layer thicknzss. For zero 

- -prassure - gradient two-dimensional flow the VO~ ;(arman ._ . - 

._ i- 3Iosentum-Intcgral: -Equation reduces to: 

2 dx Cf=X 

where, cf is the local skin friction coefficient and x is th2 

axial length. Ths inomentum thickne-ss,B, is determined as - -. 

describsd above for a plurality of positions downstriain of 

thi LEBU. Ths valuis can b2 least squars fitted to 3 powsr 

curve of thi form: 

e=axb (2.2) 

Hence, th2 skin friction coefficient can be estimated by : 

cf =2abxb-' (2.3) 

An altzrnative calculation of the skin friction coefficient 

can bi obtained by applyins a central finite difference 

scheme upon equation 2.1 

The previously describtd indiroct method of maasurinz 

cf, althoush time consuming, has certain sdvantag3s cornpar23 

to other msthods of wsll shear strsss measurement [??I. Skin 
23 

friction gaug~s have problems with the nessscary gaps and 

possible misalisnement rilated to the floating elenent. 

Preston tubas, Stanton gauges and sublayer fences caus=L flow 

obstruction, and measurements are heavily dependent _upon 

geometry and positioning. Thi method used in this study was 

- - the- most-economically sound and the most dirsctly rslated to 

provsn theory. 

2.4. VERIFICATION OF THE BASIC FLOW CONFISURATION 

The -momentum -thicknsss,@, of the turbulent boundary 

._ - ~-- - ..__layer. .is of primary interes-t .in-the -prisent investigstion 

becauss it is used for determinins ths skin friction 

coefficient. Figurs 9 shows neasured and theorztically 

- predicted -valu?s of 8 for__tht --plain flow case versus 

downstream distance x. The solid line represents valuos of 

momentum thickness predicted by Head's nethod [ 231. Thi 

expzrimental vsluis of 8 were obtained by averaging 3 valuss 

across th? spsn of th2 test surface. Hsad's method was 

applied for zero pressure gradient flow and initialized with 

a momentum thicknass prsdicted empirically at th2 end of the 

sandpapir trip (Appendix 2.1). The initial shape parameter, 

H=1.375, was selected as the averaged measured valu?. The 

shape parameter H for a boundary layer is defined as the 

ratio of displacement to momentum thickness. Yeasured valuzs 

of H at different axis1 locations arz listed in table 1 along 

with the average. The initial or starting valu3s in Hiad's 
24 

. 

c9 cv 

/ 

A 

W\ 

"y i 

.. 

a 

mc 

E4 

a) o 

m 

6, 

t 

3 

bO 

L 

.A 
25 

Tabla 1 -. Neasured shspe paramet r, H, versus axis1 

distance,x (&=0.7xlOg v m'' ). 

x bl H 

2.00 I .379 

2.25 1.332 

2.50 1.495 

2-75 1.375 

3.00 1.361 

3-25 1.363 

3.50 I .356 

3-75 1.343 

4.03 I .355 

4.25 1.358 

4.53 1.357 

* avecag2 H=1.375 

- 
26 

method are relatively unimportant except for the first few 

points of the calculation. Agreement between the predicted 

and measured values of appeared satisfactory with a 

-maximum-deviatTon of -3-percerrt;-I'k momentum thickness ,e , - - - - - 

at 9 spanwise locations across the test section centerline at 

2.0 m and 3.5 m from the test surface leading edge is shown 

orc figure -10. The maximum deviation from the mean was 4 percent. 

The local skin friction coefficient for a plain flow 

configuration was determined according to the procedure 

suggested by Bradshaw [24]. This method explained in Appendix 

2.4 determines cf from a measured boundary layer velocity 

profile. These measured results are compared with the axial 

skin friction coefficients predicted by the empirical formula 

of Ludwieg and Tillmann [I], 

(2.4) -0.268 -0.678 H 

C =0.246Ree 10 

In figure 9. The shape parameter H and momentum thickness Re 

in the above equation were predicted with Head's method. A 

maximum deviation of 2 percent was observed between the c+ 

predicted by Ludwieg and Tillmann's formula and the q 

determined by Bradshawls method. Although Bradshawls method 

predicted c+ very well for the plain flow, it was not used in 

other flow configurations because it is based upon the 

previous knowledge of the logarithmic law ; the form of the 

logarithmic law for a LEBU manipulated boundary layer has not 

been established yet. 
27 

h 

E 

Q 

*O 

E 

3 

c 

a, 

c 

€ 

0 

2 

7 

6 

5 

4 

A 

6 ~0=0.7xlO /m 

Y 

8-0.006534 m - 

f 

0 0 

a a A 

a 

-0.24 -0.12 0.0 +o. 12 t0.24 

Distance from centerline,t (m) 

Figurs 13. Spanwise variation of momefitun thickness,g, 

3t two axi31 locations. 
2E 

The measured velocity profile for ths plain flaw 

configuration was compared to a theoretically pridicted 

profile using a modified Coles' boundary layer (Appendix 

._ __ __ - :2.2). The -velocity profile was calculat2d for sn axial 

location 2.5 m from the tpst section leading edsi. The free 

streas vslocity was set at 11.35 m/s to satisfy th2 unit 

Reynolds numb5r requirimsnt of 0.7~13 ;n and the rzsultins 

theoretical and expzrimental profiles are shown in figure 11. 

The maximum deviation between predicted and measured velocity 

valuss was 2 percent. 

6 -1 

- 

- - -- -~ -- Measurements of-the-fluctuating -axial velocity component 

were obtainid across ths turbulent boundsry layer at an axial 

lxation of 2.0 rn with a hot film probe. These data ari 

- - --plotted in figure 12 and compared with classics1 msasurenents 

of Klebanoff [l]. The trend of the data agrees fairly well 

although the magnitude of ths measured data is lower than 

Klebsnoff' s classic measurements. Such deviations should b? 

expzcted since Klebanoff's dats ara for a Reynolds number of 

lo7 whereas the measurements of figure 12 were obtainsd with 

a Reynolds number of 1.4~10~. A method to scale the measured 

data to correct for the diffsrence in Reynolds numbirs was 

not available. 

The boundary layer velocity profile for a LEBU 

configuration was predicted by superimposing the turbulent 

wake velocity distribution fr3m a thin plat? upon a plain 

flow profil?. The detailed calculation pracsdure is deszribid 
29 

0 

2 

w 

J 

IA 

- 

0 

a 

e 

b 

W 

1 

0 

0 

0 

a 

v) 

\ 

E 

n 

'0 

Q, 

v) 

-a . E 

v 

. 13- 

-* 

-a 

0 
33 

. ... 

0 

0 

W 

-_ 

.. . . 

0 

0 

D 

h 

c, 

.r( 

0 

0 

rl 

a 

> 

a 

t 

3 

hn 

[i 

d 
3: 

- in Appendix 2.3 and the predicted and measured profiles are 

shown in figure 13. Their agreement was found satisfactory and 

a 4 percent maximum difference was measured. 

The structure of the turbulent boundary layer was 

investigated by using flow visualization with the Smoke-Wire 

method of Raspet and Moore [25]. The smoke was produced by 

_. - - vaporizing -oil from a fine stainless steel wire by impulsive 

resistive heating. The smoke wire was mounted vertically in 

the test section with the tunnel operating at low speed. 

Large scale eddies shaping the boundary layer intermitancy 

region and typical eddies throughout the layer can be 

observed in figure 1. 

The mean free stream velocity was uniform in the 

spanwise direction within 0.2 percent [21] and momentum 

thickness across the test section span varied within 4 percent of the mean value. These small deviations combined with 

the satisfactory agreement found between predicted and 

measured flow characteristics allow the assumption of a two 

dimensional ergodic turbulent boundary layer with the large 

eddy break-up device removed. When the LEBU is installed the 

basic velocity profile downstream of the device is also as 

expected. The wake of the plate appears normal and the slight 

increase in the velocity profile, at approximately y=1.0 cm 

in figure 13, may be attributed to the viscous drag reduction 

capability of the LEBU which manifests itself as a reduction 

in momentum thickness. 
32 

0 

a, 

m 

\ 

E 

oE 

0 

t 

a 

c 

0 

ao 

a 
33 

3. RESULTS AND DISCUSSION 

The experiments with acoustic excitation of the LEBU 

were performed in order to: 

i. Determine if proper acoustic excitation can enhance 

the effectiveness of a boundary layer plate 

manipulator. 

-- ii.-- Investigate --the -properties -of the resulting flow - - _- - - - - - 

field downstream of. the LEBU. 

iii. Search for the optimum operating parameters of the 

experiment. 

iv. Examine the effectiveness of the acoustic excitation 

with different experimental conditions. 

3.1. BASIC RESULTS 

3.1.1. SKIN FRICTION DRAG REDUCTION 

The effect of the acoustic pulse upon the plain flow 

was first examined and the momentum thickness growth for the 

unexcited and the excited plain flows is compared on figure 

14. The acoustic input caused no significant alterations in 

the flow and the average value of 0 for the acoustically 

excited configuration was found to be higher than the 

unexcited configuration by only 0.5 percent. This slight 

increase inois due to an expected small increase in mixing 

near the acoustic source. Figure 14 shows that the acoustic 

input has no significant effect on the flow when the LEBU is 
0 

a 

a 

0- 

01 

04 

4 00 

a 

0 

E 

\ 

(D 

0 

Y -- bo 

-E 

00 

.- 

.. 

40 .. . 

4 

aa 

0 

am 

43 

0 
35 

not installed. 

When the thin plate was installed turbulent bounclsry 

layer velocity profiles were obtained at midspsn locations 

downstream of ths LEBU manipulator. The mornentum thickness,Q, 

was calculated as doscribid in section 2.3 and plotted versus 

downstream distanci,~, from th2 test surface leading edsi. 

Figurs 15 shows thz axial variation of for ths following 

con f i gur a t ion s : 

~~ 

- _- 

i. Plain flow with the upstream sensor installsd 

__ - .- . ii. The -LEBU configuration with the upstream ssns3r 

_I --insta-lled but not operating. - -- - - - - - - - -_ -- 

iii. The LEBU configuration acousticslly excittd. 

The monetltua thickness of the manipulated flow is 

- greater than th? plain flow case near the LEBU bec3usI of -- 

momentum loss imposid by the embedded thin plats. Ths 

mornentum thickness near the LEBU trailing edse ( 4 boundary 

layer thicknesses downstream) is within 5 percent of the 

sun of the mornentun thickness of the plain flow cas2 and thz 

momentum thicknesses of the laainar boundary layers that 

develop on the upper and lower surfaces of the plate. 

The acoustically excited case produces an even griater 

momentum loss at this location. If the acoustic input was 

merely tripping the laminar boundary layer, one might hope to 

repeat the above superposition using a calculation for 

turbulent boundary layers on ths LEBU plat3. Tht measured 

incrsas? in 8 with the acoustic input is, how?v?r, 
36 

08 

8 

a 

C 

a .- U-JO 

Q 0 

E 

0 

0. 

0 d 

w 

n 

E 

v 

x 

Q, 

o 

c 

a 

cn 

o 

a 

X 

c 

- 

c 

N 

- 

.- 

3 

N 
37 

approximately ten times the expocted increase that c3uld bs 

attributed to turbulent boundary layers. These results 

suggest that an additional mschanis-n may bo activi during thi 

- - __ . __ . . acoustic -excitation; a mechsnisa-which alters the trailins 

edso flow from the blade in a mannar other than merely 

tripping a laqinar layer to a turbulent boundary lsyer. 

Further downstream at x=2.6 m (158 from the LEBU) thi 

momentum thickness of the acousticslly excited configuration 

relaxes to that of the unexcited LEBU but grows at a slower 

-_ - - - rate. -The same trend is noted at x=3.8 rn where the momntuq 

z k h i c k n s s s = o f = t h e z a c o u s k i c s l ly,excitad.-f low becomes less than 

ths plain flow configuration. This a clear indication of 

roduced skin friction coefficient and net drag reduction. 

-- _I --- -I- -- 

---Ths-::-approximate _. :variation of tho skin friction - - - - - -_ - - - - - - -. - - - . - - - 

coefficient,cf with the axial distance from the test surface 

leading edgg is shown in figure 16. All messuren2nts were 

obtainid at the test surface mid spsn. This location was 

aligned with the upstream sensor and the acoustic wsvc port. 

The numerical values of the skin friction coefficient w2r2 

calculated according to the procedure described in section 

2.3. All least square curve fits had a correlation 

cogfficient above 0.99. Ths LEBU configuration and thi 

acoustically excitcd flow were campsrid to the plain flow 

(hot film sensor installed). According to the nunnericsl 

vslues of the skin friction cozfficient, acoustic excitatiDn 

can enhance thz LEBU's effect by reducing cf batwzen 
i -W 

0 

< 

J 

m 

- 

n 

x 

a 

II 

a 
approximately 7 and 13 percent with respect to the unsxcitsd 

LEBU configuration. Compsrison with the plsin flow sh3ws a 

reduction of the wall shsar stress bztvzen 9 and 15 percent. 

-- 3.1.2.Z3KIN-FRICTION DRAG REDUCTION MEZHANISY - - - - - - 

Space-tine cross' corrslation functions (CZF) wers 

obtained using the hot film eddy detector probe upstrean of 

the LEBU plate as a fixed rsference location and another 

proba at various downstrean locstions as indicated in fizure 

17. A dual channel anemometer was utilizsd and ths hot film 

---I- - -- pwha signals- >.were prac-zssed=.=xith 1 x- NICOLET 550B . FFF 

analyzer. Figure 13 shows peak vsluis of the space-time cross 

corrslation functions versus probi separstion distance 96, at 

- - - - - - - -- variaus boundary -1syer -heij3ht,c.-zF3r away from the LEBU, in 

the downstream diraction, the residual acoustic far field 

produces higher cross carrelation peaks when thi acaustic 

excitation is applied. When the moving probe is locatsd near 

the LEBU's leading edgi th2 excitstion causes significant 

increases in thi cross correlation functions becausz the 

probss are sxposed to both, the large scale eddiis and ths 

acoustic field. At the trsiling edge of the plate in the 

outer region of the boundary layer the flow without 

excitation maintains a maximum CCF approxinstely equal to 

that of the leading edge. The wakz of the LEBU in this cas? 

is clearly correlated to the incident flow. When ac3ustic 

excitstion is 3ppliEd ths downstresm flow is corrzlated tq 
3 

w 

J 

m 
4" 

0.4- 

- 

A 

0 

o Without excitation 

B With excitation 

0 

0 

0 

OO 

Y -=0.95 6 

/ LEBU location 

0.0 1 - 

0.4- 

0 

-6 

0.2- 

- 

C 

0 

Y -=0.80 8 

Y -=0.60 

cc 

t Probe segixation distance, - w 

Fi3uri 13. Maxianurn space-tine velocity cross carralstion 

in the! boundary layer. 
42 

the upstream point sigificantly less. The reduction is Tori 

obvious at the outer region of the boundary layer ( -==0.95 ) 

where the large eddios doninate. This indicates that acoustic 

- - .- __ . excitstion enhances the destruction of the largo eddios which 

are sensed at the upstream location. It is assuwd that the 

impinging sound -wave at the LEBU trailing eds? sh2ds 3 

Y 

6 

vorttx of opposing rotation to the oncoaing larsi eddizs 

resulting in enhanced large eddy cancellation. 

At downstream locations deeper inside the boundary 13yer 

(-&=3.80, -=0.60 th2 reduction of the CCF, when acoustics 

- - -==-arE applied, is -moderate. because -1ac.ge. eddiis appear mainly in 

the outer part of the boundary layer. Thi reduction of th2 

CCF when the moving probt is at the LEBU's heizht signifiss 

--- __ . . --that. -the acoustic pulses-assist- the manipulator in canceling 

large eddies. All time delay values associated with the cr3ss 

correlation function peaks correspond to expected large eddy 

convection times and not to the acoustic wave propagation 

time. 

8: __ -- 

-- - - - . - . - - . 

I 

- - - - - - - - 

The turbulence intensity of the low frequency part of 

the turbulence spectrum was exanined downstream of the plste 

manipulator. A hot film probe was positioned slighty above 

(1.5 mm) the LEBU's height and the turbulence spectrum from 0 

to 2,000 Hz was measured. Figure 19 compsres the variation of 

the root mean square (RMS) of the fluctustins axial v?locity 

component u' for the acoustic2lly excit3d flow to ths 

unexcited LEBU configuration at various downstream locations. 
43 

n 

c 

0 

a 

0 

x 

Ql 

r 

.- 

c 

CI .- 

.- c 

3 

Y 

CJf 

2 

a 

1 .o 

n 

C 

.- 0 

zo.9 

0 

x 

Ql 

c 

L 

0.9 

--& 

z =O.Om 

0 

0 

(0-2000) HZ -.-. +---e 

0 

(0-200) HZ 

Q 

A 

0 

I I 0 5 10 

Distance from LEBU trailing edge, (-) f 

s 

Fizuro 13. R213tlvP varlatlon of ths low frsquoqcy RYS 

turbulince clos2 to the LEBU trailing edj,e. 
44 

The turbulence level over 2 KHz is considerably reduced when 

acoustics are applied and the effect persists for a distance 

of 88 downstream of the LEBU. When the low frequency (0 to 

--- - -2OO---Hz) Tart --o-f the 'signal i-s examined the level of the 

turbulence intensity appears further reduced. This range of 

frequencies approximately corresponds to the lsrge eddy 

- - - - - - . . . passing frequency which is estimated to occur near 110 Hertz 

and dominate the low frequency spectrum. The relatively 

higher frequency (200 to 2,000 Hz) part of the turbulence 

spectrum remains largely unaffected by the acoustic pulses. 

This indicates that only the large wavelength motions of the 

turbulent boundary layer are affected when the flow is 

acoustically excited. The measurements of the RMS velocity 

fluctuation, as for the previous CCF data, were limited to a 

distance of about 108 downstream the LEBU. 

To better understand the influence of the acoustic 

- __. .~ 

_. 

excitation on the flow manipulator, a pulsed smoke wire was 

used to obtain flow visualization photographs. The smoke wire 

was mounted downstream of the manipulator at the midspan of 

the tunnel. The fine wires ran vertically from the wind 

tunnel floor through the boundary layer. Figure 20 shows 

typical results for the three cases of concern. The large 

eddy break-up device reduces the large scale structure in the 

boundary layer and acoustic excitation of the device causes 

further reduction in coherent motion. The results were 

obtained at approximately 356 downstream of the manipulator. 
.... .- 

- 

A 

Figur2 20. Boundary layzr flow visualization for tht 

(A) plain cas2 (8) LZBU nanipulattd 2nd (C) 

acgustically exeikd LEaU confiarqtinn - 

45 

C 

-Ap- -----*- 
46 

The sound waves at the LEBU trailing edgs appsrintly shsd 

vorticity which helps cancel the oncoming large eddies. 

Ths possibility of verticsl oscillation of ths thin 

ribbon when llhit" by acoustic wavzs was exanin2d. The gosl 

of this study is to control th2 lsrge eddy break-up process 

without moving th2 LEBU. Motion _of _the devica could senerats 

- more disturbances and altsr ths boundary layer on thi device, 

._ I - thus .-altsring - the -momentum thickness downstrism. A srnall 

accelerometer was mounted on the LEBU above the acDustic wsvs 

port. Virticsl displacement messursaents were obtainsd with 

no flow; the pressure pulsi devici -was oxcitad with a 

previously recorded anemometer signs1 from the turbulent 

boundary layer. Thi messmad v2rtics1 displaceaent whir. 

acoustics wer? applied could not be distinguishsd from the 

background electronic noise. The reduced corrslation of the 

flow across the LEBU and reduction of RMS velocity 

fluctuations with acoustics, can be only attributed to the 

interaction of th2 acoustic input and the fixed LEBU, not thi 

motion of the manipulator device. This is evident because ths 

acoustic pulsss had no effect upon th2 tha plain flow; als~ 

they cause no vertical motion of the plate at zero flow 

conditions. 

According to these results an acoustic puls? of the 

proper sound pressure level and phase locked to the convected 

large scals structures can enhsnce tho effactivsness of B 

plate manipulator. Large scale 2ddies contribute 
47 

spproximstzly 50 percent of the turbulent energy and 33 percent of the Reynolds strzss whin ths outer part of th2 

boundary layer is considered [9] . Turbulent llburstingll in the 

sublayer accounts for most of ths turbulence and Reynolds 

stress close to the wall [26,27]. If the passsge of the larsa 

eddies is related to the triggering of ltburstingll events in 

the sublayer, then their enhanczd destruction can lesd to 

further rsduction of skin friction drag downstream of ths 

LEBU. Energy exchangi between tk mean flow and turbulence is 

governed by tha -dynamics of- the large eddies [25] which 

---______ ---extra&- kinskic. eLar3-y fr.m &-.mean flow. The break-up of 

the ensrsy cascade from the very largi eddies to the snall 

energy dissipsting structures can lesd to reduced monentun 

__ ___ transfer--to- ths wall-2nd reduced skin friction drsg. 

3.2. SPREAaING EFFECT 

It is clear from figure 15 that increased dras reduction 

dui to acoustic excitation persists downstream for 9 

considerable distance. Measurenents of 0 across the span of 

the test section indicated that the beneficial effects of 

excitation spread slowly in th2 spanwise direction as the 

flow convected downstrean. 

3.2.1. SPAN’UIISE MAPPING DOWNSTREAM OF THE LEBU 

The spresding of the acoustic excitation effzct 

downstream of th? LEBU wss mappid indirsctly. It has bion 
48 

obsirved (section 3.1.2) that thi output signals of two hot 

film probes across the LEBU at aidspan of thi test surface 

are less correlatzd when acoustic excitation is applied. The 

cross C~rrelat~on-function-~eeF~ between the upstream fixid 

sensar and anothzr pasitioned at various spanwisi locations 

c c F(LA) 

ccqq 

downstrzam of ths blsde was maasured. Thi ratio rc= 

was calculated; LA siSnifi2s the acoustically excitid LERU 

configration and L signifies the LEBU configuration without 

excitation. Figure 21 shows a schematic top view of the test 

surface downstrean of the LEBU with expandid z coordinates. 

Ths solid symbols indicate points on thi test surface where 

the ratio rc is snallor than unity because thi acoustic waves 

enhsncs the largs eddy dzstruction. Ths open synnbols indicst? 

points where the ratio rc is greater than unity bocause the 

acoustic pulsis mak? the prabi signals more correlated. This2 

measursasnts could not be extanded further downstream bicause 

ths large eddies have a lisited life spsn and decay after 

travelin: a distancg of approxinately 108. A slight 

spreadins of the acoustic excitation effect at a half sngle 

of abaut 2 degrses can be sezn in figure 21. This sprsading 

is verified by spanwise measureaents of momentum thickness. 

l9(L A) 

0 =@(L) Figure 22 shows the variation of the ratio r 

with the spanwise distance,^, from the test surface 

centerline for various axial locations. The variation of 

momentum thickn?ss,@, (section 3.1.1) measured at the test 

surface centerline needs to be rsconsidersd. Accarding to 
0 Q 

1 7 - -.- -.- -.- .o -.-- 0 1 a 

n 

v) 

0 

v)l 

.- 

c, 

x=2.08 m 

0 

13.01 

0 

x=2.12 m 

8 I -m-.

4 x=2.16 m 0 

II 

L 0 

J 3.01 

x=2.20 m 1 

0 4 8 12 

Distance from centerline,z (mm) 

Fisurs 21. Spanvise mspping of thi peak cross c3rrzlatim dovnstr2a.a of the LEBU (solid synT1531s 

indic3ts liss than 1.0). 
5G 

A 

c 

3 

0 

C 

c 

I3 

Y 

3 

3 

.- .-I 

1.02{ :w , 

0, 

x=2.16 m 

I 

0.98 .’ --. 

1. - - 1 

# 

x=2.88 

0 _---- -- z 

-.-. -. a - 

m 

.- 

x=3.84 m 

0 e’ Q 

I 

1 I I 

0 2 4 6 8 

Distance from centeriine,z (cm) 

Figure 22. Spanwise variation of momentum thicknsss ,e, for the excited and unexcittd LEBU at 

three axial locations. 
51 

these data the ratio rQ is greater than unity at axis1 

locations close to the LEBU trailing edge. Further downstream 

at a distancs of 68to 88 from the LEBU trailing edge ths 

__ __ - ___ ---ra.tiDrr- becomes snall?r -than uni-ty,--Ema-ining as such for th2 

e 

rost of the test section. Returning to figure 22, at x=2.15 

m, the spanwisi measurenents of 8 indicata a nar'r:,w region 

whire r,is greater than unity. Further dawnstream, at axi31 

distances of 228 and 478 from the plate manipulator, the 

ratio t-3 was found to be small2r than unity over a brciader 

extent in the z diriction. These data show a tendency for the 

- drag-- reduction- phenomena to sprsad spsnwisi at a half angli 

of about 2 degrees. The exptriintnt was limited to a distanci 

of 50 boundsry layer thicknzsses from the LEBU bzcause most 

-- - of ths przvious investisations indicated that a manipulatsd 

turbulent boundary layer rslaxes to the undisturbed flow 

after 5a to 1308. Furthsrmore, the length of the test section 

did not allow good measurements beyond this point. Thi smll 

valuz of the spreading angle is attributed to the mixing 

proctss of the surrounding turbulent boundary layer. This 

angle also agrees with the results observed for the spsnwis? 

spre3ding of the reduction in the sp3ce-ti;nZ cross 

correlation near the LEBU. 

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

The turbulence lntensity,T, of the axial flow 

velocity component, with and without excitation was measursd 

throughout the boundary layer at three axial locations. 

Figure 23 shows the variation of ths psrameter I'T =- T(L A) , T(L) 
52 

. 

I 

z=-0.02 rn x=2.08 m 

0 0 

1 .oz 

1. 

0 

0 

-. rT= 1.008 0 

0 

I - 

00 -. rT=l .0Oln 

I 

A 

d 

~22.88 rn 

x=3.84 m 

D 

O 

- 0 - -.-. 

0 

D 

0 0 

I 1 I I 

0.0 0:2 014 0.6 0.8 1 .o 

Y Distance from wall (7) 

Figure 23. Relative turbulence intznsity of the excit2d 

boundary layer across the ttwedg2tt of acoustic influsncz. 
53 

whcre T=- virsus the boundary layer height $- at a 

spsnwis? location 2cn off the test surface centerline, 2=+2.0 

cm. 

k2 

u" 

--- - - At -_ x=Z.OS-m,- _outside of- thz narraw Itwedge" of acoustic 

influence, ths averagz valu? of the parsmater rT is 1.909. 

Acoustic waves in this case make the excitzd flow mors 

perturbid. At x=2.33 m, whore this point is starting to be 

affscted by th2 acmstic influenca, the averagi ratio is 

1.001. W2ll inside th2 cone of acoustic influence, at an 

axial distance of 478 from the LEBU, the averagl valu? of 

- .-. __ -.---- . - l-c sth2. parameter -rT. isszallsr7than unity;: It should be noticed 

. that the turbulence intensity level includes 311 frequencies, 

not just the lower fraquency range which is primarily 

influenced by ths- acoustic- input. Thz difforencas in 

turbulence intensity are saall whsn acoustics is appliid 

leading to a random oscillation of rT around unity. The 

reduction of turbulence intensity seens to exist howevzr, 

inside ths narrow llw~dgslt of acoustic influence. 

3.2.2. EXPLANATION OF THE SPREADING EFFECT 

A recently proposed model of turbulent boundary layer 

cohsrent motion [29] was examined and a qualitative 

explanation of ths spreading acoustic influence w3s based 

upon it. According to this model, large scale motions are 

initiated by the instability of th2 main flow and rotate in 

ths diriction of the mean flow shear. Thi sublsyer bursting 
54 

events arz caused by the interaction of the seni-periodic 

largi scale motions with the wall. Thz burst is bound by a 

pair of counter rotating vortices which are inclined forward 

--and---thi -resulting e jec-tion and -swig? 3re flows induced by 

thzse vortices. A schematic rspreszntation of th? sugg2st2d 

model is shown on fisure 243. 

-- Using rsfarence [33] applied to ths particular 

experiaental set-up, an .approximate skstch of thi resulting 

flow field fr3m a single prassure pulsi can be made 3s sh3wn 

in figure 24b. This schematic is 3 side v'iew of the flaw 

.- -.a . _e__ - -_ -- I AI.--- _' = Sieldz?tndqsed-=by an a_cou_st& --pulsG -Cmp-ingins upon thz LEBU 3s 

sxn frDm a downstream location. The acoustic pulse is 

spread through ths air with ths vortex ring moving awsy 

fmm the acoustic input port. Thi resulting jst flow has a 

spsnwisi velocity component w' which is als:, auzmentsd by th? 

stagnation of the pulsating air upon th? LEBU. The moving 

media causzs a divsrging motion of the generated vortices 

through thi downstream boundary layer. 

A top vigw of the flow across the flst plate manipulator 

is shown on figure 25. Upstream of the LEBU thz larg? scale 

structures appiar according to thi model at a randon r3t2 and 

spacing. Only thi eddies that are convected on tht centerlini 

are detected and canceled with acoustic waves. These acoustic 

waves partially stagnate upon the flst plate and induce a 

vortex "street" which is sproad into tho boundary layor 

downstream. These varticzs interact out of phsse with soms of 
55 

uo 

__3 -- a. 

c7:7\ 

- a’-pAIRED VORTICES 

BURST 

Y b. 

WALL 

, 

ACOUSTIC PORT :/ I 

I ,/ / 

Figur? 24. Model of (a) c3hirent structures and (b) 

acDustic puis? flow field. 
56 

i, +go 

00 

\ 

\ 

LARGE ED DIES^; - -- --PASSING DOWNS'TREAM / 

&ED VORTICES I 

r 

P 

t? 

\ 

__ 

P ', 

rt 

00 - '* 

\ 

4 

- - - -_ 

\ P R E S'S b&,P u L s E I '- 0 

LEBU 

Figre 25. Top view of sugpsted acaustic spreading 

mechanism. 
57 

the large eddies which wers not detectid by the hot filln 

probe but were partislly canceled by th2 nsnipulator. This 

cancellation proceeds downstream within a narrow angle 

- ____ --because the spanw-is? velocirty campnn2nt w' of th2 induced 

secondsry flow is assuaed far saaller thsn the axial vzlocity 

conponent u. Somo of these vortices eventually decay becausi 

of strong mixins in the turbulent boundary layer. It should 

be noted that the angle of acoustic influence was reduced at 

higher free stream vilacities which supports this proposed 

explanation of how the- spanwise spresding of the phznomenon 

msy occur. 

An slternativa explanstion can bi provided based upon 

the assumption that the large eddies and tho sublay3r 

- _. .- phenomena -of Vurstft and' 11sweep71 ar9 closely 'interrzlated and 

preserve each other. It is assumed that a burst of fluid is 

counteracted by large scala motion in order to proserve 

continuity at a point of the flow field. Also, ths convected 

larp eddies, being limited spanwiss, trigger bursting events 

at other nearby locstions in the z direstion. Thes? ivints 

account for most of the skin friction production. 

Consequently, the break-up of larso eddies will spresd 

spanwisi interruptins the chain of events th3t might link th? 

cohgrent motion to the sublayer bursting and sweeping of 

fluid. 
58 

3.3. OPTIMIZATION OF THE EXISTING CONFIGURATION 

Since acoustic excitation reduces the correlati3n 

betwsen two points across the LEBU, this was utilized to 

optimize the various parameters which control the function of 

-- the analog, timne delay processor. Thsse psraaeters are thi 

voltage reference,V,, the time delay,t, and the prsssurs 

level-of the acoustic pulss. 

The downstream hot film sensor was positioned 3t a 

distance of 7cm (1.76) from the LEBU trailing edgs, and at a 

-- -_-_ height of 3.4 cm above the wall on the centerline of the test 

surface. Ths upstream hot film sens3r was positioned at ths 

usual distance of 2.58 from the LEBU trailing edga. Thi 

- -_ - ratio rc=m)is plotted versus the rslative processar 

Vr 

Va 

riference voltage, - where Vr is th2 szt reference 

voltag,? and Va is the upstream anemoaetzr voltage output. 

Thi valuzs of r, ( opsn synbols) displayed in figure 25 

indicate a minimum at - vr -9.970. The turbulence intensity 

level at the upstream sensor's height was 2 to 3 per cent. 

Ths optirnu-n range of the reference volt3iqe is very narrow (IO 

millivolts) and it was repaatedly noticed during th2 

expzriments that Vrshould be set just below thl AC RNS level 

of the detector probe output, Va. 

va 

The closed symbols of figure 26 reprisant the avzraszd 

numb9r of processor puls2s per second for different valu2s 

of the ratio- Vr . Th2 average processor respons2 frsquency 

was dzt2rminsd by counting ths number of output pulses fraa 

Va 
59 

2-0.0 rn 

~=2.07 RI 

~~0.034 m 

U0=10.91 m 

Va=2.005 volts 

CCF(L5k0.205 

1.2 

1 .o 

0.8 

0.6 

OC 

AP 

1 

CF 

uises/sec ~ 

A / 

e3--RL I 

\I 

W J 

0.94 0.98 1.02 

Reference voltage, - Vr 

Va 

280 

200 

120 

40 

Figuri 25. Relstiv? p2ak correlation,r,, and nunb-lr Df 

acoustic v pulsos par secand , vscsus rzf2rlncz 

vol tag2 - . va 
60 

- -- -the processor over an intervsl of 203 sec. For ths local 

boundary layer thicknass of about 4 cm and free strzzin 

velocity of about 10.9 m/szc, a value of approxiinstsly Ilm3 

Hertz is predicted [3] for the large eddy psssing frequsncy. 

This frequoncy is very close to that m2asured whzn V, is set 

to its optimuin value. Thus optimizstion of Vr is again 

associstsd with the large scale structure in th3 boundsry 

layer. 

The acoustic sxcitsti3n remained effectivi whin thi 

- rzfereica voltagi was _set-he-low thi optiaun vslui. In this 

cas2 only very large eddizs w2re rzcognizsd and the nunbsr of 

acoustic pulses per second wss reduc5d. Whtn ths relstiv-? 

was set at 0.91 -ths-procassor was unsble to 

trigger the pulse mechanisn. On tno othir hsnd, the acoustic 

excitation becomes less effictive when the reference vol t332 

is increaszd above th2 optimun range. In this case thz 

acoustic excitation is triggered by additional sanall2c 

eddies. The number of acoustic pulsas per second was 

incrsased to almost double th2 pridicted numbir of lsrga 

eddies per szcond. Increased correlation messursd between ths 

two points acr3ss the LEBU is then causid by acDustic wavzs. 

The optimua valu2 of the reference voltage,V,, depends upon 

the anemometer voltase output, V,, which varies with thi 

tunnel free stream velocity. Conti?uous mgnit3ring and 

periodic adjustment W~S necossary to coapansate for 

temp2rsture varistions of ths flow. 

I 

Vr 

Va 

voltage - 
GI 

The processor time-delay, t, required to allow for 9 

detected large eddy to be convected to the LEBU trailing edge 

was also optimized based upon the reduction of piak 

correlation across the LEBU when acoustics is applizd. Oq 

CCF(~*) is plotted versus tha 

rc =- figure 27 the ratio 

- pracessor tims delay t. The downstream probi rernainsd at tha 

-sanle---position and the referenca voltas? was set to the - - ___ - - 

optimum value. According to the data, a ninimuin valu2 of the 

ratio rccan b2 distinguished corresponding to a tine delsy of 

10 mscc. For the psrticular--tunn=l .-velocity setting of 13.5 

m/ssc, the time delay, t=- w3s found to be 10 IIIS~C. This 

reinforces the concept of assistins thz large eddy 

cancellation process with an acoustic pulsi which arrivas 

simultsnemsly at the trailing edge of the plate manipulator. 

Finally, the time averaged sound pressure level of the 

acoustic w8ves impinging upon the thin plate was optimizzd 

using th2 same phinoanenon of minimized CCF when acoustic 

excitation is applied. Miasurernents of the time averazid 

pressure level of the acoustic wave were obtained at 

llsinulatedll experimsntal conditions. Ths acoustic puls? 

mechanisn was mounted upon a wooden baffle plate that hsd an 

acoustic port identical to that of the test section. Thz 

S 

0.93 U, ' 

pressure pulsz mechanisn was trigg2red by a prsrecorded 

output signal from the upstrsam ssnsgr at rial flow 

conditions. Sound pressure level measuremsnts wers obtainsrl 

at ths LEBUls height above the pr2ssure port in a hard wsll 
0 

rE 

\ 

0' 

0 I 

0 / 

/ 

/ 

/ /o 

/ 

/ 

0 

/ 

'0 

I 

0 6 I 

. . F 0 

n 

0 

NQ) 

F cn 

U 

c9 

0 

62 

Y 

m 

b, 

P 

(u 

04 

kE 

c 

OC 
room with no flow. The microphone was positioned at grazing 

incidence and the reference voltage,Vr , and time delay,t, 

were set at their optimum value. In this manner the sound 

pressure level at the LEBU was determined for various power 

amplifier settings. Measurements of the CCF were then taken 

inside the tunnel with real flow conditions. A hot film probe 

was positioned at midspan of the-test section at a distance 

of 1.78 from the LEBU trailing edge and at a height of 0.828 

from the wall. CCF measurements were obtained comparing the 

- --- --.---LEBU -and the acoustically excited flow configurations for 

different settings of the acoustic wave pressure level. The 

ratio rc= a) ccF(L) versus the measured narrow band SPL at tho 

LEBU's height is plotted on figure 28. Once more a minimum 

value can be observed, which indicates that an acoustic pulse 

with a SPL of about 102 decibels is most effective for 

canceling the large eddies. 

The cross correlation across the LEBU remained reduced 

for a range of 2 dB around the optimum value but for values 

of the sound pressure level above 105 dB the acoustic wave 

field increases the correlation across the plate. The value 

of the sound pressure level required for optimum large eddy 

manipulation is of the same order of magnitude as the 

predicted and previously applied pressure pulse of 100 dB. In 

the beginning of the study it was assumed that a pressure 

pulse of the same order of magnitude as the pressure 

perturbations at the near wake of the thin plate (Appendix 1) 
G4 

0 

0 

t 

E 

c\ 

E 

00 

ON 

II II 

NX 

. 1: 

I 

I 

P 

I 

I 

I 

I 

I 

dl 

I I I I 

0 co 

1 0 

I 

. 
E5 

might benefit the large eddy break-up process. 

Ths obsirved phenomenon of reduced correlation at two 

points across the LEBU device when the flaw is acoustically 

excited can be utilized to optimize the operating psranoters 

of the acoustic input. Thg cancellation of the large eddies 

is maximized when the refsrence voltage is set to produc2 

approximately the same nunber of acoustic pulses per unit 

time approximatoly as the number of predicted larg? eddies 

per unit time. The flow is least correlated ( enhanc2rl large 

eddy cancellstion).when the time delay is set equal ta the 

large eddy convection tinno from the detector probe to the 

LEaV trsilins edze. Tho initial approximation of the pressure 

perturbation required to influence the flow downstream of the 

LEBU was found close enough to the optimum value for enhanced 

large eddy cancellation (it deviated by 2 dB). Thi optimun 

vslues of the expirinental parameters were very close to 

th~se initially projected with the concipt of acoustic 

excitation of a boundary layer plats manipulator. Thus, for 

furthsr verification, boundary layer velocity profilzs wers 

measured downstream of ths LEBU when the processor opersting 

paraseters were set at their optimurn valu2s. 

3.4. MEASUREMENTS WITH AN OPTIMIZED CONFIGURATION 

The operating parameters of the processor and power 

amplifier were set to the priviously established optimun. 

Detailed boundary layer velocity profilis wer? obtainsd 
66 

downstr3am of the plate manipulator along the midspan of the 

test surface. Thi momentua thickness was calculated and 

platted in figure 29 as a function of downstream axis1 

distance x. Ths three configurations compared were 

i. The plain flow 

ii. The acaustically ixcited LEBU, and 

- ~__ - iii. Ths optimally excited LEBU. 

Thi axial variation of moinentum thickness exhibited a 

trend similar to tht initial configurations. The moneatua 

- - .- _- thicknsss ---_close __ -tT thq- LEBU trailing edge for ths 

., 

optimally excitid flow w3s again slightly highor than tht 

plain flow's but lower than the sinply excited confisuration. 

The slope of -the curve is als3srnallerI and ths rasultinz 

momentua thickness2s downstream are less with optimum 

acoustic excitation. 

Ths valuis of 8 were least square curve fitted to a 

power law of the form 8=ax and the skin friction 

coefficient was estimated using cf =2abx . Numerical vslu2s 

of the coefficients a and b for various flow configurations 

ars shown in tabli 2. According to these values of thi skin 

friction coefficient, optimized acoustic excitation can 

enhanci the LEBU's eff~ct by reducing cfbetwezn 2 and 0 psrcent with respect to the initially excited configuration and 

by 10 to 17.3 percent when coapsred to th? plsin fl3w 

configuration. Th? improvement of about 2 pPrcent 

additional cf raduction ov2r the unoptimizsd csss w3s 

b- 1 
67 

OQ m 

e8 

am 

am 

0 

<D 

0 

x -- E 

ea 

a8 

-* 

t 4 

0 

4. 

I 0 Q 8 Q DO 
68 

moderate. -This is becausi the operating parameters of the 

initial cmfiguration were s2t close ta optimum and becausi 

the least square curve fitting procedure is itself an 

averaging process. 

Thore may be some expsrimental error in the messuremsnt 

of 8 when the absolute numbirs of fi3ures 29, 14 and 15 ars 

- .. examined. -It - must -be noticed- that alwsys during thi data 

acquisition every point of the velocity profile was measured 

with and without acoustics. All ths data indicate that 

-_ excitation - ricluces . drag and optimized -excitation irnprovss 

--* .T-.Ir 5 ~--~sli.gh-Uy- Aha2 eff2cti-vone-ss Gf,Lthe -pulse.--r Some of ths dsta 

could be coinbined to show results supPrior to those given in 

figure 29, but thi data shown are typical. 
69 

- --Table 2a. Curve fitting parameters for th2 acousticslly 

optimized LEBU f5 confizuration. 

I Configuration a b r2 

- 

- -0.002442 ----o.a5175 0.993 -. 

- --plain 

LEBU #j 

(excitsd) 

0.00291 2 0- 71 7327 0.992 

LSBU #5 0.002775 0.731 5 5 5 0.995 (optimum acoustic 

excitation ) 

Table 2b. Axial variation of the skin friction 

coefficient, cf, for ths optimized 

configuration. 

-2.0 0.093754 0.003425'- . 3.087 0.003373 0.101 

2.5 0.093532 0.303213 3.115 0.0331 77 0.125 

3.5 3.003455 3.002917 0.155 O.OO2932 0.163 

-. 

- -3i-O- 0.033535 0.003349 -- 0.137 0.003025 0.143 - ---_ 

4.0 0.033337 O.OO23O8 0.171 0.002330 0.173 

2L signifies the plain flow configuration 

Table 2c. Axial variation of thi total drag coefficisnt, 

c,. , for th? optirnizsd configuration. 

2 0 0 004437 0 004738 -0.035 0.00461 9 -0.045 

2.5 3.004254 0.004495 -0.054 0.004342 -0.013 

3.0 0.004153 0.004269 -0.029 9.094134 0.004 

3.5 0.094055 0.004387 -0.008 0.003957 0.022 

4.0 0.003977 9.003935 0.010 0.003827 0.037 
70 

3.5. NET DRAG REDUCTION 

The moinontum thickness,@, at an axial distance x from 

the-test surface leading edp -can be use3 to calculate the 

total skin friction drag coefficient,^^, at this point [2]. A 

momentum balance is applied considscing 8 control volurnc 

bounded by ths test surface and th2 undisturbzd flow, and 

- - 

extending downstreain from the test surface leading edg? to an 

axial location x. Then the total drag coefficient is giv?n 

by: 

-- , 

-- Ti-p-re -29 fs-reconsid9red 'here 'obszrving that the -. - -._ -- 

momentum thickness carrespondins to an acDusticslly excited 

flow is lower than- for the other configurations. According to 

equation 3.1 and the data listed in table 2, a 4 per cent 

net drag reduction, with respect to the plain flow, can be 

obtainid at a distance of 508 downstriam of the LEBU 

manipulator. The acoustic powsr input to the devicis was not 

taken into sccount. 

The actus1 results of optimization are, hDwevsr, more 

benaficial than thoscl rPvoaled by table 2. Comp3rinz figure 

15, which is the unoptimized L5 css2 with figure 29, which is 

the optimized L5 case, two important differences can b2 

noted. First, the momentum thickness near thi trailing edsz 

of th? blade is larger with excitati3n in both cases, but thz 

optimized cas? shDws 0 only slightly high3r with excitatioq. 
71 

I 

I initial drag into the systsm when properly optimized. 

I Secondly, for the optimized case, net dras reduction occurs 

The more effective large eddy cancellation imparts less 

I 

I 

I 

- .. - earlier- than - the unoptimized-case and-over a significsntly 

larger area. In the non optimized case of figure 15, nit drsz 

reduction is observed starting at approxinstely x=3.5 m. For 

the ssne flow and same configuration but with carsfully 

optimized acoustic input, the ragion where net drag rsduztion 

begins has moved upstream to approximately x=2.8 m (fisure 

- . _- 29). Measurements- in- the downstrean dirsction beyond ths 

-i- L-raptgg ;9f-6azwe ra:. i;nl ted-+y-th=:avaf la-Me 12 ngt h of the w in3 - 4- ,- 

- 

---- __ _._-r.-- - ---L ___v~,,tunnel tsst section. 

3.6. SKIN FRICTION MEASUREYENTS_-OF VARIOUS LEBU 

CONFIGURATIONS 

Prior to the experimental sst-up L5 (LEBU #5) various 

large eddy break-up dgvices wera studied in a mre 

prslisinary manner to establish the effectiveness of a sing12 

plate and, the effect of an acoustic pulse upon the flow 

downstrean of a large eddy manipulator. It is appropriate 

that same of this preliminsry data should be przsented here. 

3.6.1. PRELIMINARY LARGE EDDY BREAK-UP DEVICES 

All the boundary layer manipulators were mounted at a 

distance of 2.0m from the test section leading edge. The wind 

tunnel velocity was set for a unit Reynolds number of 
72 

703,000 m-' and the pressure grsdient throughout the flaw 

was zero. Thz height of the boundary layer at thi LESU 

location was approxinately 4 cm above the test surface. No 

- -:upstr.eam hot_ film sens3r was install2d- and no acoustic 

excitation was applied. Thi geometry of this? manipulators is 

given in table 3. 

Tablt 3. ';eometry of preliminary single LEB'J'S 

configuration height abova chord thic knz ss 

floor [6] length [s] [61 

Boundary layer velocity prafiles were measured 

downstream of the various LEBU platss along the centerlinz of 

the test surface. Th? messurements sxtended a distance of 63 

boundary layer thicknesses fram the LEBU, with a spacing for 

each axis1 station of 68 Thi valuss of thi mone2tun 

thickness,e, 

manipulators are shown in fisure 33. 

for th2 plain flow cas2 and ths various plate 

Ths valuss of 8 for all the axial stations wore least 

square curve fitted in a power law of the form B=ax and 

the local skin friction coefficient was estimated following 

the method of section 2.3. Table 4 contains thi nunerizal 

valuis of the curve fitting parameters s,b and r2 for tha 
73 

0 40 

a0 

C .- 

a 

e 

- 

3 

W 

J 

m 

3 

W 

J 

m 

3 

W 

J 

m 

o.og 

..- 

E 

\ 

(b 

x 

'b 0 

00 

II II 

0 go 

a3 F: 

n 

E 

Y 

X 

a, 

0 

C 

a 

cn 

'D 

a 

X 

- 

c 

.- 

- 

.- 

a 

0 

m0 

3 

m 

E> 
74 

skin friction dras reduction over a distance of 528 froa 

the LEBrJ. 

Table 4. Curve fitting parameters for various flow confipuratims (- was -msasured to a distanco of 

523 from LEBTJ). 

cmf iguration a b 

percent drag 

reduction 2 

r 

at 526‘ 

----- PLAIN FL3W 0 . 032555 0.715333 9.934 

LZBU ryl 0.033OO5 0.5595 9.991 -3.0 

__ -;LEBU 42 - - 0.033134 - - 0.52774 3.953 2.7 

Acc3rdigS to the d3t3 list3d the achieved dra5 reduction 

was negativa or moderste . These -neasureaents were preliminary 

and mostly used to devslop th2 experiwntal set-up 3nd the 

data acquisition procedure. The configuration LEBU #3 was 

considered as reasonably effective dsvice and it was dGcids5 

to proceed with the acoustic excitation after achizving sc)me 

moderate SUCC~SS with boundary layer manipulation. 

3.6.3,. PRELIMINARY AZ3USTIC EXCITATION 

The acoustically excited thin plate configurati9n w3s 

designsted as LEBU f4. The large eddy detector probe was 

installed upstream of the LFUBU at 3 distance of 2.48 from 

its trailins 2dge snd at a height of 0.9Sabove tho wall. Th2 

timo delay of the processor was sit at 9.5 mszc and the 
-5 

prsssurs live1 of the acoustic wave at tho LEBU's hzight wss 

100 dB. Thi giometry of LEB'J #4 (chord,height,thickfiess) wit-? 

identical to LEBU f3 as w3s the location of device and th? 

wind tunnel operating unit Reynolds numb2r. 

Boundary layer velosity profiles for ths following 

configurations were measured downstrsam of thi LEBU 3t 

- midspan a x i a l - l o c a t i o n s over- a- downstresm distance of 538. 

i. Plain flow (hot fila sens3r was installed) 

ii. LEB'J 54 (h3t film sensor instsllid but not 

--__ -- - ,_ - - opi rat ing) 

~ . I'ii.--LEBU #3 3kousticslly exzito3.- 

- .- - --- .. . 

- ==: :The cal-,ufatsd-valuss of: mmrontun-.thicknsss art plotttd on 

figura 31. Mo major changzs Setsreen the configurations can bs 

obsirved in the rate of mDmentum thickness growth and thP 

local skin friction drag reduction was moderate. Tht vsluis 

of e wer2 fitted to the powir law and tho locsl skin 

friction coefficient was calculated according to the method 

of section 2.3. The curvo fitting parameters and the achisvsd 

drag rtduction ar3 shown on table 5. 
n 

E 

€ 

z 

0 

a 

-- 

7 

6 

5 

o Plain flow 

0 LEBU #4 

LEBU #4 

acoustically 

excited 

E 

0 

I 

0 

R 

O 

f 

0 

4 

0 

0 

0 

8 0' . 

6 -- u0-0.7x10 Y /m 

z=O.O m 

6 

2.5 3 lo 315 410 

Axial distance,x (m) 

Figurs 31. Y3,asqtuq thicknsss,Q, versus axis1 dlstancz, 

x, for praliminsry acoustic excitation. 
77 

Table 5. Curve fitting parameter and per cent dras 

riduction for LEBU #4 configuratioq. 

Conf igura t ion a b r percent _._ draz rsduction - 

plain flow 0.33245 0.34~ 0.992 -------- 

LEBU 64 0.002576 0.51 353 0.993 -1.7 to 9.5 

- LEBU 64 0.032599 0.834223 -0.995 0.3 to 2.2 

(acoust. excited) -~ ___. 

Na3 net drag riduction was achievzd and it was decidid, bas23 

-* - -* -1_.-~zr=npon flow yisualLzation,-t3 raise theLEBU to 0.8 . in order 

- .- .. -tcr be-tter in'ter-cKpt =thz -FncFd?nt._largz eddies. This 

-- - conf-iguration was -LEBU #5 whfch-is -ext&nsiveTy doszribid in 

-- ------ 

the prsvious sections. 

Those proliminary data with little success 3ro the 

result of much time and effort to obtain drag reduction with 

acoustic excitstion. This method is not woll understood and 

requires 9 considerable effort to find a configuration which 

works woll. Because of inconsistencies with these early 

efforts, it was dicided that another independent 

configuration must be tested to provid? additional 

verification of the phenomenon. 
7€ 

3.7. ACOUSTIC EXCITATION AT UNIT iiEYNOLDS NUYBER OF 

1 O6n” 

To further verify the generality of the 3.arse eddy 

cancellation process the wind tunnel vilozity was set at a 

unit Reynolds numbir of 10 m 

6 -1 and LEBU Y5 was replaced with 

a different manipulator. LEBU RS was installed and tested in 

- orde-r to exaaine-tht effectivzness of the acoustic excitation 

at a higher speed. Thi detailed description of configuration 

LEBU #5 is givon in table 6 and compared with tho successful 

._ - optimiztd LEBU #5. 

_- - . 

m- 
Table 5: Experimental parameters for optirnizcd LE33 tS -. - -and LEBU #6 configurations. 

EXPERIMENTAL PARAMETER __ 

Unit Reynolds nurnbir 

79 

LEBU 65 LEBU 45 __ 6 -1 3.7~10 m 1 o6 m-' 

Typical man flow velocity 11 m/s 15.5 m!s 

Boundary layer sandpaper trip length 

Boundsry layer trip locatlon - 

LEBU trailing edgs location 

LEBU material 

__ Boundary layer thickness at 

LEBU location 

Acaustic input hole diarneter 

(hole location at LEBU's trailing 

edge,midspan) 

Upstream eddy detector distance from 

LEBU's trailing edge 

Time delay between largo eddy 

detection and acoustic pulse 

Upstream eddy detector height 

Momentum thickness Reynolds number 

at LEBU location 

Expected largs eddy 

passing frequency, Hz 

Predicted pressure perturbation at 

LEBU's near wake 

SPL of acoustic pulsz at LEBU's 

hoight (2 dB higher than predicted 

pressure perturbation). 

21 cm 31 c;11 

- 3-€0 24 em 3 tcl 34 ca 

2. m 2. m 

steel steel 

. . -0*-936 - 3.348 - - 

-. :0:00.50& 0.03548 

-4.1 cm -3.7 cm 

3/3 inches 3/9 inzhis 

2.458 2-58 

10.5 asec 5.5 IIIs3.c 

0.858 0.956 

3,130 3 9 730 

110 165 

100 dB 134 d3 

102 dB 105 d3 
Turbulo2t boundary layer velocity profiles were messurtd 

at midspan locations downstream of the LEBU manipulator as 

ususl. The momentum thickness,@, W~S calculated as describ2d 

- in sestion 2.3 and plotted versus downstriaa distance,^, from 

the test surface lesding edge. Figure 32 shows the axis1 

variation of 8 for the usual three configurations. 

Ths moae3tun thickness of the manipulated flow is 

greater than the plain flow case because of morninturn loss 

fmposzd -br thi- emb2dded thin plat%. -The -acousticslly excitzd ._ 

- . - 

-diir== r.-i -ease-produce =,1 ow2 r- . rnam-s n tu lossTat-this locat 

- - .- 

-‘ indicstesTthat the - acoustic-pulse -does-not subtract kin2tic -- 

energy from ths flow and it improves the efficiensy of the 

LEBU configuration in the wake region. From figure 32 it can 

be observed that the momentum thickness of the acoustically 

excitid configuration again grows at a slower rate coapsred 

to ths simply manipulated boundary layer. Further downstream 

at x=3.75 m (478 from the LEBU) the momentum thickness of 

the acoustically excited configuration fslls below that for 

thi other configuratigns indicating net drag riduction. 

The vsristion of the skin friction coefficient,^^, with 

ths axial distance from the test surface leading edge is 

shown in figure 33. All measurements were obtained at th2 

test surface mid span aligned with the upstream sinsor and 

the acoustic wave port. The numeric31 values of the skin 

friction coefficient were calculated sccordins to thi 
81 

.. 

_. E __ 

0 

C 

-t .d 

(Uk 

5r 

0 

a 

0 

4J t, 

lul f E>€ 

0 

Q. 

w ox 

.I aa . 

(\I 

M 

b, 

0 a 8 L 

3 

en 

I I A (D v) a0 
a2 

- a 

X 
83 

procedure described in section 2.3. All least square curv? 

fits again had a corrilstion coefficient abovs 0.99. Thi L39U 

configuration and the acoustically excited flow wore cornpsred 

___ .. ._ to- the. plain.flow..( hot film ssnsor instsllod ). According to 

the numerical values of the skin friction coefficient, 

acoustic excitation can enhance thi LGBU’s effect by reducing 

- cf between 3.9 snd 6.0 percsnt with-respect to the LTBU 

configuration. Comparison to the plain flow shows a reduction 

of the wall shear stress between 6.5 and 13 per cent. In 

--=:a d d i t i on a 2;parcent net dfag-reduction=was measured - et a 

-x:di s t a ac~x f - 54 6 from the LEBU.--- ---- r .- - 3- - _LI - - .- - 

.. - . -- “..- - - _4i~houghilthe:da~a_afe_not-as- impressivs as the pr2vious .- voptimizod configuration, they do suggest that the mechanisn 

of enhanc3-d large eddy canczllation is real. Anders [13], has -- 

shown that variations of the manipulator microsoonetry 

exercises a strong influonce upon the results so absolute 

numbers are not extremely meaningful. The trsnds of the data 

are, however, consistent with previous findings. 

Space-tino cross corrilation functions (CCF) were 

obtained using the hot film eddy detector probe upstrzsn of 

the LEBU plate as a fixid referent? location and another 

probP at a distance of 4.08 boundary layer thicknassas 

downstrzam (figure 17). The height of the downstream sinsor 

was 0.98. Figure 34 shows representativz space-time cross 

correlation functions for the plato manipulated snd ths 

acoustically excited boundary layers. When acoustic 
0, , 0 

E - .L 

i. 

i 

(3 

c 

I/ 6 

ei 

0 

a 

L. 

E 

6 

al t I L 

I I 

L 

03 

E I 3 I 0 

P 

0 

.d 

c1 

a 

d 

aJ 

L 

L 

0 

0 

m 
ORIGINAL PAGE rs 

OF POOR QUALITY; 

85 

- excitation is applied the downstream flow is again correlate3 

to thi upstresm point significantly loss. The peaks of tho 

CCF correspond to eddy convostion time from the upstrean to 

the downstraam sensor. This indicates that acoustic 

excitation enhances the dsstruction of the large eddies which 

3r3 ssnsed 3t the upstrzsa locstion. These messurenents ar? 

in sood agreement -with -sirnifsr -results of configur3tion LZBU 

#5. In addition measurenents of the low frgquoncy turbulence 

spectrum, downstrean of thi plate manipulator showed that 

with the spanwise distance from the test surface 

center line,^, at a distanc9 of x=1.76m from the LEBU. 

According to previous measurements of momentun thicknoss, 8, 

(figure 31) th2 ratio re was found ssallir than unity at this 

axial ststio~. In this location it was found that th? 

acoustic excitation persisted with s tendency to spread 

spanwisi at a half angle of about 1.2 desrees. Thz redustion 

of the angle of acoustic influence whon comparsd to LEBU 55 

is attributed to the increased mixing process of the 

turbulent boundary layer due to highzr free stream velDcities 

in which LEBU ,4(5 was tested. 

Prop2r acoustic oxcitstioa of a thin flat plat? 

operating in 3 higher unit Reynolds numb?r flow was assin 

found effectivi in enhsncing the lsrg2 eddy break-up procsss. 
1.01 

0.99 

0 

? 

ORIGINAL PAGE 18 

OF POOR QUALITY 

6 &=IO Y /m 

&6 

x-3.76 m 

. _. ._. -. . .' . , . _~_ ., .. ._ 0 

0 .. 

.. 

4 8 

Distance from centerline ,z(cm) 

Figure 35. Spanwise variation of momentum thickness ,8, 

for t;fe_yxcit2d and unexcited LEBU et unit 

Re=lO m . 
The processor operating parameters were set according to 

hisher free stream velocities. Ths achievid skin friction 

drag reduction, reduction of flow correlation across the 

LEBU, reduction of the low friquency turbuleice and th? 

moderate net drag reduction wers consistent -with th? results 

obtained from LEBU1YS. This reinforces tho initial concegt 

- - - that proper acoustic excitation of a plate boundary lsyer - -___ 

manipulator can lead to enhanced larg? eddy destruction. 

. - . . . . . . . . . .. . . . . . -. 
ORIGlNAE PAGE IS 

OF POOR 9um 88 

4. CONCLUSIONS AND RECOMMENDATIONS 

4.1. CONCLUDING REMARKS 

Large eddy structures in-a turbuler,t boundary layer can 

be effectively manipulated by acoustic waves resulting in a 

net reduction in skin friction drag downstream of a 

I L L-- -manipulating plate._ The- vortex . unwinding at the LEEU's 

trailing edge when the blade encounters a large .eddy is 

assisted by acoustic waves. These acoustic pulses must be 

-- pressure level: in -?order -to- be -effective. The coherent 

-:structure --was .:assumed:to be -relatedrtorthe Reynolds stress 

produc€ion and the sublayer bursting -events. Thus, The 

additional elimination of the large scale structure caused by 

the acoustic waves improved the effectiveness of a single 

plate manipulator. Skin friction drag reduction was achieved 

for two different low Reynolds number LEBU configurations. 

The skin friction coefficient cf was reduced as much as 18 

percent at a distance of 508 from the LEBU when the 

acoustically excited plate configuration is compared to the 

plain flow. In addition, a moderate net drag reduction was 

achieved at about the same distance from the manipulator. 

__ I 

_- 

The application of the proper acoustic input made the 

flow less correlated across the LEBU, and reduced the level 

of the low frequency part of the turbulence spectrum of the 
ORIGINAL PAGE W - OF - - 89 POOR gVm - 

-_ 

- manipulated boundary lsyer. In addition, flow visualization -- 

of the acoustically excitPd boundary layir showed the further 

reduction in cohirent motion. Thi initial hypothesis, thst a 

- .- - phase~1Q~ed--acousticnput to th? flow can reduce tho 

turbulence mixing and tha wall skin friction was verified. 

The effects of the acoustic excitation spread slowly in 

. .- ---.__-- L-- -:ths- spsnwisz-dirsction as the floKconv=&d downstream. This . 

was verified by carefully measuring the momentum thickness,e, 

in thi spanwise diraction downstrean of ths manipulator. Ths 

1- 

-_ -effect :spresds-at-s -half angle -of -2-degrees for the most 

- __ effectivi configuration. Th? -spriadins angle was reduce? ss 

-. 

-- Re -and turbulent mixing increased. It was assumed that 

secondsry flow vortices induced by th? acoustic pulsi are 

convected into the turbulent boundary layer and cancel some 

of th2 "weakened" large eddies passing the plate manipulator. 

An altsrnative explanation for the spreading process can be 

based upon thz assumption that the large scale structure and 

the sublayer bursting phenomana are intirrelated and pres2rve 

esch other. The passing of a largs eddy causis sidswsys 

eruptions of fluid. These bursting and swesping motions cause 

the generstion of the larga scale structure. The interruption 

of this chain of events by eliminating the l3rg0 eddies at a 

spanwise position would yield has a spreading effect upon th? 

reduction of bursting events and further generation of large 
scalos. 

90 

Ths operating psrameters of ths processor devici which 

controls the acoustic input could be set to an optimum in 

__ __ . . ordgr-to-accsuot for thzlarge- eddy -_ convestion velocity, 

their particular frequency of appearance and the level of 

thi velocity fluctuation they reprtsent. Th2 optimization of 

--_. - thi processor operating psrarnetsr was based upon the obs3rvs3 

phenomenon of riduced correlation across the LESU when 

acoustics is appliod. For msximum large eddy canc2llation 

= L~ stha k: r2e-ferg n c B yo 1 tag9 $mu& &e: r s.rtt: =_tas Ipr od uco a pprp x im s t e 1 y 

ses-w-r unit time - - 

numb3c -of predicted .1 -p?cxun3t titno. The process . . 

._ 

----- 1 -I -. - .--of---reduced correlation is -very much,dspendent upon th? 

- setting of the refersnce voltas? snd must be set within 13 

millivolts froin the optimum value for best results. The flow 

is least correlated when ths tine delay is set equal to the 

largo eddy convection time from the detector probe to the 

LEBU trailing edg2. Also, the initial spproximstion of th2 

pressure perturbation required to influence thi flow 

downstresm of the LEBU was found closi enough to the optimun 

value to achieve enhanced larse eddy cancsllation. The 

optimun vsluis of the exp2rimental psrsmeters were very close 

to those initially projected. These results verify the 

concept of increased drag reduction by acoustic excitation of 

a boundsry layer plate msnipulator. 

- -. 
I 

-_ 

4.2. RECOMMZNDATI3NS F3R FURTHER INVESTISATI3N . -- 

Acoustic excitation was proven effective in improving 

the plate manipulator effect upon a turbulent boundary layer. 

The basic concept of the larg? eddy cancellation by acoustic 

wavis should be studied in the cas2 sf a manipulator plate in 

inviscid flow. A LEBU devics should be positioned in 

-- - -- undisturbed flow so that it may encounter vortices 

artificially generated upstream. Acoustic pulses must be made 

to arriva at the blade trailing edge together with these _- -- 

-- ___-- - 

- -,_ -- 

__ :resulting- 

- - the basic mechanisa-developed in this study. 

-- I_ 

- 

Further measurements, _beyond the-range of 53& are 

recommended in order to establish the extent of the 

persistence of the acoustic effect downstream of the LEBU. 

Extensivi measurements of the axial and longitundinsl 

velocity fluctuating components ut and v' should be taken to 

determine changis in the turbulence en2rgy production. The 

production of skin friction drag is closely related to the 

Reynolds stress component -pu' v'; this quantity should be 

also examined comparing an acoustically excit2d LEBU 

configuration to single and tsndem plate manipulated 

turbulent boundary layers. 

Further investigstion of the spreading tindancy of th? 

acoustic effect upon the flow regime downstream of the LEBU 

should be pursusd. Two hot film llscout" probes can b3 
. , 

92 

'ORIGINAL PAGE IS 

OF POOR QUALITY 

installod upstream of the plate and thi acoustic pulszs can 

bs input from tyo different ports, located relatively close 

to each- other. Boundary layer traverses will show if both 

zones of acoustic influence merger downstream of the LEBU. 

A LEBU with two plates in tandea-zxposed .to acoustic 

- 

I2 3 wavesLmay b? also examined-because this configuration has 

been found most promising without excitation. The boundary 

layer upon a LEBU plate is laminar. Possible separation of 

-by rough$ning its- surface. -Such a 4,EBUzonfiguration is aiso I - __ _ _. - -worth studying when exposed to acoustic puls?s. 

wer2 carried out at a slightly higher speed than the present 

investigation. An experimental setting at higher velocities 

will require an acoustic pulse of higher frequency and sound 

pressure lsvel. Improvemznts and redesign of the prtssure 

pulse mechanism must be undertaken. Such a configuration, 

closer to real flow conditions, in conjunction with a 

variable pressure gradient and airfoil type.LEBUs should alsa 

be studied. 
93 

1. White, F.M., Viscous Fluid Flow, pp. 425-432, ?p. 

519, PP. 448, PP- 593, PP* 490, PP. 4379 PP. 513 

McSraw-Hiil Book Coapany, 1974. 

2. Schlightins ,!-I., Boundary Layer Theory, 7th 

edition, pp. 373-332, pp. 175-179, pp. 733-733, 

McSraw-Hill Book Company, New York 1979. 

3. i-Iefnzr,J.N. and Bushnell, D.M. "An Ovsrview of - -Concepts--FocrA~rcraft -Drag -R=dustion,tt ASAW-3-654, -. 4 2 ____.I 

pp. 1.1-1.30,1977. 

4. F3lcD,R.E.,I*Cohersnt Motions in thz Outer Ragion of 

Turbulent Boundary Layer ," Thi Physics of Fluids, 

132. - 

- __ I Vol. 20, No. 10, Pt 11, Octobir 1377, pp. S 124-S 

-! ?e. -_ *- - -- - - - . - - - - - - - - __ . - - - -. ~ ." Falco;':R;.E;pN The:Prodnc*tibn af Turbulence Neaf:a- - __ - __ ,----- __ :WaLl,-tt -AIAA pap2r 1999-1355. 

5. - ._ Kline,S.-J., -- Reynolds; W.C., Schrsub ,!?.A*, -- -Runstadler, P.N., nThe 'Structure of Turbulent -- - - - __ - -- -- - -Boundary- Layer-,tt Journal-of Fluid Mechanics 

-~ - - - - - __ 

(1967), Yo1 30,Pt 4, PP. 741-7730 

7. Kovasznay, L.S.G., Kibens, Y., Blackweldir, R.F., 

"Large-Scale Motion in the Intirrnittent Region of 

a Turbulent Boundary Layer ,It Journal of Fluid 

Mechanics (1979), Vol. 41, pp. 293-325. 

3. Corrsin,S., Kistler,A.L., "Free Stream Boundaries of 

Turbulent Flows,It NAZA TR 1249 (1955). 

9. Blackweldsr, R.F., Kovasznay,L.S.G., I'Time Scales 

and Correlations in a Turbulent Boundary Layir ,I1 

Thi Physics of Fluids, Vol. 15, Number 9, Sspt. 

1972, PP* 1545-1 554. 

lO.Yajnik,K.S., Acharya,M., ttNon-Tquilibrium Effests in 

a Turbulent Boundary Layer DUP to the Dzstrustion 

o f La r 52 Ed d i 5 s , Bangalore,NAL-BL-7, Aug. 1977. 

N3 t ion a 1 Ai r ona u t i c a 1 La b o r a t o r y , 

11. Hifner, J.N., Weinstein,L.M. ,and aushnell ,D.Y., 

Large-Eddy Break-up Scheme for Turbulent Viscous 

' Drag Rsduction,Synposiun on Viscous Drag Rsductiorl, 

Dsllas, Texas, NDV. 74,1979. 
. 

12. Corke,T.C.,Guezennec,Y.,Nasib, H.Y.,"Modificati3n 

in Large Scale Structures,11 Symp3siurn on Viscous 

Drag Reduction, Dallas, Texas, Nov. 7-9,1979. 

13. Corke,T.C.,Nagib, H.M., Guezzenec,Y.,l' A Now Viow on 

Origin, Role, and Manipulation of Lars2 Scales in 

- - - -- - . - __ ---Turbulent Boundary I;ayersTt1 --NASA CK-165951, Ftb. 

1932. 

_._.____I_ -- - 1-4~--Ber-teirud,A., Truong,T.-V-. , AvelZsn,F., "DraS 

Rsduztion in Turbulent 9oundary Layers usink 

Ribbons, AIAA paper 32-1370. 

of Outer Flow Structures for Turbulent Drag 

Raduction ,11 AIAA paper 93-0293. 

15. Hefner,J.N., Anders, J.B., Bushnall D.M., "Alttration 

-16. Plesniak,-_ M.W. ,Nsgib, H3, k-llNe-tDrag hduction in A - --. enk Bmrrdary-=%~ye'~ Mrlting from - - -- 

. _-c 

.e- 

--- - ~ - .'.. -- - ---" ~ -_ __- -- ._ 

_- - - . - /__----. -17.. Ander-s,-J,B. ,- Watson,R.D,, JVAirfei-l- t3r-333- AMdy.Br2aZr- - __ -- - up-Devicss Tor- Turb-ule-nt lk-2 - Reduc3ion,11 AIAA -- --p-ap?r 354520. 

18. Anders, J.B., - "Low RPynolds Number LEBU .. . Drag Reduction and Boundary Lsyer 

Control Symposium, National Academy of Sciences, 

October 1995. 

19. Guezsnnec,Y.G., Nagib, H.M., llDocumentation of 

Mschanisms Leading to Net Drag Reduction in 

Manipulated Turbulent Boundary Layers,'! AIAA 

paper 85-0519. 

20. Liss, A.Y. and Usol'tssv, A.A. ,llInfluence of Vortex 

Wing Interaction on Reducing Vortex Induction,11 

Izvestiys Vuz. Aviatsionnaya Techniks, Val. 16, 

NO. 3, pp* 5-10,1973. 

21. Nagel ,FI.T., and Alaverdizsdeh,O. "The NCSU Low 

Speed Boundary Layer Wind Tunnel," SAE Psper 

951 897, 1995. 

22. Goldstein,R., Fluid Mechanics Measurements, pp.557- 554, Hemisphere Publishing Corporation, Wsshinston 

1933 

23. Cebecci,T. and Bradshaw,P., Momentum Transfer in 

Boundary Layer, pp. 192-197, Hsmisphere 

Publishing Corporation, Wsshington 1977. 
. 95 

- -- --Ti - - - - - - - 24.?:Bradshaw;- 'P;;ttA SimplP-MsthOd for Dsternining Ski? 

Friction -Fron Velocity Profiles,lt Journsl of .- 

~- .. 

- - __ __ ._ Aerospace Science, 25, pp. 941, 1959. 

25. Yueller, T.J., "Smoke Visuslization of Subsonic and 

Supersonic Flows (The Le3acy of F.N.M. Brown) ,I1 

University of Notre Dame Report UNDAS TN-3412-1, 

June 1973. 

25. Yim,H.T., Kline,S.J., Seynolds,W.C., ttThs Production - - - - - - - - . - of -Turbulence Nsar a Snooth Wall in a Turbulent 

Boundary Layer,tt Journsl of Fluid Msshanics 

- (1971), VO~. 50, Pt.1, pp. 133-155. 

- - - - _-_--_ - - -27 . tu-; S .S:-; Wi 1 lma r t h , W . W .; Me a sur e mn t s o f the 

Structuri of the Riynolcls Stress in a Turbulent 

Boundary Layer," Journal of Fluid Mochanics 

(1973), Vol. 50, Pt. 3, pp.431-511. 

- .-,---Turbulencs , - 7th edition,:->Ch. -3, -The +$!IT ?ress,---- k h-r _. - . . Cambridge,-3972. ----- - x- - -- I -. *- '.:29. KDbashi,Y. and21chijo,Y,,p !Wall pressure and Its ~ - --- - - - ___ .._^.. Relation---to---Turbulent- Structure of a Bmndsry _-I_ __I._;.--_Layer,I'-Expsrimonts in-Fluids, Vol. 4, Yo. 1, Dp. -_- - - .- 

49-55, 19%. 

30. Sturtevart, B. and Kulgurny, V.4., Journsl of Fluid 

Mechsnics, Vol. 73, pp. 551-571, 1975. 

31. Yarsmcheti, K., privato connunication, July 1935. 

32. Yelnik,R.E., Chow,Fi., ttAsymptotic Thsory of TwoDimensional Trailing Edge Flows,11 NASA SP-347, 

pp.177-249, 1979- 

33. Cobecci,T., Chang,K.C., "Calculation of Incomprsssible 

Rough-Wsll Boundary Layor Flows,ttAIAA 

Journa1,Vol. 16, July 1978, pp.730-735. 

34. Rotta,J.C., Fluid Mechanics of Internal Flows , Elsevier, Ansterdam 1957. 

35. Chevray , R. , Kovasznay , L. S . S. , "Turbulence Mea suremen t s 

in thg Wake of a Thin Flat Plate,!' AIAA 

Journal, Vol. 7, No. 8, 1959, pp. 1541-1543. 

35. Yetka,C.,ltThe Effect of a Larse Eddy Break-Up D?vici 

on the Losarithmic Rigion of a Turbulent Boundsry 

Layer ,)I Southeastern AIAA Student Conferenc?, 1935. 
6.1. FLUCTUATING PRESSURE AT THE LEBU'S TRAILINS E335 

Based upon the procedure suggested in reference [32],a 

prediction of the fluctuating pressure at the LZBIT's trailing 

96 

- edse-. was obtainsd.- This-permitted -the time averaged sound - _.__ 

- - - - -. - . . . 

-.-. .- --- pressure. level from 0 to 2000 Hertz of the acoustic wavis 

impinging upon the flat plate to be set at a value which 

could influence the flow. The study of referencz 32 exanines 

- LEBU trailing edse. was found as (fig. 7, reference 32): 

P (TE)=-3.531 (5.1) 

The above quantity is defined by: 

DP P(TE)= 

e2P &? 1 (5.2) 

where, DP iki the fluctuating pressure. The paraneter e for 

1 

laminar flow is equal to Re,twhere, Re, is the Reynolds 

nunber based upon the LEBU's chord length. The constant 

-- 

E=0.33205 appears in the Blassius solution for a flat plate. 

The flow density,p , wss given a typical value of 1.25 Kg/m 

and U, is the free stream velocity. Considering LEBU #5 

mounted at 3 height h=3.9&, U,was approximated 3s 10.5 m/s, 

and ths psramzter % was 670,000 rn-lat the LEBU's height. 9 

The Reynolds number, Rec was found to be -25,033 and 
97 

the boundsry layer upon ths LEBU was assuixd ta b? lsainsr. 

The transition Reynolds nurnber ReX, with a 3 por cznt 

turbulence intensity (typical at LEBU's height ) wss 

approxiastely 75,900. 

4fter substitutins the given quantities into (5.2), DP 

wss=-fottnd oaual-to 99.95 decibels.-Similar calculstions for 

- - __ the LEBU #j resultid in a pressure perturbation of 104.3 dB. 

A sound wave with such a low frequency ( 0 to 203 Hirtz ) 

time averag2d pressure level w3s considired adequsts to 

- 

- ..* - __ _-___ ~ trigger .the shedding of .a vortclx-at the-LEBU's trailing edge AI -" - I-_ -~ __ -. ._ - 

. -.- 

~. , . -~ .~ 

--..I. . ..% .- .. -. -a - . . ._ . .-* .- . ion. ,- 

. 

rid:-inf fu+$c dy ._. . -cant v 

-_ e- 

.- . .. 
t 

I 

6.2. PREDICTION OF TURBULENT BOUNDARY LAYER. 

6.2.1. INPUT DATA FOR HEAD'S METHC)D 

- Head's method [23] was utilized to predict the growth of 

characteristic lengths of a plain turbulent boundary layer. 

Head's method requires th2 following data as input: 

- - .- - . . - - - ~- - -l,--The moinentum -thickne_ss --at-the beginning of the 

predicted flow regims (end of sandpaper trip). 

2. The initial shape parameter, H. 

at the end of the sandpaper trip is defined as: 

The drag coefficient at the end of the sandpaper trip was 

ern~iricslly pradicted [l] by: 

0.554 

Rex 

'[, + 0.3 Rex(+) 3 (1-- 5, 

x x C,(X)= (5.4) 

In ths above relation Re, is ths Reynolds numbir based 

upon the sandpaper trip length x, r( is th? avgrage rauqhness 

height of the sandpaper and A is a parameter defined as ~ 0.5 

Tha skin friction coefficient cf at the end of the 

sandpaper trip W~S predicted by th2 empirical formula from 

White [I]. 
99 

The average sand-paper roughness heisht K was about 0.001 

in, the sandpaper trip length was 0.24m, and th2 wind tunnil 

flow velocity unit Reynolds number "' was 700,000 IU-'. Proper 

manipulation -of the above -formulas can provids a prediction 

of the mosentum thickness at the end of ths sandpaper trip. 

- .Tha lnitial or starting .values of iI in Head's method 3r3 

__ - 

_____~~a~~v~.y_--trrrimpo~tan~~xce p t --f or t he first few po in t s of the 

-calculation. A shape parameter for a flat plate flow H=1.375 

was assumed by averaging measured values of H along th2 flat 

3L -E,,, ---pl-ate*.-'-Th+ -free -strsm +rs'lrocfty 'was 'con-sidzred to be 11-.-- m/sT - - -- - - -_.. 

-The .growth 'of Athe &menturn 'thicliness,-e:, predicted 6y Head' 6- 

5e-tho-L far-a _pLain--flo_w configuration is cornpsred with - ._ _____-. 

- - = measurad @Is in figure 9. 

6.2.2. VELOCITY PROFILE OF A TURBULENT BOUNDA2Y LAYER 

The logarithmic and ths outer region of a plain 

turbulent boundary layer wsre predicted using a modified 

Coles velocity profile [33]. The velocity u at a boundary 

layer height y is thus given by: 

where, ut is the wall skin friction velocity, is the wakz 

paraneter and y(r) is the well known wake function. The 

logarithmic velocity law constants k and B were assumed equal 

to 0.41 and 5.0 resp2ctively. The wakg function ~$7) [34] is 

defined as: 

Y 

Y 
ORIGINAL PAGE rs 

OF POOR QUALITY1 - 100 

which alsa can be approxiasted with the sine function 

proposed by Coles [I]: 

The mors- complicated rglation (6.7) was used because it __ _- 

Ssve better agreemznt with the measur2ments. 

- . At the wall thi rtlation (5.7) yields w(0)=0.0,and at 

- .. 1-i- =the --dg2=:of the-boundary--layer. -(y=8~~=-~(1.0)=2.0. Rolstion 

(5.6) then yields: 

remains- constant ; for a flat plat2 measuremsnts susgestTT=0.55 

[l]. The wall skin friction velocity ut was d2termined from 

the definition rearranged as: 

0.5 

Ut =Uo($f) (5.11) 

The local skin friction coefficient was predicted by Coles 

formula [I]: 

0.3 e 

Cf = 

( I og Ree) 

-1.3 3 H 

(5.12) 1.74+0.31 H 

The boundary layer velocity profile prsdicted by using thise 

relations in equation (6.10) is coapsred with a messurzd 

plain flow prafile in fipr? 11. 
c c 

L 

101 

6.2.3. BOUNDARY LAYEfi VELOCITY PROFILE FOR A LEBU 

CON FISURATI ON 

The velocity, uLE, at a height y of the LZBB'J 

manipulated turbulent boundary layer was predicted as: 

-~hers, -u is the velocity predicted for s plain configuration 

. and du, is the velocity defect caused by the LESU plate wake. 

PL 

For inviscid free stream flow and a two dimensional wsk2, du, 

- - ._ . - _. -- - .- - - - --_- "___ __ ____ is-estimaJed-by the relation [2]: 

- -14) 

.. _. -- -_ -L I. 

7^ --- 

-- where,dU,,-,-Fs.-the :maximum yelocity :defect at the wake's axis 

of -spmmstry,/3(x ) 'is the wake semi-width snd y, is thi 

-. -1ongitundinsl- distance from. the -wSke's axis of syrnmstry. 

According to privious studies [35] for a similar twodinznsional wake the quantitiesp and dy,,*at a distanc: x 

from the plate trailing edge, are defined as follows: 

and 

(5.16) 

where Uo is the boundary layer velocity at the LEBU height 

(free steam vslocity) and @(O) is the momentum thickness at 

LEBU trailing edge. The quantity B(0) was considered as 

being twics the momentum thickness of th2 laminar boundsry 

layer grown upon the LEBU.1 The Blassius solution [2] for a 

flat plate with a laainar boundary layer suSg2sts 

0.5 

Q(~)=0.564 (E) .UO (5.17) 
. a 0 

- ORIGINAL PAGE IS 

OF POOR QlJ.%LITY 102 

In the aSove relation c represants the LEBU chord lerlgth, and 

the paraneter -2 U was 670,000 q -1 (at the LEBU' s height). 

-The logarithmic velocity law constant k was assumed to retain 

ths value of 0.41 [361, velocity 

was calculated from-.( 5.10). The s k i n - f r i c t i o n coefficient 

LJ 

- 

and the wall skin friction 

resulted - -from previous measurements (section 2.3). A 

-- I... . 4 --T:-: theoretically- - predicted - velocity profile for LEBU 82 is 

compared with a messured profile on figure 13. 

-- ~-- - -- .- the procsdure suggested -by Bradshsw 124]-. In th2 logarithmic - 

- -- - -region of a boundary layer, th-e--velocity u at a distance y - 

from the wall is given by: 

(5.18) 

where ut is the wall friction velocity,v is the kinemstic 

viscosity and k and B are constsnts equal to 0.41 and 5.0 

respectively. For a flat plate the logarithnic region 

extends approxinately ovsr 35<9<350. So, for 

(5.19) -- "'-200 

V 

relation (6.18) is valid and yields 

U 

-- -I 7 . 923. 

Ut 

Ths skin friction coefficient is given by: 

(5.20) 

(5.21) 

wh2re U, is thc fr2e streaa valocity. Only on2 point (y,u) on 

thc losarithmic region of a measured boundsry layer satisfizs 
103 

all the above relations. Dnotermining this point can providi a 

value for c at a certain axial location. After traversing 

across a boundary layer various values of u at= substitutsd 

f 

__ into-rela~iorr-~6.2OL)~_Theresu1-ti-ng u and corresponding y 

are used to detirmini thi point on thi logarithmic region 

which gives y+ closest to 200. This requires a local least 

__ __ -----_- - -square fitting of the form 

u=3y (5.22) b 

which is applied for measured values of u and y in thi 

- - -I-- - -__ - .---vFcfnl'Zy" __ __ - - - of __ -this point.= Thus 

t havg 3een 

can.- b1--approx i nnsted vz r y accur a tz 1 y. 

-___ _- 1 *hers y?_=230. may- 

._ and y forY+=33 ---1_. - , 

- __ .- - __ a __ I- I 34snipulation -of -t,hsse formulas yiilds: 

The resulting value of y and u satisfies the relation (6.20) 

and can bi used to detsrmine cf from (5.21). 

Exasple calculation: 

Yeasured quantities at x=2.75 m, z=3.0 m. 

-=730,835 m-l, ~=1.514 13 U,=11.311 m/s "0 -5 

J 

Y Ut Yhl uc m/ SI ut[ m/ SI V 

0.035 7- 525 0.420 139.1 

0.006 7.700 0.433 159.709 

0.039 8.033 0.449 222.376 

Least squsrz curve fitting of the mnossurad valuos of u at 2 

distance 0.004 to 0.016 m from thno wall risults in 

~=0.007255~ with corrilation cosfficient equal t3 

0.1 5 5 6 
104 

0.993. Then substituting -into the proper relations one can 

get: y=0.007255 m, u=7.961056m/s, ut=3.4442m/s, and 

cf=0.003064. The value of cf is the desired r2sult. 
c 

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4 

15 

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3 

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Lr, 

4