Orderly three-dimensional processes in turbulent boundary layers on ablating bodies

'« N69-10l9a

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ORDERLY THREE-DIMENSIONAL PROCESSES IN TURBULENT BOUNDARY LAYERS ON ABLATING BODIES

By Thomas N. Canning, Michael E. Tauber, Max E. Wilkins,
and Gary T. Chapman

Ames Research Center, NASA, Moffett Field, California, 94035, USA

1. INTRODUCTION

Careful experimental studies have revealed the presence of a remarkable degree of order in
turbulent boundary layers. Two examples of this, which will also be cited as bases for the discus-
sion of the present paper, are the work by Gregory and Walker (1) and by Mochizuki (2,3). These
papers illustrate quite clearly that the wedge of turbulent flow produced by affixing a single
element of roughness in a flat-plate boundary layer contains a highly regular system of longitudinal
vortices which extend from the wedge leading edge to great distances downstream.

A number of studies have shown the existence of laterally spaced, time-variant disturbances in
transitional subsonic and supersonic flows (4-ft) . More recently, the present authors (9,10) found
.vhat appeared to be regular markings on recovered oallistic-range cone .tiodels showing longitudinal
as well as lateral periodicity, that is, a cross-hatching of the ablated surface, in addition to
longitudinal vortices which ablated streamwise grooves in the surface. An example of this cross-
hatching is shown in Fig. 1, taken from Ref. 10,

The possible implications of these crosshatched ablation patterns on the heat-shield performance
of entry bodies have prompted the present study. This paper describes an attempt to link the observed
sculpturing of the surfaces to the aerodynamic and thermodynamic test conditions under which they
were produced.

2. FACILITIES AND TESTS

Most of the data and discussion will concern observations of Plexiglas models (polymethyl-
methacrylate) , as affected by the hot hypersonic flow in the NASA Ames 3.5-foot wind tunnel. Where
appropriate, comparison will be made with models recovered after flight in a ballistic range.

The 3.5-foot hypersonic wind tunnel is a blowdown facility, in which air stored at high pressure
is heated as it passes upward through a cylindrical tank filled with hot zirconia pebbles. The hot
air then passes through an axially symmetric, contoured nozzle (Moo ^ 7), the walls of which are pro-
tected by a thin film of helium injected upstream of the nozzle throat. The tunnel exhausts into
four evacuated spheres and can provide test times in excess of 1 minute at the conditions used in the
present tests (stagnation pressure of 115 atm and stagnation temperatures of 750° and 1075** K) .

The models were mounted on a movable sting, inserted into the test section after steady flow
was established, and withdrawn after the desired test interval (before the flow was stopped) .
Insertion and withdrawal each required only a fraction of a second.

The models used in the experimental study were designed to reveal the influence of both gradual
and abrupt, and positive and negative, pressure gradients on the patterns produced by ablation.
Shapes were selected that would result in large pressure and heating-rate changes on a given model,
along with large changes in boundary- layer-edge Mach number, M^ , (1.3 to 3,5) and unit Reynolds
number (67,000 per cm to 640,000 per cm). The models (Fig. 2) were solid, homogeneous bodies of
revolution (except for laminations) made of Plexiglas. Cone angles at the tip were 25**, 30°, 40*^,
and 50°; surface inclination was, in every case, changed by a 15** increment, which produced compres-
sions on the two smaller tip angle cones, and expansions on those with larger tip angles. 'ITie slope
was changed in two ways, disrontinuously at a corner, and continuously on surfaces described by
cubic equations. Pointed steel tips, about 1.2 cm in diameter, were used on the models to prevent
ablation at the apex.

3. DATA

The data presented represent a detailed visual study of the bodies during and after testing.
During the tests, the model sui faces were watched by one or more observers and were photographed by
a 16 mm motion-picture camera at 128 frames per second. The observers' purpose was co determine the
rate of formation of the surface patterns by the airflow and to signal the time for termination of the
run by withdrawing the model. Since the plastic material is transparent and the surfaces appear
frosted, many subtle details are better revealed by surface replicas than by the original surface.
Two types of replica were made.

The more sensitive of the two consisted of epoxy plastic cast in a silicone-rubber mold made
from the actual n;odel. The rubber used adheres only weakly to the model and to the epoxy, and is
easily separated with a small air jet. The rubber used for making the female impression is Dow
Corning 3110 RTV Enca^jsulant, and the epoxy resin .'s Epocast Resin No, 4-L with hardener No. 9111.
Tn the course of making these replicas it was found desirable to provide hollow liners in order to
save rubber and epoxy material and make the final bodies light. Liners were made by vacuum-forirtng
clear-plastic sheets of 0.508 mm to l.i!70 mm thickness over the models. A rather high degree of
detail was replicated in both of these processes, and many features difficult or impossible to see

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and photograph on the actual models are made easily visible. Photographs o*" all of the epoxy
replicas are shown in Fig. 3. There are more replicas than models since two models were tested
twicfi in the wind tunnel and replicas were made after each *est.*

Several techniques were used to measure dimensions and angles of surface patterns from the
models and replicas. Cine very sensitive process was to make pencil rubbings by pressing a piece of
bond paper tightly against the model or replica surface and stroking lightly with the side of a lead
pencil or a soft, colored pencil. Both longitudinal and lateral strokings were used to get best
results. The features were then identified and measured in the flat.

On very subtly sculpted models (Fig. 3(e)) or deeply ablated models (Fig. 5(f)), it was found
desirable to hand-mark the features with a grease pencil while studying them with different lighting
and viewing angles. After the principal features were thus accentuated, the pencil marks could be
either "transferred" using pressure-sensitive tape (and transported to flat paper as in the case of
rubbings) or measured in place. Some features, however, were so clearly marked that there was no
difficulty in ineasuring them directly.

In order to minimize any personal bias in the measurement of pattern si2es and shapes, two of
the authors made totally independent measurements of the sweep angle and longitudinal and lateral
wavelengths of the Crosshatch patterns at positions on the bodies selected by each for clarity of
markings. Several measurements were made in each region so that the results would have some
statistical value, but no averaging has been done in the data presentation. The results of the
independent stuaies were substantially identical.

3.1. Appearance of Ablated Surfaces

After ablation by the hypersonic test stream, the present models exhibited most of the features
seen on the earlier ballistic-range models (9) . For completeness of the present discussion these
features are described briefly herein and related to those reported by other authors, as

appropriate.

Each model had small regions of apparently uniform laminar flow, for at least a part of the
test time, which produced little in the way of surface sculpting. These regions usually ended at
a highly irregular transition front characterized by roughness elements and their resultant more
deeply eroded "wedges." The wedges appear similar in planform to those observed in Refs, 1-3, 9,
and 10. Their lateral rate of growth is similar as is the occasionally observed longitudinal
grooving inside them.**

The most striking feature in the turbulent wedges and elsewhere in the regions of presumably
turbulent flow is the cross-hatching produced by the flow. That the patterns result from intersect-
ing grooves which spiral in both directions around the bodies is clearly evident from the slightly
ablated bodies (Fig. 3(e)). As the ablation proceeds, the grooves appear to influence the nature
of the adjacent flow more and more strongly. Instead of clearly intersecting, the grooves appear
to join longitudinally at the spiral intersections and produce a set of wavy longitudinal grooves
like those shown in Fig. 3(f) on model 4.

The clarity and depth of the Crosshatch patterns is occasionally enhanced by disturbances pro-
duced by flaws or joints in the models as seen in Fig. 3(d). A cursory examination showed that new
grooves were being created iriore or less continuously along the surfaces so that the spacing did not
increase proportionately with body radius.

3.2. Correlations

In general^ the sculpture produced by ablation is seen to be quite complicated, and our first
effort at relating the forms produced to the test conditions is necessarily limited. In the present
case we have sought to correlate the spiral angle of the grooves, that is, the angle between the
groove and the body-generator lines, and the size of the patterns with the boundary- layer-edge
flow conditions.

3.2.1. Spiral Angle Correlation

Although the influence of material pioperties has not been ruled out, it was postulated at the
outset that the surface patterns were governed by the boundary layer and perhaps the exterior flow.
Accordingly, the spiral angle data for all the models were plotted against the boundary- layer-edge
Mach number to obtain Fig, 4. A rather convincing coirelatioi* is seen between the observed spiral
angle and the Mach an^le. If the spiral is established by a standing wave, it must of necessity be
at a greater angle than the Mach angle at the boundary- layer edge. The quality of the correlation
suggests that a standing wave system does in fact exist, and hence that the cross-hatching should

*In general, the replicas do not extend fully to the base of the original model. For the pui*pose
of making the replicas only, in some cases the steel tip was removed from the model nose ari replaced
with a screw. The apparent blunting of model tips, such as in Fig. 3(c), was caused by air trapped
during casting and does not represent the actual condition of the model during the test.

**The bodies also exhibited, in varying degrees, two other types of mai^kings. One consisted of
very fine scale longitudinal ridges along body generators (see Fig. 3(h)); these may be a product of
small longitudinal vortices. TTi** other markings are small surface craters partly surrounded by cres-
cents immediately downstream of each crater (see Fig. 3(c)); these are thought to be produced by the
impact of zircona dust particles present in the test stream.

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not exist in subsonic flow. Mateer and Larson (11) conducted a test series using cones of various
materials and a range of apex angles in the same facility and found cross-hatching only on bodies
with supersonic flow outside the boundary layer. The points above the Mach angle curve suggest that
the disturbance source of the standing wave can be well inside the boundary layer where the Mach
numbers are lower than M^. One level in the boundary layer which might be critical is that at
which temperature is maximum.

3.2.2. Lateral-Spacing Correlation

Since the shape of the pattern, that is, the spiral angle, is related to the flow properties,
a length was sought to which the size of the pattern (longitudinal or lateral spacing of grooves)
could be satisfactorily related. Several lengths were considered: the various boundary- layer
thicknesses, the distance from the surface to the shock wave, the wetted length along the surface
from the apex, the radius of curvatut^e of the surface, and the depth of melted surface material, if
any. In addition to these lengths, the influence of such factors as absolute heating rate and Mach
number on pattern size was checked as well.

Even a cursory examination of the models showed a wide variation of groove spacing at any
particular body station. New grooves continuously appear as the flow stretches around the expanding
body; this means that the minimum groove spacing is» at the very greatest, half the maximum. Also,
since there are doubtless random influences affecting groove initiation, the ratio of maximum spacing
to minimum must exceed 2. At a particular streamwise location on model 4 a groove variation of
fourfold over the minimum was observed. In view of these variations, only an approximate character-
ization was possible with the data available. No obvious effect of the pressure gradient on such
features as the cross-hatching has been found; however, because of the influence of the pressure
on the heat -transfer rate, significant changes occurred in the depth of the surface markings.

Many dimensionless groupings were attempted in the course of studying these data and almost all
appeared to yield substantially poorer correlation than that given by a Reynolds number based on
f; boundary- layer-edge conditions and the lateral spacing between the oblique grooves, Re^ , plotted

r as a function of the Reynolds number based on local thickness of the turbulent boundary layer, Re^,

The correlation showed that Rex increased with Re^ (Fig. 5). This finding has two weaknesses:

first, it is based on one test of model 3 at higher total temperature (filled symbols). Second, in

\ two-dimensional flow it would be necessary for grooves to disappear selectively in order to permit

\ the spacing to increase so as to avoid passing out of the correlation band. Mateer and Larson found

\ no such selective disappearance in tests with plast.c wedges. An alternative to selective dis-

-, appearance might be that the entire periodic system might simply decay generally and produce imper-

^ ceptible ablation patterns. In view of the slow decay of longitudinally disposed vortices this

might require great distances.

I

A few measurements of \y were made on the ballistic-range models of Ref. 9. Since there is
little chance of accurately determining when during the flights the final patterns formed, accurate

i calculations of Re^ and Reg are not possible. The complications added by the possibility of

' y ' ,;

f sizable mass transfer at the suriace add to the difficulty of interpretation. Rouglily, the values j

^ of Re^ fell near the bottom jf the scatter band in Fig. 5. i

} y \

^ ''

j. The present findings tc^^tther with those of earlier experiments (clearly defined laterally ^

I periodic structure in turbulent boundar)'- layer flows) lead to a possible model for the inception of i

'j cross-hatching and other sculpture of ablated surfaces. ^

I i

I 4. POSTULATED MODEL \^

K' The flow processes in the boundary layer, which are thought to be capable of sculpting the J

{ present patterns (and some other patterns observed earlier as well), are described without qualifying }

J remarks in this section. Subsequently, supporting observations taken from the present experiments \

i and from the literature are presented to lend weight to the description. 1

r 4.1, Postulated Flow |

The establishment of a turbulence wedge, such as diagrammed in Fig. 6, starts with a single*
f disturbance source a (e.g., a roughness element) in a laminar boundary layer b. The trailing

{ vortex system c from the disturbance may be steady downstream for a distance, depending on sue*"

f factors as disturbance size and flow Reynolds number, and then suddenly break down into intense

I oscillation and turbulence at d in Fig. 6. The disturbance generated by this breakdown produces

a nearly perfectly symmetrical spreading pattern of turbulent flow containing a regular array of
discrete longitudinal vortices e, which are formed at the wedge leading edge. The disturbance f
along the leading edge either produces or is produced by a vortex rcighly hyperbolic in form near

Near the beginning of the test periods of some of the models a much smaller Crosshatch pattern
of waves was seen in the thin melt layer. The spiral angle of these wavelets appeared to be the same
as that 01 the grooves produced later, but the spacing of the waves was perhaps smaller by a factor
of 3 or 4 than the final markings. They may be like the line cross-hatching shown in Ref. 10. Their
smaller size and impermanence suggest that some change in material response,, such as temporary
development of melt layers of critical thickness, surface tension, or viscosity, may have an important
influence on wave spacing in either the small temporary or large permanent patterns observed.

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its apex. Tho longitud '.il vortex filaments are regularly spaced. The pressure disturbance result-
ing from the formatio.. of each filament propagates within the Mach cone g, as indicated in Fig. 6.
The array of pj^esstr' ^.alses c^n e\;;ite oscillations ir the boundary layer as might a multitude of
randomly spaced disturbances in view of the potential for self-aggravation (i.e., feedback) and
stabilization introiucf*d by the sculptured pattern. These disturbances do not produce noticeable
local increases in h/ at transfer or ablation outside the wedge h where the flow is laminar; within
the wedge, where the flow is turbulent, the wave-boundary- layer interaction is concentrated i and
yields sharply defined increments in heating. liVhere the surface contouring by concentrated ablation
becomes deep enough, tiie resulting disturbances become severe enough to supplant the hyperbolic-
front vortex mechanism responsible for the earlier spread of turbulence, as shown at j, toward the
rear of the sketched flow in Fig. 6. As the boundary layer stretches over the ever-expanding
perimeter of the body, new three-dimensional elements (probably vortex pairs) are created and pro-
duce additional wave systems (and hence grooves) .

4.2. Supporting Evidence

The observations of Gregory and Walker (1) and of Mochizuki (2,3) are examples indicating that
the breakdown of the smooth trailing vortex system from a roughness element is hastened either by
increasing the free-stream Reynolds number or the size of the roughness clement. The suddenness of
the breakdown is well documented (2). The disturbance generated by this breakdown is so strong and
the resulting breakdown so regular that an almost perfectly symmetrical wedge is produced. Among
the scores of turbulence wedges seen by the authors, no highly asymmetric turbulence wedges have
ever been seen, so it is concluded that the ensuing spread of turbulence is fully controlled. That
transition fro*^t laminar to turbulent flow, well known for uncertain behavior, should b'e so regular
in this case ;'ttests to the dominance of this mechanism.

Both Ref s . 1 and 2 note clearly the regular array of streamwise vortices found in the wedge.
The extremely regular breakdown along the wedge leading edge is described in Ref. 3: *', . . the
photographs of the smoke pattern show distinctly the turbulent region behind the sphere [roughness

[ element] and the laminar region outside of it. At the boundary of the two regions, we can see the

smoke filaments grther one after another and take winded forms and then become obscure by strong

I mixing downstream. This state indicates that there might be a longitudinal vortex near the

boundary. The measurements of the mean velocity profiles show clearly that a pair of longitudinal
voitices appears outside of the four longitudinal vortices existing already, just at the boundaries
of the turbulence v;edge, and much closer to the flat plate than the former vortices." The indication
that all of these outer vortices (in each half of thc^ wedge) are co- rotational also suggests that
the mechanism controlling filament forraation is not simple induction by the downwash fields of

] existing vortices, but is the result of a continuous vortex filament or a pressure wave passing

obliquely across the flow.

V An unusual observation on recovered ballistic-range models (9,10) may be further evidence of

I this postulated leading-edge vortex. The surface shown in Fig. 7(a) has a clearly visible low ridge

called a "hyperbolic front" by the authors; several such fronts have been preserved on ballistic-
range models. If the leading- edge vortex described in Ref. 3 does exist, it should induce a lateral

t flow near the surface such that the surface streamline will trace out a line following the ridge

S found. The flow detail here is suggested at f in Fig. 6.

\

f; The pressure disturbances proauced by the start of each vortex filament forming at this front

; should produce sharp pulses propagating along the Mach cones from each formation point. In subsonic

\ flow no such obvious mechanism exists for concentrating the effect of the pulses, and cross-hatching

is not observed. Also, a convincing correlation is found between spiral angle and edge Mach number.

I In a laminar boundary )ayer h (i.e., along the outbound waves, g) , the streamwise action of

I each wave should be spread out over many boundary- layer thicknesses, perhaps over several wave

\ spaces, because of the extensive interaction typical of waves with laminar boundary layevi., and

\ therefore produce no important sculpture unless i:: is stjong enough by itself to cause transition

{ (j in Fig. 6), as illustrated in Fig. 7(b). The inward-bound waves, g, on the other hand, are inter-

acting with a boundary layer of much higher shear, so that the interaction is concentrated sharply.
^ This should permit the cutting of grooves in the turbulent -flow area. As the flow is stretched over

the body, new grooves appear. That the lateral wavelength does not exceed some poorly defined maxi-
mum probably related to the boundary- layer thicVnois is shown by the present data. The observations
using hydrogen-bubble flow visualization in two-dimensional flow (7) show that even at very large
Reynolds numbers there is a clear later. i^ periodicity in turbulent-boundary- layer profiles. Consis-
tent with the results of Ref. 7, Black *s analytical formulation (12) points strongly to the possibil-
ity of vortex- loop discharges into the rv;er part of th*5 layer from near the surface at preferred
lateral spacings.

This overall flow model for the inii^iation and development of turbulence and cross-hatching is
believed to reconcile many of thj observe^jl phenomena in transitional and turbulent flow. The high
degree of order found is consistent with the orderliness of the markings.

'■

t 5. CONCLUDING REMARKS

It has been shown herein that there can be a great deal of order in the supersonic turbulent
boundary layer. The presence of both lateral and longitudinal, nearly time-invariant, spatially
fixed waves or vortex systems or both has been deduced from studying ablated surfaces under widely
varying test conditions, ranging from those of ballistic ranges to wind tunnels. The sizes of the

6-5

models ranged over an order of magnitude, while surface pressures and ht^ -it -transfer rates varied over
two to three orders of magnitude. The generally good agreement of "crosshatch" spiral angle with the
boundary-laver-edge Mach angle up to about M^ = 2 and then spreading,, at timers, at an angle greater
than the Mach angle, suggests that the disturbance causinjj the standing-wave system responsible can
bT near the edge ox deeper within the boundary layer as Mach number increases. The attempt to cor-
relate the spacing of the cross-hatching against a boundary-layer thickness has been on^ partially
successful; typically, the wavelength is equal to a few boundary- layer thicknesses. Lastly, the
model proposed herein for the formation of the cross-hatching is fe)t to be compatible with many of
the critical elements of orderly flow found by uarlier investigators.

ACKNOWLHDGMHNT

The authors would like to acknowledge the contribution of Mr. Hartmut Legner in designing the
models and doing many of the flow-field calculations.

6. REFERHNCES

1. Gregory, N.; and iValker, W. S. : "Tnc Effect on Transition of Isolated Surface Excrescences in

the Boundary Layer." Part I, R. § M. Nc. 27*'t\ Aeronautical Research Council, London,
October 1956.

2. Mochizuki, Masako: *'Smoke Observation on Boundary Layer Transition Caused by a Spherical Rough-

ness Element." J. Physical Society of Japan, vol. 16, no. 5, May 1961, pp. 995-1008.

3. Mocnizuki, Masako: "Hot-Wire Investigations of Smoko Patterns fiused by a Spherical Roughness

Element." Natural Science Report, vol. 12, no. 2, Ochanomizu Univer:.ity, Tokyo, Jappn, 1961.

4. Hama, Francis R. : "Some Transition Patterns in Axisymmetric Boundary Layers." Physics of

Fluids, vol. 2, no. 6, November-December 1959, pp. 664-667.

5. Kama, Francis R.; and Nutant. John: "Detailed Flow-Field Observations in the Transition Process

in a Thick Boundary Layer." Proceedings of the 1963 Heat Transfer and Fluid Mechanics
Institute (Stanford University Press, Stanford, California, 1963), pp. 77-93.

6. Coles, Donald: ^'Tiansition in Circular Couette Flow." J. Fluid Mechanic:*, vol. 21, part 3.

March 1965, pp. 365-425.

7. Schraub, F. A.; Kline, S. J.; Henry, J.; Runstadler, P. W., Jr.; and Littell, A.: "Use of

Hydrogen Bubbles for Quantitative Determination of Time Dependent Velocity Fields in Low Speed
Water Flows." Report MD-10, Stanford University, Stanford, California (February 1964).

8. Knapp, C. F.; and Roache, P. J.: "A Combined Visual and Hot-hire Anemometer Investigation of

Boundary-Layer Transition." AiAA J., vol. 6, no. 1, January 196£, pp. 29-36.

9. Canning, Thomas N.; Wilkins, Max E.; and Tauber, Michael E.: "Boundary- Layer Phenomena Observed

on the Ablated Surfaces of Cones Recovered After Flights at Speeds Up to 7 km/sec." Presented
at AGARD Specialists' Meeting on Fluid Physics of Hypersonic Wakes, Fort Collins. Colorado.
May 10-12, 1967.

10. Canning, Thomas N.; Wilkins, Max E.; and Tauber, Michael E. : "Ablation Patterns on Cones Waving

Lamin%r and Turbulent Flows." AIAA J., vol. 6, no. 1, 1968, pp, 174- 175.

U. Mateer, George G.; and Larson, Howard K.: "Unusual Boundary- Layer Transition Results on Cones
in Hypersonic Flow." AIAA Preprint 68-40, 1968.

12. Black. Thomas J.: "Some Practical Applications of a New Theory of Wall Turbulence." Proceedings
of the 1966 Heat Transfer and Fluid Mechanics Institute, edited by M. A. Saad and J A. MiUer
(Stanford University Press, Stanford, California, 1966), pp. 366-386.

6-6

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Fig. 1. Example of cross-hatching (Ref. 10)

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SECTION A-A

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PAPER 7

This pq;>er has been cancellsd
by mutual agreement

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REYNOLDS AND MACH NUMBER SI!4ULATI0N OF APOLXiO AND
GEMINI RE-ENTRY AND COMPARISK>N WITH FLIGHT

By

i B. J. Griffith and D. E. Boylan

^ ARC, Inc., Arnold Air Force Station, Tennessee

SUMMARY

A comprehensive investigation in the AEDC-VKF wind tunnels
was conducted on the Apollo Oil and Gemini 3 spacecraft config-
urations in order to resolve several anomalies between prefllght

predictions and flight data. Attention was focused on simu- i
lating the actual Apollo Command Module (Oil) and Gemini space-
craft (GT3) ''as flown" in model construction over a Mach number ^
range of 3 to 20.

Ilie investigation indicated that the influence of the ' j

ablator (heat shield) geometry of the Apollo Command Module \

causes a significant change in trim angle of attack and j

resulting decrease in available litt-to-drag ratio. In addi- I

tion, a very strong viscous influence exists in the initial |

portion of re-entry for both the Apollo and (Semini space- i

crafts. Also, the Mach number influence extends up to about }

Mach 14 which is substantially higher than previous blunt body |

investigations have indicated. Comparisons of the AEDC wind I

tunnel data with existing flight data are made and generally f

excellent agreement exists. \

i