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Maïlys
title: Design of a Spatially Resolved VUV Spectroscopy System for Shock Tube Flows
source_pdf: RHTG_Buquet_et_al_2022[1].pdf
conversion_note: Two-column PDF linearised to Markdown. Figures inserted inline where captions were detected; extracted figure crops are used where available, page renders are included as backup.
Design Of A Spatially Resolved Vuv Spectroscopy System For Shock
TUBE FLOWS
Maılys Buquet, Alex Glenn, Peter Collen, Benjamin Williams, Matthew McGlivray, and Tobias Hermann
Hypersonics Group, Oxford Thermofluids Institute, University of Oxford, Southwell Building, Osney Mead OX2 0ES
Oxford, United Kingdom
1. INTRODUCTION spheres as thin as Mars’, equilibrium states take more
time to be reached. The non-equilibrium component of
the shock layer, where dissociation, ionisation and exciOne of the side effects of using drag to slow-down space- tation are not in equilibrium with their backwards reaccraft during their entry into an atmosphere is the resulting tions, can account for a large proportion of the emitted
substantial heating to the vehicle. The resulting heat flux, radiation [BJC16]. Although critical, the quantity of exwhich can lead to failure of the structure, is strongly influ- isting spectra dataset in the VUV region is limited due to
enced by a change in gas composition due to the sudden its challenging acquisition.
and steep temperature gradient through the shock near
the surface [Jr.19]. These strong thermochemical reac- This paper first describes the experimental arrangement
tions take place within the shock layer, in which the im- and working principle of the VUV spectroscopy system
balance in gas species initially results in a state of non- under development in the Oxford Hypersonics laboratory,
equilibrium where the internal degrees of freedom of the followed by a detailed description of the optical system
gas are excited, heavily influencing radiation. For mis- design and of its analysis through ray-tracing simulation
sions such as Mars return, during which entry veloci- in Section 3. Section 4 explains the calibration and charties can be as high as 15 km.s−1, radiative heating be- acterisation of the system, and Section 5 defines the test
comes the primary source of heat load on the vehicle’s conditions selected through shock tube and nonequilibsurface [BJ14]. As this process involves complex models rium radiative transport and spectra simulations using the
and is computationally expensive, laboratory ground test- simulation tools Poshax3 and NEQAIR for future test
ing can reduce uncertainty by providing validation data. campaign.
Shock tube experiments are a tool to recreate these
thermochemical phenomena in a ground-based facility.
2. EXPERIMENTAL ARRANGEMENT
Emission spectroscopy can be used to investigate a slug
of gas thermochemically similar to the gas encountered
by the vehicle during re-entry in order to measure radia- This section presents the VUV-system working principle
tive emission and spatially resolve temperature and gas and how it will be used on the T6 Stalker wind tunnel.
species densities. Knowledge of these quantities offers a
better understanding of the flowfield around the vehicle,
2.1. Facility
and a better prediction of the contribution from radiative
heat transfer, currently predicted with an uncertainty of
the order of 80% [JMG+13]. This uncertainty leads to The T6 Stalker Tunnel shock tube was previously used
excessive safety margins in the design of thermal protec- to perform emission spectroscopy in the wavelength
tion systems, which amount to a substantial portion of the regime of 300-850 nm to measure radiation in the shock
vehicles’ mass. It is therefore crucial to be able to quan- layer [CDM19a, GCM21, GCJ+]. A VUV emission
tify it. spectroscopic system is currently under development to
use on T6 in its shock tube mode, with the goal to perAs velocity increases, vacuum ultraviolet (VUV) radia- form spectroscopy for shots in the velocity range of 10tion presents an increasing contribution to the total ra- 15 km.s−1.
diance [HLZ+16]. This radiative heat flux arises from
high-energy electronic transitions of atomic nitrogen and The T6 Stalker Tunnel is a high enthalpy ground testing
oxygen, characterised by short wavelengths and strong facility, able to perform as a reflected shock tunnel, an exintensity radiation. By comparing the relative line in- pansion tube, or a shock tube of different diameters. Its
tensities of their multiplets, the ground state densities latter mode is of interest in this paper, but details of the
can be determined, which makes VUV spectral data par- facility’s development were reported in various publicaticularly useful to characterise the flow. As density is tions [CDS+21, SCG+]. A schematic of the tunnel in its
especially low during high-altitude flight, or in atmo- different configurations is shown in Fig.1.
Figure 1. T6 Stalker Tunnel schematic [CDM+19b].
The driver section contains a piston separating highpressure reservoir gas and lower-pressure, low molecular weight compression tube gas. The piston is accelerated by the reservoir gas and quickly compresses the
driver gas to high pressure and temperature against a
metal diaphragm separating the driver and the shock tube.
When the diaphragm ruptures, the driver gas is free to expand into the low-pressure test gas, driving a shock wave,
while still compressed by the piston to maintain pressure
in the driver section and avoid expansion waves to travel
downstream and interact with the shock. The slug of gas
following the shock undergoes the same non-equilibrium Figure 2. Schematic of the VUV system’s different parts
thermochemical processes as the stagnation streamline in and of its dynamic features. From top to bottom: VUV
front of a (re-)entering vehicle, allowing investigation of system inserted in the shock tube, bellows and purple sysemitted radiation of interest. tem adjusting for tunnel recoil during a shot, VUV system
extracted from the tunnel. Not to scale.
2.2. Working Principle of the VUV spectroscopic
system
Because molecular oxygen and water vapour absorb
VUV wavelengths in ambient air, any acquisition set-up
must operate either using oxygen-free gas or under a high
level of vacuum, the latter being the approach of the current work. The collection optics system is designed to be
contained in vacuum chambers fitted to the shock-tube
via the test section window. The different parts of the
set-up can be seen in the schematic in Fig.2 and in the
CAD model in Fig.3. This system consists of one circular and one square vacuum chamber attached to a VUV
Spectrograph (McPherson 207V). An intensified P43 iStar sCMOS camera is connected to the spectrograph to
record the spectra. The red window holder is attached
to the barrel and allows connection of the VUV system
via the green interface fitter plate. The mounting of the
chambers is separated into a static yellow system which is
fixed to the laboratory floor, and blue and purple dynamic
systems respectively moving in the lateral and axial directions with respect to the main T6 barrel, as shown in
Fig.2. The whole system is pumped down to a low vac- Figure 3. CAD model of the VUV system, inserted (top)
uum level (10−3 Pa range) up to the test section’s win- and extracted (bottom). Purple parts allow for axial
dow using a dry scroll pump (Edwards nXDS10i) and a movement during tunnel recoil, blue parts for lateral
turbopump (Edwards nEXT300D) mounted in series. movement while yellows parts are fixed
2.3. T6 experiments and turn-around During tunnel turn-around, the test section’s window and
its insert move together with the VUV system to main-
tain the vacuum isolated on the largest volume possible.
Before being secured to the tunnel, the VUV system can The red window holder stays attached to the barrel, and
be positioned next to the test section and the length of will be reconnected to the interface fitter plate when turnthe legs adjusted for correct alignment of the window around is finished.
with the shock tube’s axis. As can be seen in Fig.4,
the window insert tightly fits in the red window holder
previously bolted to the tunnel. A set of four rod guides
helps to ensure alignment. Once in position, the green
2.4. Calibration
interface fitter plate and the red window holder can be
bolted together. At this point, the entire VUV system up
to the window can be pumped down. A gauge positioned
Once the tunnel is pushed upstream for turn-around, the
on the cylindrical chamber allows to keep track of
VUV system can be pushed back to its nominal position,
the level of vacuum. When a satisfactory threshold is
200 mm closer to the tunnel’s axis. The calibration box
achieved, the VUV system is ready for a shot. The
shown in Fig.6 and the deuterium lamp can then be fitted
set of bellows connecting the VUV system to the test
to the interface window holder as shown in Fig.5, and the
section as well as the purple system allow the system to
extra volume contained in the calibration box between
accommodate the tunnel’s recoil movement.
the light source and the window pumped down using the
pipework shown in schematic in Fig.7. Calibration of a
single point can be performed during tunnel turn-around,
When T6 is back at atmospheric pressure after a shot, in conditions as similar as possible to the shot’s ones.
the VUV system can be detached by unbolting the
interface fitter plate from the window holder. The
VUV system is then pulled backward across the rails
using the handles, to the maximum length of 200 mm
allowed by the bellows joining the vacuum chambers.
The cylindrical chamber’s movement along the rails is
limited by hard stops in both directions, ensuring precise
realignment and repeatability for the next shot. On the
other end of the bellows, the optics table supporting the
spectrometer and the square vacuum chamber remains
static. When the tunnel is free of the VUV system,
it can be pulled upstream to proceed with the tunnel
turn-around procedure.
Figure 5. Deuterium lamp and calibration box mounted
on the window to perform calibration during tunnel turn-
around
Prior to the test campaign, a range of spatial calibrations
can be performed independently of T6 to use as compar-
ison for the daily single point calibrations taken during
the test campaign, between the tunnel’s shots. In this sce-
nario, the sliding plate in Fig.6 on which the deuterium
lamp is mounted can take different positions along the
window. This allows to obtain calibrations for a range
of axial locations, modelling the shock moving along the
Figure 4. Mechanical attachment of the VUV system to tube. By shortening the length of the tables legs, the systhe tunnel for a shot, and detachment for turn-around and tem can be put on wheels and moved within the laboracalibration tory with minimal dissasembly.
3.1. Mirrors Characteristics for Telecentric System
The mirrors were designed using an optimisation ap-
proach, and comprise two plane mirrors forming a
periscope system, two powered mirrors respectively col-
limating and focusing the light onto the spectrometer slit,
and a cylindrical mirror between the latter two to correct
for astigmatism. The numbers they were assigned and
will be referred by in the following section can be found
in Table 1.
Table 1. Mirrors denominations and characteristics
N◦ Name Shape
1 High periscope Rectangular plane
2 Low periscope Rectangular plane
Figure 6. Calibration box details (exploded view). The 3 Collimating Spherical plano-concave
sliding plate with the deuterium lamp can be moved along 4 Cylindrical Cylindrical plano-concave
the tunnel’s axis to generate a set of calibration points 5 Focusing Spherical plano-concave
along the window.
In a telecentric system, light is collimated by placing a
VE1 Edwards powered mirror at a distance equal to its focal length
SP10K
KF10 to from the region to be imaged, i.e the center-line of the
KF25
Dry scroll shock-tube in this case. The rays leaving the mirror focus
pump towards infinity, creating chief rays parallel to the opti- Edwards Cross KF25 KF25 nXDS10i
Deuterium cal axis. Maintaining lines of sight perpendicular to the
lamp shock can greatly reduce spatial blur [GCGY09], which
Reducing KF16 to V3
bulkhead KF10 centring ring VE3 is particularly important for study of the non-equilibrium LewVac Edwards clamp + KF16 bulkhead Tee V1 25KF LewVac AV-25KF-M assembly clamp SP10K KF25 KF25 Calibrationset-up KF16
AV-25KF-M region where the gradients in emission characteristics are V2
KF25
Turbopump AV-25KF-M LewVac Window very strong with distance from the shock. The second
Edwards connection KF25 to nEXT300D powered mirror focuses the light onto the spectrometer KF40 CF100
Cylind. KF40 CF100 gauge slit. To ensure telecentric imaging characteristics, it has plate KF40 Sqr. PfeifferKF40 chamber vac. vac. KF25 KF25 VacuumPKR360 KF40 Spectrometer to be located a distance equal to the sum of the powered KF16 chamber AdaptorVUV-02-03
KF40 Reducing KF16 to mirrors focal lengths away from the collimating mirror.
KF10 centring Camera
+ KF16 bulkhead Andor ring As its virtual object is located at infinity due to the col-
clamp iStar sCMOS
limation of the incoming rays, this also means that the
VE2
Edwards SP10K mirror must be located one focal length away from the
spectrometer’s slit. The geometry of the system is shown
in Fig.8.
Figure 7. Pipework schematic to pump down the VUV
system and the calibration box
3. OPTICAL DESIGN
The optical system presented in this work consists of a
set of five mirrors, redirecting the light from the centerline of the shock tube to a high spectral resolution
spectrograph on which an intensified sCMOS camera is
mounted. Windows have to be made of magnesium fluoride (MgF2) and mirrors of VUV-Enhanced Aluminium
and MgF2 to allow transmission and reflection of VUV
light. To reduce spatial blur and obtain the highest fidelity and intensity of signal, the collection optics set-up
was designed in a telecentric configuration [GCGY09].
Telescopic systems suffer from larger spatial blur due to Figure 8. Geometry of telecentric system.
ray divergence. Numbers correspond to numbering shown in Table 1.
These optical constraints, coupled with the geometri- An aperture the size of the window is placed at a discal constraints from the pre-existing vacuum chambers tance equal to the tunnel’s radius from the light source.
shown in Fig.9 were used in an optimisation procedure The mirrors were located and angled using the informato obtain the mirrors’ positions, angles, focal lengths and tion obtained from the optimisation code, and modelled
diameters for optimum spatial imaging of the test sec- using the refractive indices of MgF2. Various apertures
tion. This code also enforces that all optics have the same were added to model the bellows and vacuum chamf-number (F#) as the spectrometer to avoid under-filling bers’ flanges and confirm no light was cut. Light sources
or risking stray light interferences, and sets limits to the of wavelength 150 nm propagating in vacuum were sent
magnification of the system, which is defined by the ra- from different points along the window’s length.
tio of the two powered mirrors’ focal lengths following
. In summary, focal lengths of theMsystem = fcollimatingffocusing
powered mirrors are constrained by their distance from
each other, their respective distances from the center-line
of the tunnel and from the spectrometer slit, as well as the
magnification of the system.
Finally, as the collimated light has to travel through a set
of bellows parallel to the shock tube between the two vacuum chambers, the light exiting the collimated mirror has
to be perfectly parallel to the tunnel’s axis. This puts an
additional constraint on the position of the periscope mirrors, which are used at an unconventional angle shown in
Fig.9. The angle necessary to redirect the light coming
from the test section to the collimating mirror generates
an extra component to the light path, such that the second periscope mirror has to be shifted further towards the
collimating mirror in order to collect as much light as Figure 10. Ray-tracing simulation using Optometrika.
possible from the first periscope mirror, from which it is The chiefs rays travelling to and from the periscope mirtilted at an angle lower than the common 45◦. rors are angled, while they remain parallel to the optical
axis when leaving the collimating mirror (bottom right).
Ray-tracing simulations allowed observation of astigma-
tism and loss of intensity along the light path. The fourth
mirror, initially flat with sole purpose to redirect the light
from the collimating to the focusing mirror, was replaced
by a cylindrical mirror to correct the astigmatism shown
on the top half of Fig.11. Before correction, the circu-
lar light source gets strongly uni-directionally deformed
Figure 9. Position of mirrors in the vacuum chambers. along the light path, and intensity is so spread out that
any signal is hardly recovered by the time it reaches the
spectrometer slit. Figure 12 shows that the astigmatism
is already present when the light reaches the collimating3.2. Ray-tracing simulations
mirror, where the ideal circle of light is turned into an
ellipse. This type of optical aberration is uni-directional
Ray tracing simulations were performed to observe, because rays lying in perpendicular planes on the optical
quantify and correct optical aberrations using the Op- axis focus at different distances. Astigmatism could be
tometrika MATLAB library [Yur02]. This allowed to introduced by the large angles of the periscope mirrors
confirm collimation of the rays with the current mirrors’ generating light paths of different lengths for rays emaconfiguration, expected magnification from Gaussian op- nating from the same source, which can be seen by the detics as well as expected field of view. Simulations were formation of the signal received by the periscope mirrors
carried out by collecting the light at the spectrometer slit on Fig.12. By using a cylindrical mirror, convergence of
by modelling a virtual object of equal dimensions and the rays in the dimension suffering from astigmatism is
pixel resolution as the camera’s sensor, and sending light introduced and an axisymmetric signal of satisfying infrom different point sources located at the center-line of tensity is recovered. This same strategy was used for the
the tunnel. Samples of the simulations are shown in VUV spectroscopy set-up in EAST [GCGY09]. Figure
Fig.10, for the case of three 3 mm diameter light sources 12 shows the effect of the cylindrical mirror on recovereach made of 20,000 rays. ing a circle at the spectrometer slit.
from the cylindrical mirror. With such a small distance
between the two mirrors, the large turning angle of the
rays led to large astigmatism. By pushing the focusing
mirror further away to limit the angle of incidence of the
rays to 30◦, linearly increasing the focusing mirror’s fo-
cal length, simulations showed better signal intensity and
a lower curvature of the cylindrical mirror necessary to
compensate for aberrations. This however led to a change
in magnification of the system from Mideal = 10.4967
to Mpractical = 7.1777, which corresponds to a field of
view along the test section’s window of approximately
100.5 mm. The field of view calculated through Gaussian
optics was confirmed by simulations, as shown in Fig.13.
Figure 11. Simulation of the signal collected at the spectrometer slit from 5 light sources before (top) and after
(bottom) the use of a cylindrical mirror. For the noncorrected image, the signal is shown with increased contrast and saturation to compensate the loss of intensity.
Figure 13. Field of view measured from simulation is
99.7 mm, which is close to the theoretical 100.5 mm ob-
tained from Gaussian optics. The 6.5×6.3 µm pixel size
shown corresponds to the sensor. The resolution will
however be limited by the intensifier, which has a coarser
pixel size of 25 µm.
4. CALIBRATION OF THE SYSTEM
To obtain correct absolute radiation values, the system
must be calibrated in three dimensions, λ (wavelength),
y (space) and z (intensity). The methodology presented
in [Cru14] and previously used to calibrate spectral data
recorded in T6 [CDM19a, GCM21] was followed to the
extent possible with the current state of development of
the system, and Table 2 summarises whether the calibra-
tion curves were obtained experimentally or through simFigure 12. Projected light on every mirror in the light
ulations.
path, generated by a diverging light source of 1 mm diameter located at the tunnel axis. Using the cylindrical
mirror, a circle is recovered at the spectrometer slit where Table 2. Smearing functions summary. Details and exthe object is imaged. Light is traveling from bottom to planations can be found in subsequent subsections.
top.
Calibration function Method Figure Dimension
A compromise had to be made on the ideal magnification ILS Experiment 16 Wavelength
of the system, defined by the ratio of the maximum length SRF Simulation 17 / 21 Space
along the test section collected by the mirror and the size LSF Simulation 20 / 21 Space
of the camera’s sensor. Ideal magnification led to a small Shock motion Simulation 21 Space
focal length of the focusing mirror, which directly im- Rad. per count Experiment 23 Intensity
pacts its distance from the spectrometer slit and therefore
4.1. Wavelength calibration the best fit for VUV cameras, and that neither Gaussian
nor Lorentzian functions alone could accurately capture
4.1.1. Wavelength to pixel fit the ILS with intensified CCD arrays [Cru14]. Lines
of lower intensities are then passed through the same
Measurement of known atomic lines from a mercury function to validate the quality of the fitting. Knowledge
lamp in the 253-580 nm range was used to linearly fit the of this function will also be used following experiments
peaks to their expected wavelengths, as shown in Fig.14. to obtain an estimation of electron densities [Cru12].
For each spectral image taken, all identifiable spectral 4 104
lines were used to perform independent linear fittings
(Fig.15) and cross-compare the pixel location to wave- 3.5
length correspondance obtained. The fitted wavelengths 3
axis is then used to find the instrument line shape function 2.5
(ILS).
2
0 105 500 1000 1500 2000 2500 1.5
2.2
4 1
2
0.5
1.8
0
350 355 360 365 370 375 380 385
1.6
1.4 Figure 16. ILS fitting using the square root of a Voigt
1.2 3 function
2
1 As seen in Fig.16, the ILS obtained is asymmetric, which
0.8 1 could be due to slight misalignment of the optics inside
the spectrometer, or of the light source in front of the
0.6 300 320 340 360 380 400 420 440 460 480 slit itself. The full-width half-maximum Gaussian and
Lorentz coefficients from a square root of Voigt func-
tion fitting were found to be 1.3221 and 0.0476 nm reFigure 14. Pixel to Wavelength Calibration - Sample set spectively. EAST experiments performed using the same
from mercury lamp emission slit width of 100 µm and same grating of 150 gr.mm−1
had ILS with similar Gaussian and Lorentz coefficients
480 of 1.3299 and 0.0294 nm [AAts].
460
4.2. Spatial calibration 440 4
4.2.1. Resolution of optics
420 3
400 35
380 2 30
360
340 25
320 1
20
300
0 500 1000 1500 2000 2500 3000
15
Figure 15. Pixel to Wavelength Calibration - Linear Fit.
Numbers corresponds to the peaks shown in Fig.14.
10
4.1.2. Spectral Instrument Line Shape (ILS) 5
An accurate characterisation of the ILS is essential to be
able to both model and quantify physical effects affecting -0.050 -0.04 -0.03 -0.02 -0.01 0 0.01 0.02 0.03 0.04 0.05
the spectral line shape, such as pressure broadening or
Stark effect, dominant at the speeds of interest [Cru12].
Using the most intense spectral lines on each calibration Figure 17. Approximated optical resolution function, usimage recorded, the square root of a Voigt function is fit ing the signal received by the collimating mirror from a
to the signal. It was empirically found that these were point source at the center-line of the tunnel.
Using the ray-tracing simulation results, the signal re- to its derivative, is shown in Fig.20. If the optical system
ceived at the position of the collimating mirror was ob- provided perfect imaging, this function would correspond
tained to measure the angle between the edge rays ema- to a Dirac impulse function located at the sensor’s centernating from a point source on the tunnel’s axis. The op- line.
tical resolution function in Fig.17 was approximated by
a triangle of the same angle, as the light from the point
source captured by the camera is described by the vol- 1800059.06 59.11 59.16 59.2 59.25 59.3 59.34 59.39 59.44 59.48 59.53
ume of the cone contained within the edge rays [Cru14]. 16000
This approximation confirms the effectiveness of the telecentric system to keep this volume and therefore the as- 14000
sociated spatial smearing small. As shown in Fig.17, 12000
the angle of the cone is 43% smaller than the one from
the EAST collection optic system presented in [Cru14] 10000y
which recorded VUV spectra with satisfying spatial res- 8000
olution, which suggests less spatial merging of emission 6000
characteristics.
4000
2000
4.2.2. Resolution of collection optics and CCD array 0
8.22 8.24 8.26 8.28 8.3 8.32 8.34
By simulating 2E6 light rays emanating from the tun- Figure 19. Approximated Spatial Edge Spread Function
nel’s axis, clustered to form a square light source of
known dimension and location, a sharp edge was simulated (Fig.18) and used to obtain an approximation of the
resolution function and estimate the spatial smearing of The LSF curve was found to be slightly shifted from the
the optics. center of the camera’s sensor. It can be seen on Fig.18
that the image is shifted to the left by a few pixels, and
suffers from some astigmatism deforming its shape from
a perfect square. It can also be observed that the intensity
tends to be higher towards the right, which could also be
observed to a lesser degree in the simulation in Fig.11.
This could be due to the lack of symmetry of the optical
system creating a higher ray concentration to one side,
which generates an asymmetric and slightly shifted spa-
tial smearing function.
59.11105 59.16 59.2 59.25 59.3 59.34 59.39
18
16
14
12
10
y
8
6
Figure 18. Light received by the virtual sensor from the
sharp edge simulation. Location of the middle pixel of 4
the sensor is shown. 2
0
8.22 8.24 8.26 8.28 8.3 8.32 8.34
The camera sensor was modelled by positioning a virtual
screen of equal dimension and resolution at the spectrom- Figure 20. Approximated Spatial Line Spread Function
eter slit location. The outer edge of the emitting square
was positioned in the middle of the field of view, ideally creating a step in intensity right in the middle of the
camera’s sensor. The intensity of each column of pix- Some additional smearing may also be introduced by the
els, representing spatial location along the window, was optics contained in the spectrometer, which also combinned to obtain the edge spread function (ESF) shown prises a cylindrical mirror to correct for the astigmatism
in Fig.19. The line spread function (LSF), corresponding measured by the manufacturer.
4.2.3. Shock motion 4.3.2. Raw signal corrections
106The loss of resolution due to the shock motion during 15
the camera shuttering was approximated by defining the
smearing length as the product of the shock velocity and
the camera’s gating time. The corresponding spatial resolution function was modelled as a square wave of equiv- 10
alent width. An example can be seen in Fig.21.
5
4.2.4. Total spatial smearing function
The functions presented in section 4.2 were convolved,
0
and the resulting spatial smearing function applied to the 120 130 140 150 160 170 180
radiance simulations as shown graphically in Fig.21.
Figure 22. Comparison of raw and corrected signals
A picture of the background noise for the same spec-
trometer and camera parameters was recorded at the same
level of vacuum, and subtracted from the calibration sig-
nal. As the deuterium lamp underfills the spectrometer
slit which has the same F# as the rest of the optics, the
calibration signal was multiplied by the ratio of the spec-
trometer and lamp solid angles Ωspectrometer to compen- Ωlamp
sate for the extra signal which will be collected during a
shot. Finally, the signal was multiplied by the reflectiv-
ity curve of the Al+MgF2 mirror coating for each mirror
used in order to simulate the optical loss through the fo-
cusing optics which are not present in the current state of
the set-up. The effects of these corrections can be seen in
Fig.22.
4.3.3. Intensity fit
10-4
Figure 21. Spatial smearing function applied to all radi- 4
ation simulations
3
4.3. Intensity calibration
2
Finally, an intensity calibration was performed using a
deuterium lamp (Hamamatsu L7292). The light source
and camera were mounted on the spectrometer, and the 1
120 130 140 150 160 170 180
system pumped down to 1.35E-5 mbar before recording
spectra and fitting it to the manufacturer’s spectral radiance curve.
Figure 23. Radiance per count calibration for each wave-
length
4.3.1. Wavelength fit
The corrected signal was finally fitted using the expected
A linear wavelength fit was found to be insufficient to radiance curve from the deuterium lamp. The obtained
satisfyingly fit the signal, and was therefore refined by values of counts per spectral radiance as a function of
performing linear interpolations on smaller sets of pix- wavelength shown in Fig.23 can be used to convert the
els. Once the signal was fitted in wavelengths, corrections spectra to units of radiance.
could be applied.
5. TEST CONDITION SELECTION
Table 3. Flow conditions simulated in view of the next
test campaign. Freestream mass fractions are assumed to
be 0.767 for N2 and 0.233 for O2.
The smearing functions parameters obtained in Section Shot P∞(Pa) u∞(km.s−1) T∞(K)
4 were applied to the simulations presented in this sec- EAST 57-8 26.66 10.66 293
tion to create a more representative model of a non-ideal
Fire II 2.08 11.36 195
physical optical collection system.
Non-eq 6.66 11.38 293
Shock-tube post-shock relaxation simulations were performed using Poshax3 [JG22], and the results of temperatures, pressures, and species number densities along
lines of sight perpendicular to the window’s test section used as an input for radiation simulations using
NASA’s code NEQAIR. These simulations aim at reproducing conditions from either experiments performed by 5.1. Poshax3 and Neqair Simulations
NASA in their Electric Arc Shock Tube (EAST) facility
which showed experimentally measurable levels of radiative emission in the VUV, data points from previous test
5.1.1. EAST shotcampaigns performed in the Oxford T6 wind tunnel, or
re-entry points from the Fire II mission.
Three conditions with flow parameters shown in Table Experiments performed in EAST were simulated and
3 were selected for showing good trade-off between the compared to shots previously performed in T6. Shots
high level of radiance shown by simulation in the wave- highlighted by NASA for showing measurable spectral
length range of 120-200 nm, and the spatially large region radiance levels in the VUV range of the spectrum were
of non-equilibrium. It is therefore believed that these selected.
points will generate measurable data during experiments,
as the level of radiance intensity and the non-equilibrium
region are large enough to be respectively spectrally and
spatially resolved by the camera and the optical collection system. These data points are shown in the context
of the facility’s history and literature in Fig.24.
103
102
EAST 57-8 (lower VUV)
221 Figure 25. Post-shock three-temperature variation from
101 simulation of the EAST shot 57-8 [AAts]
229Non-eq
231230
Fire II
228 227 As seen on the temperature trace in Fig.25, shot 8
100
6 8 10 12 14 16 18 from the EAST test campaign 57 was found to give a
non-equilibrium region of about 5 mm length behind the
shock. Although short, this can be sufficiently resolved
Figure 24. Tests of interests in facility and context in by our optical system which has a spatial resolution of
literature. The T6 shots data is presented in [CDS+21, 0.047 mm per pixel.
HCG+]. EAST shots data can be found in [AAts].
Figure 26. Radiance obtained from simulation of the
EAST shot 57-8 [AAts] Figure 28. Radiance obtained from simulation of the Fire
II mission re-entry point
The spectral radiance shown in Figs.26 and 27
in the 120-200 nm range reaches a maximum of
1200 W.cm−2.Sr−1.µm−1 over this region, giving measurable radiance in the EAST facility which uses an optical system of similar resolution [GCGY09, Cru14]. The
next test campaign will therefore aim at recreating this
condition. Corresponding flow characteristics are shown
in Table 3.
This datapoint was however judged particularly inter-
esting because of the large non-equilibrium region it
presents. Figure 25 shows a length of 24.24 mm behind
the shock before temperatures start to plateau, which cor-
responds to a quarter of our available field of view. In this
case, temperatures seem to keep on rising slightly long
after the shock has passed, instead of completely plateau-
ing to a steady value. Corresponding flow conditions can
be found in Table 3.
Figure 27. Spectral and cumulated radiance from simulation of the EAST shot 57-8 [AAts]
5.1.2. Fire II re-entry point
A simulation of a trajectory point from the Fire II mission, corresponding to t = 1634 s shown spectral radiance
levels lower than the first point selected in Section 5.1.1,
with a maximum of 430 W.cm−2.Sr−1.µm−1 at 120 nm Figure 29. Spectral and cumulated radiance from simuas shown in Figs.28 and 29. lation of the Fire II mission re-entry point
Figure 32. Radiance obtained from simulation a previous
T6 shot
Figure 30. Post-shock three-temperature variation from
simulation of the Fire II mission re-entry point
5.1.3. Non-equilibrium point
Finally, a data point from a previous test campaign performed in T6 was simulated. As shown in Figs.33 and 31,
temperature and radiance plateau shortly after the shock,
after just less than 10 mm. However, the spectral radiance profile shown in Fig.33 presents a few high peaks at
120, 131, 149.4 and 174.4 nm with spectral radiances as Figure 33. Spectral and cumulated radiance from simuhigh as 1000, 1026, 1056 and 1125 W.cm−2.Sr−1.µm−1 lation a previous T6 shot
respectively. This point was therefore selected as the radiance from this shot should be easily measurable. Corresponding flow conditions can be found in Table 3.
6. CONCLUSION
A VUV spectroscopy system is currently in the final de-
sign stage to be mounted on the Oxford T6 Stalker steel
shock tube to perform emission spectroscopy. The col-
lection optics were designed as a telecentric system using
an optimisation code, and widely characterised through
ray-tracing simulations. The system in its current state
was calibrated in all three dimensions of wavelength,
space and radiance. A few experimental points of interest
for investigation of the non-equilibrium region have been
highlighted. These conditions of interest were simulated
using Poshax3 and NEQAIR to obtain predictive levels of
radiance in the VUV. Before the test campaign to come,
further study of absorbance and individual spectral lines
in these regions will be conducted through simulations,
as well as further characterisation of the system using the
optics to compare with simulations. Some phenomena
observed in previous test campaign in T6, such as slight
Figure 31. Post-shock three-temperature variation from hydrogen contamination and underestimation of electron
simulation a previous T6 shot density will also be added to the simulation model.
7. ACKNOWLEDGMENT [GCM21] A. B. Glenn, P. L. Collen, and
M. McGilvray. Experimental non-
equilibrium radiation measurements for
This research was funded by the UKRI Future Leaders low-earth orbit return. AIAA SCITECH
Fellowship scheme (grant number MR/T041269/1), and 2022 Forum, 2021.
we extend our gratitude to UKRI. For Open Access, the
[HCG+] Tobias Hermann, Peter Collen, Alexauthor has applied a CC BY public copyright licence to
Glenn, Tamara Sopek, Matthewany Author Accepted Manuscript (AAM) version arising
McGlivray, , and Luca di Mare. 9thfrom this submission.
International Workshop on Radiation of
High Temperature Gas.
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Additional extracted image crops
The following extracted crops could not be confidently mapped to a numbered caption and are included for completeness.
Summary
The T6 Stalker Tunnel shock tube was previously used to perform emission spectroscopy in the wavelength regime of 350-850 nm to measure radiation in the shock layer. A VUV emission spectroscopic system is currently under development to use on T6 in its steel shock tube mode, with the goal to perform spectroscopy for shots in the speed range 10-15 km.s−1 and for various gas densities. This system was designed to offer fast turn-around, easy calibration and ensure repeatability between experiments. It comprises a telecentric optical system developed using an optimisation approach, and ray tracing simulations were run to observe, quantify and correct optical aberrations.