High Speed Wind Tunnel Testing Alan Pope
Short Description
Book...
Description
High-Speed Wind Tunnel Testing
Courtesy Naiiona! Aeronautics and Space Administration
Schlieren photograph of the flow field
around the X-15
aircraft
(Mach
3.24,
a
=
8°,
|3
= 0°).
High-Speed
Wind Tunnel
Testing
Alan Pope Director of Aerospace Projects, Sandia Corporation
Kennith Staff
L.
Coin
Member, Aerodynamic Testing
John Wiley
Division, Sandia Corporation
& Sons,
Inc.,
New York London Sydney |
|
Copyright
©
1965 by John Wiley
& Sons, Inc.
All Rights Reserved
This book or any part thereof
must not be reproduced in any form without the written permission of the publisher.
Library of Congress Catalog Card
Number: 65-21435
Printed in the United States of America
Preface
The extension of
made
regimes has
the field of wind tunnel testing into the higher-speed it
advisable to revise
Wind Tunnel
Testing into low-
and high-speed coverages. In this, the high-speed edition, the design, calibration, and operation of nearsonic, transonic, supersonic, and hypersonic tunnels are covered.
but the relatively rare corrections
may
field
This book
is
a separate entity for
all
of nearsonic testing, where low-speed wall
have to be obtained from Wind Tunnel Testing.
The purpose of High-Speed Wind Tunnel Testing remains the same as that of
its
parent book; to furnish a reference for engineers using tunnels,
help students taking laboratory wind tunnel courses, and to aid
to
beginners in the field of wind tunnel design.
Attention should be called to the format of the book.
of
tests
may
duplication
Nearly
all
we have had
to select a place to discuss a test
and make only
such additions as seem necessary in the remaining speed ranges. suggest, therefore, that
when studying a
We wish to acknowledge it
this
Albuquerque, June, 1965
the help
we have
book would have been
New Mexico
We
particular type of test the reader
check the speed ranges of reduced interest to see therein is of use.
Without
types
be performed in any of the speed ranges, and to avoid
if
the material contained
received
from our
associates.
substantially delayed.
Alan Pope Kennith
L.
Coin
Contents
ix
Abbreviations 1.
High-Speed Wind Tunnel Theory
2.
Design of Intermittent Blowdow'n Tunnels
3.
Design of Intermittent Indraft Tunnels
135
4.
Design of Pressure-Vacuum Tunnels
146
5.
Design of Continuous Closed-Circuit Tunnels
166
6.
Air Measuring Devices
198
7.
Force and
8.
Models, Testing, and Data Reduction
Moment Measuring
Devices
I
66
242 284
9.
Calibration and
Use of Nearsonic and Transonic Tunnels
305
10.
Calibration and
Use of Supersonic Tunnels
349
11.
Calibration and
Use of Hypersonic Tunnels
402
12.
Hypervelocity Facilities
442
Index
469
Abbreviations
In view of the large
number of aeronautical research
centers being set up, a
incomplete. However, list such as this must be considered publications. particular in identifying the source of
may
be of help
Complete Meaning
Abbreviation
AAL ACA AEDC
it
Ames Aeronautical Eaboratory (NASA), Moffett Australian Council for Aeronautics, CSIR
Field, California
Arnold Engineering Development Center (Air Force), Tullahoma, Tennessee
AFAC AFCRC
Air Force Armament Center, Eglin Field, Florida Air Force Cambridge Research Center, Cambridge, Massachusetts
AFFTC
Air Force Flight Test Center, Muroc, California
AFMTC AFSWC AFWL AGARD
Air Force Missile Test Center, Cocoa, Florida Air Force Special Weapons Center, Albuquerque,
AIAA APL
American
New
Mexico
Air Force Weapons Eaboratory, Albuquerque, New Mexico Advisory Group for Aeronautical Research and Development, a
North Atlantic Treaty Organization and Aeronautics Applied Physics Eaboratory, Johns Hopkins University, Spring, Maryland Aeronautical Research Association, England division of the
ARA ARC ARDC ARDE
Institute of Astronautics
Silver
Air Research Committee, Australia Air Research and Development Center, Wright-Patterson Air Force Base, Ohio
Armament Research and Development Establishment Fort
ARE ARE
Halstead, England Aerospace Research Institute, University of Tokyo (Japanese) Aeronautical Research Eaboratory, Whitley, England Aerospace Research Eaboratory, Wright-Patterson Air Force
ASD
Aerospace Systems Division, Wright-Patterson Air Force Base,
ATE
Aeronautical Test Eaboratory, U.S. Navy, Pt. Mugu, California Aerodynamische Versuchsanstalt (Gottingen Institute for Aero-
ARI,
UT
Base, Ohio
Ohio
AVA
dynamics), Gottingen,
BAC BOE BRE
Germany
British Aircraft Corporation,
England Boeing Engineering Report, Boeing Company, Renton, Washington Ballistic Research Eaboratory, Aberdeen Proving Ground, Maryland
ix
X
I
High-Speed Wind Tunnel Testing
CAI CSIR
Central Aerohydro dynamic Institute, Moscow, U.S.S.R. Council for Scientific and Industrial Research, Australia
CNRC DTMB DVL
Canadian National Research Council, Ottawa, Canada David Taylor Model Basin (Navy), Carderock, Maryland Deutsche Versuchsanstalt fiir Luft- und Raumfahrt (German Institute for Aeronautical and Space Research) Berlin and
ETH
Gottingen, Germany Eidgenossische Technische Hochschule (Swiss Institute of Tech-
GALcrr
nology) Flygtekniska Forsoksanstalten, Stockholm, Sweden Guggenheim Aeronautical Laboratory of the California Institute
HMSO
Her Majesty’s
IAS
Institute of Aeronautical Sciences
JAM JAS
Journal of Applied Mechanics Journal of the Aeronautical Sciences (United States)
JPL
Jet Propulsion Laboratory, California Institute of Technology,
JRAS
Journal of the Royal Aeronautical Society (British) Langley Aeronautical Laboratory (NACA), Langley
FFA
of Technology, Pasadena, California Stationery Office, London, England
(United States)
Pasadena, California
LAL
Field,
Virginia
LFA
Hermann Goring (Hermann Goring Braunschweig, Germany Laboratory (NACA), Cleveland, Ohio
Luftfahrtforschungsanstalt
Institute for Aeronautics),
LFPL
LRBA
Lewis Flight Propulsion Laboratoire de Recherches Ballistique France
et
Aerodynamique, Vernon,
MAI MIT
Moscow
NACA
National Advisory Committee on Aeronautics (now the National Aeronautics and Space Agency)
NAE NAE NAL NASA NLRL
National Aeronautical Establishment, Bedford, England National Aeronautical Establishment, Ottawa, Canada National Aeronautical Laboratory, Tokyo, Japan
Aviation Institute, Moscow, U.S.S.R.
Massachusetts Institute of Technology, Cambridge, Massachusetts
National Aeronautical and Space Agency, Washington, D.C. National Lucht-en-Ruimtevaartlaboratorium, Amsterdam, Netherlands
NOL
Naval Ordnance Laboratory, White Oaks, Maryland
NPL NRTS NSL OAL
National Physical Laboratory, Teddington, Middlesex, England National Reactor Testing Station, Arco, Idaho Naval Supersonic Laboratory, Cambridge, Massachusetts
ONERA
ONR ORNL PRS
Ordnance Aerophpics Laboratory, Daingerfield, Texas Office National d’fitudes et de Recherches Aeronautiques (National
Bureau of Aeronautical Research), Paris, France Naval Research, Washington, D.C. Oak Ridge National Laboratory, Oak Ridge, Tennessee Office of
Proceedings of the Royal Society of London (British)
High-Speed Wind Tunnel Testing
QAM R&M
Reports and Memoranda (of the Air Research Committee)
/
xi
Quarterly of Applied Mechanics
RAE
Royal Aeronautical Establishment, Famborough, Hants, England
RM
Research
SAE
Society of Automotive Engineers (United States)
TCEA
Training Center for Experimental Aerodynamics, Belgium
Memorandum of the NASA
TM
Technical
TN
Technical Note of the NASA Technical Report of the NASA
TR
USNMC
Memorandum of the NASA
WRE
United States Naval Missile Center, Pt. Mugu, Caliform'a Wright Air Development Center, Wright Patterson Air Force Base, Ohio Weapons Research Establishment, Australia
ZAEA
Zhukovsky Aeronautical Engineering Academy, Moscow, U.S.S.R.
WADC
:
chapter one
High-speed wind tunnel theory
Tunnel Types and Uses
1:1
tunnels are devices which provide an airstream flowing under controlled conditions so that items of interest to aeronautical engineers
Wind
High-speed tunnels, as far as this textbook is concerned, are those whose usual operating speeds require the inclusion of compressible flow effects. This, it turns out, means that in the high-speed field we
can be
tested.
usually talk about
“Mach number”
—
^the
ratio of a given velocity to the
—as a more typical parameter approximately 0.5 —about 380 mph for
speed of sound in the air about the body
A lower limit
than velocity.
where the
Mach number
of “high speed” might be considered to be
is
standard sea level conditions.
wind tunnel varies as the cube of the wind tunnel. Although this rule does not hold into the high-speed regime, the implication of rapidly increasing power requirements with increasing test speed is correct. Because of the power requirements, high-speed wind tunnels are often of the “intermittent” type, in which energy is stored in the form of pressure or vacuum or both and is allowed to drive the tunnel only a few seconds out of each pumping
The power
to drive a /ow-speed
velocity in the
hour. Essential features of the “continuous” tunnel
mittent” tunnels are tunnel (Fig.
1
:
blowdown and
1) is
shown in
Figs.
1
:
1,
1
:2,
1
:
and three types of “inter3, and 1 :4. The continuous
used throughout the speed range.
The
intermittent
and 1:3) are normally used for Mach numbers from 0.5 to about 5.0, and the intermittent pressurevacuum tunnels (Fig. 1:4) are normally used for higher Mach numbers. Both intermittent and continuous tunnels have their advantages and indraft tunnels (Figs. 1:2
disadvantages.
Advantages claimed for intermittent tunnels are 1.
They are simpler
2.
A single drive may easily run several tunnels of different capabilities.
to design
and
less costly to build.
2
j
High-Speed Wind Tunnel Testing
Fig. 1:1
Diagrammatic layout of
closed-circuit,
continuous flow, supersonic wind
tunnel.
Fig.
1
:2
Diagrammatic layout of intermittent blowdown tunnel.
Vacuum pump Fig. 1:3
Diagrammatic layout of intermittent indraft wind tunnel.
High-Speed Wind Tunnel Theory
port
^Inspection
tunnel,
port-'^
pressure-vacuum
Blow-off
hypersonic
pebble-heater
Corporation
Sandia
of
drawing
Schematic
:4
1 Fig.
/
3
— 4
I
High-Speed Wind Tunnel Testing
Model testing is more convenient, since a lot of time need not be spent in pumping down the whole circuit and getting the drive motors up 3.
to speed.
model
4.
Failure of a
5.
Extra “power”
6.
is
will usually
not result in tunnel damage.
available to start the tunnel.
Loads on a model during the establishment of high-speed flow because of faster starts.
(starting loads) are less severe
Advantages claimed for the continuous tunnels are: 1.
We
are
more
in control
given flow condition with 2.
of conditions, and
may
usually return to a
more accuracy.
Since the “panic” of rapid testing
is
removed, check points are more
easily obtained. 3.
Testing conditions can be held constant over a long period of time.
Although intermittent tunnels seem to have more advantages, the fact remains that very few intermittent tunnels would be built if cost were of no consequence. We should also note that a tunnel’s being continuous does not guarantee that it will turn out more data than an intermittent tunnel. For one thing, faster instrumentation is usually employed with intermittent tunnels, and even if continuous tunnels were to have such equipment (for some curious reason, they never seem to), the time lost pumping the pressure tunnels up and down, bringing the drive up to speed, and stopping it may offset the advantage of being able to run for longer periods.
Particularly,
a desired pressure
may be
pumping a continuous tunnel
circuit
up
to
a problem, since some tunnels require two hours
or more. It is sometimes amusing to listen to an operator of an intermittent tunnel and one of a continuous tunnel discuss their problems. It is almost as if they were talking two different languages. This is particularly true when the subject is the need for higher compression ratios (ratios of supply to
discharge pressure) to start a tunnel than to keep
mittent tunnel
—
it
running.
The
inter-
particularly the indraft or the pressure-vacuum type
When the valve on one of snapped open, a near vacuum is provided against the stagnation pressure, and the pressure ratio is very large. Getting the tunnel started is no problem at all. On the other hand, the operator of a continuous tunnel is very well aware of the fact that his
almost automatically provides these ratios. these intermittent tunnels
is first
compressors will yield only a particular pressure ratio for a particular
mass flow. There is
choice in the type of intermittent tunnel to be used at the numbers. The compression ratio requirements are so high that a pressure-vacuum tunnel is dictated. It is not practical to operate
higher
little
Mach
High-Speed Wind Tunnel Theory
/
5
with atmospheric inlet pressure (as with the indraft tunnel) or with atmospheric discharge pressure (as with the blowdown tunnel). However,
high-speed wind tunnels operating at
many
there are
and blowdown
Mach numbers
tunnel are practical.
for
Lists of the
which both the indraft advantages of these two types of tunnels when compared with each other follow.
Some advantages of the 1. is
indraft tunnel over the
blowdown tunnel are:
Total air temperature at supply conditions (stagnation temperature)
constant during a run. 2.
Total air pressure at supply conditions (stagnation pressure)
constant during a run although in total pressure
no variations
it
may
is
be lower than desired. There are
such as those a pressure regulator
may
cause. 3.
(but 4. 5.
The airstream
is
free
from contaminants such
as
compressor
oil
may
contain dust from the desiccant of the air drier). The headaches and dangers of pressure regulators are removed. Loads on a model during the establishment of the high-speed flow
(starting loads) are smaller. 6.
Vacuum
7.
The noise
8.
Obtaining low air density (corresponding to high altitude) in the
tunnel 9.
is
not
The
heating
is
is
safer to handle than pressure. level
is
lower.
difficult.
indraft tunnel can operate at higher
Mach numbers
before
required to prevent the liquefaction of air during the expansion
to high speeds.
For a given
10.
cost, indraft tunnels are larger.
Advantages of the blowdown tunnel over the indraft tunnel are: 1.
It is
possible to vary the Reynolds
Mach number. In some may be reached. 2.
Cost
from
number widely
at a particular
cases the value corresponding to full-scale flight
lower than to less than one-fourth of that of an Reynolds number. Short-time burning tests are usually possible. is
slightly
indraft tunnel of equal 3.
Although we risk antagonizing friends who swear by indraft tunnels by saying this, few such tunnels are built without the stimulus of strong external factors
1:2
Summary
—such as
gifts
of Compressible Flow Theory
In low-speed aerodynamic fluid,
that
is,
of equipment or free vacuum pumps.
work we assume
that air
is
an incompressible
that the density of air does not change as the air flows
6
I
High-Speed Wind Tunnel Testing
around a vehicle in flight or in a wind tunnel. This assumption is perfectly satisfactory from an engineering standpoint up to Mach numbers of 0.2, for flows to this speed will have only minor changes in air density. At Mach num'bers above 0.2 the density changes increase, but the most of compressibility are not realized until the local velocity at some point in the flow field exceeds the speed of sound. This, it turns 0.5. We may count on it above out, almost never occurs below important
M=
effects
M=
0.85.
a marked change in the character of the air flow which begins as soon as the speed of sound is exceeded. These effects include (1) the localizing of the effects of a body into a “zone
The reason
for the serious effects
is
of action” and a “zone of silence”; (2) a reversal of the subsonic laws governing “streamline flow”; and (3) the formation of “shock waves.” We shall describe these effects, discuss their relation to the flow over an airfoil,
and then summarize the laws of flow that govern
their application.
The “Zone of Action'’ and “the Zone of Silence." An understanding of phenomenon is based on the fundamental concept that disturbances in a fluid will propagate away from the point of a disturbance at the local speed of sound. This effect can be described by Fig. 1 :5. which illustrates the propagation of sound waves relative to a particle in flight in different speed regimes. In Fig. 1 5fl it may be considered that a particle has been fired into still air from a gun at time zero and at half the speed of sound (3/ = 0.5). At time zero, the particle rushing into the air sets up a disturbance that travels at the speed of sound a in all directions. At a time Ac later, the region affected by the initial disturbance is bounded by a sphere of radius a At. Meanwhile, the particle moving at half the speed of sound has moved through a distance of only 0.5a At, so that the initial disturbance wave is preceding the particle. At time At, another disturbance is created. Between times At and 2 At, the sphere affected by the disturbance initiated at time zero expands to a radius of 2a At, while that iniated at time At is expanding to a radius of a At. The particle is now preceded by both waves. Continuing in this manner in Fig. 1 5a, we see that the air ahead of the particle will alw'ays be affected by the disturbance waves before the particle reaches it. This is typical of subsonic flow. The disturbance waves, which are pressure pulses, go out ahead of the body to prepare the air ahead to move aside. Similarly, pressures at the rear of a body or behind it can reach forward and contribute to the flow pattern. Thus, the complete flow field is affected by ever}' other this
:
:
point in the subsonic flow
field,
Looking at Fig. 1:56, which a gun at the speed of sound
so that there
is
no “zone of silence.” of a particle fired from
illustrates the case
{M =
1.0),
we
see that the disturbance
High-Speed Wind Tunnel Theory
(a)M = 03 Fig. 1:5
(c)M =
(b)M=1.0
Propagation of disturbance waves (sound waves) due to
Mach numbers (M
= Mach
propagation pattern
is
number, a
somewhat
= speed
/
7
2.0
flight at
various
of sound).
different.
In this case the disturbances
bow of the particle and form a concentrated wave front. of Mach 1.0, the particle moves through the air at the speed
coalesce at the
For
this case
of the advancing waves, so that the air ahead of the particle has not received a signal of the particles approach. Thus, the region
ahead of the
is a zone of silence. For the case of the particle moving
particle
at a speed greater than the speed of sound, the disturbance propagation pattern is shown in Fig. 1; 5c. In this case the radius
the rate of
of each disturbance wave increases at a rate less than
movement of
the particle.
The
result
is
that the disturbance
8
High-Speed Wind Tunnel Testing
/
waves coalesce into a cone-shaped envelope that is a Mach wave having its apex at the particle. The region outside this cone is a zone of silence. As indicated in Fig. 1:5c, the half angle of the cone is sin“^ Streamline Flow. For air flowing through a duct at
than
increases in
1.0,
Mach number
and decreases
velocity
will
The
in density.
Mach numbers
less
be accompanied by increases in
velocity of the air increases faster
than the density decreases; a 10 per cent increase of velocity, say, yields an 8 per cent decrease in density. In such a case the number of pounds per second flowing through each square foot of duct cross section increases with increasing Mach number. Consequently, the duct area must decrease to remain filled with flow.
if it is
Above
M=
the
1.0,
(See also Ref. 1:15.)
phenomenon
is
decrease in density.
In this case, the
As
reversed.
increases, a 10 per cent increase in velocity
might
the
Mach number
yield, say, a 12
per cent
number of pounds per second
flowing through each square foot of duct cross section decreases, so that
accommodate the flow at increasing Mach number of a supersonic flow, the duct area must be decreased, an action that would increase the Mach number of a subsonic flow. In free air flows, we speak of “stream tubes” instead of ducts. Stream must be increased
the duct area
Mach number.
to
Conversely, to decrease the
tubes are imaginary ducts in which constant mass
is
considered to flow.
“Streamlines” are the lines forming the boundaries of two-dimensional
stream tubes. Stream tubes, and therefore streamlines, assume the shape of perfectly designed ducts, decreasing in cross section when a subsonic
and increasing in cross section when a supersonic flow Thus, the subsonic laws governing streamline flow are reversed when the speed of sound is exceeded.
flow is
accelerated
is
accelerated.
Shock Waves. As noted above and illustrated in Fig. 1 5, concentrated wave fronts are established when a particle is moving through the air at speeds of Mach 1.0 and above. If these waves are very weak, so that :
changes in air properties occur as they pass through the said to be a “Mach wave” and is inclined at an angle sin-1 {ijM) with respect to the flow direction. Waves of finite strength (through which air properties change significantly) are caused by a infinitely small air,
the
wave
is
concentration of
Mach waves and
are called “shock waves.”
Mach wave formation caused by compression of a supersonic flow with that caused by the expansion of a supersonic flow. Changes in flow direction require a small, though Figure
1 -.6
presents a comparison of the
Thus,
finite,
time.
When
the corner
is
approaching a corner tends to round the corner. tending to compress the flow, disturbance waves will
air
develop, as illustrated in Fig. \:6a.
A
weak disturbance (Mach wave)
High-Speed Wind Tunnel Theory
1
:
6
9
(b) Expansion
(a) Compression Fig.
/
Disturbance-wave formation
in
a compression and an expansion of supersonic
flow.
develops,
which
slow the flow very slightly and turn
will
A number of following weak disturbances
will
it
very slightly.
do the same. The decreased
flow velocity and changed flow direction are such that each successive
wave has a greater inclination with respect to the original The result is a coalescing of a large number of weak compression
disturbance direction.
disturbances into a shock wave.
When
the corner
is
such as to cause the
expand (Fig. 1 66) a series of weak disturbance waves also develop. In this case, however, each succeeding disturbance occurs at a higher Mach number. The higher Mach number as well as the changed flow direction cause the disturbance waves to diverge, resulting in a series of expansion air to
:
waves called a “Prandtl-Meyer expansion fan.”
The shock wave its
in Fig.
1:6a
is
called
angle relative to the flow direction.
an “oblique shock” because of
If the turning angle of the flow
is
downstream of the oblique shock will be less than the will remain supersonic. If the turning angle is large, the shock will become normal to the flow and detached from the wedge, and the velocity downstream of the “normal shock” will be subsonic. Between these extreme turning angles, the oblique shock will become steeper and the downstream velocity lower as the turning angle small, the velocity
mainstream flow velocity but
increases.
Now
normal and oblique shocks have been introduced, we shall of shocks in more detail. Upon passing through a shock wave, the properties of the air change almost instantly. The pressure, temperature, and density increase and the velocity decreases. The entropy increases with the result that the total pressure of the air that
discuss the properties
upstream of the shock cannot be recovered. rest at the total
lower than the
A
shock
supersonic.
will
The air can be brought to temperature upstream of the shock but only at a pressure
initial
pressure.
always develop
If the flow
when
the flow velocity over an object
over the object
is
slightly
above Mach
1.0,
is
the
10
I
High-Speed Wind Tunnel Testing
be normal and the losses through the shock will be small. If is higher, the shock may be either oblique or normal, depending on the angle through which the object turns the air. At a given Mach number losses through a normal shock are always greater shock
will
the flow velocity
than losses through an oblique shock. Normal shocks occur in the supersonic flow of air through a duct such as a wind tunnel when conditions are such as to require a reduction in speed to subsonic flow. The importance of normal shocks to wind tunnel operation will be discussed later.
Now
let
phenomena described above to The air passing over the surface of
us discuss the relation of the
the flow over the airfoil of Fig.
must average
1
:
la.
portion of the airfoil in
mainstream flow because it has a time. Over the forward subsonic flow where the thickness is increasing,
the effective flow area
being reduced, so that the velocity
the airfoil
faster than the
greater distance to travel in the
is
same length of
is
increasing
and the stream tubes are getting smaller. Over the aft portion of the airfoil, where the thickness is decreasing, the effective flow area is being increased, so that the velocity is decreasing and the stream tubes are getting larger. The distribution of local velocity over the airfoil is illustrated in Fig. 1 :1b for a flow Mach number of about 0.6. Note that for the ideal case an integration of the pressure loading over the airfoil -at
Mach
0.6 will yield a zero force in the flow direction (zero “drag”).
(b)
High-Speed Wind Tunnel Theory
/
II
(c)
(d)
Fig.
1:7
freestream
Illustrative local velocity variation
over surface of an
airfoil at
various
Mach numbers.
The high velocities over the forward portion of the airfoil are accompanied by reduced pressures, which tend to pull the airfoil forward. Similarly, the higher velocities over the aft portion are accompanied by reduced pressures, which tend to pull the airfoil aft. The forces in the two directions exactly cancel each other. In practice, the airfoil will
have a
slight pressure
The major portion of drag, however, will be due to friction between airfoil surfaces and the air in proximity to these surfaces, that is, the
drag.
the
boundary layer. With the same
airfoil in
(Fig. l;7c), the velocity
an airstream moving
at
about
Mach
0.85
of airflow in the stream tube again increases rapidly over the forward portion of the airfoil and in this case reaches
12
/
High-Speed Wind Tunnel Testing
and passes through Mach 1.0. At the point where this occurs, the airfoil surface is turning away from the direction of local supersonic flow, which corresponds to an increasing stream tube area and consequently to an increasing velocity. The result is a tendency for the velocity to continue to increase with distance toward the trailing edge of the airfoil. Before rejoining the mainstream flow downstream of the airfoil, the flow must be decelerated to the original subsonic velocity. Deceleration is accomplished by a shock wave that forms on the surface of the airfoil. An integration of the ideal pressure loading for this case would yield little drag. In the actual case, however, the airfoil would exhibit a substantial increase in drag over that at Mach 0.6 because of interaction between the shock and the boundary layer. Finally,
when
the airfoil
is
placed in a supersonic airflow (Fig. l:ld)
no resemblence to incompressible flow. In this case, conditions exist for a shock wave ahead of the airfoil. A decreasing stream tube area and 'an increasing velocity are required to get the air approaching the airfoil around the leading edge of the airfoil. Since these conditions are consistent only for subsonic flow and the main flow is supersonic, a shock wave develops ahead of the airfoil, causing a decrease in speed to subsonic between the shock wave and the airfoil the flow over the airfoil bears
leading edge.
From
subsonic velocity, the speed in the stream tube
this
will rapidly increase to supersonic
passes over the airfoil. will
At
and then
be above the main airstream velocity.
edge of the
airfoil to
will
continue to increase as
it
the trailing edge of the airfoil, the velocity
A shock will occur at the trailing
bring the velocity back
down
to the mainstream
In this case, the velocity over the forward portion of the airfoil below freestream velocity, so that the pressure is above freestream.
velocity. is
Over the aft portion, the velocity is above freestream, so that the pressure below freestream. An integration of the pressure loading in this case yields a substantial drag because the drag components of the forward and is
aft portions
With
of the
airfoil are additive.
background
in compressible flow theory, we shall now develop equations defining compressible flow. Air flow in general is governed by the five following laws. this
1. At any point in a flow field, the pressure, density, are related by the equation of state:
P = pRiT — pressure, Ib/ft^, p = density, slugs/ft®, T = temperature, °R, i?i = gas constant, ft-lb/slug-°jR.
where p
and temperature
(1:1)
:
High-Speed Wind Tunnel Theory
13
/
For continuous flow in a duct or stream tube, the equivalence of mass flow at any two stations is specified by the continuity equation. 2.
Pl-AiUi
A
where
U is
—
(i*^)
P2^2^2
the cross-sectional area of the duct at a given station (ft“), and subscripts 1 and 2 denote two stations
is
the flow velocity (ft/sec),
in the duct. 3. If no energy is added or lost during the flow of a sample of fluid between two stations in a duct (that is, if the flow is adiabatic), the
following energy equation
valid
is
where
c,, is
script 5.
t
+ -y =
^
CpTi H-
CpT,
(1
the specific heat at constant pressure (ftVsec“-°.R)
:
3)
and the sub-
denotes conditions at zero velocity or, identically, stagnation
conditions. 4.
If the
another
change of
state
of a fluid during
isentropic, the following
is
7i
p(j-iyr
where y
is
flow from one station to
thermodynamic
relation
is
applicable:
To _ p(v-i)/v
(1:4)
the ratio of specific heat at constant pressure, c^, to specific
heat at constant volume,
From
its
c^.
summation of forces between two stations in a constant area stream tube or duct with no friction, the following momentum equation is
the
obtained:
Pi
+
Pi^^
= P2 +
P 2 U2
(1:5)
In addition to the above equations, the following definitions are needed for the development of the desired relations for compressible flow:
U a
= aM = ^yR,T
(1
is
the speed of sound (ft/sec),
M
is
6)
(1:7) (1
where a
:
Mach number, and
i?i is
:
8)
the
gas constant (ft^/sec2-°i?).
From the energy equation we get:
(1 :3)
_ T2
1 1
+ +
and the
[(y [(y
-
definitions of eqs. (1:6) to (1:8)
1)/2]M,^
l)/2]Mr
(1:9)
:
:
14
I
High-Speed Wind Tunnel Testing
Combining
eq. (1:9) with the equation for isentropic flow (1:4) yields:
El
f
ll
p,
Combining
and
eqs. (1:9)
(1
ll
P,
[(y
==
Mill
[(?
+ +
:
[(y
-
[{y [(y
1C
1) yields
.1.11
l)/2]M/j
we
get
l)/2]M/ rttv+i)/2(v-i)] ^
l)/2]Mi^j
the definitions of eqs. (1:6) to (1:8), the following equation for
dynamic pressure (pU^j2)
is
obtained:
4
From
.
l)/2]M,^j
in the continuity equation (1 2),
dl Aa
From
-
[(y
10) with the equation of state (1
:
+ +
El ==
Adding
+ +
i
=
=
(1:13)
the preceding equations, together with the knowledge that stag-
M=
nation conditions will exist at
0,
the following isentropic flow
relations are obtained
=
1
(i
— M*)
+
(1:14)
+Lii1mA 2
\
Pt
[y/(y-i)]
(1:15)
1 '
I=
+ Z-ILi
T,
\
Pt
2
jwA
2
(1:16)
/ 1
(1:17)
Using an area
at
M=
nozzle) as a reference,
A= A* The at
1
(A*, corresponding to the throat of a supersonic
we 1
obtain the following from eq. l
+
Ky [{y
:
12):
(1:18)
f
m\
(1
-1-
1)/2]
/
relations of eqs. (1:14) to (1:18) are tabulated in
Mach numbers of 0.1 to 10.0. When a normal shock wave exists
Table 1:1 for air
in a flow, there is an entropy change Consequently, the preceding isentropic flow equations are not valid. The equation of state (1 1), the continuity equation (1:2), the energy equation (1:3), and the momentum equation (1:5) are used in
across the shock.
:
High-Speed Wind Tunnel Theory
/
15
to
be
Table 1:1 Isentropic
Flow Parameters, y
=
1.4
The plus and minus numbers indicate the number of spaces the decimal moved, plus to the right, minus to the left.
M
g
Pipt
0.1000 0.9930 0.9725 0.9395
0.4
0.8956
0.5
0.8430
+ 01 + 00 + 00 + 00 + 00
0.4374
+ 00 + 00 + 00 + 00 + 00
0.3950
+ 00 + 00 + 00 + 00 + 00
0.6897
0.3609
1.4
0.3142
1.5
0.2724
1.6
0.2353
1.7
0.2026
0.5853
2.6
0.5012
2.7
0.4295
2.8
0.3685
2.9
0.3165
3.0
0.2722
3.1
0.2345
3.2
0.2023
3.3
0.1748
3.4
0.1512
0.1475
00
1.3
2.5
+ 00 + 00 + 00 + 00 + 00
0.4829
0.4124
0.6840
0.9524
00
1.2
2.4
0.1003
0.5311
0.4684
0.7997
00
00
0.5283
1.1
0.9352
+
0.8052
1.0
2.2
0.9690
0.8333
0.5913
2.3
+00 + 00
0.2723
0.9823
0.9921
00
0.9
+ +
0.1094
0.6951
+00 +00 + 00 + 00
0.6560
0.1278
0.0000
+
0.8
2.1
01
0.5817
+
2.0
0.9243
+ + + + +
+ + -
-
00 00 00 00 00
0.8852 0.8405
0.7916
0.7400
0.3557 0.3197 0.2868
0.2570
00
0.2300
00
0.2058
01
0.1841
01
0.1646
01
0.1472
01
0.1317
01
0.1179
01
0.1056
01
0.9463
01
0.8489
01
0.7623
01
0.6852
01
0.6165
01
0.5554
01
0.5009
+ + +
+ +
0.9328 0.9107
0.8865 0.8606
0.7764 0.7474 0.7184
0.6614 0.6337 0.6068 0.5807
00
0.5556
00 00 00
0.5313
00
0.4647
+00 + 00 + 00 - 01 - 01
- 01 - 01 - 01 - 01 - 01
+ +
0.5081
0.4859
+ + + + +
0.5919
0.1976 0.2473
0.2939 0.3352
00
0.3698
00
0.3967
00 00 00
0.4157
+ 00 + 00 + 00 + 00 + 00
0.4290
0.4270 0.4311
0.4216 0.4098
0.3947 0.3771
+ + + + +
00
0.3579
00 00 00
0.3376
00
0.2758
0.3169 0.2961
0.4444
+
00
0.2561
0.4252
+
00
0.2371
0.4068
+ + +
00 00
0.2192
00
0.1863
00 00
0.1577
0.3147
+ + + +
0.3019
+
0.3894 0.3729 0.3571
0.3422 0.3281
AlA*
9lPt
00
0.6339
0.7209
0.1492
0.9564
0.1000 0.9980
00 00
0.7840
0.1740
0.9803
+ 01 + 00 + 00 + 00 + 00
0.6870
0.6 0.7
1.8
0.1000 0.9950
+ 00 + 00 + 00 + 00 + 00
+ +
1.9
TITt
pIpt
00 00 00
0.2022
0.1715
0.1450 0.1332 0.1224
is
+ 00 - 02 - 01 - 01 + 00
CO
5.822
2.964 2.035 1.590
+ 00 + 00 + 00 + 00 + 00
1.340
+ 00 + 00 +00 + 00 +00
1.000
+ 00 + 00 + 00 + 00 + 00 + 00 + 00 + 00 +00 + 00 + + + + +
1.188
1.094 1.038 1.009
1.008
1.030
1.066 1.115
1.176
1.250 1.338 1.439 1.555
1.687
1.837
2.005 2.193 2.403
00
2.637
00 00 00 00
2.896
+ 00 + 00 + 00 + 00 + 00
4.235
3.183
3.500 3.850
4.657 5.121
5.629
6.184
16
I
High-Speed Wind Tunnel Testing
Table 1 1 (continued) :
M
Pipt 0.1311
0.1138
-
01
0.4523
01
0.4089
0.3702
IsffiisiBa
BE
0.7532
a la a a 4.0 4.1
0.6586 0.5769
0.5062 0.4449 0.3918
0.3455 0.3053 0.2701
4.8
0.2394
4.9
0.2126
5.0
0.1890
5.1
0.1683
5.2
0.1501
5.3
0.1341
5.4
0.1200
5.5
0.1075
5.6
0.9643
5.7
0.8663
5.8
0.7794
5.9
0.7021
0.3355
-
TjTi
pIpt
02
0.3044
- 02 - 02 - 02 - 02 - 02
0.2766
- 02 - 02 - 02 - 02 - 02
0.1745
0.2516
0.2292 0.2090 0.1909
0.1597
0.1464 0.1343
0.1233
- 02 - 02 -02 - 02 - 02
-
0.2899
0.2784 0.2675
0.2572 0.2474
01
0.2381
01
0.2293
01
0.2208
01
0.2129
01
0.2053
- 01 - 01 - 01 - 01 - 01
0.1980 0.1911
0.1846 0.1783
0.1724
0.1134
-01
0.1667
0.1044
-
01
0.1612
02
0.1561
02
0.1511
02
0.1464
- 02 - 02 - 02 - 02 - 02
0.1418
0.9620 0.8875
0.8197
- 02 - 03 - 03 - 03 - 03
- 01 - 01 - 01 - 01 - 01
0.7578
0.7012 0.6496 0.6023
0.5590
0.1375
0.1334
0.1294 0.1256
AjA*
^IPt
+ 00 + 00 + 00 + 00 + 00
0.1124
+ + + + +
00
0.7376
00 00 00 00
0.6788
+ 00 + 00 + 00 + 00 + 00
0.4898
+ 00 + 00 +00 +00 + 00
0.3308
+ + + + +
00 00
0.2276
00
0.1970
00 00
0.1835
+ 00 + 00 + 00 + 00 + 00
0.1596
+ 00 + 00 + 00 - 01 - 01
0.1140
0.1033
0.9490 0.8722 0.8019
0.6251
0.5759 0.5309
0.4521
0.4177 0.3861
0.3572
0.3065
0.2842 0.2637 0.2449
0.2117
0.1711
+ + -
00 00
7.450
01
8.169
01
8.951
01
9.799
01
10.719
01
11.715
01
12.792
01
13.955
01
15.210
- 01 - 01 - 01 - 01 - 01
-
6.790
16.562 18.018 19.583
21.264 23.067
01
25.000
01
27.070
01
29.283
01
31.649
01
34.175
01
36.869
01
39.740
01
42.797
01
46.050
01
49.507
j
6.0
0.6334
6.1
0.5721
6.2
0.5173
6.3
0.4684
6.4
0.4247
6.5
0.3855
6.6
0.3503
6.7
0.3187
6.8
0.2902
6.9
0.2646
- 03 - 03 - 03 - 03 - 03 - 03 - 03 - 03 - 03 - 03
0.5194 0.4829 0.4495 0.4187
0.3904 0.3643
0.3402 0.3180 0.2974 0.2785
- 02 - 02 - 02 - 02 - 02
- 02 - 02 - 02 - 02 - 02
0.1220 0.1185 0.1151
0.1119 0.1088 0.1058
0.1030
0.1002 0.9758
0.9504
0.1490 0.1392 0.1301
0.1218
0.1068 0.1001
0.9395
0.8820
- 01 - 01 - 01 - 01 - 01 - 01 - 01 - 01 - 02 - 02
53.180 57.077
61.210 65.590 70.227
75.134 80.323 85.805
91.594 97.702
High-Speed Wind Tunnel Theory
/
17
Table 1:1 {continued)
M
pIPt
7.0
0.2609
7.1
0.2446 0.2019
0.1848
0.1694
- 03 - 03 - 03
0.2295
0.2155 0.2025
7.8
0.1207
- 03 - 03 - 03 - 03
7.9
0.1111
-03
0.1498
8.0
0.1024
-
0.1414
0.1554 0.1427
wXm
8.1
0.1312
0.9449
8.2
0.8723
8.3
0.8060
8.4
0.7454
8.5
0.6898
8.6
0.6390
8.7
0.5923
8.8
0.5494
8.9
0.5101
9.0
0.4739
9.1
0.4405
9.2
0.4099
9.3
0.3816
9.4
0.3555
9.5
0.3314
9.6
0.3092
9.7
0.2886
9.8
0.2696
9.9
TITt
pIpt
03
- 04 - 04 - 04 - 04 - 04 - 04 - 04 - 04 - 04 - 04 - 04 - 04 - 04 - 04
0.1904 0.1792 0.1687 0.1589
0.1334 0.1260 0.1191
0.1126 0.1066 0.1009 0.9558 0.9059
0.8590
0.8150 0.7737 0.7348
0.6982 0.6638
- 02 - 02 - 02 - 02 - 02 -
0.9259
0.9024 0.8797 0.8578 0.8367
02 02 02 02 02
-
04
0.6313
04
0.6008
04
0.5719
04
0.5447
0.2520
-
04
0.5191
-
0.2356
-
04
0.4948
-
0.6494
01
0.4589
0.7081
-01
0.4339
-
01
0.4106
01
0.3887
01
0.3682
0.6767
0.6617 0.6472 0.6332 0.6197 0.6065
0.5938
0.5814
03
0.6895
-
0.6921
03
0.7326
0.7246
0.7777
0.7594
- 02 - 02 - 03 - 03 - 03
104.143
0.7788
0.7417
0.7967
- 02 - 02 - 02 -02 - 02
- 01 - 01 - 01 - 01 - 01 -
0.8163
0.5694 !
-
01
0.6120
01
0.5771
01
0.5445
01
0.5140
01
0.4855
01
0.3489
01
0.3308
01
0.3138
01
0.2978
01
0.2828
- 01 - 01 - 01 - 01 - 01
03
0.5578
03
0.5465
03
0.5356
03
0.5249
03
0.5146
03
0.5046
03
0.4949
03
0.4854
-
03
0.4762
-
A!A*
^IPt
1
0.2687
0.2554 0.2428
0.2310 0.2199
- 02 - 02 - 02 - 02
-
02 02 02 02 02
-
02 02 02 02
02
- 02 - 02 -02 - 02 - 02 -
02 02 02 02 02
01
0.2094
01
0.1994
01
0.1901
01
0.1812
01
0.1729
- 02 - 02 -02 -02 - 02
0.1649
-
01 I
02
110.931
118.080 125.605
133.520 141.841
150.585 159.767 169.403 179.511
190.109
201.215 212.846
225.022 237.762 251.086
265.014 279.567
294.766 310.633
327.189 344.458 362.463
381.227
400.775 421.131 442.321
464.370 487.304 511.151
535.937
(
18
:
:
High-Speed Wind Tunnel Testing
I
Let subscripts 1 and 2, upstream and downstream of a normal
the derivation of normal shock flow equations. respectively, represent conditions
shock.
The solution of the energy equation (1 :3) again The combination of eqs. (1 1) and (1 5) gives :
yields eq. (1:9).
:
_ 1 + yMi 1 + yM/ Pi
(1:19)
The combination of the continuity equation
(1
2) with eqs. (1:9)
:
and
(1:19) gives
+ M/ 1)] - 1
[2/(y-l)] '
When eq.
(1:20)
is
[2yMi=‘/(y
-
used with eqs. (1:9) and
(1
(1
19), the
:
:
20 )
following relations
for flow across a normal shock, in terms of the upstream
Mach number,
are obtained. 1
-
+
1
2y
M,
71
El Pi
When the
+ 1)^ Ml 2(y - 1) = 2yMi" - (y y + 1 (y
equation of state
(1
:
1) is
the density ratio across the shock
p,_ Pi
(y
2
1
1 (1
:
21 )
(1
:
22 )
2
1)
combined with
is
-
Ml"
—
Ly
eqs. (1 :21)
and
(1 :22),
obtained
+
l)Mi"
+ (y -
(1:23)
l)Mi"
The stagnation pressure downstream of a normal shock is less than that upstream of the shock. The relation of static to stagnation pressure downstream of the shock is obtained from eq. (1 14) when the Mach number downstream of the shock is used. A relation for the total pressure downstream of a normal shock is obtained as follows :
Pt2
^
(PilPnXpJPi) iP2lPt^
Ptl
r
The
(y
+ i) 1 1
r
(y
L(y
-
+
l)Mi"
1
+
2]
l)Mi"
(1:24)
relations of eqs. (1:20) to (1:24) are tabulated in
Mach numbers Pi//’ 2 .
which
is
Table 1:2 for of 1 to 10. Also included in Table 1:2 is the parameter obtained by dividing eq. (1 14) by eq. (1:24). :
High-Speed Wind Tunnel Theory
/
19
Table 1:2
Normal Shock
M
Relations, y
pdpi
pdpi
—\A TdT^
Palpti
Pdpn
+ 00 + 00 0.4154 + 00 0.3685 + 00 0.3280 + 00
1.1
1.245
1.169
1.065
1.2
1.513
1.342
1.128
1.3
1.805
1.516
1.191
1.4
2.120
1.690
1.255
+ 01 + 00 0.9928 + 00 0.9794 + 00 0.9582 + 00
1.0
1.000
1.000
1.000
0.1000 0.9989
1.5
2.458
1.862
1.320
0.9298
1.6
2.820
2.032
1.388
0.8952
1.7
3.205
2.198
1.458
0.8557
1.8
3.613
2.359
1.532
0.8127
1.9
4.045
2.516
1.608
0.7674
2.0
4.500
2.667
1.688
0.7209
2.1
4.978
2.812
1.770
0.6742
2.2
5.480
2.951
1.857
0.6281
2.3
6.005
3.085
1.947
0.5833
2.4
6.553
3.212
2.040
0.5401
2.5
7.125
3.333
2.137
0.4990
2.6
7.720
3.449
2.238
0.4601
2.7
8.338
3.559
2.343
0.4236
2.8
8.980
3.664
2.451
0.3895
2.9
9.645
3.763
2.563
0.3577
3.0
10.333
3.857
2.679
0.3283
3.1
11.045
3.947
2.799
0.3012
3.2
11.780
4.031
2.922
0.2762
3.3
12.538
4.112
3.049
0.2533
3.4
13.320
4.188
3.180
0.2322
3.5
14.125
4.261
3.315
0.2129
3.6
14.953
4.330
3.454
0.1953
+ 00 + 00 + 00 + 00 + 00 + 00 + 00 + 00 + 00 + 00
+ 00 + 00 + 00 + 00 + 00
+ 00 + 00 + 00 + 00 + 00 + 00 + 00 + 00 + 00 + 00
0.5283
1.0000
0.4689
0.9118
0.2930 0.2628 0.2368 0.2142 0.1945 0.1773
0.1622 0.1489 0.1371
0.1266 0.1173
0.1089 0.1014 0.9461
0.8848
+ 00 + 00 + 00 + 00 + 00 + 00 + 00 + 00 + 00 + 00 + 00 + 00 + 00 - 01 - 01
- 01 - 01 0.7323 - 01 0.6900 - 01 0.6513
0.6157 0.5829
4.395
3.596
0.1792
4.457
3.743
0.1645
3.9
17.578
4.516
3.893
0.1510
4.0
18.500
4.571
4.047
4.1
19.445
4.624
4.205
+ 00 + 00 0.1173 + 00 0.1080 + 00 0.9948 - 01
- 01 - 01 0.4314 - 01 0.4120 - 01 0.3938 - 01
- 01 - 01 0.7809 - 01 0.7214 - 01 0.6670 - 01
- 01 - 01 0.3459 - 01 0.3319 - 01 0.3187 - 01
20.413
4.675
4.367
21.405
4.723
4.532
4.4
22.420
4.768
4.702
4.5
23.458
4.812
4.875
4.6
24.520
4.853
5.052
4.7
25.605
4.893
5.233
4.8
26.713
4.930
5.418
4.9
27.845
4.966
5.607
0.9170
0.8459
0.7011
0.6684 0.6405 0.6165
0.5956
0.5774 0.5471
iMcm
0.4956
0.5526 0.5247 0.4987
0.4596
- 01 0.4512 - 01 0.4474 - 01 - 01 EESin - 01 0.4377
15.805
4.2
0.7397
-01
16.680
4.3
0.7860
0.8291
3.7
0.1388
0.8422
0.7785
3.8
0.1276
Afj
0.4747
0.4523
0.3768
0^9 0.4236
0.3609
0.4167
20
I
High-Speed Wind Tunnel Testing
Table 1:2 (continued)
M
pdpi
pdpi
Tdn
5.0
29.000
5.000
5.800
0.6172
5.1
30.178
5.033
5.997
0.5715
5.2
31.380
5.064
6.197
5.3
32.605
5.093
6.401
5.4
33.853
5.122
6.610
- 01 - 01 0.5297 - 01 0.4913 - 01 0.4560 - 01
5.5
35.125
5.149
6.822
0.4236
5.6
36.420
5.175
7.038
0.3938
5.7
yirn'i
5.200
7.258
0.3664
5.8
39.080
5.224
7.481
0.3412
5.9
40.445
5.246
7.709
0.3179
pnipn
-
pdpn
M,
0.3062
- 01 - 01 0.2834 - 01 0.2730 - 01 0.2631 - 01
0.4152
0.2945
0.4138
- 01 - 01 - 01 - 01 - 01
0.4090
01
0.2537
01
0.2448
01
0.2364
01
0.2284
01
0.2208
0.2002
6.0
41.833
5.268
7.941
0.2965
43.245
5.289
8.176
0.2767
0.2067
6.2
44.680
5.309
8.415
6.3
46.138
5.329
8.658
6.4
47.620
5.347
8.905
- 01 - 01 0.2584 - 01 0.2416 - 01 0.2259 - 01
0.2136
6.1
6.5
49.125
5.365
9.156
0.2115
6.6
50.653
5.382
9.411
0.1981
6.7
52.205
5.399
9.670
0.1857
6.8
53.780
5.415
9.933
0.1741
6.9
55.m
5.430
10.199
0.1634
7.0
57.000
5.444
10.469
7.1
58.645
5.459
10.744
60.313
5.472
11.022
62.005
5.485
11.304
63.720
5.498
65.458
67.220
0.1939 0.1880
- 01 - 01 - 01 - 01 - 01
- 01 - 01 0.1716 - 01 0.1667 - 01 0.1619 - 01
0.4125 0.4113 0.4101
0.4018 0.4011
-01
0.1823
0.4004
- 01 - 01 - 01 - 01
0.1768
0.3997
0.1535
0.3974
0.1530
0.3968
11.590
- 01 - 01 0.1357 - 01 0.1277 - 01 0.1202 - 01
0.1573
0.1443
5.510
11.879
0.1133
12.173
0.1068
69.005
5.533
12.471
0.1008
7.8
70.813
5.544
12,772
0.9510
7.9
72.645
5.555
13.077
0.8982
- 01 - 01 - 01 - 02 - 02
0.1372
5.522
8.0
74.500
5.565
13.387
0.8488
76.378
5.575
13.700
0.8025
0.1177
8.2
78.280
5.585
14.017
8.3
80.205
5.594
14.338
8.4
82.153
5.603
14.662
- 02 - 02 0.7592 - 02 0.7187 - 02 0.6806 - 02
0.1207
8.1
8.5
84.125
5.612
14.991
0.6449
- 02
0.1070
8.6
86.120
5.620
15.324
0
6114-02
0.1045
8.7
88.138
5.628
15.660
- 02 0.5504 - 02 0.5226 - 02
wSk
H msk
8.8
90.180
5.636
16.000
8.9
92.245
5.644
16.345
.
0.5799
- 01 - 01 0.1488 - 01 0.1448 - 01 0.1409 - 01 -
01
- 01 0.1302 - 01 0.1269 - 01 0.1237 - 01 0.1336
0.1149
0.1122 0.1095
0.1021
0.9983 0.9761
- 01 - 01 - 01 - 01 - 01 - 01 - 01 - 01 - 02 - 02
0.3991
0.3985
0.3979
0.3963 0.3958
0.3954 0.3949 0.3945 0.3941
0.3937 0.3933
0.3929 0.3925
0.3922 0.3918
0.3915
0.3912 0.3909 0.3903 0.3901
High-Speed Wind Tunnel Theory
/
21
Table 1:2 ^continued)
M
pdpi
9.0 9.1
9.2
pdpi
niT
94.333
5.651
16.693
96.445
5.658
17.045
98.580
5.665
17.401
100.738
5.672
17.760
9.4
102.920
5.679
9.5
105.125
9.3
0.9546 0.9338
18.124
- 02 0.4486 - 02 0.4267 - 02 0.4061 - 02
5.685
18.492
0.3866
0.8572
0.3683
0.8395
- 02
0.4718
9.6
107.353
5.691
18.863
9.7
109.605
5.697
19.238
9.8
111.880
5.703
19.617
9.9
114.178
5.709
20.001
- 02 - 02 0.3510 - 02 0.3346 - 02 0.3191 - 02
10.0
116.500
5.714
20.387
0.3045
1:3
0
.
- 02 - 02
0.3898
9137-02
0.8943
0.8754
- 02 - 02
0.3891
0.3888
0.3886
0.7895
- 02 - 02 - 02 - 02 - 02
0.7739
- 02
0.3876
0.8223
0.8057
0.3884 0.3882
0.3880 0.3878
Real Gas Effects
The preceding equations and air
Mi
pjptz
ptdpti
relations
which define the properties of
flow in wind tunnels are based on the premise that the specific heat
ratio for air, y,
is
invariable. This premise holds true for practical purposes
as long as air temperatures of the flow are below about I000°R.
lower temperatures, the internal energy of the air
is
At
these
completely defined
by the degree of excitation of the translational and rotational degrees of freedom of the molecule, and y is constant. At temperatures above 1000°R an additional degree of freedom of the molecule, termed the “vibrational degree of freedom,” begins to reach significant proportions. air
When
this occurs, the
with further additions of heat
is less
than
it
temperature increase of
would have been
at
lower
temperatures because a significant portion of the heat energy goes into excitation of the vibrational degree of freedom. This results in values of y that vary with temperature. Relations pertaining to the flow of air in wind tunnels with vibrational included have been derived in Ref. 1:1. From this reference the
effects
following equation for specific heat ratio, including the effects of molecular vibration, is obtained:
y
=
1
+
(1:25)
JIT 1
+
= a constant, 5500°R for air, y = specific heat ratio, yp = perfect gas value of specific heat ratio, T = temperature, °R.
_
1)2
where
1.4 for air,
22
High-Speed Wind Tunnel Testing
I
Equation (1:25) is satisfactory for engineering purposes at air temperatures up to 5000°R and yields the results of Fig. 1 8. Examination of eq. (1 :25) quickly reveals that this is not one of the “slide rule” type of equations. :
Equations for flow relations pertinent to wind tunnels are similarly complicated. In fact, solutions for the case of a normal shock require
and the reader is referred to Ref. 1:1, whose solutions in graphical form are reproduced in Figs. 1:9 to 1:18. Results of the figures are presented in terms of the ratio of the real gas flow parameter iteration,
(including vibrational effects) to the
same flow parameter calculated by
assuming a value of y = 1.4 throughout the flow. The subscript “therm perf” indicates a thermally perfect gas, which in turn indicates that the equation of state p = pR^T is valid. This validity holds as long as the diatomic molecules of nitrogen and oxygen in air (N, and Oo) do not dissociate into atoms.
Example 1:1
The use of the
Determine the
figures
is
real gas static
illustrated as follows.
temperature of air in a
Mach
5 flow with a total temperature of 3000°R.
From
Fig.
1:11 at a
3000°R, a value of 1.10
Mach number is
of 5 and a total temperature of
read for the ratio (T/7))therm perf (T/T,)pert
From Table y
=
1.4.
1
1,
a value of J/E,
= 0.1667
is
read for air at
5.0 with
is
the value of E/E, including vibrational effects. Multiplying
value of E/E, by the total temperature of 3000°R yields a static
temperature of 550°R, as compared to 500°R when y
1:4
Mach
Multiplying the ratio of 1.10 from the figure by 0.1667 yields
0.1834, which this
:
Ideal
Flow
in a Supersonic
=
1.4.
Tunnel*
The establishment of a supersonic stream
in a duct has many interesting not the least of which is the odd-shaped passage that must be provided. In order for the flow to become supersonic, it must first become
facets,
Because of the marked change in the characteristics of air flow Mach 1.0, a sonic velocity can occur only at a minimum cross section of a duct. Hence a supersonic nozzle must first contract sonic.
that occurs at
and then expand (see Fig. 1:19 and Ref. 1:15). The relation between area and Mach number has been given in eq. (1 1 8). Unfortunately, however, the simple provision of the proper duct area will not assure uniform supersonic flow because increases in supersonic flow velocity do not occur through planes normal to the duct axis. As :
discussed previously, expansion disturbances in a supersonic flow are
The not-inconsequential
effects
of viscosity will be discussed in the next section.
High-Speed Wind Tunnel Theory
Fig.
1
:8
The
/
23
variation of the ratio of specific heats, y, with temperature.
(P/PtK^ri
Fig.
1
;9
Effect of caloric imperfections
on the
ratio of static pressure to total pressure.
24
/
Fig.
1
High-Speed Wind Tunnel Testing
:
10
Effect of caloric imperfections
on the
ratio of static density to total density.
Mach number Fig. 1:11
Effect of caloric imperfections
on the
ratio of static temperature to total
temperature.
Fig. 1:12
pressure.
Effect of caloric imperfections
on
the ratio of
dynamic pressure
to total
.
j
25
ratio of local cross-sectional area
of a
High-Speed Wind Tunnel Theory
Fig.
1
:
13
Effect of caloric imperfections
on the
stream tube to the cross-sectional area at the point where
Fig. 1:14
Effect of caloric imperfections
shock wave.
on the
M=
1
static pressure ratio across
a normal
28
/
High-Speed Wind Tunnel Testing
“Mach lines” or “characteristic lines,” which are lines inchned at the angle sin-’-(l/M) with respect to the flow direction. Regions of flow upstream of the area bounded by the characteristic line are not influenced by the disturbance. Thus, an increase in duct area caused by diverging the walls of the duct does not aflect the flow at the
propagated along
duct centerline until the characteristic lines originating at the beginning of the divergence cross the centerline as shown in Fig. 1 20. Because of :
delayed efiect of changing area ratio on the flow throughout the duct, great care must be exercised in obtaining the proper axial distribution of
this
be obtained. We shall discuss the details on supersonic nozzle design. The shock wave is the mechanism by which most supersonic flows, including those in a wind tunnel, are slowed down. * When a supersonic area ratio
if
uniform flow
of this problem in Section
is 1
to
:8
The
flow passes through a shock wave, a loss in total pressure occurs. losses
through the shock wave represent a large portion of the power
requirements for higher
Mach number
to the other losses to
supersonic tunnel operation.
power loss through the shock
In
added be replaced by the tunnel drive compressor, and may
the continuous-type wind tunnel the
is
under some conditions represent 90 per cent of the total loss. The loss in total pressure associated with the return to subsonic speed through a normal shock is plotted in Fig. 1:21. Clearly it is a great waste of power to shock down at operating Mach number instead of reducing the if the
Mach number before the final normal Mach number is above 1.5 or 2.0.
shock, particularly
operating
The above observation has
led to the design of
most supersonic wind
tunnels with a diffuserf having a converging section, a
minimum
cross-
section zone termed the “second throat,”
and then a diverging section. The purpose of this design is that the flow leaving the wind tunnel test section will be compressed and slowed down in the converging section of the diffuser, will pass through the second throat at a speed considerably below that of the test section, will begin to speed back up in the diverging section of the diffuser, and will establish a normal shock in the diverging portion of the diffuser at a Mach number considerably below the test section Mach number, and with a correspondingly smaller loss. It would be desirable to have a Mach pumber of 1 .0 at the second throat in the hope that the normal shock would occur at a Mach number only slightly above 1.0 under conditions where the normal shock losses would be insignificant. It would appear, then, that the diffuser with a sonic flow in the second throat is the answer to the power requirements problem in *
They may
also
be slowed by
friction
or cooling.
t The diflfuser is the section of the tunnel in which the flow conditions to a low subsonic speed.
is
slowed from design
High-Speed Wind Tunnel Theory
Fig.
1
waves
;20
Flow region
BC and DC is
affected
by diverging duct
walls.
(The flow upstream of
/
29
Mach
unaffected by the divergence.)
a supersonic wind tunnel.
Practical considerations, however, tend to
negate this conclusion, as will be seen below. As we start a supersonic tunnel there is at
first
a low subsonic speed
throughout the tunnel circuit and the power required corresponds to the subsonic drag of the complete circuit. At this time the highest Mach
power is increased, the speed throughout the circuit rises until the Mach number at the nozzle throat (Station a. Fig. 1:22) becomes 1.0 and a normal shock develops a short distance downstream of the throat. At this point the power required still corresponds to the subsonic drag of the complete circuit. A slight increase in power now will not change the Mach number at the nozzle throat but will move the normal shock further downstream
number
in the circuit occurs in the nozzle throat.
Fig.
1
;21
As
the
Ratio of stagnation pressures across a normal shock wave.
30
I
High-Speed Wind Tunnel Testing
Fig. 1:22
Normal shock
positions in a nozzle during the tunnel starting process.
b), where the Mach number is supersonic and the through the normal shock are finite. The losses through the normal losses point account for the slight increase in power. As the power at this shock increased, the normal shock moves downstream through the is further (Stations d, and occurs at progressively higher Mach numbers. nozzle c, e), The resulting increased shock losses are added to the subsonic drag of
of the throat (Station
power requirements. where it Finally, the normal shock moves into the requirements power occurs at the test section Mach number, and the correspond to the normal shock losses at the design Mach number. At this point in the tunnel starting process the power requirements are not influenced by the diffuser design because flow in the diffuser is still subsonic. Hence, in spite of the diffuser, the power requirements for getting a supersonic tunnel started correspond to normal shock losses at the design Mach number and are high at the higher Mach numbers. More the circuit and correspond to progressively increasing
test section (Station /),
customarily, the tunnel engineer, rather than speaking of “power,” uses
the ratio of necessary stagnation pressure to diffuser exit pressure, which
he
calls
related.
“pressure ratio.”
The
By
including mass flow the
theoretical pressure ratio required with a
shown as Case 3 in Fig. 1:23. With the normal shock in the test section, only a
two are
affinely
shock wave in the
test section is
should be required to
move
slight increase in
power
the shock through the second throat of
the diffuser because the normal shock
Mach number, and
the normal shock losses, should decrease as the shock
consequently
moves through the
converging section of the diffuser.
With
the normal shock in the test section during the tunnel starting
process, another limitation to the second-throat diffuser effectiveness
Downstream of the normal shock, the flow is subsonic. Hence the flow velocity in the converging section of the diffuser must be inappears.
creasing, until a
maximum
velocity
is
reached in the second throat.
High-Speed Wind Tunnel Theory
1234 56789
j
31
10
Mach number Fig. 1:23
Theoretical values of the compression ratio for Case 2
and
3 operation.
Since the Mach number in the second throat (minimum cross section) cannot exceed 1.0, the second throat must be sized to pass the mass flow of the nozzle with an expansion of the air downstream of the normal shock to a Mach number no greater than 1.0. Sizing of the second throat to allow the normal shock to pass through during the starting process is
The Mach number in the second throat is assumed to be 1.0. The expansion of the air from the conditions downstream of the normal shock in the test section to Mach 1 .0 at the second throat is assumed to be an isentropic process. With these assumptions eq. (1 12) is used to obtain the ratio of second throat area to test section accomplished as follows.
;
area in terms of the
Mach number downstream
of the shock. The
Mach
32
High-Speed Wind Tunnel Testing
/
number downstream of the shock is related to the upstream Mach number eq. (1:20). Combining these two equations and substituting y = 1.4
by
yields (5
-
+
1)"
(1:26)
216
= second-throat area, ft^, = test section area, ft^ M = test section Mach number.
where As*
Values from eq.
(1 :26)
are plotted in Fig.
1
:24.
The Mach number
in the
second throat after the tunnel has started, corresponding to isentropic may be obtained by using the area ratios of
flow between the two throats, Fig.
1
:
24 in conjunction with eq.
(1
:
12).
When
done we find that
this is
the requirement that the tunnel be able to start results in a fixed second throat considerably larger than that needed to bring the second-throat
Mach number close to 1.0 during running. For example, when the test section Mach number is 6.0 and the second throat is sized for starting, its Mach number is 5.38. Similarly throughout the range, the second throats that permit starting theoretical pressure ratios that
throat are It is
shown
as
reasoned that
Case 2 if
do very little supersonic diffusing. The would ensue for the optimum fixed second
in Fig.
1
:23.
the tunnel to start and could then be closed
Fig.
1
:24
The
Mach number, y
enough to allow more nearly ideal
the second throat could be open
down
to a
variation of the theoretical fixed geometry second throat area with
=
1.4.
High-Speed Wind Tunnel Theory
/
33
shock has passed through, the pressure ratio requirements for running the tunnel could be reduced considerably. In theory, with a very gentle (no shock) diffuser, second throat Mach number could area ratio after the
made equal
be
to 1.0.
ahead of ourselves to consider a practical case, we note wind tunnels have incorporated this idea of an throat, always with a degree of success far below ideal. adjustable second As a matter of fact, the usefulness of such a technique has generally been Getting a
little
that several high-speed
many tunnels with variable second
so limited that
tlu'oats
do not use them.
High tunnel starting power requirements must be provided, and when they are, the power requirements for operation are no longer a problem. Actual Flow in a Supersonic Tunnel
1:5
In Section
:4
1
we
discussed flow in a supersonic
standpoint of ideal flow. the
Although
this discussion
wind tunnel from the is
useful in describing
mechanism of the flow, the correlation with actual flow
is
quite poor
unless viscous effects are included.
Viscous effects
may be
through a tunnel there
is
described in the following way.
next to the wall called the ness
and the
from the
first
total loss
“boundary
of
high
first
and
of air in a layer
The boundary
layer thick-
increase with increasing distance
and become quite important
Mach number
Viscous effects between the
momentum
layer.”
momentum
throat of the nozzle
section, particularly in
air flows
a friction force developed between the air
This causes a loss in velocity and
the walls.
As
in the test
nozzles.
throat and the test section of a nozzle
importance during the steady-state operation of The growth of the boundary layer thickness with distance from
are not usually of great the tunnel.
the
first
throat
is fairly
predictable (see Section
1 '.9),
and can be accounted boundary layer
for in nozzle design so that the desired flow outside the
can be achieved.
During the transient process in which the tunnel effects are
is
started, viscous
extremely important and not very well understood.
So im-
portant are these effects that compression ratios required to start most high Mach number tunnels now in operation are usually at least 100 per cent greater than the
saying that losses
normal shock pressure ratio pnlpa. In effect, we are due to viscous effects during the starting process are
usually at least equal to the
planation gives
normal shock
losses.
The following
some insight into the flow complexities high viscous losses occur.
ex-
from which these
Boundary layers are normally stable when the pressure is decreasing of boundary layer growth. However, they become unstable and have a tendency to break away or “separate” from the wall in the direction
34
/
when
High-Speed Wind Tunnel Testing the pressure
is
increasing in the direction of growth.
As a normal
imposes a severe unfavorable pressure
shock passes through a nozzle it gradient on the boundary layer, which will in some cases cause separation. If the boundary layer does separate, the flow across the nozzle will be severely altered over a large portion of the nozzle length. If the boundary layer does not separate, high pressure in the boundary layer downstream of the shock will cause air to flow forward into the subsonic portion of the boundary layer upstream of the shock, with the result that the boundary layer
and consequently the flow
in the duct are altered over a significant
portion of the nozzle length. In the diffuser of the wind tunnel viscous effects are probably pre-
dominant during starting and steady-state operation. In the starting case, normal shock moves into the converging section of the diffuser, an unfavorable pressure gradient is established at the beginning of the convergence. The unfavorable pressure gradient produced by the normal shock exists as in the general case mentioned above. “Oblique shocks” from the convergence create additional unfavorable pressure gradients after the
when they
After the tunnel is started, all these with the difference that the normal shock has moved to a stable position downstream of the second throat stable because small strike the opposite wall.
effects still exist,
—
draw the shock farther downstream, where a higher Mach number and a larger loss.
reductions in diffuser loss the greater area results in
In summary, there are six compression ratios (ratio of the total pressure in the settling
chamber
to that at the diffuser exit) that are of interest,
three for ideal (theoretical) frictionless flow
and three for the
real or
practical case.
The
is the ratio required to run the tunnel after an adjustable been closed down to the minimum area. In theory, this ratio approaches 1.0, which corresponds to negligible loss.
1.
smallest
diffuser has
2.
The next
is
the ratio required to run the tunnel
(of throat area just large 3.
The
largest
to the condition
is
enough to
let
when a
the tunnel start)
is
fixed diffuser
employed.
the ratio needed to start the tunnel. (This corresponds
when
the normal shock
is
in the test section.)
Compression ratios for Conditions 2 and 3 are shown in Fig. 1:23 for the theoretical case. The range of actual compression ratios for starting and running, as obtained from a number of wind tunnels, is shown in Fig.
1:25.
The area between
actual tunnel has as
the curves for starting and running an
lowest values the compression ratios for tunnels with adjustable diffusers; higher values correspond to fixed diffusers. its
The actual starting ratios are higher yet, as shown. The starting compression ratios in Fig. 1 25 may be reduced by using :
High-Speed Wind Tunnel Theory
/
35
Mach number
The probable maximum pressure ratios needed for starting, and the minimum needed for running, as obtained from data from eleven tunnels over their range of Mach numbers. Data include tests with models installed. Fig.
1
;
25
an adjustable nozzle and adjusting it to a higher Mach number after the The running compression ratios may be reduced by means of injectors in the diffuser which reduce separation. (In one tunnel has started. instance
known
to the author
ratio of 5.0, a very ically
by
M=
low figure.) Both
special considerations
5.0
was obtained by a compression must be justified econom-
alterations
of available equipment.
:
36
High-Speed Wind Tunnel Testing
j
In high-speed wind tunnel design the importance of providing adequate compression ratio cannot be overemphasized. The power supply is a
major portion of the wind tunnel and cannot be easily altered in the event that sufficient compression ratio is not provided in the original design. It will be noted that a second throat as much as 30 per cent or more above the ideal size required for tunnel starting will be needed in order to make allowance for the increased losses produced when a model is installed This allowance (see Section 1:6) is another extremely important item in wind tunnel design. It can be quite embarrassing to have enough compression ratio to operate a wind tunnel and to have a in the test section.
second throat too small to get it started. In conclusion we note the following general items concerning flow in supersonic nozzles which have to this point only been implied
The Mach number
a supersonic nozzle
is
locked in by the nozzle
area ratio and will not be changed (as long as
it
remains supersonic) by
1.
either
in
upstream or downstream pressure.
2. If the
downstream stagnation pressure is lowered without changing no change in the test section flow, but
the upstream pressure, there will be
the losses in the diffuser shock system will be increased.
This increased
normal shock’s being pulled farther downa higher Mach number.
loss is usually attributed to the
stream, where
it
occurs at
upstream pressure is increased, the flow in the test section occur at a higher pressure but at the same Mach number. 3.
If the
will
Items 1 and 3 neglect secondary changes in Mach number produced by changes in boundary layer thickness and consequent changes in the effective area ratio.
1:6
Starting with a
Our
Model
in the
discussion of flow in a supersonic tunnel has been generally limited
now consider the effects of a of a supersonic tunnel. can be shown that the area of a second throat sized for Mach 1.0
so far to the case of a clear tunnel.
model It
Test Section
in the test section
on the
Let us
starting
flow during the starting process varies as the loss of total head in the test section. Using a value of 1.4 and eq. (1 18), we obtain the ratio of y
=
:
area at the nozzle throat to area at the test section. ratio of eq. (1:26)
by
this area ratio gives the ratio
area to the nozzle throat area.
When
compared with
that
eq. (1 :24)
we And
this is
Dividing the area
of the second-throat
done and the
results are
High-Speed Wind Tunnel Theory This relation implies that losses in total
37
/
head resulting from the shocks on
a model during the starting process require a second throat larger than that for the clear tunnel. This has been found to be true in actual wind
tunnel operation.
Another important consideration is the maximum model size for tunnel starting. This may be studied in the manner of the second throat analysis. With a normal shock ahead of the model, the flow ahead of the model is subsonic. A minimum cross-sectional area will exist at the station where the cross-sectional
the
area of the model
Mach number cannot exceed
is
1.0.
At
greatest.
this
minimum
area,
Hence the model must be small
enough to allow the mass flow of the nozzle to pass through the unobstructed nozzle cross section with of a normal
shock to a
shock does not pass across the tunnel
is
said to
model during the
model required for
throat area of Fig. 1:24.
In practice,
smaller than this analysis suggests. size
small, the
greater than
air
1.0.
downstream normal
If the
starting process, the
be “choked.” The theoretical unobstructed nozzle cross-
sectional area at the
model
an expansion of the
Mach number no
may have
starting
it is
If the
is
the
same
as the second
wise to size a model somewhat
model
to be further reduced.
normal shock envelops the model
is
particularly blunt, the
If the in the
model
manner
is
sufficiently
illustrated
by
Fig. 1:26.
on model size for starting from several high-speed wind tunnels are summarized. At Mach numbers to 10.0, allowable model sizes are much smaller than theoretical, again indicating the danger of considering purely theoretical flow. Surprisingly, in a few instances, sharp models have permitted tunnel starts when their sizes were In Fig. 1:27, experimental data
above the “theory” line.
Fig.
1
:26
a model.
Sketch showing the progress of the normal shock through a The flow is finally established in (rf).
test section
with
38
I
High-Speed Wind Tunnel Testing
Mach number
Maximum model
Fig, 1:27
Sharp-nosed models
A —
may
diameter for certain start of blunt models.
be larger than blunt ones. d„
physicial test section cross-sectional area less the product of
displacement thickness and
test
Occasionally a model
The following luck to 1.
is
(Ref. 1:2.)
= maximum model
diameter;
boundary layer
section perimeter.
put in the tunnel and the tunnel will not
actions (not in any particular order)
start.
may be tried, and good
all.*
Moving
the model forward in the test section.
Squirting a spray of water in to the stagnation chamber. 3. Adding an afterbody to the model. 2.
4.
Blowing
5.
Increasing the diffuser area.
air
out of holes near the nozzle throat.
6.
Increasing the tunnel pressure ratio.
7.
Adding a removable sharp nose
Since an increase in
to the model.
model angle of attack requires an increase of
pressure ratio, the tunnel
may
“unstart” during a run. This effect
is
often
accompanied by a change in tunnel noise that the operators may notice. However, visual means for detecting “unstarting” are much preferred. The authors know of one small a wire
is
fed into the entrance cone
(I-inch test section) indraft tunnel that starts to “tickle the tunnel’s throat.”
and wiggled
when
High-Speed Wind Tunnel Theory
]
39
connected Typical visual means include schlieren systems or manometers orifices. pressure to test section 1:7
The Method of
Characteristics
a method for defining the properties of supersonic flows in the presence of varying boundaries such as in a wind tunnel nozzle or in the presence of some aerodynamic configuration in a supersonic air stream. The method as normally used requires constant
The method of characteristics
is
having shock waves. In general, this limits the method of characteristics to the case of a continually expanding flow because weak compression waves have to be widely separated to avoid the formation of a shock and consequent
entropy flow. Hence
it
cannot be used in a flow
field
entropy changes.
The method of characteristics is probably the most frequently used method for defining the internal contours of supersonic nozzles in the region between the first throat and the test section. It is this application which
is
of primary interest here.
been developed for both twodimensional and three-dimensional flows. We shall discuss only the twodimensional flow method. The two-dimensional flow considered is one
The method of
in
characteristics has
which flow changes occur
in
two dimensions such as a rectangular
supersonic nozzle with parallel side walls and contoured upper and lower walls.
If a parallel flow at a
Mach number
of 1.0
is
expanded around a corner, Mach number will be
the direction of the flow will be changed and the increased.
The Mach number
to
which the flow
will
be expanded by the
corner
is related to the angle of the corner. This relation is tabulated in Table 1:3, where v is the turning angle. Also included in the table are angles of Mach lines with respect to the direction of flow, a„„ and ratios of static to total pressure, pjpf. The data of Table 1 :3 are based on the assumption of perfect gas flow. The values are not limited to cases in which the flow is expanded from Mach 1.0 by a single turn. They are
applicable to cases in which the flow
is
turned from one direction to
some
maximum inclination with respect to that direction through any number of steps.
They
are also applicable to the case, as in a supersonic nozzle,
where the flow
is
turned
to the direction of flow at
of flow at
Mach
1.0.
first
to
Mach
some maximum
1.0
and then
is
inclination with respect
turned back to the direction
In this case, the angles of turning out and back are
additive in determining the total turning angle,
v.
In order to describe the method of characteristics let us examine the flow around a corner illustrated in Fig. 1:28. The Mach number ahead of a 5-deg corner is 1.950. From Table 1 :3 we find that in order to reach
40
I
High-Speed Wind Tunnel Testing
Table 1:3
Pmndtl-Meyer Corner Data, y
Deg
Mach Number
Deg
=
1.4
pipt
Deg
Mach Number
Deg
pIpt
90.00
0.5282
20.0
1.7743
34.31
0.1813
0.5
72.10
0.4975
20.5
1.7915
33.93
0.1763
1.0
67.70
0.4792
21.0
1.8090
33.54
0.1718
1.5
64.50
0.4634
21.5
1.8268
33.19
0.1668
61.96
0.4492
22.0
1.8445
32.83
0.1624
0.0
2.0
1
1.1328
2.5
1.1559
59.89
0A267
22.5
1.8622
32.48
0.1584
3.0
1.1770
58.17
0.4250
23.0
1.8795
32.15
0.1539
56.68
0.4136
23.5
1.8973
31.82
0.1498
3.5
4.0
mmwM
55.29
0.4036
24.0
1.9150
31.49
0.1459
4.5
1.2362
53.99
0.3926
24.5
1.9325
31.16
0.1419
5.0
1.2554
52.77
0.3834
25.0
1.9502
30.85
0.1383
5.5
1.2745
51.66
0.3737
25.5
1.9680
30.54
0.1342
6.0
1.2935
50.63
0.3638
26.0
1.9861
30.23
0.1306
6.5
1.3120
49.66
0.3552
26.5
2.0041
29.93
0.1270
7.0
1.3300
48.75
0.3463
27.0
2.0222
29.64
0.1234
7.5
1.3478
47.90
0.3385
27.5
2.0402
29.35
0.1201
8.0
1.3649
47.11
0.3298
28.0
2.0585
29.06
0.1166
46.33
0.3215
28.5
2.0770
28.78
0.1133
8.5
9.0
1
4005
45.57
0.3136
29.0
2.0957
28.49
0.1100
9.5
1.4178
44.58
0.3067
29.5
2.1145
28.23
0.1067
10.0
1.4350
44.18
0.2991
30.0
2.1336
27.97
0.1037
10.5
WEsm 1
43.52
0.2917
30.5
2.1530
27.68
0.1007
42.92
0.2847
31.0
2.1723
27.41
0.0977
11.5
1.4858
42.30
0.2778
31.5
2.1913
27.16
0.0949
12.0
1.5028
41.72
0.2711
32.0
2.2105
26.90
0.0919
12.5
1.5195
41.15
0.2648
32.5
2.2298
26.65
0.0892
13.0
1.5365
40.60
0.2585
33.0
2.2492
26.40
0.0866
13.5
1.5540
40.05
0.2518
33.5
2.2688
26.15
0.0839
14.0
1.5710
39.53
0.2454
34.0
2.2885
25.91
0.0814
14.5
1.5875
39.04
0.2398
34.5
2.3090
25.66
0.0789
15.0
1.6045
38.54
0.2336
35.0
2.3288
25.43
0.0764
15.5
1.6213
38.08
0.2281
35.5
2.3485
25.21
0.0740
16.0
1.6380
37.63
0.2222
36.0
2.3688
24.99
0.0718
16.5
1.6550
37.17
0.2167
36.5
2.3895
24.77
0.0695
17.0
1.6723
36.73
0.2116
37.0
2.4108
24.53
0.0672
17.5
1.6892
11.0
^
36.30
0.2058
37.5
2.4316
24.29
0.0651
18.0
35.88
0.2009
38.0
2.4525
24.07
0.0630
18.5
35.48
0.1955
38.5
2.4730
23.86
0.0611
19.0
1.7401
35.08
0.1905
39.0
2.4942
23.64
0.0591
19.5
1.7572
34.69
0.1860
39.5
2.5156
23.43
0.0571
High-Speed Wind Tunnel Theory
/
Table 1 :3 {continued)
Mach Number
Deg
40.0
2.5372
23.22
40.5
2.5590
23.01
V,
Deg
V,
^m» PlP‘
Deg
Mach Number
a-m.
Deg
PiPt
2.5810
22.80
0.0516
61.0
41.5
2.6028
22.59
0.0499
61.5
2.6948
ISi wSm WSm mgm
42.0
2.6254
22.38
0.0482
62.0
3.7288
15.56
0.00951
0.0466
62.5
3.7632
15.41
0.00907
63.0
3.7980
15.26
0.00866 0.00825
41.0
60.0
3.5937
0.0534
60.5
3.6270 3.6610
0.0115
0.0110 0.0105
0.00998
42.5
2.6484
22.19
43.0
2.6716
21.98
43.5
2.6948
21.79
0.0433
63.5
3.8332
15.12
44.0
2.7179
21.59
0.0418
64.0
3.8690
14.98
0.00786
44.5
2.7412
21.39
0.0403
64.5
3.9052
14.84
0.00748
45.0
2.7643
21.21
0.0389
65.0
3.9417
14.70
0.00712
45.5
2.7879
21.02
65.5
3.9788
14.56
0.00678
46.0
2.8120
20.83
66.0
4.0164
14.42
0.00644
46.5
2.8361
20.65
0.0349
66.5
4.0548
14.28
0.00612
47.0
2.8610
20.46
0.0336
67.0
4.0940
14.14
0.00581
47.5
2.8855
20.28
0.0323
67.5
4.1338
14.00
0.00552
48.0
2.9105
20.09
0.0311
68.0
4.1738
13.86
0.00524
48.5
2.9360
19.91
0.0300
68.5
4.2135
13.73
0.00497
49.0
2.9616
19.73
69.0
4.2543
13.60
0.00472
49.5
2.9873
19.56
69.5
4.2960
13.46
0.00447
50.0
3.0131
19.38
70.0
4.3385
13.33
0.00423
50.5
3.0393
19.21
70.5
4.3820
13.19
0.00401
51.0
3.0660
19.06
0.0247
71.0
4.4257
13.06
0.00379
51.5
3.0925
18.87
0.0237
71.5
4.4704
12.92
0.00359
52.0
3.1193
18.70
0.0228
72.0
4.5158
12.79
0.00339
52.5
3.1463
18.53
0.0219
72.5
4.5620
12.66
0.00320
53.0
3.1737
18.38
0.0210
73.0
4.6086
12.53
0.00302 0.00285
53.5
3.2015
18.21
0.0202
73.5
4.6558
12.40
54.0
3.2293
18.04
0.0194
74.0
4.7031
12.28
0.00269
54.5
3.2576
17.87
0.0186
74.5
4.7505
12.15
0 00254
55.0
3.2865
17.72
0.0178
75.0
4.7979
12.02
0.00240
55.5
3.3158
17.55
0.0171
75.5
4.8504
11.89
0.00226
0.00212
56.0
3.3451
17.40
0.0164
76 0
4.9032
11.76
56.5
3.3747
17.24
0.0157
76.5
4.9557
11.64
0.00199
57.0
3.4055
17.08
0.0150
77.0
5.009
11.52
0.00187
57.5
3.4365
16.92
0.0144
78.0
5.119
11.27
0.00165
58.0
3.4675
16.76
0.0137
79.0
5.232
11.02
0.00145
58.5
3.4985
16.61
0.0131
80.0
5.349
10.78
0.00127
59.0
3.5295
16.46
0.0126
81.0
5.470
10.53
0.00111
59.5
3.5612
16.31
0.0120
82.0
5.595
10.29
0.000970
41
42
/
High-Speed Wind Tunnel Testing
Table 1:3 (continued) V,
Deg
Mach Number
Deg
PiPt
Deg
V,
^mj
Mach Number
Deg
pIpt
83.0
5.724
10.07
8.622
6.67
0.0000628
5.867
9.81
0.000845 0.000727
98.0
84.0
99.0
8.907
6.45
85.0
6.008
9.58
0.000628
100.0
9.210
6.23
86.0
6.155
9.35
0.000541
101.0
9.539
6.02
0.0000507 0.0000407 0.0000322
87.0
6.311
9.12
0.000463
102.0
9.887
5.80
0.0000254
88.0
6.472
8.88
0.000396
103.0
10.260
5.60
0.0000198
89.0
6.643
8.66
0.000336
104.0
10.658
5.38
90.0
6.820
8.43
0.000285
105.0
11.081
5.18
0.0000154 0.0000118
91.0
7.008
8.21
0.000240
92.0
7.202
7.98
0.000202
93.0
7.407
7.77
0.000169
94.0
7.623
7.54
0.000140
95.0
7.852
7.32
0.000116
96.0
8.093
7.10
0.0000950
97.0
8.350
6.88
0.0000776
the
Mach number
of 1.950, the flow at this point has been turned through
its direction at Mach 1.0. We also find that at a of 1.950, the angle of the Mach wave OA with respect to the direction of flow is 30.85 deg. Turning the flow through an additional 5-deg angle results in a total turning angle v of 30 deg, so that the Mach
an angle of 25 deg from
Mach number
the corner is 2.134 and the Mach wave OB has an angle of 27.97 deg with respect to the new flow direction or 22.97 deg
number downstream of
with respect to the original flow direction.
Between the
Mach waves OA and OB
the flow
Mach number and
High-Speed Wind Tunnel Theory
Fig.
Sketch demonstrating by a solid boundary.
1:29
reflected
how
characteristic lines
43
/
from an expansion are
direction are continuously changing.
In the method of characteristics,
these variations in the fan-shaped zone
AOB are replaced by a step change
from the conditions upstream of the corner to the conditions downstream of the corner across a line OC which bisects the fan shaped zone AOB. For the flow of Fig. 1 :28, this corresponds to saying that the flow is at
Mach
OC
1.950 in
its
its
original direction until
Mach number
is
instantly
it
reaches
OC. When
changed to 2.134 and
its
it
crosses
direction
is
changed by 5 deg. The line OC is called a characteristic line. It is apparent that the changes in Mach number and flow direction across the fan-shaped zone AOB will be decreased as the turning angle is decreased. Thus, the assumptions of the method of characteristics approach the actual flow as the turning angle approaches zero. instantly
In some supersonic flow problems, particularly in nozzle design, necessary to determine what happens solid
when an expansion wave
boundary. Let us examine this case by reference to Fig.
1
it is
strikes :29.
a
The
Mach number of 1.950 between the parallel walls XA and POM. At point A the upper wall makes a turn of 5 deg upward. From our previous example we have defined the characteristic AO and the Mach number downstream of AO, Now, let us draw a line OZ parallel to A Y. If the area between A Y and OZ is allowed to represent initial
flow
is
at a
downstream of AO, then no characteristics occur downAO because no further turning of the flow is required. In this case the characteristic wave AO would be said to be “canceled” upon striking the boundary POZ. However, is the actual boundary of the flow downstream of and the flow along this boundary must be parallel to the boundary. Hence a characteristic wave is required to turn the flow from the 5-deg up direction to the horizontal direction. We can see that having the actual boundary instead of the boundary OZ for uniform flow allows more room for the air flow downstream of AO. Thus, the flow is expanded to a higher Mach number by the 5-deg turn the flow channel
stream of
OM
OM
:
44
/
:
High-Speed Wind Tunnel Testing
back to a horizontal direction. This being determined, the second characteristic line OR and the Mach number downstream of OR are obtained in the previously described manner. Supersonic Nozzle Design
1:8
The supersonic nozzle consists of a subsonic portion which accelerates the settling chamber flow up to sonic speed, and a supersonic portion which further accelerates the flow and finally delivers it as a uniform stream to the that
it
Considering
test section.
first
the subsonic portion,
is exceedingly difficult to accelerate the settling
without having some areas of deceleration near the walls thicken the boundary layer undesirably. Usually this effect
by nozzle
designers, apparently without serious
completely arbitrary procedures
is
we
find
chamber flow which tend to is
neglected
harm, and one of three
used to determine the subsonic shape
a smooth curve of Mach number against nozzle length from = 1.0, and then using eq. 1:18 chamber Mach number to compute the corresponding area ratio. (The reason for not drawing the area curve directly is that the extra step yields a much more gradual curve than intuition would normally indicate.) 2. Draw an arc of 5/i* where h* is the height of the sonic throat. 3. Use the curve made by an ellipse having the major axis equal to the throat height and the minor axis equal to one-half throat height. A 45-deg line is then faired from settling chamber to the ellipse. 1
.
Draw
M
settling
In the usual case of fairing from a round settling chamber to a rectangular section at the sonic point (nozzle throat), about twenty control stations should be used.
the nozzle should end at station,
In actual construction the subsonic portion of
M = 0.9 or below to avoid a joint at the sonic
and whatever joint
finally evolves
should cause a step of no more
than 0.001 inch.
For designing the portion of the nozzle between the throat and the test method of characteristics is normally used. An outline of the
section, the
steps required in the design of a two-dimensional nozzle
by the method
of characteristics will be given.
Note that use of the method of characteristics requires dividing the diverging portion of the nozzle into a series of straight sections in order to define the characteristic lines and their reflections and cancellations. However,
after the characteristic calculations
possible to obtain a for the
boundary
smooth curve which,
layer,
is
stream of a predetermined as follows
have been completed,
after allowance has
suitable for creating a
Mach number. The
it is
been made
uniform supersonic
general steps to take are
3
High-Speed Wind Tunnel Theory
——
O Fig.
1
:30
j
45
H
Illustration of first step in supersonic nozzle design.
Read the turning angle v for the desired Mach number from Table 1 the maximum wall angle Omax from Omax = r/2. compute and 2. Since a nozzle symmetrical about a horizontal centerline will have :
1.
is somewhat shortened if we design only Hence we now draw (Fig. 1 30) the centerline OH and a horizontal section AB representing the downstream end of the
symmetrical flow, the problem the
upper half.
very short
:
subsonic portion.
smooth and arbitrary curve BCD that expands the minimum section to 0max at some distance downstream. Both the distance downstream and the curve are unimportant except in the way they effect the overall distance between the nozzle throat and the test Construct a
3.
section.
In supersonic nozzles, this distance
to 8 test section heights,
is
usually in the range of 3
Mach
with the lower values occurring at lower
numbers.
Divide the curve into
4.
of not over 2 deg
enough equal
straight sections to
make an
between each section. The shorter the sections
greater the accuracy,
and, of course, the greater the
angle
are, the
number of calculations.
than \ deg are probably unnecessary. Construct the expansion waves and their reflections according to
Steps smaller 5.
our previous
work and the examples that follow Step
6.
Construct the section canceling
7.
Redraw the nozzle to an expanded
all
8.
the expansion waves. vertical scale
and
fair
a smooth
curve through the points of intersection of the
Check the
8.
final
section with that
Example 1:2 final
is
Other
selected
:
1.503, test section to
because
it
yields
Mach numbers merely
M=
1.0.
1
Construct a single-step supersonic nozzle to obtain a
Mach number of
1.503
with
waves with the wall. by comparing the area ratio of minimum to of eq. (1 18). Agreement should be within per cent.
final result
be 9.44 inches high.
(M =
an even number of degrees of
require interpolation in the table.)
turn. Start
46
High-Speed Wind Tunnel Testing
I
E
D
Fig. 1:31
1.
2.
Construction of a single-step characteristic net for a supersonic nozzle.
From Table 1 :3 v = From eq. (1:18) the
distance
AO
12 deg for
M = 1.5028.
area ratio for
M=
Hence 0max
1.5028
is
—
6 deg.
1.180, so that
of Fig. 1:31 should be constructed as 9.44/ (2
X
1.18)
=
4.0 inches.
have only one step of 6 deg, no smooth curve need be laid in. It should be noted, of course, that 6-deg steps are too large, and this example is presented only as the simplest case, useful as a starting 3.
Since
we
shall
point.
The Mach number produced by a 6-deg turn is, from Table 1:3, = 1.0 is 90 deg, and for — 1.2935 it is 1.2935. The Mach angle for 50.63 deg. Sketching in the Mach wave for the initial flow BC' and the Mach wave for the turned flow BC", and bisecting the angle thus formed, we get the first characteristic line BC, which is inclined 67.32 deg with 4.
M
M
respect to the horizontal. 5.
turn
We is
have determined that the
Mach wave downstream
inclined 50.63 deg with respect to the flow, so
we
of the
first
sketch in such a
wave CD'. When the 6-deg-up flow is turned down 6 deg to obtain the design Mach number of 1.5028, we find in Table 1:3 that the Mach wave is inclined 41.72 deg with respect to the flow. Such a wave, CD", is sketched in. The angle between these two waves is bisected to obtain the second characteristic line CD, which has an angle of 49.17 deg with respect to the horizontal. 6.
At
the point of intersection of the characteristic line
BD,
the second 6-deg turn of the wall
CD
made
with the
form a DE. Since the flow everywhere downstream of the characteristic CD is parallel to the boundary DE, no further turning of the flow is required. Consequently the wave CD does not reflect when it
nozzle wall
is
to
horizontal segment
strikes the wall. strike the wall
This portion of the nozzle where the characteristics
and are not
reflected
is
called the “cancellation region.”
High-Speed Wind Tunnel Theory
47
D
D’
Illustration of the effect
Fig. 1:32
/
of starting the constant-area section of a nozzle too
far upstream.
Measurement of the area ratio to 1.18 fromeq. It is noted that in the design compared 18). (1 yields 1.15, of a nozzle by the characteristic method, the Mach waves of Fig. 1:31 Tliis
completes the single-step nozzle.
;
are usually not sketched in
drawing.
angle formed
Mach wave
Mach waves
by the two
characteristic line It is
because they increase the complexity of the
Instead, the pertinent
drawn on the
is
angles are obtained, the
are bisected analytically,
and the
figure.
of interest to consider the result of starting the constant-area
section too early, say at
D'
(Fig.
1
:32).
the positively (to the flow) inclined surface
At D' the flow is up 6 deg, and would produce an over-pressure
wave that would ricochet down the duct. Further, the rarefaction wavelet CD would not be canceled, and it too would continue downstream. The field in which the model is to be tested would have a lattice of horizontal, up-and-down-flow regions of varying speed, and successful testing would be most doubtful.
Example 1:3
Construct a two-step supersonic nozzle 9.44 inches high
Mach number of 1.5028. An additional step must be used, but this problem now embraces wave intersection and demonstrates the complete case, so that any number of steps may be employed in an to yield a final
identical
manner.
manner
Example
1.
In a
2.
The nozzle throat dimension
similar to
1
;2,
OA
Fairing of a curve to define the length
unnecessary.
The
first
is
BE.
At E,
is
6 deg.
again 4 inches (Fig. 1:33).
of steps
step turning the flow
constructed with a length
up an additional 3 deg
Omax
is
in a two-step nozzle
up
3
deg
is
is
arbitrarily
the second step turning the flow
constructed.
The network of waves will form a number of spaces, each having its individual flow angle and Mach number. It is convenient to label each space according to a coordinate system {a, b) where a denotes the number of degrees of turn produced so far by waves from the upper 3.
;
48
/
Fig.
1
High-Speed Wind Tunnel Testing
:33
The
characteristic
network for design of a nozzle with a two step expansion.
4.
and b is the number of degrees of turn produced so far by waves from the lower surface. Since waves from the upper wall turn the flow upward and those from the lower wall turn the flow downward, the local flow angle 0 is equal to a — b, and the flow is hence horizontal when a is equal to b. The total v is (ct + b) degrees. Our preliminary grid is hence as shown in Fig. 1 :33. surface,
An we
will
examination of the preliminary grid of Fig. be concerned with total turning angles v of 0,
with respect to lines.
It is
;
33 indicates that
and 12 deg. form angles of pertinent Mach waves the horizontal as an aid in determining characteristic
convenient to
It is
1
list
3, 6, 9,
in tabular
noted that the inclination with respect to the horizontal of
downward-moving Mach waves, 3^, is the difference between the Mach angle and the upward flow angle, c/.^ — 6. Similarly, the inclination with respect to the horizontal of upward-moving Mach waves, is a„, -F 6. Using these two relations together with Table 1:3 allows the following tabulation for
M
“m
0
1.0000
90.00
3
1.1770
58.17
6
1.2935
50.63
9
1.4005
45.57
12
1.5028
41.72
V
Flow
Up
for
Flow
Up
6°
3°
55.17
52.17
61.17
64.17
47.63
44.63
53.63
56.63
42.57
39.57
48.57
51.57
38.72
35.72
44.72
47.72
3°
6°
—
5. The characteristic line BC is determined by averaging a,„ for a zero turn angle with 3^ for a 3-deg turn angle and 3-deg up flow. The angle of BC with respect to the horizontal is thus (90.00 55.17)/2 72.58 deg.
=
The
EH
determined by averaging 3^ for a 3-deg turn angle and 3-deg up flow with 3^ for a 6-deg turn angle and 6-deg up 6.
characteristic line
flow: (55.17 -f 44.63)/2
=
is
49.90 deg.
High-Speed Wind Tunnel Theory
j
49
CH is determined by averaging 8^ for a 3-deg with a„ for a 6-deg turn angle (horizontal flow up 3-deg and turn angle The
7.
(61.17
flow):
The
8.
characteristic line
-1-
50.63)/2
=
characteristic line
55.90.
HD
is
determined by averaging
for a 6-deg
and 3-deg up = -!deg. Since the flow downstream of HD 52.60 48.57)/2 flow: (56.63 is 3 deg up, the nozzle contour must turn down 3 deg to that flow direction at D to avoid a reflection of HD from the wall. 9. The characteristic line HF\s determined by averaging a„, for a 6-deg turn angle with
(1:33) c.
The
dynamic pressure obtained by using and calibrated Mach number is given by
error in determining
measured
total pressure
yM'^
_
d_q
q~ Ml To
l+Ky-
+
1)/2]M-
(1:34) Pt
carry this tie-in of calibration accuracy to final data accuracy a step
further,
it
would be necessary
pressure-measuring system, that by, say, a 0.01-inch error in
to consider the absolute is,
to determine
what
accuracy of the
errors are
manometer reading. This
step
is
because of the great difference between the magnitude of
produced necessary
static
and
pitot pressure previously indicated, but is not amenable to general treatment because of the wide range of total pressures used in wind tunnel work. Even this step will not give the complete picture because it ignores
the fundamental fact that pitot pressure
is
much
easier to
measure than
static pressure.
References
1
:
1
Ames
Research
NACA 1:2
C.
J.
Schueler,
Numbers 1:3
Antonio
An
Equations, Tables and Charts for Compressible Flow,
Investigation of
1.5 to 19.5,
Ferri,
Company, 1 :4
Staff,
Report 1135, 1953.
Hermann
Model Blockage
AEDC TN 59-165,
for
Wind Tunnels
at
Mach
1960.
Elements of Aerodynamics of Supersonic Flows, The Macmillan
1949. Schlichting,
Boundary Layer Theory, McGraw-Hill Book Company,
1960.
1:5
1:6
and Robert G. Payne, A method of Calculating Boundary Layer Hypersonic Mach Numbers, AEDC-TR-59-3, ASTIA Document
James C.
Sivells
Growth
at
AD-208774, 1959. H. Maxwell and J. L. Jacocks, Nondimensional Calculation of Turbulent Boundary Layer Development In Two-Dimensional Nozzles of Supersonic Wind Tunnels,
AEDC TN 61-153, 1
:7
1:8
1962.
Charles B. Johnson, Lillian R. Boney, James C. Ellison, and
Wayne D.
Erickson,
Real Gas Effects on Hypersonic Nozzle Contours With a Method of Calculation, NASA TN C-1622, 1963. Paul Chambre and Lin Chia-Chiao, On the Steady Flow of Gas Through a Tube
With Heat Exchange or Chemical Reaction, JAS, 13
(10), (1946) p. 537.
High-Speed Wind Tunnel Theory 1:9
1:10 1:11
1:12 1:13
/
65
Richard M. Head, Investigation of Spontaneous Condensation Phenomena, Ph.D. Thesis, California Institute of Technology, 1949. J. Lukasiewicz, Effects of Air Humidity in Supersonic Wind Tunnels, R & 2563, June 1948. G. A. Lundquist, Recent Experimental Work at NOL on Condensation in Compressible Flows, Geophysical Research Paper No. 37, ARDC, July 1955. P. Wegener, On The Experimental Investigation of Hypersonic Flow, Naval Ordnance Laboratory Report 9629, 1948. Fred L. Daum, Air Condensation in a Hypersonic Wind Tunnel, AlAA Journal,
M
May
1963.
1:14 D. E. Morris and K. G. Winter, Requirements for Uniformity of sonic
Wind
Tunnels,
RAE TN Aero 2340,
Flow
in
Super-
1954.
1:15 Alan Pope, Aerodynamics of Supersonic Flight, Pitman Publishing Corporation, 1958, p. 28.
Chapter two
Design of intermittent
blowdown 2 1 :
tunnels
General
The basic problems in the design of any high-speed wind tunnel are always those of providing suitable duct work and flow control devices to ensure that air will pass through the test section of the tunnel at the desired flow conditions. Going one step further, we can say that these problems always include those of providing air (1) with enough pressure ratio across the tunnel to achieve the desired flow velocity, (2) with enough
mass per second and total mass to meet the tunnel size and run-time requirements, (3) dry enough to avoid condensation, and (4) hot enough to avoid liquefaction.
The ways of tunnels:
solving these problems result in four basic types of
blowdown,
indraft,
pressure-vacuum, and continuous.
following discussion of tunnel design in the order listed above,
is
wind The
divided according to tunnel type
with the discussion of the
blowdown
tunnel
The various types of wind tunnels have many common design problems and in the subsequent discussion of the other types of tunnels, reference is made to the discussion of blowdown tunnels where in this chapter.
necessary to avoid repetition.
2:2
Design of Intermittent Blowdown Tunnels
Although some variations
blowdown
in
arrangement are possible, the intermittent
tunnel (Fig, 1:2), usually consists of a basic circuit of
com-
pressor, air storage tank, stagnation pressure control system, test section,
and exhaust. The sizing of components and the selection and matching of components is a large portion of the science of blowdown tunnel design. Often the design of a blowdown tunnel is greatly influenced by some For example, some major component (a building, a
special condition.
compressor, or an air storage tank) for
66
economy, or the tunnel
will
is already available and must be used be used only for a particular type of test
Design of Intermittent Blowdown Tunnels
/
67
and hence must be optimized for that type of test. Under such conditions, operating range, and versatility of the tunnel will be restricted somewhat. However, designing the tunnel is often made somewhat easier because some of the major decisions regarding the design it is
probable that the
are dictated
size,
by the special condition. we shall assume that there are no conditions imposed
In our discussion
on the design of the tunnel, except that the desired operating Mach number range is known and there is a limitation on cost. Our discussion will not be completely relevant to the case
when some
special condition
is
imposed on the design but will be directly applicable to the most frequent case in which there is a cost for the tunnel that must not be exceeded. Once a decision to build a tunnel is reached, one of the more important tasks is finding a place to put it. Buildings of some sort are required for every wind tunnel, and these can cost from a sizable fraction of to well over half the total cost of a wind tunnel, depending on the type of building, the amount of equipment that must be sheltered, whether office space is to be provided, the amount of floor space allowed for a work area and for setups, the
amount of floor space allowed
for controls, the type of equip-
ment and instrumentation, the type and extent of heating and air conditioning, and many other factors common to building design. If the engineer can find a building suitable for his tunnel, he
agonizing experience of seeing a large portion of his
is
money go
spared the
for buildings
instead of tunnel.
2:3
Establishing the
Minimum
Allowable Operating Pressure
When the Mach numbers at which the tunnel minimum pressures at which operation is
the
is
to operate are
known,
possible at these
Mach
numbers are obtained by using Fig. 1:25. Since the blowdown tunnel under discussion exhausts to atmosphere, the tunnel exit pressure is known and the minimum allowable operating pressure is easily determined by using a ratio from the figure. It is strongly suggested that in 1:25 for determining minimum operating one use the top of the band rather than the middle or lower part of the band, or better yet, that one use a figure 25 per cent greater selecting
ratios
from
Fig.
pressures,
than that at the top of the band. within the
band were
The
whose data fall and it is doubtful
designers of tunnels
striving for operating efficiency,
that the uninitiated can
do better. The construction of a tunnel that will not work because of insufficient compression ratio can be extremely embarrassing to the tunnel designer and can require extensive and expensive modifications.
Mach number is below the lower limit of the band in minimum compression ratio of 2.0 is suggested for design
If the design Fig. 1:25, a
68
High-Speed Wind Tunnel Testing
/
purposes. instead of
The selection of some lower ratio
this
compression ratio for design purposes of the blowdown tunnel
will affect the cost
by only a small amount. Once the minimum pressure to ensure satisfactory operation at the design Mach numbers is established, the tunnel designer may wish to consider higher operating pressures. However, at this point in the design he is in no position to do so because of the many ramifications of operating pressure on the design of components that have not yet been considered. 2:4
Determining the Size of Tunnels
The
size
of the wind tunnel
the tunnel designer must
test section is
make with
components must be scaled
perhaps the most basic decision
respect to cost.
All wind tunnel
and naturally component and
in proportion to the test section
the larger the test section, the greater the cost of each
hence of the complete wind tunnel. Within reasonable cost limitations, the tunnel engineer usually wants to get the largest test section possible
with the
money he has more
larger (and usually
available.
Larger
costly) models.
test sections
make
built in direct proportion to a full-scale aircraft or missile.
the installation of
model
possible
Larger models are more easily
They allow
more instrumentation such as pressure orifices in the
surfaces, together with associated tubing to vent the individual
They are much by the way, is extremely important because the person in wind tunnel work who has the talent and patience of a jeweler in working with very small mechanisms is rare indeed. Reynolds number, which is an important parameter with respect to correlating wind tunnel data of a model with flight characteristics, increases in direct proportion to model size. With all of these reasons for making the tunnel as large as possible, it is appropriate to state that useful and significant work has been accomplished in wind tunnels with test pressures to measuring instruments outside the tunnel. easier to
work on than small models, and
sections as small as It is
section.
1
inch square.
appropriate to state the arguments for the smallest usable test Actually, for a given air supply and a given run time the largest
Reynolds number
is
obtained by using the smallest test section and the
highest available stagnation pressure.
number
this,
is
Except when
maximum Reynolds
the sole criterion, the arguments against extreme smallness
given above are overwhelming. Probably, cost of a tunnel decreases with size in spite of designing (in this case) for higher pressure.
The possible options and the possible degrees of sophistication are too numerous to allow determination of the size of a wind tunnel that can be built with a specified amount of money. By contacting other people with wind tunnels of the type he wants to build, the tunnel designer can get a
Design of Intermittent Blowdown Tunnels
/
69
general idea of the size he can afford. This provides a starting point from which he can calculate his complete tunnel installation and come up with
an estimated cost. If this estimate is less than he has available, he simply selects a larger test section size and goes through the complete tunnel installation calculations a second time to obtain a second estimated cost.
manner he \s'ill arrive at a tunnel size compatible with the available money. A word of warning is appropriate at this point. The cost estimates should be thorough and carefully obtained because there is much equipIn this
ment and often many subsystems in addition to the basic tunnel circuit which are required for satisfactory use of the tunnel and which can account for a very substantial portion of the complete tunnel cost. 2:5
Specifying
Run Times
Tunnel run time
is
normally determined from considerations of the
type and amount of data required during a given run.
In turn, this
depends on whether pressure or force tests are to be made. tests,
several pressure orifices are
in the surface orifices
In pressure
normally installed at various locations
of the wind tunnel model. Connections are
made
with flexible tubes that run to the outside of the tunnel.
to these
Outside
manometers or to some other form of pressure-measuring device from which the pressures are recorded.
the tunnel, the tubes are connected to
In this type of
test,
a significant amount of time
is
usually required for
the pressure at the measuring device to stabilize at the orifice pressure, particularly if the orifice pressure
is
low.
The reason
for this
is
that air
has to flow' through the tube between the orifice and the measuring device.
The tubes
are normally quite small (because of
resistance to air flow is developed.
As
model
the pressures at
and a high the orifice and at size)
the measuring device air flow'
approach each other, the pressure differential for decreases, with the result that the measured pressure approaches
When the orifice pressure is lower than the measured pressure, the stabilization time is greater than when the orifice pressure asymptotically.
the reverse pressure air in
is
and
true.
While the measured pressure
is
less differential is available for flow,
the measuring device
approaching the
orifice
the specific volume of
and hence an increasing This effect on stabilization time increases rapidly with pressures below' psia. In the blow'down 1 tunnel it w'ould be unw'ise to depend on pressure stabilization in less than
volume of
flow’ is
is
getting greater
required for stabilization.
15 or 20 seconds with a system of the type described. This factor in specifying run-time requirements. a large model, and pressure transducers
is
Of course, with
an important
a large tunnel,
located very near the orifices
model a much faster response can be obtained. In force tests the model is usually attached to a strain gage balance for
w'ithin the
:
70
High-Speed Wind Tunnel Testing
j
measurement of loads. During a
test,
the model
is
driven through a range
of attitudes with respect to the airstream to obtain a record of forces and moments as a function of a. The time required to do this is, of course,
dependent on the drive mechanism, the a range of interest, and the speed of the electronic data system that indicates and records the strain gage signals. However, for this type of test, a minimum run time of 15 seconds is
usually required.
Because of the data recording times required for force and pressure tests, and the time for the pressure control valve to provide a stable operating pressure, blowdown wind tunnels are usually designed for
minimum run least
times of 20 to 40 seconds.
30 seconds at each
A
run-time requirement of at
Mach number is probably
at this point in the design.
reasonable, particularly
Later detailed analyses of data recording
instrumentation and techniques and of the a drive mechanism in a
may
result
change in the estimate of run-time requirements.
2:6
Calculating Air Flow Rates
The rate of flow of air through the tunnel is one of the primary considerand the associated equipment. It is
ations in sizing both the tunnel calculated as follows H’
= pUA
(2:1)
= mass flow rate of air, slug/sec, p = mass density of air, slug/fH, U = velocity, ft/sec, A = duct cross-sectional area, From eq. (1 15) with y = 1.4, we get where w
ft^.
;
P
=
which, with the equation of state P
=
0.2M2)-5^
p,(l -F
(1
:
1)
becomes
{ptlR^T,)il
(2
= gas constant, 1716 fF/sec^ — Pf = total pressure, Ib/fH, Tf = total temperature, °R. From eq. (1 16) with y = 1.4, we get where
:
2)
°R,
:
T= From
eqs. (1 :6)
and
(1:7),
we
Ttil
+
Q.2i\Pr^
(2:3)
get
U = MilARJ'fi
(2:4)
Design of Intermittent Blowdown Tunnels
Combining
eqs. (2:3)
and
U= Eq. (2;
we have
(2:4),
M[1 ARiTjil
+
(2 : 5)
0.2M")]’'^
then becomes
1)
If the flow rate
evaluated
u'
=
w
= Q.02%56MpiAl[Tt^{l +
+
being calculated
by using the
is
supersonic
Mach number,
at the nozzle throat,
O.lM^y
0.2M"-y]
for a subsonic
is
in conjunction with the
If the flow rate being calculated
usually convenient to
it is
(2:6)
Mach number, eq. (2:6)
Mach number
test section
temperature and pressure.
total
71
/
where Mach number equals
make
1.0.
is
for a
the calculation
For
this case eq.
(2:6) becomes:
w blowdown
noted that
It is
= 0.0l653piA*lTf'^
(2:7)
tunnels invariably operate at an essentially
The primary purpose of this mode of flow while data are being recorded. Thus
constant pressure during each run. operation
is
to obtain a steady
the total pressures to
be used
The area
2:7
pressures determined as in Section 2:3.
at the throat of a supersonic tunnel
test section area,
from eq.
evaluating eqs. (2:6) and (2:7) are the
in
minimum allowable operating
(1
:
and the
ratio
of
of course obtained from the throat area (A IA*)
18) or Table 1:1.
Calculating
Run Times
There are two ways in which operated:
is
test section area to
(1),
with constant
q,
blowdown wind and
(2),
tunnels are customarily
with constant mass flow.
For
constant q operation, the only control necessary is a pressure regulator that holds the stagnation pressure constant. The stagnation temperature falls
according to the polytropic process in the storage tank; n
—
1.4 for
=
high-mass runs, approaching « 1.0 for long runs with thermal mass (open cans, spheres, etc.) in the tank. short,
For constant-mass runs the stagnation temperature must be held conand either a heater or a thermal mass external to the tank is required.
stant
Since heat energy
is
added to the pressure energy for constant-mass
running, a longer run time
is obtained. Even more important, the constant temperature of the constant-mass run keeps the Reynolds number constant. Since a 200°F drop during a run is quite common without heat
addition, this
is
a substantial point.
72
High-Speed Wind Tunnel Testing
I
Assuming, then, 1.
polytropic expansion in the storage tank,
2.
a heater that keeps the temperature constant,
3.
a pressure regulator that keeps the pressure constant,
4.
no heat
5.
isentropic expansion
work, from the
loss in the duct
settling
chamber
to the test section,
and 6.
a supersonic tunnel.
we may proceed to compute run The rate of mass flow through
time.
the tunnel is given by eq. (2:7). Setting the product of flow rate and run time equal to the change of mass in the tank,
we
get
0.01653^ = p,F-p,K /
or
=
t
60.5 Pt
A* L
A.
where
=
t
run time,
V= and subscript
i
denotes
sec,
storage tank volume, ft^
initial
conditions in the tank, and / denotes final
conditions in the tank. For a polytropic expansion of air in the tank Pf Pv
The equation of
state (1
t
=
:
1)
yields p,
= pjR^T,.
The run time
is
then
_
0.0353
A*
T.
p,
(2
:
8)
I
Eq. (2:8) gives the run time for the general case of blowing under constant-mass-per-second conditions.
The maximum run time obviously occurs when pf
is
down
a tank
a minimum. Note
that the run does not continue until the tank pressure drops to the stag-
nation pressure p^, but rather stops
higher value Pf
and
= Pt +
when
the pressure reaches
some
Ap denotes the losses in the duct work of Ap varies from about O.lpt for very-
Ap, where
in the regulator. The value small-mass runs (hypersonic tunnels) to somewhere around
1
.Op, for
high-
mass runs. Values for eq. (2:8) in parametric form have been plotted in Fig. 2:1 for The proper value of n itself is a function of the rate at
the range of n.
Design of Intermittent Blowdown Tunnels
.
Run
Fig. 2:1
which the tank. Fig.
From
the total
preliminary data
amount is
appears that
the tank
it
more toward
approaches isothermal
1.4, (tj
=
1.4.
used, and the shape of the storage
=
=
ti
may be
estimated from
The value of n
for more and with heat storage material in
2:2 for cylindrical tanks for which Ijd
spherical tanks tends
73
a*Tp!
time for blowdown tunnel; constant mass operation, y
air is used,
/
1).
3.0.
Equation (2:8)
may
also be
used with good accuracy for constant-pressure runs in which the change in
2:2 Very approximate chart for estimating polytropic process in cylindrical pressure storage tank, length^iameter
Fig.
exponent n of expansion
= 3.0.
74
/
High-Speed Wind Tunnel Testing
total temperature
small, since these
is
approach the constant-mass-rate
condition.
Compute
Example 2:1
the run time for a
M=
air storage
2600
sink material in 1.
3.3,
2.
From
A A
ft®
at 300 psig
blowdowm wind tunnel
by 12 inches, and 100~F. The storage tank has heat
with the following specifications:
2.5, test section 12
it.
M = 2.5 for M = 2.5
Fig. 1:25, a sufficient starting pressure ratio for
x
=
be reasonable duct and regulator valve pressure loss
satisfactory/?, will
3.3
14.7
48.5 psia.
=
is
=
(I.5)(4S.5) 72.S psia. could be 50 per cent, yielding Pf 2.5 2.637. the area ratio for is 3. From eq. (1 : 18).
M=
Substituting in eq. (2;
_
1),
w’e
have
(0.0353)C2600)(v5i^)(3I4.7)
*“(12 X
f
12/i44)(l/2.637)(560)(48.5)L
/
'
7S.5y'"-‘n
314.5'
J
= 49.8 sec 2:8
Specifying the Frequency of
Runs
After calculating the air flow rates and specifting tunnel run times,
we
can readily calculate the amount of air to be used during a run at each design Mach number. This does not give us all the information we need for determining the size of the air supply system, however, unless it is correlated with the required run frequency. The specification of the frequenc}’ of runs is an item with numerous ramifications. For e.xample. if the blowdown tunnel is transonic (high subsonic and low supersonic speeds), changes in Mach number usually require only changes in operating pressure because one nozzle is normally used for this speed range. These changes require only changes in pressure regulator valve adjustment. Consequently, essentiallx' no time is required for changes between runs. With this sort of operation there are two extreme possibilities regarding the air supply compressors and storage tanks. One possibility is to make the compressors and storage tanks of such a size that it would take 24 hours for the compressors to fill the air storage tanks, and when the tanks were full the air stored would be adequate to make perhaps a dozen runs during a one-hour period, ^^fith this arrange-
ment
would be busy with the test during hour of the day. would get the model changed and ready for the next series of runs in perhaps half an hour, and would be free fbr other work during a large part of the day. The other extreme possibility would be to make the compressors and storage tanks of such a size that the storage tanks would be essentially emptied during one run and it would the
the tunnel operating personnel
first
Design of Intermittent Blowdown Tunnels take 20 or 30 minutes to
refill
the tanks.
With
this
/
75
arrangement, there
would be considerable time during which operating personnel would be day. idle but runs could be made at any time during the transonic, a change in a instead of supersonic If the blowdown tunnel is model or a change in the wind tunnel nozzle is required between runs
Reynolds number studies). Generally, a series of runs is made at one Mach number, and then the series of runs is repeated at the next Mach number. With this type of operation the time required for changing a model and getting set up for the next run is usually (except for occasional
The time to change from one Mach number to the next typically varies from 5 minutes or less to more than an hour, depending on about 20 minutes.
the design of the nozzle
assembly for changing
Mach number. To
obtain
and to have continuous of the maximum utilization of a operations chores for operating personnel, the compressors and air storage tanks should be of such a size that the pressure tanks will be pumped up and ready for the next run in about 20 minutes following a run. This is the reasoning usually followed by wind tunnel designers. facility
However,
it is
this type
not particularly recommended because each designer should
have a good knowledge of the type of tunnel operation he
is
trying to get
and should design accordingly. 2:9
Compressors and Pumping Time
There are various types of compressors that could be used for pumping up the storage tanks of a blowdown wind tunnel, but by far the most frequently used type
is
the piston compressor, the reasons generally being
economy and commercial availablity in many sizes. Piston compressors can be obtained with one stage of compression for providing up to about 1 50 psia of discharge pressure, with two stages of compression for providing up to about 500 psia of discharge pressure, and with a third stage of compression for providing still higher pressure. For a given pumping capacity there is a marked difference between the cost of a single-stage and that of a double-stage compressor, as might be expected. After calculating the minimum allowable operating pressure for each Mach number at which the tunnel is to be operated, the tunnel designer can look at the required operating pressure for the highest Mach number and usually can tell quickly whether he is going to require a single-stage or a double-stage compressor. The air storage pressure, and consequently the discharge pressure of the compressor,
must of course be greater than
maximum tunnel operating pressure if the pressure control system is to work satisfactorily. The margin may be as small as 20 per cent, or pos-
the
sibly less, size
depending on the characteristics of the control system and the of the air storage tank relative to the mass flow of the tunnel.
A
76
I
High-Speed Wind Tunnel Testing
tunnel designer would consider margins of this magnitude only if his minimum required operating pressures were on the verge of crossing over single- to a considerably more expensive double-stage comand then only if the mass flow at the highest operating pressure were small compared to the maximum tunnel design mass flow. The
from a
pressor,
when
latter is frequently the case
range of
the tunnel
is
designed to cover a large
Mach numbers. For low Mach numbers
for operation are low but the nozzle throat
is
the pressures required
As Mach number
large.
increases, the pressure required for operation increases but the nozzle
throat decreases in area at a
more
rapid rate, with the result that the
mass flow requirements are generally lowest at the highest Mach numbers. In compressors a great deal of heat is added to air by the compression process. Because of this, cooling water is normally required to keep the temperature of the working parts of any sizable compressor at an acceptably low level. In multistage compressors, cooling water is also used between stages in order to take away the heat added by one stage of compression before the air enters the next stage. This is called “intercooling.” If cooling water requirements are large, a cooling tower may be required along with associated piping, valving, and pumps in order to reuse rather than waste the cooling water. If the compressor is of significant size, several safety features are usually incorporated.
provided to shut if
down
the compressor
if
the lubricating oil level gets too low, or
high.
It is
Controls are
the cooling water stops fiowing, if
the discharge pressure gets too
usually desirable, also, to provide controls which will shut
the compressor
down when
the storage tank reaches
design pressure
its
and which will start the compressor back up when the tank pressure falls below some limit. In addition to the above “accessories” for a compressor, a motor control center is usually required for switching the large amounts of electrical power required in turning the compressor on and off. All of these extras must be taken into account in arriving at a reasonable cost estimate because they
may represent
a very significant portion of
the compressor cost.
Small amounts of safety hazard,
and
oil in
high-pressure circuits present a considerable
several serious air-oil explosions
wind tunnel systems.
Because of
tunnel design to minimize the first
oil
this hazard,
it
is
have occurred in
important in wind
entering the high-pressure system.
The
step in doing this can be taken at the compressor.
cylinder piston rings of compressors are usually steel lubrication.
With
this
arrangement the probability that some
into the high-pressure circuit steel rings
is
high.
However,
at a very
can be replaced by carbon or teflon rings,
oil lubrication.
Compression and require oil oil will get
nominal cost the which do not require
Design of Intermittent Blowdown Tunnels
Fig. 2:3
Time
to
pump; standard
sea level
/
77
air.
The primary disadvantage of this substitution is that the carbon or must be replaced more frequently than the steel rings. Carbon rings are normally expected to wear about 0.003 inch per year of 8-hour day operation, and in this case would have to be replaced after about 5 years. The newer teflon rings in some installations might have to be replaced as frequently as every 600 hours of compressor operation. teflon rings
Compressors are rated at a specific number of cubic feet of sea level per minute. The time to pump a tank from an initial pressure ofp,- to a final pressure may be found from pf air
t
V
—
K 14.7(2
(Pf
-
Pi)
(2:9)
78
I
High-Speed Wind Tunnel Testing
=
where
Q =
pump time, min, compressor rating (cfm at sea
= final pressure, psia, = initial pressure, psia, — volume of pressure tank,
Pf p, Vj,
level),
ft*.
In practice Pf corresponds to the run start pressure, and p, to the run end pressure. For computing pump times at altitude, the sea level
constant of 14.7 in eq. (2:9) should be replaced with the corresponding atmospheric static pressure. Times required to pump each 1000 cubic feet
of air storage tank are shown in Fig. 2:3.
Example 2:2
Compute
the
14.7 psia to 300 psia using a
pump
time to
2600 (300
tv
-
a 2600 300 cfm.
fill
compressor rated
at
ft*
tank from
14.7)
(I4.7)(300)
= The number of cubic
feet
168 minutes.
of inlet air
pumped each minute (Q)
is
simply
converted to pounds per minute by using the equation of state (1:1):
M’ C
_
gQPo
(2
:
10 )
RiT,
where
= rating of compressor, Ib/min, acceleration of gravity, 32.174 ft/sec*, = g = pressure at compressor inlet, Ib/ft*, air Po Ri = gas constant, 1716 ft*/sec*-°R, T„ = air temperature at compressor inlet, °R.
Using eq. (2:10) together with the mass flow through the tunnel from we can easily derive the relation of pumping time to running
eq. (2:7),
time:
=
w-t^ where
w^-tjg
(
2 11 ) :
=
tunnel run time, sec. If the tunnel is to be designed so that following a maximum flow run the storage tanks will be back up to pressure and ready for the next run in some specified time, eqs. (2:10) and (2:11) can be combined to define the compressor capacity:
^i2o tr ^ G = >»'^-2.
Po
^
(2:12)
For very small and simple blowdown wind tunnels, an ordinary “filling may be used. These compressors are usually air cooled and very economical to purchase and maintain. As they wear station” air compressor
Design of Intermittent Blowdown Tunnels / lot
of
the possibility of
an
they
do put a
oil into
the air which
79
must be removed to eliminate
air-oil explosion.
Aftercoolers
2:10
An
aftercooler
is
usually provided to
remove the heat of compression
of air leaving the compressor. The aftercooler is a very simple device in which the hot air from the compressor is allowed to flow at low velocity
A
typical aftercooler conthrough or over water-cooled tubes or pipes. of large pipe, perhaps 25 to 50 diameters long, section straight of a sists
with several small pipes passing through the inside.
The
small pipes are
manifolded together at each end and provide an air flow passage. The cooling water enters at the air-exit end of the large pipe, flows through the large pipe
Fig.
2:4
pression
and over the small pipes that carry the
Maximum amount
air,
and leaves
at
of moisture remaining in atmospheric air after com-
and cooUng to mdscatod tomp^ratoTe flow piessuTe range).
80
I
High-Speed Wind Tunnel Testing
Maximum amount
Fig. 2:5
of moisture remaining in atmospheric air after
com-
pression and cooling to indicated temperature (high pressure range).
the air-inlet end of the large pipe.
would
come from
typically
The cooling water
for the aftercooler
the circuit that supplies cooling water to the
compressor.
Cooling the
air
several purposes.
and the
It
immediately after
it
leaves the compressors serves
reduces the temperature to a point where the
oil filter
2:11 and 2: 12) can be effective. It reduces the temperature of piping, valves, and other components between the comair drier (Sections
pressor and the air storage tank to a point where there
burns to personnel.
It eases
is
no danger of
the requirements on valves to the point where
regular commercial valves rather than high-temperature valves used.
and
It
reduces the volumetric flow rate and thus the size of
may be
oil filters
between the compressor and the storage tank. It also air, as illustrated by Figs. 2:4 and 2:5. If saturated atmospheric air at 70°F is compressed to 10 atmospheres and air driers
reduces the moisture content of the
Design of Intermittent Blowdown Tunnels
81
/
cooled back to 70°F, 90 per cent of the water will be condensed out. If the air is compressed to 3000 to 4000 psia and cooled, the moisture vapor content of the air will probably be reduced to levels satisfactory for highspeed tunnels without further drying. For more typical pressures, a drier
be required. In any event, a moisture separator to collect water and from which water may be drained should be installed downstream of the will
aftercooler.
Oil Filters
2:11
needed
Oil filters are
keeping
oil
in
most systems for the very obvious purpose of
with which the air comes in contact out of the system.
The
most important reason for keeping oil out of the compressed air systems Other reasons are that oil passing is the danger of air-oil explosions. through the air drier will rapidly reduce its effectiveness, and that oil may
on windows of the nozzle
collect
test section
and cause a deterioration of
the quality of photographs. Basically, the oil filter is
upon which the
oil
type often used in the air
is
a mechanical device that provides a great area
vapor can condense.
blowdown
tunnels
A
sketch of an
shown
is
oil filler
in Fig. 2:6.
of the
In such a
filter
forced to pass through a bed of desiccant (drying agent) in the
The granular form of the desiccant provides a large on which oil vapor can condense. The desiccant used in the oil filter will usually be the same as that in the air drier for convenience of facility operation. If a large filter settling chamber is provided, one pound of alumina can clean 3000 pounds of air. form of granules. surface area
Usually, a
commercial
one for the simple reason that considered.
The
filter is,
The
the compressor.
be used rather than a
oil filter will it is
more economical when design time
is
of course, sized according to the air flow from
desiccant in the
filler will
have to be removed and
cleaned with an oil solvent or replaced periodically because
when
homemade
it
will lose its
becomes covered with oil. This operation may be necessary every few weeks or only after several months, depending on the amount of oil in the air leaving the compressors. An oil filter of the type shown in Fig. 2:6 will serve as an effective moisture separator for collecting the water droplets condensed out by the aftercooler. Water will naturally collect in the cavity at the bottom of the effectiveness
filter
2:12
the surface of the granules
and can be drained
off.
Air Driers
Air driers for that operate
and the
blowdown wind tunnels
somewhere between the
are usually “high-pressure” driers
maximum
maximum compressor discharge
air storage
pressure.
tank pressure
Among the reasons
for
82
j
High-Speed Wind Tunnel Testing Compressed
air
to drier
Fig. 2 6 ;
Schematic drawing of oil
filter.
the operation of the drier at high pressure are that the size and consequently the cost of the drier are reduced because the volumetric flow of air
through the drier
blowdown tunnel
is
less,
and that the desiccant normally used
in
more water at higher pressure. Of the various possible methods for drying, the method usually used in blowdown wind tunnels is the adsorption method in which moisture is collected in condensed form on the surfaces of a desiccant. The desiccant used in driers will hold
Design of Intermittent Blowdown Tunnels
/
83
driers is almost always either silica gel, activated These desiccants are in the form of granules having alumina, or zirconia. an extremely porous structure. Moisture condensing on the outer surfaces of the granules is drawn into the pores of the granules by capillary action.
blowdown wind tunnel
The moisture trapped by the desiccant is removed in a “reactivation” cycle in which the granules are simply heated to temperatures about 100°F above the boiling temperature of water. The action of the desiccant is purely physical, no change in the shape, or appearance of the granules being noted as they
size,
become saturated.
The granules adsorb water vapor until the pores are filled to a point where the internal pressure of the adsorbed fluid in the pores at a given temperature approaches as a limit the partial pressure of the vapor in the surrounding atmosphere at the same temperature.
When
moisture
is
adsorbed by the desiccant, heat
is
liberated equivalent
of evaporation of the adsorbed liquid plus an additional amount of heat known as the heat of wetting, the sum of the two being
to the latent heat
known as the heat of adsorption. This heat is dissipated into the adsorbent, its container, and the dried air. The temperature rise in the dried air in a typical installation amounts to 10°F for each grain of moisture removed In a typical system this amounts to a temperature rise of from 15 to 30°F during one drying cycle. While some tunnel engineers use silica gel, it is believed that most use per cubic foot of air at atmospheric pressure.
activated required.
alumina unless the higher temperature capacity of zirconia
The
gel loses
some of
the alumina, while less efficient
a
drying capacity above 70°F, whereas
than at lower temperatures can
still
dry to
— 90°F while is at 100°F. Alumina is also less susceptible powdering. A comparison of pertinent characteristics of activated
dew point of
to
its
is
alumina and
silica gel is
it
given below. Activated
alumina Suggested moisture capacity, pounds of water per pound of desiccant
Silica gel
0.02
0.03
275°F
325°F
fiOO^F
dOO'-F
Specific heat, Btu/Ib-°F
0.21
0.22
Density for typical granule size, Ib/ft®
50
40
550.20
S0.40
Suggested temperature for reactivation
Maximum
temperature without
damage
Cost in small quantities, per pound
84
I
High-Speed Wind Tunnel Testing
may be determined when the following are dewpoint of the tunnel air, (b) the total amount to be passed through the drier between reactivation cycles, and (c)
The capacity of a specified:
of air
drier
(a) the desired
amount of moisture in the air entering the drier. The dewpoint required for condensation-free flow has been
the
1:10 and
in Section
Mach number
of the
is
readily obtained as a function of the
facility.
It is
discussed
maximum
sometimes suggested that regardless of
the dewpoint required for condensation-free flow, the drier should be
designed for a dewpoint of
and provides operating
The
— 40°F.
This
air suitable for higher
Mach number amount of
is
easily
and cheaply accomplished
Mach numbers
range of the
in the event that the
facility is increased in
the future.
be passed through the driers between reactivation cycles is, of course, dependent on the rate at which air is passed through the driers and the time between reactivation cycles. The rate at
which
total
air is
air to
passed through the drier depends only on the pumping
capacity of the compressor, since
through the
drier.
type of facility operation desired.
compressors
all air
The time between
will operate 8
leaving the compressor passes
reactivation cycles
If the facility
hours a day and be
is
is
defined by the
designed so that the
idle the
remaining 16 hours,
a drying cycle of at least 8 hours would be required, and the design would
As in all components, a margin for trouble should be included in drier design, and in the above type of operation it would be reasonable to design the drier for 16 hours between reactivation cycles. In the event that the reactivation cycle fails one night, it would still be possible to run the next day. A more versatile drier system is obtained by using “twin tower” driers, which are simply two driers arranged so that one drier is always being reactivated while the other drier is being used. With “twin tower” driers the operating cycle is defined by the time required for reactivation. As previously stated, the amount of moisture in the air leaving the aftercooler is essentially independent of the conditions of the air entering the compressor. If all the water condensed out of the air by the afterprovide for reactivation during the idle hours.
cooler
is trapped, then the moisture content of the air entering the drier dependent only on the pressure to which the air is compressed and the temperature to which it is cooled by the aftercooler (Figs. 2:4 and
is
2:5).
As an example of moisture-handling calculations, let us take a 500-cfm, 300-psia compressor handling atmospheric air at 80°F and 80 per cent relative humidity with an 8-hour cycle between reactivations and with an 80°F aftercooler. The atmospheric density is 0.075 Ib/fF, so that the air handled is 500 x 0.075 x 8 x 60 = 18,0001b. From Fig. 1 36 we find the :
Design of Intermittent Blowdown Tunnels
/
85
pound of dry compressor during a cycle is
moisture content of the atmospheric air to be 0.0176 lb per air,
so that the total moisture entering the
0.0176
X
=
18,000
drier design
but
317
0.0011
0.001
is
1
is
the drier at
is
not pertinent to the
compare with the moisture
Following aftercooling the water vapor content of
pound of dry air (Fig. 2:4), which 20 pounds of water entering the drier.
yields a total of
lb per
18,000 =
X
This amount of water
an interesting figure to
handled by the drier. the air
lb.
— 40°F dewpoint,
the moisture content
of that entering the drier, so that the drier
water during the cycle.
For
this
must
is
If the air leaves
than 10 per cent about 20 lb of
less
collect
20 lb of water to be collected by the drier,
would be reasonable to provide 700 lb of
silica gel (3 per cent moisture alumina (2 per cent moisture content) or, more typically, a commercial drier with a 20-lb water capacity at — 40°F dewpoint. If the — 40°F dewpoint is considerably below that for condensation-free flow at the highest tunnel Mach number, the above drier it
content) or 1000 lb of activated
capacity
is
quite adequate because the drier capacity
increased as the
is
dewpoint goes up. At a — 20°F dewpoint the drier can times as much moisture as a dewpoint of — 40°F.
blowdown tunnel engineer
Ordinarily, the air drier
is
hold about three
not called upon to design an
system. Instead he gives a commercial drier supplier information
Valve-open
for
drying, close during
reactivation
Wet
from
air
Atmospheric
aflercooler
air
from low pressure blower -Electrical
power
and cold water
for heating for cooling
the coil in desiccant bed
Valve for high pressure discharge before reactivation
—Cy"'—
-Desiccant
temperature monitor
_ From Air
coil in
desiccant bed
temperature monitor Dry
ait to
backReactivation
pressure valve and-er
air
to storage tank
Valve open for
Valve closed during
drying, closed
drying, open for
during reactivation
Fig. 2:7
discharge
reactivation
Schematic drawing of typical high pressure drier system.
86
I
High-Speed Wind Tunnel Testing
pertinent to the compressor, the aftercooler, and the drier use
ation cycles, and lets the supplier
A schematic drawing When
it
recommend a
of a typical drier system
becomes time to
and
reactiv-
system.
reactivate the drier, the
is
presented in Fig. 2:7.
two valves that are open
for drying air are closed, trapping pressure in the drier bed. This pressure is
released slowly through a small valve exhausting to the outside of the
building because rapid exhaust through a large valve could
damage
desiccant bed or the grate and screen supporting the desiccant. the pressure has been released, the
and a small blower turned on to
two reactivation
circulate
air valves are
room air through the bed
the
When opened
to carry
out moisture that will be released during the reactivation. This air is usually exhausted outside the building. At the same time, a low-voltage electrical
desiccant.
copper
power is supplied to coils of copper tubing embedded in the Over an extended period of time, electrical heating of the
coils will raise the
that will cause
bed
it
to give
will carry this
up
temperature of the desiccant to a temperature all its
water out.
water and the
When
air circulating
through the
the proper reactivation temperature
power to the coils is turned off, the reactivation and cooling water is circulated through the coils is embedded in the desiccant. This gradually removes the heat stored in the bed, and when the bed temperature is reduced to the neighborhood of 100°F, the reactivation cycle is complete and the bed is again ready for is
reached, the electrical
air
blower
turned
off,
use.
The major
from the schematic are method of heating the desiccant during the reactivation This may be accomplished by passing steam through the coils or deviations of existing drier systems
usually in the cycle.
by passing hot products of combustion directly through the bed. Driers are usually designed for an automatic reactivation cycle because it is not practical from an economic standpoint to provide a person to monitor each reactivation cycle. A reactivation cycle can usually be set up on a time basis, so that each step in the reactivation process takes place at a specified time relative to starting time. several interlocks required to prevent drier
When
this
damage
is
done there are
in the event that
something does not work properly. For example, the large reactivation must not be allowed to open until the pressure has been released through the small valve, and electrical power for heating coils must be valves
turned off if the desiccant temperature or the reactivation air discharge temperature exceeds prescribed values.
Like any type of mechanical apparatus, driers have their difficulties. In cases troubles may be located rapidly and corrected easily. Some
most
typical troubles
facing page.
and
their causes
and corrections are outlined on the
.
D esign of Intermittent
Blowdown Tunnels
Possible Causes
Difficulty
Dust passing through the
/
87
and Corrections
rapid blowoff of drier pressure causing
1.
Too
2
tumbling and rubbing of desiccant. Reduce size of blowoff line or add a constriction. Pulsing from compressor is tumbling desic-
tunnel
.
Add
cant.
a length of pipe for acoustic
damping. Poor dewpoints at
all
times
Aftercooler not working and air entering drier
1
too hot or too wet. Repair aftercooler. 2
.
Improper
Check
reactivation.
reactivation
cycle. 3.
Oil
filter full
of water and excessively moist
air entering drier. 4.
Drain
Desiccant covered with
oil filter.
oil.
Clean or replace
desiccant.
Besides the heat-regenerated driers described above, there is a drier
now
available that regenerates without
any heat.
It
new type of
uses two towers
and is arranged so that part of the air dried at high pressure in one tower expanded (and made still drier) and bled through the second tower to regenerate it. A switching circuit sends the air from tower to tower in is
2- to
4-minute cycles.
A
greatly reduced
wear on the drier material, and
new type of heatless
for the
2:13
it
at high pressure.
storage tank,
being used,
drier.
This
and the
is
was noted that
air driers are
Since air leaving the drier
which
will
is
almost always operated discharged into the air
always be below design pressure when the drier
some means
required to maintain a high pressure in the accomplished by a “back-pressure valve” between the drier
air storage
is
tank which
is
automatically adjusting to maintain a
The valve
is,
of the pressure in the air storage
of course, designed to be compatible in size with the
compressor capacity and pressure and 2:14
electric load, less
drier.
specified pressure in the drier regardless
tank.
maximum
maintenance are advantages claimed
Back-Pressure Valves
In Section 2: 12
is
less
is
obtained commercially.
Air Storage Tanks
The major aspects of deciding on the size of the air storage tanks are covered in Sections 2:5 to 2:8. It is sufficient to say at this point that their size
is dependent primarily on mass flows during a wind tunnel run and the frequency of runs desired.
Since a pressure regulator is used to reduce storage tank pressure to tunnel stagnation pressure, a choice will exist with respect to storage pressure selection if the available compressor discharge pressure is significantly
88
I
High-Speed Wind Tunnel Testing
above the
maximum
tunnel stagnation pressure.
It
turns out that the
about the same no smaller but requiring higher pressures matter what the pressure, the compresmargin of safety on offers a stronger tanks. High pressure standpoint from the of for starting the tunnel, advantages sion ratio has higher tunnel changes for Mach air, later drying the and makes possible numbers. On the other hand, from the standpoint of safety and minimum cost of storing a given
number of pounds of
air is
stagnation temperature drop during a run, low air storage pressure
is
advisable.
Pressure tanks are used by the call
them
“air receivers”)
shelf basis. In the smaller sizes (400 to
and may be mounted
and chemical industries (they
4000
ft^)
they are usually cylindrical,
either horizontally or vertically, depending
Spherical tanks frequently prove
space available. larger sizes,
gas,
oil,
and are hence usually available on an off-the-
and
in
some
less
on the
expensive for the
cases, especially for the highest storage pressures
(5000 psi or so), high-pressure pipe or oxygen containers are used.
The tank should be Installed with some sort of flexible joint between compressor and tank, and if installed horizontally, should be on a slight incline with the drain at the lowest point. There should be a lead-off pipe from the drain air blast will
valve, so that if draining
is
necessary under pressure, the
not strike the person operating the valve. The tank should
be painted black
in
by
However,
solar heating.
tank, say four or
order to attain the if
maximum
temperature produced
circumstances have resulted in a fairly long
more diameters,
it
may
well be worthwhile to forgo the
heating, by using a sunshade over the tank, rather than risk excessive tank
and inlet pipe bending. If the tank is outside and exposed to cold weather a commercial steam blanket will serve to keep it (and in turn the air in it) warm.
The tank should be equipped with a
safety disc that
is
designed to
fail
no greater than the design pressure of the tank. Such a safety disc, which can be obtained commercially, will fail and allow discharge of the tank pressure before the tank pressure can become at a pressure
dangerously high in the event of some malfunction.
The run
is
previously noted decrease in air stagnation temperature during a
due to expansion of the
air
remaining in the tanks to a lower
pressure as part of the air in the tanks
The expansion of the
air in the
tanks
is
is
removed
as the air temperature in the tank drops, heat
of the tank to the
The
to operate the tunnel.
not an adiabatic process because is
transferred
from the walls
result is a polytropic
expansion process with a value of n between 1.0 (for isothermal) and 1.4 (for adiabatic) in the air.
equation (2:13)
:
:
Design of Intermittent Blowdown Tunnels
where
T=
/
89
temperature, °R,
= pressure, Ib/ft^, = initial conditions in tank, f = final conditions in tank.
p
i
A
chart showing approximate values of n for typical conditions
The
is
tank stagnation temperatures after 1.2 expansion to lower pressures for an assumed expansion exponent n are presented in Fig. 2:8, where it may be seen that variations to about 2:2.
presented in Fig.
final
=
200°R are possible. This drop in stagnation temperature as the can become bothersome.
It affects
the
air leaves the storage
Mach number
tank
in the test section
boundary layer thickness, but it can gage readings significantly, and it does change the
only secondarily through a change in affect
balance strain
Reynolds number during a run.
Some
effort
is
therefore justified to see if
drop can be reduced or perhaps completely nullified. downstream of the tank could be designed to yield heater Obviously a essentially zero temperature drop, and such heaters are sometimes employed. However, a simpler method is to fill the tank with crumpled metal the temperature
or “tin” cans. air
As
the air temperature drops, heat
is
transmitted to the
is much reduced. The cheapest cans are dog food, but rimmed paint cans are worth the avoid can crushing. The design of a can installation may be
from the metal, and the drop
those intended to contain difference to
worked as follows
Compute
1.
amount of heat needed
the
to bring the air
=
1.2 up to the desired temperature. Pi to Pf with n obtain the final temperature.)
expanded from
(Use eq. (2:13) to
2. Select a can size and determine how many can be put (Assume a packing factor of from 60 to 75 per cent.*) 3. From the specific heat of the metal of the cans and the
of the cans, determine the final can temperature
if
in the tank.
total
the required
weight
number of
Btu’s are removed.
From
number of Btu’s, the can surface area, the run and the heat transfer coefficient (assumed equal to 0.01 Btu/ft-sec-°R), compute the difference between can and air temperature needed 4.
the required
time,
to effect the necessary heat transfer.
The example below
will serve to illustrate the
method.
Example 2:3 Compute the final air temperature for the conditions described below if cans are installed in the air storage tank tank volume 400 initial
final *
ft®
pressure 150 psia
initial air
temperature 520°R
run time 30 sec
pressure 50 psia
Some may have
to be crushed to get this
many
in.
90
I
High-Speed Wind Tunnel Testing y„ ‘9jn}Ejaduis; UOIJBUSbJS
|BI}]U|
600
n
assuming
tank
Pf P, storage
pressure
pressure
a in
tank
Fmal
tank
tnitial
temperatures
Final
2:8
Fig.
‘^'l
=
ti
JO} ajn}ejaduj9}
U0HBu3e}S
>(UB} |BUIJ
Design of Intermittent Blowdown Tunnels 1.
From
the gas law the initial air density
weight of air 2.
From
is
hence 311
is
91
/
0.778 Ib/fF and the initial
lb.
temperature would be 433°R with n
eq. (2; 13), the final
=
1.2.
The average temperature of the air leaving the tank would be 477°R. 3. If it is assumed that the cans permit no temperature drop, the final air density is 0.260 Ib/ft®, and the final weight is 104 lb. 4. Using a specific heat of air of 0.24, we find that the heat needed by the air will be
Btu
=
-
0.24(311
104)(520
-
477)
=
2140
Assuming a can 3 inches in diameter and 4i inches long with an 0.013-inch wall (a commercial dog food can), we find that the surface area is 0.688 fU, the nominal volume is 0.0184 fU, the metal volume is 0.000373 5.
ft®
and the weight 6.
is
0.18 lb.
The maximum number of cans that can
actually be put in the tank,
=
16,300.
letting the heat
needed
8.
assuming a packing factor of 0.75, will be (400)(0.75)/(0.0184) Their weight will be 2940 lb and their surface 7.
The
by the
final
air
temperature of the cans
is
1
1,200
found by
ft®.
equal the heat taken from the cans and using 0.11 as the specific
heat of iron:
= 0.11(2940)(520 520 - To = 6.6°R Fa = 513.4°R
2140
Jo)
The next step is to find out how much temperature difference between and the air is needed to develop the desired heating rate:
the cans
2140
T=
0.6°R
(0.01)(11,200)(30) 9.
Thus, as the cans cool
temperature very closely. perature 10.
tank
is
513.4
—
0.6
=
off,
The
the air temperature follows the can
first
approximation of the
final air
tem-
512.8°R.
Recalculating using 512.8°R as an end temperature of air in the is
not
justified, since the
accuracy of the heat transfer coefficient
is
not that good.
The tank will be hydraulically pressure tested by the manufacturer, sometimes being supported during the process by being set in sand. Accordingly, should the need for retesting the tank arise because of age or the welding of additional fittings, a stress check should be made before filling it with water in the customary mounting saddle. Some tanks will
be broken
when loaded under such conditions. The very high pressure tanks have no such problem, since the density of air in the 5000-psi range approaches that of water.
92
High-Speed Wind Tunnel Testing
/
Fig. 2:9
The
effect
of solar heating during the hydrostatic pressure check of an air
storage tank.
A problem to watch while checking for leaks and strength is the pressure increase due to solar heating
such
test are
if
the tank
presented in Fig. 2:9, where
is
outside.
it is
The data from one
seen that the tank pressure
increased by 75 psi as the tank walls, heated by the sun, transmitted their heat to the water inside. This process, to the uninitiated, is a baffling thing,
and many a student,
back with clipboard
sitting
tank leakage rate has been
in
terrified to see the pressure
down. The senior author had one such lad back off head, and exclaim “I’ve got a negative leak!” 2:15
in
awe, shake his
Pressure Regulators
Blowdown wind
tunnels are almost invariably designed for operation
at a constant stagnation pressure during any run. is
hand to record a go up instead of
The
pressure regulator
a special valve used to provide a constant wind tunnel stagnation
pressure while the available pressure in the storage tank
is
decreasing.
theory, almost any valve could be used for this purpose.
however, valves not designed for
this
air passes varies fairly
purpose make very poor regulators.
a valve in which the opening through uniformly with valve position from fully
Basically, the pressure regulator
which the
In
In practice,
is
Fully open, the flow area through the valve should be approximately equal to that of the pipe supplying air to the valve. If the flow area through the valve is less than that of the lead-in pipe, higher storage tank pressures will be required to maintain a given tunnel stagnation pressure and tunnel run times will be reduced. closed to fully open.
Design of Intermittent Blowdown
Tiinrieis
/
93
Operating
A
schematic diagram illustrating the design principle of a pressure
control valve
is
presented in Fig. 2; 10.
In the design, the flow opening
is
by gradually moving two spherical plugs out of their seats. Two plugs are used instead of one to increase the flow area through the valve. The plug-seat configuration of pressure control valves may vary considerably from that of Fig. 2: 10. However, the basic idea of lifting a plug
varied
out of
its
seat to vary the flow area
figure, regulator
is
very
common. As
illustrated in the
valves are often operated by applying pressure to
side of a bellows to
overcome the tension of a spring which
is
one
designed to
keep the valve closed. Pressure control systems can have almost any degree of sophistication is willing to pay for. With control valves similar to those of Fig. 2:10, satisfactory pressure control can be obtained manually by
that the designer
an experienced operator. In this case a pressure regulator valve to apply operating force to the valve
and a pressure gage
for the operator to
watch
94
High-Speed Wind Tunnel Testing
j
would be the only requirements. The other extreme of control system sophistication would be one in which the difference between desired and actual stagnation pressure is sensed, an electric signal proportional to this difference is fed into an analog computer, the computer continuously calculates regulator valve corrections from considerations of both difference between the desired and actual pressure and its rate of change, and a signal from the computer is continuously supplied to a device that regulates the pressure to the valve operator to
make
corrections to valve
position. With this type of control system working properly, stagnation per cent. pressures may be controlled to within \ of The regulator causes a drop in pressure and thus controls the downstream pressure by means of a throttling process. With the regulator valve only partially open the velocity in the constricted area of the valve is greater than in the pipe leading to the valve, and may vary anywhere from the velocity in the lead-in pipe to sonic, depending on the pressure drop across the valve, which is in turn dependent on mass flow rate and valve position. If the pressure drop across the valve is 47 per cent or greater (see Table 1 1) the flow through the constriction will be sonic. As the flow through the constriction fills the pipe downstream of the valve, it is at a lower total pressure and a higher velocity than in the pipe 1
;
entering the valve (assuming the
same pipe
size).
It
may be
at a higher or
a lower stagnation temperature than the entering airstream, depending on its initial
and
is
conditions. Throttled flow
a constant-enthalpy process.
is
known
as
“Joule-Thomson”
However because of
flow,
the changes in
the coefficients of specific heat at constant pressure with temperature pressure, the stagnation temperature of the stream throttling occurs.
The phenomenon
is
rise
and
or fall as
such that for low pressure storage,
say around 300 psia, regulated to around 50 psia there
is
a loss of a few tens
For very high pressure storage, moderately
of degrees Fahrenheit. throttled, there
may
may be
a small
rise
in stagnation temperature.
(See
Fig. 2:11.)
Regulator valves are used in various ways in wind tunnel operation. tunnels are started by quickly opening the regulator valve and then
Some
adjusting
its
position either manually or automatically to maintain a
constant stagnation pressure. in series with
and used
Some
tunnels have a quick-opening valve
in conjunction
tunnels the regulator valve
is
with the regulator valve. In these
pre-set to the approximate position required
The tunnel is quickly started by operating the quick-opening valve and then the regulator valve takes over the control. In large tunnels, where it is necessary to conserve air, regulator valves have been used in for the run.
still
another way. In such tunnels, the operation of the regulator valve is so that it is quickly opened to provide the pressure required
programmed
Design of Intermittent Blowdown Tunnels
/
95
The change of temperature with throttling. Curves a,b,c,an6 d are isenand show that in general the temperature falls during throttling. For very high pressures moderately throttled (points to the right of the dashed maxima line) there may be a small rise in temperature.
Fig. 2:11
thalpy lines
to start the tunnel, held in this position for starting, closed
pressure ratio,
down
2 or 3 seconds to allow tunnel
to a position needed to provide a
minimum operating
and then allowed to control the pressure
at this value
during the run. Pressure regulators should be fail-safe so that loss of operating air
cannot permit the opening to increase and throw storage pressure into the
wind tunnel. However, even those “fail-safe” regulators, after being put into operation,
can sometimes be made to flop suddenly open
if
not used
properly.
One
fault with
some regulators
fluctuation (“noise”)
that they seem to put a high-speed
into the airstream.
authors this fluctuation has been total
is
In instances
known
to the
from
^ of 1 per cent to 3 per cent of the head in magnitude and with a frequency of 500 to 700 cps. This
oscillation
must be
in total head, since
it
represents as
much
as 200 per
96
High-Speed Vilnd Turznel Testing
/
cent of the dynamic pressure, but methods of alleviating
Another difnculw with some
obscure.
it
are as yet
regulators concerns the asNin-
when the regulator is at a very small opening. regulators are made which combine the duties of gate valves
metrical fiovr created
Pressure
(sealing), butterfly valves (fast-opening),
operated hydraulically, pneumatically,
and
regulators.
electrically,
These
may be
or manually, and give
good control with fast action. Even if such a regulator valve
is used, however, it is highly desirable to have a quick-operating valve in series with it which can be used as a backup valve in the event of regulator vah e failure. The selection of a pressure regulator for a blowdown wind tunnel can sometimes be difncult. If the Mach number range of the tunnel is wide, the range of operating pressures and mass Sows will also be wide. It is
difncult to obtain a single regulator valve that will give satisfactoiy pressure
control over a wide range of operating pressures and nows.
2:16
Piping and Valves
The
and valves increases rapidly with diameter
cost of piping
given pressure), and hence there
diameter possible.
To
is
(for
a
a natural tendency to use the smallest
avoid objectionable whistling and pressure losses,
the piping should be selected so that, at the ma.vimum mass flow (usually at the lowest operating
Mach number of the
the pipe will be below 0.4.
between the
air storage
calculated because
may
drop
result in
if
The
used
in
is
marginal, this pressure
a significant reduction in available run time. 15.
some
tunnels have a quick-opening
valve in series with the regulator valve that operation.
Mach number
tank and the pressure regulator valve should be
the air storage capacitv'
mentioned in Section 2:
-As
tunnel), the
pressure drop in the piping and valves
In the event that such a valve
is
is
used in normal tunnel
not used or that the valve
not a tight shutoff tnive. another val\ e will usually be required in with the regulator to provide a tight shutoff and to double as a valve. The tight shutoff is required to prevent leakage of high-
is
series safets’
pressure air from the storage tanks through the tunnel.
In addition to
and a draft of air through the tunnel which makes model changes immeasurablv
coriserving air. the tight shutoff valve eliminates an annoting whistle
more
difficult.
In view of the need for at least one valve in series with the regulator valve as well as the need for
blowdown tunneL some of
many the
valves in the various subsvsiems of the
more common
tspes of valves will be
discussed briefly: I.
Butterfly valve.
which
is
This valve consists of a disc in the flow passage
rotated about an avis through
its
center.
The
disc
is
aligned with
Design of Intermittent Blowdown Tunnels
when
the flow
the valve
when the valve
is
is
open and
is
97
essentially perpendicular to the flow
Butterfly valves
closed.
/
can be operated quickly because
90' deg of rotation of the valve stem changes the valve from fully closed to fully open. They are normally not tight shutoff valves but can be
obtained with an inflatable sealing ring to provide tight shutoff for
some
applications.
Gate valve.
2.
This valve
essentially
is
across the flow passage of the pipe.
one on which a plate
is slid
In the closed position, sealing surfaces
on the plate and on the valve body are forced into intimate contact by the pressure difference. The gate valve is not normally a quick-operating valve because of relatively large friction forces developed is
when
the valve
and the pressure load holding the sealing surfaces together. Plug valves consist of either a cylindrical or a conical a seat with a hole through the plug equal to the inside diameter of
closed
Plug valve.
3.
plug in
For operation the plug is rotated 90 deg, so that the hole in the Plug valves are quick-operating and tightconical plug has an advantage in severe flow environsealing valves. The ments in that it can be lifted out of its seat slightly, rotated, and then
the pipe.
plug
is
aligned with the pipe.
reseated, thus
minimizing the torque required for operation. Ball valves consist of a sphere with a
Ball valve.
4.
to the inside
diameter of the pipe.
outlet flow passages in the valve
and provide a very good
through hole equal
Teflon rings around the inlet and
body maintain
the proper ball position
These valves are quick-operating
seal.
in that
90 deg of ball rotation opens or closes the valve.
Wide-Angle Diffusers
2:17
known
many years that the uniformity of flow in a wind improved if a large-area, low-velocity section is provided immediately upstream of the nozzle, so that a large contraction It
has been
for
tunnel can be greatly
of the flow
is
section
termed the “settling chamber.”
is
previously,
provided as
it is
desirable
it
enters the nozzle. This large-area, low-velocity
As we have pointed out
from an economic standpoint to use the smallest from the storage tank to the tunnel proper
practical pipe size to deliver air
and
this
small pipe size corresponds to high flow velocities.
device in
decelerated to a low-velocity flow, Relatively
A diffuser is
which high-velocity flow, such as that in the small piping, long,
a is
such as that in the settling chamber.
shallow-angle diffusers have been tried between the
piping and the settling
chamber as a means of recovering the dynamic pressure in the piping while reducing the flow velocity. As far as the writers IS
know, these have not been successful. Among the possible reasons and unsymmetrical flow leaving the pressure regulator valve
a turbulent
which
persists into the settling
chamber and consequently
into the nozzle.
98
I
High-Speed Wind Tunnel Testing
(c)
Fig.
2:12
Type of
(6) Drilled plate,
Blowdown
id)
flow-spreaders,
(a) Perforated can, perforated plate
flow control screens,
(c) Full
perforated cone,
and
screens.
(d) Reverse entry.
tunnel designers typically use wide-angle diffusers for the
from the pipe to the settling chamber. Commonly included angles between opposite walls are 45 to 90 deg. Because of the highly turbulent and non-uniform flow usually existing at the diffuser inlet, various devices are used to spread the flow from the inlet pipe to the settling chamber. There are almost as many spreader designs as there are tunnels. transition
A
few typical spreaders are illustrated in Fig. 2:12.
Many
failures of
spreaders similar to those of Fig. 2:12a and 2:12b have occurred and these are attributed primarily to the high-pressure-drop design of the perforated
can or plate in the small-diameter section. is
illustrated in Fig. 2:12c.
The
A recommended configuration
perforated cone facing upstream from the
chamber allows ample perforations for a low-pressure-drop design and has been found to spread the flow satisfactorily. The perforations settling
should be designed with a flow area sufficient to keep the average velocity through the perforations well below Mach 0.5 at the most severe operating conditions. This point should not be disregarded. In one tunnel using a perforated plate spreader with J-inch holes and insufficient flow area, the blast out of the holes
was strong enough to tear out a welded screen four The perforations should be positioned in the
inches from the hole exit.
Design of Intermittent Blowdown Tunnels
/
99
cone to provide a uniform distribution of flow area over the duct. The spreader should be of rugged construction because it will be probably subjected to shock loads during starting and stopping of the tunnel in addition to pulsations
from the control
valve.
An
estimate of pressure
drop through the spreader should be made because this could have a typical design significant effect on the tunnel run time in some cases.
A
value
is 1.0^'^,
The
2:18
where
Settling
is
dynamic pressure
the
in the inlet pipe.
Chamber
The settling chamber is usually a cylindrical shell, one diameter or more long, which accepts the air from the wide-angle diffuser, provides a length for settling to obtain uniform flow, provides screens for promoting uniformity of flow and for reducing turbulence in the air stream, and then exhausts into the subsonic portion (inlet) of the nozzle.
The
chamber is higher than at any downHowever, it is normally considerably below
pressure in the settling
static
stream point in the tunnel.
that in the storage tanks or in the piping to the pressure regulator. it is
economical, the settling
tunnel are usually designed for their the tank pressure.
settling
Because there
is
normal operating pressures rather than usually the possibility of a malfunction
component which could
of a tunnel
Because
chamber and downstream portions of the
result in excessive pressures in the
chamber, such as the pressure regulator’s suddenly being fully
opened with
maximum
pressure in the air storage tanks, the settling
chamber normally contains a blowoff stack extending through the roof
The blowoff stack
is equipped with a commercially availblowout diaphragm) rated to fail before an unsafe pressure is reached in the settling chamber. The exhaust stack and safety disc should be sized so that adequate flow passages are available to prevent
of the building.
able “safety disc” (or
chamber in the case of the worst conceivable emphasized that the “worst conceivable malfunction” does not correspond to the most severe condition expected during normal over-pressurizing the settling
malfunction.
operation.
It is
diffuser will
it will be found that a blowoff stack and a safety disc comparable to that of the pipe entering the wide-angle
Often,
with a flow area
be adequate.
should be noted that blowout diaphragms
come in two types, those and those internally supported against vacuum failure, but designed for outward over-pressure blowout. The onedirectional types are not satisfactory for blowdown tunnels, since sudden It
for one-directional loads
shutdowns can result in subatmospheric tunnel pressures as the
momentum
of the tunnel air carries it outside, dropping the tunnel pressure below ambient. The loss of diaphragm strength with temperature is shown in Fig. 2:13.
If the flow spreader in the
wide-angle diffuser
is
properly
100
High-Speed Wind Tunnel Testing
I
Air temperature, °F
Fig. 2:13
Loss of strength with temperature for blowout diaphragms.
chamber with a fairly uniform distrimost spreader the air enters through perforations and bution. In designs a finite distance will be required for the individual jets of air from the individual perforations to coalesce to form a uniform flow. However, turbulence of the flow emanating from the control value or elsewhere will not be removed by the spreader. In fact, additional turbulence is almost certain to be induced by a perforated spreader. The turbulence level of air in low-speed wind tunnels is extremely important because the point on a model at which a boundary layer has a transition from laminar to turbulent is related to the turbulence level. The aerodynamic drag of a model at low' speeds is greatly influenced by designed, air will enter the settling
this
point of transition.
The importance of turbulence
level
is
generally
considered to decrease as the wind tunnel speed increases into the transonic
and supersonic range.
At
these speeds the
model drag
is
primarily a
function of pressure distribution and the effects of boundary layer tranNevertheless, most high-speed wind tunnels are designed with screens in the settling chamber to promote flow uniformity
sition are secondary.
and
to reduce the turbulence level before the air
is expanded through the Experiments to determine the turbulence damping accomplished by screens in low-velocity flows have been reported in Ref. 2:1. Results
nozzle.
Design of Intermittent Blowdown Tunnels
j
101
Solidity, s
Fig.
2:14
Pressure drop through screens.
of these experiments indicated that the reduction in turbulence level function of the pressure
=
1
Vl
~ root mean square of velocity = Cl mean flow velocity, ft/sec,
fluctuation, ft/sec.
u'jU (with screen)
__
’
“
A/7
(2:14)
+K
u'
p
a
drop through the screen:
/..
where
is
u'jU (without screen)
= =
air density, slugs/ft^,
pressure drop through a screen
=K
•
IpU^.
Values of the screen pressure-drop coefficient as a function of Reynolds
number and
solidity (ratio of area
area) are presented in Fig. 2: 14.
screens are presented in
blocked by wires of screen to total duct
Values of solidity and wire size for various
Table 2:1.
It is
noted
in Ref. 2:
1
that at large
may be caused by screens and it is recommended that several low-pressure-drop screens are preferable to a single high-pressure-drop screen. This is the practice normally followed in blowdown tunnel design. pressure-drop coefficients, turbulence
A characteristic of flow in wind tunnels fluctuations in the settling
the expansion of air
is
that the magnitude of velocity
chamber will remain essentially constant during through the nozzle. The result is that the turbulence
102
High-Speed Wind Tunnel Testing
I
Table 2:1 Values of Solidity s for a
level
u'lU
is
Screen Meshes
Wire
Solidity
per Inch
Diameter
s
22 30 40 50
0.0075
0.303
0.0065
0.352
0.0065
0.452
0.0055
0.474
much lower
in the settling
Number of Screens
in the test section
of a high-speed tunnel than
it is
chamber.
The concensus of wind tunnel engineers
is
that settling
chambers should
be designed for flow velocities no greater than 80 to 100 feet per second. If possible, the lowest velocity in the settling
than about 10
feet per second.
A
low
limit
chamber should be no less on velocity is desirable to
prevent convection currents from causing a non-uniform temperature distribution that section.
would
significant differences
and the walls of the tunnels.
persist
from the
settling
chamber through the
test
Convection currents can become a problem any time there are
If the air
between the air temperature in the settling chamber chamber, which is not unusual in blowdown
settling
is
hotter than the walls, the air adjacent to the walls
be cooled. This cool air near the walls will have a tendency to drift toward the lower portion of the duct. If the flow velocity through the duct will
is
small, there will be
ample time for a temperature gradient to be
before the air leaves the settling chamber. This problem in high-temperature air
blowdown
Mach number
set
up
very Important
tunnels, but has been noted in tunnels with
temperature of about 200°F.
for a fairly large
is
It usually
shows up
range. If a tunnel
is
in tunnels designed
designed for a settling
chamber flow velocity of 100 feet per second at Mach 1.0 and is operated with the same size test section at a Mach number of 5.0, the settling chamber velocity at Mach 5.0 will be only 4 feet per second. An ideal solution for this problem has not been worked out. Possible solutions are the use of more than one settling chamber or the use of an air bleed system to maintain reasonable settling chamber velocities at the higher
Mach numbers. The
settling
access to will
its
chamber should be designed for easy removal or for easy some maintenance. It
interior, since the screens will require
have a provision for a connection to a pressure-measuring instrument.
Normally this will need to be only a static pressure port because the velocity head will be negligible. If the tunnel is to have an automatic pressure
Design of Intermittent Blowdown Tunnels control system, a second pressure port will
/
103
be required for obtaining a
process pressure to be used by the control system. The settling chamber should also have a provision for measuring total air temperatures. Pressure
and temperature measurements should, of course, be
made downstream
of the screens.
The settling chamber and wide-angle diffuser should be designed according to pressure vessel code and should have a hydraulic pressure check at 150 per cent of the design pressure. The pressure check will require blind flanges for the ends of the individual components or of the assembly. It will also require fittings for filling with water and bleeding off air. Nozzles
2:19
Blowdown wind tunnel nozzles depending on whether the tunnel
is
will
be designed
quite
differently,
to operate at transonic speeds, super-
The entrance section for a transonic nozzle is usually designed to give a smooth variation of Mach number with -distance between the settling chamber and the minimum section of the nozzle. Typical lengths for the entrance section are one or two test section heights. Downstream of the minimum, the nozzle usually has rectangular sections with parallel side walls and with flat top and bottom walls having provisions for being varied from parallel to perhaps ±2 deg. The walls of the nozzle are vented from a point downstream of the minimum to the end of the rectangular section by means of slots or numerous holes either straight through the walls or inclined in a downstream direction, going sonic speeds, or both.
from inside to outside the nozzle. Typical hole diameters in perforated nozzles are
Work on
about equal to the wall thickness.
wind tunnels was pioNASA. The primary purpose of venting the nozzle walls is to minimize their effects on the air flow over the model. At transonic speeds (high subsonic and low supersonic), shocks and expansion waves developing in the vicinity of the model will be nearly ventilated test sections for transonic
neered by Wright of the
normal to the flow. If shocks are allowed to strike a solid wall, they will and strike the model, causing a flow over the model much different from that required to obtain data applicable to flight. If shocks are allowed reflect
to strike a free air
and
will
boundary, they
will
be reflected as expansion waves
again strike the model, causing bad data.
The ventilated walls, being partly open and partly closed, are designed to minimize the effects of reflections
A
of shock waves and similarly, of expansion waves. second purpose of venting the walls is to generate a low supersonic Mach number. In Chapter 1 it was noted that the generation of supersonic flows in nozzles requires a
convergence to a minimum area cross section and then a divergence to a larger area, with a specified area distribution required for
104
/
High-Speed Wind Tunnel Testing
each individual Mach number. For tests in the transonic speed range, data are normally required at small Mach number intervals. This would require a large number of solid wall nozzles. However, by taking advantage of the ventilated walls, one can use a single nozzle to generate an almost unlimited number of low supersonic Mach numbers. To do this, the pressure outside the nozzle is reduced to a value near the static pressure
Mach number and total pressure. In the portion upstream of the vents, the Mach number is 1.0 and the static of the nozzle above that outside the nozzle. When this higher-pressure air pressure is vented section the nozzle, a flow to the lower pressure outthe of reaches through the vents continues until the nozzle begins. This flow side the at the desired operating
pressure inside the nozzle becomes almost equal to that outside the nozzle.
When this point is reached the air in the nozzle is flowing at the desired Mach number. Thus, the flow out through the vented walls gives the same end
result as flow in a diverging solid wall nozzle.
Ventilations of the tunnel wall illustrated in Fig. 2:15.
is
usually accomplished in the
The gradual
manner
increase of the slot or hole area
allows a more gradual expansion of the nozzle flow to the desired Mach number and minimizes the likelihood of overexpansion with consequent
nonuniform flow in the test section. The ratio of open area to total wall area will typically be between about 16 and 30 per cent. With the smaller percentages of open area it will be more difficult to generate the higher transonic Mach numbers because the pressure drop through the ventilated area will be higher. No configuration for the vents has been found completely satisfactory from the standpoint of canceling both compression and expansion waves from the model. From published test results it appears that the best shock and expansion wave cancellation has been achieved with circular holes slanted 60 deg from a normal to the wall in a direction to encourage outward flow. The slanted holes provide cancellation of shock waves comparable to that of normal holes but do a better job of canceling expansion waves. The reader is referred to Refs. 2:2 and 2:3 for a bibliography of work on ventilated walls for transonic test sections.
Whether or not the previously mentioned variable-angle walls are used appears dependent to a large extent on the particular tunnel. They have been used to improve the test section flow or to improve the disturbance cancellation properties of the nozzles under specific operating conditions. is enclosed in a plenum chamber and one of two used for reducing the pressure outside the nozzle (in the plenum chamber) Fig. 2:16. The most commonly used method is that of variableangle flaps hinged on the diffuser walls and extending forward to the
Generally the nozzle
means
is
downstream end of the perforated
walls.
The
diffuser
is
somewhat
larger
Design of Intermittent Blowdown Tunnels
"
Mmpr on, c speed a super from air enterirlT
reduciU?
/
105
the test section at
expands
to.
a higher
Mach number and
lower pressure Rotation of the forward end of the flaps away centerline provides a gap through which the low-pressure the plenum chamber, thus
sometiiefo",
S
The second method of controlling pressure
in the test section
is
with an
106
High-Speed Wind Tunnel Testing
/
To
auxiliary suction
or atmosphere
Fig.
auxiliary
2:16
Arrangement of devices to
alter flow
through ventilation.
pumping system or by directly exhausting the plenum chamber When the plenum chamber is directly vented to the
to the atmosphere.
atmosphere, an excess of operating pressure is required in order to raise and consequently the plenum pressure to the
the test section static pressure
point where air will flow from the plenum to atmosphere.
noted that auxiliary suction
It is
is
more commonly a
continuous tunnels than blowdown tunnels.
part of large
In large tunnels with in-
adequate power for the desired operating Mach number, auxiliary suction with a relatively small pumping system is usually an economical means of increasing tunnel performance.
Some
transonic tunnels use a choke for subsonic operation.
Such a
sometimes a variable diffuser and sometimes a special diffuser design with a center body which can be moved to vary the diffuser minimum cross section. At a constant supply pressure, the choke can be used to vary the Mach number in the test section because it forms a sonic
choke
is
second throat.
The choke may
also be used to operate with increased
tunnel stagnation pressure and consequently Reynolds
number
if it is
used
in conjunction with plenum chamber exhaust.
Operation at subsonic speeds does not require flow out through the ventilated walls of the test section. Consequently it is not necessary to reduce the pressure in the plenum chamber below that in the test section.
This
is
fortunate because with subsonic flow, the air
is
compressed in
passing from the nozzle into the diffuser and this compression has a
tendency to increase the pressure in the plenum chamber above that in the nozzle.
Some
transonic tunnels are operated at subsonic and super-
same flap setting. When this type of operation is from the plenum chamber into the nozzle, causing a thickening of the boundary layer but apparently having no adverse effects on the test section flow.
sonic speeds with the used, air flows
Design of Intermittent Blowdown Tunnels
A point of importance with flaps.
Positive
regard to safety
means should be provided
is
j
107
the design of the diffuser
to ensure that the flaps will not
it could easily cause an disastrous results. A safety chamber with overpressure in the plenum disc is an excellent idea if there is any conceivable way for high pressures to be developed in the plenum chamber.
come loose and block the
If they did,
diffuser.
The aerodynamic design of supersonic nozzles has been discussed in Chapter
1.
mechanbecome an important factor. The cost
In translating the calculated nozzle coordinates into a
ical design the allowable tolerances
of a nozzle will increase rapidly with decreasing tolerances on the nozzle contours. Experience has shown that a low tolerance on the actual is of considerably less importance than low and continuity of curvature downstream of smoothness tolerances on Small supersonic nozzles with the initial expansion at the throat. tolerances of 0.002 to 0.005 inch or even more may be expected to yield satisfactory flow if the contour is smooth and has a continuous cur-
coordinates of a nozzle
vature.
Nozzles for supersonic
blowdown
ing to one of four basic designs.
tunnels will generally be built accord-
(It is
noted that only two-dimensional
inasmuch as axially symmetric nozzles are not commonly used in blowdown tunnels.) The first basic design is one in which the two side walls and the two contoured walls are fabricated into a rigid semi-permanent assembly and are inserted into the tunnel circuit as a piece of pipe would be with bolted flanges or with some other positive coupling device. Another basic design is one in which one side wall of the nozzle is a fixed part of the tunnel circuit. The other side wall and the two contoured walls are fabricated into a rigid semi-permanent assembly. This assembly is installed by placing it against the fixed side wall, using a positive coupling to attach it to the side wall, and then using positive coupling to the tunnel circuit at the upstream and downstream end. Another basic design is one in which a rectangular channel with a removable side wall is a fixed part of the tunnel circuit. The two contoured walls of the nozzle are secured in place in the channel and the movable side wall is then positively clamped to the channel. The last and by far the most complicated nozzle design is one in which the contoured walls of nozzles are considered
the tunnel are flexible plates (Fig. 2:17). Screw-type jacks are attached to the outer surfaces of the flexible plates and the nozzle contour is adjusted to that for the desired
Mach number by use of the jacks. The flexible wall nozzle has advantages over the fixed wall nozzles in that Mach number can be set at any desired value in the operating range. theoretical
than
real, since
few
flexible nozzles
This point is more have been arranged for
more than a reasonable number of customarily used
Mach
numbers.
Fig.
A
2:17
flexible
plate
nozzle.
(Courtesty Arnold
Engineering Development
Center.)
However it
is
distribution,
quite possible to miss developing the desired
and
this
omission
may
easily
Moreover, any nozzle
laborious recontouring by using flexible plates.
contour
is
right for only
small corrections to be
Problems of using
one Reynolds number;
made
Mach number
be corrected without a lot of flexible plates enable
simply.
flexible wall nozzles include the extra cost
of their
construction and maintenance, and the difficulty of sealing the flexible plates
where they contact the
flat walls.
This problem exists to a lesser
degree with any built-up nozzle.
With the exception of the
flexible wall nozzle, the material
construction of the contoured walls
work can go
into the nozzle
aluminum, and
When speeds,
steel all
a nozzle it
is
work
is
and how well
and
used for
how much last. Wood,
selected according to
long last
it is
expected to
according to their strength.
designed for use at both transonic and supersonic
will typically
be designed as the transonic nozzle previously
discussed with provisions for inserting contoured blocks in the upstream
portion of the nozzle. These blocks form the converging-diverging portion
of the nozzle and the test section of the transonic nozzle
A photograph
is
not changed.
of a transonic nozzle with contoured blocks for
Mach
3.0
Design of Intermittent Blowdown Tunnels operation
is
109
The ventilated walls of the test section adverse effects on the flow in the test section but
presented in Fig. 1:19.
have no large
generally
/
may have an adverse
on the pressure
effect
ratio required for operation.
The Test Section
2:20
The primary consideration in the design of a test section is to ensure that model length will not be limited by the length of the uniform flow portion of the nozzle. It is necessary in transonic tunnels to keep model sizes
such that cross-sectional areas will not exceed
section area in order to minimize wall interference
1
per cent of the test
effects.
For a
cylin-
would mean that the model and therefineness ratio length for a (length to diameter) model 9 model fore that the should not exceed one test section height. The aft end of the model should be at least 4 or 5 model diameters into the uniform flow region of the nozzle to minimize the effects of disturbances from the end of the nozzle on the wake behind the model and possibly on the flow over the model. drical
model
in
a square
test section, this
diameter should not exceed one-ninth of the test section height,
Thus, a test section length of for testing fineness ratio
1
.5 test
section heights should be adequate
9 models. If tests of higher fineness ratio models
are anticipated, the test section length
In supersonic tunnels the
should be increased accordingly.
model length
bow shock waves from the tunnel determining allowable model lengths of
will be limited
walls. is
An
by the reflections
exact procedure for
not available.
However, by
making a few approximations, reasonable estimations of model lengths
up as illustrated in Fig. 2:18. The bow assumed to be reflected from a plane located a distance equal
can be made. shocks are to the
The problem
is
set
boundary layer displacement thickness inside the tunnel wall.
Although
it is
layer rather
certain that the
bow wave
will
be reflected by the boundary
than the tunnel wall, the point in the boundary layer at which
take place cannot be specified. Although it would more conservative to assume reflection at the surface of the boundary layer, it is reasonable to assume reflection from a plane equal to the disreflection will actually
be
away from the wall. The angle of the bow shock on a cone at an angle of attack cannot be readily determined. The assumption placement thickness that this angle is
wave angle on a cone at zero angle of moderate angles of attack (to between 5 and 10 deg). As the distance away from the cone apex increases, the bow shock will begin to curve toward the Mach angle, making the calculation conservative. The allowable proximity of the reflected shock to the base of the model depends to a large extent on the model configuration. For the model shown in Fig. 2:18, if the shock passes the model base 1.5 diameters from the model centerline, the only effect will be on the wake attack
is
equal to the shock
reasonable, particularly at
110
High-Speed Wind Tunnel Testing
I
i
Approximation of shock pattern for determining allowable model lengths 6 is the shock wave angle, and p the angle of shock reflection. The Mach wave angle may often be used for both with little error. Fig. 2:18
at supersonic speeds.
behind the model.
This
is
not particularly important because the wake
influenced to a large extent by the sting which holds the tunnel,
and model base pressures measured
will
model
is
to the
not equal those of
flight
even in the absence of the reflected shock. If the model were boat-tailed at the base (having
a diameter decreasing with model station), the flow
over the boat-tailed portion could be influenced by the reflected shock.
In this case,
it
would be desirable to
specify an intersection of the shock
with the wake a few diameters downstream of the model base. If the model
were equipped with vertical fins, the model length would be specified from the consideration of proximity of the reflected shock to the fins. It is
obviously not possible to specify model length in completely general
However, the simple cone cylinder should be one of the longest models that can be tested in a particular supersonic tunnel. Since the test section is to be designed for the maximum allowable model lengths, an analysis of Fig. 2:18 should be applicable to the determination of test terms.
section length.
From
geometrical considerations the following equations
can be derived. The model length limited by the shock reflection on the compression side of the model (i Q- C o o
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