The high temperature aspects of hypersonic flow; proceedings of the AGARD-NATO Specialists' Meeting sponsored by the Fluid Dynamics Panel of AGARD, held at the Technical Centre for Experimental Aerodynamics, Rhode-Saint-Genèse, Belgium, 3-6 April 1962

776 Pages·1964·68.7 MB·English

by  Wilbur Clifton Nelson

THE HIGH TEMPERATURE
ASPECTS OF
HYPERSONIC FLOW
Proceedings of the AGARD-NA TO Specialists' Meeting
Sponsored by the Fluid Dynamics Panel of AGARD
held at the
Technical Centre for Experimental Aerodynamics
Rhode-Saint-Genèse, Belgium
3-6 April 1962
Edited by
WILBUR C. NELSON
Department of Aeronautical and Astronautical Engineering
University of Michigan
Ann Arbor, Michigan
Published for and on behalf of
ADVISORY GROUP FOR
AERONAUTICAL RESEARCH AND DEVELOPMENT
NORTH ATLANTIC TREATY ORGANIZATION
A Pergamon Press Book
THE MAGMILLAN COMPANY
NEW YORK
1964
THE MACMILLAN COMPANY
60 Fifth Avenue
New York 11, N.Y.
This book is distributed by
THE MACMILLAN COMPANY · NEW YORK
pursuant to a special arrangement with
PERGAMON PRESS LIMITED
Oxford, England
Copyright
©
1964
ADVISORY GROUP FOR
AERONAUTICAL RESEARCH AND DEVELOPMENT
NORTH ATLANTIC TREATY ORGANIZATION
Library of Congress Card No. 63-17827
Set in Baskerville 10 on 11 pt and printed in Great Britain by
PAGE BROS. (NORWICH) LTD.
DEDICATION
With heavy hearts we dedicate this volume to Theodore von Karman—
the man who made NATO-AGARD possible. As his foreword indicates,
he was deeply and intimately involved in AGARD's many activities. His
inspiration and humor made life brighter and more meaningful for all of us.
His loss is immeasurable. We are truly thankful that he was active and happy
throughout his entire life span.
FLUID DYNAMICS PANEL
6 June 1963
V
FOREWORD
THE AGARD Fluid Dynamics Panel has for several years followed the prac-
tice of sponsoring specialists' meetings as one means of achieving its objectives.
Experience has shown that the success of these meetings depends on a wise
and timely choice of subject, on confining the meeting to a single specific
subject and on getting the active workers in the field to attend. The present
meeting was one in a series which includes: "Pressure Measurements",
"Interference Effects", "The Use of Wind Tunnels in Aircraft Development
Testing", "High Temperature Gas Characteristics", "Boundary Layer
Research", "Stability and Control" and "The Use of Rocket Vehicles in
Flight Research".
It has been the custom of the AGARD Fluid Dynamics Panel to arrange
for publication of the papers presented at specialists' meetings in the AGARD
Report Series. This had the advantage of making the material available to
readers with little delay in that the printer could publish corrected copies of
individual papers as they were received. In addition, from the standpoint of
economy, readers could obtain copies of only those papers in which they
were actively interested. The advantages of publishing the papers and
discussion in a bound volume as "Proceedings" are obvious, if it could be
done within a reasonable time limit. I believe that this objective has been
achieved in the present volume.
THEODORE VON KÂRMÂN
Vil
ACKNOWLEDGEMENT
IN the interests of timely publication, it unfortunately has been necessary to
delete several papers which were still unavailable at the time of going to
press. These will undoubtedly appear at a later date in the various scientific
journals.
The Editor wishes to express his thanks for the extremely helpful work of
L. Moulin and his colleagues at the TCEA in editing the discussion of the
various papers as well as the round table discussion.
WILBUR C. NELSON
ix
CHAPTER 1
HYPERSONIC AERODYNAMIC PROBLEMS
OF THE FUTURE
H. JULIAN ALLEN*
National Aeronautics and Space Administration
Ames Research Center, Moffett Field, Calif., U.S.A.
Blunt shapes were of interest for the speed regime of ballistic missiles and satellite
vehicles, in the main, as a result of the necessity for minimizing convective heating.
But as speeds exceed escape speed, the heating due to air radiation assumes an even
more important role than does the convective heating. It is shown that this change
revives interest in the more slender configurations and that when the speed of a vehicle
entering the atmosphere of a planet becomes sufficiently great, it may be economical
to decelerate in part by retrorocket rather than entirely by aerodynamic braking.
The factors discussed determine the speed limit for which retrorocket braking be-
comes desirable.
The change in the basic characteristics of flow brought about by gas radiation
at speeds well in excess of escape speed are then analyzed. It is shown that when
the gas radiation energy becomes a significant part of the total energy of the flow,
it is no longer possible to analyze aerodynamic flow fields with the assumption that
the energy of elemental volumes remains constant, since for such cases a transfer of
energy by radiation from one elemental volume to another significantly alters the
flow. The increase in complexity in the analytical approaches to the problems of
these hypersonic flows necessitates, more than ever, continued experimental research,
even though such experiments are exceedingly difficult to perform. Extension of our
experimental knowledge of these hypersonic flows is shown to be possible by study
of tracked trajectories of bright meteors. Some analyses of meteor tracking data are
presented which demonstrate that the tracking camera systems employed at present
can provide sufficiently accurate results to yield useful aerodynamic heating
information.
SYMBOLS
A reference area (usually base area) for definition of coefficients
CD drag coefficient
D drag force
F function of flight speed in Eq. (20)
G multiple of g
g earth gravitational acceleration
h altitude
/ luminosity
i specific impulse of propellant
K constant in Eq. (6)
m body mass
n exponent in Eq. (20)
* Assistant Director.
1
H. JULIAN ALLEN
q aerodynamic heat input
R earth radius
r body radius defined in Eq. (31)
t time
V flight velocity
ß inverse scale factor defined in Eq. (14)
y angle flight path makes with local horizontal
ζ heat capacity of coolant per unit mass of coolant
6 6 angles defined in Fig. 20
Wy C
λ heat-transfer coefficient
p local air density
r luminous efficiency
Φ, φ functions of flight speed in Eq. (18)
Ψ, φ functions of flight speed in Eq. (19).
Subscripts
C coolant
c convective
E entry
e equilibrium
g gas cap
lim limit
max maximum
m meteor
n non-equilibrium
o sea level
P payload
£ satellite
v vaporizaticn
1. INTRODUCTION
It is the purpose, in this paper, to enumerate and discuss future problems
in hypersonic aerodynamics. Hopefully, the list of problems would be com-
plete but past experience indicates that such is not likely to be the case, for
as the science progresses, there will arise problems of a nature not now antici-
pated. It is hoped that the paper may provide some readers with an impetus
to give more serious thought to the problems that are discussed and might
help others to foresee additional problems.
Before listing and discussing future hypersonic aerodynamic problems, it
is of value to review the problem of the past and the methods employed in
their solution. In this way some methods for solution of future problems
may suggest themselves.
2. THE SUBSATELLITE-SPEED VEHICLE PROBLEMS
OF THE PAST
It is only about a decade since serious consideration was first given in the
United States of America to constructing and flying ballistic missiles having
intercontinental range capability. The development of rocket engines capable
of producing the large thrusts required at what then seemed absurdly low
weight was, of course, only one of the major problems. Equally important
2
HYPERSONIC AERODYNAMIC PROBLEMS OF THE FUTURE
was the construction of large ultralightweight tankage structures and guid-
ance systems capable of reliable performance with required accuracies far
more stringent than anything that had been attempted before. To the aero-
dynamicist, the major problem of comparable import concerned aero-
dynamic heating of the vehicle during atmosphere entry on the return to
Earth. The principal difficulty was then, as it is now, that mere solution of
these problems was not enough. The chemical fuel rocket has such low
efficiency that weight is at an absolute premium. The propellants constitute
approximately nine-tenths of the "take -off "mass. The higher the speed the
arger the fraction of fuel required, other things being equal. With one-tenth
or less of the launch weight available for the rockets, the entire structure,
the required accessories and the payload, it is readily apparent that the least
carelessness in design can produce a situation wherein no payload at all can
be carried, if, in fact, the required flight speed is even attainable.
The fundamentals of aerodynamic heating on entry of these vehicles are the
following: When the vehicle begins its entry into the atmosphere it enters
at a very high speed, VE, dictated by the desired long range. The deceleration
experienced during the portion of the entry wherein the aerodynamic heat-
ing is important is so large compared to the acceleration of gravity that the
latter may be ignored. Hence, the equation of motion gives
dV 1
m^ = - C V*A (1)
(? DP
and the equation of heating gives
à£=\\ V*A (2)
P
where
m entry body mass
V local velocity at any time
t time
p local air density
A reference area (usually base area) for definition of coefficients
q aerodynamic heat input
CD drag coefficient
λ heat-transfer coefficient
Then combining Eqs. (1) and (2) gives
λ λ im dV2\
ΎΤ ΛΊ7
(3)
If for the moment the heat-transfer coefficient, the mass, and the drag co-
efficient are considered to be essentially constant, then the total heat input
is
_ _ fonV*\v° _ XmV *
E
(4)
2CD \V=VE ~ %CD
since V will generally be small compared to the speed at entrance to the
0
atmosphere.
B 3
H. JULIAN ALLEN
The heat-transfer rates for ballistic vehicles of usual size are so great that
only a negligible amount of the heat input may be radiated from the vehicle.
Therefore, the mass of required coolant is directly proportional to q, and
since the vehicle mass in an ideal case is the sum of the payload mass, mp,
plus coolant, mc, then
mc = - (XVE*I2CD()\ mP (5)
where ζ is the heat capacity of the coolant per unit mass of coolant.
To minimize the cooling system weight, then, attention must be paid to
the following: First, reducing the mass of the entry vehicle to the bare
minimum by jettisoning the spent rockets, tankage, etc. ; second, using a
coolant with the highest employable heat capacity per unit mass, ζ; and,
third, keeping the ratio of the heat-transfer coefficient to the drag coefficient
as small as possible. That is, as large a fraction as possible of the heat energy
must be spent in heating the atmosphere to assure that the remainder, which
is retained by the vehicle, is a minimum.
Historically, the role played by several of the factors was not immediately
appreciated. The necessity for jettisoning all but the essential mass required
was recognized first. The advantage to be accrued by use of a coolant which
vaporized, thus adding the latent heat of vaporization to the value of ζ, was,
of course, apparent. However, the most suitable vaporizing materials from
the heating standpoint were those having low thermal conductivity, and
there were justified fears that such materials would not be able to withstand
the accompanying high thermal stresses. If spalling of the surface due to
thermal stress were to occur, then, at the least, the value of ζ would be
reduced by the fact that some coolant would be jettisoned in the solid state
before it had received its share of the heat. At most, such local structural
failure might be progressive and promote complete collapse of the entry
vehicle, a phenomenon well known to commonly occur with large stone
meteors. Since, at that time, there were no facilities available for investigating
these structural problems, it was decided to employ metals as heat sinks for
the cooling systems for which calculation indicated no insurmountable
structural problems existed. With regard to the heat-transfer coefficient and
the drag coefficient in the heating process, the role of the former was clearly
recognized but not that of the latter at first. The earliest designs attempted to
minimize the heating problem by lessening the friction coefficient and so
the heat-transfer coefficient. This approach led to entry body shapes having
high fineness ratios. Such an approach naturally appealed to the missile
designers ofthat time who, from their earlier experiences as aircraft designers,
had been accustomed to directing their efforts toward the attainment of
minimum frictional drag. When the role of drag coefficient was seen in
proper perspective and designs were sought which provided minimum ratio
of heat-transfer coefficient to drag coefficient, an order of magnitude im-
provement became possible. Bodies with such properties, contrarily, have
very low fineness ratios. The attendant bluntness of such shapes was readily
appreciated to be particularly attractive in minimizing intense local heating
of the surface such as usually occurs at the bow of bodies.
4
HYPERSONIC AERODYNAMIC PROBLEMS OF THE FUTURE
The principal weakness of the early blunt entry bodies was, as noted
earlier, that the heat sink as a heat shield was most inefficient. On the early
entry vehicle such heat shields constituted as much as one-third of the entry
body mass. An ardent and successful effort was made to provide facilities in
which entry heating rates could be duplicated in the laboratory. Many
materials were then found which, as desired, would ablate as vapor without
attendant danger of spalling or structural failure. Thus a great improvement
in the efficiency of heat shields became possible and heat shield mass was
reduced to a relatively small fraction of what it had been. The gains were so
great, in fact, that it was no longer mandatory to employ the extremes in
bluntness of shape that had been necessary with the heat sink designs.
For sundry reasons the low drag shapes were desirable for missiles. The
present missiles reflect this trend.
There are additional advantages associated with the use of heat shields
employing vapor ablation. One advantage recognized by many (see, e.g.
Refs. 1-4) is that the issuing vapor fends off the air so as to reduce the heat-
transfer coefficient itself. For laminar flow the reduction is in the ratio (4)
1 (6)
where K is a constant depending upon the molecular weight of the vapor
(0-3 represents a usual value) and ζ is the total energy required to vaporize
ν
a unit mass. Thus, the reduction in heat-transfer coefficient becomes more
important the higher the flight speed.
A second advantage not generally appreciated, and one which will become
more important as we increase flight speed, is that as the coolant is vaporized,
it is automatically jettisoned; therefore the ensuing heat load is diminished
by the continuous reduction of unnecessary body mass. Thus the heat-
transfer equation becomes
ζν d = xpV3A (7)
£ " I
(7)
Combining this with the motion equation gives
(8)
so that if the quantity in parentheses is assumed to be essentially constant,
then the mass, m, at any time when the speed is V, is related to the entry
mass, niEi and entry speed, VE, by
m = m exp[A(F2 - V *)I2C C ] (9)
E E D V
if we consider the idealized case wherein the final mass is the payload only,
then for a final velocity, negligible compared to the entrance velocity,
(10)
\ exp[— XVE2I2CDCV\ J
Figure 1 gives the optimum ratio of coolant mass to payload mass for an
ablative heat shield obtained from Eq. (10) and, for comparison, the optimum
5