AOSR ..TR 8 10 4,0 ,
tkj r)SR TR7
Air Force Office cf Scientific Research
Eglin Air Force Base
Grant *-AFOSR 78-3569-4
0Z(M
0 THE EFFECTS OF WARHEAD-INDUCED DAMAGE ON THE AEROELASTIC
lCHARACTERISTICS OF LIFTING SURFACES
VOLUME II - AERODYNAMIC EFFECTS
by Cj7 .
DEC 19 1980.J.C. Westkaemper
and AR. M. Chandrasekharan
Department of Aerospace-Engineeringand Engineering Mechanics
CENTER FOR AERONAUTICAL RESEARCH
Bureau of Engineering ResearchThe University of Texas at Austin'I
[AJ This da.%Ou.ut boon epp o0"t . " . for puibbc roic,'w,% o d s.1o; ,' .
0dtrlton 0 m93
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Re TIL. rfd Su i II IIe) S. TYPE OF REPORT & PERIOD COVERED
TJh ffects of Warhead-Induced Damage on the Final cientific ReportAeroelastic Characteristics of Lifting Surfaces 2-1---Zi to 3-1-80Volume II- Aerodynamic Effects 6. PERFOMrIbG ORG. REPORT NUMBER
7. AUTHOR(s) 8. CONTRACT OR GRANT NUMBER(')
J. C. Westkaemper AFOSR 78-3569R. Chandrasekharan
9. PfRFORMINf ORGANIZATIOJ NAMT TO AOOPEPS O. PROGRAM ELEMENT. PROJECT. TASK
Lenter TOr Reronau tica Iesearch AREA a WORK UNIT NUMBERS
Dept. of Aerospace Engr./Engineering M4chanicsThe University of Texas @ Austin/Austin TX 78712 //9Of ,c///96
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_4
L 18. SUPPLEMEI:TARY NOTES
19. KEY WORDS (Co,.tinue on ,ot'trse side If necessary nnd Identtify by block number) " ,
Damaged Lifting Surfaces. Drag Divergence
r Aeroelasticity & Ballastic Damage
* AV TRACT (Conti n s If neessarX and Identify hy block numbet)-es aerdnmic In a SUbSOnIC Wind tunnel to Determine the effects of damage on
'Ithe aerodynamic characteristics of a T-38 aircraft stabilator half. Six damageconfigurations wre used, one circular and the reaminder trapezoidal in planform,with areas of up to 2 percent of the stabilator area. The damage holes were allahead of the 50 percent chord line, with centers at 43, 60 and 75 percent span.
i ,-FT Surface pressure distributions and lift and drag coeffecients were measured.The 65A004 airfoil used is subject to leading edge separation which strongly in-
A fluenced the results. In the absence of separation, damage effects tended to-:
- _. ... --- 44, _ # t'A #JS,,4 ., __
X- -
WR WITY CLASSIFICATION OF THIS PAGE(Ir7in Daf Enlerod"
be'loalized and aerodynamic degradation was modest. With extensive separa-tion, the damage influence propagated completely across the span, with moresubstantial degradation. There was up to 300 percent ;ncrease on Doh butat moderate lift coefficients t ,e drag increase was generally in- D S
,.l significant. The decrease in was more consistent, ranging up to 10 percent- for the larger damage holes.
t
C *,
[ -I
IMf
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I.-.--- -- --
Air Force Office of Scientific Research
Eglin Air rorce Base
Grant FAAOSR-78-3 569
.THE EFFECTS OF yRHEAD-INDUCED DAMAGE ON THE.AEROELASTIC
CHARACTEr.STICS OF LIFTING SURFACESo
VOLUME I,- AERODYNAMIC EFFECTS
-by-
,--i- / 'I Y/ C J. Weetkaompe~r
R .MChandrasokharan
Department of Aerospace Engineering,and Engineering Mechanics
CENTER F~OR AERONAUTICAL RESEARCH _qT- Gr(A&I.uronu of Engineering Research
The Unive Sity of Texas at Austin t n ---------
T ,niz'Tnn/. __
,Julia 108A' ,t S .o S
ip",
TABLE OF CONTENTS
Page A
.Q
ACKNOLYLEDGEMENT.................. . . .... ... .. .. .. . .....
ABSTRACT .. ............................. a
INTRODUCTION................... . . ... . .. .. .. .. .......
TEST FACILITY. ........................... 2
MODEL .. ............. ................. 2
. . . . . . .
TEST CONDITIONS. .. ......................... 4
RESULTS. ................................
Pressure Measurements .. ................... 6Spanwise Lift Distribution. .. ................ 8
Direct Lift and Drag Measurements .. ............. 9
REFERENCES. ............... ............. 13
~ TABLES .. ............................. 14
.FIGURES. .. ............................17
APPENDIX I -THREE-DIMENSIONAL PLOTS. ............... 47
APPENDIX II -TABULATED DATA. .............. ..... 84
A1IR FORCE OFFICE OF SCIENTIFIC RESEARCH (APSC)
This technical re-oj't h-as been reviewed and isapproved f'or public rel ease IAIN APR .190-12 (7b).Distribution is unlimited.A. D. BLOSEPechnical InIfoematioi Officer
7
-
ACKNOWLEDGEMENT
I. ~This research was sponsored by the Vulnerability Assessments Group
of the Air Force Armament Laboratory, Eglin Air Force Base, through the
Air Force Office of Scientific Research. Mr. J.M. Heard was technical
monitor on the program carried out under Grants -AFOSR 78-3569 and 3569#
during the period February 1, 1978 through January-31.1980.
Austin, Texas
June, 1980
!1N
-iL~ I
MN
Li - ..
ABSTRACT
Tests were made in a subsonic wind tunnel to determine the effects
of damage on the aerodynamic characteristics of a T-38 aircraft stabilator
half. Six damage configurations were used, one circular and the remainder
trapezoidal in planform, with areas of up to 2 percent of the stabilator
area. The damage holes were all ahead of the 50 percent chord line, with
centers at 43, 60 and 75 percent span. Surface pressure distributions and
lift and drag coefficients were measured. The 65A004 airfoil used is sub-
ject to leading edge separation which strongly influenced the results.
In the absence of separation, damage effects tended tn be localized and
aerodynamic degradation was modest. With extensive separation, the damage
influence propagated completely across the span, with more substantial
degradation. There was up to 300 percent increase on CD , but at moderate
0' 1lift coefficients the drag increase was generally insignificant. The de-
crease in CL was more consistent, ranging up to 10 percent for the larger
damage holes.
4
-~ iii
5
V
INTRODUCTION
This report covers the second phase of a study of the effects of
damage on the aerodynamics of lifting surfaces. The work is part of a
larger study of the effect of damage on the aeroelastic characteristics
of lifting surfaces. In Reference 1, the report on the first phase of this
study, it was observed that suitably accurate aeroelastic predictions
could not be made because of the unknown changes in aerodynamic forces
caused by damage. A limited amount of two-dimensional test data and
results for one actual aircraft were found. These produced a very sparse
data base that did not include surface pressure measurements which would
aid in understanding the aerodynamics of damage holes or permit predictions
of the effects of holes other than those tested. In addition, the airfoil
sections were characteristic of subsonic aircraft, in contrast to the
current interest in supersonic aircraft.
As a consequence, a test program was initiated to measure lift
and drag coefficients and surface pressure distributions using a surplus
T-38 horizontal stabilizer with a limited but systematic series of damage
configurations. The phase covered herein is the subsonic, imcompressible
regime; planning is in progress for the next phase which will extend test-
ing to the transonic regime.
43
TEST FACILITY
All aerodynamic tests were made in the University of Texas
5 x 7 ft. subsonic wind tunnel at a Mach Number of 0.186 + .005. The
ti-nnel is an atmospheric-intake, open-circuit type, hence the test
zonditions vary slightly with seasonal variations in the weather. The
turbulence level at the test section was 0.6%. All data were recorded
using a Hewlett Packard 3052 programmable data acquisition system.
The pressure measurements were made using four 48-port Scannivalves,
each with a DRUCK PDCR22, I psid pressure transducer.
MODEL
The models used in all the aerodynamic tests were left-half,
T-38 stabilizers which had been removed from service because of local
delamination of the skin from the honeycomb core. The majority of the
delaminations were small enough in area to ignore aerodynamically, but
in one case a repair was made. The surface conditions on the stabilizers
were thus the same as on the T-38 aircraft; no attempt was made to obtain
an aerodynamically-smooth surface. A small triangular planform section
was added to the root of each stabilizer (Fig. 1) to give a root chord
perpendicular to the torque tube which was then used to mount the stabilizer
in the tunnel. This addition was necessary because the original root chord
was oriented parallel to the boattailed fuselage of the T-38. The torque
tube was supported by two pillow blocks mounted on a stand outside the
tunnel; an angle-of-attack drive was also attAched to the stand.
A-7-
3
Because of the honeycomb construction, the pressure taps were in-
stalled using stainless steel tubing cemeted to the lower-surface skin,
passing through the lower skin and honeycomb to the inner side of the
upper skin which contained the 0.81 mm diameter pressure orifices. Fabri-
. cation details are given in Ref. 1, and the location of the orifices is
listed in Table 1. The stabilizer airfoil section is a symnetrical one,
and the pressure data from the upper skin taps was measured at equal posi-
tive and negative angles of attack; data from the negative angles was used
in place of measurements on the lower skin surface which was distorted by
the pressure tubing. Thus, the data from the upper skin at +8 degrees,
for example, was combined with data from the same orifices at -8 degrees to
tobtain overall lift and pressure coefficients. This method is not com-
pletely rigorous because of the -4 degrees dihedral r the stabilizer,
bv: any error may be expected to be minor compared to the effects of Lhe
damage being studied.
The direct-measurerent forces were obtained from a stabilizer having
four-arm strain gage bridges at two stations on the cantilevered section of
the torque tube, between the tunnel wall and the first pillow block. Two
bridges were located in the axial-force plane and two in the normal-fr..rze
I plane; conversion to lift and drag coefficients was done by the comp-iter
I in the data acquisition system. This stabilizer had no pressure -'nstru-
mentation, hence data were obtained for both positive and negative angles
of attack.
-I
DAMAGE CONFIGURATIONS
One circulamr and five trapezoidal damage holes, as detailed in
Table 2, were tested. In all cases, the openings were perpendicular
to the plane of sywetry of the stabilizer. For -ost pressure distri-
bution measuremei.ts, the honeycomb cells exposed by cutting each hole
were filled with putty to produce a s=ooth-sided openin-. However,
after tests of the effect of filling the honeyco-b showed no difference,
the filling was discontinued. The hole areas ranged from 1/2 to 2
percent of the planform area of the tested stabilizer hal:. The trape-
zoidal ;hape was selected to aid in evaluating computer calculations cf
pressure distributions since curved hole shapes are more complex to model
in computer studies.
TEST CONI1TIONS
As previously noted, the tests were madc at an average Mach Nunber
of 0.186, uhich resulted in an average Reynolds Numvber of 5.29 :million
based on a mean aeredvnaric chord of 1.15- (45.15 in.). Corrections for
tunnel wall effects were =de using the method of Ref. 2. The corrected
angle of attack in degrees was
= + 3.27C.ML
The corrected lift coefficient was
CL =0.937 C_
and the corrected drag coefficient
% - CD + 0.035 Cj
where the subscript m indicates the measured value.
Oil flow visualization was by means of dye in SAE 20 motor oil.
At angles of attack where flow separation was present, model vibrations
4. and unsteady flow resulted in correspondingly unsteady pressure trans-
ducer and strain gage readings. These were recorded continuously on a
strip chart recorder, to determine the mean values. Studies were then
made to determine the number of digital-system readings which when
averaged gave a value equal to the dynamic mean. Although not as
precise a study as that repcrted in Ref. 3, the repeatability of data was
improved by approximately one order of magnitude. For pressure measure-
meats, five readings over a 1.5 second period were averaged, and for
strain gage (force) measurements, 60 readings over 60 seconds were
averaged. The indicated angle of attack range for pressure measurements A
was 0 to +100 in 2C increments, and for force from -12* to +12* in
10 increments.
The stabilizer was supported by a single, hollow steel torque
tube, and as a consequence, substantial vibration was initially observed
at the higher angles of attack where flow separation occurred. This
vibration was a significant factor in the unsteadiness of the data.
A small amount of lead shot was sealed in cavities at several positions
in each stabilizer to supply dynamic damping. This reduced the motion
of the tip to approximately + 0.25 inch, compared to + 0.75 inch without
damping.
4
- -- _ 4- , : '',d o I, I. '''ll A1 1 'l !'
6
RESULTS
Pressure Measurements
The results of all the pressure tests are presented in the Appen-
dices in two forms. Appendix 1 consists of plots in three-dimensional
form of AC for all six configurations for which data were taken. Asp
noted previously, pressure taps were installed on the upper skin surfaceonly, thus ACp was obtained by combining data for runs made at equal
positive and negative angles of attack, e.g. + 2, + 4, etc. Although
equal positive and negative geometric angles of attack were used, the
tunnel corrections produced some minor deviations in actual angles of
attack; this may be seen in Appendix II which is a tabulation of all
pressure data. For example, for the undamaged case, + 80 geometric
- angle resulted in + 9.80 and - 10.10 after wall corrections were applied.
The variation is primarily the result of uncertainty in setting zero
angle of attack. For the pressure model, this was done by aligning the
tip chord with the tunnel axis. Subsequent testing with the force model
f. disclosed some misalignment.
The sharp leading edge of the thin 65A004 airfoil causes a
leading edge separation bubble to form at approximately 40 angle of
attack (Ref. 4) and the length of the bubble increases with increasing
angle of attack. As a consequence the data obtained without separation
were generally of better quality than when separation and reverse flow
were present. Separation also influenced the effects of damage on
pressure distributions. Without separation, as in Fig. 2, there was
little spanwise flow, and pressure changes were concentrated ahead of
and aft of the damage. Separation produced both spanwise and reverse
A- --.-.- --
7777A-
7
flow (Fig. 3), and the strongest damage influence was observed outboard
and forward of the hole for this case. The damage also substantially
reduced the spanwise and reverse flow in some cases, as shown in Figures
3 to 5. The regions of perturbed pressures were small for the attached
flow case, and generally were limited to a distance ahead of and behind
the hole approximately equal to the hole chordwise dimension. For holes
centered at 75% span with separated flow, the influence was concentrated
at the leading edge and extended approximately to the stabilizer tip.
The hole centered at 44% span caused less change .n pressure than did the
same area hole at 75% span, and influenced a smaller region of the skin.
Figure 6 shows the chordwise pressure distribution at 75% span
for the undamaged stabilizer and the 1% area trapezoidal hole, for an
angle of attack of 2.40. The undamaged-case data are consistent with
the two-dimensional results of Reference 4. For the 1% hole which had a
length of 20% chord, the influence is concentrated in a region of 10%
chord ahead of and behind the hole. Immediately aft of the hole, the
pressure is reduced on both the top and bottom surfaces. A reduction is
I also observed ahead of the hole on the lower surface. These are all com-
patible with the expected flow into and out of the cavity formed by the
damage. (The data points at 20% chord are the "base" pressure at the
center of the forward face of the cavity.) Figure 7 shows similar data
for a hole of 2% area, with similar trends but a larger change on the
lower ,urface. Again, the pressure plotted at 10% chord is the base
pressure within the cavity.
Ar
8
Figure 8 shows the influence of the 1% hole at 83.5% span; com-
parison with Figure 6 indicates only minor changes at this location,
primarily on the upper surface. Inboard of the same hole, at 67% span,
the perturbations are also small, as seen in Figure 9. This is consis-
tent with the earlier observation that there is limited spa-iwise propa-
gation of damage effects at lower angles of attac', where the flow is
not separated.
Figures 10, 11 and 12 show the pressure distribution for the 1%
hole, at 83.5, 75 and 67% span, and 9.80 angle of attack. The influence
of separation is evident since the damage-induced disturbances are
stronger at the outboard position than at the damage station or the
inboard location. However the local lift from integration of the pressures
is diminished inboard of the damage as will be shown in detail later.
SPANiSE LIFT DISTRIBUTION
The surface pressure distributions were integrated for several
representative cases in order to show the spanwise lift distribution.
The local lift coefficient C is shown in Figures 13 through 16 in the
$ 1
same form as used in References 1, i.e. referred to the mean geometric
chord, c, and to the angle of attack in radians. The data for the un-
damaged case is included for comparison.
Figures 13 and 14 present the results for the 1% and 2% trapezoidal
holes at 75% span, based on pressure data at 2.40 angle of attack. The
localized nature of the disturbance is again evident at this angle, for
which the flow is attached. The 1% hole reduced the total lift by 2.1%,
32
r9
whereas the theoretical prediction of Reference 1 was approximately 5% for
a very similar planform. Figure 15 presents the results obtained at an
angle of attack of 9.80, at which substantial flow separation exists. The
damage effect is seen to propagate to the row of pressure taps nearest the
root and thus is substantially stronger than at the lower angle of attack.
Data for the 1.96% hole located at 43% span, with a = 2.4' is shown in
Figure 16. This hole was between pressure-tAp rows 8 and 9, so the lift
at the hole centerline was obtained by spanvzise interpolation of pressures
prior to integration for lift. The loss .n lift of 2.6% is only slightly
higher than for the 1% hole at 75% span.
DIRECT LIFT AND DRAG MEASUREIENTS
As noted in Reference 1, investigation of the aeroelastic effects
indicated that damage-induced drag is a possible source of sLructural11 failure. For this reason, a second T-38 stabilator half was instrumented
with strain gages to directly measure normal and chordwise forces which
were then coverted to lift and drag coefficients by the data system com-
puter. No pressure instrumentation was installed in this stabilator. For
both pressure and force tests, the angle of attack was varied with a lever
arm bolted to the stabilator torque tube using pre-existing holes in the
tube. The zero angle of attack position was initially determined with the
pressure model by aligning the symmetrical airfoil with the tunnel axis.
This same setting was used for the force tests; however, it was found during V
these tests that zero lift did not correspond to the zero angle of attack
setting. Consequently there is a slight offset in the results, as shown
it. Table 3 which gives the results of the force tests, in equation form.
. I -,
- 10
These equations and the test data are shown in Figures 17 through 28 as C1
vs a and C vs C.D. L*
For all d.amage configurations, Table 3 shows an increase in zero-
tslift drag, C although the relationship as shown in Figure 29 is sensitive
I to the orientation of the damage as well as the size. The four cases
indicated by the circular symbols all had the same spanwise dimension; the
area was progressively increased by increasing the chordwise dimension of
the damage hole. The approximate ratios vf chordwise to spanwise dimen-
sion were 1, 1.5, 2.0 and 2.7 for the 0.5% to 2% area holes. The results
indicate that C decreases as this hole "fineness ratio" exceeds 2. By
contrast, the 2% spanwise damage which had a fineness ratio of 0.8, i.e.
1 its long dimension was oriented spanwise, resulted in a C which was
nearly twice as large as for the 2% chordwise hole, even though the actual
dimensions were nearly the same. This characteristic is evident in Figure
30 for small lift coefficients as well.
It is likely that increased C is partially the result of reduced
pressure on the cavity forward face, i.e. base pressure, and of increased
pressure on the aft Lace. In several instances these two pressures were
measured. As seen in Figures 6 and 7, a negative base pressure coefficient
was observed. The pressure on the rear face was found to be essentially
the free-stream dynamic pressure. By this rationale, spanwise holes would
increase CD by more than equal chordwise holes, which is the trend in0
Figures 29 and 30. However, the uncertainty in the data at these low drag
levels does not justify drawing more exact conclusions.
•A
=M t __ -
Reference 5 reports the results of measurements of the effect of
circular holes on drag, using a two-dimensional model having a NACA
65 -012 airfoil section; these results are discussed in some detail in1
Reference 1. There were three configurations tested which were circular
holes at 25% chord. For these, the C based on hole area was -0.1,D 0
+0.1 and +1.1. The results from the present tests was +0.38 for the
circular hole, and +0.40 for the 1% area trapezoidal hole (which had a
fineness ratio of 1.5). These two most nearly correspond to the damage
of Reference 5, and the results fall close to the center of the range
reported in that reference.
The influence of damage on drag is summarized in Figure 30 which
shows the effect of orientation of 2% holes, and in Figure 31 which shows
the effect of chordwise holes of 1 and 2%. Both figures demonstrate that
at higher lift coefficients, the increases in drag diminish to the point
where they are obscured by the uncertainty in the data. In general, the
increase was less than 10%, with only the 2% spanwise hole showing a
consistent increase. This is contrary to the results of Reference 5, in
which both CD and K of the parabolic drag polar equation were found to
increase.
Figure 32 shows typical effects of damage on lift coefficients,
at angles of attack below and above the separation angle; both force and
pressure data are included. Generally, the reduction in CL was small and
approximately constant up to a = 50, beyond which the reduction increased
markedly to a peak at 100 or 11, followed by a decrease. There was
substantial scatter in the force data, particularly for the smaller damage
i - -- -I - "-" - "
12
cases, because the magnitude of the changes was small compared to the full-
scale capability of the strain-gage measuring system. This was parti-
cularly true at smaller angles of attack. At a = 2.40, for example, the
lift force of the undamaged stabilator was about 30 kg and the damage
effect was about 4 kg, whereas the maximum lift force was approximately
275kg. As seen in Figure 32, the integrated pressure distribution gave a
more consistent result than did the force data; at a = 2.40 the change in
the lift curve slope of Table 3 was also a good indicatoi, although it
under-predicts the effect in the presence of separated flow as at a 9.80.
I.I
43b:79_d3I
SI
= --- r ~ - ~ = ~ ~ S V - - ' v--- if
--------
t. A
13
REFERENCES
a • 1. Scott, D.S., et al., "The influence of Ballistic Damage on the Aero-elastic Characteristics of Lifting Surfaces:, AFOSR TR 80-0220,May, 1979.
2. Pope, A., and Harper, J.J., Low Speed Wind Tunnel Testing, JohnWiley & Sons, New York, 1966.
3. Muhlstein, L. Jr. and Coe, C.F., "Integration Time Required to ExtractS4 Accurate Data from Transonic Wind-Tunnel Tests," J. Aircraft,Vol. 16, Sept. 1979, pp. 620-625.
4. Gray, V.H., and von Glahn, U.H., "Aerodynamic Effects Caused by Icingof an Unswept NACA 65A004 Airfoil," NACA Technical Note 4155,Feb., 1958.
5. Shatz, R.E., "Aerodynamic Vulnerability of Aircraft", Final ReportNo. Gl-634-G-14, Cornell Aeronautical Laboratory Inc., Mar.31, 1952.
-
14
TABLE 1
PRESSURE TAP LOCATIONS
ROW # % SEMISPAN
91.7
2 83.5
3 79.3
4 75.2
5 71.1
6 66.9
7 58.7
8 50.4
9 35.8
10 17.4
In each row, chordwise tap locations, numbered from the
leading edge, were at the following positions in percent of
the local chord: 0, 1.25, 2.5, 5.0, 10, 15, 20, 30, 40, 50,
60, 70, 80, 90, 95.
L
- - - - - - -t£. r
15
TABLE 2
DAMAGE CONFIGURATIONS AND DIMENSIONS
SHAPE AREA HOLE CENTER LOCATION ORIENTATION, TYPE DATA% % Span % Chord Long Axis
Circle 0.5 75 25 --- Pr., F
Trapezoidal 1.0 75 27.2 Chordwise Pr., F
Trapezoidal 1.5 75 22.5 Chordwise Pr., F
Trapezoidal 2.0 75 27.1 Chordwise Pr., F
Trapezoidal 1.96 43.4 19.9 Spanwise Pressure
Trapezoidal 2.0 58.9 16.5 Spanwise Force
HOLE HOLE EDGE LOCATIONSAREA Percent Span Percent Chord
1.0 71.6 78.6 17.4 37.01.5 8.0
iI2.0 46.2
II 1.96 36,9I 49.8 12.8 27.0
2.0 47.8 69.9 11.5 21.4
2. _ __ _ _ __ _ _ _ _ _ _ _
7: ______ _______ ________ _______
:1 16
00 0 0 0 0 -
0 - n Lnc
0 0. 0r ~ 0 C)
0 0 n 0 0 0
* .1
'0~ LA ~ ( N ."q
0 a~( *~. 2 2 Iej p to C 0 cEU 0a U - 4 ( ( V
~-~ -- -Eto c N* "! UI* 6*.e
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-4 = * o* -
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ca_:I I I I I I I I II-
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cj E 0 i ra
0 -H a
18
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19
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~ FIGURE 4.
OIL FLOW PATTERN, 1.5% HOLE, a =9.80
I m__; M-
FIGURE 5.OIL FLOW PATTERN, 1.96% HOLE, a 9.80
~S
uAM,
20
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' . 377 . 2 ). -1 ..3 X) 0 . 2 0 . A.2 0- .133
22 e% n,30 ?.7 1.1 0 2.21 1 ) '1.-) . 3 9 -97 r" '7n1-. 2 0. .- 07 ?4e 10 .. 0!')1 0.1 n . '.51 .32 "1 . ,0.252
_ f7 0S -00 15-9 P ~ 2'' 1.11 1 7V~ ' 1 *.1 3 Iq!, 2.f) In -01,- 0 I 1 1 -1 0'1 010 5 ) ')i7 0 ..1 133
10;; -0.033c -I12 A~.'2 -200 n02 -162 Of.IO 0.075 f! .029
-- C..,o , n, 1 4s~~~ .,,1 1)) . 9.3 ";,'
l -1 .-132
2 n ,. 4 1Pi 0 3 3
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Tnci ,--nce: -7.1 , 5 . .,- oe iati n:1.0 Ww-- .. , row I Po,,,? c . . r .,". [ow -.%w , o 7, , ,,. , q -'-o 9 ow M
] nwci C': ." (.5. .f ,v75%iro25..,3
2 - '5 , - f i. 1 0. 1 -1 - P72 5 O n %n g , - = '55 - 1 '71 fl. , 6 4 ' A% 0 "5
4 .' , 0 ~ 0. % 0 "l * 22' 1 ' q "'* g "-1 " " ' C ) A4
-0.035 O.Of] - .03V -0.1~1 rj.075 I 'g r'g2 ' 0. )2 fl12 0.04 0. , . V1 , ..2t-1 ") . n7, _ j;1;) , v.
61 0. 5 0.0?1 -r.,i 1 - .99% -- 0 3 fl.137 0 .0c; oo 0 .800*flI.~~~~~~ C,/; 11 ." -- O7' r,73 .- 2~
H. 3P.5 -0.1 -. 07 .93-.0 -300 0129 7 0 -11) 900712 -0.042 -0.02;' -0.026 -. ),3 -0.019 -r.I11 0.00, 0.103 -S.0l1 0 016
3.3 -0.037 -0.031 -. 0 25 -0.9'I -0.017 -0.01 1 -0.009 -9. 03 0.009 0 .01I4 -0.043 -0.034 -0.016 -C.003 -0.018 -0.005 0.003 -0.005 9.015 0 .02115 -0.019 -0.002 0.007 0.018 0.0 8 -0.000 0.00S 0.002 0.010 0 .030
Incidence: -2.5 d!ec. R'mq .Deviation: 0.040Tan Row 1 Row 2 Row 3 Pcw 4 Row 5 Pow 5 Row 7 Pow 8 Pow 9 Powl0
1 -0.448 -0.976 -0.339 -0.966 -0.799 -1.336 -1.500 -1.210 -0.5652 0.455 0.452 0.407 0.392 0.3R7 0.346 0.419 0.425 0.381 0.3793 0.248 0.259 0.259 0.264 0.260 0.230 0.297 0.285 0.2604 0.143 0.178 0.159 0.161 0.190 0.135 0.193 0.205 0.217 0.18395 0.061 0.092 0.050 0.037 0.075 0.073 0.098 0.0qg 0.100 0.12216 0.025 0.050 -0.00q -0.082 -0.005 0.041 0.051 0.055 0.069 0.0617 -0.007 0.028 0.030 -- -0.108 0.013 0.032 0.028 0.036 --8 -0.039 -0.00-0.00t 0.001 0.0009 -0.066 -0.046 -. 121 -0.309 -0.075 -0.020 -0.02 -0 0 2 -0.01) -0.0221
10 -0.071 -0.061 -0.045 -0.053 -0.053 -0.039 -0.043 -0.046 -0.022 -0.033111 -0.073 -0.960 -0.047 -0.04? -0.042 -0.941 -0.041 -0.031 -0.032 -0.042l12 -0.058 -0.037 -0.041 -0.039 -0.037 -0.031 -0.027 -0.016 -0.027 -0.020-13 -0.042 -0.033 -f.031 -0.022 -0.026 -). 021 -0.018 -0.015 -0.006 -0 .00414 -0.027 -0.021 -0. 903 -0.001 -n.Oll -f.002 0.012 -0. 001 0.013 0 .01415 -0. 005 0.01! 0.021 0.0?4 1.03.3 3.00t 0.-107 0.001 0.013 3. 0211
1 ncide ce: , ? , "1ei t o 0.033a' 3 "e-; , , ,; " "o 7 Pow " "o q Pow;A07I .. 53 0..3 0.3P2 0i 41 0 .7 10.i5r 0.S% 9.S14 0.622 -2 0.O'6 0.SE 0.0- -51.'?7 -1.0:5 -0.112 - L.hl 0.07; 0 .11. 0 .02,3 0.024 0.013 -0.013 '1.052 0. 1 " 0.311 0.053 0.03 3.06A --4 -0. 1 0.030 - .033 0.011 . 005 - 32 -0.)00 .. 0913 0 0215 -9. 53.9 - .. -.. 07 ) V 1 57 - 1, Q 5 0. - 3 0 - .,) A - 15 - .0 -5070 -0.4 - ..086 -0. 1; -3 .01 -,).)7- -0.070 -0.05') -0.052 - 35-f,
7 -0.076 -0.041 -0.001 -- -3.155 -0.076 -0.074 -0.66 -0.076S -0.093 -0.068 0.53 -- 0.146 -0.075 -0.0 035 -0.05 -0.086 -0 056
-0.093 -0.105 -0.231 -92. 1 -0 -0.09! :)0;0 -0.00? -0.093 -90 1310 -0 .3Z -0.102 -0 .101 -3.120 - .113 -0 1.0 -0. 0, -0.9 7 -0.09i -0 032111 -0.035 -0.)4 -. 306 - 0.,1 -1.177 -0.33 -n.0P6 -0.071 -0.08 9 .67412 -0. 64 -0.05q -6..06G -0.03,. .070 -0 '1 -0.03 -0 r.1C7 -0.071 -0 0413 -0 .37 -0.042 -.. ,37 -n. 37- 0 0,A4 -0.3 - -0.045 -. 94 -0. 02 -0. 0214 -0.023 -0. r1 -(r.00-% .011 -0. f1.7 -0.011 -009 -0.023 -0 .(0G 3 0015 0.007 C.022 0.0!1 0.019 0.038 0.004 -0.003 -0.005 -0.004 0.017
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2 -,,.-,7,3, 0.33 . - .I' -. :I1 i., .- .,. "-K ; ".~-, " ).3" :;.] -- .
2 -0..24 -0.22, - -C.4 -C.";i -3.237 -3.%: --22:;; -0.1 -3 3 3 -0.293 -9 .2017 -..- 0 -t:.13. -0).221 -').2-'2 -K .U -". 2.01 -. .'> -V.9.5 -- 246-0.179 _n ,'- _..2l 3 3 -3*?,0 -? "-" -e V9- -n "-,. -O - 57 - 01 -9.l3 0 C .1)1 -- ;9 -0.2" -1* -7; ̂ 9r -.... V-K~ -
T.lQ A
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3;- 0~ .. 31 2-J -713 -02 _,.0 -'K>4 -4- -4.0!7 -C- -. 2 2"% 0 2 ' =- -.3152
5 0 0u.i -192 C 1' -1 -7, 2314.10 .1
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-- 122O -1.!2131 - 1 ",- .- 17 -'. o",1 -. s -"h "'' --- : "" -3.-'12
3! -0.37: -¢.!27 -0.120 -'.! -. 172 -7 'K- -- 01 ..
4 '~ 'Y -. ~ -. .7. - -- 7- -. , . -o~!2 -0.303 -0.3",7 -0-1 -, " A. o. ." ', - -' - e
13 -0.951 -P.2 -r.9 4 -0A'! -3 _.31' _.3. -333 " -. -3.053
-0.25 - .222 -2 0- -525 n R .2 0O2 027-.i -0.2 -.214 32-0.137 -- ? -3.934, -0.2 :.-. --. ?U- 0.223,, -0.0!4 i
.2 -2.13-0.12? -0.113 -,.'2, -0..2. -.. 2" -,.11 -9.115 -0.122 -0 .523 -0.5 _..9P. -0.07 -. *31 -0.,75 -0.0-! -,.- , -.. 2 -0.073 -1 .32
5 -314,-0.053 -0. t -3 7 - ,.0 ] - -. 4 _.0. -_. 3t - .9 "" - '.0'" - ' .- ',
13 _0.0.2', _-,.2,l' -0.2 % -3. t. -',0., I , -).03 -(,.01 , -0].010, -0.." ) 0< - 0. _
1 0_9-.2-.~ l07-.7 -0. " -i .2i' -01 -1.2-% -
--0.0252 - -.3 -2. 2 . 0 . - 7 0 -1 5
-0.220 --. .4, -(..1-' -G- - . - . 5 - 1 .0.23. -0.-0.235 0.5 7 " -0. -7 -7 .... -07.5 - '. 0_- .0 -
10 -0. 173 -0.1. -. 277 - :024 -j32 -0.V- -0.317 -0.593 -0.1 7 -0.194i 7 -0.12 -0.176 -. -. -. 17- -7.4 -. 77 -0. 57 -3.153 -0.1671.2 -0. ! -0.1 . -0.15 -,,. i5 - 2.7 -4. 121 -0.1 -. !5 -0.156 -0 .11513 -0.,9 6 - C.07 -C7.l -0.1. 70 -0. -3.31 -0. 2S -0 on C .73 -0 0 714 3 . -0.053 -. 07- -0.031 -7 2 -"."O7 -0.072 -0. 31 , 0(31-0 02 '415 - . - W.03 -0 P. r - 002 -* -0."40 -0 1,lc -0 007 0 004-
1 nci:: e r.. c?-: r".'e ti n 0.16 7
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"7 -0 .- 2 5 6 51 -2. , . -- 7' ,q -: .. 4 0 0. 3-q - 1]9 -- {; q -0.353 -0.35" 61 ="3 -- -3 2 9 -)2 ' 9 132 (.1 7-1.. qt - . :
11 -0,.216 t.3.. .. .. ... -,.9 2 22 22"-1iel
12 1o"', -o 6 -0. 157 - 1. 6 -0 . 1 "7 -,'1. 1'' -0.1s; C.1 -0.].-3-6 -0O.i1-A.513 -0. 1 ,2 "2 -C. ' 6 -0 . 12 0 -0 .121 - -.. 13 - 12 1 1 0" - . 1,03 - 'O3{
14 -0.13]7 -0.08.3 - 0. 071 -n 07'i - C-. rn7 2 -(1. C7 , -" .07 - 0. 0 31 0049C15 -0. 086 -0.043 - 0.f,4 5 -G.0,15 -0.023 -,.9 - O 0.O04 - (.n-331 . 0- 2.,.- - 0. 0!0
*i.. . = I7 -- ' 0 T! S - .. .--. ' n -- -1 1 . e o o
7 '. , -'-1 7 - . - -
7- -7 .0 3 -I "''- -f.l'1 --l -34 " - J' -.a ._ . .:_' 3 - . l ----
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-' - 27 o,
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72 -0.3 3- -0.3' -¢..73 -3' -. - - . 3 33 1-
11 - 0.75 -- 2"57 - 0 7 C - _ -- - : r 2 55 - 0. 1 t - 0 .2 -. 1 47
14 -0.42" -0.3 . - 0.. , .. --1 -. 11 -. 3';.7 -0.-17-12 -0.2 .-0 .. 1 -0. -O.3! -(. 1'9 C.. -. 3 -2 1 _ - .2 -n 3
1.7 270 - 3... . - . .... -2.14 -0. 2.5 -0.217 -0.213 -1.21 -. 7' - ' -. 1" -0.121 -1.075 -0.077
' 1 -0. 22 -3., :q -O.-J]1 -07.'33" -9.7&7 -0.* V' -1.002 _]l-.,7 1 -1.007 --
, -G.P21 ~~o~os~ ~P. , '77. n I -N7 ~*''-C iM 1.0' I2 -- 7. 03 -0.71n - .7 "'e -n.. ' -'. - ': 1 - 0.-5" -2.2'-
3 -0.774 -0. - . -.. _ -A' - 73 -P..g3 -].l52 - -30
11 -0.015 _0.A 7 0.604-,i _ 0l -. '. -O.$17 -0, -.- 57 -0 .7 ._ 32
12-3.47 -3.50. _..,57 -053. . -2.-. -- -.. 5 -.. 2 -1.3"' -.. 2.7
17 0, . qT0 51 7n ,,V- .7 -r., I 1 1 7 0. -,f- ,.- f- 7 1: 7 1o 4
0] . 7 1"). " - 0. -6 0. ,-', .n e .- -f'j;. A0 'I .. "7 n 1 4 .oj7 _n,. CV). -0 . 2 3 ,-'
12 -0.674 - 0. 506 - 0. 5 A 2 - 0. 5 - ' , -5i - ." - . I - -0.452 -0. 309 - 0.- 2-57
13 -0.432 -0.449 -0.49 -0.17 -C - .4 ,, 0 --. 4.. -0.371 -0.209 -O.132
14 -0.357 -0.401 -0.415 -0.404 -0.419 -0.407 -0.345 -0.212 -0.149 -. 104
15 -0.366 -0.37A -0.380 -0.382 -0.388 -0.390 -0.304 -0.254 -0.115 -0.06!
I'C
7 7
t
- - - L -,
1.5% TVDEZOIDAL IiOT,3 e75%5S,25%C
Incidence:-12.4 dec. r'iq neviF ion: 0.007,Pr Roa 1. Pow 2 ow 3 P-w .. Pow 5 i'ow 6 Row 7 -cw 3 Dow !z oW,:
-1.551 -1.950 08 -. 007 -0.q12 -0..F05 -0.901 -1.057 -1.44. -
2 0.655 0.682 0.610 0.524 0.577 -0.623 0.670 0.616 0.720 3.7523 0.609 0.613 0.459 0.376 0. '69 0.549 0.599 0.620 0.6584 0.492 0.503 0.252 0.096 0.307 0.436 0.499 0.529 0.555 0.569
5 0.347 0.387 0.043 -0.991 -0.143 0.215 0.372 0.306 0.419 0.4306 0.255 0.331 0.115 -- -0.297 0.173 0.290 0.314 0.336 0. 364
7 0.138 0.298 0.156 -- -0.2,4 0.132 0.233 0.259 0.281 --
8 0.0q6 0.244 A.364 0.457 -0.065 0.130 0.119 0-1'30 0.197 0.210
9 0.031 0.150 0.282 0.453 0.319 0.15- 0.112 0.118 0.129 0.143
10 -0.019 0.062 0.110 0.140 0.144 0.112 0.071 0.070 0.085 0.094
11 -0.067 -0.002 0.023 0.036 0.055 0.052 0.032 0.045 0.049 0.054
12 -0.00-8 -0.039 -0.027 -0.020 -0.015 -0.003 -0.001 0.015 0.020 0.049
13 -0.104 -0.084 -0.080 -0.070 -0.064 -0.059 -0.048 -0.025 0.011 0.0314 -0.143 -0.144 -0.137 -0.13R -0.139 -0.124 -0.111 -O.O6 -0.016 0.013
15 -0.147 -0.161 -0.173 -0. 166 -0.146 -0.1(0 -0.163 -(.1 3- -0.054 0.002
Incidence: -9.9 deg. D-3 Deviations: 0.019
Tao Pow I Row 2 Pow 3 Pow I c, 5 Pc-, 6 'vow 7 Pow Z qow q rowlF 1 -1.487 -2.341 0.911 -0.q28 -0.79q -0.735 -0.-2q -1.097 -1.5032 0.673 0.6R3 0.596 0.94 0.564 0.+ ,O n.657 0.490 0.702 0.717
3 0.582 0.500 0.434 0.134 0.441 0.51 0.5;4 0.5c! 01.4-.40.454 0 262 0.233 0.0 8i 2n 0.2 lA ' f) 0 :350 0. -. . ... 5 A. .0 . 66+ , 3. O:q .. ..- 5
5 0.309 0.345 0.077 c -,"1 l 2.. 3.- 2"- -1 .. 1 1 3 - 3.155
6 0. 22 l"'.21 0. 12.4 -0 n1i 0. 5 .1. I'l . -1 7 1 .3. 01 0 3. 1)7 0.163 0.25 3.1 3 -- -0.230 .l " 3.1) 0.123 0.237
0.052 3.211 0.333 0.553 -0.033 .) 1 7 9.122 0 .II 0.1 3 0.1J
= 0.327 .130 0.2..2 0.3' -0.2-":0.i "0 0'7 0 .0' 0.I05 3 .1n10 -0.005 0.057 10.100 0.3 ) . - e A i P. 0 5 n 07 7 011 -0.041 0. f0) 0.033 0.053 0.15, ').* -' "3.012 ,. 3 3.41 .
12 -0.051 -0.91 -0.00- 0..00P 0.032 1.fl 5 0.)21 .? 0.f22 2-113 -C.0 , -,-.12" _-.02. -, -'3 -.. . 0.. 2 . 11,...14 - 2. . -0. 3 c3 -G.076 -- . 7 -0. -1.047 -0.031 .01A .G,215 -0.0.2 -0. Wl -0.0F2 -0.'q.1 -1 .c; 0. ...
I ncilence: -7. -ei. fl'3D':i~t'): 0.010e, 1 2 7 -0 - . " - N
1 -1.133 -I.035; ] .q3 -0. 'l1 -'0.'01 -'.1'15 -i .90 -i. n" -1 .343 -
2 . 7 0.77. .5Iq 0. :8 0.:33 1. " n .. ,. 6- 1 .-"5 13 0.521 0.537 0.-11 '.310 0. 105 31 . .52 0- 1 54 0.3Pn. 0.413 0.220 0.067 0.251 1.360 0.414 0.43 -1 42 9 0.1 3.5 0.252 0.2(3 0.106 -0.7.! -0.10 q 9.214 0.2R02 0.2 n 0.301 1?6 0.175 0.237 0.12'3-0.177 1" c2 0 .210 0.225 0 .234 0 . i67 0.122 0.107 0.138 -- -3.l'1 14 .8)7 0.;- . .I ; 0.I :7 -
! ,.051 0. iI6 0.7")2 .0(I I " .1 , 3 0.091) 02. 7 0 123 0 .1!.( 0.017 0.398 0.l~fl 3.9L' 0.2 12 7.12 1.076 , f) 17 G.97 3.)k " 10 -0.008 0.04? 0.090 0.10 a .14 ... 8 k .. .0" .84 0t.1 - 0 ) .1" 0 _4- 1 . , . n 8 001 0 .8 5 : 0 0 . 4 0 . ".3
11 -0.031 0.002 .07 0.0 1 0.052 1.0-2 1.137 . ' 7.... . 312 -0.033 -0.002 0.012 0 P:17 .011 0.033 .27 1 ,2" - 0-.02-- 0.03-
13 -0.,31 -0.0l3 -0.005 002 0.000 0.11 3.013 3.117 0.032 G .03714 -0.04- -0.)34 -. 3.0110 -0.13 -0.020 -1.005 0.005 0.0 o i.02l 9.03613 -0.035 -0.017 -0.011 -0.007 0.009 -0.^17 -0.003 1.10 , "..n3 0 t33
Sa M
1~~~-* .5% --! 7 I - T 251
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5 25 1" ' Z T '[ 20,.,: t- 5 121'1 -
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35 0.OCS0.01 0.2 7 .3 3.A -- 1' 0.1 -171 7.1
3 . .o 1 2 r 3 c, 4 !;o, S ,. . 7 '-,A ( 2 1 1I7 1 1
1 -_.3, - ? 271 -7 - -07 ---1.37--_ -1 -0 " --
2 19.427 0. 13- . 3 .5 0'00351.5 .7 i l37
3 0.51 0.S43 0.07A 0.177 .71" .' ,.n ".C. 4 1. 1. ,
1 0.0 3 0.1 0.003 ,.0n. ,.11 '.... , 2 0. 7 7 0.0)-
12- 0. 3 -,*, 0 . * 0 - .0 . 219' 0 .01 ,1 . I .1 0 )7 f .')I -0
13 -0.0270 0 *3 n 0 .002 0 .001 ,1! 1. 0. 0 03 MI74 -(0.02 -0.0S 0.001 - -3 .. 01 . 0 10 . C; I . 7- 0.2.7
3 -0.037 0.017 0.-2 3. 0.. '0.. 02. 0 __
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14 -0.030 -0.009 0.00!7 0.00 ).00 0.010 o.01y (0. !] 0..5 0.02
15 0 .02. 0.17 . .3 .a, q 0 2 0 07 8.9 - .! .
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7 02 0 P O."e .5 l> "- 5 7 -0 0 37
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4 . 0.0 C... 37 -0.Q."1 Q. -. 7 043-
L7 -0.07 -0.03" 0r .2 -- -0.02 -,.0S -0.077" -Cl .37 .... 7 -
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. 2-00:." -. O,:-0.073 -0.0% -0.02 -3.3;-~ _0.5 _13.0-r 43 --.7 g13 -0.01' -4.'3-1 -3.033 _n.1 0 , '". 3'. 3. 0 ,.3$ _- .. . .. _,. 0 f3 _3 -~ -3.'17
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7 -0.074 -0. 0 1P 0.023 -- -0.025 - 0. 0 55 -0077 V A 7 i -0.0-' -- .'I -. ".. £ - S0 6 0n. Or%: 0.7 r7 0 .1n-, -3 .~ -01.qo _,0 l S -0. -S5 I),.I 'D 4
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