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1 1. TITLE tincousse Security Claaaalacetions SOME UNSTEADY AERO- ~43oDYNAMIC CHARACTERISTICS OF SEPARATED AND ATTAC ED FLOWI

12. PIERSONAL AUTHOR(S)

Dr. Eugene E. Covert, Mr. Peter F. Lorber, Ms. Carol M. Vaczy13&. TYPE OF REPORT I13b. TIME COVERED 14. DATE OF REP0OR7 (Yr. Mo.. Da, 15. PAGE COUNT

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FIELD /1 (ROUP .SUB GR. UNSTEADY FLOW, BOUNDARY LAYERS, FLUID MECHANICS,

i AIRFOIL AERODYNAMICS -

1.3. ABSTRACT sConeinue an reverse if flDcssa' ad identify by biocif numberi

. Aerodynamic characteristics of separated and attached unsteady flow about a NACA 0012

airfoi l have been measured for reduced frequency from 0 to 6.4 and angles of attack up tol8r .<Results from boundary layer and near wake ensemble averaged velocity, Reynolds stressan~ surface pressure distributions are presented. The flow was determined to be locally

two-dimensional away from the separation point (if present) , within + 1/4 span of theairfoil centerline. A convected component of the unsteady separateiipressure field wasidentified, and the dependence on reduced frequencylangle of attack, Reynolds number andform of transition is discussed. A geometric similarity model is suggested to explaine*

presence of a periodic component measured for the ensemble averaged Reynolds stresses IrFinally, studies of the relative importance of acoustic and upwash velocity compone,~of the excitation are summarized. 1

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MICHAEL S FRANCIS, Capt, USAF 202/767-4935 AFOSR/NA

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A AFOSR-TR- 8 3- 1 34 4

MASSACHUSETTS INSTITUTE OF TECHNOLOGY

DEPARTMENT OF AERONAUTICS AND ASTRONAUTICSCAMBRIDGE, MA 02139

ANNUAL REPORT

Grant # AFOSR-80-0282

entitled

SOME UNSTEADY AERODYNAMIC CHARACTERISTICSOF SEPARATED AND ATTACHED FLOW

Prepared for

Air Force Office of Scientific ResearchBolling Air Force Base, D20332

Attn: Capt. Michael Francis

Period of I"Investigation: September 1, 1982 - August 31, 1983

Investigators: Eugene E. Covert Accessi~n ForProfessor of A-ronautics and Astronautics NTIS GRA&I

Peter F. Lorber DTIC TABGraduate Research Assistant Unannounced

Justification

Carol M. VaczyGraduate Research Assistant By

Distribution/

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Avail and/or

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" ized for public release ;

•Mtribution unlimited

Ai 0, 1, , lob

INTRODUCTION

With one notable exception, this year's activities on Grant

APOSR-80-0282 were much different than the activities of preceeding

years. This fact in a simple consequence of the evolutionary nature of

this program. The first few years were spent demonstrating the

feasibility of the experiment and recording and evaluating velocity

and pressure data to be used as the forcing function for the boundary

layer itself1 92 . During the next year the initial boundary layer data

were recorded for a variety of test conditions3 . This was a very

useful and exciting period, since much of the data represented a new

combination of parameters. The last year was spent largely in

consolidating the data, "filling in the envelope," as it were. It was

also a period of reflection, consolidation and improved understanding of

both the older and the newer data, which included studies of additional

features of the experiment, such as near wake velocity profiles and

separated flow pressure distributions. Additional tests were also

conducted to help delineate the velocity part of the unsteady forcing

function from the acoustic or pressure part. In some circumstances

teots vere conducted either to demonstrate, say, the two-dimensionality

or lack of it, on the metric surface or to confirm or reject hypotheses

or explanations of various features tn the data. These results will be

discussed briefly below. Some interpretations of this data will also be

briefly set forth.

The notable exception referred to in the opening sentence is a

result of a failure to either find a suitable research student or to

"i :et I%.... . : 1 I-,ormntion .11vision

* ' 2

hire a suitable engineer to complete the development of the floating

element shear gauge. The experience from the preceeding two years

suggested that unless a suitable student or engineer was available, the

results were not worth the cost. This short term loss now appears to

have resulted in a long term gain for two reasons. First a cheaper,

more reliable method has been adapted for our use, and second we have

reprogrammed the assets and improved our ability to take simultaneous

data from many hot wire and pressure sensors. Such data appear to be

* very valuable in the region of near separation in unsteady flow.

In this report the important aspects of the last year's studies

will be briefly outlined. The results of the last few years will be

placed in a more general context. This discussion will lead to a

discussion of some important unanswered questions and their importance.

Technical Sumary

The important technical points to be discussed are as follows:*

1. The nature of the various correlation terms in unsteady flow.

2. Experimental demonstrations of the two dimensionality of the flow

field.

3. Experimental delineation of acoustic effects from unsteady velocity

effects.

4. Characteristics of unsteady separated flow in this experiment.

*The geomietry and the detailed nature of the experimental conditionsand data acquisition system are described in detail in References 2and 3.

, . 3

5. Comments on the trailing edge flow.

6. On the proposed method of measuring shear.

Results of a study of the turbulent unsteady near wake completed in the

fall of 1982 are given in the attached copy of AIAA paper 83-0127.

On the nature of the several correlation terms

Recall that our signals for, say, the tangential component of

velocity are defined to contain three parts (Refs. 4, 5, 6): a time

mean part, a periodic but not necessarily sinusoidal part, and the part

left over. Thus if u(x,t) is our measured signal, then the time mean is

defined

- 1- u(x,t)dt

T.m 2T J-T

Further we can take an ensemble or phase lock average

S-.1N-I

-- ± E u (x,t + n -+ 0)N n-0 W

where 0 < 0 < 21/u , but is constant for each average. Note then

<u(x,t)> - u(x) + u(x,t)

This equation is, in fact, the definition of the periodic part of

the signal, u. The remaining term is, by definition

u'(xt) - u - <u> - u - u - u

Note u' has two properties, by definition

'pI

9, , . , -, , , . . . . . " .. . ' ... . - .. - .. - . - . .. - . .. , " - .. . . . . ' . . , . " . . . . '

.M Al7 r 11 W7 T'C 4

A) u(xt)dt 0T-a 2T LT

B)i N-1 ul21

E u'(x,t+n --+G)u-0n-0

That is to say u' has zero time mean and has zero ensemble average.

We are assuming that u' corresponds to the usual turbulent velocity

coponent that one measures in steady flow. In turbulent boundary

layer theory the term <uv> is of great importance since it leads to the

*Reynolds Stressu terms. Based upon the decomposition above we find

<uv> -v+uv + uv +uv u>+(UV>+ UV>

+ <uv > + <U v >

* The time average of this term gives

1T -- T fT -_ --lra _ (uv)dt uv + lim- i(v + uv + uv)dtT., 2T LT T.a 2T JT

+ iu -T (uv + uv + uv)dt

T.. 2T JT

But by definition u and v have zero mean, so

(uv) - uV + uv + u v + uv + u v

The term uv is non-zero because it may contain a rectification

effect. Further this sort of term will appear in the left hand side of

the momentum equation for each periodic velocity term (i.e. vaii/ay,

-... - - - - -*J-

*j **!' .*f**~ *

4 5

etc.). The terms u'v' is the classic Reynolds stress term. The

last two terms would seem to have a small value (random rectifications).

The real issue is whether or not u' as a function of time is of finite

or zero measure. In the latter case u'l is identically zero. In the

former it should be small. According to our data terms like u'l and

uv' are less than 10-4 of U9 or less than 1% of u'v'.

Similarly we may take an ensemble average, subtract out the mean

and end up with

1V - uv + uV + uV UY u v + u v

M UV + ;V + UV + UOVO

The appearance of the non-zero term u'v' is a curiosity. The basic

premise is that the periodic part of each term in u and v had been

removed by the previous manipulation. Figure I shows typical values of

u'v' across the wake layer7 . It is definitely not zero. It was

suggested by Lorber 3 that a simple geometric argument accounts for

this term. To follow this argument keep in mind that u is really a

function of x and y as well as time. In the unsteady boundary layer we

expect each of the several thicknesses characterizing the boundary layer

to vary over a cycle. It is well known that the turbulent intensity is

a function of the distance from the wall. Hence the probe sees a

variation in scale position (i.e., y/g with y fixed). So since the u'

and v' correspond to different heights in the boundary layer over a

cycle, so u'v' is non-zero. Thus, there is an unsteady contribution to

the Reynolds stress, at a fixed y that varies over the cycle. This

.p.

.8I

*8*,•

6

model will be discussed further below.

Experimental Demonstrations of Two-Dimensionality

The two-dimensional characteristics of the flow pattern were

measured in two ways. First, pressure taps were mounted in the lateral

positions ±12.5% and ±25% of chord from the mid span location at 6

8chordwise locations betwe4n x/c-0.025 and 0.98 . Figures 2A, B, and C

show the comparison of this data for attached flow. The data show the

flow is locally two-dimensional. Figures 3A-C show the same kind of

data when a laminar separation bubble is present near the leading edge.

This separation point location can be predicted by Stratford's

criteria 9 when based upon mean flow properties to within about 20% (or

about 1/2% of the chordwise position). The reattachment zone is

predicted by Oven and Klanfer's criteria 0 equally well. Figures 4A-C

show results for massive separation of an artificially tripped boundary

layer, while Figure 4D shows the mean pressure distribution with natural

transition. Lack of two-dimensionality in the leading edge bubble

separation has been observed by Winkleman at the U. of Maryland 110

More important, our data shows the separation zone for the case of

artificial transition is more three-dimensional than either the

laminar bubble or the massive separated region.

The other procedure to test the two-dimensionality is

through wake measurements. Typical data is shown in Figures 5 and 6.

The conclusion is that locally, the flow is two-dimensional for at least

the distance of ± one quarter span on either side of the airfoil

centerline. The two regions selected, the location of the separation

6 7

bubble and the near wake, are regions where one would expect the

departure from two-dimensional flow to be the largest. Hence we are

confident our conclusion that the flow is essentially two-dimensional is

valid.

Characteristics of Unsteady Separated Flow

In this discussion we will deal with bulk characteristics associated

with separated flow. This restriction is primarily due to problems

associated with measuring the details associated with unsteady separated

flow. (It is likely that a computer contolled laser anemometer could track

the separation point; while there is no substantiation of this conjecture

on separated flow, such measurements have been made in the wake of a

propeller.) Thus separation is located more or less by examination of the

man and fluctuating pressure distribution. Hence the final separation

point location is known no more accurately than the distance between

pressure taps. Figure 7 shows the variation of cp vs x/c as a function

of reduced frequency, k, in the fully attached case8 . Note the high

value of the peak suction pressure coefficient (-6.2), and the tendency of

the mean pressure coefficient difference to approach zero at the trailing

edge. Figure 8 shows the change in mean difference when separation is

present on the upper surface8 . In this case, the mean lower surface

pressure coefficient is as it was before, except near the leading edge, but

the man upper surface pressure coefficient is radically transformed.

.9. Figures 9 and 10 summarize the current data on attached flow, separated

flow and the boundary regions dividing the two8 . The transition strip is

#120 grit 0.1250 wide at the leading edge. In these figures "dynamic

4,e

.v.

separation" implies the flow varies between attached and separated in an

intermittent way as shown in Figure 11 (which is also taken from Ref. 8).

The attached- interval varies from 2-30 ellipse revolutions, as is also true

in the separated state.

The data allows comparison of separated and attached flow for the

same s, k and Reynolds number. Figure 12 shows the first harmonic of

Cp as a function of x/c and Figure 13 shows the phase lag under the

same conditions. The non-attached unsteady flow seems to be convected

over the front 40% of the chord, and acts as if it were attached over

the last 60%. This supposition is based upon a comparison of Cp and

its phase in attached flow. At the present time it is not clear what is

being convected at approximately 0.55 U,, in the separated flow

regime. However the data (Fig. 14) suggests that whatever it is, it is

roughly the same whether the boundary layer has natural or artificial

transition. Figure 15 shows the variation of convected velocity with

"k". This variation is consistent with that reported by Carta et

A1.12. We note too that when A, is added to p, the angle of attack

at stall is increased by the unsteady process, as reported by Mccrosky

et al. 1 3 .

We note the oscillating variation of term C on the upper surface

over the front half of the airfoil acts as a convected process, not an

acoustic process, because a change in speed of about 50% does not change

the behaviour (Fig. 16).

An examination of two summary plots (Figs. 17A, B) for a range ofI

"k's", at a-15 degrees and for natural transition shows the amplitude

9

and phase of the fundamental of the unsteady pressure coefficient (Cp)

varies from the leading edge to the trailing edge as follows:

a.

k humps #valleys phase speed comments

0.5 2. 1 slow downstream, sign rises slowly, sharpchange at .8. Last drop off at TEvalue of the slope isslightly negative(-.08)

1.0 2 2 .14 over last 70% more or less likeof chord .-0 over k-.5 for front 1/2lot 30% chord, oscillation

amplitude growstoward TE

2.0 3 2 0 over let 20% more or less conat) .27 over last 80% ampl, rising slope

toward TE

3.9 3 2(3) .45 over lot 50% decreasing ampl.zero after towards TE flat

at TE

6.4 4 4 .55 over 1st 40% decreasing ampl.zero or slightly toward TE, rising

negative last 60% characteristic atTE, flat at midchord

Three features stand out on this chart. The number of cycles

increase with "kw. The character of the distribution changes

-. 4i drastically with uk". For these conditions, at low "k" the amplitude

Increases with nk", strongly so, over the last 20% of the airfoil.

There is little going on over the front of the airfoil. At higher "k"

the oscillation is maximum near the leading edge and decreases as one

moves aft towards the trailing edge. Further the convection

W SG%

104.:

characteristic is the strongest where the fundamental amplitude of the

unsteady pressure is the largest. In the case of artificial transition,

the implication is a change-over from trailing edge separation at low

Ok" to a leading edge separation at higher "k". This dependence at high

*k" is extraordinary because at high "k" the mean plus unsteady pressure

gradient effects are largest at the trailing edge. Note the unsteady

flow field seems to be superimposed on the relatively constant pressure

mean flow field on the upper surface.

Clearly this flowfield is not understood.

Comsnts on Trailing Edge Conditions

The data from References 1 and 2 show the pressure difference

between the upper and lower surface seems to approach zero as the

trailing edge is approached. At low values of k the variation of Ap is

approximately as the square root of distance from the trailing edge. As

k increases the variation is more nearly linear. Examination of Figures

7 and 8 indicates the pressure difference is finite and varies smoothly

as the trailing edge is approached, whether the flow is separated or

* not. This implies the extended Kutta condition 14

1 (u2 _ 2)

2 u Z dt

my well be applicable here. (Note here uu is the tangential

velocity, just outside the boundary layer at the upper separation

point, while utis the tangential velocity just outside the boundary

layer at the separation point on the lower surface. The latter point

.1

is nominally at the trailing edge.) For rough purposes one could argue

-i - -- -2 ~2S- u U u

CC + 2 tItp p 2

U U

Thus the pressure difference has a part proportional to the mean, one to

the fundamental frequency and as indicated by the third term, a term

proportional to the second harmonic, as shown in Figure 18, for the

upper surface pressures. However the fact that the second harmonic

appears only near the trailing edge reduces the validity of this

argument.

On the Effect of Acoustic Excitation

The effect of the noise generated from the rotating ellipse was

investigated. This was accomplished by first measuring the sound

pressure level at 7 locations near the airfoil. This pressure was then

reproduced using a speaker. The airfoil/speaker configuration is shown

in Figure 19. Many difficulties were encountered in accurately

reproducing the acoustic wave characteristics, particularly at low k.

Therefore only reduced frequencies of k-2.0 and 6.4 were reproduced.

For these two cases the sound pressure level could not be duplicated

over the entire airfoil at the same time because the amplitude decay of

the pure sound wave excitation with distance was different than the

combination of effects due to the rotating ellipse. Therefore three

separate sound pressures were used, one corresponding to that at the

leading edge, one to that at the trailing edge, and one that is4

somewhere in between. (This adds a large degree of uncertainty to the

- * - ..-.--. . .| . -

12

validity of the results.) The surface pressure distribution and

boundary layer profiles were measured and then compared to those for

the airfoil/ellipse combination.

The conclusion was reached that at low values of "k" (2 or less)

the acoustic part of the response is some 30 decibels below the measured

pressure with wind on. At k of 6.4 the acoustic pressure level

recorded on\ the airfoil is 5-6 db less than the wind-on measurement.

Hence the threshold for effects of compressibility on the flow must lie

in the neighborhood of these higher values of k. For the most part the

4 acoustic excitation had a negligible effect on the measured boundary

layer characteristics.

On the Measurement of Shear

'4 The detailed measurement of the velocity profile shows that (in

inner coordinates) there is a region where

u + YU T-my Wu v

VT

In this region then one can measure u near the wall and find, if v and

y are known

u2 y u 1 U 2 CT 2 afy 2S

For our boundary layers if we can measure u at y corresponds to y+ = 6

or less we can deduce Cf. Such probes are under construction and will

be calibrated in known flows.

.4A;

4".

131

~~13=.

On the Relation of These Results to Other Results

Certain of these results discussed above indicate for example that

the unsteady Reynolds stress term (u'v') seems to be present in all the

data40 18 in the literature, vhether the data vas obtained in a channel

with forced excitation, or on an airfoil which is the configuration of

our experiment. Lorber's geometric argument3 seems to apply to both

channel flow and our external flow. If variables such as <u> and <uev'>

depend only on distance and some thickness 6(t), such that

<u(y,t)> - <u(y/a(t))>

<u'v1(y,t)> - <u'v'(y/s(t))> , then

time and space derivatives are related by

a<u) -<u> Ad. .d and

at ay 6 dt

3D<ulv'> . 3<u'v' > y d--.

at ay 6 dt

If the mean and first harmonic are considered, so that

<u> (y,t) - u(y) + Q(y)exp(i(wt-#u(y))), and

<uIvI> (y,t) M 717(y) + u'v (Y)exp(i(wt-4uIvI(Y) time

differentiation and division produce the relation

3<UeVe>

- exp(i( u (Y) -u y)

u 3<U>ay

Finally, for small unsteady amplitudes and for profiles similar at each

;-" time,

.

Lwha1bJ2k§ .

14

<U'v> uv'v and l- <u> :- , and thereforeay ay ay ay

au'vI

uav Y-m ~:~~ . exp(iAu-u'v)u

ay

This relation predicts the amplitude of <u'vl> based upon i ' and

uev °. Also, since the left hand side is positive and real, <ulvl> and

.<u> must be in phase if au've/ay has the same sign as iu/y and

1800 out of phase if the signs are reversed. Figure 20 shows a

comparison of computations from this model and data from our experiment.

References 3 and 16 provide further details and comparisons with other

data, both for phase and amplitude.

A second issue here is the relation of the "Kutta Condition" in

steady and unsteady flow. There are two characteristics of the airfoil

associated with the Kutta condition. The first is the statement that

the pressure jump is non-infinite at the trailing edge. The data which

has been developed in this program shows

(1) for all attached flows hp.0 at the trailing edge;

(2) for all separated flow ap is not infinite at the trailing edge.

This aspect of the "Kutta Condition" in absolutely satisfied in every

case. The second consequence of the "Kutta Condition" is to fix the

value of the circulations about the airfoil. These calculations for

lamina suggest a value for the circulation is

15

.'

u

4," This value increases linearly with the thickness ratio for an

airfoil with a cusped trailing edge, and decreases with included

trailing edge angle, and decreasing Reynolds number. For an 0012

* .. airfoil the net result is that

CL - (0o.9)CLIDEAL

where CLIDEAL is the zero thickness lamina value (2va)

Figure 21 shown the value of the mean CL at a-10 0 for two

Reynolds numbers as a function of k. Two clear conclusions are reached.

*First CL mean increases with Reynolds number, and second CL

increases with reduced frequency. Figure 22 shows the unsteady

increment is. of the order of 0.15. This represents a substantialimprovement in effectiveness of developing lift on heavily loaded

airfoils in unsteady flow. The improvement in the ability of an airfoil

to generate lift in unsteady flow is in substantial agreement with the

data in Ref. 13. This improvement comes about in spite of the great

difference in the source of the unsteady flow.

These sorts of results for the lift coefficient were not

unexpected. However the data on the unsteady pressure coefficient in

Figs. 12-17 have yet to be explained. The variation of cp with x/C

shown there is unexpected and unexplained. (These matters are under

study15.) This confusing situation is further complicated by

i. . .* . . ... . - - , . .**

:.:.

16

data (Figs. 11, 23) which demonstrates intermittent separation in

unsteady flow.

To further compound the complexity of the situation, Figure 24

shows a rough plot of our boundary layer data on a Clauser [A/6 - 6(G)]

plane. The steady state "self-similar" profiles are shown as flat

plate, Clauser #1 and Clauser #2. The unsteady data at small a is well

away from this line (although the steady data are not too far from it)

lying at a value of "G" that is too high. That is, the unsteady losses

exceed those expected in steady flow. As k increases, the relative size

of the unsteady losses decrease. At higher a, the unsteady losses seem

to be too small compared to the "self-similar" thickness. The

implications here seem simple. As the Stokes layer becomes thinner with

respect to the boundary layer thickness (i.e., as k increases) more and

more of the boundary layer acts approximately as a quasi-steady layer.

The smaller unsteady amplitudes seen at higher frequencies may also be a

factor. The consequences of this are treated in Ref. 16.

Closing Remarks

At the present time, many of the characteristics of the unsteady

flow field as measured in this program are unexplained. These vary from

the frequency doubling at the trailing edge for low frequency separated

flows to the appearance of a transition from a downstream convected

process to a standing wave as one proceeds downstream following a

leading edge separation. Understanding of some of these details may or

.- may not be improved by measurement of shear at the wall under these,unsteady flow conditions. In other words the primary question is which

,J -

Q-

* -- . * . ' a . *

i~°j

17

of these characteristics are a result of this particular test

configuration and which are characteristic of general unsteady flows.

At the present time the results suggest that the determination of the

characteristics of the separation point may be a clarifying result.

Because of the detailed balance at the separation point, it is suggested

that non-obtrusive ins trumentation may be the only way one can obtain

unbiased data under these circumstances.

Status of Research

We have met the following program goals during the last grant year.

(1) The unsteady boundary layer computer program is operational using

an algebraic turbulence model. Work in continuing on a version using a

three transport equation turbulence model.

(2) We have demonstrated the two-dimensional character of the flow and

find it satisfactory, except possibly near the leading edge laminar

separation bubble or at the separation point if transition is forced.

(3) The behavior of the unsteady turbulent near wake has been studied

for a wide range of flow conditions, revealing many interesting

features.

(4) In this experiment at low reduced frequencies the unsteady flow is

primarily an upvash effect, and the flow behavior is like that

predicted by unsteady potential flow of an incompressible fluid. At

higher reduced frequencies the pressure on acoustic wave may account

for up to 10% of the excitation. The boundary layer characteristics

seem to be unaffected by the acoustic excitation.

(5) More of the test matrix in a, k and Re has been filled in for

4. "I'.'''%. ' ,- , ' . ¢ ", ,..2 "" 2 .42 ''' . _r''''..,.." ' ' ' . -".-, ._. . '.'.. .. " ... '.. ..

turbulent boundary layer profiles, including measurements of <u>, <v>,

<'UII t <vv'> and <u vl>.

(6) The unsteady separated flow zone has been mapped out. Although the

surface pressure distribution has revealed many interesting

characteristics, the details are not yet completed. (For example, we

have yet to maure the motion of the unsteady separation point.)

-4

ID

'iI

"Fq 4 ---.

.i* ~ *4 ~ 4 . * . . . . .~,o,-

19

INTERACTIONS

Seminars

Ames Research Center, Dr. S.S. Davis

University of Maryland, Dept. of Aeronautics

Royal Institute of Technology, Dept. of Mechanics, (Stockholm)

ONERA (Paris)

Dept. of Ocean Engineering, MIT

Dept. of Aeronautical Engineering, MIT (twice)

Presentations

AIAA 21st Aerospace Science Meeting, JanA 1983

AFOSR - U. of Colorado - Seiler fub Workshop, Aug. 1983

Thesis

Cordier, Stephane, J.; "Characteristics of an Acoustically

Excited Unsteady Turbulent Layer in an Adverse Pressure Gradient." MIT

S.M. Thesis, Department of Ocean Engineering, August 1983.

.4,

.4..,

S S

20

References

1. Lorber, P.F.; "Unsteady Airfoil Pressures Induced byPerturbation of Trailing Edge Flow." Department of Aeronauticsand Astronautics, MIT, S.M. Thesis, February 1981.

2. Lorber, P.F., and Covert, E.E.; "Unsteady Airfoil PressuresProduced by Periodic Aerodynamic Interference." AIAA Journal,20, 9, pp. 1153-1159 (1982).

3. Covert, E.E. and Lorber, P.F.; "Unsteady Turbulent BoundaryLayers in Advance Pressure Gradients." AIAA paper 82-0966, to bepublished in AIAA Journal.

4. Parikh, P.G., Reynolds, W.C., and Jayaraman, R.; "Behavior of anUnsteady Turbulent Boundary Layer." AIAA Journal, 20, 6, pp.769-775 (1982).

5. Simpson, R.L., Shivaprasad, B.G., and Chew, Y.T.; "The Structureof a Separating Turbulent Boundary Layer. Part 4: Effects ofPeriodic Freestream Unsteadiness." J. Fluid Mechanics.

6. Telionis, D.P.; "Unsteady Viscous Flows." Springer-Verlag, NY,1981.

7. Covert, E.E., Lorber, P.F., and Vaczy, C.M.; "Measurements of theNear Wake of an Airfoil in Unsteady Flow." AIAA paper 83-0127,January 1983.

8. Covert, E.E., Lorber, P.F., Vaczy, C.M.; "Flow Separation Inducedby Periodic Aerodynamic Interference." Presented at AFOSR/FJSRC/U. of Colorado Workshop on Unsteady Separated Flows; Aug. 10-1i,1983.

9. Stratford, B.S.; as cited in Rosenhead, L., ed, Laminar BoundaryLayers; Oxford University Press, Oxford, 1963, pp. 324-329.

10. Oven, P.R., and Klaufer, L.; "On the Laminar Boundary LayerSeparation from the Leading Edge of a Thin Airfoil." British ARC,CP, 220 (1953).

411. Winkleman, Allen; Personal Communication; also "An Experimental

Study of Mushroom Shaped Stall Cells." AIAA paper 82-0942,presented at AIAA/ASME 3rd Joint Thermophysics, Fluids, Plasma andHeat Transfer Conference, St. Louis, Missouri, June 7-11, 1982.

12. St. Hilaire, A.O., Carta, F.O., Fink, M.P., and Jepson, W.D.;"The Influence of Sweep on the Aerodynamic Loading of anOscillating 0012 Airfoil." NASA CR-3092 (May 1979).

-.. . . . . . . ... ,.................................................................

%.4

21

13. McCroskey, W.J., Carr, L.W., and McAlister, K.M.; "Dynamic StallExperiments on Oscillating Airfoils.0 AIAA Journal, Vol. 14, 1,pp. 57-63, Jan. 1976.

14. Sears, W.R.; mUnsteady Motion of Airfoils with Boundary LayerSeparation." ATAA Journal, Vol. 14, No. 2, pp. 216-220 (February1976).

15. Vaczy, C.M.; "Unsteady Separated Flow Fields Around a NACA 0012"-,q Airfoil." MIT S.M. Thesis, in preparation.

* N 16. Lorber, P.F.; "The Turbulent Boundar Layer on an Airfoil inUnsteady Flow." MIT PhD. Thesis, in preparation.

17. Cordier, S.J.; "Characteristics on an Acoustically Excited UnsteadyTurbulent Layer in an Adverse Pressure Gradient." S.M. Thesis, MITDepartment of Naval Architecture and Marine Engineering, September1983.

18. Cousteix, J., LeBalleur, J.C., and Houdeville, R.; "Response of aTurbulent Boundary Layer to a Pulsation of the External Flow Withand Without Adverse Pressure Gradient." IUTAM Symposium onUnsteady Turbulent Shear Flows, Springer-Verlag, 1981.

.,.,,4., . I . .,.,- .. . .. . . ,.-. . - . , . . . .,..,. .. . . ,,.. -. ...- - .. - . . - . .. . .'. . -. . -. . -

' .'.22

'm

*(THIS PAGE WAS LEFT~ INTENTIONALLY BLANK)

,4,.

4'.

'4

A

' ,# 4/ S , . , . , , . - , , . - , ' . .. . -, . ' - . - . - - , ' - . - . - - - . - . . . -- . - - . - . - ' . . - . .. . . ;

44L .*

23

* 0.20cc 2I I I I0

. -Rea7xiOS:" K- 2.0U.

w.1.0oI 1II .

E0

,

0

0 0 0 0 .001 .002

AMPLITUDE OF THE FUNDAMENTAL HARMONIC OF (U'V')/UE.UE

FIGURE 1 : AMPLITUDE OF ACROSS WAKE

., 0 " .--* .- . .: . .-. . . . -..: , . ...... .. ......-: ..... .. ... .-,,;-.. .',','.. ,u I- . 0 .'.2 --,5. .-.-. .: ...-. X /C,- .- . 0. .X... .C.,I . 20. . ., .. ; i:-,:

24

RE~MEP1 PRSSURE COEFICIENT

SS 0.59 LH-U K-0.5R RE7000LOE UFC

EF

SUFCC

T' I -IC.59

-1.990.

-2w

-1.509.88 9.29 9.48 9.68 9.69 1.88

DISTANCE A".OG AIRFOIL CHOR, X#'C

FIGURE 2A: SPANWISE DISTRIBUTION OF MEAN PRESSURE COEFFICIENTATTACHED FLOW

25

AM'PLITUDE OF FIt4IAWENTAL, HARM1ONICAM 6.160 4.H- LWRSLFCPK-.L R-0,0ITUD 0.120E

o.o86N%,,LFPE

S'RFC

Z:6 XY

+

-.1;5-. 50

0.00 0.20 0.40 0.60 0.86 1.66DISTANCE ALONIG THE CHORD, X/C

FIGURE 2B: SPANWISE DISTRIBUTION OF AMPLITUDE OF FIRST HARMONIC OF Cp

-A

26

HA PI-WEE LAG OF TH-E FUNDETL HpOnIC

L K.8.

A sw70~o

1563. +.02 xD tD

G -. 1.

LFbER

58.

9.99 0.29 0.40 9.66 0.60 1.08DISTANICE ALO.NG AIoROL CHOR, X-'C

FIGURE 2C: SPPANWISE DISTRIBUTION OF PHASE OF C

27

PRE -1.0 MEN PIlESS1NE DISTRIBUTIONSS ALPHAi8 DEGREES

U POSITION CR -2.0 RE-720,M66E K-2.0

C -3.90E

* F SWMOL Z/C POSITION

I + .125TO RIGHTE-5.9A . iM TO RIGT

1 .125 TO LEFT

T

9.96 9.29 0.40 9.69 9.6Be 1.06DISTANCE A~LON4G TH1-V HRD, X/C

FIGURE 3A: SPANWISE DISTRIBUTION OF MEAN PRESSURE COEFFICIENT -

WITH LAMINAR SEPARATION BUBBLE

28

.428

P AFPLITUDE OF THE FLDDAIENTL HpiRe IC

A ,. LP - DEGREES.1. 160 POSITION CP RE-720,0"L K-2.0I

* T SYMIBOL Z-'C POSITIONLOR

D 8.1M9 X .00(CENTERLINE)E + .125 TO RIGHT

.. .250 TO RIGHT:-'. • .125 TO LEFT

.- AW .250 TO LEFT-

* e.em4.,

. 0.213 0.40 9.60 0.80 1.00

DISTANCE F LOG THE AIRFOIL CHOR, X/C

FIGURE 3B: SPANWISE DISTRIBUTION OF AMPLITUDE OF FIRST HARMONIC OF C -WITH LAMINAR SEPARATION BUBBLE P

.4., ,,.,,.. .. ,z -,' .. .. 4., . - . . ... -'.:. - . .. . .. -.. . .. . . -.- ." . . . , . .". . - . . - .,

29

,

H 59 5. I 'I 'I

HA PI-%ESE LAG OF THE FUND4lVIALS 2m. UPPERE FLHA-10 DEGRES

L POSITION CA . R r15 8.,8-

D 188.E

* G

50.

LOWER SYMBOL Z/C POSITION

x .88(CENTEJINE)*-53. + .125 TO RIGHT

.25 TO RIGHT

.125 TO LEFT-a. I,< ,. TO [-100. 0.5 OLF

0.88 9.29 0.49 0.60 0.90 1.00DISTANCE ALONG THE AIRFOIL CHORD, X/C

FIGURE 3C: SPANWISE DISTRIBUTION OF PHASE OP C - WITH LAMINARSEPARATION BUBBLE P

* , . " 4, • . - . . .I -,, ,, • . .. ..*

p 30

EAm

RES

R

E

F SYMBOL Z/c POSITION

4 x .008CMETERL.I4E)I-3.93 + .125TO RIGHT

E .0 .25 TO RIGHTN A .125TO LEFTT 0 -2 TO LEFT

-4.09.98 0.20 0.40 0.69 9.88 1.89

DISTANCE ALONG THE CHORD IN X/C

FIGURE 4A: SPANWISE DISTRIBUTION OF MEAN C WITH TURBULENT SEPARATIONp

31

Cp

-d

/ A'LITUDE AT THEFUNAMETAL FREQJ04CY

AM 0.400 _ LPH--14 DEGREES - K-1.0P RE-700,0WL ARTIFICIAL TRANSITIONIT SYMBOL Z/C POSITIONUlD 0.3M X .00(CETERLIE)

* E + .125 TO RIGfr~0 • .250 TO RIGHT

.125 TO LEFT

.250 TO LEFT0.2

-1.90 -0.50 0.00 0.50 1.00DISTANCE ALONG CHORD IN X/C

"" FIGURE 4B: SPANWISE DISTRIBUTION OF C WITH TURBULENT SEPARATION

p

bp

- :a i - * * a * *1 -

32

* I' ' aI' ' ' ' ' ,

* . . TiRe i

5.,.

PH PHASE LAG AT THE FUNDAMENTAL FREQUENCYA "-PA-14 DEGEES K-1.0S D E-700,0DE 4F. 4 ATIFICIAL TRONOSITION

LAG

N

% ,YBL VCPSTO

D~' E X .80(CENTERLI1E)

G 200. + .125 TO RIGHT* -. R 0.250 TO RIGHT

E .125 TO LEFT* E .250 TO LEFT

S

LOWER SURFACE URFACE(

-1.99 -9.50 0.90 0.50 1.0S.. DISTANCE ALONG CHORD IN X/C

FIGURE 4C: SPANWISE DISTRIBUTION OF PHASE LAG OF Cp WITH

TURBULENT SEPARATION

,9'* ".

4.." "-

33

CP

EA

-2.9 MOHLE5PI*W-1.4 DEG - RE-700,666

SYMBOL Zo'C POSITION

4-3.9 x .00(CTRLD)* .125 TO RIGHTO .25 TO RIGHTA .125 TO LEFT

-4.9 .25 TO LEFT

4. -5.99.99 0.29 0.49 9.69 0.130 1.90

-DISTAN4CE ALONG CHORZD; X.'C

* FIGURE 4D: SPANWISE DISTRIBUTION OF MEAN C FOR MASSIVE

LAMINAR SEPARATION

Ut • . - . - . . - --

34

0.20

HE TWO DIMENSIONALITY TESTI

* G 0.15 ALPHA-10 DEG - POSITION CHT K-2.0 - RE-700,000 - X/C-i.025/

A(I CENTERLINE

R 0.10 A Z/C - .125F - Z/C - .2500

* L

CH0RD 0.00

-0.050.00 0.20 0.40 9.60 0.80 1.00

MEAN U VELOCITY / MEAN EXTERNAL U VELOCITY

FIGURE 5A: SPANWISE DISTRIBUTION OF MEAN TANGENTIAL WAKE VELOCITY

.'4

"p.

35

HE TWO DIMENSIONALITY CHECK-IG 0.15 ALPHR-10 DEG - POSITION CHT K-2.0 - RE-700,00 X/C-i.025

1 CENTERLIN~EC 0.10 nZc -. 1H - Z/c - .2w00RD <-(U "V " > l

0.05

(VV > Aa (Uul

...00

-0. .995 0.0m 0.005 0.010 0.015 0.020N. T-RBL NE IMITEISITY, <U'U' >/Ue*Ue

FIGURE 5B: SPANWISE DISTRIBUTION OF TURBULENT CHARACTERISTICS

IN WAKE

4.

n.

-II

.°

"- 36

0.20H. H

"" E TWO DIMENSIONALITY CHECK*.-

'- G 0.15 ALPH-10 DEG - POSITION C

T K-2.0 - RE-700,000 - X/C-1.025

~'C- H CIENTERLIE;' 0 0.10 AZ/C - .125

R C'Z/C - .250D

0.05

0.00

I I I I I~ I I I I I I I I I I I ! I I-0.05

0.00 0.05 0.10 0.15 0.20 0.25AMPLITUDE OF THE FUNIAM.ENTAL HIAROIC OF <U> M'EWr Le

FIGURE 6A: SPANWISE DISTRIBUTION OF U IN WAKE

:'.5

'I.5.

.

V ,., . .- • '- - . -. • ' : " "- . . - -, - * " - - ~ ." .'. . .,, ''*- - ,.". ,' - " " ," ** . . ' -. ". ' " ". '""" - .' ." " ' " . .. o- , " ' " " " ." " "

'I, 37

0.20

H TWO DIMENSIONALITY CHEOEI ALPHA-10 DEGG 0.15 POSITION CH K-2.0T RE=? 7, 000

X/C=1.Q5 4 _

<U> 4 <V>C 10-H0RD

OcErITELIIESAZ/C - .125

OZ - .250

* S

*4,

-100. -5. 0. 50. 100. 150.PIE LAG OF T-E FUNDAENTAL HARMONIC (DEGREES)

FIGURE 6B: SPANWISE DISTRIBUTION OF PHASE OF U AND V IN WAKE

4, ,. " ,, '. , -.- ., . "., -," -- ,- , -., . " .-,, . -, - . -_ -. . . : . . .. - . , -. . -. -, -. .. . . • ,, . . .. ., . - - , , . ,.

"* 38

P-1.0

M

0.0

PR -1.0

* E

S -2.0 UPPERUSUFC MEAN~ SURFACE PRESSURES

R __

E-3.0 - ,PH10 DEG

* C ATTACHED FLOW0E -4.0 SYMBOL KF X 0.5

* F A 1.0* I-5.0 + 2.0

* c 02 3.9I 3 6.4

T

4.-7.0

0.0 0.20 0.48 0.60 0.80 1.0DISTANCE ALONG AIRFOIL CHORD, X/C

FIGURE 7: EFFECT OF "k" UPON C DISTRIBUTION IN ATTACHED FLOW

='

. .C.

* - .

* 4"* .* 'f q.Z

EALOESUFCm 0.0

pR -1.0UPESUFC-7E

S -2.0UR MEANt SURFACE PRESSUESE -3.0

C ALPH-1-0 DEGREES0 K-6.4E -4.0F 03 ATTACH-ED FLOWF x SEPARTED FLOW

* I -5.0C

E -6.0

T

0.00 0.20 0.40 0.60 0.60 1.00DISTANICE ALOMi AIRFOIL CHORD, X/C

FIGURE 8: EFFECT OF SEPARATION ON C AT K6-r.4p

..::~.. -. . ,.-- .

40

I .

7.0

.5R

-.v _ FLOW REGIME MAPD 6.0 RE-700, 000.. u NTURAL :

C TRNSITION

- _D 5.0

FRE 4.0

Q ~~ATTACHEDSEIADU STATE STATE:, E 3.0 _

~C"cy-

2.0

K BORDERLINE" ' 1.O __- STATE --- _

1S EDYNAMICSEPARATION

0.0

0.0 3.0 6.0 9.0 12.0 15.0 18.0AIRFOIL GEOMETRIC ANGLE OF ATTACK (DEGREES)

FIGURE 9: CHARACTERISTIC STATE WITH NATURAL TRANSITION (R e=700,000)

°.

• .

41

7.01

*17.9 . '1-~ -rr ._

E FLOW REGIME MAP.:

D 6.0 SE PARATEU ARTIFICIAL SEPARATEDC T4*SITIOt4 STATE

* ED 5.0

.4aF

R ATTACHEDE 4 . STATE BORDERLINEQE 3.0

Cy

2.0 DYNAMIC

," SEPARARATION

.. 0.9

0.0 3.0 6.0 9.0 12.0 15.0 18.0AIRFOIL GEOMETRIC ANGLE OF ATTACK (DEGREE-)

FIGURE 10: CHARACTERISTIC STATE4 ARTIFICIAL TRANSITION

hi

"..,. .... ,. . .. -.... -,., -. . .,....... :.-... ,....... ........... ,-,-....-..-.,-....-..-,,... . .... -.. ,, -.- ,•. .. :.:....,"

42

Z -. OF

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P PSUR APLITDE AT THE FlMENITIL FREQUENCYIE=7 9660W - ALPIHA-10 DEG - K-6.4

A NATURAL TRANSITIONMo. 8.5PL

13 ATTAC-ED FLOWT B. 200 x SEPARTED FLOWUDE

0.1

LOWAER U

8.0m - -

g -1.09 -9.58 0.68 0.58 1.06

DISTICE ALONG AIRFOIL CHORD, X/C

FIGURE 12: AMPLITUDE OF C AS A FUNCTION OF X/C FOR K-6.4p

_..44]

,4l"'p

.4-

. .. . . . . .. . . . ,. . . . . . . ... 4. . . . , . , :.;,

". ' ,," *.," - -- "5" . - 4 % ' , . % ", , ." "," ""•" , . '"""" . % " , % " " "

44

P.K- HA P! LA AT THEs F M.RrDIENTAL

"E FLRENCY

L 6M. - I-7008,0A HAP-1D DEG

2 G K-6.4RRAL DSTRANSITIONO

N E3 ATTACHED FLOW400. X SEPARTED FLOW

D

Rp

sue.

E- --E

-1.98 -6.56 6.00 0.50 1.98DISTAN1CE ALONG AIFOIL a-ORD, X/C

4FIGURE 13: DISTRIBUTION OF PHASE OF C pAT K=6.4

Je-* r

I'-.45

__ 0.350C

.F, R A'MLITU1DE AT THE FL4I'{ENTA.. F'REQLE-YA 9.309HRE -700,W00 - iLPI' -14 DEG - K-6.4

L X NATLRAL TRANSITION1 0.5 l ARTIFICIAL TRANSITION-TUDE S.200

9.158

0.10 -o.5o LOWER LPPERSURFACqI:E SURFACE

8.999-1.99 -.. 58 9.9 9.59 1.00

DISTAN1CE ALOtNG AIRFOIL CHORD, X/C

FIGURE 1'-: EFFECT OF TRANSITION ON AMPLITUDE OF Cp

d.P

4 ,''% '' - '.''':'-'"- - " " "" "" "' ", ", ' " ' ", ' .,", - - " . ..

46

H CALCULATED UPE SUIRAE PRESSURE RIASE VELOCITIESAS 1.00 SYMBOL FLlPIVA TRANSITIONE 1 10 NAWTRAL

a 3 12 NATURALV -w 12 ARTIFICIALE 0.80 x 14 NATRAL~L + 14 ARTIFICIAL00 15 NAUAC & 15 ARTIFICIAL.1 9.68 09 ISATIFICIAL.T

9.409

R

E '.2135 RE-700, 000 UL.ESS

T OTHERWiISE NOTED

8 .00P1 1.9 1.9 2.9 3.9 4.0 5.8 6.0 7.9

p REUCED FRECIENCY, K

FIGURE 15: PHASE VELOCITY AS A FUNCTION OF "K"

* .4

~~~ . . .~* . . .L . L~. - *

47

A ALH-15 DEG - K-2.0"+ 500. NFATURA:L TRANISITION

' LA' 48B. -- x RE41,-7188,O8G . + REtIl,M ,8W

200.

lee

pp

P 16 0. -- .*

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,'-.B-.5 .8 .014

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48

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AMPLITUDE AT TH-E FUNDAMENTAL FREQUJENCYA ALPHAM-15 D~EG -K-.M NATURAL TRPIVSITIONPLI x RE#-7900WOT0.100 + RE# -1, 000, 00UDE

-.-

p1p

o0o

-1.i9--05 8.98 0.5 1.90

DTSTI~iICE .N CHORD TNX/

FIGURE 16B: EFFECT OF REYNOLDS NUMBER ON AMPLITUDE OF CP

F,

49

p

q

G " I I, I..l T' ITI I,

L <0> RE70,8

-'L.4 Ps.

A NURFI A A ,SITI

0.

AE

EITAC SYMBOL AIKI l-:

A .

+ 2.0IP

N0 3.13 '6..

- OE SCCSUFC

R10 05 .005

FIUR 17.4 FET FXFNPASEAGORLC~aERsLN~Ac

..

.s

0.300

P AMPLITUDE AT TI-E r LMMENTA. FREXE:NCY

A R-700, 800 SYMBOL KMI 9.248 FLPHA~-15 DEG. X 0.5P N4T:1 A 1.0

L TRPZSITION + 2.0I '> 3.9T -3 6.4UD 0. 18E

0.129

I.0, ._

0.96I9.-e

-1.99 -. 59 0.09 0.50 1.09DISTINCE A..cG AIFOIL CHORD, X/C

FIGURE 17B: EFFECT OF K ON AMPLITUDE OF C

'pq8.-'i

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