Pressure distribution of spherically-blunted 60 deg half-angle cone in hypersonic flo

Kurtz, D. W.

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NATIONAL AERONAUTICS AND SPACE ADMINISTRATION
Technical Memorandum 33-404
Detailed Pressure Distribution on a
Blunted 60-deg Half-Angle Cone at
Mach Numbers of 6.08 and 9.46
Donald W. Kuriz
1,
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JET PROPULSION LABORATORY
CALIFORNIA INSTITUTE OF TECHNOLOGY
PASADENA, CALIFORN IA
September 1, 1968
q..
NATIONAL AERONAUTICS AND SPACE ADMINISTRATION
Technical Memorandum 33-404
Detailed Pressure Distribution on a
Blunted 60-deg Half-Angle Cone at
Mach Numbers of 6.08 and 9.46
Donald W. Kurtz
Approved by:
ate'- <D 	 ,	 .
Bain Dayman, Jr., Manager
Aerodynamic Facilities Section
JET PROPULSION LABORATORY
C A L I F O R N I A I N S T I T U T E OF T E C H NO LO G Y
PASADENA, CALIFORNIA
September 1, 1968
TECHNICAL MEMORANDUM 33-404
Copyright © 1968
Jet Propulsion laboratory
California Institute of Technology
Prepared Under Contract No. NAS 7-100
National Aeronautics & Space Administration
Contents
I. Introduction .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 1
U. Model .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 2
Ill. Test Procedure	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 2
IV. Results of Investigation . 	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 2
V. Conclusions	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 5
Nomenclature	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 6
References	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 6
Figures
1. Test model, front and side views . 	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 2
2. Test model mounted on 1-in.-diam sting carrying external base
	
thermocouple, with pitot tube-cooling shield down . . . . . . . . . . . 	 3
3. Pressure distriburion along ray, indicating the compression cusp
at the leeward breakpoint .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 3
4. Comparison of pressure distributions at the two Mach numbers . . . . . . .	 4
5. Variation in pressure coefficient on the nose port as a function of
angle of attack for the two Mach numbers . . . . . . . . . . . . . . 	 5
6. Maximum CP location as a function of angle of attack for the two
	
Mach numbers	 .	 .	 .	 .	 .	 .	 .	 . .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 5
JPL TECHNICAL MEMORANDUM 33-404	 iii
Abstract
An investigation of the detailed pressure distribution on a spherically blunted
60-deg half-angle cone was conducted in the hypersonic wind tunnel at the
Jet Propulsion Laboratory. Wind tunnel tests on a specially designed model
indicated that the pressure coefficient distribution over the surface seemed to
be almost independent of Mach number at 6.08 and 9.46. At both Mach numbers,
the nose pressure remained within a band of 3% through angles of attack from
0 to 6 deg. Beyond 2 deg, the displacement of the stagnation point from the
longitudinal body axis was not a linear function of angle of attack. Although
base pressures were measured, they are not included here because support inter-
ference yielded questionable data.
iv	 JPL TECHNICAL MEMORANDUM 33-404
Detailed Pressure Distribution on a Blunted 60-deg Half-angle
Cone at Mach Numbers of 6.08 and 9.46
I. Introduction
The requirements for a suitable atmospheric reentry
body involve a multitude of trade-offs and compromises
that include:
(1) High drag characteristics.
(2) Aerodynamic stability.
(3) Heat dissipation.
(4) Suitable packaging.
The vehicle must exhibit high drag characteristics, so
as to utilize the planetary atmosphere for initial de-
celeration, simultaneously demonstrate a fair degree of
stability, and provide suitable packaging for the experi-
ments. At hypersonic speeds, the heat dissipation in
the boundary layer, which surrounds the skin of the
vehicle, creates extremely high temperatures. This dic-
tates another essential consideration. Highly blunted
bodies afford a compromise capable of satisfying the
demanding requirements of the vehicle. Wind tunnel
studies, performed on a variety of configurations at sub-
sonic, supersonic, and hypersonic speeds, indicate satis-
factory drag, stability, and heating characteristics. Be-
cause of their geometric simplicity, highly obtuse cones
are well suited for this purpose.
To obtain a detailed pressure distribution over the
face, edge, and base of a blunted core, a high-speed test
program was undertaken in the 21-in. hypersonic wind
tunnel at JPL. The test was conducted at two Mach
numbers. At Mach number 6.08, the angle of attack was
— 8 to + 16 deg. At Mach number 9.46, the angle of attack
was 0 to + 12 deg. The principal results of the investi-
gation+, derived from testing a model and recording
pressure measurements, are summarized.
'The complete results of this program are contained in JPL docu-
ment SR 900-183, available on request to J. Jackson, Support
Section Technical Information and Documentation Division, Jet
Propulsion Laboratory, Pasadena, Calif.
JPL TECHNICAL MEMORANDUM 33-404 	 1
Il. Model
The model consisted of a "sharp edge" 60-deg half-
angle cone with a nose bluntness ratio S of 0.23. The
edge was constructed (see Fig. 1) such as to approximate
the structural considerations necessary for a full-size cone.
A total of 25 pressure ports (Fig. 1) were installed on
the model; 21 on the face, one on the edge, and three on
the base. Those on the face were aligned in two com-
plementary rays with staggered radii in order to ac-
complish a maximum of coverage with a minimum of
interference. The edge and three base ports were co-
linearly aligned with one of tLe forebody rays, but were
in the opposite quadrant.
Two chromium-alumel thermocouples were installed
on the model to continually monitor and record local
temperatures for thermal-creep" considerations. One
thermocouple was mounted on the base and one was
mounted internally behind the model nose.
The 4-in.-diam stainless steel model %vas mounted on
a 1-in. hollow sting, which housed all 25 pressure tubes
and the nose thermocouple, and carried the base thermo-
couple in such a manner as to allow roll angles of ±90 deg
without any interference or damage to the tubes or
thermocouples.
III. Test Procedure
The investigation was conducted at Mach numbers of
6.08 and 9.46 with Reynolds No./in, of 2.7 X 10 and
1.18 X 10'', respectively. The model was sting-supported
and had a sting diam-to-model-base-diam ratio of 0.25.
The hollow sting, which housed the pressure port tubes
and thermocouple leads, was pitched to angles of attack
of — 8 to + 16 deg and 0 to + 12 deg at Mach numbers of
6.08 and 9.46, respectively. To obtain a detailed pressure
distribution, the model was rolled through a total of
180 deg at either 30- or 45-deg intervals at each angle
of attack. Hence, the two complementary rays were ro-
tated through a common quadrant and these data, when
incorporated, resulted in a more detailed radial pressure
distribution in this region.
The JPL 100-port multiple pressure measuring system,
an updated version of the system described in Ref. 1,
"Thermal creep may occur with high temperature. low pressure
measurements in small diameter tubes in which the molecule mean
free path becomes of the order of the tube diameter. These con-
ditions c4use the settled pressure in the tubing; to have a higher
pressure at the hot end of the model than at the cold end, where
the transducer is located.
VERTICAL RAY IS SHOWN
AT A ROLL ANGLE 0 OF 0 deg
A
+—	 FACE PORTS
BASE PORTS (3)—^ i^
	 \\	 (21)
^ ^
	
4.0
0;9000	 0l
7
EDGE PORT (1)	 i
HORIZONTAL RAY SHOWN
A	 AT A ROLL ANGLE 0 OF
-90 deg
^0.062ODx0.006
SS TUBING
0.823 P,---- ;Z_ 7711/11 1°
NOSE PORT
BREAKPOINT
	
0.372
60 deg
45 dcq
ALL DIMENSIONS
ARE IN INCHES	 SECTION A-A
was employed to measure and record all surface port
pressures. The system was advanced manually to enable
the operator to monitor and account for the pressure
lag. The pressures at the one edge and three base ports
were measured by means of a precision oil microma-
no.neter (Ref. 2) and were subsequently recorded on a
digital channel. Settling times for these low pressures
were upwards of 5 min. A retractable cooling shield was
installed in the tunnel (Fig. 2) to permit model surface
cooling by injecting gaseous nitrogen into the flow
stream immediately in front of the model. Model cool-
ing was employed near the end of the test to observe
possible thermal-creep errors related to the high model-
temperature and low base-pressure measurements at the
high Ma,_h number (Ref. 3). The entire test was con-
ducted in the 21-inch hypersonic wind tunnel (Ref. 4)
at JPL.
IV. Results of Investigation
The results of this cone study are presented in the
form of a pressure coefficient as a function of a non-
dimensional distance from the nose port. On leeward
rays at angles of attack, a characteristic cusp in these
curves resulted at the break-point (Fig. 3). The break-
2	 JPL TECHNICAL MEMORANDUM 33-404
WINDWARD LEEWARD MACH 9.46(0, deg 0
I
R e /n. x 10-5
Q, deg
O	 10
q 	 4
COMPRESSION CUSP
(NEAR BREAKPOINT)
2.0
1.8
U
Z
1.6
U
w
w
w
O
U
w	 1.4
w
a
1.2
1.G
0.6	 -0.5	 -0.4	 -0.3	 -0.2	 -0.1	 0	 0.1	 0.2	 0.3	 0.4
NON-DIMENSIONAL DISTANCE FROM NOSE PORT 5
Fig. 3. Pressure distribution along ray, indicating the compression cusp at the leeward breakpoin
0.5	 0.6
Fig. 2. Test model mounted on 1-in.-diam sting carrying external base thermocouple,
with pitot tube-cooling shield down
JPL TECHNICAL MEMORANDUM 33-404	 3
1.8
'ANDUM 33-404
v
Z 1.6W
U
OV
W
oc
N 1.4
W
cr.
2.0
1.0
-0.2
1.2
Mach No.	 R, 	 in. x 10-
5
	a and	 0, deg
O	 6.08	 2.70	 0
q 	 9.46
	
1.18	 0
e e 0
MODIFIED 0	 8
NEWTONIAN e
PRESSURE 8DISTRIRUTIOi
e
0
EDGE OF MODEL—^
0.5	 0.6-0.1	 0	 0.1	 0.2	 0.3	 0.4
NON-DIMENSIONAL DIS T ANCE FROM NOSE PORT S
Fig. 4. Comparison of pressure distributions at the two Mach numbers
^ ear ^... ..
point is the point (Fig. 1) corresponding to the inter-
face of the spherical nose and conical section. This cusp
is the result of an al,rupt flow compression at that point;
i.e., the flow over the spherical nose acquires angular
momentum as it accelerates over the surface. At the
interface of the spherical and conical surfaces ;Fig. 3),
the flow undergoes a compression, which manifest- itself
in it rise ahruptly changing t1w slope of the
pressure coefficient curve at this point. The flow over ;he
face accelerates from a stagnation point near the nose
to the sonic point near the sharp edge. In this flow region,
the surface pressure is inversel y proportional to the square
of the local surface velocity. The characteristic negative
pressure coefficient gradient over the conical portion of
the hcxly is a result of this flow acceleration.
The Mach numhcr variance frc,m 6.08 to 9.46 resulted
in a surface pressure coefficient increase of less than 1%
at 0-deg ankle of attack (Fig. 4). A Newtonian distribu-
tion is presented for comparison.
The pressure coefficient on the nos(- of the cone (Fig. 5)
is relatively constant for certain angle-of-attack regions.
At angle of attack of —6 deg to +6 dcg inclusive, the
nose pressure coefficient (S = 0) varies only 2T at Mach
number 6.08 and W at Mach number 9.46. It is interesting
to note that beyond 2 deg (Fit;. 6), the displacement of
the stagnation point from the longitudinal bod y axis is
1.85
`v
1.80
O
a
O	
1.75
z
z
O	 1.70
z
v
LL	 1.65w
O
v
1.60
w
1.55
1.50
-8	 -4	 0	 4	 8	 12	 16	 18
ANGLE OF ATTACK a, deg
Fig. 5. Variation in pressure coefficient on the nose
port as a function of angle of attack for
the two Mach numbers
^z 5
X	 0.04v 10
15
0 - 0.08 20
z 
U
O-
_	 0.12
25
30
a ^,
O N
0.16
—
Moch No.
O	 6.08
q 	 9.46
C	 2	 4	 6	 8	 10	 12	 14	 16
ANGLE OF ATTACK a, deg
Fig. 6. Maximum CP location as a function of angle
of attack for the two Mach numbers
not a linear function of angle of attack. This trend results
in a favorable static stability
 contribution.
The results of the base presstirc investigation are not
presented. Due to the low pressures at these Mach
numbers, the settling times were extremely large and
not clearly defined. Also, a: ,hese hypersonic Mach num-
hers, it is expected that the sting support has a significant
effect on the measured base pressure. The base pressure
is, to it degree, a function of the wake neck diameter
and position, both of which are greatly affected by the
presence of a sting. These combined effects resulted in
base pressure measurements that were as great as 211^2
times the free stream static pressure at '.\iach 9.46. Due
to these high measured pressures, thermal-creep correc-
tions were found no. to be applicable.
V. Conclusions
A wind-tunnel test has been performed to determine
the detailed pressure distribution over a blunted 60-deg
half-angle cone at Mach numbers 6.08 and 9.46. The
ma;or conclusions were:
(1) A distinct pressure rise occurred on leeward rays at
the breakpoint due to an abrupt flow compression
at that point ( Fig. 3).
(2) Mach number variance from 6.08 to 9.46 resulted in
a pressure coefficient band of less than 1% (Fig. 4).
(3) The displacement of the stagnation point from the
longitudinal body axis is not a linear function of
angle of attack beyond 2 deg (Fig. 6).
(4) To a large extent, the base pressure of a cone is a
function of the wake neck diameter and position,
both of which are greatly affected by the presence
of a sting.
<3 %
<2
Mach No.
O	 6.08
q 	 9.46
I
JPL TECHNICAL MEMORANDUM 33-404 	 5
Nomenclature
D base diameter, in.
d dimensional distance along model surface on
a ray from nose port, in.
CP pressure coefficient, p — p„/q,
M Mach number
p surface pressure, psi
pm
 free stream static pressure, psi
q. free• stream dynamic pressure, psi
R,/in. Reynolds No./in.
r. nose radius, in.
S non-dimensional distance from nose port, d/D
n angle of attack, deg
S nose bluntness ratio, r„ 'D
,I angle between longitudinal body axis and
position vector emanating from nose radius
origin, deg
0 angle of roll, deg
References
1. Covey, 11. E., "Activities in the 21-in. Hypersonic Wind Tunnel," in Suppor!ing
Research and Advanced Development. Space Programs Summary 37-21, Vol. IV,
pp. 59-67. Jet Propulsion Laboratory, Pasadena Calif.. June 30, 1963.
2. Kendall, J. M., The Design and Performance of Precision Oil .11icromanometers,
NAVORD Report 6803, U.S. Naval Ordnance Laboratory, White Oak, Mary-
land, July 1961.
3. iloward, W. M., An Experimental Investigation of Pressure Gradients Due to
Temperature C:radients in Small Diameter Tubes, Memorandum No. 27
GALCIT, California Institute of Technology, Pasadena, Calif., June 10, 1955.
4. let Propulsion Laboratory lVirul Tunnel Facilities, Technical Memorandum
33-335. Jet Propulsion Laboratory, Pasadena, Calif., Apr. 1967.
6	 JPL TECHNICAL WMORANDUM 33-404


Detailed pressure distribution on a blunted 60-deg half-angle cone at Mach numbers of 6.08 and 9.46

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