Radiative interaction between driver and driven gases in an arc-driven shock tube, CHEMIA I PIROTECHNIKA, Chemia i ...
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Shock Waves (2002) 12: 205–214
Digital Object Identifier (DOI) 10.1007/s00193-002-0157-y
Radiative interaction between driver and driven gases
in an arc-driven shock tube
D.W. Bogdanoff, C. Park
ELORET Corporation, Moffett Field, CA 94035, USA
Received 3 January 2002 / Accepted 6 May 2002
Published online 12 August 2002 – c
Springer-Verlag 2002
Abstract.
An electric-arc driven shock tube was operated with hydrogen as the driven gas and either
hydrogen or helium as the driver gas. The electron density was measured behind the primary shock wave
spectroscopically from the width of the hydrogen beta line. The intensity of the radiation produced by the
driver and driven gases and directed along the axis of the shock tube was measured with a photomultiplier
tube. The temperatures behind the primary shock wave were 3 to 4 times those calculated from the Rankine-
Hugoniot relations. A proposed explanation for this difference is developed, involving strong heating of the
driven gas at early times due to higher shock velocities and radiative energy transfer from the driver arc.
The electron density ahead of the shock wave agreed roughly with the calculation based on the precursor
phenomenon due to radiative transfer.
Key words:
Radiation, Arc-driven shock tube
1 Introduction
understand the cause of this high electron density, the
intensity of radiation produced by the driver and driven
gases and directed along the shock tube axis was measured
with a photomultiplier tube. A proposed explanation for
the high observed electron densities is that the driven gas
is heated very strongly early in the driven tube due to
higher shock velocities at early times and radiative energy
transfer from the driver arc.
One well known method of producing a strong shock wave
in a shock tube is to use an electric arc-heated driver (see,
e.g., Sharma and Park 1990). At NASA Ames Research
Center, one such shock tube is in operation. Tests were
made in this shock tube with hydrogen as the test gas
originally with the intention of studying the nonequilib-
rium radiation phenomenon occurring in the shock layer
over the Galileo Probe vehicle. The Galileo Probe vehi-
cle, which entered the atmosphere of the planet Jupiter
in 1995, had a sphere cone geometry with a cone angle of
44
◦
. The present test was motivated by the fact that the
surface recession of its heatshield was different from the
prediction: recession was less in the stagnation region and
more in the frustum region than predicted (Milos 1996).
At the peak-heating point in the entry flight, the flight
velocity of the vehicle was about 40 km/s. The frustum
region produced a shock wave inclined at 45
◦
, producing
an equivalent normal shock velocity at the peak-heating
point of about 28 km/s.
Because radiation intensity is closely related to elec-
tron density, electron density was measured in the present
tests. The tests produced unexpectedly high electron den-
sity values behind the primary shock wave. In order to
2 Method of measurement
2.1 Shock tube
The electric arc-driven shock tube facility of NASA Ames
Research Center is described in detail in Sharma and Park
(1990) and Sharma and Park (1990a). The internal diam-
eter is 10 cm for both the driver and the driven tubes.
Both the driver and the driven section are made of stain-
less steel. The present tests were made with a driver which
is 23.5 cm in length, at a distance of 5.34 m in the driven
section from the diaphragm (see Fig. 1). The driver was
filled with either hydrogen or helium. An arc discharge is
initiated in the driver by exploding a tungsten or stainless
steel wire. The mass of the tungsten and stainless steel
wires used are approximately 11% and 48%, respectively,
of the mass of the driver gas. The driven section of the
shock tube was filled with hydrogen to a pressure of 1
Torr. The capacitance of the driver capacitor bank was
1530
µ
F. The shock velocity was varied primarily by vary-
ing the charging voltage of the capacitor bank between
Correspondence to
: D.W. Bogdanoff
(e-mail: dbogdanoff@mail.arc.nasa.gov)
An abridged version of this paper was presented at the 23rd
Int. Symposium on Shock Waves at Fort Worth, Texas, from
July 22 to 27, 2001.
206 D.W. Bogdanoff, C. Park: Radiative interaction between driver and driven gases in an arc-driven shock tube
Fig. 1.
Schematic of experimental setup
at one time. The first 60 test runs were made with the
configuration shown in Fig. 1, but without the radiome-
ter and its sacrificial mirror. Then the special electrical
conductivity test section (skimmer, insulated test section,
electrodes) was removed, leaving an open, 10 cm inside
diameter driven tube all the way to the dump tank. Op-
tical ports in the tube section replacing the conductivity
test section continued to allow monochromator and spec-
trograph data to be taken essentially as shown in Fig.
1. The radiometer was still not in place. Nine test runs
were made with this configuration. Finally, the radiome-
ter and its sacrificial mirror were added for the last 5 test
runs. Five piezoelectric pressure tranducers (not shown in
Fig. 1) spaced along the driven tube were used to measure
shock velocities. One or two photomultiplier tubes (also
not shown in Fig. 1) along the driven tube were used to
monitor the arrival of driver gas contamination and the
end of the useful test time.
The spectrograph was a 0.30 m McPherson Model 218
unit with a 384
×
576 pixel CCD array mounted at the exit
plane. Spatially-resolved, time-frozen spectral snap-shots
were obtained with the spectrograph. Gratings with 1200
and 2400 lines/mm were used, giving spectral widths of
26.3 and 10.0 nm, respectively. The spectrograph was op-
erated centered on the hydrogen beta line at 486.13 nm.
The monochromators were Bausch and Lomb 0.25 m units
operated with 600 lines/mm gratings. The passbands of
the monochromators were about 0.090 nm. Time-resolved
light intensity histories were obtained with the monochro-
mators at 486.13 nm (center of hydrogen beta line) and
488.69 nm (center of a tungsten line). The radiometer con-
sisted of a 1p28 photomultiplier tube, viewing a sacrificial
mirror through a pair of slits. The mirror allowed the pho-
tomultiplier tube to look along the axis of the shock tube
towards the driver. To measure the gas conductivity, cur-
rent was passed through the gas by means of a pair of
3.10 cm square main electrodes (‘E’ in Fig. 1). To allow the
true gas conductivity to be measured, the insulated wall
between the main electrodes was fitted with three 0.24 cm
diameter floating potential electrodes with a 0.89 cm sep-
aration in the current direction.
10
18
10
17
10
16
10
15
10
14
10
13
10
12
10
11
10
10
EAST Facility
Test Runs 40/16 - 60
Driven gas: 1 Torr H
2
New Griem-Kepple Theory
(from Griem (1974))
10
9
10
8
10
7
Exp. - Stark broadening of H
β
line
Theory - from shock wave eqns. and u
s
10
6
10
5
15
20
25
30
35
Shock velocity, km/sec
Fig. 2.
Theoretical and experimental electron densities vs
shock velocity
13.9 to 34 kV. In addition, for the highest velocity shots,
the hydrogen fill pressure of the driver was reduced from
897 kPa to 276 kPa. The shock velocities produced for the
present study were in the range from 12 to 34 km/s.
For 60 of the 74 test runs, the shock tube was fitted
with the special test section shown in Fig. 1 in order to
measure the electrical conductivity of the test gas. This
test section included a boundary layer skimmer 22.9 cm
long with an inside diameter of 3.5 cm. The flow was then
led through a transition section to a 3.10 cm square in-
sulated channel, where conductivity measurements were
made.
2.3 Diagnostic technique
From the spectrograph, for each shot, 64 individual spec-
tra are obtained at various distances behind the shock
wave. Running averages over 4 adjacent spectra are made
and smoothing is applied to reduce high frequency noise.
For most of the data, the full widths of the Stark broad-
ened hydrogen beta at half maximum are 2.0 nm or more.
The Doppler widths of the lines are, at most, 0.05 nm
and the instrumental line width is estimated at 0.09 nm.
Hence, the corrections due to Doppler and instrumental
line widths are small, of the order of 5% or less and have
not been applied to the data. For a small number (6) of
test runs, at the lowest electron number densities, these
corrections can be larger, up to 20% or even 50%, for the
very lowest electron densities. The data have been cor-
rected for optical density effects by modifying the the-
2.2 Diagnostic equipment
Figure 1 shows the spectrograph, two monochromators,
the radiometer and the electrodes used to measure the
electrical conductivity of the gas. For brevity, more di-
agnostics are shown in the Fig. 1 than were ever used
D.W. Bogdanoff, C. Park: Radiative interaction between driver and driven gases in an arc-driven shock tube 207
oretical spectral curves for various optical densities and
choosing the curve with the optical density that best fits
the experimental data. The theoretical Stark broadened
curves were taken from Griem (1974). Curves are given
therein for temperatures from 5,000 to 40,000 K and elec-
tron densities from 10
14
to 10
18
cm
−
3
. The curve for the
temperature and density closest to that indicated by the
experimental data is chosen. By fitting the theoretical
curve to the experimental data, a value for the electron
number density is obtained. The estimated errors in the
electron density are
±
15%, except for the cases of low
electron densities mentioned above.
A 1p28 photomultiplier tube (PMT) was used as a ra-
diometer. The tube was calibrated using a DXW lamp op-
erated at a current of 8.3 A. Spectral irradiance curves are
available from the Eppley Laboratory, Inc. for this type of
lamp. The PMT assembly has very narrow viewing angles,
due to the two slits in front of the PMT. The angular sen-
sitivity of this assembly was measured and a viewing angle
correction applied when the PMT was used as a radiome-
ter. A wavelength correction factor must also be applied
for radiometry. This factor is obtained by taking the PMT
photocathode sensitivity curve, allowing for the Plexiglas
window cut-off (at
∼
400 nm) and convoluting this curve
with the spectrum of the calibration lamp and an assumed
spectrum of the driver or driven gas radiation. (The latter
spectra were either black body or calculated equilibrium
gas radiation spectra.) Using these two convolutions and
the integrated radiation spectra of the two sources, the
required wavelength correction factor is constructed.
the method of McBride and Gordon (1996). The experi-
mental electron densities can be as much as six orders of
magnitude above the theoretical predictions.
On account of these rather unexpected results, it is
worth briefly reviewing some considerations that were
made to guard against presenting erroneous experimental
results. The spectrograph was calibrated using spectral
lamps, the H
β
line itself and tungsten impurity lines. The
Doppler and instrumental line widths were, for the most
part 5% or less of the H
β
line width (see Sect. 2.3). The
data were corrected for optical depth effects. The experi-
mental line profile shapes agreed very well with the theo-
retical profiles. Shock reflection could cause much higher
theoretical electron number densities, but, particularly
with the conductivity test section absent, there is no place
for the shock to reflect and photographs of the shock wave
in the conductivity test section during air conductivity
tests Baughman et al. (1997) showed a nearly perfectly
formed normal shock. In the shock tube environment, the
boundary layer is cooler, not hotter, than the core flow, so
excess heating in the boundary layer cannot explain the
high observed electron densities. In the conductivity tests,
current was passed through the test gas, but estimates of
the maximum Joule heating of the gas are only a few per-
cent of the gas enthalpy. More importantly, 6 test runs
were taken without current with the conductivity test sec-
tion in place and 14 runs were made without the conduc-
tivity test section in place, and all of these “no-current”
runs showed the same unexpectedly high electron densities
as the runs made with electric current. Finally, one might
argue that, in some way, through a glint or reflection, one
is actually observing the driver arc at the driven gas opti-
cal observation station. This seems very unlikely, since the
electron number density histories were always observed to
follow exactly the times of arrival of the shock wave and
later, the cooler driver gas. The driver arc current follows
a totally different time history. In particular, for many
test runs, the driver arc current has fallen to essentially
zero when the pulse of electron number density is observed
at the driven gas optical observation station. Our conclu-
sion is that the driven gas electron number density and
temperature are, in reality, far above the adiabatic val-
ues expected based on shock velocity. We note that the
driven gas is highly ionized for most of the experimental
data range. The electron number density divided by the
total estimated particle density is
∼
0
.
03 at a shock veloc-
ity of 13 km/sec,
∼
0
.
12 at a shock velocity of 16 km/sec
and
∼
0
.
50 for shock velocities of 18 km/sec and above.
For the block of data points at a shock velocity of
∼
23 km/sec, the maximum experimental electron number
densities average
∼
1
.
2
×
10
17
cm
−
3
. At this shock velocity,
one may readily calculate a theoretical driven gas pressure
of 400 Torr for an adiabatic shock wave. By trial and er-
ror, one obtains the best match between the theoretical
and experimental electron number densities for a driven
gas temperature of
∼
18,000 K at this same gas pressure.
By constrast, theoretical calculations for a 23 km/sec adi-
abatic shock wave in 1 Torr room temperature hydrogen
give a theoretical driven gas temperature of only 4250 K.
3 Measurements – state of driven gas
3.1 Test time
The end of the useful test time was determined from the
abrupt drop in conductivity, electron number density and
radiation observed by the monochromators upon arrival
of the much colder driver gas after the driven gas. Arrival
of tungsten trigger wire contamination (monitored by a
monochromator) also signals the end of the test time. For
the present tests, with the electrical conductivity test sec-
tion in place, the test times were found to decrease from
∼
7to
∼
4
µ
sec as the shock velocity increased from 12 to
34 km/sec. In general, test times without the conductivity
test section were found to be somewhat longer than those
with the test section. The latter test times were typically
∼
10
µ
sec at shock velocities of
∼
21 km/sec.
3.2 Electron number density measurements
Figure 2 shows the experimental measurements (solid data
points) of the maximum electron number density behind
the shock wave plotted vs shock velocity. These data were
obtained from measurements of the Stark broadening of
the H
β
line as described in Sects. 2.2 and 2.3. The solid
line in Fig. 2 shows theoretical predictions of the elec-
tron number density based on the shock velocity using
208 D.W. Bogdanoff, C. Park: Radiative interaction between driver and driven gases in an arc-driven shock tube
The theoretical driven gas temperature referred to
above was calculated for adiabatic flow with no radia-
tion losses. If the driven gas acts like a black body, if
the driven gas radiation intensity (=
σ
T
4
, where
σ
is the
Stefan-Boltzmann constant and T is the gas temperature)
is comparable with the flow energy flux (
ρ
V
3
/2, where
ρ
is
the gas density and V is the shock velocity), this adiabatic
assumption cannot be used. This phenomenon is discussed
in some detail in Hall (1966). We have calculated the ra-
tioR=(
σ
T
4
)/(
ρ
V
3
/2) for various shock wave velocities
of the present study. R is between 0.027 and 0.037 for
shock velocities of 13 to 23 km/sec, but rises to 0.15 and
0.48 for shock velocities of 27 and 33 km/sec, respectively.
However, the hydrogen gas is nearly transparent in the
important energy-containing wavelengths of 100–1000 nm
for these temperatures. The minimum absorption lengths
range from 300 to 5000 cm, depending upon the driven
gas temperature, whereas the driven gas slug thickness
is typically 10–20 cm. Under these conditions, the driven
gas radiation can be calculated to be, at most, 2 to 3% of
the black body value. Hence, the radiation loss from the
driven gas slug is, at most, of the order of 1% of the flow
energy flux, and the adiabatic assumption used herein to
calculate the theoretical driven gas temperatures should
be very accurate.
100
9
8
7
6
5
4
3
2
10
9
EAST Facility
Test Runs 40/16-60
Driven gas: 1 Torr H
2
8
7
From E, I with low-moderate noise levels
From E, I with high noise levels
From n
e
+ AVCO report (Yos (1963)) theory
6
5
4
15
20
25
30
35
Shock velocity, km/sec
Fig. 3.
Experimental conductivity values versus shock velocity
10
1
EAST Facility
Test Runs 40/19, 20, 23, 24, 25, 26
27, 29, 32, 51, 52
Shock velocities = 21.4 - 25.8 km/sec
Driven gas: 1 Torr H
2
0.1
Individual runs - experiment
Average - experiment
Theoretical - parameter is T (K)
0.01
3.3 Conductivity measurements
14,000
0.001
19,000
Figure 3 shows the experimental measurements (solid and
open data points) of the electrical conductivity at the time
of maximum measured electron number density. Noise
pickup problems in the conductivity voltage measure-
ments from the driver discharge current (up to 1200 kA)
were significant. The open circle experimental data points
in Fig. 3 (at shock velocities above 26 km/sec) had high
noise levels and conductivity values derived from these
points would be very uncertain. The solid circle data
points of Fig. 3 (at shock velocities up to
∼
25 km/sec)
had low to moderate noise levels and, with averaging,
yield reasonably accurate conductivity values. Averaging
the nine data points at 22–24 km/sec gives a conductivity
value of
∼
40 Mhos/cm. From the driven gas tempera-
tures estimated from the electron density measurements
and the shock velocities (see previous section), a calcula-
tion can be made of the state of the driven gas. For this
driven gas state, a gas conductivity can obtained using the
theoretical conductivity calculations of Yos (1963). These
values are shown as the solid curve in Fig. 3. These con-
ductivity values are higher than the directly measured val-
ues. Thus, the measured conductivities imply somewhat
lower driven gas temperatures than the measured elec-
tron densities. Taking the average measured conductivity
of
∼
40 Mhos/cm at a shock velocity of
∼
23 km/sec, the
estimated driven gas pressure of 400 Torr for this condi-
tion from the previous section and using the theoretical
conductivity calculations of Yos (1963) yields a driven gas
temperature of
∼
12,000 K. While somewhat lower than
the temperature obtained using the electron number den-
12,780
16,000
0.0001
-30
-25
-20
-15
-10
-5
0
Time before shock passage, microsec
Fig. 4.
Experimental and theoretical conductivity values in
front of shock wave
sities, this value is still far above the adiabatic shock wave
value of 4,250 K.
3.4 Measurements of along-axis radiation
with radiometer
Good along-axis radiometer measurements were obtained
in test runs 72–75. For the last three of these test runs,
electron number density data was also obtained. The av-
erage shock velocity for these three runs was 21.6 km/sec.
From the average maximum electron density of 4
.
38
×
10
16
cm
−
3
and the shock velocity, a driven gas tempera-
ture of 13,600 K can be estimated following the procedures
of Sect. 3.2. From the shock wave equations, for an adia-
batic 21.6 km/sec shock wave, the calculated temperature
and pressure behind the shock are 3,950 K and 4
.
70
×
10
4
Pa, respectively. To obtain temperature estimates from
the driven gas radiation along the axis, a number of dif-
ferent driven gas temperatures between 10,500 and 13,500
K were assumed, all at the adiabatic shock wave equation
pressure of 4
.
70
×
10
4
Pa. From the monochromator traces
for runs 72–75, an average driven gas slug thickness of
D.W. Bogdanoff, C. Park: Radiative interaction between driver and driven gases in an arc-driven shock tube 209
14.8 cm was estimated. Using the methods of Karzas and
Latter (1961), Lasher et al. (1967) and Griem (1974a),
theoretical values for the radiation intensity along the
shock tube axis were calculated for each temperature.
With a theoretical radiation wavelength distribution avail-
able for each temperature, the wavelength correction fac-
tor required for interpreting the radiometer measurements
(see Sect. 2.3) can readily be calculated. For each of the
four test runs, by trial and error, the temperature giv-
ing a match between the theoretical calculations and the
radiometer measurements was found. The radiation in-
tensity was evaluated at the time of the maximum mea-
sured electron number density. The resulting temperatures
range from 11,050 to 13,020 K, with an average value of
11,980 K. While slightly lower than the temperature ob-
tained using the electron number densities, this value is
still far above the adiabatic shock wave value of 3,950 K.
experimental comparison, we ignore the very high exper-
imental conductivities for t later than
−
1
µ
sec. For very
low conductivities (below 0.01 Mhos/cm), the current data
are not reliable, being based on only one or two bits in the
digitizers. Nevertheless, there is a considerable amount of
experimental data between
−
20 and
−
5
µ
sec which is very
much greater than the theoretically predicted values. It
is di
N
cult to account for these high early conductivities
based on a pure hydrogen driven gas and the most likely
explanation would seem to be the presence of small quan-
tities of impurities which are much easier to ionize than
pure hydrogen. The conductivities of
∼
0
.
1 Mhos/cm at
times of
∼−
5
µ
sec, which are the highest which are pos-
tulated to be due to impurities, require electron number
densities of
∼
6
.
8
×
10
11
cm
−
3
. Taking this electron num-
ber density to be equal to the impurity number density, we
obtain a ratio of impurity number density to total number
density of
∼
2
×
10
−
5
. The impurity could well be sodium
chloride from the atmosphere, as discussed in Sharma et
al. (1990a) and Schneider et al. (1975). It is important
to note that ratios of the electron number density to the
total number density obtained after shock passage (see
Sect. 3.2) range from
∼
0
.
03 to
∼
0
.
5, thus being three to
four orders of magnitudes greater than the impurity ratio
estimated above. Hence, the impurity concentrations es-
timated above are completely incapable of explaining the
electron number densities observed after shock passage.
To try to estimate the temperature of the driven gas
slug based on the conductivity values of Fig. 4, we concen-
trate on the range
−
2
.
5to
−
1
µ
s, where the shock wave
has not yet reached the edge of the electrodes, but it is
believed that the conductivity due to ionized hydrogen
dominates over ionization due to impurities. In this time
range, the best fit for the temperature of the driven gas is
∼
15
,
500 K. For this driven gas slug temperature, the slug
radiation would heat the gas in front of the shock wave to
∼
760 K, with
∼
75% of the heating occurring in the last
microsecond before shock passage.
3.5 Conductivity measurements before shock arrival
Low, but measurable conductivities were measured before
arrival of the shock wave at the conductivity electrodes.
Radiation from the hot driven gas slug can photo-ionize
the driven tube gas in front of the shock wave. This phe-
nomenom was modelled starting with the assumption of
various driven gas slug temperatures and calculating the
radiation forward from the slug using the methods of the
previous section. Absorption and ionization coe
N
cients
for hydrogen are available in Cook and Metzger (1964).
Recombination rates for electrons and ionized hydrogen
molecules are available in Trainor (1978). Using this data,
the absorption of the radiation from the hot driven slug
in the hydrogen in front of the shock, and the consequent
photo-ionization and recombination were modelled, lead-
ing to predictions for the build-up of the electron number
density in front of the shock wave. The conductivity chan-
nel (see Fig. 1) was modelled as a 3.556 cm inside diameter
cylinder and the vacuum ultra-violet radiation of impor-
tance in the modelling was considered to be absorbed by
the cylinder wall. Thus, the solid angle of the light source
decreases rapidly as one moves further ahead of the shock
front. With predictions now available for the electron num-
ber density in front of the shock, the conductivity can be
estimated if the drift velocity of the electrons in the ap-
plied electric field is known. The applied electric field is of
the order of 1.4 V/cm for the measurements in question.
From Massey (1969), the drift velocity of the electrons will
then be
∼
1
.
3
×
10
6
cm/sec. With this information, theo-
retical predictions can be made of the conductivity profile
in front of the shock wave. Different profiles will be ob-
tained for different assumed driven gas slug temperatures.
Figure 4 shows experimental and theoretical conduc-
tivities in front of the shock wave, plotted versus time be-
fore the shock wave passage. Experimental data for 11 test
runs at shock velocities of 21.4–25.8 km/sec are shown.
The average shock velocity is
∼
23 km/sec. At times af-
ter
−
1
µ
sec, the shock wave has actually passed over the
leading edge of the 3.1 cm wide electrodes, leading to a
large increase in conductivity. Hence, for the theoretical-
3.6 Summary of driven gas temperature data
Table 1 gives a summary of experimental and theoretical
driven gas temperature data for two key blocks of data
discussed in Sects. 3.2 to 3.5. For the first block of data,
the conductivity test section was in place and the average
shock velocity was 23 km/sec. Data from this data block
can be seen in Figs. 2 and 3 between 21.5 and 25 km/sec.
For the second block of 4 test runs, the conductivity test
section was not in place and the average shock velocity
was 21.6 km/sec. Shown in the table (in order) are the
temperatures calculated from the electron number densi-
ties (Sects. 3.2 and 3.4), those calculated from from the
conductivity measurements after the shock wave passage
(Sect. 3.3), those calculated from the driven gas radiation
forward along the tube axis (Sect. 3.4) and those calcu-
lated from conductivity measurements ahead of the shock
(Sect. 3.5). Finally, theoretical driven gas temperatures
based on the adiabatic shock wave equations and the shock
velocity are also given.
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