Effect of blockage ratio on drag and pressure distributions for bodies

11

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NASA TECHNICAL NOTE

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NASA TN D-7331

EFFECT OF BLOCKAGE RATIO ON DRAG

AND PRESSURE DISTRIBUTIONS FOR BODIES

OF REVOLUTION AT TRANSONIC SPEEDS

by Lana M. Couch and Cuyler IV. Brooks, Jr.

Langley Research Center

Hampton, Va. 23665

NATIONAL AERONAUTICS AND SPACE ADMINISTRATION • WASHINGTON, D.C. • NOVEMBER 1973

https://ntrs.nasa.gov/search.jsp?R=19740001903 2018-04-02T19:02:15+00:00Z

, , /_ i _

1. Report No. 2. Government Accession No. 3. Recipient's Catalog No.

NASA TN D-7331

5. Report Date

November 19734. Title and Subtitle

EFFECT OF BLOCKAGE RATIO ON DRAG AND PRESSURE

DISTRIBUTIONS FOR BODIES OF REVOLUTION AT

TRANSONIC SPEEDS

7. Author(s)

Lana M. Couch and Cuyler W. Brooks, Jr.

9. Performing Organization Name and Address

NASA Langley Research Center

Hampton, Va. 23665

12, Sponsoring Agency Name and Address

National Aeronautics and Space Administration

Washington, D.C. 20546

6. Performing Organization Code

8. Performing Organization Report No.

L-8449

10. Work Unit No.

501-06-09-01

'11. Contract or Grant No.

13. Type of Report and Period Covered

Technical Note

14. Sponsoring Agency Code

15. Supplementary Notes

16. Abstract

Experimental data were obtained in two wind tunnels for 13 models over a Mach

number range from 0.70 to 1.02. Effects of increasing test-section blockage ratio in the

transonic region near a Mach number of 1.0 included change in the shape of the drag curves,

premature drag creep (i.e., transonic creep), delayed drag divergence, and a positive incre-

ment of pressures on the model afterbodies. Effects of wall interference were apparent in

the data even for a change in blockage ratio from a very low 0.000343 to an even lower

0.000170. Therefore, models having values of blockage ratio of 0.0003 - an order of

magnitude below the previously considered "safe" value of 0.0050 - had significant errors

in the drag-coefficient values obtained at speeds near a Mach number of 1.0. Furthermore,

the flow relief afforded by slots or perforations in test-section walls - designed according

to previously accepted criteria for interference-free subsonic flow - does not appear to be

sufficient to avoid significant interference of the walls with the model flow field for Mach

numbers very close to 1.0.

t7. Key Words (Suggested by Authoris))

Transonic wall interference

Drag

Facilities

19. Security Classif. (of this report)

Unclassified

18. Distribution Statement

Unclassified - Unlimited

20. Security Classif. (of this page)

Unclassified

21. No. of Pages

109

*For saleby the National Technical Information Service,Springfield, Virginia 22151

22. Price*

Domestic, $4.2_Foreign, $6.7!

i

EFFECT OF BLOCKAGE RATIO ON DRAG AND PRESSURE DISTRIBUTIONS

FOR BODIES OF REVOLUTION AT TRANSONIC SPEEDS

By Lana M. Couch and Cuyler W. Brooks, Jr,

Langley Research Center

SUMMARY

In an attempt to determine the severity of wind-tunnel wall interference under near-

sonic test conditions, aerodynamic force and pressure measurements were obtained at

zero normal force for 13 bodies of revolution over a Mach number range from 0.70

to 1.02.

Three specific effects on the drag data occurred near a Mach number of 1.0 as a

result of increasing the test-section blockage ratio for a given model profile:

i. The shape of the drag curves changed from a relatively rapid increase to a very

gradual increase in drag with increasing Mach number. This change occurred for

increases in test-section blockage ratio above approximately 0.0010. The shape of

the drag-coefficient curves, obtained at values of test-section blockage ratio less than

0.0010, is relatively insensitive to changes in blockage ratio.

2. Increasing the blockage ratio above approximately 0.0003 produced a premature,

positive deviation, or transonic creep, of the drag curve from the trend of the subsonic

data. Since the Mach number at the initiation of transonic creep agrees with the calcu-

lated Mach number for choked flow in a solid-wall tunnel, transonic creep may be the

first indication of significant wind-tunnel wall interference near a Mach number of 1.0.

3. The occurrence of drag divergence was delayed by approximately 0.013 in Mach

number because of an increase in blockage ratio from 0.0002 to 0.0010. For blockage

ratios greater than 0.0010, the drag-divergence Mach number was essentially constant.

Therefore, near a Mach number of 1.0 increasing the blockage ratio delays the occurrence

of drag divergence - the result that would be expected because of an effective decrease in

the free-stream Mach number at the model.

There was only one obvious effect of wall interference on the model surface-

pressure distributions obtained for a given model shape at different values of blockage

ratio. For Mach numbers greater than approximately 0.96, a region of supersonic flow

existed around the models. An increase in the value of blockage ratio for Mach numbers

greater than 0.96 caused a positive increment of pressure to occur on the model. The

effect on the drag data of this pressure-drag increment coincided quite well with the

change in shape of the drag curves.

The results of this investigation indicated that models having values of test-section

blockage ratio of 0.0003 - an order of magnitude below the previously considered "safe"

value of 0.0050 - had significant errors due to wall interference in the drag-coefficient

values obtained near a Mach number of 1.0. Furthermore, the flow relief afforded by

slots or perforations in test-section walls - designed according to previously accepted

criteria for interference-free subsonic flow - does not appear to be sufficient to avoid

significant interference of the walls with the model flow field for Mach numbers very

close to 1.0.

INTRODUCTION

In the past, numerous experimental investigations have been conducted in transonic

wind tunnels to determine the drag of both complete aircraft configurations and various

aircraft components at high subsonic and transonic Mach numbers. For these investi-

gations, data obtained at test-section blockage ratios of 0.0050 or less were generally

considered to be free of wall-induced blockage effects. However, the advent of the super-

critical design concept and the effort to develop a near-sonic transport have placed

renewed emphasis on accurate drag measurements in the near-sonic speed range (Mach

numbers of 0.95 to 1.0). As a result of this increased emphasis, it was believed that the

severity of wind-tunnel wall interference should be reexamined at near-sonic Mach num-

bers. Therefore, geometrically similar bodies of revolution were tested in two wind

tunnels and in flight under the same conditions. The model-to-wind-tunnel blockage ratios

were 0.0028 and 0.000684. A comparison of the results obtained in the flight test and

wind-tunnel test, at a blockage ratio of 0.0028 (ref. 1), indicated differences in drag char-

acteristics of sufficient magnitude to cause concern about the validity of drag data obtained

in the wind tunnel near a Mach number of 1.0. This discrepancy was believed to be the

result of wall interference due to test-section blockage in the wind tunnel. To investigate

this result further, bodies of revolution which provided a systematic variation in blockage

ratio from 0.00017 to 0.0043 were tested in the Langley 16-foot transonic tunnel and the

Langley 8-foot transonic pressure tunnel to assess the extent of wall interference effects

near'a Mach number of 1.0. The significant variables included in the investigation were

Mach number and model diameter and length.

SYMBOLS

Values are given in both SI and U.S. Customary Units. The measurements and calcu-

lations were made in U.S. Customary Units.

2

A local cross-sectional area of model

d2A

dx 2

Amax

A s

C D

CD ,b

Cp

Cp,b

Cp,sonic

d

K

iref

M

NRe

P

q_

reference area, maximum cross-sectional area of model

cross-sectional area of sting

drag coefficient at zero normal force, adjusted to a condition of free-stream

static pressure at model base, Dragq_Amax

base-drag coefficient

pressure coefficient

base-pressure coefficient

pressure coefficient corresponding to

maximum diameter of model

M = 1.0 local flow

curvature constant in model profile equations

length of model

reference length of model (length to body closure)

free-stream Mach number

Reynolds number based on model length

model surface pressure

model base pressure

free-stream static pressure

free-stream dynamic pressure

R radius of model

longitudinal center-line distance from model nose

X m longitudinal center-line distance from model nose to maximum diameter

of model

(7 standard deviation of variable

APPARATUS

Model Description

The five model shapes investigated in the wind-tunnel tests were (I) the blunt-nose

supercritical body of type A, (2) the blunt-nose, finned body of type B, (3) the blunt-nose,

supercritical body of type C, (4) the blunt-nose, supercritical body of type D, and (5) the

pointed-nose body of type E. Sketches of all models are shown in figure I; the letters

indicate the profile type and the numbers are coded to the diameters - as indicated in

the following table:

Configurationnumber

code

1

2

3

4

5

6

cm

6.35

8.99

12.70

15.70

22.25

27.08

Diameter

in.

2.50

3.54

5.00

6.18

8.76

10.66

Pertinent dimensions of all models and stings are listed in table I, and model coordinates

are listed in table II.

Generally, the models had machined metal noses and were otherwise constructed of

wood with fiber-glass-covered surfaces, or they were made totally of aluminum. The

models were turned on a lathe to obtain the required profiles within a tolerance of

+0.0025 cm (+0.001 in.) in radius. Although the models were generally smooth, deviations

in the radius of the models may have been as much as ±0.0127 cm (+0.005 in.) due to

warping or shrinking of the wood. These deviations were well within the limits for hydrau-

lic smoothness for the test conditions and model sizes of this investigation. (See ref. 2.)

4

The surface-pressure orifices were constructed of metal tubing with 0.076-cm(0.030-in.) inside diameter, installed flush with andperpendicular to the model surface.Onelongitudinal row of pressure orifices was installed in each model, and eachmodelwas tested with the orifices in the sameorientation in roll. The locations of all surface-

pressure orifices are listed in table III.

Type A.- The profile of the blunt-nose, supercritical body of type A is defined by

the following equations:

For 0 < x < Xm=lref =lre f'

A,,/' x _ = K x\iref ) - A (l_ef_

Xm < x <0.990and for lref = lref

Xm 1where = -. The profile is symmetrical fore and aft of the point of maximum diam-

lre f 2eter, except for truncation at the base to accept the sting. Three models of this profile,

having maximum diameters of 8.99, 12.70, and 15.70 cm (3.54, 5.00, and 6.18 in., respec-

tively) and a fineness ratio (i/d) of approximately 9.0, were investigated.

Type B.- The profile of the blunt-nose, finned body of type B was identical to the

type A profile, except that the aft 12.7 cm (5.0 in.) of the body were modified. The cross-

sectional area distribution of the body including the four 3-percent-thick delta biconvex

fins was equivalent to the cross-sectional area distribution of the A-3 body. One model

of this profile having a 12.70-cm diameter (5.00 in.) was investigated in the wind tunnels

and in a flight test (ref. I).

Type C.- The profile of the blunt-nose, supercritical body of type C is defined by

the following equations:

X < XmFor 0 <=lref - lref,

K x '

\lref)

5

and for Xm < x <0.990,iref - iref -

A,,fx _= K\ire f] Amax

Xm 1.0 Xmwhere - The profile for 0 _-< x _<_ is identical to that of type A;

lref 1.0 + (2/_)" lref lref

however, aft of the location of the maximum diameter, the profile has a constant second

derivative in the area distribution. The model is truncated at the base to accept the sting

and to give a ratio of base diameter to maximum diameter equivalent to that of the type A

models. Consequently, the type C models have a fineness ratio (l/d) of approximately

9.5 - a value slightly larger than the fineness ratio of the type A models. Five models

of this type, having maximum diameters of 8.99, 12.70, 15.70, 22.25, and 27.08 cm (3.54,

5.00, 6.18, 8.76, and 10.66 in., respectively), were investigated in the wind tunnels.

Type D.- The profile of the blunt-nose, supercritical body of type D is defined by the

following equations:

X (: XmFor 0 <=lre f - lref'

Xm xand for <_ -< 1.052,

Iref iref

/l_e f/ [(v/2)(x - Xm_A" x =Ccos_ l__efLX_ _

where Xm_ 1.0 and C

Iref 1'2( 1 A-_a;\) +1"0

( lm;C = (A s - Amax) lref - x

is a function of the base area and is defined by

Therefore, the actual base is slightly larger than As, and the actual length of the model

is slightly less that that predicted by the equations in order to provide clearance for the

sting. Three models of this type, having maximum diameters of 6.35, 8.99, and 15.70 cm

(2.50, 3.54, and 6.18 in., respectively), were investigated in the wind tunnels.

Type E.- The pointed-nose model of type E has a modified Sears-Haack profile, as

given in reference 3. This model has a maximum diameter of 12.70 cm (5.00 in.), a

i ¸ / H / _ •

fineness ratio I/d of approximately 9, and Iref/d of 12.0. The free-flight model of

reference 3 also had a fineness ratio iref/d of 12.0, but the maximum diameter was

25.4 cm (i0.0 in.) and there was no simulated sting-type support.

Stings

All tests were made with models sting supported through an access hole at the

model base, except for the model which was tested in flight. The model support stings,

except for configuration C-6, were scaled to approximately the model size and were

designed in accordance with the criteria of reference 4 in order to minimize the effects

of sting interference on the flow over the aft end of the model. This reference specifies

the minimum length of straight_-sting section aft of the model base and the maximum angle

of the sting flare. The ratio of cylindrical sting length to sting diameter for configura-

tion C-6 was smaller than desirable. Pertinent dimensions and flare angles of the stings

are presented in table I.

Wind Tunnels

This investigation was conducted in the Langley 16-foot transonic tunnel and the

Langley 8-foot transonic pressure tunnel. The 16-foot transonic tunnel (TT), which has

a nominally 4-percent-open, slotted, octagonal test section, as shown in figure 2, is an

atmospheric wind tunnel with continuous air exchange. This wind tunnel has continuously

variable airspeed through a Mach number range from 0 to 1.30. Test-section plenum

suction is used for speeds above a Mach number of 1.10. In order to eliminate any lon-

gitudinal static-pressure gradients that might occur along the center line, the test-

section wall divergence is adjusted. These adjustments are based on the results of the

wind-tunnel calibration. The average distance from center line to wall is 2.37 m

(93.31 in.), and the cross-sectional area is 18.50 m 2 (199.15 ft2).

The 8-foot transonic pressure tunnel (TPT) has a Maeh number range from 0

to 1.30. The test section is 2.16 m square (85.2 in. square) with filleted corners so that

the total cross-sectional area is 4.52 m 2 (48.70 ft2). The top and bottom walls have four

slots each, as shown in figure 3(a). The sidewalls are normally flat and solid; but for

this investigation, a set of wooden fairings was installed in an attempt to reduce the wall

interference effects. Two sidewall fairing strips were mounted in the streamwise direc-

tion on each wall, as shown in figure 3(b). The cross-sectional area of these fairings is

constant through the test section, except in the vicinity of the model being tested, where

they are contoured to account for 40 percent of the model cress-sectional area (i.e., the

cross-sectional area of the fairing decreases in the vicinity of the model). Forward of

the test section the fairings taper smoothly into the wall of the entrance nozzle. Down-

stream of the model, the fairings are contoured to represent 40 percent of the cross-

/i i

sectional area of the support sting and are tapered to near zero thickness in the vicinity

of the large tunnel sting. The maximum cross-sectional area of the fairings is approx-

imately 0.27 percent of the cross-sectional area of the test section.

Configuration C-3 was also tested in the 8-foot transonic tunnel at the Calspan

Corporation (TT CAL).

Test Conditions

All models v_ere tested at zero normal force over the Mach number range from

0.70 to 1.02. Close spacing of test points at Mach numbers between 0.90 and 1.02 gen-

erally was maintained in order to improve the definition of the drag-divergence region.

Boundary-layer transition was fixed according to the criteria of reference 5 on all models

at about 2 percent of the model length downstream of the nose. The 0.25-cm-wide

(0.10-in.) boundary-layer transition strip consisted of grit sparsely distributed in a thin

film of lacquer. Grit size determined from criteria of reference 6 for all configurations

is included in the following table:

C onfigu ration

A-2

A-3

A-4

B-3

C-2

C-3

C-4

C-5

C-6

D-I

D-2

D-4

E-3

Grit number

180

120

120

120

180

120

120

120

120

180

180

120

120

am

Grit height

0.0064

.0102

.0102

.0102

.0064

.0102

.0102

.0102

.0102

.0064

.0064

.0102

.0102

in.

0.0025

.004

.004

.004

.0025

.004

.004

.004

.004

.0025

.OO25

.004

.004

In the 16-foot transonic tunnel, the test Reynolds numbers varied from 11.48 x 106

to 13.7.8 x 106 per meter" (3.5 x 106 to 4.2 × 106 per foot) for each model and the stag-

nation temperature varied between 310.93 K and 355.37 K (I00 ° F and 180 ° F). During

the iavestigation data were generally taken at dewpoint temperatures of about 269.26 K

(25 ° F); however, data were taken in two separate runs on the same model at dewpoint

temperatures of approximately 269.26 K and 283.15 K (25 ° F and 50 ° F). In comparing

these two runs, no effects of condensation could be observed in the pressure distributions

or the force data.

8

•'.. •i. "• /•" . • .

! •

Tests in the 8-foot transonic pressure tunnel were conducted at a Reynolds number

of 13.12 × 106 per meter (4.0 x 106 per foot). The stagnation temperature was held

constant at 322.04 K (120 ° F) with the airstream dried to a dewpoint temperature less

than 272.04 K (30 ° F) to avoid condensation effects.

Comparisons of the Reynolds numbers, based on model length, at which each model

was tested in the various facilities are shown in figure 4.

Instrumentation

Aerodynamic forces were measured with internal six-component strain-gage bal-

ances. The model surface pressures were measured with 34.47-kN/m 2 (5.0-psi) and

6.90-kN/m 2 (1.0-psi) differential pressure transducers in the 16-foot and 8-foot tunnels,

respectively. The transducer was mounted inside the model in a scanning unit, which

was capable of scanning 48 orifices with a dwell time per orifice selected to insure that

each pressure had settled out. The base pressures and any nose orifice that would be

subjected to near-stagnation conditions were measured on individual pressure transducers

located outside the test section. Free-stream static and stagnation pressures were meas-

ured on precision mercury manometers. The stagnation temperature was measured with

a platinum resistance thermometer in the 16-foot tunnel and with a thermocouple in the

8-foot tunnel.

Accuracy and Corrections

iAccuracies of the various parameters obtained in the wind-tunnel tests were deter-

mined by the root-sum-square method for combining errors from independent sources.

This method was described and used in reference i. The standard deviations at a Mach

number of 1.0 of the parameters of interest in the Langley 16-foot transonic tunnel and

8-foot transonic pressure tunnel are presented in the following table:

Parameter

M ..o....°°...°..°.....

CD .....................

Cp ....................

P_, kN/m 2

q_, kN/m 2

p, kN/m 2

Pb' kN/m2

(psi) .............

(psi) .............

(psi) ...........

(psi) .............

Standard deviation (i_)

0.002

0.001

0.001

0.007 (0.001)

0.138 (0.02)

0.014 (0.002)

0.007 (0.001)

, - • • . "4

Root-mean-square deviations are included in reference 7 for the data obtained in the

8-foot transonic tunnel at the Calspan Corporation (formerly Cornell Aeronautical

Laboratory, Inc.) and are comparable with the values presented above.

The values of drag coefficient were corrected for a base-drag coefficient computed

over the total base area. No buoyancy corrections were made to the data.

The effect of the sidewall fairings on the test-section calibration in the 8-foot tran-

sonic pressure tunnel cannot be determined, since each fairing is designed to be tested

with its corresponding model installed.

PRESENTATION OF RESULTS

Figure

Data obtained for finned model (configuration B-3) in

wind-tunnel and flight tests ........................... 5

Variation of drag coefficient with Mach number for the6various configurations .............................

Variation of base-pressure coefficient with Mach number for the

various configurations ............................. 7

Variation of drag-coefficient increment with Mach number ........... 8

Variation of drag-coefficient increment with Mach number for models of

comparable blockage ratio ........................... 9

Variation of drag-coefficient increment with blockage ratio at discrete

Mach numbers .................................. I0

Variation of drag-divergence Mach number with blockage ratio ......... 11

Variation of transonic creep Mach number with blockage ratio ......... 12

Pressure-coefficient distributions obtained for type A confi_drations ...... 13

Pressure-coefficient distributions obtained for configuration B-3 ........ 14

Pressure-coefficient distributions obtained for type C configurations ...... 15

Pressure-coefficient distributions obtained for type D configurations ...... 16

Pressure-coefficient distributions obtained for configuration E-3 ........ 17

Comparison of drag-coefficient increments obtained from both

force-balance and pressure integration ..................... 18

DIS CUSSION

Effects of Blockage Ratio on Drag

Drag coefficients.- A comparison of the variation of drag coefficient with Mach num-

ber obtained for the finned model (type B) in both wind-tunnel and flight tests is presented

10

r ¸

r

k -

in figure 5(a). The flight data are reported in reference i. The same model-sting com-

bination was tested in the 16-foot and 8-foot tunnels; the ratios of model to test-section

blockage for these tests were 9.000684 and 0.0028, respectively. The model used in the

flight test was identical to the wind-tunnel model, except that the sting was not present.

Since there was essentially no variation of axial-force coefficient over an angle-of-attack

range in the wind-tunnel data (ref. I), the axial-force coefficients from the flight test can

be compared with the drag coefficients obtained in the wind tunnel. The subsonic drag-

coefficient levels obtained in the wind tunnel agree quite well through a Mach number of

approximately 0.95, although the wind-tunnel data indicate a lower drag-coefficient level

than that of the flight data. In general the shapes of the drag curves obtained for the

model in the 16-foot tunnel (blockage ratio of 0.000684) and in flight are very similar.

The model in the 8-foot tunnel (blockage ratio of 0.0028) shows sizable differences in both

the shape and magnitude of the drag curves near M -- 1.0. These differences were

believed to be the result of wind-tunnel wall interference.

The variation of base-drag coefficient with Mach number obtained for the finned

model (configuration B-3) in both wind-tunnel and flight tests is presented in figure 5(a)

and on an expanded drag-coefficient scale in figure 5(b). The base-drag coefficients

obtained in the three tests are in good agreement throughout the Mach number range. In

figure 5(b) the expanded drag scale shows that although the trends of the data are similar

at Mach numbers below 0.95 and above 1.00, some differences occur in the levels of the

three sets of data. The main differences observed in the data can be attributed not only

to the lack of a sting in the flight test, but also to the differences in the Reynolds numbers,

since the curves tend to converge near M = 1.0 as do the Reynolds numbers (fig. 4 and

ref. i).

In order to further explore the effects of increasing the blockage of the test section,

a systematic investigation was made in the Langley 16-foot and 8-foot transonic wind

tunnels. The model-to-test-section blockage ratio varied from 0.00017 to 0.0043 in the

investigation.

The variation of drag coefficient with Mach number for each of the models tested is

presented in figure 6. Data obtained from the five type C models - three of which were

tested in two different facilities - are presented in figure 6(a). Effects similar to those

observed for configuration B-3 are apparent when comparing the data on a model tested

both in the 16-foot tunnel (the lower blockage ratio case) and in the 8-foot tunnel (the higher

blockage ratio case). As the blockage ratio is increased, the drag divergence is delayed

and the drag curve has a much less rapid rise. Furthermore, the models (configura-

tions C-5 and C-6) which have relatively large blockage ratios in the 16-foot tunnel exhibit

drag characteristics similar to those observed for the large blockage ratio cases in the

smaller tunnel. The data obtained for the type D models (fig.6(b)) also show the same

ii

effects due to increase in blockage ratio. A comparison of the data obtained for the

smallest model tested (configuration D-l), which had a blockage ratio of only 0.00017 in

the 16-foot tunnel and 0.00070 in the 8-foot tunnel, shows effects similar to those observed

for the comparison of larger blockage ratio models. The pointed-nose model (configura-

tion E-3) shows the same relative drag characteristics for the two blockage ratio cases

as the blunt-nose models. Flight data for the RM-10 (ref. 3), which was geometrically

similar to configuration E-3 for the forward three-quarters of the model, are also pre-

sented in figure 6(d). The flight model was different from the wind-tunnel model in that

it had no similar base, since the afterbody was faired into the tail boom. Also, as stated

in reference 3, the error in the drag coefficient is ±0.009 at M = 1.0 and the error in the

Mach number is no worse than +0.01. Unfortunately, the magnitude of the possible errors

in the flight data precludes any firm conclusions based on the comparison with the wind-

tunnel data.

The variation of base-pressure coefficients with Mach numbers for each model

tested is presented in figure 7. In general, the base-pressure data obtained for each of

the models in the 16-foot and 8-foot tunnels are in fairly good agreement, considering the

differences in Reynolds numbers. The only difference which may be attributable to wall

interference in the base pressures is that the Mach number at which the maximum value

of the base pressure occurs increases slightly with increase in blockage ratio - an effect

comparable to the delay in the drag divergence with increase in blockage ratio, as will be

shown in figure 11.

Drag-coefficient increments.- The variations of drag-coefficient increment with

Mach number are compared for models within a geometrically similar profile type and

are presented in figure 8 with expanded scales to show the data trends more clearly.

These drag coefficients have been adjusted to an arbitrary common level by subtracting

the value of the drag coefficient at M = 0.90 for each model. The delay in the drag diver

gence and the change in shape of the drag curves with increasing blockage ratio are quite

apparent at these values of blockage ratio whether comparing flight and wind-tunnel data

(fig. 8(a)), data from different wind tunnels (figs. 8(c) and (d)), or data for various values

of blockage ratio from one wind tunnel (figs. 8(b) and (c)).

It should be noted that for models tested at values of blockage ratio less than approx-

imately 0.0010, the shapes of the drag-coefficient curves within a profile type are essen-

tially the same near M = 1.0 (except for some creep in the curves). At first glance, this

appears to be encouraging for successful application of a fairly simple correction to data

obtained for models tested at blockage ratios less than 0.0010. However, in an 8-foot tun-

nel a limit of 0.0010 in blockage ratio would require that a body of revolution have a diam-

eter no greater than 7.62 cm (3.00 in.).

12

: i:i

Since the same model-sting combinations were tested in two different wind tunnels

at different blockage ratios and the differences in the drag data still were present, it can

be assumed that the drag differences were not due to model support interference.

For models tested at blockage ratios of 0.0028 (figs. 8(a) and (b)) and 0.00311

(fig. 8(c)), the shape of the drag curve appears to be somewhat erratic, having a bump or

increase near a Mach number of 1. The phenomenon is apparently real since it occurred

on three different models and in two different wind tunnels. The bump did not occur in

the data of models tested at smaller blockage ratios nor did it occur in the data of config-

uration D-4 (fig. 8(d)), which was tested at a blockage ratio of 0.0043 in the 8-foot tunnel.

Data obtained from geometrically similar models (type C), which have comparable

blockage ratios in different wind tunnels, are presented in figure 9. The variations of the

drag-coefficient increment with Mach number for the models tested at comparable block-

age ratios are nearly identical throughout the Mach number range from 0.90 to 1.01. This

agreement indicates that the discrepancies observed for the models tested at various

blockage ratios apparently result from effects of wall interference due to model blockage

of the test sections. Since models tested at similar unit Reynolds numbers and at com-

parable blockage ratios in different size test sections have different model Reynolds num-

bers, this agreement also indicated that there were no significant Reynolds number effects.

The variation of incremental drag coefficient with blockage ratio at which a model

was tested is presented in figure 10. Each faired line and its symbol represent the data

obtained at one Mach number for models tested at several blockage ratios. The data

obtained for all the profile types tested show similar variations of drag coefficient with

blockage ratio. Since the data being compared were obtained for models which were geo-

metrically similar in profile, the drag-coefficient levels should have been the same except

for very small differences in this Mach number range due to model Reynolds numbers.

For Mach numbers of 0.99 and higher, the data obtained at the low blockage ratios show

fairly large drag-coefficient increments. However, as the blockage ratio increases, the

drag-coefficient increments decrease, and models tested at blockage ratios greater than

approximately 0.0010 show only a very small, nearly constant increase in drag increment.

A value of blockage ratio of 0.0050 generally has been considered to be sufficiently low to

avoid significant effects of wall interference. However, it should be noted in figure 10(b)

that a model such as type B tested at a blockage ratio of 0.0028 (approximately one-half of

the previously accepted "safe" value) at a Mach number of 1.00 yielded a drag-coefficient

value which was 0.057 lower than the flight value. Furthermore, at a blockage ratio of

0.00068 and a Mach number of 1.00 the wind-tunnel drag coefficient was still 0.042 lower

than the flight value.

The data obtained for type B at the three values of blockage ratio indicate the gen-

eral trend of drag coefficient with blockage ratio; however, no data were obtained for this

13

i ¸¸ : i • •

model which could show the trend as zero blockage ratio is approached in the wind tunnel.

It does appear from the type D data in figure 10(d) that obtaining data near M = 1.0

which are free of significant effects of wall interference would require extremely small

models permitting only meager instrumentation.

Drag-divergence Mach number.- The variation of drag-divergence Mach number

with blockage ratio of the four types of geometrically similar models is presented in fig-

ure 11. Drag-divergence Mach number is defined as the free-stream Mach number at

which the direction of the tangent vector to the curve of drag coefficient plotted against

Mach number is changing most rapidly with distance along the curve, that is, the Mach

number at which the radius of curvature is a minimum. The drag-divergence Mach num-

ber increased by approximately 0.013 (from M = 0.980 to 0.993) for an increase in block-

age ratio from about 0.0002 to 0.0010. For values of blockage ratio greater than 0.0010,

the drag-divergence Mach numbers for types A, C, and D remain approximately constant.

Only three values of blockage ratio were tested for type B, and the curve is not well

defined. The trend of increasing drag-divergence Mach number with increasing blockage

ratio is opposite from the result that would be expected for subsonic flow in which the

test-section walls are too closed (i.e., an increase in the effective free-stream Mach

number at the model causing a premature rise in drag). In contrast, near M = 1.0 the

results are more like those that would be expected for subsonic flow in which the test-

section walls are too open (i.e., a decrease in the effective free-stream Mach number at

the model accompanied by the delay in the drag rise).

Transonic-creep Mach number.- The variation of transonic-creep Mach number

with blockage ratio is presented in figure 12. The experimental wind-tunnel data, repre-

sented by the symbols, were obtained by determining the Mach number at which the drag

curve begins to deviate consistently by 0.0010 or more in drag coefficient from a straight

line passed through the subsonic data (i.e., 0.70 < M = 0.92). The curve in figure 12 is

faired through the free-stream Mach numbers that would correspond to choked flow at the

point of minimum cross-sectional area of the test section due to the presence of each

model. This calculation assumes that the walls are solid and neglects the relieving effects

of the slots. The free-stream Mach number is calculated for each value of blockage ratio

by using the stream-tube area relations of continuous, one-dimensional flow. By com-

paring figures 12 and 11, it appears that for blockage ratios less than 0.0003 the transonic

creep is masked by the beginning of the drag-divergence region. The agreement of the

Mach numbers at the initiation of creep in the drag curves with the calculated Mach num-

bers for choked flow in a solid-wall tunnel indicates that the creep results from the inter-

ference of the wall with the rapid lateral growth of the model flow field as a Mach number

of unity is approached. Consequently, the transonic creep may be the first indication of

significant wind-tunnel wall interference near M = 1.0. Therefore, the flow relief

afforded by slots or perforations - designed according to previously accepted criteria

14

for interference-free subsonic flow (for example, ref. 8) - does not appear to be sufficient

to avoid significant interference of the walls with the model flow field for Mach numbers

very close to 1.0.

Effect of Blockage Ratio on Pressure Distributions

Surface-pressure-coefficient distributions are presented for all models in figures 13

to 17. Pressure data were obtained in both the 16-foot and 8-foot transonic tunnels at the

Langley Research Center and also in the 8-foot transonic tunnel at the Calspan Corporation

for configuration C-3. The pressure coefficients are plotted against the center-line dis-

tance from the model nose which is nondimensionalized by the reference length of the

particular model. Pressure data are presented for each model at all test conditions in

each facility; unfortunately, no pressure data were obtained in the flight test.

For Mach numbers below approximately 0.96, the general trend of the pressure

distributions obtained for the model types A and C (figs. 13 and 15) is a smooth distribution

consisting of a rapid expansion around the nose, a rather flat distribution over the mid-

section of the model, and a fairly rapid compression to the base. The pressure distribu-

tions obtained for the models of types B and D (figs. 14 and 16) are quite similar to the

distributions obtained for types A and C. The pressure distributions of the type D models

generally show a small region of overexpansion around the nose and have a more gradual

compression to the base which begins nearer the longitudinal midpoint of the model than

do the compression regions for types A and C. The pressure distributions obtained for

the same model tested at two different blockage ratios show good agreement, provided

that the local flow around the model is substantially subsonic. However, for Mach num-

bers greater than approximately 0.96, a supersonic region develops around the model. As

the free-stream Mach number is increased toward unity, a discrepancy begins to appear

in the data obtained for the same model tested at identical free-stream conditions but at

two different blockage ratios. Comparlson of the pressure distributions for the two

values of blockage ratio shows a positive increment of pressures on the moclel tested at

the larger value of blockage ratio. The affected region typically maintains a constant size

and tends to move downstream on the model as the free-stream Mach number is increased.

(See configuration C-2 in figs. 15(c) and (d).) The location of the region of increased sur-

face pressures in conjunction with the geometry of the model determines the extent and

direction of the interference effect on the drag coefficient. Increments in pressure drag

that result from these differences in the pressure distributions obtained for configura-

tion C-2, at two different blockage ratios (figs. 15(a) to (d)), correspond quite well with the

trend of the differences observed between the two sets of drag data obtained for this con-

figuration (fig. 6(a)). The correspondence between the interference effects in the pressure

and drag measurements obtained from M = 0.90 to 1.02 was typical of the data obtained

15

for models tested at various blockage ratios, as canbe seen for three configurations in

figure 18. Therefore, in the transonic Machnumber region, the interference of the wallwith the model flow field apparently producesanadditional pressure increment, thus

altering the value of the drag coefficient.

Surface-pressure-coefficient distributions obtainedfor configuration E-3, thepointed-nosemodel, in the 16-foot and 8-foot transonic tunnels at Langley andin the flighttest of the RM-10 (ref. 3) are presented in figure 17. The data obtainedin the wind tunnelsagree fairly well through a Machnumber of approximately 0.95; at higher Machnumbers,discrepancies similar to those observedfor the blunt-nose modelsbegin to appear. Theeffects of wall interference on the pressure distributions are the same for the pointed-nosemodel as for the blunt-nose models. The distributions obtainedfor the RM-10 in theflight test generally showonly fair agreementwith the wind-tunnel data over the similarportion of the models and, as expected,no agreementnear the back where the models weredifferent. These results are not surprising, since the estimated maximum inaccuraciesin the pressure coefficients from the flight test were stated in reference 3 to be =_0.04atM = 0.75 to ±0.02 at M = 0.95 and to +0.004 at M = 1.27. Therefore, no firm conclu-

sions can be drawn by comparing the pressures measured in the flight test with those

measured in the wind-tunnel test.

Pressure coefficients, calculated for configuration E-3 by the program of refer-

ence 9, are indicated by the faired lines in figure 17. The comparison of this theory with

the experimental data shows good agreement through a Mach number of 0.997, which was

unexpected since this is a subsonic theory.

CONCLUSIONS

The results of this investigation of bodies of revolution confirm that drag-coefficient

values obtained at transonic flow conditions near a Mach number of 1.0 in wind tunnels are

affected by wall interference with the model flow field.

There were three specific effects on the drag data that occurred near a Mach num-

ber of 1.0 as a result of increasing the test-section blockage ratio for a given model

profile:

i. The shape of the drag curves changed from a relatively rapid increase to a very

gradual increase in drag with increasing Mach number. This change occurred for

increases in test-section blockage ratio above approximately 0.0010. The shape of the

drag-coefficient curves, obtained at values of test-section blockage ratio less than 0.0010,

was relatively insensitive to changes in blockage ratio.

2. Increasing the blockage ratio above approximately 0.0003 produced a premature,

positive deviation, or transonic creep, of the drag curve from the trend of the subsonic data

16

Since the Mach number at the initiation of transonic creep agrees with the calculated

Mach number for choked flow in a solid-wall tunnel, transonic creep may be the first

indication of significant wind-tunnel wall interference near a Mach number of 1.0.

3. The occurrence of drag divergence was delayed by approximately 0.013 in Mach

number due to an increase in blockage ratio from 0.0002 to 0.0010. For blockage ratios

greater than 0.0010, the drag-divergence Mach number was essentially constant. There-

fore, near a Mach number of 1.0, increasing the blockage ratio delays the occurrence of

drag divergence - the result that would be expected due to an effective decrease in the

free-stream Mach number at the model.

There was only one obvious effect of wall interference on the model surface-

pressure distributions obtained for a given model shape at different values of blockage

ratio. For Mach numbers greater than approximately 0.96, a region of supersonic flow

existed around the models. An increase in the value of blockage ratio for Mach numbers

greater than 0.96 caused a positive increment of pressure to occur on the model. The

effect on the drag data of this pressure-drag increment coincided quite well with the

change in shape of the drag curves.

The results of this investigation indicated that models having values of test-section

blockage ratio of 0.0003 - an order of magnitude below the previously considered "safe"

value of 0.0050 - had significant errors due to wall interference in the drag-coefficient

values obtained near a Mach number of 1.0. Furthermore, the flow relief afforded by

slots or perforations in test-section walls - designed according to previously accepted

criteria for interference-free subsonic flow - does not appear to be sufficient to avoid

significant interference of the walls with the model flow field for Mach numbers very

close to 1.0.

Langley Research Center,

National Aeronautics and Space Administration,

Hampton, Va., July 2, 1973.

17

i_ ..... _ i

L

REFERENCES

I. Usry, J. W.; and Wallace, John W.: Drag of a Supercritical Body of Revolution in

Free Flight at Transonic Speeds and Comparison With Wind-Tunnel Data. NASA

TN D-6580, 1971.

2. Schlichting, Hermann (J. Kestin, transl.): Boundary Layer Theory. Fourth ed.,

McGraw-Hill Book Co., Inc., c.1960.

3. Thompson, Jim Rogers: Measurements of the Drag and Pressure Distribution on a Body

of Revolution Throughout Transition From Subsonic to Supersonic Speeds. NACA

RM L9J27, 1950.

4. Cahn, Maurice S.: An Experimental Investigation of Sting-Support Effects on Drag and

a Comparison With Jet Effects at Transonic Speeds. NACA Rep. 1353, 1958.

(Supersedes NACA RM L56FI8a.)

5. Braslow, Albert L.; and Knox, Eugene C.: Simplified Method for Determination of

Critical Height of Distributed Roughness Particles for Boundary-Layer Transition

at Mach Numbers From 0 to 5. NACA TN 4363, 1958.

6. Braslow, Albert L.; Hicks, Raymond M.; and Harris, Roy V., Jr.: Use of Grit-Type

Boundary-Layer-Transition Trips on Wind-Tunnel Models. NASA TN D-3579, 1966.

7. Chudyk, D.W." Transonic Wind Tunnel Tests of Several NASA Bodies of Revolution.

Rep. No. AA-4018-W-5 (Contract No. NAS 1-10649), Cornell Aeronaut. Lab., Inc.,

Jan./Mar. 1971. (Available as NASA CR-I12069.)

8. Goethert, Bernhard H.: Transonic Wind Tunnel Testing. AGARDograph No. 49,

Pergamon Press, 1961.

9. Hess, J. L.; and Smith, A. M.O.: Calculation of Potential Flow About Arbitrary Bodies.

Progress in Aeronautical Sciences, Vol. 8, D. K_chemann, ed., Pergamon Press,

Ltd., c.1967, pp. 1-138.

18

_'i_:!_ i i__

/

TABLE I.- MODEL DESCRIPTION

Configuration

A-2

A-3

A-4

B-3

C-2

C-3

C-4

C-5

C-6

D-I

D-2

D-4

E-3

Maximum Length Reference Basediameter length diameter

cm in. cm in. cm in. cm in. 16 ft TT

8.99 3.54 80.85 31.83 81.64 32.14 2.29 0.90 .......

12.70 5.00 114.30 45.00 115.45 45.45 3.18 1.25 .......

15.70 6.18 141.22 55.60 142.72 56.19 4.14 1.63 .......

12.70 5.00 114.30 45.00 115.45 45.45 3.18 1.25 0.000684

8.99 3.54 85.34 33.60 81.64 32.14 2.29 .90 .000343

12.70 5.00 120.65 47.50 115.45 45.45 3.18 1.25 .000684

15.70 6.18 149.10 58.70 142.72 56.19 4.11 1.62 .00104

22.25 8.76 210.24 82.77 202.03 79.54 6.35 2.50 .00210

27.08 10.66 257.02 I 101.19 245.95 96.83 7.06 2.78 .00311

6.35 2.50 60.58 23.85 57.73 22.73 1.78 .70 .000170

8.99 3.54 85.85 33.80 81.64 32.14 2.29 .90 .000343

15.70 6.18 150.22 59.14 142.72 56.19 4.14 1.63 .......

12.70 5.00 137.62 54.18 152.40 60.00 3.18 1.25 .000684

CylindricalBlockage Sting sting

ratio diamete r length

8 ft TPT cm in. cm ] in.

m

0.00140 1.78 0.70 21.59 / 8.50

.00280 2.54 1.00 35.31 13.90

.00430 3.51 1.38 43.94 17.30

.00280 2.54 1.00 34.93 13.75

.00140 1.78 .70 17.02 6.70

.00280 2.54 1.00 22.56 8.88

.00430 3.51 1.38 25.63 10.09

....... 5.72 2.25 44.20 17.40

....... 5.72 2.25 25.76 10.14

.000698 1.27 .50 17.78 7.00

.00140 1.78 .70 17.02 6.70

.00430 3.51 1.38 35.05 13.80

.00280 2.54 1.00 28.50 11.22

Included

angle ofsting flare,

deg

6

6

6

6

6

6

6

8

8

6

6

6

6

i ¸ : •

i• ,

x//lref

0

.002

.004

.005

.006

.0075

.008

.010

.0120

.0125

.0140

.0160

.0180

.0200

.0250

.0400

.0500

.0600

.0750

.0800

.1000

.1200

.1400

.1500

.1600

.1800

.2000

.2400

.2500

.28OO

.3000

.3200

.3500

.4000

.4500

TABLE II.- NONDIMENSIONAL MODEL COORDINATES

R//lref

Type A

0

.00696

.00946

.01134

.01291

.01422

.01539

.01645

.01742

.01832

.01916

.02556

.03005

.03357

.03648

.03894

.04108

.04295

.04460

.04607

,04855

.05052

.05207

.05412

Type B

0

.00696

.00946

.O1134

.01291

.01422

.01539

.01645

.01742

.01832

.01916

.02556

.03005

.03357

.03648

.03894

.04108

.04295

.04460

.04607

.04855

.05052

.05207

.05412

Type C

0

.00696

.00946

.01134

.01291

.01422

.01539

.01645

.01742

.01832

.01916

.02556

.03005

.03357

.03648

.03894

.04108

.04295

.04460

.04607

.04855

.05052

.05207

.05412

Type D

0

.OO713

.00969

.01159

.01316

.01450

.01570

.01678

.01777

.O1868

.01954

.02604

.03060

.03416

.03709

.O3958

.04172

.04360

.04525

.04671

.04915

.05108

.05256

.05443

Type E

0

.00232

.00298

.00428

.00722

.0121

.0161

.0197

.0259

.0309

.0347

.0374

.0393

.0406

.0414

2O

i ¸ : •

TABLE II.- NONDIMENSIONAL MODEL COORDINATES - Concluded

X/iref I R/lref

Type A Type B Type C Type D Type E

0.4800

.5000

.5200

.5500

.6000

.6500

.6800

.7000

.7200

.7500

.7600

.8000

.8200

.8400

.8500

.8600

.8800

.9000

.9030

.9200

.9400

.9600

.9700

.98OO

.9900

1.0000

1.0100

1.0200

1.0300

1.0400

1.0450

1.0532

0.05497

.0550O

.05497

.05412

.05207

.05052

0.05497

.05500

.05497

.05412

.05207

.05052

0.05497

.05500

.05497

.05413

.05213

.05065

0.05500

.05495

.05483

.05358

.05107

.04934

.04855

.04607

.04460

.04295

.04108

.O3894

.03648

.03357

.03005

.02556

.02271

.01916

.01422

.O4855

.04607

.04460

.04295

.04108

.03894

.03602

.03178

.02650

.02047

.01745

.01511

.01422

.O4881

.04658

.04530

.04390

.04235

.04066

.03879

.03673

.03444

.03186

.03044

.02892

.02728

.02549

.02354

.02136

.01888

.01596

.01423

.04725

.04481

.04344

.04196

.04037

.03867

.03683

.03484

.03268

.03032

.02906

.02773

.02632

.02483

.02323

.02150

.01962

.01753

.01642

.01423

0.0417

.0413

.0402

.0384

.0356

.0313

.0253

.0185

.0113

.0104

21

k

" ) i •

b_

TABLE Ill.- NONDIMENSIONAL PRESSURE-ORIFICE LOCATIONS

Pressure i

orifice Configuration Configuration Configuration

A-2 1 A-3 A-4

1 0 ..... 0

2 .0311 ..... .0178

3 .0467 0.0297 .0257

4 .0622 .0396 .0356

5 .0778 .0594 .0446

6 .0933 .0891 .0534

.1089 .1069 .0623

8 ,1245 .1287 .0712

9 .1556 .1485 .0801

10 .1867 .1683 .0890

11 .2178 ..... .0979

12 .2489 .2079 .1067

13 .2800 .2475 1246

14 .3111 .2970 1424

15 .3422 .3465 1780

16 .3734 .3960 .2136

17 .4045 .4455 .2492

18 .4356 .4950 .2848

19 .4667 .5445 .3203

20 .4978 .5940 .3559

21 .5269 .6435 .3916

22 .5600 .6831 .4272

23 .5911 .7227 .4626

24 .6223 .7623 .4984

25 .6534 .8019 .5339

26 .6845 .8217 .5695

27 .7156 .6415 .6051

28 .7467 .8613 .6408

29 .7778 .8811 .6764

30 .8089 .9009 .7119

31 .6400 .9207 .7475

32 .6556 .9405 .7631

33 .8712 .9603 .8187

34 .8667 .8543

35 .9023 .8721

36 .9176 .6900

37 .9334 .8988

38 ,9489 .9077

39 .9645 .9166

40 .9255

41 .9344

42 .9433

43 .9522

44 .9611

45 .9700

46

47

48

X/lref

:onfigur ation I : on f __nfi_llr a-tion

B-3 C-2 _ _ C-3 C-4

O0o9 66. l-0. o:o-o8;.0311 I .0196 .0176

I

.0196 .0467 I .0297 .0267I

.0297 .0622 .0396 .0356

,0396 .0776 .0594 .0445

.0594 .0933 .0691 .0534

.0891 .1089 .1089 .0623

.1089 .i245 .1287 .0712

.1287 .1556 .1485 .0801

.1485 .1867 .1683 .0890

.1683 .2178 .1881 .0979

.1981 .2489 .2079 .1068

.2079 .2800 .2475 .1246

.2475 .3111 .2970 .1424

.2970 .3423 .3465 .1780

.3465 .3734 .3960 .2136

.3960 .4045 .4455 .2492

.4455 .4356 .4950 .2846

.4950 .4667 .5445 .3204

.6445 .4978 .5940 .3560

.5940 .5289 .6435 .3916

.6435 .5600 .6831 .4272

.6831 .5912 .7227 .4628

.7227 .6223 .7623 .4984

.7623 .6534 .8019 .5339

.8019 .6845 .8217 .5695

.8217 .7156 .6415 .6051

.8415 .7467 .8613 .6407

.8613 .7778 ,8811 .6763

.8811 .8090 .9009 .7119

.9009 .8401 .9207 .7475

.9207 .8556 .9405 .7831

.9405 .8712 .9603 .8187

.9603 .8867 .9801 .6543

.9801 .9023 .9999 .6721

.9179 1.0197 .8899

.9334 1.0395 .9077

.9490 .9255

.9645 .9433

.9956 .9611

1.0112 .9789

1.0268 .9678

.9967

1.0056

1.0145

1.0234

1.0323

Configurat_ion] Configuration Configuration

C -5_ C -6 D-Io o--.0089 .0089 0.0175,0219

.0178 I ,0178

.0267

.0356

.0445

.0534

.0623

.0712

.0801

.0890

.0979

.1068

.1246

.1424

.1780

.2136

.2492

.2848

.3204

.3560

.3916

.4272

.4628

.4984

.5339

.5695

.6051

.6407

.6763

.7119

.7475

.7831

.8187

.8543

.8721

.8899

.0967

.O356

.0445

.0534

.0623

.0712

.0801

.0890

.0979

.1066

.1246

.1494

.1780

.2136

.2492

.2848

.3204

•3560

•3916

.4272

.4628

.4984

.5339

.5695

.6051

.6407

.6763

.7119

.7475

.7831

.6187

.8543

.8721

.6899

.9077 .9077

.9255 .9265

.9433 ,9433

.9611 ,9611

.9789 .9789

.9878 i .9878J

.9967 .9967

1.0145 1.0056

1.0234 1.0234

1.0323 1.0323

.0329

.0438

.0548

.0657

.0876

.1095

,1314

.1534

.1753

.1972

.2191

.2410

.2629

.2848

.3067

.3505

.3943

.4382

.4820

.5256

.5696

.6134

.6572

.7010

.7449

.7666

.7887

.8106

.8325

.8544

.6763

.8982

.9201

.9420

.9596

.9771

.9946

1.0121

1.0297

0.014

.0311

,0467

.0622

.0778

.0933

.1089

.1245

.1556

.1867

.2176

.2489

.2800

.3111

.3423

.3734

.4045

.4356

.4667

.4978

.5289

.5600

.5912

.6223

.6534

.6845

.7156

.7779

.8090

.6245

.6401

.8556

.8712

.8868

.9023

.9179

.9334

.9645

.9956

1.0266

1.0517

1.0517

.0979

.1067

.1246

.1424

.1780

.2136

.2492

.2848

.3204

.3560

.3916

.4272

.4628

.4984

.5339

.5695

.6051

.6407

.6763

.7119

.7475

.7831

.8187

.6543

.8721

.6899

.9077

.9255

.9433

.9611

.9789

.9876

.9967

1.0056

1.0145

1.0234

1.0323

_onfiguration ]

E-3

0.0050

.0130

.0250

.0500

.0750

.1000

.1500

.2000

.2500

.3000

.3500

.4000

.4500

.5000

.5500

.6000

.6500

.7000

.7500

.8OOO

.8500

.8750

H:

c_ c

A 2 80.85,31.83}

8.99 c_____3. 541

A 5 114.30 12.70 _._

(45.001 (5.00)

15.70_ 141.22(55.601 (6.181

B 3 114.30 12.70 ____

(45.00) 15.00l

o

___ -=

C 2 85.34 8.99 _

(33.60) (3.54}

c 3 120.65 12.7o C_._147.5m (5.oo)

C 4 149.10 15.70(58.70} (6.18}

f

C 5 210./4 22.25(82.77) (8.76)

fC 6 257.02 27.08 k._

(I01.19) (10.66)

ZCc]

E 3 137.62 !2.7054.18) (5.00)

D 1 60.58 6.35 (

123.85) (2.50)

D 2 85.85 8.99 _

(33.80) (3.54)

D 4 150.22 15.70(59.14) (6.18)

Figure 1.- Model sketches. (Dimensions are given in centimeters (inches).)

boOo

• /

Slots

Body of revolution

Movable circular-arc

support strut

Cross-sectional view of test section showing location of eight slots

Region ofmodel installation

Total slot openingI

Ipercent of wall perimeter)____.,. 4, ill 16

\\

Slot configuration

Figure 2.- Test-section configuration o£ Langley 16-foot transonic tunnel.

24

Movable circular-arc support strut

.Body of revolution

_--Diffuser entrance flap

Cross-sectional view of test section showing location of eight slots

Total slot opening

(percent of

wall perimeter)----'-

._-Region of model installation-_i

2

i

5 10

/.---J

\

Slot configuration

(a) Distribution and shape of slots.

Figure 3.- Test-section configuration of Langley 8-foot transonic pressure tunnel.

25

b_

Flow

_X/--I ndented to_' match model

cross-sectional

ar ea

distribution jFairings

""-- Fairings

Test section - top view

\ Fairings_

_--Fairings % \"\Model

Photograph of sidewall fairing strip installed in the test section

Test section - end view

Location of sidewal fairing strips

(b) Installation of sidewall fairing strips in test section.

Figure 3.- Concluded.

Conf.No

A-2

A-3

20 x 106 A-4

16

12-

Re

8

d

Oy-Conf.

slo.

C-2

C-3

C-4

C-5

C-6

36 Io

28

-- Z

24

20

NRe ._

16 Ib

12 --

8

]6 Ft. 8 Ft.-_ TPT

16 Ft. 8 Ft.

TT TPT

< - _ >

-- - -v- (

Type C

8 Ft.TT-CAL

0.7 .8 .9 l.O 1.1

M

Conf. 16 Ft, 8Ft.No.

IT TPI

3-3 o -

E-3 -

__ _( _A---- - ----

q

q

Flignt

I

C -_-_- Types B and E ' 1

Conf. 16 Ft. 8Ft.No. TT TPl

D-I o

D--2 ......

D-4

..... C_] _

.7 ,8

5:]

FType D

[[.9 1.0

M

Figure 4.- Variation of NRe with M for the various models.

27

.28

.... 16 Ft. _"

---o--- 8Ft. TPT

,_ Flight , reference1

.24

.2O

.16

CD

• 12

(

.08

.Oa

CD.b )

-. 0468

4S<>

I

!

I

76 .84 .92 1.00 1.08M

(a) Variation of CD and CD, b with M.

CD.b

-.Ola

-.012

-.010

E-. 008

-. 006 -

---o---I6 FI TT

cG 8 Ft. "i-PT

Flight reference 1 )

IJ

0_.- _

,--/ 0<-©

<0

0

_Oc bO,<>

-.004. 68 76 .84 M .92 1.00

I

1.08

(b) Variation of CD, b with M (expanded CD, b scale).

Figure 5.- Data obtained for finned model (configuration B-3) in wind-tunnel

and flight tests.

28

• 16

• 12

08

CD

08

04

• 04

• 04

04

Configuration C-2

/'I,V

Configuration C-3

C fig ration C-4

i I I Ii t I ti I It

I t

Configuration C-5

"I'/IIi

Configuration 0-6

Conf. ].6 Ft. 8 Ft. 8 Ft. TTNo. TT TPT CAL

C-2 _ -- ,oC-3 ---m-- - ,m _,_--

C-4 ---O--- - _ -

C-5

C-6

-- -=

.90¥

/

_4 _- _

0.80 .85 .95 1.00 1.05

(a) Type C.

Figure 6.- Variation of CD with M for the various configurations.

29

¢oo

.16

•12

.08

•04

0

CD.08

.04

Configuration

Configu ration

Conf. 16Ft. 8 Ft.No. TT TPT

D-1 + ---_t_----D-2 _ ---_ ....D-4 ----_---

........... )_,..... E---::___q,;._ ___ :z._-q_

_% ............ _:_:_ >--c .--_ >_:_

I

/

/

.08

•04

0•80

Configuration

....... •-t .............

•85 .90 .95M

(b) Type #.

Figure 6.- Continued.

i1.O0 1.05

• 16

Conf•No.

A-2

A-3A-4

8 Ft. TPT

• 12

.08

• 04

0

CD

.08

.04

.08

.04

(c) Type A.

CD

.24

20

• 16

• 12

.08

I

.04 --

O.80

Configuration E-3

• 85

16Ft. "iT

---,,_---- 8 Ft. TPT---¢<--- Flight -eference 3 )

k----Z

L/

/

/i

/

• 90 .95 1. O0 l. 05M

(d) Type E.


31

.24

Conf. 16 Ft. 8 Ft. 8 Ft. --No. TT TPT CAL

C-2 _ ---,o- - -C-3 _ --=a .... -_-

C-4 _ ---9-- -C-5 _--C-6

.2O

• 16

• 12

.08

.04

0

.08

04

CP,b 0

.08

.04

.08

• 04

.O8

.04

080 .85

Figure 7.- Variation of

.90 .95 1.00 1.05

(a) Type C.

Cp, b with M for the various configurations.

32

"j.20

• 16

• 12

.08Configuration D-1

Conf 16Ft. 8 Ft.No. TT TP[

D-1 + .... : ....D-2 _ --- © ....

D-4 .... _ ....

n\

Cp,o

.04

.08

.04

.08

Configuration )-2[

ConfigurationI[:)-4

.04

8C • 85 .90 .95M

I1.O0 1,05

(b) Type D.


33

•24

.20

• 16 Co_figuration

Conf• 8Ft.No. TPT

A-2 -- p----A-3 ---;_ ....

A-4 - - -42---

• 12

.08

.04Configuration

...... _.__- ZY- ' "5

0

Cp,b

.08

• 04

Configuration A-4

\x

,>

.08

• 04

20

15

12

Cp,b

.08Configuration E-3

•O4

(c) Type A.

----o--- 15Ft. TT--_-- 8Ft./PT

\

080 .85 .90 .95 t. O0 1.05

(d) Type E.


34

•• _ k,i ¸,

',___i_._,_i,_i_"•••' ' i_ :i _i _ '

CD

0

oo_

b--b---

\

\\ \

K

\

\

\

\

,I 1

\

0

00

cxDCr_

C_

C_d

CO

0 .v._

o0

0 ,-_c.)_ 0

0

1

g

00 0

06"=W0 0

0 00

0C_

0

I

35

.... ?

_:i ;i i/_ i _

.... iii;_ _

L

I--I--

O0 I----

On "_" O00_CO 0 r"_ C',,J _r

0_ rYm

. CX.I 0"_ '_t"t-- 0 I I I

0

\

\

\

\ \

l!

il

0

00

O0

C_

g.

C_

0

0-,

0

0I

O0

ol.-I

Cx.J

0"

0 0 0 0

06"=Wfl 3 _ 0 3

C_

0C_

C)

I"

36

- • • • .

. • . .: - ,

- .- . . ..

._> i ¸¸. •

i

.r

• 12

. I0

•08

0

,,• •06

0

I

.04

•02

.92

I_6Ft. TT

BlockageRatio

.00034

.00068.00104.00210.00311

i"

.94

8 Ft. TPT

Conf• BIockageNo. RatioC-2 .o .0014C-3 p .0028C-4 _ .0043C-5C-6

.96

M

/

.98

:

/ 1!

11tl

I//

/ f-

I. O0

/

J//I

/ /i1 I

/ /

//i

/

/

!

//

/ !

/

1.02

(c) Type C.


,k ¸ .

oo

12

16 Ft. TT

BlockageRatio

.00017

.00034

Conf.

NO.

D-1D-21:)-4

8 Ft. TPT

BlockageRatio

.00070

•00]40•00430

10

.08

oo',

:_ .06

(_3

I

C.D.04

• 02

///

It

II

I II

,/

/

i!/

1!

1/

zl

/

/

//

/!

/

_J

.92 •94 .96

M

(d) Type D.


.98 1. O0 I. 02

Conf. BlockageNo. Ratio

.O4

0

°i. 02II

I

-. 02

z_ C-.5 .0021

c-3 .0o2t16 Ft. TT8Ft. TT -CAL

LI

O

I

.04 - -L.....!

O

_.. 02II

0 "_

-. 02.90

Conf. BlockageNo. Ratio

C-3 .0028

C-6 .0031

8 Ft. TPT

16 Ft. TT

• 94 .98 I. 02M

Figure 9.- Variation of drag-coefficient increment with

comparable blockage ratio.

M for models of

39

i : • •

0

• O5

Mach 8 Ft.No. TPT

.98 P

.99 P1.00 _>1.01 /_

o

E_0

I

r-_

.O4

•O3

• O2

.01

_k

<_

/

00 .0008 .0016 .0024 .0032 .0040

BIockage ratio

©

.0048

(a) Type A.

Figure i0.- Variation of drag-coefficient increment with blockage ratio at discrete Mach numbers.

,i

)

O0

c_ Z

0

0

_o '-4

°,,._

o

Tsa

06 GO"=W(]3 _

41

7

:\

! 4

• 12

.11

%\

• 10

\.09

• 08.07 _

v_°_o_ _

_"-" ..0405

.03

.02

.01

1\

\

\\

\

MachNo.

•980•985•990• 99.5

I. 000I. 010I. 020

16 Ft.

TT

o

[]©

8 Ft.TPT

P

P

\

\

\\

\\

\\

\

\\

_ --_---_:: =--::_

-.01.0008 • 0016 .0024

Blockage ratio

(c) Type C.


•0032 .0040 .0048

42

• _i : i!_ L •...... i iiil

i ¸¸ / ,

oO

C_

F

_L

0 0 0 0 CD 0 0

06"=W(l3 _ (I3

43

44

Jaqwnu q3eW a3uaQa^!p-6eJ(]

00m

,,..)0

t",m

k

bb

0r_

o,_

,.O

bO

Ibb

©

©0r-i

0,_,-4

I>I

,i.,-.I

(D

bb

_#00"

"o_l_a o_mtoolq ql_maoqtunu qo_IAI doa2o-o_uosu_a] 3o uo!l_a_A -'_I o_n_,;[

@00" _00" _00" 9100" 8000" 0_6"

I.O

[]

-IV3 - II "_.J8 vIdl q.-I8 []

II q-J 9[ o

e_ep le_UOW!Jadx3 - sloqLuXS

lauum, lleM-p!los _oj W po)loqo - aAJn3

"--_C-.,..,

,-...,

iqB!IJ

\\

\D

_6"

96"

_6"

O0"I

W

- _. -

il :, i _i:!:i/_:_ i ;

, "=7 • • L /-

i¸ :: C" : " :

• U_ ,i__, •

-2

Mach 8 Ft.No, TPT

•85 ,0.90.95 9.98

/ :iI • •

-1

2

-.1

-.2

-.I

0

.I

.2

-.2

-.]

2

46

0 .i .2 .3 .4 5 .6 .7 8 .9 1.0

xl I ref

(a) Configuration A-2; 0.85 < M < 0.98.

Figure 13.- Pressure-coefficient distributions obtained for type A configurations.

_iiiii _ : :!

"u _ _ , _ i_ . _

_ii_;: :i _i I:i_,':/

ii_ •

Cp

-.2

-.1

.1

.3

-.2

-.1

.1

.3

-.2

-.1

.3.2 .3 4 5 .6

x/I ref

.7 .8 9 1.0

(b) Configuration A-2; 0.991 < M < 1.011.

Figure 13.- Continued,

47

"_ _, _i _'

•_:I_II• •

-.i

.I

.2

.3

-.I

Math 8 Ft.No. TPT

• 85 ,O

.90 E3

.95.98

.3

Cp

.i

.2

.3

.i

I .2 3 .4 .5 .6 .7 .8 .9

X/Ire f

(c) Configuration A-3; 0.85 <_-M -< 0.98.


1.0

48

Math 8 Ft.

No. TPT

.991 ,0

1.0001.01].

] .2 .3 .4 .5 6 .7 .8xl I rel

(d)Configuration A-3; 0.991 _-<M _-<1.011.


10

49

i ¸

: !il i ¸ :

-.2

0

.i

.2

-.2

.I

Mach 8 Ft.No. TPT

• 85 ,0

• 9o p.95 <#.98

.2C

D

_2

_2

0 .l 2 .3 .4 .5 .6 7 .8 9 1.0x/

ref

(e) Configuration A-4; 0.85 _-<M -<0.98.


50

ii__i ::i_i!_

'9' i

• i _

i _i:_

-.2 --

=1

0

.1

.2 >

.3

-.2

=1

Cp 0 --

.1

3.2

.3

=2

-.1

0 --

1

g.2

.30

Math

NO.

.99

].00

1.01

3 J

b

8 Ft.TPT

,oP9

.1 .2 .3 .4 x/I .5ref

¢>

.[ [3

) ;

;>,

.E: 3

.8

(f) Configuration A-4; 0.99 -<M _-<1.01.


1.0

51

Mach 16 Ft.

No. TT

• 699 0

• 800 []

CP

.3

0 ] .2 .3 .4 .5 .6 .7 .8 .9 1.0

X/Ire f

(a) 0.699 < M < 0.800

Figure 14.- Pressure-coefficient distributions obtained for configuration B-3.

52

:i

_ L _ . :

Cp

3

Mach 16 Ft. 8 Ft.

No. TT 1-PT

• 849 O ,C,

•900 []

.3 .4 5 6 .7

x/I ref

(b) 0.849 < M -< 0.900.


53

.2

Mach 16Ft.

No. TT

.9]9 0• 94O []

i _ "

=l

.1

-.2

-1

.1

.2

P

.3

.6

1.0

1.1

1.2

].3.3 .4 .5 .6 7

Xllre f

(C) 0.919 __-<M < 0.940.


54

+. .,

_ • i_I_I ,+il

, , +,_

/,'+ ,_/,+/ .

C

P

Mach ]6 Ft. 8 Ft.

No. [T TPT

• 950 O ,O

• 958 C] P

(d) 0.950 _ M _ 0.958.


8

55

_._.

-.2

-.I

.I

-.2

-.I

.i

.2

Mach 16 Ft. 8Ft.No. TT TPT

• 968 0 _3• 975 [] ,_

.3C

P

.4

.5

1.0

ii

1.2

1.3.3 .4 .5 6 .7

x/Iref

(e) 0.968 < M -< 0.975.


8 1.0

56

Mach 16 Ft.No. TT

• 979 O• 985

1

.l

C .20

3

i.I

1.2

1.3

(f) 0.979 =<M =<0.985.


57

x • • :

• i: ! ,/

L

-.2

CP

--.i

0

.i

n2

-.1

0

.i

.2

.3

Mach 16 Ft. 8 Ft.N0, TT TPT

• 990 0 ,0•994 [] ,E3

.4

.5

.6

.7

.8

1.0

1.1

1.2

1,3l 2 .3 .4 .5 6 .7

x/l rel

(g) 0.990 =<M =<0.994.


1.0

58

-.2

Mach ]6 Ft. 8 Ft.No. TT TPT

.999 0 ,01.010 0 ,3

=I

-.2

-.]

.3

CD

.z_

.5

.6

.8

1.0

l.l

1.2

1.30 i3 .4 .5 .6 7

xllref

(h) 0.999 _-<M -< 1.010.


.8 .9 1.0

59

: "j

/'i _!,/ i _ L i

• ) _ii _

/

?

i.i !_ .il •

/

CP

-.2

-.l

.I

.2

-l

.l

Mach 16 Ft. 8Ft.No. IT TPT

•698 © P.8ol [] P.85o 0•901 z_ ,_

-.i

.l

.2

-.l

.l

2 0 .i .2 .3 4 5 .6 .7 8 .9 l.O i.I

x/I ref

(a) Configuration C-2; 0.698 =<M <_-0.901.

Figure 15,- Pressure-coefficient distributions obtained for type C configurations.

6O

k

• ::ii!__I:i:

,r

: i_ _'//! ::! y" •

CP

Mach 16 Ft. 8 Ft.

No. TT TPT

.921 0

.94o []• 960

.971 ./x

.2 .3 .4 .5 .6 .7 8 .0

Xllre f

(b) Configuration C-2; 0.99.1 _-<M _-<0.971.


61

CP

-.2

Macn 16Ft. 8Ft.

No. TT TPT

• 976 O

.980 [] D•984 0 ©.990 A A

_ z A / A A A

----C

0 p, sonic _

.i

.2

-.l

.1

sonic

.2

9

-.1 0 )O(_@DOD oO _°_0 _COC,OO([ (: ODc_EL_

0 o_ _%_-C

0 p, sonic

.1

Qi

.20 .l 2 .3 .4 .5 .6 .7 .8 .9

X/Ire f

0

(

0

0

I1.0 1.1

(c) Configuration C-2; 0.976 _-<M < 0.990.


62

Mach 16 Ft. 8Ft.No. TT TPT

•995 0.999 [] P

1.010 O _>1.019 A

0c

P

.1

.2 .3 .4 .5 6 .7 .8 .9x/I rel

(d) Configuration C-2, 0.995 <-M < 1.019.


63

cp

-.2 _ I I

---C

_ p, sonic_

1

o _

1

2

-.1

0 _ ....... _'_<

.l

.2 >

Mach 16Ft. 8Ft. 8Ft. TTNo. TT TPT CAL

•697 © O,• 8O0 3 C,• 849 _ <_ Q

•900 zx .A

A

-.1

0

.1

_,E'=_.--@z'__ _-_ _E ,, _ _,a _

E]E

-1

0 .i .2 3 .4 .5 .6 .7 .8 .9xll re[

(e) Configuration C-3; 0.697 _-<M -<0.900.


c,

I10 l l

64

Mach 16 Ft. 8Ft. 8Ft. TT

No. TT TPT CAL

• 921 0

.940 []

.951 o _

.961 zx

.1

CP

2

(f) Configuration C-3; 0.921 -< M _-<0.961.


65

CP

-.2I

__ r--Cp, sonic

A0 _

A

A

Mach 16 Ft. 8Ft. 8Ft. TT

No. TT TDT CAL

•969 q

.977 D

.979 C _ #•985

Z

A A

A_

A

A

A2

C-- p, sonic-

---Cp, sonic

_/ __ _][]LJD[]] ] E E E L [] [] [] T][[][ ],r'l,

-I

30

.l[]

_E

[]

.2

- ]

0

_Cp, sonic

cJ_)o_ D_ c c c c c c c0

c

0

.1 o

CO0 D

OCD@(0 C

Do

)

0

.2 .3 .4 .5 .6 .7 .8

X/Ire I

.q

C

I1.0 I.i

(g) Configuration C-3; 0.969 _-<M -<_0.985.


66

L •

7, 'ii.

]i • ,_

-.2

-.1

.1

.2

.3

-:1

Cp 0

.i

I I

--C

t%

'_ --C

m p, sonic-

L E:_d_Dd

[]

rn

Mach 16 Ft. 8Ft. 8Ft. If

No. Ti- TPT CAL

•990 O ,O q

• 995 []

1.000 0 <_ Q

< z <>

L E q E E LEBnE3 E

HE3EU

3

[]

.3 N-

I4

0 .1 .2 .3 4 5 .6 .7 .8 .9 1.0x/I

ref

(h) Configuration C-3; 0.990 _-<M < 1.000.


1.1

67

[:'- , .':

_'/'/.L.i.i.

.2C

P

-.2

7- Cp, sonic-i

E]Z]L_

.I

.3

[]

C

- I p, sonlc

o

0.i

-6.2

[

NlachNo.

I. 008I. 020

] [

16 Ft. 8 Ft.TT TPT

o ,o[]

[

8Ft. TTCAL

n.

F- []

-q

[], [z1,

oo :_cC C C 0

E3E3

()

P

)

8

©

.3

.4

()

0 .1 .2 .3 .4 .5 .6 .7 .8

x/I ref

(i) Configuration C-3; 1.008 < M < 1.020.


.9 1.0 1.1

68

Mach 16 Ft. 8Ft.X]o. Fl TPT

•699 0.801 [].85_ © 9• 900 z_ .&

2

CP

3

.2

.3

-:I

.2 .3 .4 5 .6 .7 .8 .9

x/Ire f

(j) Configuration C-4; 0.699 _-<M -<_0.900.


1.0 1.1

69

Mach 16 Ft. 8Ft.

No. TT TPT

.921 0

• 941 []

•95o 0 S>

0

P

.i

.4 o .2 .3 .a .5 .6 .7 8

X/'re f

(k) Configuration C-4; 0.921 _<M -<_0.950.


1.0 1.1

7O

i ¸ i:: ¸ /

CP

0

Mach 16 Ft. 8Ft.

No. TT TPT

.961 O• 970 []

.976 _ _)

.2 .3 .4 5 .6 .7 .8 .9

X/Ire f

(1) Configuration C-4; 0.961 _-<M _-<0.976.


11

71

.; ': , t . " .

/ -

/

:;:_i I¸:¸• _

: <.i, i: ,_ : '_i

-.2

-.I

.I

.4

nl

0C

P

.3

.4

-t

.2

.3

1

Mach 16Ft. 8Ft.No. TT TPT

•981 O.9_ [].992 <} 9

.2 I 3 4 .5 .6 I 7 8 I 9

Xllre f

t.0 l.]

(m) Configuration C-4; 0.981 _-<M < 0.992.


72

i':/¸ / " // 'L

Mach 16 Ft. 8Ft.No. TT TPi-

• 995 ©1.000 [] E3].olo _ 9

!i :: !_:ii__

Cp

.2 .3 4 .5 .6 .7 .8 .9

xllre f

(n) Configuration C-4; 0.995 < M _-<1.010.


73

/

/

CP

-.2

=I

0

.i

.2

.3

.4

.I

.2

F

F

[][]

[]

3

00

0

Cp, sonic

[].nlZt []

Cp,sonic

]E] [] q

O0 DC

Mach 16Ft.No. TT

1.020 01.O99 []

E [] [][] E] [] 3_

0 o( ooDC

[]E]E []

oOC 0 0 DOG:pc D0

0C

[]

[]

[]

D

©0

.3

.4

.5.] .2 .3 .4 .5 .6 ,7 .8

x/Ire f

(o)Configuration C-4; 1.020 < M -_<1.099.


.9 1.0 I.I

74

2

-1

Mach 16Ft.No. TT

• 698 C• 802 []

E Fj 7

Dm DE F1E] E L:J U D" D LJ U E:]EDDE

E][]

[]

CD

0

o

.1

D

.2

O0 On Dr" Ooc 0_ DoG O

0©

0

.4

.5

.6

.I

.8

.9

1.0

1.1

1.2

1.32 .3 .4 .5 .6 .7 8 .9

x/I"ef

(p) Configuration C-5; 0.698 =<M < 0.802.


1.0 1.1

75

i •

_i i I _ •

• •'i

i• L

.I

Cp

.2

Math 16Ft.

No. IT

•850 ©

•901 []

(q) Configuration C-5; 0.850 _-<M < 0.901.


76

-.2

Mach 16 Ft.

No. TT

.921 0

.941 []

-.I

.2

-.I

.2

C0

.3

.4

.5

.6

.7

8

.9

1.0

Iii

L.2

1.3m2 3 m_ 5 16 17 m8

X/Ire f

.9 1.0 1.1

(r) Configuration C-5; 0.921 _-<M _-<0.941.

Figure 15,- Continued.

77

Math 16Ft.

Xlo. TT

.952 co•961

2

CD

.3

1.0

l.l

1.2

1.3

(s) Configuration C-5; 0.952 -<M -<0.961.


78

Mach I6 Ft.No. TT

.972 0

.977 []

[ 3

)

©

I

L

3

.6Ii .2 ,3 _ I5 .7

x/I ref

I

[

) SE

(t) Configuration C-5; 0.972 < M < 0.977.


3

I

]

)

9

)D

G

I

I

I

lIO 1.1

79

-.2! I I

--C

p, sonic

--.1 d___ E [] DE E

o 'g_

.2

-I

.2

CD

.3

[]

f--Cp, sonic-

J/ @_¢ o o o

©

Mach 16Ft,

No. TT

.982 O• 987 []

UdED EU L []q mD3 [] []

q

EE

O De 0 3 O0 )C Oc3 0 o )oc

3 E3

[]E

3C0

R

3

Eq

[]

L)0

©

.5

.8

3

.9 --

1.0

1.1

1.2

1.32 .3 .4 .5 .6 7 .8 9

X/Iref

(u) Configuration C-5; 0.982 _-<M <_-0.987.


Il0 ].l

80

! i i¸¸ _

_' , ; _,/i _ • _

i

0

.I

.2

Cp

.3

Mach 16 Ft.No. TT

.991 0•997 []

.8

.9

1.0

I.I

1.2

1.30 .1 .2 .3 .4 .5 .6 .7 .8 .9

X/Ire f

(v) Configuration C-5; 0.991 =<M <: 0.997.


1. I

81

-.2

Mad 16 Ft.

No, IT

1.000 0

1.012 Z

-.1

.2

=L

.2

CD

.3

.7

.8

.9

1.0

1.1

1.2

1.3.1 .2 .3 .4 .5 .6 7 .8 9

x/Iref

(w) Configuration C-5; 1.000 -<_M < 1.012.


L.0 l.l

82

.. . i _.

k ,

"'V .

CP

Mach 16Ft.No. TT

1.O22 O

I

I

I

I

I

I

I

I

I

i

I

I

I

I

I__ e-

l

I

I

i

I

I

I

I

I

__+_

.3

I

f.4 .5

x/Iref

C

II

I

I

i

.6 .7 .8

__

.9 1.0 1.1

(x) Configuration C-5; M = 1.022.


83

2

,i

. L

i__ ,"i __k_::

.1

Mach 16Ft.No. TT

.700 0• 8O2 []

1.0

I.I

2 .3 .4 .5 .6 .7 .8 9

X/Iref

(y) Configuration C-6; 0.700 < M -< 0,802.


LO ].1

84

: :>i:: i/:¸

:ii_, _._ _ i_

0

.l

-,2

.2

Cp

.3

Mach 15 Ft.No. TT

• 851 0• 902 []

.2 .3 .4 .5 .6 7 .8 .9

x/l ref

(z) Configuration C-6; 0.851 -<M -< 0.902.


85

p, ,Oli(

I

p, nJ,

0 .1 .2

I

_5i

I.4

Mach 16 Ft.

No. TT

922 1942 []

E

J

C

.5 .6 7

x/I ref

TTZ]-

I Fq

DIC)

©

C

k.8 .9 1.0

(aa)Configuration C-6; 0.922 <_-M -<_0.942.


86

j _ ,i,/_ ' _ .

C _i_:::i;/

¸%:.¸ <j_ : !

• /

-.2 --_

Cl,soric

[]0

.1 3_

-.2 •f -C

), SOl liC_

(

Co

0

)

.4

.6

.7

.8

]

.9

1,0

L1 --

1,2

q]

1.30 .l .2

.I

.2

CP

.3

Mach 16 Ft.No. TT

•052 0•961 []

_ -

_- 1'

C

o )

m

3 .4 5 .5

x/I ref

E D

O

E

(

.g

__ r

E

]D

_ E

L)

(

o

C _

i __ __

I1.0

(bb) Configuration C-6; 0.952 =<M < 0.961.


87

-.2

Mach 15 Ft.

No. TI

• 970 O• 976 []

.I

.I

-.2

-.l

.3

CP

.4

.7

8

.9

1.0

1.1

1.2

1.31 .2 .3 4 .5 .6 .7 .8 .g 1.0 ].1

x/I ref

(cc) Configuration C-6; 0.970 =<M _-<0.976.


88

Mach 16 Ft.'40. IT

.982 0

.988 []

.]

cP

2

7

8

.9

1.0

I.I

1.2

• i .2 3 .4 5 .6 .7 8 .9

X/Ire t

(dd) Configuration C-6; 0.982 < M _-<0.988.


l0 11

89

Mach 16 FLNo. TT

.992 0

.995 []

9O

.1 .2 .3 .4 .5 .6 .7 .8 .9

X/Iref

(ee) Configuration C-6; 0.992 _-<M < 0.995.

Figure 15.- Continued:

Mach 16Ft.No, ]-T

1.002 O].011 []

1

-.2

7

8

1.0

L.1

L2

.1 .2 .3 .4 .5 .6 .7 8 .9

x/I ref

(ff) Configuration C-6; 1.002 =<M -< 1.011.

Figure 15,- Continued.

91

H .2

_1

.1

.2

.3

CP

(DC OOC

----C

-- -- p, sonicC

0

©

Mach 16Ft.No. TT

1.02] o

0

(' oO o OOC 0

I

I

Io o _oo cDO U C: O Do

.4 w_.

.5

.6

r

I

.7

.8

o

C

oo

.... _ • _-__--

.9

1.O

1.1

1.2

1.30 1 .2 .3 4 .5 6 .7 .8 .9

x/lref

(gg) Configuration C-6; M = 1.021.


l0 ]l

92

L

/,

i , i :/

ii

Mach

No.

• 697

• 799• 849

• 899

16 Ft.

TT

0

[]

<>z_

8Ft.

TPT

<>

0

CP

.i

--.i

.20 .i .2 .3 .4 .5 6 .7 .8 .9 1.0 1.1

Xllre f

(a) Configuration D-l; 0.697 < M < 0.899.

Figure 16.- Pressure-coefficient distributions obtained for type D configurations.

93

_" %1

-.2

-.l

.l

-.2

-.i

0

P

.i

-.2

-.l

.l

-.2

.2

Mach 16 Ft. 8 Ft.

No. TT TPT

.918 O

• 940 []

•949 <> <_• 959 A

.2 .3 .4 5 .6 i7 8

X/I ref

.9

(b)Configuration D-l; 0.918 -<_M < 0.959.


1.0 l.l

94

r

I

©B

©

_°

o

I

_°

ITA

I1^

Q

CO

i

_ ,_, _i_ _ _"; "_ i .... i_i_"

.... qi! ; i ¸ r _ : : ; :i I .

_ _ __ _ - • ; _i_:ii_ ,_;!_ii_,_i__i- _-

i

.i ?

• i

LL

"/ ' L"

f

x

-.2

-.1

_A

.1

5-.2

=1

C ,_,P

.i

--]p, sonic

[]-.I --

[]

Nlach

No.

• 989

• 995• 996

1.011

16 Ft.

TT

0

[]

©A

8 Ft.

TPT

<>.A

2L_,

.i

-.2

Cp, sonic

Cp, sonic

F _ [] [] [3 =3 3 EIDEDE3•[

^/N,

yq

:]_---

0

;PGOp,sonic

i .2 .3 ._ .5 .6 7 .8 .9xll

ref

(d) Configuration D-l; 0.989 =<M < 1.011.


DO ( )

[2E

F]F1

,4L

t>

<>9 ¸

E_

[3

O0

I1.0 1.1

96

• _i _i____ _ _,_

i _ _

_ ; ,'_ , -_ _ _i_

:i

_1

CP

0


._o p

._8 p

.951 _ 9

.3

.2 3 4 .5 .6 .7

X/Ire f

8 .9 l.O 1.1

(e) Configuration D-2; 0.850 < M < 0.951.


97

• "i' _

" . , . - • •

98

cp

-.2

Mach ]6 Ft. 8 Ft.No. TT TPT

•970 ©

.976 E

•981 0

?0 _<_ p, sonic _

.1

'__ [

-_ Cp, sonic .... 40 -[!] ........

.1

.2

-.2

[]

1 b 0

_) ,._.O 0 )©q_- oOC 0 .0 ( 0_J'-C

p, sonic

0

1 I

• ] .2 3 .a .5 .6

X/Ire f

0 _ )0

D

.7 .8 .9

I

c-i

1.0 1.1

(f) Configuration D-2; 0.970 < M _-<0.981.


,_ _ii_ • -, "

! ,{__ii _i}i____!

• v -

i.... i_•/_;-.

i •ii•_!_ }

-.2

-.1

.2

.3

-.2

__;><>p,sonic

Y

3C

cO-- p,


•984 ©• 990 [] P.995 0 ©

sonic - E_

-.2

0

C 3

G_

) o,DO0(r_) OCn _@0_

° Das_q:_t°Cp,somc

.2 .3 .a .5 .6 .7 .8 Q

X/I ref

(g) Configuration D-2; 0.984 -_ M _ 0.995.


c

o

I]0 I I

99

• k " •

y

:i_ i ,h _

ii _ i i

-.2

0 _

1

2

E_

2 --

]

.3

-.1 0

_D0 -- --

[

.2_

•3 0

.3

:l

po

3,scnicI

Ii

I

F-i

II

" i

]E 31 E]

_FIICP,

)

)

p, sonic


•999 0 ,01.00] E]I. 0]9

3[ _J[ 1::] flz

4x/I ref

!

.6

sr n cs_: TjsE

D! © )

.7 8 .9

(h) Configuration D-2; 0.999 =<M < 1.019.


!

>

[3L_[]

1.1

lOO

-.2

-.1

[CI or

0

P p,

o

0

1

.2

-.2

-.1 _ -

0

.1

.20

.2

-.2

-.1

.1C

P

.2

-.2

Mach 8Ft.No. TPT

• 85 P.90 }:3

.95 ©

.98 A

i

tj

5; )

.2 .3 4 .5 6

Xllre f

.7 .8

s

(i) Configuration D-4; 0.85 _-<M _-<0.98.


1.0 11

101

-.2

Mach 8 Ft.

No. TP]

.985 Z• 99] 13

1.ooo _,1.01o

-.1

.1

.2

-.2

-.1

0

CP

.1

.2

-.2

-.]

2

-.2

-.1

.2.2 .3 .4 ,5 ,6 7 .8 0

xll rel

(j) Configuration D-4; 0.985 _-<M _-<1.010.


1.0 1.]

102

CP

-.2

_l

.2

.3

-.2

.l

"4

.( '

/

0

/

r

]

/.

0 - _C

-q/

I

.2 5

.3 --

0 1 .2

.3

-.2

-.1

MacY

No,

• 698

• 800

•850

L

16 Ft. 8Ft. FligmTT IPI

0[]

]

5 .6

x/I ref

Theory Iref. 9_ ....

!

4_ " __

}S>

\

\

.8 .9 1.0

(a) 0.698 _-<M <_-0.850.

Figure 17.- Pressure-coefficient distributions obtained for configuration E-3.

103

_':.,i.: i_:I'_

L

-.2

-.1 _:iCp, sonic-

_<0 /,

Q-

.1/

.2 I

0

.3

-.2

._< _,--<

7

Mach 16 Ft. 8Ft. FlightNo. TT TPT

•901 O ,O Q•920 [].94o O

Theory (ref. 9) .....

\\

-.l --

Cp ..'I:: -_

0 _[]/

.I [/

I

[]I

I.2 I

.3

-.2

]_]"

\\

-.I

0

.i

!

.2 ©

6

.3o l

.f

.___ ___ _ __A_--L_-_-c_-_

I2 .3 .4 .5 6 17

x/l ref

(b) 0.901 =< M =<0.940.


.8

C

9 1.0

104

Mach 16Ft. 8Ft. FlightNo. TT TPT

950 0 ,_ Q.961 [].97] 0

Theory (ref. 9) ....

.3 .4 .5 .6 .7

x/I ref

(c) 0.950 < M < 0.971.

Figure 17.- Continued,

8 . 9¸ 1.0

105

Mach 16 Ft. 8Ft.

No. -_ TPT

.976 O

.981 [] El Theory (ref. gl ---

.986 Q

-.2 i i

__f -%,sonic_ ,-] < <>_ > __>/<

0 --I_" \v

f

.1<

//

.2 "_II

.3 7

-.2

p_l __j/Z

0

J

.1 j:i///

[].2 /

IIi

I

--Cp, sonic-

__ ---E

3

-.2

__ p,son_c_

-.1 )

.1

.2

.3

0 ,,,(

Y

//

®/III

©

0 l .2 .3 4 .5 .6 .7

x/I ref

",\\\

\

q,,

\\

\

\\,(

.8 .9 1.0

106

(d) 0.976 =<M =<0.986.


-.2

Mach 16 Ft. 8Ft.

No. TT TPT

• 99O 0

• 997 []

].ool © ©Theory (ref. 9) .....

4

-.2

-.1

C13

0

.3

-.2

=]

.2

.3.2 .3 .4 .5 .6

x/I ref

.7 .8 .9 1.0

(e) 0.990 =<M =<1.001.


107

_ _" iI, _ , _ _

-.2

_i

.I

.2

CP

.3

.4

[]

]

I

sonic

[

]

]


1.011 0 PI. 021 [] ,_

LJ _ '

[] EE "I r, r

C ,E3 _-J _-

]

rl

j LJ

F:I

,[3[]

-.2

=1

0

.l

.2

--Cp,

/

©

sonicC

() ()

() ()

.3 0

108

.4.I .2 .3 .4 .5 .6

X/Ire f

(f) 1.011 < M < 1.021


.7 .8 .9 1.0

c3)C.Dc"

(1)(,Dk_O

Ll..

OO

r'_

¢D

.08

.O7

.O6

.O5

.O4

.O3

F---

.02kl-

.01

0 2I

//

/

© C-2

[] C-3

<> C-4

//i

/////

z_Z]/

-.01. Ol 0 . Ol .02 . 03 . 04 .05 .06 .07

CD16 Ft. TT CD8 Ft. TPT) pressure integration

Figure 18.- Comparison of drag-coefficient increments obtained from both

force-balance and pressure integration•

/

.O8

.ASA-La.gley,1973 , L-8449 109

'k_• -_ I_ILI_I.•_•I_ _ill , • kii,!i k i i¸

J_xI_Iii__ _irl __¸I_ir____!_ivl!rL

Documents

Effect of blockage ratio on drag and pressure distributions for bodies