NASA TECHNICAL NOTE
NO
NASA TN D -6865
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■OAN COPY: REr^M I
AFWL (DOUitii^ ;5
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ANALYSIS OF THE FLOW IN
A l-MJ ELECTRIC-ARC SHOCK TUNNEL
by John 0. Keller, Jr., and N. M. Keddy
Ames Research Center
Moffett Field, Calif. 94035
'iri iy/2
NATIONAL AERONAUTICS AND SPACE ADMINISTRATION • WASHINGTON, D. C. • JUNE 1972
TECH LIBRARY KAFB, NM
DiB33aa
lllllll
1. Report No.
NASA TN D-6865
2. Government Accession No.
4. Title and Subtitle
ANALYSIS OF THE FLOW IN A 1-MJ ELECTRIC-ARC SHOCK TUNNEL
7. Author(s)
John O. ReUer, Jr., and N. M. Reddy
9. Performing Organization Name and Address
NASA— Ames Research Center
Moffett Field, Calif. 94035
12. Sponsoring Agency Name and Address
National Aeronautics and Space Administration
Washington, D. C. 20546
15. Supplementary Notes
3. Recipient's Catalog No.
5. Report Date
June 1972
6. Performing Organization Code
8. Performing Organization Report No.
A-4341
10. Work Unit No.
117-07-04-15-00-21
11. Contract or Grant No.
13. Type of Report and Period Covered
Technical Note
14. Sponsoring Agency Code
16. Abstract
An investigation has been conducted in the Ames electric-arc-heated shock tunnel to evaluate the performance of the
facility over a range of shock Mach numbers from 7 to 19. The efficiency of the arc-heated driver is deduced using a new
form of the shock-tube equation. A theoretical and experimental analysis is made of the tailored-interface condition. The
free-stream properties in the test section, with nitrogen as the test gas, are evaluated using a method based on stagnation-
point heat-transfer measurements.
17. Key Words (Suggested by Author(s) )
Shock tunnels
Nozzle flow
Arc-discharge heating
Calibrating
Test facilities
19. Security Classif. (of this report)
Unclassified
18. Distribution Statement
Unclassified — Unlimited
20. Security Classif. (of this page)
Unclassified
21. No. of Pages
28
22. Price
3.00
' For sale by the National Technical Information Service, Springfield, Virginia 22151
TABLE OF CONTENTS
Page
NOTATION V
SUMMARY 1
INTRODUCTION 1
THEORETICAL CONSIDERATIONS 2
The Shock-Tube Equation 2
Driver Efficiency 3
Tailored-Interface Operation 3
Test Section Flow 5
EXPERIMENTS 6
The Test Facility 7
Driver Performance V
Reservoir Conditions 8
Test Section Measurements 9
The three-probe rake 9
The survey rake 10
DISCUSSION ..11
Nozzle Test Core 12
Total Enthalpy 12
Free-Stream Properties 14
Atom concentration 15
Velocity 15
Density 16
Shock-layer viscosity 16
Shock-layer Reynolds number 17
Mach number, Reynolds number, and ylM * IV
CONCLUDING REMARKS 17
REFERENCES 19
TABLES 21
ui
■iiiiiiiiiiiiiiiiin^niH^niiiiBinininiiiiii i mill
NOTATION
a speed of sound
A constant in equation (21), ^4 =6X10^° cm^ °K/mole sec; effective area of inviscid nozzle
flow
cjj coefficient of specific heat for Pyrex 7740
d diameter
E internal energy
E^ capacitor bank energy
hj^ heat of dissociation per unit mass
H total enthalpy
H^ reference enthalpy (300 J/g)
/ for two-dimensional flow; 1 for axisymmetric flow
Kfj coefficient of conductivity of Pyrex 7740
Le Lewis number
m molecular weight
M^ shock Mach number (f/^/fli )
p pressure
Pf pitot pressure
Pr Prandtl number
q convective heat-transfer rate
R gas constant per unit mass of undissociated molecules
Ryi dimensionless velocity number defined in equation (1 )
S entropy
S^ shock tube number defined in equation (2a)
T absolute temperature
U flow velocity relative to tube wall
C/y shock velocity
C/3 limiting velocity, 2a4/74 - 1
V volume of the driver
Z compressibihty, 1 + a
a atom concentration
ap temperature coefficient of resistance of platinum film
7 ratio of specific heats
6 * boundary-layer displacement thickness
e density ratio across a normal shock wave, Pi /p2
M dynamic viscosity
p gas density
p^ density of Pyrex 7740
T} efficiency of the driver
^ parameter involving 7, defined in equation ( 1 0)
6 characteristic dissociation temperature; 1 13,260° K for nitrogen
Subscripts
reservoir condition at end of shock tube
1 quiescent test gas ahead of incident shock wave
2 test gas between incident shock wave and contact surface
3 driver gas behind incident contact surface
4 driver chamber conditions after arc discharge
e edge of the boundary layer
eq equilibrium boundary-layer model
fc fully catalytic
fm free molecule flow model
fr frozen boundary-layer model
vi
/ initial driver condition before arc discharge
nc noncatalytic
T tailored interface
oo free-stream condition at exit of nozzle
Superscript
* nozzle sonic throat
vn
ANALYSIS OF THE FLOW IN A 1-MJ ELECTRIC- ARC SHOCK TUNNEL
John O. Keller, Jr., and N. M. Reddy*
Ames Research Center
SUMMARY
An investigation has been conducted in the Ames electric-arc-heated shock tunnel to evaluate
the performance of the facility over a range of shock Mach numbers from 7 to 19. The efficiency of
the arc-heated driver is deduced using a new form of the shock-tube equation. A theoretical and
experimental analysis is made of the tailored-interface condition. The free-stream properties in the
test section, with nitrogen as the test gas, are evaluated using a method based on stagnation-point
heat-transfer measurements.
INTRODUCTION
The shock driven wind tunnel has played an important role in the study of hypervelocity
aerodynamics, in part because of the wide range of flow velocities available and the relative ease
with which the composition of the test stream can be varied. Relatively long duration test flows
may be obtained with the tailored-interface mode of operation, as discussed in references 1 and 2.
Heated hydrogen drivers (ref. 3) and combustion drivers (refs. 4, 5, 6) have been extensively used to
produce tailored shock Mach numbers in the range of 6 to 9. However, higher shock Mach numbers
are necessary to dissociate and ionize gases such as nitrogen and carbon monoxide, which are of
interest in planetary entry studies. To achieve such conditions within the constraints imposed by
the tailored mode of operation requires driver gas temperatures in excess of 2000° K. Arc-discharge
heating (refs. 7 and 8) has been used successfully in this application; a wide range of driver
temperatures is made available by varying driver loading pressure or discharge energy. This attractive
scheme has been used for the Ames electric-arc shock tunnel (EAST), which has a capacitor storage
system rated at 1 MJ.
In the present study, the characteristics of the heated driver and the tailored-interface
operation of the shock tube (with nitrogen) have been considered, both theoretically and
experimentally. The major emphasis, however, is on evaluating the properties of the highly
expanded nitrogen stream in the test section. In this low-density environment, the more
conventional methods of stream evaluation, which rely on probe measurements of static pressure,
are inaccurate, largely because of substantial corrections for orifice and probe boundary-layer
effects. Thus, in this study a number of quantities characterizing the flow in the EAST test section
have been deduced using a new technique based on stagnation-point heating-rate measurements.
Other flow properties were obtained from these measurements by application of the sudden-freeze
concepts of reference 6. The results are compared with numerical solutions of nonequilibrium
nozzle flow using the method of reference 9.
*NASA— NAS Research Associate. Presently at Indian Institute of Science, Bangalore — 12, India.
■ II ■■■iiii^ii III ■■■■■III ■■■■■^■^■■■■■illii
THEORETICAL CONSIDERATIONS
The idealized performance of an electric-arc-heated driver and shock tube can be predicted
easily for any driver gas or test gas mixture using the generalized form of the classical shock-tube
equation presented in reference 10. This form of the shock-tube equation presents simple
expressions for the tailored mode of operation and provides an easy method of calculating the
actual efficiency of the electric-arc-heated driver. This information is the basis for estimating
reservoir conditions at the nozzle inlet for an arbitrary test gas. These conditions in turn are input
quantities for calculating the flow properties in the expansion nozzle and test section. The concepts
of reference 10 are reviewed briefly and applied to the arc-heated driver; comparisons are made of
predicted and realized reservoir conditions.
The Shock-Tube Equation
It is shown in reference 1 that by defining a dimensionless velocity
Rr,^^ (1)
the classical shock-tube equation, relating particle velocity behind the incident shock wave to driver
gas properties before diaphragm opening, can be reduced to a universal form given by
74/(74-')
Sn-- ""l, -" (2a)
where
^ ^'^1 __^li_ ^ _^24_ / Pxlp^ .2b)
'" 74 ~ 1 yJlxPjPi 74 " 1 V 74
and
R =(7^n(l-e)M, ^20
" 2(aja^')
In equations (2) the driver gas is assumed to be perfect, but no assumption as to the thermodynamic
state of the driven gas is made. (Equations (2) are for a constant-area tube and represent the exact
solution for perfect gases to within 3 percent at Ms > 4.)
In an electric-arc-heated facility, the driver gas is heated at constant volume and hence the
initial density p^ is equal to the final density p^ after heating. Hence
---'''- (3)
Also
:i=^ _i (4)
Pi Pi "'i
since in general Tj = T^. With the use of equations (3) and (4), the shock-tube equation can be
reduced to
,74/(74-0
y ^ R (5)
74 ^n
Thus, the dimensionless shock-tube number Sn, for constant-volume heating of the driver gas,
depends only on the initial pressures and molecular weights of the driver and driven gases.
Equation (5) is convenient to use for estimates of shock-tube performance for any combination of
gases; in graphical form, the variation of Rn with S^i is a single curve for a given 74 • The value of Rfi
that corresponds to a particular Sn is unique in the sense that it is independent of the
thermodynamic state of the gas behind the shock wave. Having R^, we use equation (2c) to relate
Ms directly to 04 and T4, the speed of sound and temperature in the heated driver gas. Obviously, if
Ms is measured, then an effective T^ can be determined.
Driver Efficiency
In an electric-arc-heated driver with constant volume heating of a perfect gas (ref. 1 1 )
and
Ij^Il) (7,
v7i m^ T^
These driver-heating equations can be combined with shock tube equations (2c) and (5) to obtain
the efficiency of the driver. With a^/ai derived from measured Ms, and equation (2c) with the
appropriate value of Rn, equation (6) will yield 17. In the present study, 1? was based on Ms
measured at the downstream end of the shock tube, and as such includes losses associated with
shock-wave attenuation. It could be reasoned that this approach results in a lower estimated driver
efficiency, because it does not account for viscous losses in the shock tube; however, the result does
give an estimate of overall driver effectiveness. The efficiencies so determined are discussed in a later
section on driver performance.
Tailored-Interface Operation
At the downstream end of the shock tube a reservoir of heated gas is produced by reflection of
the incident shock wave from the end wall. An optimum condition exists if the downstream wave,
resulting from the interaction of the reflected shock wave with the contact surface, is a Mach wave.
When this occurs, the contact surface (interface) is said to be "tailored." Since this secondary
reflection is vanishingly weak, the reservoir conditions remain steady for a longer period — in
theory, until the arrival of the main driver expansion. For tailored operation a matching condition
can be derived for the perfect driver and driven gas case, as shown in reference 12; for example.
[
^1
74 + ^ 7i -1
74-1 7i + 1
M^ » 1
(8)
The dimensionless number Rn can be used to write the ratio of internal energies, following
reference 10, as
E2
3 _ T4-I (l-Rn
274
Rr
From equations (8) and (9) the tailored value of Rn is
1
^^n]T -jT^
(9)
(10)
where
Then equation (5) reduces to
^
74 + 1 274
1
274
74-1
74-1 74-1 7i + 1
74/2(74-0
nil /mi
n 1/2
74(P//Pl)
^
(1 +,// 1^2) 1/(74-1)
(11)
Equations ( 1 0) and (11) represent the tailoring conditions for thermodynamically perfect gases.
From equation (11) it is evident that for a given combination of driver and driven gases, the ideal
loading pressure ratio Pj/p^ required for tailored operation is a constant, regardless of the quantity
of energy discharged into the driver gas. The loading pressure ratios for tailored operation with the
different gas combinations used in these experiments are given in table 1 .
The tailored shock Mach number is given by
_ 2(^4 /a 1)
[M
s^T
[Rn\ x
(74-l)(l-e)
Using equations (6) and (7) to obtain a^/ui , equation (12) can be written as
(12)
[Ms]j= [Rn^T
(74-l)(l-e)
74 ^1
7i fn^
l+(74-l)
vEc
Vp
-, \l/2
I J
(13)
where e «i(7i - iy(7i + 1) is the perfect gas value of the density ratio across a normal shock wave
for Ms » 1, and [Rn] f is the constant given by equation (10). The tailored shock Mach number
[Ms] T depends on the initial loading pressure p^, the driver volume V, the stored capacitor energy
Ec, and the choice of gases. A typical variation of [Ms] f with Pj , with He driving N2 , is given in
figure 1, for £'c = 10^ J and V- 0.0209 m^ (Ames 2.90 m arc-heated driver). As shown, this result
from equation (13) compares favorably with a similar result from reference 2 where, for the same
He-N2 combination, nitrogen is treated as a real gas.
'Ng real gas (ref. 2)
17=1.0
He-Ng
Ec = 10^ joules
V = 0209 m^
The preceding analysis indicates that if
the appropriate ratio of p^ to p j is chosen the
contact surface will be tailored at all shock
Mach numbers. With the assumption of ideal
shock-tube theory with thermodynamically
perfect working gases inherent to this
analysis, each tailored shock Mach number
has a unique ratio of temperatures across the
contact surface {T^IT2). In practice, this is
not the case, however, because the
temperature T^ is influenced by real-gas
effects, viscous losses, heat transfer to the
wall, and nonuniform distribution of energy
within the driver chamber. The temperature
T2 is affected by similar viscous and heating
losses, real-gas effects, diaphragm opening,
etc. Thus, these nonideal effects make it
impossible to predict from ideal theory the ratio of pressures that will give a tailored condition.
However, a near-tailored reservoir can be obtained by adjusting p^- and Pj , as discussed later.
Figure 1.— Variation of tailored-shock Mach number with
shock-tube loading pressure.
Test Section Flow
This section considers methods of evaluating flow properties in the high-velocity test stream
issuing from a steady reservoir of quiescent, shock-heated gas. It is assumed v|:hat the reservoir gas is
in equihbrium, with respect to both vibrational and chemical energies. In reference 13 a method is
described for determining the Reynolds number, viscosity, and atom concentration in a
hypervelocity nozzle from the measurement of stagnation-point heat-transfer rates to three probes
placed side by side (the three-probe method). The physical nose dimensions of the probes should be
chosen so that one probe measures the heating rate q^^ in the presence of an equilibrium (chemical)
boundary layer, the second qfy. in a frozen shock layer, and the third qr^^ in the free-molecule flow
regime. With a pitot-pressure measurement, in addition to these three heating rates, the following
relationships can be used. (The derivation of these equations and the probe design considerations
are given in reference 13. The present results are subject, of course, to the assumptions of the
reference analysis.) The shock-layer Reynolds number is
2m^
K^fr
(14)
where
C = 0.64(7+ \y'^Pr
l/2p^-O.6^-0.2 5
The ratio of dissociation to total enthalpy is
^eq'^eq '
■ .1/2
"eq eq
+ (Le
0.52 _
)qf,
r^fr^
(15)
In equation (15) the two heat-transfer probes are assumed to be geometrically similar. Using the
approximations
one obtains
Pt '^ PooUo,
f/o,
and -^oo *** 2 ^°°^ "*" ^/?"°°
(16)
Mp =
2Al
\dfr Pt qf r
4 C^~ q}^'
(17)
(18)
Hr.
Ov
2Le
0. 52
• .1/2
^eq"eq
kfrdf,
II
+ {Le
0.52
I)
(19)
U ^
_ ^eq eg _ . '
(20)
All the flow properties in the preceding equations are expressed in terms of the measured quantities,
stagnation heating rate and pilot pressure. The unknowns are the two transport properties, Lewis
and Prandtl numbers, and the shock density ratio e, which must come from another source.
Fortunately, they are relatively insensitive to test conditions and can be matched by an iterative
solution if desired. An examination of equations (14) through (20) shows that the derived values of
free-stream velocity U^, density p^, shock-layer viscosity /ig, and Reynolds number [Re] ^ require
only two of the three measured heating rates, namely q^y and ^^^; and that the free-stream Mach
number M^o and Reynolds number Re^ cannot be obtained by this method, since the static
temperature of the stream is not directly available. However, these latter properties can be derived
from the present measurements by an adaptation of the sudden-freeze method of reference 6, as
vnh be shown later. To assess the validity of this combined approach, a comparison will be made
between the stream densities from the three-probe and the sudden-freeze methods, while U^ from
equation (16) will be compared to the stream velocity obtained by a completely independent
analysis.
EXPERIMENTS
In this section the methods discussed for determining driver efficiency, tailored-interface
conditions, and flow properties are apphed to the EAST facility.
The Test Facility
An electric-arc driver and energy storage system has been developed for shock-tunnel
application, with provision for driver lengths up to 3 m. Such driver lengths are required to match
the reservoir time requirements for tailored-interface operation (ref. 2). The energy for the arc is
supplied by a 1250-/xF capacitor bank capable of storing 1 million joules when charged to a
maximum of 40 kV. The arc is contained within a 10.2-cm-diam insulated chamber and is initiated
by a tungsten wire. Details of the operating characteristics for the driver system are given in
reference 14. (Dannenberg and Silva have developed methods to improve driver performance and
range of operation; these are described in a forthcoming publication.) For the present experiments,
driver lengths of 1.37 and 2.90 m were used. The energy per unit volume Ec/V was kept the same
for both lengths (about 42 J/cm^) with capacitor bank voltages of 28 and 40 kV, respectively. The
driver is coupled to a 10.2-cm-diam, 1 1.3-m-long shock tube, which discharges into a 10° half angle,
conical supersonic nozzle. A 76-cm, hexagonal test section and a vacuum tank are located
downstream of the nozzle. Figure 2 is a schematic diagram of the facility. Interchangeable sonic
Driven tube
I 1.3 m
=^
20° _ Test ^
nozzle section
Vocuum chamber
4.3m
0.76ni \
exit diQ/
rf/"^"^
J,___jj
Collector
ring
Mom
diaphragm
Loading
valve
Nozzle
diaphragm
Model support
spool
Figure 2.— Schematic of Ames electric-arc shock tunnel.
throats can be inserted at the nozzle entrance to permit operation at different flow Mach numbers.
The shock wave arrival was monitored at six stations in the shock tube using the ion-probe system
described in reference 15. Shock Mach number was calculated from the measured velocity and the
initial gas temperature in the tube. The initial pressure p, was measured with a precision dial gage at
the gas loading station, and the reservoir pressure po with a piezoelectric transducer located in a
sidewall port at 0.64 cm from the endwall. Test gas impurities were estimated to be less than
1.0X10"^ of the total sample.
Driver Performance
Driver efficiencies, determined by the method described earlier, are shown in figure 3 for the
range of loading pressures p^ of the present tests. Equivalent driver temperatures computed from
equation (6) are included for reference. Experimentally determined efficiencies were based on the
shock velocity measured near the end of the 1 1.3-m tube and thus include the energy loss associated
with shock attenuation. At values of p^ from 10 to 15 atm, the He and N2 drivers operate with an
overall efficiency of about 50 percent. With the addition of argon to the driver gas, which lowers Mg
because of the decrease in a^, the driver efficiency varied substantially from run to run. In all cases
17 was better than for helium alone, but the wide variation from 0.60 to over 1.0 is a surprising
result. It is inferred that the arc-discharge and heat-transfer processes in the driver chamber are
variable, perhaps because of local variations in gas mixture ratio. Since the basis of comparison is a
1.2
1.0
T4,°K 7500 6000 4500
3000
8
Flogged symbols = 2.90 m driver
1 ]
24 32
16
Pi I atm
Figure 3.— Overall driver efficiency and equivalent temperature;
1.37- and 2.90-m drivers.
uniformly heated driver gas, it is obvious
that nonideal effects can be strong
enough to create shock waves that
exceed the ideal velocity. It should be
noted, moreover, that rj > 1.0 has been
reported in reference 8 for pure helium
drivers at relatively low temperatures T^ .
Here again one logical explanation is
nonuniform driver heating. Further
investigation of this behavior is
warranted since it will influence
interface temperatures T2 and T3 , which
determine tailored operation.
Reservoir Conditions
In an earlier section, the ratios of initial driver-to-driven-tube pressures were predicted for
tailored interface operation with ideal gases. For a given combination of gases the ratio is a fixed
constant, although absolute values can be changed to vary Ms- As part of the experiment, an effort
was made to validate this prediction, using the pressure ratios listed in table 1 . It was quickly found
that nonideal effects resulted in undertailored conditions — an undertailored condition is a
mismatch of internal energy at the contact surface such that E^ > £'2 , causing a downstream
expansion wave to emerge from the reflected shock-contact surface interaction. This situation can
be corrected by lowering pj, while keeping a^/ai constant, or by decreasing a^/ai with Pj
constant, until the tailored condition is achieved. To obtain reasonably constant reservoir pressure
histories with nitrogen as the test gas, it was necessary to increase the ratios p^/p ^ by about an order
of magnitude by a reduction in p j . This is not surprising since the shock Mach numbers attained in
most high-energy shock tubes are below ideal predictions at the initial pressures considered here.
The observed departure from the ideal pressure ratio in this experiment is attributed to an elevated
temperature behind the contact surface T^ , partly due to deceleration of the incident shock wave
and partly to a timewise variation of total temperature in the gas issuing from the driver. These
nonideal effects are the subject of a separate investigation.
Figure 4 shows representative reservoir pressure histories for the Ms range and the driver gases
used. Figure 4(a) is a record of a somewhat undertailored condition at Ms = 18.5, which has a fairly
constant pressure after the arrival of the expansion wave from the contact surface. This pressure
level corresponds to an enthalpy in the test gas of about 40 kJ/g, considerably above that obtainable
in combustion or heated hydrogen driven facilities. The tailored condition would occur at a slightly
lower Pj foT Ms> 1 8.5. Figures 4(b) and 4(c) show slightly overtailored conditions for which weak
compression waves augment the reflected-shock pressure.
An independent check of the reservoir gas quaUty was obtained by monitoring the radiant
emission of the shock-heated nitrogen, using a photodiode detector with S-1 response. The reservoir
gas was observed through a sidewall window masked by a 0.025-cm vertical slit for coUimation;
signals were recorded on an oscilloscope. Although the detector was not calibrated for absolute
intensity, care was taken to operate in the linear response range. Typical results (fig. 5) show that
8
U— JsOO/isec ^Expansion Wave
li— ■■■
■■■hBR
23.8 atm
(a)Ms=i8.5 Pi= 10.2 atm (He), P|=:. 0092 atm (Ng)
iWW Pim jPi 36.1 atm
(■■■■T
{b)Ms=l2.7 Pi=l2.2atm (.4A+.6He), P| =.OI32atm (Ng)
25.6 atm
{c)Ms=6.9, P|= 10.2 atm (Ns), P| = . 0264 atm (N2) J
Figure 4.— Reservoir pressure histories at near-tailored
conditions.
(b)Ms = l5.4, P|=0.0I32 atm
Figure 5 .— Pressure and radiation histories in the
reservoir, 0.64 cm from end wall.
the radiation from the reservoir varies with the pressure for at least 1 msec at Af^ = 6.9, and for
about 0.5 msec at Ms = 15.4. In a quahtative sense, this finding indicates that no large dilution of
the test gas occurs in these times.
Test Section Measurements
As the shock-heated, partly dissociated nitrogen in the reservoir expands into and beyond the
throat of the supersonic nozzle, a point is reached where the recombination and vibrational
relaxation become rate limited and can no longer follow the rapid change of temperature. When this
occurs, the flow changes over a relatively short distance from local equilibrium to a state in which
one or both of the two forms of internal energy (vibration and dissociation) are nearly invariant. In
effect, the flow "freezes" at an intermediate level of dissociation and vibrational energy
distribution, and remains essentially in this state as it sweeps through the test section.
Consequently, the properties of the test stream differ from those in an equilibrium expansion; the
temperature, pressure, and velocity are lower while the Mach number is higher. The calibration
method must determine these differences, measure the dissociation level, and if possible, the
vibrational energy defect of the flow.
The three-probe rake— The flow quantities in the test section were evaluated, in part,
using the three-probe method described earlier. The probes were mounted together on a single rake
for simultaneous measurements of stagnation-point heating rates in the equilibrium boundary layer,
frozen shock layer, and free-molecule flow regimes. The nose diameters were <ig„ = 5.1cm,
dff. = 1.0 cm, and df^ = 0.10 cm; the largest probe was hemispherical and the two smaller probes
were cylindrical in shape. Figure 6 shows a diagram and a photograph of the three-probe rake
immersed in the test flow. For the present range of conditions, the computations presented in
reference 13 show that a cylindrical probe of 0.10 cm diam is sufficiently small to obtain
-0.5 cm radius cylinder
(a) Rake assembly
(b) Rake in fest stream
Figure 6.— Three-probe heat-transfer rake.
free-molecule flow at the stagnation point. On
the basis of estimates and experimental results
presented in reference 16, a cylindrical probe of
1.0-cm diam should result in frozen shock-layer
conditions.
Estimates of the probe size for equilibrium
boundary-layer flow in the stagnation region
were based on the theory of reference 17.
Although the reference analysis is specifically
for air, it was assumed that the functional
dependence of gas-phase reactions on local
conditions would be similar for pure nitrogen.
The resulting estimates of probe size, in the limit
of a fully equilibrium boundary layer, exceeded
the physical dimensions of the facility for many
of the expected test conditions. Therefore, it
was decided to relax the requirement of full
equilibrium, retain the concept of three
simultaneous measurements, and resolve the
defect in heating rate by analytical means. A
5.1-cm-diam hemisphere was used for this
measurement; for convenience, this probe will
be referred to as the equilibrium heat-transfer
probe.
(A:^P^c^)1/2 =0.153 J cm""2 °K~^sec"
The sensing elements on the three probes were thin film platinum gages. To avoid shorting due
to shock-layer ionization, all the gages were coated with a 1-^-thick layer of silicon monoxide by a
vacuum evaporation technique. (The response time of a l-/i glass layer is about 50 jUsec for
5 percent accuracy.) The backing material used was Pyrex 7740, which has the following properties:
'^''^ and ap=2.18X10~3 fi/fl °K. The heat-transfer rates
were determined directly with the use of analog
networks. The methods of reference 16 were
followed closely in the design and construction
of both the gages and the analog networks.
The survey rake— During test core sur-
veys, other heating rates were measured on
hemispherical models 2.5 cm in diam mounted
on a rake spanning the test region (fig. 7). These
models were copper shells, 0.013 cm thick,
instrumented with 40 gage chromel-constantan
thermocouples formed by soldering the
individual wires of each pair into two closely
spaced holes at the stagnation point. AU the
heat-transfer data were recorded by a high-speed
data acquisition system (ref. 18), which provides
digital information at the rate of one reading
13 cm
adjustment ,
(a) Rake assembly
(b) Rake in test stream
Figure 7.— Pressure and heat-transfer survey rake.
10
Tg = Flow Starting time
Test time
2 3 4
Time, ms
Figure 8.— Rate of heat transfer to the equilibrium
boundary -layer probe (Ms = 12.4, Pj = 0.0132 atm).
every 2jLtsec. The data were punched on a paper
tape and processed on an IBM 7094 computer.
A sample of the machine-plotted heat-transfer
data is shown in figure 8.
Pitot pressures were measured, in repeat
runs at each test condition, with a piezoelectric
pressure transducer (Kistler, model 701 A).
These measurements were obtained with both a
flush mounting (gage face exposed to the flow)
and a recessed mounting arrangement. In both
cases the gage face was coated with a very thin
layer of silicone rubber to reduce the heating
effects. (Reservoir pressures were measured with
similar transducers (Kistler, model 60 IH).) Pitot
pressures were also measured during test core
surveys with an adjustable rake, which contained
as many as seven variable-capacitance pressure
transducers. These gages were mounted behind a
heat-sink baffle to shield the active element (a pretensioned Invar diaphragm, 0.0013 cm thick)
from heating effects.
The heat-transfer rates and the corresponding pitot pressures were measured for a wide range
of shock Mach numbers (hence reservoir enthalpies) with nitrogen as the test gas. The driver gases
were nitrogen, pure helium, and helium diluted with different amounts of argon; for each case the
ratio of initial driver pressure to driven tube pressure Pj/p^ was adjusted until a near-tailored
condition was achieved. The three-probe rake was mounted in the horizontal center plane at the
exit of a conical supersonic nozzle with a 0.32-cm-diam throat. The pressure and heat-transfer
survey rake was mounted vertically in the same nozzle, at the same axial station, and offset to
position pitot probes at the same radial distance as the outer models on the three-probe rake.
Throat sizes of 0.32 and 1 .27 cm were used with this rake. For the present range of experiments,
the corrections to measured pitot pressures for rarefaction effects were estimated by the method of
reference 19 and found to be less than 2 percent. The flow starting time in the nozzle (as in ref. 20,
the time required to estabHsh uniform flow after arrival of initial disturbance) is estimated from
probe response to be between 1 50 to 300 Msec, and in general, varies inversely with A/5.
DISCUSSION
The data are summarized in table 2 ; the measured heating rates, pressures, and test times are
grouped into two sets according to the instruments used. Test 1 refers to the runs made with the
three-probe heat-transfer rake, using thin-film detectors. Test 2 results are from the survey rake that
used thin-wall calorimeters to measure heat-transfer rates and variable capacitance transducers for
pressure.
Analysis of the heat-transfer data from three-probe rake (test 1 ) gave inconsistent results over
the range of test conditions. To isolate the cause of this erratic behavior, test 2 repeated several runs
11
at identical starting conditions and extended the scope to include a larger nozzle throat size,
d* = 1.27 cm. Furthermore, as a check on the measuring techniques of test 1, a different type of
heat-transfer sensor and pressure transducer were used. These were mounted in the survey rake that
spanned the test region. The results of test 2 showed that the inviscid test core was smaller than
predicted at the higher reservoir enthalpies. This result can be seen in 'table 2 where, for test 1,
columns 7 and 1 indicate when the pitot pressure at the off-centerline location of the frozen-flow
and free-molecule probes was lower than centerline pitot pressure. Column 13 of table 2 lists the
time interval of useful data for each run, while column 14 gives an estimate of the duration of test
gas flow based on reservoir radiation and test section heating rate measurements. In general, the
longer flow times of column 1 4 could not be fully utilized because of pressure disturbances in the
reservoir.
Nozzle Test Core
Rake surveys of the nozzle flow at the exit station, using the 0.32-cm-diam throat, showed
that inviscid test cores varied in diameter from about 23 to 10 cm as the total enthalpy was
increased from 8 to 40 kJ/g. Pressures were relatively constant across the core area and repeatable
from run to run. At H^o > 27 kJ/g, the stream core size decreased to the point where the outer two
probes on the heat-transfer rake (located 8.4 cm from the centerline) were in the outer edge of the
nozzle wall boundary layer. For these conditions, the frozen-flow probe data were discarded, but the
free-molecule probe results were assumed to represent a velocity close to the inviscid core value,
since in the outer edge of a hypersonic boundary layer the density decreases much more rapidly
than the velocity. For example, for the first run listed in table 2 the local pitot pressure was about
0.7 the centerline value; the corresponding defect in velocity is estimated to be less than 1 percent,
while the local density decrease is nearly 30 percent. The corresponding local Mach number is only
about 1 5 percent lower, so that the free-molecule probe should remain within the appropriate flow
regime.
With a nozzle throat diameter of 1.27 cm, the measured test core diameter was greater than
40 cm over the entire range of reservoir conditions.
Total Enthalpy
As shown in table 2, the stagnation region boundary layer on the largest probe, as expected,
did not come to chemical equilibrium. Therefore, it was not possible to compute the stream total
enthalpy directly using equation (19). An alternate method was devised for indirect verification of
the enthalpy, using the measured q^^^ and q^^, along with an H^j derived from reflected shock
conditions. The first step in this approach was to determine the chemical state of the shock layer by
comparing the product of the rate of nitrogen dissociation and the flow residence time to the
limiting value of equilibrium dissociation. The dissociation rate was estimated using the
characteristic equation, as given for example in reference 21, which describes a diatomic gas with a
binary collision mechanism
doc AP -a IT .« , .
— =(l-a) —— e-G'^ (21)
dt Rp+CO
12
where 00= 1.5 is half the number of degrees of freedom contributing energy during a collision and
A is a constant determined by experiment for a particular gas. In the present case da/dt was
maximized by using the ideal gas (a= 0) temperature just behind the shock wave.
Residence time was estimated from shock detachment distance and average local velocity. The
uniform result was that even for this maximum dissociation rate the residence time was so short
that the inviscid shock layer was effectively frozen at the stream composition (on the largest model)
for all test conditions. Similarly, for the stagnation region boundary layer, a recombination rate
parameter (the ratio of atom diffusion time across the boundary layer to characteristic atom
lifetime)
C, = L6X10iVd_ (22)
2r*zi^2
was used after the manner of reference 22, with pressure in atomspheres and nose diameter in
centimeters. Values of Cj varied from 1 0~* to 1 0~^ over the test range and indicate atom lifetimes
much in excess of transit time. Thus, the boundary layer in the stagnation region of the 5.1 -cm
probe is frozen to atom recombination for all test conditions.
With the chemical composition of the probe shock layer thus defined (frozen at stream
composition) and assuming that reservoir enthalpy can be evaluated from the measured reservoir
pressure at the entropy level associated with the reflected shock wave, the second step is to
compute the convective heat transfer to a noncatalytic (glass covered) surface for several assumed
values of a^. When the expression for a frozen free stream and frozen shock layer is used (ref. 22),
where the heating rate to a fully catalytic surface q^^ is essentially the same as that for an
equilibrium boundary layer q^ . As suggested in reference 22, this latter value can be closely
approximated for nitrogen by
^^'i \dj V 10,000/ V ^00/
where Uoo — (2^oo)^^^ . the flow velocity for an equilibrium expansion; that is, Uoo includes
the dissociation energy. The resulting values of q ^ were interpolated to match the measured
heating rate on the 5.1 -cm probe, which yields Ooo and the corresponding stream velocity Uoo-
Alternately, U^o can be computed from equation (16) using the measured data for each test
condition
29/m
U^= -^ (16)
Pt
13
200
i"
^ 160
I
I 120
C
a>
•o 80
m
o
E 40
Test
I
O
Compufed from measured
reservoir pressure at reflected
shock entropy
ref. 23
8 12 16
Stiock fvlach number, Mg
Figure 9.- Variation of total enthalpy with Al^ for
nitrogen.
20
The results of this analysis are shown in table 3 ,
where the two sets of Uoo are seen to be in good
agreement. This finding implies that there are no
significant energy losses in the reservoir for the
range of conditions tested, and that the total
enthalpy of the test core matches that of the
reservoir.
The variation of total enthalpy with Ms is
shown in figure 9. Symbols denote computed
values based on the measured reservoir pressure
and the entropy level associated with the
reflected shock wave. Computed enthalpies are
compared with a theoretical, reflected shock
curve taken from reference 23 ; differences are
due to the change of reservoir pressure after
shock reflection.
Free-Stream Properties
A nonequilibrium nozzle flow program similar to that of reference 9 was used for comparing
the measured flow properties with theoretical predictions. The major uncertainty involved in this
program lies in the assumption that the vibrational energy mode always remains in equilibrium with
translational and rotational modes. (While the energy in vibrations is at most about 20 percent of
the total enthalpy, its disposition can make a noticeable difference in stream properties, as will be
shown later.) The reservoir temperature and pressure are specified as initial values for the numerical
solution. In the present cases the initial values were the measured reservoir pressure and the
corresponding equilibrium temperature obtained from thermodynamic charts for nitrogen, using the
appropriate reservoir enthalpy. Energy losses from the reservoir gas were assumed to be negligible;
thus, the computed quantities represent a limiting set for the entropy associated with each test
condition. The numerical computations showed that the nitrogen atom concentration was frozen in
the test section for all the cases considered.
The semiempirical method of reference 6 also can be used to predict certain stream properties,
without knowledge of the specific relaxation processes or rate constants. It is assumed that the
gasdynamic properties at the test station (having undergone relaxation of several internal degrees of
freedom) are approximately the same as if the gas had made a sudden transition from equihbrium to
a zero rate of internal energy exchange at some location in the expansion. The location of the
transition is characterized by a single parameter, the freeze Mach number. Downstream of this point
both the chemical composition and vibrational energy distribution of the gas are constant (frozen).
A computing program for one-dimensional nozzle flow, using equilibrium reservoir conditions
as input quantities, was used to generate stream properties as a function of area ratio for a specified
set of freeze Mach numbers. The pitot pressure was calculated assuming the vibrational mode and
chemistry remained frozen behind the bow shock wave — a realistic choice for the flow conditions
of the present experiment. The details and an experimental verification of this method are given in
reference 6.
14
Vibrational
energy
Frozen Equil.
• O
■ D
d«
cm
0.32
1.27
Kest 2
38 42
Reservoir entropy, Sq/R
Figure 10.— Free-stream atom concentration.
Atom concentration— The measured and
computed values of (x^ are compared in
figure 10 as a function of reservoir entropy.
Reservoir atom concentration a^ is common to
both theory and experiment. The open symbols
represent concentrations deduced from
measured heat transfer, using equations (23) and
(24) as described earlier, with vibrational energy
assumed to be in equilibrium. For test 2 the
probe surface was partly catalytic (copper
oxide), and allowance was made for surface
recombination by the method of reference 24.
The recombination energy fraction varied from
4 to 26 percent of the available dissociation
energy.
The filled symbols in figure 10 represent a similar analysis in which both vibrational and
chemical energy exchanges become inactive simultaneously in the nozzle expansion and remain so
in the probe shock layer. Comparisons of shock-layer residence time with vibrational relaxation
rates showed this a reasonable assumption except at the highest enthalpy conditions. Tables 4 and 5
summarize reservoir conditions, stream atom concentrations, and other flow quantities.
The results of figure 10 indicate that a relatively small amount of recombination occurs in the
expanding nitrogen flow over most of the operating range, and that the numerical solution (with
vibrational equilibrium) substantially underestimates the stream atom concentration. For frozen
vibrations, the sudden-freeze approximation indicates that the internal energy adjustment stops just
downstream of the nozzle throat, between M^= 1 and 2. The effect of nozzle throat size on atom
concentration appears relatively minor over the test range. At SqIR > 42, recombination is
enhanced and ol^ approaches the numerical prediction.
86
J) 5
E
34
^
D d< i:27;Test 2
O d* -- 0.32 Test 1
Filled symbols denote
frozen vibrations
38
Reservoir
42 46 50
entropy, Sq/R
Figure 1.— Comparison of measured and predicted
stream velocity.
Velocity- Experimental and predicted
free-stream velocities are compared in figure 1 1 .
The sudden-freeze predictions are shown as
dashed lines, shifted downward slightly relative
to the numerical solution and the a^ curve to
account for the frozen vibrational energy. The
experimental values are consistent with the atom
concentrations of figure 10 and, as expected, are
substantially lower than the numerical
prediction. At the lowest values of SoJR the
data fall below the curve for a^ = a.^ because of
frozen vibrational energy. At the higher values
of Sq/R, the velocities move toward the
numerical prediction.
In the present analysis, the flow velocity
was derived from experimental measurements in
two ways: (1) using the stagnation heating rate
15
20
cm
O d* = 0.32\ ^ , „
D d*= 1.27; ^«=' 2
O d*n 0.32 Test I
Filled symbols-eqn. 17
Open symbols -method of ref. 6
Flagged symbols- frozen vibration
Symbol superscripts = po, otm
= 2500
Computed -ref. 9
for a frozen shock layer, and (2) using the
free-molecule heating rate as in equation (16).
Comparisons are given in table 3. The first
method requires a prior knowledge of the stream
total enthalpy; the second does not. For this
reason, the ^f^ rn^^^od is preferable and, in
fact, is a relatively simple way to determine the
velocity of a nonequilibrium stream. For best
accuracy, both q.c^ and p^ should be measured
simultaneously.
Density— The computed and measured
stream densities are shown in figure 12, where
the filled symbols represent values from
equation (17) and the open symbols are from
the sudden-freeze analysis. The curves are from
the exact numerical solutions (with vibrational
equilibrium) at two representative nozzle area
Figure 12.- Free-stream density. ratios A I A* and reservoir pressures p^. The
experimental results agree in general with predictions on this summary plot; more exact
comparisons would require a point-by-point analysis since p^o is sensitive to both reservoir pressure
and local area ratio. (The area ratios shown are average values for each d* as determined from the
sudden-freeze analysis, while p^ is within 1 percent of experiment except for the symbols with
superscript values. For more detail see tables 4 and 5). The results for test 1 , using the sudden-freeze
analysis, compare favorably with the more direct values from equation (17). This agreement
between stream densities appears to justify the assumption that the sudden-freeze analysis can be
used to supplement the stream properties obtained by the three-probe method.
Shock-layer viscosity— The viscosity in the stagnation-region shock layer is obtained from
the relationship of pitot pressure and heating rates given in equation (18)
^e ATI
AO
^fm
(18)
where
C= 0.64(7 -1- 1)1/ 2^^-0.6^-0 .2 5
The density ratio across the bow shock e was evaluated using either 7 = (8 -i- )/(8 - ) for
equihbrium vibrations, or 7 = (4 -I- 3 )/(4 + ) for frozen, in the normal shock relation
PooIPp ^ (7 ~ l)/(7 + 1) for Mao >^ 1 ■ A Prandtl number of 0.7 was used throughout. The results
are listed in table 4, where the values are seen to increase with H^ in a regular manner. As a check
on the magnitude of these values, equation (A4) of reference 24 was used to determine the
shock-layer temperature T^. Figure 13 shows that the resulting temperatures exceed the estimated
values for dissociated flow with equihbrium vibrational energy; thus the measured viscosities appear
consistent with the other findings of this investigation.
16
20
15
10
Test I
Symbols are for T^ from
72 + 1
[^e = l 58X10"^ Te°^'
28 dco
I + aco
ref 24, eqn (A4)
30
34
38 42
S„/R
46
50
Shock-layer Reynolds number— Reynolds
numbers in the stagnation - region shock
layer were obtained from equation (14) and are
listed in table 4. They remain fairly constant
over the operating range, varying from 4.2 to
6.9/cm, as a result of the relatively small changes
in density and viscosity observed earlier. These
low Reynolds numbers reflect the high viscosi-
ties in the frozen shock layers of the present
experiments.
Much number, Reynolds number, and
A/A*— The sudden-freeze method was used
to evaluate the additional flow quantities,
free-stream Mach number, Reynolds number,
and effective area ratio. Results are listed in
tables 4 and 5. For the smaller throat size
(0.32 cm) the Moo increased with total enthalpy
from 20 to 32 and for the 1.27-cm throat from
14 to 23. The Reynolds number did not vary in
a consistent manner with increasing enthalpy, apparently because of the increase in freeze Mach
number (see fig. 1 1); values between 200 and 1000/cm were obtained. A substantial difference was
observed, at intermediate enthalpies, between the Reynolds numbers for frozen and equilibrium
vibrations (see table 5). Thus, a knowledge of the vibrational energy distribution is important in
evaluating the properties of nonequilibrium streams at these energy levels.
The effective area ratio of the test stream comes directly from the sudden-freeze analysis, as
shown in reference 6. The ratio A/A* decreased with increasing reservoir enthalpy from 12,000 to
about 9,000 with the small nozzle throat and from about 3,300 to 2,300 with the large throat. (The
corresponding geometric area ratios are 56,000 and 3,600.) Representative boundary -layer
displacement thicknesses 6* at the nozzle exit are listed in the last column of table 5. The very
substantial 20- to 23-cm thicknesses that occur with the small nozzle throat correspond to the small
inviscid core size noted earlier. Obviously, for the present reservoir pressure, 0.32 cm is about the
smallest throat diameter that can be used in this nozzle.
Figure 13.^ Shock-layer temperature.
CONCLUDING REMARKS
The operating characteristics of an electric-arc-heated driver and shock-tube system, and the
properties of high energy nitrogen flows expanded in a supersonic nozzle have been investigated.
Driver temperatures up to 8000° K and pressures up to 340 atm were used to obtain
tailored-interface conditions at shock Mach numbers from 7 to 19, enthalpies in the reflected-shock
reservoir of test gas from 7 to 40 kJ/g, and test-section Mach numbers from 14 to 32. The
gasdynamic processes in the shock tube and nozzle have been compared with theoretical, real-gas
predictions. Local equilibrium conditions were assumed to exist everywhere in the shock tube; the
nozzle flow was not so restricted, and substantial nonequilibrium effects were observed. The
primary results of this investigation are summarized as follows.
17
1. The overall efficiency of the driver and shock-tube system was found to vary with the
composition of the driver gas. Argon-heUum mixtures were the most effective but did not give
consistent shock-tube performance. Pure helium and pure nitrogen were less effective driver gases
but produced mor^ uniform results. Efficiencies from 40 to 100 percent were recorded.
2. An ideal, theoretical analysis of tailored-interface, shock-tube operation, which predicts a
constant ratio of initial driver pressure to initial shock-tube pressure for tailoring at all shock
velocities, was not confirmed by experiment. However, the nonideal effects that invalidated this
prediction could be offset by increasing the pressure ratio, so that near-tailored operation was
achieved for shock Mach numbers from 7 to 19.
3. Reflected shock relationships and a reservoir pressure history can be used to define reservoir
conditions at total enthalpies between 7 and 40 kJ/g, if successive pressure changes are
considered to be isentropic. There was no significant loss of energy from the reservoir gas during
the 0.5- to 1.5-msec test period.
4. The proposed method of evaluating the properties of a nonequilibrium nozzle flow of nitrogen,
using simultaneous measurements of stagnation heating rates (to noncatalytic surfaces) in three
gasdynamic regimes, could not be fully utilized under current test-section conditions. Limitations
on probe size prevented the attainment of an equilibrium boundary layer in the stagnation
region. In future work, however, it may be possible to use a catalytic probe surface to recover the
dissociation energy of the shock layer.
5. By combining elements of the three-probe diagnostic method with a sudden-freeze
approximation of the flow behavior it is possible to define most of the properties needed for
hypervelocity, gasdynamic studies in a nonequilibrium stream. This technique has been shown to
give consistent results in a single-component gas (nitrogen) over a wide range of specific energies,
with initial dissociation up to 75 percent.
6. Theoretical predictions were found to underestimate the energy retained in the inert degrees of
freedom (dissociation and vibration) in a rapidly expanding stream of nitrogen. Typically, the
flow departed from thermodynamic equilibrium just downstream of the nozzle throat and was
effectively frozen at a local Mach number of about 2.
Ames Research Center
National Aeronautics and Space Administration
Moffett Field, Calif., 94035, March 21, 1972
REFERENCES
1. Wittliff, C. E.; Wilson, M. R.; and Hertzberg, A.: The Tailored-Interface Hypersonic Shock
Tunnel./. Aerospace Sci., vol. 26, 1959, pp. 219-228.
2. Loubsky, W. J.; and Reller, J. O., Jr.: Analysis of Tailored-Interface Operation of Shock Tubes
With Helium-Driven Planetary Gases. NASA TN D-3495, 1966.
3. Hertzberg, A.; Wittliff, C. E.; and Hall, J. G.: Development of the Shock Tunnel and Its
Application to Hypersonic Flight. ARS Progress in Astronautics and Rocketry; Hypersonic
Flow Research, F. R. Riddell, ed., Academic Press, Inc., vol. 7, 1962, pp. 701-758.
4. Nagamatsu, H. T.; and Martin, E. O.: Combustion Investigation in the Hypersonic Shock
Tunnel Driver Section./. Appl. Phys., vol 30, July 1959, pp. 1018-1021.
5. Mason, R. P.; and Reddy, N. M.: Combustion Studies in the UTIAS Hypersonic Shock Tunnel
Driver. Proc. 5th Shock Tube Symposium, U. S. Naval Ordnance Laboratory, April 1965.
6. Hiers, R. S., Jr.; and Reller, J. O., Jr.; Analysis of Nonequihbrium Air Streams in the Ames
1-Foot Shock Tunnel. NASA TN D-4985, 1969.
7. Camm, J. C; and Rose, P. M.: Electric Arc-Driven Shock Tube. Phys. of Fluids, May 1963,
pp. 663-677.
8. Warren, W. R.; Rogers, D. A.; and Harris, C. J.; The Development of an Electrically Heated
Shock Driven Test Facility. Second Symposium on Hypervelocity Techniques, Univ. of
Denver, March 1962.
9. Lordi, J. A.; Mates, R. E.; and Moselle, J. R.: Computer Program for the Numerical Solution of
Nonequilibrium Expansions of Reacting Gas Mixtures. NASA CR-742, 1966.
10. Reddy, N. M.: Shock-Tube Flow Analysis With a Dimensionless Velocity Number. NASA TN
D-5518, 1969.
1 1. Glass, I. I.; and Hall, J. G.; Handbook of Supersonic Aerodynamics. Shock Tubes (Section 18).
NAVORD Rep. 1488, vol. 6, Dec. 1959.
12. Flagg, R. F.; Detailed Analysis of Shock Tube Tailored Conditions. RAD-TM-63-64, AVCO
Corp., Wilmington, Mass., Sept. 1963.
13. Reddy, N. M.; A Method for Measuring Reynolds Number, Viscosity, and Atom Concentration
in Hypervelocity Nozzles. AIAA J., vol. 6, July 1968, pp. 1398-1400.
14. Dannenberg, R. E.; and Silva, A. F.; Exploding Wire Initiation and Electrical Operation of a
40 kV System for Arc-Heated Drivers up to 10 Feet Long. NASA TN D-5126, 1969.
19
15. Dannenberg, R. E.; and Humphry, D. E.: Microsecond Response System for Measuring Shock
Arrival by Changes in Stream Electrical Impedance in a Shock Tube. Rev. Sci. Instru., vol. 39,
Nov. 1968, pp. 1692-1696.
16. Reddy, N. M.: The Use of Self-Calibrating Catalytic Probes to Measure Free-Stream Atom
Concentrations in a Hypersonic Flow. NASA CR-780, 1967.
17. Inger, G. R.: Nonequilibrium Stagnation Point Boundary Layers With Arbitrary Surface
Catalycity..4/y4y4/., vol. 1, 1963, pp. 1776-1784.
18. Seegmiller, H. L.; and Mazer, L.: A 500,000 Sample per Second Digital Recorder for the Ames
Electric-Arc Shock Tunnel. IEEE Pub. 69 C 19-AES, 1969, pp. 243-247.
19. Potter, J. L.; and Bailey, A. B.: Pressures in the Stagnation Regions of Blunt Bodies in Rarefied
Flow. AIAA J., vol. 2, April 1964, pp. 743-745.
20. Dunn, M. G.: AppHcation of Microwave and Optical Diagnostic Techniques in Shock-Tunnel
Flows. AIAA Paper 68-394, 1968.
21. Hammit, A.: The Flow of a Dissociating Gas Around and Behind a Blunt Hypersonic Body.
BSD-TDR-62-107, May 1962.
22. Pope, Ronald B.: Stagnation-Point Convective Heat Transfer in Frozen Boundary Layers.
AIAA J., vol. 6, no. 4, April 1968, pp. 619-626.
23. Lewis, C. H.; and Burgess, E. G., Ill: Charts of Normal Shock Wave Properties in Imperfect
Nitrogen. AEDC-TDR-64-104, Arnold Engineering Development Center, Tenn., May 1964.
24. Okuno, A. F.; and Park, Chul: Stagnation-Point Heat Transfer Rate in Nitrogen Plasma Flows:
Theory and Experiment. ASME Pub. 69-WA/HT-49, Nov. 1969.
20
TABLE 1 .- RATIOS OF INITIAL DRIVER PRESSURE TO DRIVEN TUBE PRESSURE FOR TAILORED OPERATION
Driver/driven gases
He/Nj
(0.3A + 0.7He)/N2
(0.4A + 0.6He)/N2
A/N2
N2/N2
PilPi
117
31.5
25.5
11.7
25.0
TABLE 2.- SHOCK TUBE, NOZZLE RESERVOIR, AND TEST STREAM QUANTITIES FOR NITROGEN
1
2
3
4
5
6
1
8
9
10
11
12
- 13
14
Test
P.XIO^,
^s
Po-
^0'
t?*,
t
Theoretical
Measured
Local
Measured
Measured
Test
Test flow
atm
atm
kJ/g
cm
PfXlo^
atm
'^eq
"ieq
P^XIO^
¥
'Ifm
interval
duration
W/cm^
atm
W/
cm^
msec
1
9.22
18.5
41.1
40.6
0.32
6.94
197
127
4.97
116
161
0.5
17.8
43.5
38.7
8.03
191
119
5.24
127
.6
,
17.7
39.1
38.5
7.21
181
123
4.62
120
153
.5
0.5
13.2
16.0
40.8
30.6
6.12
142
—
6.12
119
165
.4
.4
15.3
38.8
28.8
6.18
134
74
5.37
108
131
.4
.4
14.9
38.1
27.0
5.71
124
68
5.71
136
.7
13.0
35.4
21.6
5.30
100
58
5.30
91
125
.6
1.2
11.4
39.5
17.9
5.24
83
55
5.24
83
108
.9
'
'
11.3
34.7
17.1
4.56
75
49
4.56
79
108
.7
—
f
26.3
6.9
19.4
6.9
2.58
22
18
2.58
28
40
1.2
1.6
2
13.2
15.8
59.8
31.8
9.80
265
162
1.2
1.5
13.2
13.7
42.5
24.4
6.73
177
111
1.2
1.7
26.3
7.6
22.1
8.2
T
2.79
39
29
.9
1.3
9.22
17.9
44.2
39.2
1.27
22.6
437
341
2.0
2.4
13.2
16.2
47.6
31.7
36.6
475
388
1.2
2.5
12.3
34.0
19.3
23.7
259
184
1.4
2.8
■ '
11.6
36.7
17.9
23.1
236
185
1.4
2.2
'
26.3
7.3
22.1
7.8
\
11.7
77
71
2.0
2.4
to
Measured
Calculated
Po'
atm
He
kJ/g
41.1
40.6
43.5
38.7
39.1
38.5
40.8
30.6
38.8
28.8
38.1
27.0
35.4
21.6
39.5
17.9
34.7
17.1
19.4
6.9
TABLE 3.- EVALUATION OF STREAM TOTAL ENTHALPY, TEST 1
Equivalent
0.57
.58
.53
.50
.47
.43
.30
.22
.20
Measured
%
Qfr'
W/cm^
E(
0.74
127
.68
119
.69
123
.51
119
.48
74
.44
68
.32
58
.22
55
.20
49
.02
18
Equivalent
Measured
Equivalent
m/sec
W/cm^
(f4o)/;„'
misec
6430
6590
161
6220
—
—
6480
153
6450
5260
165
5310
5120
131
4800
5030
136
4710
4800
125
4650
4590
108
4600
4560
108
4660
3290
40
3160
(£4c)/,
m
0.977
.996
1.008
.938
.937
.970
1.003
1.022
.962
TABLE 4.- F
LOW(
:ONDITION
fS AND TE
PcoXlO^,
ST-SECTIC
N FLOW I
M^XIO*,
'ROPERTIES, TEST 1
Sudden freeze
P^,
<L
H „
PooX10^
^s
^0'
atm
p^xlo^
atm
kJ/g
So/R
%
Ooo
Kg/m^
1.78
[Re/cm]^
Nsec/m^
A/A*
M^
[Rel cm] ^
kg/m^
2.27
18.5
41.1
6.94
40.6
45.1
0.74
0.57
4.49
2.61
8,900
29.8
289
17.8
43.5
8.03
38.7
44.1
.68
.58
2.10
4.98
2.61
8,600
31.8
328
2.59
17.7
39.1
7.21
38.5
44.4
.69
.53
1.74
4.17
2.70
9,000
29.3
233
2.20
16.0
40.8
6.12
30.6
41.5
.51
.50
2.25
5.54
2.19
9,700
32.2
446
2.58
15.3
38.8
6.18
28.8
40.8
.48
.47
2.40
5.68
2.20
9,500
30.1
436
2.92
14.9
38.1
5.71
27.0
40.2
.44
.43
2.29
5.32
2.15
10,000
29.4
370
2.45
13.0
35.4
5.30
21.6
38.2
.32
.30
2.33
5.71
2.03
10,300
25.0
318
2.67
11.4
39.5
5.24
17.9
36.5
.22
.22
2.51
6.30
1.85
11,800
24.5
318
2.93
11.3
34.7
4.56
17.1
36.3
.20
.20
2.23
6.30
1.64
11,800
24.0
266
2.78
6.9
19.4
2.58
6.9
31.8
.02
2.45
6.86
1.22
11,800
19.5
207
2.22
22
ta
TABLE 5.-
- FLOW CONDITIONS AND TEST-SECTION FLOW PROPERTIES, TEST 2
'2.
X atm cm
P^xlo^
atm
kJ/g "^o/^
%
Theoretical
g g ^ a Measured
Theoretical
F-B-L.*^
E.V.'^
W/cm'
Theoretical
F.B.L.*^
F.V.'^
%\
W/cm^
E.V.*^
F.V.'^
Sudden freeze approximation
CO
-3
to
A/A*
[i?e/cm]^
Moo
PooX10^
kg/m^
5*, cm
15.8 59.8
0.
1.
32
r
27
1
9.80
31.8 41.3
0.53
309 162
158
173
157
171
0.50
.46
8900
9600
832
640
31.5
29.6
4.19
3.94
22.9
22.4
4i>
13.7 42.5
6.74
24.4 39.0
.36
192 101
109
115
110
116
.33
.27
11,000
303
24.0
2.78
21.3
7.6 22.1
2.79
8.2 32.4
.02
41.0 29.2
37.6
29.6
.02
12,700
169
19.8
2.10
20.1
17.9
44.2
22.5
39.3 44.4
.70
574 341
330
346
...
.56
3200
705
22.7
6.75
2.29
16.2
47.6
36.6
31.8
41.7
.53
590 388
377
407
...
.40
2250
452
17.5
12.4
8.14
12.3
34.0
\
23.7
19.3
37.4
.26
287
184
178
193
179
192
.25
.19
2400
675
15.7
12.0
7.12
11.6
36.7
23.1
17.9
36.6
.22
261
185
178
186
179
186
.19
.13
2600
2800
981
518
17.0
15.2
13.6
10.4
5.84
4.57
7.3
22.1
11.7
7.8
32.2
.02
80.6
71.1
80.6
71.0
.02
3300
453
13.7
9.48
1.78
^E.B.L. = equilibrium boundary layer
F.B.L. = frozen boundary layer
''E.V. = equilibrium vibrations
F.V. = frozen vibrations
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