Temperature recovery factors on a slender 12° cone-cylinder at Mach numbers from 3.0 to 6.3 and angles of attack up to 45°

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Material Information

Title:
Temperature recovery factors on a slender 12° cone-cylinder at Mach numbers from 3.0 to 6.3 and angles of attack up to 45°
Series Title:
NACA RM
Physical Description:
56 p. : ill. ; 28 cm.
Language:
English
Creator:
Reller, John O
Hamaker, Frank M
Ames Research Center
United States -- National Advisory Committee for Aeronautics
Publisher:
NACA
Place of Publication:
Washington, D.C
Publication Date:

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Subjects / Keywords:
Heat -- Transmission   ( lcsh )
Laminar boundary layer -- Research   ( lcsh )
Aerodynamics -- Research   ( lcsh )
Genre:
federal government publication   ( marcgt )
bibliography   ( marcgt )
technical report   ( marcgt )
non-fiction   ( marcgt )

Notes

Abstract:
Abstract: Temperature recovery factors were determined for a slender, thin-walled cone-cylinder, having a 12° vertex angle and a 1.25-inch-diameter cylinder, at Mach numbers from 3.02 to 6.30. The angle-of-attack range was 0° to 45° at Mach numbers up to 3.50, and about 0° to 20° at Mach numbers from 4.23 to 6.30. A transverse cylinder of the same diameter was also tested at Mach number 3.02. Free-stream Reynolds numbers varied from 1.8 to 11.0 million per foot. Flow visualization studies of boundary-layer transition and flow separation were made and the results correlated with recovery-factor measurements.
Bibliography:
Includes bibliographic references (p. 19-21).
Statement of Responsibility:
by John O. Reller, Jr., and Frank M. Hamaker.
General Note:
"Report date July 20, 1955."
General Note:
"CONFIDENTIAL"--stamped on front and back covers
General Note:
"Copy 390."--stamped on front cover
General Note:
"Classification changed to unclassified Authority: NASA Technical Publications Announcements #14 Effective date: February 8, 1960 WHL."--stamped on front cover

Record Information

Source Institution:
University of Florida
Rights Management:
All applicable rights reserved by the source institution and holding location.
Resource Identifier:
aleph - 003854733
oclc - 156189461
sobekcm - AA00006146_00001
System ID:
AA00006146:00001

Full Text

c Copy
.- RM A55G2











RESEARCH MEMORANDUM


...... TEMPERATURE RECOVERY FACTORS ON A SLENDER 120

S, CONE-CYLINDER AT MACH NUMBERS FROM 3.0 TO

6.3 AND ANGLES OF ATTACK UP TO 450

By John O. Reller, Jr., and Frank M. Hamaker

., Ames Aeronautical Laboratory
Moffett Field, Calif.




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I maw=n r .to am mulnired peson is poblbi ed b law.
NATIONAL ADVISORY COMMITTEE

FOR AERONAUTICS
WASHINGTON
October 3



.i s E .: -











NACA RM A55G20 CC'liFIDETLAL


NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS


RESEARCH ME IORA -DUM


TEMPERATURE RECOVERY FACTORS ON A SLENDER 120

CONE-CYLI;fDER AT MACH :J-IER;3 FROM 3.0 TO

6.3 AND AliGLES OF ATTACK UP TO 450

By John 0. Reller, Jr., and Frank M. Hamaker


SUMMARY


Recovery temperatures were measured on a slender cone-cylinder, having
a 120 vertex angle and a 1.25-inch-diameter cylinder, at Mach numbers from
3.02 to 6.30. The angle-of-attack range was 00 to 450 at Mach numbers up
to 3.50, 00 to 250 at Mach number 4.23, and 00 to 150 at Mach numbers from
5.04 to 6.30. The free-stream Reynolds numbers varied from 1.8x106 to
11.0X106 per foot. A transverse cylinder of the same diameter was also
tested at 3.02 Mach number. At angles of attack up to 100, the tempera-
ture distribution varied in a complex manner apparently in response to
changes in the location and extent of the boundary-layer transition region.
For larger angles, the effects of adiabatic compression and flow separation
became prominent; resultant recovery factors based on free-stream condi-
tions ranged from 6 percent above to 7 percent below those measured at zero
angle of attack. A circumferential recovery-temperature pattern similar
to that for a transverse cylinder was developed on the cylindrical after-
body at angles of attack greater than 250. In the high Reynolds number
range of this investigation, the average recovery factor (based on free-
stream conditions) for the entire surface did not exceed that for zero
angle of attack by more than 1 percent for angles of attack up to 350.

Recovery factors based on local stream conditions for laminar
boundary-layer flow, at zero angle of attack, were in agreement with the
square root of the Prandtl number based on wall temperature, while for
turbulent flow the cube root of the Prandtl number established an upper
limit. Compared to the predictions of Van Driest, Young and Janssen, and
Tucker and Maslen, the laminar boundary-layer data at Mach numbers greater
than 4 were about 1 percent low and the turbulent boundary-layer data were
high by about the same percentage. With increasing angle of attack, recov-
ery factors (based on local flow conditions) on the windward meridian of
the conical nose gradually decreased, dropping at 450 to as much as 6 per-
cent below the zero-angle-of-attack value. No significant variation of


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recovery factor with either Mach number or Reynolds number was observed,
in regions of either laminar or turbulent boundary-layer flow, for the
range of conditions of this investigation.


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Aerodynamic heating is one of the foremost considerations in the
design of aircraft for flight at high supersonic speeds. The recovery
temperature is a controlling factor in the heating phenomenon since the
rate of heat transfer is proportional to the difference between this
temperature and the actual surface temperature. The prediction of recov-
ery temperatures for a body of revolution at angle of attack is of par-
ticular interest because this shape often constitutes a major component
of supersonic aircraft. At present there is little theoretical infor-
mation on this problem, and existing experimental data refss. 1 and 2)
are available only over a limited Mach number and angle-of-attack range.

The purpose of this investigation is, then, to provide experimental
values of temperature recovery factors on a slender body of revolution at
angles of attack from zero to 450 and at Mach numbers from 3.0 to 6.3.
Experimental recovery-factor data for the limiting case of a cylinder
inclined 900 to the flow are also presented. The more significant results
of the investigation are discussed briefly and, with the aid of several
flow visualization methods, are related to boundary-layer phenomena.


NOTATION


a speed of sound, ft/sec

Pe Po
Cp surface pressure coefficient, q dimensionless


Cp constant-pressure specific heat, BTU per pound, OF

g acceleration of gravity, ft/sec2

k coefficient of thermal conductivity, BTU per second, sq ft, OF/ft

V
M Mach :iumt-r, -, dimensionless
a
N reciprocal of exponent defining boundary-layer velocity profile,
dimensionless

gCpNp Pandtl nbe, dimensionless
Npy Prandtl number, k dimensionless
.k


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p static pressure, lb/sq ft

Pt stagnation pressure, lb/sq ft

q dynamic pressure, p2, Ib/sq ft
2
VcxPogX
R Reynolds number, dimensionless


S surface area of model, sq ft

T absolute temperature, OR

V resultant velocity, ft/sec

x distance along surface measured from model tip, in.

a angle of attack, deg

Te T
Ir temperature recovery factor, Tt dimensionless


Trav average recovery factor for entire model surface, P r,, dS,
dimensionless

0 circumferential angle measured from windward meridian line, deg

pi absolute viscosity, lb-sec/sq ft

p mass density, slugs/cu ft


Subscripts


t stagnation condition

a free-stream condition at a location in the test section corre-
sponding to the midpoint of a test model

1 local condition adjacent to the body at the outer edge of the
boundary layer

e local condition at the surface of an insulated body in thermal
equilibrium


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EQUIPMENT AND TEST PROCEDURE

Wind Tunnel and Auxiliary Equipment


The experimental data of this investigation were obtained in the Ames
10- by 14-inch supersonic wind tunnel at Mach numbers from 3.0 to 6.3.
This tunnel is supplied with dry air at pressures up to 6 atmospheres abso-
lute. At Mach numbers above 4.2 the supply air is heated to prevent air
condensation in the test section. Details of the construction, operating
range, and calibration of the wind tunnel may be found in reference 3.

A center-of-curvature-type schlieren apparatus and a simple shadow-
graph system were used interchangeably to make visual studies of the flow
about models. Additional visual evidence was obtained with the vapor-
screen technique described in reference 4 and the china-clay method
(ref. 5).


Test Bodies and Instrumentation


The basic body of this investigation was a 120 included angle cone-
cylinder combination of over-all fineness ratio 12. This shape was chosen
because it is relatively simple, hence enabling some comparison between
theory and experiment. Temperatures and pressures were measured with
separate models. A cylinder with a length-to-diameter ratio of 5-1/2 was
used to obtain temperature data in the limiting case of 900 angle of
attack.

Temperature models and measuring equipment.- The recovery temperature
was measured on a model of the basic body made of a free-machining stain-
less steel. Except for an inaccessible region near the tip and a support
adapter at the base, the wall thickness was a uniform 0.025 inch. With
this thin wall, the heat capacity of the model and the heat conduction
within the shell were minimized. Thirty copper-constantan duplex thermo-
couple wires were soldered into holes through the surface in a plane
passing through the axis of symmetry (meridian plane) as shown in fig-
ure l(a). The outer surface of the model was then polished to a finish
of about 10 microinches. A thin layer (< 0.0005 inch) of hard chromium
was electroplated on the surface and the model was again polished to the
same finish. The result was a highly polished and durable surface (see
fig. 2).

The cylinder model had a shell thickness of 0.013 inch (see figs. l(b)
and 2) and was constructed in the same manner as the cone-cylinder.
Tw.e rty-four thermocouples were distributed along two opposing elements of
the cylinder and in two circumferential planes as shown in figure l(b).


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The output voltages of all model thermocouples were measured on a record-
ing, self-balancing potentiometer.

The cone-cylinder model was supported from the base by various double-
bent stings which positioned the midpoint of the model on the wind-tunnel
center line at approximately the same axial station for all angles of
attack. The crossflow cylinder was held at both ends in a forklike sup-
port. Typical support assemblies are shown in figure 3.

Reservoir temperatures were indicated by 19 copper-constantan thermo-
couples distributed, in one plane, over the cross-section area of the
wind-tunnel settling chamber. Output voltages of these thermocouples were
measured on an indicating, self-balancing potentiometer.

To evaluate the effect on test-section total temperature of heat
transfer at Mach numbers 5.0 and 6.3 from the heated air stream to the
tunnel walls, especially in the vicinity of the minimum section, a shielded
total temperature probe similar to that of reference 6 was used. The body
of the probe was stainless steel, while the hemispherical support was
micarta and the thermocouple lead was temperature-insulated. Thermocouple
voltage was measured with a manually operated precision potentiometer. No
effect of heat transfer on test-section total temperature was indicated,
there being negligible difference between the measured total temperature
and the average reservoir temperature.

Pressure model and measuring equipment.- The surface pressures were
measured on a model of the cone-cylinder similar in construction to that
used for the temperature measurements. Wall thickness was a uniform 0.025
inch, and thirty O.040-inch-diameter pressure orifices were spaced along
opposite meridian lines in the same locations as shown in figure l(a).
Pressures above 7 centimeters of mercury were measured on conventional
U-tube mercury manometers, while lower pressures were measured with McLeod
type mercury manometers. Reservoir pressure was measured with a sensitive
Bourdon type pressure gage; static and dynamic pressures in the test sec-
tion were determined from wind-tunnel calibration data and the reservoir
pressure.

Pressures were not measured on the transverse cylinder inasmuch as
representative data were obtainable from other sources (see, e.g., ref. 7).


Test Procedure


Model surface temperatures at each test condition were continuously
recorded until the difference between successive readings for all thermo-
couples was equal to or less than the repeatability of the recording
equipment. At this time several sets of equilibrium data were taken.
Likewise, model surface pressures were observed at short intervals of

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time until the difference between successive readings was within the
measuring accuracy. Equilibrium pressures were then recorded.

Data were obtained in several meridian planes by rotating the test
model relative to its support. Wind-tunnel flow blockage was the limit-
ing factor in high angle of attack, high Mach number operation. Data
were obtained at angles of attack up to 150 for all test fM ch numbers,
up to 250 for Mach numbers of 3.02 through 4.23, and up to 45 for Mach
numbers of 3.02 and 3.50 only. Testing of the 900 crossflow cylinder was
restricted to Mo~ = 3.02. Free-stream Reynolds numbers varied from 1.8x10l
to 11.0x106 per foot. A summary of the test conditions for models with
polished surfaces is given in tables I and II.

Limited temperature data were obtained with the cone-cylinder model
for two types of surface roughness, one type being a distributed roughness
of the order of 0.0003 inch in height and the other a localized roughness
consisting of two 0.020-inch-diameter wire rings (l/4-inch spacing) about
1/2 inch from the tip of the model.


INTERPRETATION AND ACCURACY OF TEST RESULTS

Interpretation of Visual Evidence


Spark shadowgraph pictures (5-microseconds exposure) were taken in
the a = 00 and 1800, and 900 and 2700, planes to aid in the analysis of
the surface temperature and pressure measurements. Boundary-layer con-
dition, whether laminar or turbulent, and the approximate location of the
transition region were determined from these pictures. Although some evi-
dence of the character of flow in separated regions could also be deduced,
better definition of separated flow was obtained in a similar set of
schlieren photographs (6-milliseconds exposure). To provide additional
information on the region of separated flow, two other visual methods, the
vapor-screen technique and the china-clay method, were employed.


Reduction of Temperature Data


The measured surface temperatures are presented in the form of temper-
ature recovery factors based on either free-stream or local flow condi-
tions. Preference is given to recovery factors based on free-stream con-
Te T,
editions, qr, = Tt T., since they provide a direct measure of surface
J, Tt T.
temperatures in separated as well as nonseparated flow regions and are
not influenced by the errors inherent in the determination of local flow
c:rditions. The assumption is made that surface temperatures are essen-
tially the same as would exist on a perfectly insulated body in thermal


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equilibrium. Deviations from this assumed condition are discussed in the
Te TI
section on accuracy of results. Local recovery factors, 1r, Tt TZ'

are used primarily to evaluate the effect of angle of attack on local
boundary-layer temperature conditions in regions of nonseparated flow and
to provide a basis for comparison of the data of these tests with those
of previous investigations.

The determination of local recovery factor requires a knowledge of
local Mach number. Local Mach numbers around the conical nose were deter-
mined by the following method: The ratio of stagnation pressures across
the nose shock wave in the 8 = 00 plane was calculated from a measurement
of the shock-wave angle taken from a shadowgraph picture. This ratio was
used in conjunction with the measured wind-tunnel stagnation pressure and
surface static pressures to calculate the local Mach number distribution.'
This method is known to be applicable in regions of nonseparated flow.


Reduction of Pressure Data


Surface pressure measurements are presented in the form of pressure
coefficients where free-stream static and dynamic pressures were taken
from the wind-tunnel calibration data (ref. 3). The free-stream static
pressure used was that of the undisturbed stream at the location of the
model surface pressure orifice, while the dynamic pressure corresponded
to the undisturbed stream value at the location of the midpoint of the
model.


Accuracy of Test Results


The model support system was calibrated for deflection by applying
static loads to simulate estimated lift forces. The resultant uncertainty
in angle of attack is estimated to be 0.10. The longitudinal location
of the boundary-layer transition region from shadowgraph pictures gener-
ally is known within 1/2 inch, while the location of separation by the
china-clay method is estimated with an absolute error in circumferential
angle of less than 80.

Model surface pressures and wind-tunnel stagnation pressures were
measured with an error of less than 1 percent, while free-stream static
and dynamic pressures (from wind-tunnel calibration data) are of similar
precision. A small additional uncertainty is inherent in the pressure
'This calculation derives from the fact that for this body the entropy
on the surface just outside the boundary-layer is essentially constant and
equal to the entropy in the plane 0 = 00 (see, e.g., ref. 8).


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8 COITFIDEITIAL NACA RM A55G20


data, since no correction was made for stream angle or Mach number gra-
dients in the test region. As a result, the estimated error in pressure
coefficient varies with the magnitude of the measured surface pressure
and, to a lesser extent, with the free-stream Mach number. Thus, in the
vicinity of the highest measured surface pressures (high angles of attack
in the low Mach number range), the probable error in pressure coefficient
for all test conditions does not exceed 0.014. The corresponding error
in the low pressure range is 0.004. These values are in general somewhat
high since with increasing free-stream Mach number the probable error
decreases to about half the foregoing estimates.

The precision of the calculated local Mach number is dependent on the
accuracy of both surface-pressure and shock-wave-angle measurement. On
this basis the probable error in local Mach number is 0.03.

The accuracy of recovery factors based on free-stream conditions is
influenced by the variation of Mach number in the test section, the uni-
formity and stability of settling-chamber temperatures, the precision with
which temperature measurements were made, and the local heat conduction
through the model shell. The probable error in free-stream recovery factor
from the first three sources is 0.3 percent. The effect of shell conduc-
tion on the accuracy of free-stream recovery factors will, in all likeli-
hood, be most pronounced in those areas where aerodynamic heat-transfer
rates are relatively low. A numerical analysis of the conduction effect
in regions of low velocity flow (low heat-transfer rates), such as near the
6 = 00 meridian at high angles of attack and in separated flow, indicated
that the most critical locations are those where large changes of tempera-
ture gradient occur and where temperatures are at a maximum or minimum.
Thus, the most severe case encountered in this investigation was in the
vicinity of the stagnation point on the transverse cylinder. At this
location the experimental data, which are in good agreement with the
results of the numerical analysis, indicate a conduction error of about
1.2 percent (the deviation from Tr = 1.00) in the measured recovery
factor. Similarly, the substantial temperature gradient changes that
occur on the cone-cylinder model at a > 150 can introduce errors of
almost 1 percent in the vicinity of the 0 = 00 meridian. The estimated
errors at smaller angles of attack and in separated flow regions are less
than 1/2 percent as the result of shell conduction. Thus, while in certain
localized r._ ions free-stream recc-.-ry factors may be subject to a probable
error fr-r.i all sources of about 1 percent, in general, the probable error
is about 1/2 percent.

Recovery factors based on local flow conditions are subject to an
additional error in the determination of the local Mach number. However,
it is demonstrated in figure 4 that a sizable relative error in local
Mach number will refle-ct a small relative error in local recovery factor,
and further, that this error is re luce,- as the Mach number increases. The
effect shell conduction on local recovery ifctors is also illustrated
in fi,-u'. 4 where it is seen that errors can be sizable in localized


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regions of maximum or minimum temperatures. Except for this shell conduc-
tion error at large angles of attack, the probable error in local recovery
factor is less than 1 percent.


PRESENTATION OF RESULTS

Visual Evidence


The photographI3 presented in figures 5 through 8, for Mo = 3.02, are
representative of the results obtained with the four flow-visualization
methods used in this investigation. Figure 5 is a group of shadowgraph
pictures which shows the location of boundary-layer transition in the
e = 00 and 1800 plane on the cone-cylinder model. Figure 6 is a similar
group of schlieren photographs which illustrates the character of flow
separation regions. The circumferential location of the flow-separation
line is seen in the china-clay photographs of figure 7, while the vapor-
screen photographs of figure 8 show flow separation in a plane perpendicu-
lar to the wind-tunnel axis. Note that parts (a) through (c) of figure 8
are photographs of the flow taken from a downstream location, while
part (d) is a view from an upstream position.

Temperature Distributions


The main body of recovery temperature data is presented in figures 9
through 13 as a function of longitudinal and circumferential position on
the model. Unless otherwise stated, all the data shown in these and the
subsequent figures are for the basic cone-cylinder shape and are based on
free-stream conditions. Figures 9 and 10 show the longitudinal variation
of free-stream recovery factor on the 0 = 00 and 1800 meridian lines for
all Mach numbers over the angle-of-attack range (to retain clarity, the
data at large angles of attack are shown separately in fig. 10). Repre-
sentative variations of 1r,0 along other meridians are shown in fig-
ure 11, while circumferential distributions of ir at selected cross
sections appear in figure 12. (It will be noted that fig. 12 presents
data which are not shown in fig. 11.) The results for the transverse
cylinder are plotted in figure 13.

Figures 14, 15, and 16 illustrate some effects of stream Reynolds
number and Mach number on recovery factor, and figure 17 shows the effect
of model surface finish and isolated roughness elements on recovery factor.

Pressure Distributions

Representative pressure data are shown in figures 18 and 19 for the
cone-cylinder model at a free stream Mach number of 3.02. Pressure


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coefficient is given as a function of 0 both on the cone and at the mid-
point of the cylindrical afterc...iy for i:-les of attack up to 250. Com-
parison is made with the second-order theory of Stone refss. 9 tuhr'.uich 12)
and the inclined-body r-pr1i-:.:inat ion of Allen (ref. 4).


Summary Figures


Figure 20 presents the location of the end of boundary-layer transi-
tion as a function of angle of attack at Mach numbers from 3.02 to 4.23.
Two indepe.-e it sets of data are shown on the figure; one set was obtained
from the longitudinal recovery-factor patterns of figures 9 and 10, while
the other was taken from a series of shadowgraph pictures similar to
those of figure 5. No curves have been faired through the data, since
this figure is used only to illustrate general trends. Figure 21 presents
the estimated circumferential angle of flow separation at the midpoint of
the cylindrical afterbody as a function of angle of attack. This infor-
mation provides the basis for a qualitative correlation of temperature-
distribution patterns with flow separation. Separation points were deter-
mined from china-clay ph t graphs similar to those of figure 7 and from
surface-pressure distributions. The latter data are the result of com-
parisons between experimental and theoretical pressure distributions as
illustrated, for example, by figures 18 and 19. Specifically, a deviation
of the experimental trend from the trend of the theoretical curve (i.e., a
decreasing rate of lee-side pressure recovery) was assumed to indicate the
approximate location of flow separation.

Recovery factors at two axial locations, one on the cone and one on
the cylindrical afterbody, are shown as a function of angle of attack in
figure 22, while in figure 23 an average recovery factor (area-weighted
average for entire surface) is presented.

The variation of local Mach number on the cone with angle of attack
and cir.~murc'erential location is given in figure 24 for a free-stream Mach
number of 3.50. Local Mach numbers computed from surface pressures and
nose shock-wave measurements are compared with those predicted by the
Stone theory.

Recovery factors based on local stream conditions are given in fig-
ures 16, 25, and 26. Figure 16 shows the variation of local recovery
factor with axial location on the model, at zero angle of attack, for
regions of laminar-boundary-layer flow. In fi-re 25, local recovery
factor on the cone is plotted as a function of angle of attack and cir-
cumferential location for Mo = 3.50. Local Mach number is the ir-d-epend-
ent variable in figure 26, where the zero-angle-of-attack data of this
investigation are compared with theoretical predictions.


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DISCUSSION OF RESULTS


Recovery temperature is obtained on an insulated _.urfa.e when a
balance is reached between the generation of heat, due to viscous dissi-
pation and compression of air, and the removal of heat by conduction and
convection within the boundary layer. (Radiant heat transfer is presumed
negligible.) It might be expected, then, that the recovery temperature
would be considerably altered by large boundary-layer changes such as
occur over the angle-of-attack range of this investigation. The tempera-
ture recovery factors did, in fact, vary substantially with angle of
attack, exhibiting a behavior that was apparently a response to several
distinct phenomena. In the following discussion consideration is given
to some of these phenomena.


Recovery Factors Based on Free-Stream Conditions


Small angles of attack.- Temperature recovery factors on the forepart
of the model at angles of attack from 10 to 50 are markedly higher than at
zero angle of attack as seen in figure 9. This result is rather surprising
and to some extent the reasons for it are not understood. It has been
observed in previous investigations, however, that transition on the lee-
ward side of a body moves forward with increasing angle of attack. This
movement of transition is very likely due to the upwash of low-kinetic-
energy boundary-layer air from the windward side. Although the data of
this investigation show a similar forward movement of transition (see
fig. 20) it is not at all clear that the effect of upwash could be so
pronounced at small a, say 10 or 20. The windward side recovery-factor
rise is thought to be due, in part, to a 'forward movement of transition
as a result of contamination from the lee-side turbulent boundary layer,
with turbulence spreading circumferentially as it is washed downstream
after the manner proposed in reference 13.2 (Note that the calculated
effect of heat conduction through the model shell is much smaller than
this observed recovery-factor rise.) Aside from the effect of transition
movement, there is an apparent increase of recovery temperature in regions
of predominantly laminar flow, as seen in figure 10(e) over the first
6 inches of the model. A small portion of this increase could result,

2Except for M = 3.02, this effect is not seen in the transition data
of figure 20, where the change in appearance of the boundary layer on
shadowgraph pictures is compared, as to location, with the end of the tran-
sition region determined from longitudinal recovery-factor distributions.
The difference between the trend of figure 20 and that discussed here is
attributed to the "stretching out" of the transition zone as mentioned in
the next paragraph. For further discussion of transition see a later sec-
tion entitled "Correlation of Temperature Patterns With Boundary-Layer
Transition and Separation."


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NACA RM A55G20


of course, from the change in local Mach number; the remainder is not
understood. A similar behavior is shown by the data of reference 2.

Coupled with this observed increase of recovery factor in the laminar
regiJ;!n and the apparent forward movement of the start of transition is a
considerable "stretching out" of the transition zone on the windward side
of the body. This is most clearly shown in figure 9(c) where the change
of slope of the curves and the rearward movement of the point of maximum
recovery factor with increasing angle of attack can be seen. This delay
of transition to fully turbulent flow probably results from the removal
of low-kinetic-energy boundary-layer air from the vicinity of the 0 = 00
meridian by the cross component of the flow.

Large angles of attack.- As the angle of attack approaches 100, there
is a tendency for recovery factors along the windward side of the body to
decrease (e.g., fig. 10(a)). This is attributed to a return to more nearly
laminar flow as the influence of crossflow boundary-layer removal becomes
more pronounced. As the angle is increased beyond 100, recovery factors
on the windward side begin to rise as a result of adiabatic compression.

The recovery-factor distribution around the model follows no obvious
pattern for angles of attack below 150, because of the relatively large
influence of transitional boundary-layer flow (see fig. 12). It will be
noted, however, that in some cases lee-side recovery factors approaching
the base of the model are as much as 0.02 to 0.05 higher than the opposite
side at a = 100. (In ref. 1 this effect was attributed to the proximity
of vortex centers in the separated flow.) At angles of attack of about
150 there appear circumferential distributions in which the maximum recov-
ery factor is on the windward meridian and the minimum is on the lee
meridian of the model. For angles of attack above 25 these characteristic
patterns evolve into a distribution similar to that obtained on the trans-
verse cylinder, namely, that the minimum value occurs in the vicinity of
the separation line as shown in figures 12(a) and 12(b).

Figure 22 summarizes the variation of windward and leeward recovery
factors with angles of attack to 45. To retain clarity, only representa-
tive curves are shown. Recovery factors at angles of attack to 100 are
generally from 1 to 4 percent higher than those at the same location at
a = 00. As angle of attack is increased to 450, windward-side recovery
values rise to about 0.95. In contrast, lee-side values reach minimums
at a = 250 to 350 which are as much as 5 percent below those at a = 00,
with a subsequent increase at larger angles of attack.

For the limiting case of a = 900 (see fig. 13) a recovery factor of
about 0.99 was measured on the stagnation line (as shown earlier, shell
conduction in this critical region caused the deviation from nrYo = 1.00)
while a minimum of about 0.89 occurred in the vicinity of 0 = 900.
Although the lee-side values of the present investigation were considerably
higher than those reported in reference 7 (respectively, 0.95 and 0.89 at
COIFFIDEITIAL


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NACA RM A55G20


e = 1600), a significant difference between the two tests was the Reynolds
number, which was larger by a factor of 8 in the present investigation.

The average recovery factors plotted in figure 23 are area-weighted
values which summarize the effect of angle of attack on the temperature
level of the entire body.3 It is apparent that the variations previously
discussed are of sufficient magnitude to affect the over-all trend. Thus,
for angles of attack up to 100, the effect of lee-side temperature rise
disappears at Mach numbers above 3.50 (generally decreased Re...o'1s number)
and the small-angle laminar-boundary-layer effect becomes predominant.
For 100 < a < 250 there is a general decrease of average recovery factor
which, in the low Mach number range (high Reynolds number), results in
minimum values which are less than the averages at a = 00 and which do
not exceed the zero-angle values for angles of attack up to 350

Effect of Reynolds number and surface roughness.- The Reynolds number
effects encountered in this investigation were, in the main, evidenced by
changes in the location and extent of the boundary-layer transition region.
These effects were not confined to the windrward side of the body but were,
to a lesser extent, also shown in regions of separated flow on the lee
side. In a sample comparison shown in figure 14, a reduction in Reynolds
number from 11.0 to 4.2 million per foot lowered windward meridian recov-
ery factors by about 2 to 4 percent, primarily as a result of the aft
movement of the transition region. Corresponding leeward values dropped
from 1 to 2 percent. This feature was also noted in the comparable
transverse-cylinder data of figure 13, as mentioned in the previous sec-
tion. Other effects of Reynolds number include a small decrease of recov-
ery factor with length of run that was characteristic of both laminar and
turbulent flow, and, as shown for example in figure 15, an increased length
of run in the transition region in response to a reduction in stream
Reynolds number. The data also appear to show that, for laminar-boundary-
layer flow, larger recovery-factor variations occurred in the low Reynolds
number range of this investijati'::- in response to Mach number chances. An
example of this effect is presented in figure 16, where recovery factors
on the forepart of the m:ldel show a pronounced Mach number response at
R = 4.2 million per f'.:ot, compared to the small change at R = 8.6 million
per foot. This could be due, in part, to a decrease of effective surface
roughness as a result of increasing boundary-layer thickness with Mach
number. Further investigation is necessary to establish the extent of
this influence in low Reynolds number flows.

The effect of surface roughness on recovery factor is shown in fig-
ure 17. The square symbols represent recovery factors for a surface with
distributed roughness elements of the order of 0.0003 inch in height,
while the diamond symbols are data for a localized rcu.brness consisting
of two 0.020-inch-diameter wire rings (1/4-inch spacing) located about
1/2 inch from the tip of the model. Comparison of these results with the
3Angles of attack from 10 to 40 are omitted because of insufficient
data.


COI[FIDEIITIAL


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NACA RM A55G20


data obtained with the polished surface shows, as expected, that roughness
causes a forward movement of transition at both a = 00 and 150. The
effects of roughness are similar for both 00 and 150 angle of attack,
although the recovery-factor rise is somewhat less pronounced at a = 150
for M = 4.23 and 5.04. There are indications that roughrnes may lower
recovery factors in turbulent regions, in particular as shown in fig-
ure 17(a). It also tends to "wash out" the distinctive sharp temperature
rise normally associated with the transition region. An interesting fea-
ture is noted in figures 17(b) and (c), where the decrease of recovery
factor for a short distance downstream of the localized roughness suggests
that the disturbance introduced by the roughness is partially damped by
the boundary layer and that transition is completed some distance down-
stream. This behavior is in agreement with the experimental results
reported in reference 14, where it is shown that roughness elements smaller
than a critical size promote transition in regions downstream of the ele-
ment location, rather than at the element.


Correlation of Temperature Patterns With
Boundary-Layer Transition and Separation

The recovery temperatures on a body of revolution at angle of attack
have been stated to be significantly dependent upon several characteristics
of the boundary-layer flow. The location and extent of boundary-layer
transition, the upwash of air of low kinetic energy from windward to lee-
ward side, the location of the flow separation point, and the phenomena
associated with the separated flow are several of the more important fea-
tures that have been mentioned. The observed recovery-factor variations
have been related to these features by the four flow-visualization methods.

Boundary-layer transition.- For the most part, transition effects have
been related to the observed temperature patterns in the previous discus-
sion. The general trend of longitudinal transition location with angle of
attack has, however, received only passing mention. Now, it is recognized
that boundary-layer transition is not a stationary phenomenon; in fact,
there is ample experimental evidence that it is a time-dependent composite
of a large number of turbulent "bursts." Consequently, the evidence of
transition obtained from surface temperatures and shadowgraph pictures
represents some average or most probable location of transition. It was
found that at small to moderate angles of attack, a rough comparison could
be made between the shadowgraph indication and that segment of the
recovery-factor curve just aft of the peak value.4 Thus, in figure 20
the location of transition is seen to move forward on the lee side and
aft on the windward side with increasing angle of attack. At a greater
than 100 there is an apparent reversal of trend on the windward side, with
transition (as defined herein) moving toward the nose.

4A similar comparison of temperature data and schlieren photographs
in reference 14 showed agreement at the location of the peak temperature.


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NACA RM A55G20


There remains the possibility that these transition data are being
influenced by the flow expansion at the shoulder, in a manner similar to
that described in reference 15. It was found therein that a strong flow
expansion (580 included angle cone-cylinder) resulted in the growth of a
"new" laminar boundary layer behind the juncture. However, from examina-
tion of the present data it is apparent that the relatively weaker shoulder
flow expansions of the present investigation were too weak to cause a simi-
lar behavior, altl .:.ugh just a suggestion of this effect may be seen at
e = 1800 in figure 9(c). Hence, although recovery temperatures in transi-
tion zones may have been slightly influenced by the flow expansion at the
shoulder, it is believed that the location of the transition zone is not
significantly altered and that the present results are representative of
slender bodies.

Boundary-layer separation.- The circumferential location of boundary-
layer separation as a function of angle of attack, shown in fi-ur- 21, is
for flow conditions at the midpoint (lengthwise) of the cylindrical after-
body. Separation moved rapidly around the body as angle of attack was
increased to about 100. With further increase in angle of attack there was
relatively little change. A rough correlation exists between the location
of the separation line and certain features of the recovery-factor distri-
butions shown in figure 12. At angles of attack above about 150 either a
definite decrease in circumferential recovery-factor gradient or a minimum
recovery-factor value is associated with the separation point. A tentative
conclusion based on the china-clay studies is that the separated flow
region, for a from 100 to 250, is by no means a "dead air" or low-
velocity region. In fact, it appears from the drying patterns (e.g.,
a = 150 in fig. 7) that the heat-transfer rate to the surface on the lee
side of the model is of considerable magnitude.

It is also interesting to note that some of the variations observed
in lee-side recovery factors (fig. 12) can be associated with the different
separation flow patterns shown in figures 6 and 8. For angles of attack
less than 150, where the effect of boundary-layer transition on tempera-
ture distributions is relatively large, there is the flow visualized in
figure 8(a) at an angle of attack of 100. Here there is thickening of the
boundary layer on the lee side with some separated flow that has not broken
free of the surface. At a = 150, where lee-side recovery factors have
started to drop, there is the flow indicated in figure 8(b) where the
vortices have broken free of the model but are still symmetrical, while at
a = 250 (fig. 8(c)) the vortices have fallen into a vortex-street pattern.
This last condition corresponds to the minimum recovery factor on the lee
side of the model.5 At a = 350, where the temperature pattern is assuming
50ne characteristic of the separation vortex pattern deserves mention.
At a = 250 a certain flow instability, as a function of time, was observed
to occur. The pattern of figure 8(c) was apparently a semisteady condition
which was frequently interrupted by alternate shedding of vortices in what
might be termed "bursts." Frequency or lenirth of "burst" periods was not
determined.


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NACA RM A55G20


characteristics of transverse-cylinder flow, the vortex street disappears
and, as shown in figure 8(d), is replaced by a dead air space followed by
a turbulent wake.


Recovery Factors Based on Local Conditions


Effect of angle of attack.- A representative variation of recovery
factor based on local stream conditions with angle of attack and circum-
ferential location is shown in figure 25. The data are based on the exper-
imental Mach number distributions of figure 24 and are presented both as
measured and as corrected for shell conduction error. Recovery factors on
the free-stream basis are also shown for comparison. With increasing angle
of attack the corrected local recovery factor decreases from about 0.86 at
a = O to 0.81 at a = 450, while free-stream recovery factor, in contrast,
increases from 0.86 to 0.93 over the same interval. The variation of
recovery factor with circumferential angle at a = 250 shows, as would be
expected, that the substantial difference between Tr,~ and Tr,I at 0 = 00
is diminished as the flow is accelerated to about the free-stream Mach
number at 0 = 900. Now, the reasons for the decrease of local recovery
factor at high angles of attack are not clearly understood, although it
has been suggested that a portion of the drop could be attributed to the
effect of strong local pressure gradients. Indeed, to date, the results
of several theoretical investigations indicate that such an effect could
exist, and in at least one experimental investigation a small decrease of
recovery factor was noted in the region of strong pressure gradients on a
spherical nose (ref. 16). However, there remains the possibility that
other factors may be contributing to the observed decrease.

Mach number effect.- A sizable decrease of surface temperature, in
response to the change of local flow conditions at the shoulder of the
cone, is illustrated in figures 10(e) and 16(b) for regions of laminar
boundary-layer flow. It is believed that for the most part this decrease
can be related to the change in local Mach number, for when recovery fac-
tors are evaluated on the, local-stream basis (shown in fig. 16(b)), there
is a good alinement of the data in the entire laminar flow region at lower
free-stream Mach numbers and a sizable reduction in the recovery-factor
decrement at the shoulder for M, = 5.04. In the high Mach number range
of these tests, however, the local-stream basis of evaluation appears to
lose effectiveness, that is, it no longer accounts for the temperature drop
at the shoulder. For example, the Tir decrement shown in figure 10(e)
for M. = 6.30 at a = 00 can be reduced only from the indicated 0.018 to
0.014 when the temperature data are evaluated on the basis of local flow
conditions. Although the reason for this change of behavior at high Mach
numbers is not understood, a similar decrease of local recovery factor
(alti u.Q for a much blunter nose cone) has also been observed by Sternberg
(ref. 15) at M, = 3.02 and 3.55. He c nclides that the pressure drop at


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NACA RM A55G20


the shoulder ':i a lasting effect on the subsequent boundary-layer develoo-
ment a..: that it is not _-fficient to describe the bc ... ---layer proper-
ties (in this r.-ion) in terms of the local Mach number. Thus, although
further investigation is necessary to fix the relationship between these
two i..'ie~er:e..t observations, it is indicated that under certain conditions
a str,:n pressure gr -. can, of itself, influence recovery temperatures.

Local recovery factors at zero :1:.- of attack for the polished model
surface are given as a function of local ..:. number in figure 26. The
experimental data are 2- r-' with the theoretical predictions of
Polhausen (IJPr li2), Van Driest (ref. 17), :. Yc 'e- and Janssen (ref. 18)
for laminar boundary-layer flow. The turbulent boundary-l-.-, data are
compared with the theories of Ackerman ('...17 ), Van Driest (ref. 19), and
TucK.r-- and Maslen (ref. 20). The Prandtl numbers of the present investi-
gation are referred to the .:.rfa.:- t.em r r-tie, since it is probable that
the temperature of the air -.iice:.t to the surface has a stro..- influence
upon the mri-.itu :- of heat transfer within the 1 :I.-.-' layer. (Note that
Prandtl numbers decrease at Mach numbers -re t-r than 4.5 as a result of
the heated wind tunnel airstream.) The data present, are indicative *f
the range of recovery factors at each test Mach number; int i--r:.- .ite values
are omitted for the sake of clarity.

The laminar-boundary-la~er data do not agree over the entire Mach
number range with any of the theoretical curves alt-. u .. comparison is
pe:ira.s most favorable with the p p,e 1/2 prediction. This is not sur-
prising since model surface temperatures are relatively low. It is of
greater significance, however, to compare with the theories "' .an Driest
and of Ycun- and Janssen, since each of these T'y also be cpp.lie- to the
prediction of recovery factors for actual flight conditions where surface
temperatures are much higher and the lPre 1/2 prediction may not be
valid. It can be seen that both of these theories give about the same
agreement in the Mach number range of this investigation. The comparison
is g:od at Mach ni.L.Tb rs up to 4, with an overestimate of about 1 percent
in the higher sper-*. rnret. It might be well to mention, in passi:r, that
a significant decrease of :liint recovery factor with Mach number is indi-
cated in reference 18, while, in contrast, a much smaller decrease is
shown in reference 17. Eckert (ref. 21) has shown that this difference
is, for the most part, du- to the definition of sta.:i tiCn temperature in
reference 18. In reference 18, the stagnation temperature used is that
for a constant specific heat (equal to the free-stream value) and, since
a variable specific heat was ued in computing the insulated-surface
temperature, it is readily seen that the resultant recovery factor will
decrease considerably at high flight speeds. If either a variable or
average specific heat is used throughout (e.g., ref. 21) the recovery-
factor predictions of reference 18 would not differ appreciably from those
of reference 17.


CoI ITDEUIT IAL


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IHACA RM A.'G120


In the turbulent case the 1]Pr,e1/3 prediction appears to e- an
'.!r r boundary for recovery factors representative of fully devel_-r.e
turbulent flow, while maximum transition values lie above. The modified
T'..-:r-Maslen theory6 agrees favorably at lower Mach numbers but is about
1 percent low in the i...r speed range. The turbui.:lit theory of
Van Driest, which in its present development is applicable to both wind-
tunnel and fli *-t, conditions at Mach numbers up to about 4, does not
compare as favorably with the experimental data.


C'.:I'LUSiIONS


Experimental temperature recovery factors were determined on a slender
cone-cylinder model at Mach numbers up to 6.30 and enecl3s numbers from
1.8x106 to ll.Ox106 per foot. The angle-of-attack range was 00 to 450 at
Mach numbers less than 3.50, 00 to 25 at Mach number 4.23, and 00 to 150
at Mach numbers from 5.04 to 6.30. The following conclusions have been
drawn from the results of this investigation:

1. Temperature recovery factors at angles of attack up to 100 vary
in a complex manner, apparently in response to changes in the location
and extent of the boundary-layer transition region.

2. At angles of attack above 100, windward-side recovery factors
(free-stream basis) gradually rise as a result of adiabatic compression
to above 0.95 at an angle of attack of 450, a value some 6 percent above
the zero-angle case. Lee-side recovery factors decrease, as a result of
flow separation, to minimum values in the angle-of-attack range from
250 to 350. At Mo = 3.02 the minimum was 0.83, about 7 percent below
the corresp:onring. zero-angle value.

3. At angles of attack greater than about 25, a circumferential
recovery-temperature pattern similar to that for a transverse cylinder
is developed on the cylindrical afterbody.

4. In the high Reynolds number (low Mach number) range of the present
investigation, the average free-stream recovery factor for the entire sur-
face does not exceed the value for zero angle of attack by more than 1 per-
cent for angles of attack up to 35

5. When based on local flow conditions, recovery factors on the wind-
ward meridian gradually decrease with increasing angle of attack (except

61.l.:'ified after the manner suggested in reference 22, where the
arithmetic mean temperature of the boundary layer was used to define a
r N+l+o.528 M2
Prandtl number in the equation r, = I"Pr sN+l+ ME


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NACA RM A55G20


for the interval between 00 and 5), dropping at Mm = 3.50, from 0.86
at zero angle of attack to 0.81 at an angle of attack of 45 on the cone.

6. At zero angle of attack, recovery factors (local flow basis) for
laminar boundary-layer flow are in agreement with NPrel/2 (Prandtl num-
ber based on wall temperature), while the Van Driest or Young and Janssen
predictions overestimate by about 1 percent at Mach numbers greater than 4.
For turbulent flow Npr,e /3 establishes an upper limit for recovery fac-
tors based on local conditions while the modified Tucker-Maslen theory is
about 1 percent low at higher Mach numbers.

7. For the range of conditions in this investigation there is no
significant variation of recovery factor with either Reynolds number or
Mach number in regions of either laminar or turbulent boundary-layer flow.
However, the effect of Reynolds number on transition location is a deter-
mining factor in lee-side surface temperature levels.


Ames Aeronautical Laboratory
National Advisory Committee for Aeronautics
Moffett Field, Calif., July 20, 1955


REFERENCES


1. Gazley, C., and Adams, P.: Temperature Recovery Factors on a Body of
Revolution at Mach Uumbers of 1.79 and 4.50. Rep. R52A0509, General
Electric Co., Guided Missiles Department, Aug. 1952.

2. Jack, John R., and Moskowitz, Barry: Experimental Investigation of
Temperature Recovery Factors on a 100 Cone at Angle of Attack at a
Mach ijumber of 3.12. NACA TN 3256, 1954.

3. Eggers, A. J., Jr., and Nothwang, George J.: The Ames 10- by 14-Inch
Supersonic Wind Tunnel. NACA TN 3095, 1954.

4. Allen, H. Julian, and Perkins, Edward W.: Characteristics of Flow
Over Inclined Bodies of Revolution. NACA RM A50L07, 1951.

5. Gazley, Carl, Jr.: The Use of the China-Clay Lacquer Technique for
Detecting Boundary-Layer Transition. Rep. R49A0536, General Electric
Co., General Engineering and Consulting Lab., Mar. 1950.

6. Goldstein, David L., and Scherrer, Richard: Design and Calibration
of a Total-Temperature Probe for Use at Supersonic Speeds. NACA
TN 1885, 1949.


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NACA RM A55G20


7. Walter, L. W., and Lange, A. H.: .i:-:'ace Temperature and Pressure
Distributions on a Circular Cylinder in Supersonic Cross-Flow.
NAVORD Rep. 2854, '.-1-'1 Ordnance Lab., June 5, 1953.

8. Savin, Raymond C.: Application of the Generalized :i:'..:-Expansion
Method to Inclined Bodies of Revolution Traveling at High Supersonic
Ai :e: s. NACA TN 3349, 1955.

9. Staff of the Computing Section, Center of Analysis, under the direc-
tion of Zdenek Kopal: Tables of Supersonic Flow Around Yawing Cones.
M.I.T. Dept. of Electrical Eng., Center of Analysis, Tech. Rep.
No. 1, Cambridge, 1947.

10. Staff of the Ci:.~r.iting Section, Center of Analysis, under the direc-
tion of Zdenek Kopal: Tables of Supersonic Flow Around Yawing Cones.
M.I.T. Dept. of Electrical Eng., Center of Analysis, Tech. Rep.
No. 3, Cambridge, 1947.

11. Staff of the Computing Section, Center of Analysis, under the direc-
tion of Zdenek Kopal: Tables of Supersonic Flow Around Cones of
Large Yaw. M.I.T. Dept. of Electrical Eng., Center of Analysis,
Tech. Rep. No. 5, Cambridge, 1949.

12. Roberts, Richard C., and Riley, James D.: A Guide to the Use of the
M.I.T. Cone Tables. NAVORD Rep. 2606, Naval Ordnance Lab., Apr. 1,
1953.

13. Emmons, H. W.: I'. Laminar-Turbulent Transition in a Boundary Layer,
Part I. Jour. Aero. Sci., vol. 18, no. 7, July 1951, pp. 490-498.

14. Brinich, Paul F.: Boundary-Layer Transition at Mach 3.12 With and
Without Single FPu!. .-, Elements. NACA TN 3267, 1954.

15. Sternberg, Joseph: T"I Transition from a Turbulent to a Laminar
Boundary Layer. BRL Rep. No. 906, Ballistic Research Labs.,
Aberdeen Proving Ground, May 1954.

16. Stine, Howard A., and Wanlass, Kent: Theoretical and Experimental
Investigation of Aerodynamic-Heating and Isothermal Heat-Transfer
Parameters on a Hemispherical Nose With Laminar Boundary Layer at
Supersonic Mach Numbers. NACA TN 3344, 1954.

17. Van Driest, E. R.: The Laminar Boundary Layer with Variable Fluid
Properties. Rep. AL-1866, North American Aviation, Inc., Jan. 19,
1954.

18. Young, George B. W., and Janssen, Earl: The Compressible Boundary
Layer. Jour. Aero. Sci., vol. 19, no. 4, Apr. 1952, pp. 229-236,
and 288.


CL'iiFIDEZITIAL


CC'i IF 1 E"TI i-J_1






iACA EM A55G20


19. Van Driest, E. R.: The Turbulent Boundary L.:,- L with Variable Prandtl
:umntr. Rep. AL-1914, North American Aviation, Inc., Apr. 2, 1 -4.

20. Tucker, Maurice, and Maslen, Stephen H.: T .-' t -: --.ry-Layer
Tempe-rature Recovery Factors in T. o-Dimensional Supersonic Flow.
NACA TN 22 ., 1951.

21. E.ck-rt, Ernst R. G.: Survey on ;it Tr=::.i:er at High :.: --. Tc...
Rep. 54-70, Wright Air Dev l: r..:t Center, Apr. 1;-.

22. Stine, Howard A., and Scherrer, Richard: E:.-2 rimental Investigation
of the Turbulent-Boundary-Layer T -r.p- ierature-Recovery Factor on
Bodies of Revolution at Mach :.'.l -ers from 2.0 to 3.8. NACA TN 2664,
1--=2.

23. The HES3-NACA Tables of Thermal Properties of Gases. Table 2.44,
Prandtl Number of Dry Air, C:..: iled by Joseph Hilsenrath, National
Bureau of Standards, U.S. De-rrt.rjnt of Commerce, 1')0.


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NACA RM A55020


TABLE I.- TEST C''-LDITI'1:i.3, TEMPERATURE MODELS


TABLE II.- TEST C.:' DITII:''i, PRESSURE :MO'DEL


Angle Meridian Free-stream Mach number
of anle, 3.02 3.50 I 4.23 5.04 6.30
attack, eg' Free-stream Reynolds number per ft/106
deg g8.6 11.3 88.6 4.2 8.6 4.2 4.2 1.8 1.8
0 0,180 x x x x x x x x x
1 0,180 x x x x__
2 0,180 x x x x__
4 0,180 x x x x_
0,180 x x x x x
5 45,90,
135,270 x x x x
0,180 x x x x x x x x x
10 45,135 x x x x x x x
90,270 x x x x x x x x
05180 x x x x x
15 45,90,
X X X X
135,270
0,180 x x x x
25 45,90,
135,270 x x
35 0,180 x x


C,'iIIFIDEIITIAL


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NACA RM A55G20 CONFIDENTIAL 23





I I
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I 1


S's



L b T .1 I
-R -


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C',NF rDENTIAL


NACA RM A550G2"'


A-19147.1

Figure 2.- F'. tograph of cone-cylinder and crossflow cylinder models.


(a) Cone-cylinder on


a = 15 supp.rt.


FigurI- 3.- Model support assemblies.


C,:'.FIDE!JTIAL


A-19148


~1111 1 I -r- *y






NACA RM A55G20


A-19149. 1


(b) Cone-cylinder on a = 350 support.


A-19625


(c) Crossflow cylinder on fork support.

Figure 3.- Concluded.

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NACA RM A55G20


-0 2 3 4 5 6 7
Local Mach number, M,
Figure 4.- Error In local temperature recovery factor resulting from either shell conduction or
error in local Mach number.


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I4


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NACA RM A55G20


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NACA RM A55G2,0 CONFII
Plane of e = 00 and 1800


a = 50






a =100


a = 150


a = 250

C'


a = 350
Figure 6.- Schlieren rph:.. r:graphs of cone-cylit. ier model; M. = 3.02,
R = 8.6x106 per foot.
CONFIDENTIAL


)ENTIAL


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NACA RM A.c5-2')


SI -1-80


4 6 8 /0
Distance, x, inches

(e) M -- 6.30, R = /.8 x/0 per foot


a, deg
0
50
9.8
151


Figure /0.- Concluded.


CONFIDETIAL


.92



.89


.86



.83



.80


I I I I


Cone Cyli-nder
Cone -* Cylinder


CONFIDENTIAL





IACA RM A 2OC20


~GI-II


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S/

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CONFIDENTIAL


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NACA RM A55G20


S____________


4, deg
0
45
90
/35
180


.86


.83

.92


.898_
.89


4 6 8 /0
DisOance, x, inches
(b) M, = 504, R = 4.2x 106per foot

Figure I/.- Concluded.


CONFIDENTIAL


B







qJ
8


.86


.83


~i~


CONFIDENTIAL





NACA RM A55G20


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CONFIDENTIAL


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:A'A RM A."






NACA RM A55G20


.92
92 a, deg
o O
0a 0
o 50
o 9.8
.89 151
X= ___3 in.


86-


30 60 90
Circumferentia/ angle, 8,

(e) M, 6.30, R /.8 x


/80


120 150
degrees

10 per foot


Figure 12.- Concluded.


CONFIDENTIAL


.89



.86



.83


x 20 .in.
_ p~


_ I


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(


CONFIDENTIAL






NACA RM A.5G,20


o Moo 3.02, R =8.6x
06/ft, di. = .25 in.
O Mc=3.24, R =2.2x
10/fft, dia.=.50 in.
fref. 7)


- I t -


8

.96


.94


.92
I-

.90
I.-

.88


.86
O >


/20
degrees


140


160 /80


Figure /3.- Recovery-foctor distribution on transverse cylinder.


CONFIDENTIAL


2N0


Io.U


0-

______ ______ ______ ______ 0 ______ ______


60 80 100
Circumferential angle, A,


.1Y r


N x I I I


-T~11~


CONFIDENTIAL


-


-





1[ACA RM A55G20


86




.84



.92



.90


Distance, x, inches

Figure 14.- Effect of Reynolds number on measured recovery factor
at = O10- M = 3.50.


CONFIDENTIAL


CONFIDENTIAL





NACA RM AGJ20


.92


.90


.88


.86

W.84



.82

S .



i ,


YU R/ft
o 4.xl/06
S.Bx /O6
88 ---


86______


C84one Cyinder

_2_9 one Cylinder I


0 2 4 6 8 /0 /2 /4 16
Distance, x, inches
(b) M = 5.04

Figure /5- Effect of Reynolds number on measured recovery factor at a= 0

CONFIDENTIAL


R/ft
0 10.9x106








I__ i f __I I __ I __.I __1
0 8.6
Cone---- Cylinder-- < 4.8
o 4.3

() Moo = 350


CONF I DENTIAL


K.





NACA RM A55G20


90 _

S------ --- -


.86


e .84


.82


QL


Cone Cylinder-

SR = 8.x/ per foo
(a) R = 8.6x10 6per foot


.92 7r Vr, w MW
o 302
-- 350
.90E _6 0 4.23
< 504


.88


.86





Cone- Cylinder
.82 .......


stance, x, chess
Distance, x, inches


(b R = 4.2x106 per foot

Figure 16- Variation of recovery factor with distance along model for several
Mach numbers, R constant, a = 0


CONFIDENTIAL


CONFIDENTIAL


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NACA RM A55G20


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CONFIDENTIAL


CONFIDENTIAL






NACA RM A55G20

.15r-


CONFIDENTIAL


.30

a /10'

.156




0o i





1 | o10 Experiment


Circumferential angle, 9, degrees

(a) a = 51 /0 and 15*
Figure 18.- Circumferential pressure distributions at midpoint of conical
nose at Moo 302, R =8.6x /06 per foot and angles of attack to
25V comparison of theory and experiment.


CONFIDENTIAL






NACA RM A55G20


S.45







.30
.15




-.30-












(b) a = 250


Figure /18.- Concluded.

CONFIDENTIAL


/80


CONFIDENTIAL







NACA RM A55G20


.JU



./5

a=15*
0 -
C \ /

\ o -o / -

N _


-Vacuum limit



SExperiment
--Allen (cylinder
crossflow,
ref 4)


'0 30 60 90 120 150 180
Circumferential angle, 0, degrees
Figure 19.- Circumferential pressure distribution at midpoint of cylindrical
afterbody at Ma, = 302, R = 86 x 1O6per foot, and angles of attack
to 25' comparison of theory and experiment.


CONFIDENTIAL


.13

a= 5

0 o
Co 7. 1 -7-_



_/<; -


U25
a= 25


0\
\ o/o /


--Vacuum limit


Y


CONFIDENTIAL






NACA RM A55G20


sa3oI/ 'x 'a3uoDsiQ


CONFIDENTIAL


CONFIDENTIAL






NACA RM A55G20


b


UUL 0

30 China clay study
o0 "5 Pressure survey
o 3.50
160 \- o 4.23
< 5.0/
4* q 6.30
/40



120



/00



80



e n-------------------


Figure 2/. Flow separation


/0 /5 20 25 30
Angle of attack, a, degrees
of midpoint of cylindrical afterbody as a function of angle of attack


CONFIDENTIAL


CONFIDENTIAL






NACA RM A55G20
.1121


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c







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CONFIDENTIAL


CONFIDENTIAL





IJACA RM A55G20


CONFIDENTIAL


0 O


o a o v v

\





\







__\__
-----^-------

rkpll.00V





--^--'


,1 'J oDJ XAJ9A03J anJlJ9adwa/ a96olaJ9V


CONFIDENTIAL


(I)





Ir,.
U)






NACA RM A55G20


Circumferential angle, A, degrees


Figure 24.- Variation of local Mach number on cone with angle of attack
and circumferential location, Mo = 350.


CONFIDENTIAL


CONFIDENTIAL






NACA RM A55G20


Angle of attack, a, degrees

Figure 25- Comporison of local and free-stream recovery factors at M =350,
x = 3 inches.


CONFIDENTIAL


CONFIDENTIAL





NACA RM A55G20


AI






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CONFIDENTIAL


NACA Langley Field, Va.


CONFIDENTIAL











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CONFIDENTIAL

UNIVERSITY OF FLORIDA

3 1262 08106 598 8




UNIVERSITY OF FLORIDA
DOCUMENTS DEPARTMENT
120 MARSTON SCIENCE LIBRARY
P.O. BOX 117011
GAINESVILLE, FL 32611-7011 USA






































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