The cryogenic concept and the advantages it offers with respect to achieving full scale Reynolds number in a moderate size tunnel at reasonable levels of dynamic pressure are described. Aspects which must be considered during the development of a facility that uses gaseous nitrogen as the test gas are examined. These include the properties of nitrogen, particularly at high pressure; isentropic expansion and normal shock flows in nitrogen; real gas ratios; and the problem of condensation. Sources of information on cryogenic technology are cited

Kilgore, R. A.

English

NASA Technical Reports Server

CRYOGENIC WIND-TUNNEL TECHNOLOGY
Robert A. Kilgore
NASA Langley Research Center
SUMMARY
As a result of theoretical studies and experience gained during the deve-
lopment and operation of both a low-speed cryogenic tunnel and the Langley
0.3-m transonic cryogenic tunnel, the cryogenic wind tunnel has been shown to
be a practical concept and to offer many advantages with respect to achieving
full-scale Reynolds number in a moderate size tunnel at reasonable levels of
dynamic pressure. After a brief review of the cryogenic concept, this paper
presents some of the aspects which must be considered during the development of
a cryogenic wind tunnel that uses gaseous nitrogen as the test gas. Based on
work by Adcock, it is shown that even though the values of the compressibility
factor and the ratio of specific heats of nitrogen depart significantly from
their ideal-gas values at cryogenic temperatures, both the isentropic flow
parameters and the normal-shock flow parameters are insignificantly affected by
these real-gas effects. Based on work by _all, it is shown that it is possible
to operate at stagnation temperatures even lower than those corresponding to
the free-stream saturation boundary without encountering condensation effects.
Should this mode of operation be possible for arbitrary models, an additional
increase in Reynolds number of about 17 percent may be realized at a given
operating pressure. Alternatively, for a given Reynolds number, operating at
the free-stream saturation boundary temperature will allow testing at reduced
pressure, drive power, and liquid nitrogen consumption.
INTRODUCTION
The cryogenic wind tunnel is a relatively new aerodynamic research tool.
The first cryogenic tunnel was built at Langley in 1971. Although the demon-
strated application to wind tunnels is relatively recent, it is interesting to
note that the science of cryogenics, just as the wind tunnel itself, dates back
to the previous century. As will be discussed, the technology developed has
been very valuable in the present application.
Historically, capital and operating costs have tended to keep transonic
tunnels small, while the host of problems encountered at high pressures have
tended to keep operating pressures low. The net result has been that existing
(ambient temperature) tunnels operate at Reynolds numbers which are too low to
insure adequate simulation of the flow experienced in flight - particularly
with regard to shock -- boundary-layer interactions encountered on modern high
subsonic and transonic aircraft. The application of cryogenics to wind tunnels
53
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has thus been brought about by the need for higher test Reynolds numbers in
tunnels of reasonable size operating at reasonable pressures.
Although the study which started in the fall of 1971 was directed toward
application of the cryogenic concept to increase the Reynolds number capability
of a small wind tunnel equipped with a magnetic suspension and balance system,
the advantages and possibility of applying the concept to a large transonic
tunnel were recognized at that time. In the late 1960's and early 1970's there
were several transonic tunnel concepts being studied in the United States which
were to provide this country with a greatly increased Reynolds number capabili-
ty. Because the cryogenic tunnel concept avoided many of the shortcomings of
the various competing ambient-temperature tunnel concepts, our efforts for the
past five years have been spent full time on the cryogenic tunnel concept and
only now are we resuming our work on magnetic suspension and balance systems.
SYMBOLS
a
c
c
M
P
R
T
V
v
Z
Y
0
speed of sound
chord of two-dimensional airfoil
mean geometric chord
linear dimension of model or test section
Mach number
pressure
Reynolds number, 0V_/v
Universal gas constant
temperature
velocity
specific volume
compressibility factor, Z = pv/RT
ratio of specific heats
viscosity
density
54
Subscripts:
c
C
L
max
t
1
2
OO
based on c
based on c
local conditions
maximum
stagnation conditions
upstream
downstream
free stream
THE CRYOGENIC CONCEPT
The use of low temperatures in wind tunnels was first proposed as a means
of reducing tunnel drive-power requirements at constant values of test Mach
number, Reynolds number, and stagnation pressure. Reynolds number, which is
the ratio of the inertia force to the viscous force, is given by
R = Inertia force = pV2_ 2
Viscous force pVg
which reduces to the well-known equation
R = pV& _ pMa&
P
As the temperature is decreased, the density p increases and the viscosity
p decreases. As can be seen from these equations, both of these changes re-
sult in increased Reynolds number. With decreasing temperature, the speed of
sound a decreases. For a given Mach number, this reduction in the speed of
sound results in a reduced velocity V which, while offsetting to some extent
the Reynolds number increase due to the changes in p and _, provides advan-
tages with respect to dynamic pressure, drive power, and energy consumption.
It is informative to examine the underlying mechanism through which
changes in pressure and temperature influence Reynolds number. To the first
order p and a are not functions of pressure whereas p is directly propor-
tional to pressure. Thus, increasing pressure produces an increase in Reynolds
number by increasing the inertia force with a commensurate increase in model,
balance, and sting loads. Also, to the first order, p = T-I, V = T0.5, and
= T0"9. Thus, decreasing temperature leaves the inertia force unchanged at a
55
given Machnumberbecause of the compensating effects of temperature on 0
and V2. The increase in Reynolds numberwith decreasing temperature thus is
due strictly to the large reduction in the viscous force term as a result of
the changes in B and V with temperature.
The effect of a reduction in temperature on the gas properties, test con-
ditions, and drive power are illustrated in figure i. For comparison purposes,
a stagnation temperature of 322 K (120° F) for normal ambient temperature tun-
nels is assumedas a datum. It can be seen that an increase in Reynolds num-
ber by more than a factor of 6 is obtained with no increase in dynamic pressure
and with a large reduction in the required drive power. To obtain such an in-
crease in Reynolds numberwithout increasing either the tunnel size or the
operating pressure while actually reducing the drive power is extremely attrac-
tive and makes the cryogenic approach to a high Reynolds number transonic tun-
nel muchmore desirable than previous approaches.
ASPECTSCONSIDEREDDURINGCRYOGENICTUNNELDEVELOPMENT
Planning for the design of a cryogenic wind tunnel falls into two basic
areas. First is the area of fluid dynamics. There is a question as to whether
the test gas at cryogenic temperatures will provide data from the wind tunnel
(e.g., forces, moments, and pressures on the model) which can be used to pre-
dict the loads and aerodynamic characteristics of the full-scale vehicle in
free flight. The second area includes the design of the tunnel and its opera-
tion at cryogenic temperatures. Figure 2 lists the items under the areas of
"Fluid Dynamics" and "Design and Operation."
Fluid Dynamics
The first item under Fluid Dynamics is "Knowledge of gas properties." Its
obvious that one needs to know such things as the speed of sound and the vis-
cosity of the test gas. Although nothing thus far in the operation of the low-
speed cryogenic tunnel (ref. i) or the Langley 0.3-m transonic cryogenic tun-
nel (ref. 2) has indicated that existing values for any given property of nitro-
gen are not sufficiently accurate, the magnitudes of someof the probable
errors are somewhatlarger than one would like, especially at the high pres-
sures proposed for the NTF. In order to be sure there are no problems in this
area, Langley is funding work at the Cryogenics Division of the National Bureau
of Standards (NBS) in Boulder, Colorado, which will improve our knowledge of
the properties of nitrogen, especially at the higher pressures, and at the same
time provide a simplified equation of state limited to the range of tempera-
tures and pressures of interest for cryogenic wind tunnels.
Jerry Adcock is in charge of the area of "Proper flow simulation" which,
as indicated in the figure, includes both analytical and experimental work.
The early experimental work was done in the low-speed tunnel at atmospheric
pressure whereas the recent work has been done at pressures up to 506.5 kN/m2
(5 atm) in the Langley 0.3-m transonic cryogenic tunnel.
56
Typical of the analytical studies being made (ref. 3) are those related
to isentropic expansions and normal-shock flows in nitrogen. First, the ther-
modynamicproperties for nitrogen were obtained from an NBSprogram based on
work by Jacobsen (ref. 4). The NBSprogram was then modified so that isen-
tropic expansions could be made. The various ratios which describe an isen-
tropic expansion were then c@iculated by using the real-gas properties of nit-
rogen and were comparedwith ratios derived from ideal-gas equations and ideal
values of the compressibility factor (Z = i) and the ratio of specific heats
(y = 1.4) for a diatomic gas. An example of the results is presented in figure
3, where the ratio of the real and ideal pressure ratios necessary to expand
isentropically to M = 1.0 is presented as a function of tunnel stagnation
temperature and pressure. As can be seen, the real-gas effects are extremely
small and, for R_ = 50 x 106 at cryogenic temperatures, the real-gas pressure
ratio differs from the ideal-gas pressure ratio by only about 0.2 percent. It
is interesting to note that the real-gas effect at cryogenic temperature is
actually less than the real-gas effect at ambient temperatures, where for the
samesize test section a considerably higher stagnation pressure is required to
obtain R-_c= 50 x 106.
The other real-gas ratios used to describe an isentropic expansion in
nitrogen also differ from the ideal-gas ratios by this samesmall percentage.
In manycases, such as the determination of tunnel Machnumber, the real-gas
equations can be used to avoid even this small error of 0. I percent to 0.2 per-
cent. However, errors of such magnitude are of the sameorder as the un-
certainty in measurementsand would be considered insignificant in most wind-
tunnel work.
For the normal-shock flow studies, Adcock modified the NBSprogram so that
the various ratios which describe normal-shock flow Could be calculated by
using the real-gas properties, and comparedthese with the corresponding ideal-
gas ratios. An example of the results is shownin figure 4 where the ratio of
the real to the ideal static pressure ratio across a normal shock is shownas a
function of tunnel stagnation temperature at stagnation pressures of 101.3 and
506.5 N/m2 (i and 5 atm). As in the case of isentropic expansions, the effects
are extremely small, and for R_= 50 x 106, the real pressure ratios differ
from the ideal-gas pressure ratio by only about 0.2 percent. The other real-
gas ratios associated with normal-shock flow in nitrogen also differ from the
ideal ratios by this samesmall percentage. As in the case of isentropic ex-
pansion, even in those situations where the real-gas equations cannot be used
to take these effects into account, an error of this magnitude would usually be
considered insignificant. Thus, even though the values of Z and y for
nitrogen depart significantly from their ideal-gas values at cryogenic tempera-
tures, both the isentropic flow parameters and the normal-shock flow parameters
are insignificantly affected by these real-gas effects.
Design and Operation
In figure 2, under the heading "Design and Operation", are listed several
areas which, depending on the type of cryogenic tunnel being considered, will
receive various amounts of attention. Each of these areas has been covered to
some extent in previous publications so it will not be necessary to consider
57
them here. The one area that will be discussed briefly is "Condensation,"
which is being studied here at Langley under the direction of Robert Hall.
As shownin figure 5, the test Reynolds number increases rapidly as tem-
perature is reduced. Marked on the curve of Reynolds number against tempera-
ture are three "boundaries" which, for the conditions of this exampleare set
by a maximumlocal Machnumber over the model of 1.2, a free-stream Machnumber
of 0.85, and a settling chamberMachnumberof 0. As reported in detail by
Hall (ref. 5), effects of condensation were not seen on the airfoil used for
these tests until the tunnel was operated at temperatures below those associat-
ed with free-stream saturation. His results indicate that for a given size
tunnel and model and for a constant tunnel pressure, an additional increase in
test Reynolds numberof about 17 percent may be realized by operating at tem-
peratures corresponding to those of the free-stream saturation boundary.
Another way to take advantage of being able to operate beyond the local
saturation boundary would be to reduce the operating pressure for testing at a
given Reynolds number. This should be of considerable practical importance for
the NTFwith its extremely high (by present standards) operating pressures. If
the minimumoperating temperature in the NTF can be reduced from the present
arbitrary limit (corresponding to a saturation boundary based on an assumed
local Machnumber of 1.4) to a lower temperature without condensation effects
occurring, then the tunnel operating pressure can be lowered correspondingly.
And, of course, when the operating pressure is reduced, both drive power and
LN2 consumption are also reduced.
As can be seen from figure 6, if operation is possible at temperatures
corresponding to free-stream saturation, tunnel pressure can be reduced by
about 15 percent (from 895.5 to 760.8 kN/m2 (8.84 to 7.51 atm)) and LN2 flow
rate, which is directly related to operating costs, is reduced by about 16 per-
cent.
SOURCESOFINFORMATION
Relative to the cryogenic tunnel development areas listed in figure 2,
several sources of information have been found useful and are generally avail-
able. Since there is familiarity with the design of ambient temperature tun-
nels, sources related to the aerodynamics of tunnel design are not listed. The
problem is really one of applying good cryogenic engineering to the type of
tunnel required.
In the United States the best source of information by far on the cryo-
genic aspects of a cryogenic tunnel are the publications and people of the
Cryogenics Division of the National Bureau of Standards. Although the cryo-
genic wind tunnel is a recent application of cryogenic technology, most of the
information needed on materials, insulation, instrumentation, liquid nitrogen
systems, safety, and so forth has been documentedby the NBSand is readily
available. If there is need to know something that is not documented, the
chances are excellent that the NBSCryogenic Division can be of help.
58
In addition to the NBSand the work being done here at Langley in the
0.3-m transonic cryogenic tunnel and on the NTFdesign, there are several
other places where cryogenic tunnels are being designed and built. Figure 7
lists the varioustunnels and provides information about each of the projects
such as the size of the test section, the type of tunnel, the location, and the
actual or anticipated date of operation. As one can see, there is considerable
activity going on around the world related to the development and use of cryo-
genic wind tunnels. Since this is such a new field, one must keep informed as
to what is going on, not only on his own projects, but around the world, if
duplication of effort is to be avoided and the full potential of the cryogenic
wind tunnel is to be realized as quickly as possible.
REFERENCES
l.
.
.
.
.
Kilgore, Robert A.; Go.dyer, Michael J.; Adcock, Jerry B.; and Davenport,
Edwin E.: The Cryogenic Wind-Tunnel Concept for High Reynolds Number
Testing. NASA TN D-7762, 1974.
Kilgore, Robert A.: Design Features and Operational Characteristics of
the Langley 0.3-Meter Transonic Cryogenic Tunnel. NASA TN D-8304, 1976.
Adcock, Jerry B.: Real-Gas Effects Associated With One-Dimensional
Transonic Flow of Cryogenic Nitrogen. NASA TN D-8274, 1976.
Jacobsen, Richard T.: The Thermodynamic Properties of Nitrogen From 65 to
2000 K With Pressures to i0,000 Atmospheres. Ph.D. Thesis, Washington
State Univ., 1972. (Available as NASA CR-128 526.)
Hall, Robert M.: An Analysis of Data Related to the Minimum Temperatures
for Valid Testing in Cryogenic Wind Tunnels Using Nitrogen as the Test
Gas. NASA TM X-73924, 1976.
59
VALUES
RELATIVE
TO 322K
GAS PROPERTIES
6-
4-
a
I.l
I I I
100 200 30O
TEST CONDITIONS AND
DRIVE POWER
NOLDS NUMBER
DYNAMIC
PRESSURE7
POWER,
I I II I
0 4_ 0 1_ 2_ 30O 4_
STAGNATION TEMPERATURE,K
Figure i.- Effect of temperature reduction on gas properties, test conditions,
and drive power. Moo : 1.0; constant stagnation pressure and tunnel size.
• Fluid dynamics
- Knowledge of gas properties
- Proper flow simulation
• Analytical
• Experimental
- Low-speed tunnel
- Transonic tunnel
• Design and operation
Materials of construction
- Drive system
- Insulation
- Method of cooling
- Vent system
Models
- Instrumentation
- Operating procedure
• Tunnel dynamics
• Condensation
- Safety
Figure 2.- Some aspects considered during cryogenic tunnel development.
60
1.004
I.'002
(P/Pt) NITROGEN
(P/Pt) I DEAL 1.000
•998
•996
SATURATION, ML =
1.0
R_,= 50 x 106 12.5 BY 2.5m TESTSECTION)
Pt
atm
--1
5
_10
R- = 50 x 106 (2.5BY 2.5m TEST SECTION) ------®
c --15
I I I I I I
50 loo 150 200 250 300
STAGNATIONTEMPERATURE,K
Figure 3.- Isentropic expansion pressure ratlo of nitrogen.
Pressure ratio P/Pt; M_ = i.
kN/m2
101.3
5O6.5
1013.0
1519.5
I
350
1.004 - M 1 = 1.4 IN NITROGEN
1.002
1.000
.998
.996
.994
.992
pt o atm kN/m2
__,,, 55,/"- 5O6.5
-SATURATION e= 50 x 106
- (2.5-BY 2.5-m TEST SECTION)
.990 I I I
0 100 2OO 300
STAGNATION TEMPERATURE,Tt. K
Figure 4.- Normal shock pressure ratio in nitrogen.
]
4OO
61
Chord
Reynolds
number,
R c
× 106
S0-
4O
30-
20-
10-
0
50
Moo • 0.85; Pt • 456 kN/m2(4.5 atm); c m 0.137 m
_ . o.85sa_at_on _- 0 2_: _
1 I I I I I
100 150 200 250 300 350
Total temperature, Tt, K
Figure 5.- Potential benefits of operation below saturation temperature.
100
LN 2
flow rate, 90
percent
.80
100
R-dc 120 × 106 //_Pt = 896 kN/m 2 (8.84 atm)
M_ = 1.0; = Saturation at M L = 1.4
p t ffi 761 kN/m 2 (7.51 atm)
ree°stream saturation
I I I
110 120 130
Total temperature, _, K
Figure 6.- LN 2 consumption as a function of temperature.
62
• Initia!
0.178 × 0.279 m Low-speed/fan NASA-LRC
• Present
0.3 m Transonic/fan NASA-LRC
0.I0 x 0.I0 m Low-speed/fan University of Southampton
• Studies of conversion of existing tunnels
0.30 x 0.30 m TWT/blowdown
1.22 x 1.22 m TWT/blowdown
1.22 x 1.22 m Transonic/blowdown
McDonnell - E1 Segundo
McDonnell - E1 Segundo
British Aircraft Corp.
• Design of new cryogenic tunnels
2.5 x 2.5 m Transonic/fan
Transonic/Ludwieg tube
1.4 × 1.4 m Transonic/blowdown
1.6 × 2 m Transonic/fan
NTF (Langley)
DFVLR - AVA (Holland)
FFA (Germany)
LEHRT (AGARD)
Figure 7.- Some sources of cryogenic tunnel design and
operational experience.
1972
1973
1977
1977
1978
1981
63


Cryogenic wind-tunnel technology

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