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Expansion tunnel characterization and development of non-intrusive microwave plasma diagnostics

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EXPANSION TUNNEL CHARACTERIZATION
AND DEVELOPMENT OF
NON-INTRUSIVE MICROWAVE PLASMA DIAGNOSTICS
by
Aaron T. Dufrene
February 1, 2013
A dissertation submitted to the
Faculty of the Graduate School of
the University at Buffalo, State University of New York
in partial fulfillment of the requirements for the
degree of
Doctor of Philosophy
Department of Mechanical and Aerospace Engineering
UMI Number: 3554446
All rights reserved
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a note will indicate the deletion.
UMI 3554446
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Copyright by
Aaron T. Dufrene
2013
ii
Acknowledgements
I would first like to acknowledge my advisor Professor Matthew Ringuette for working
with me despite my unconventional status as a part-time student. He brought a different
perspective to the table that helped expand the way I thought about various issues to improve my
research. I also have to acknowledge my MS advisor, Professor Joanna Austin, who got me
started down the path of experimental hypersonics, which has turned to an exciting and fulfilling
career path.
I would also like to thank Dr. Michael Holden for finding me at a conference in Reno and
giving me the opportunity to work with the amazing staff and the world-class facilities at
CUBRC. Dr. Matt MacLean played the key role in developing numerical tools to help
characterize LENS XX, and both he and Tim Wadhams have provided invaluable insight over
the years. Manu Sharma helped me setup HET at UIUC and then continued to provide helpful
and relevant measurements and analysis on his own that was useful when characterizing
LENS XX. Professor Stephen Andre introduced me to microwave measurements and provided
input every step along the way. Dr. Chris Davis worked with me on EDA’s microwave
resonance probe and loaned us equipment to do testing in LENS XX. There have been too many
fellow students, technicians, machinists, and mechanics to thank all of them by name, but I
would especially like to thank Zakery Carr, Adam Devoria, Gary Paone, Dan Czora, Tom
Offhaus, and Alice Miller for their extra effort in helping me with this work.
This would not have been possible without the love, support, and encouragement of my
family. Emily, I can’t thank you enough for all you have sacrificed to help me succeed with this
goal; I love you so much. Finn and Sophia, you’re my inspiration and I’m so excited to finish
iii
this up so we can spend more time playing, exploring and growing together. To my parents,
thank you for everything along the way, the examples you set and your continuous support
inspired me to keep going one step further. I’d also like to thank all my friends for their
encouragement and well needed distractions throughout this long process.
This research was funded in part through a Multi-University Research Initiative (MURI)
granted by the Air Force Office of Scientific Research (AFOSR), as well as, NASA, and
CUBRC, Inc.
iv
Table of Contents Acknowledgements ............................................................................................................ iii List of Tables .................................................................................................................... vii List of Figures .................................................................................................................. viii List of Symbols ................................................................................................................ xiv Abstract ............................................................................................................................ xvi 1. 2. 3. Introduction ............................................................................................................... 1 1.1. Historical Background ....................................................................................... 1 1.2. Motivation for Current Work ............................................................................ 3 LENS XX Facility Description ................................................................................. 5 2.1. LENS XX Design and Expansion Tunnel Gas Dynamics ................................. 7 2.2. Determination of Test Condition ..................................................................... 11 2.3. LENS XX Capabilities .................................................................................... 12 2.4. Typical Measurements in LENS XX ............................................................... 25 2.5. Expansion Tunnel Test Gas Disturbances ....................................................... 29 Development of Microwave Shock Speed Measurement for LENS XX ............... 32 3.1. Details of Microwave Shock Speed Measurement .......................................... 32 3.2. Antenna Selection and Shield Design ............................................................. 41 3.3. Shock Speed Measurement Upgrades ............................................................. 44 v
4. 5. 6. Development of Plasma Diagnostics for Expansion Tunnels ................................. 48 4.1. Microwave Frequency Domain Reflectometry Measurements ....................... 50 4.2. Results from Resonance Probe Reflection Measurements .............................. 53 4.3. Langmuir Probe Development......................................................................... 60 Results from Microwave Shock Speed Measurements ........................................... 64 5.1. Measuring Primary and Secondary Shock Speeds .......................................... 64 5.2. Shock Speed Attenuation................................................................................. 68 5.3. Effects of Secondary Diaphragm ..................................................................... 78 5.4. Low Density Microwave Shock Speed Measurements ................................... 80 5.5. Summary of Microwave Standing Wave Measurements ................................ 85 Conclusions ............................................................................................................. 88 6.1. Summary of Completed Work ......................................................................... 88 6.2. Future Work..................................................................................................... 89 Appendix A List of Microwave Components ................................................................ 90 Appendix B HET and Langley Expansion Tube Data and Noise Correlations ............. 91 References ......................................................................................................................... 95 vi
List of Tables
Table I. Freestream Conditions for Extruded Capsule Model .......................................... 56 Table II. Average Shock Speed Comparison Between Standard TOAs and Microwave
Measurement (Run 75) ................................................................................................................. 66 Table III. Average Shock Speed Comparison between Standard TOAs and Microwave
Measurement (Run 76) ................................................................................................................. 66 Table IV. Average Shock Speed Comparison between Standard TOAs and Microwave
Measurement (Run 77) ................................................................................................................. 67 Table V. Microwave Shock Speed Attenuation Compared to Mirels’s Boundary Layer
Theory ........................................................................................................................................... 70 Table VI. Equilibrium Freestream and Stagnation Properties from Low Density MURI
Runs .............................................................................................................................................. 81 Table VII. Secondary Shock Properties from the Low-Density MURI Runs .................. 83 Table VIII. Miller’s Test Conditions and Correlation with Noise .................................... 93 Table IX. HET Test Conditions and Correlation with Noise............................................ 94 vii
List of Figures
Figure 1. Dissociation and ionization in air for shock/expansion tunnel
comparison at 10 MJ/kg condition [6] ................................................................................ 3 Figure 2. LENS XX - 61- cm. large-scale expansion tunnel at CUBRC ................ 7 Figure 3. Schematic of LENS XX .......................................................................... 7 Figure 4. X-t Wave Diagram of an Expansion Tunnel ......................................... 10 Figure 5. Capability of LENS XX to Duplicate Hypersonic Conditions in Air and
CO2 .................................................................................................................................... 11 Figure 6. Reynolds Number vs. Stagnation Enthalpy in Air for Various Driver
Gases ................................................................................................................................. 14 Figure 7. Density vs. Stagnation Enthalpy in Air for Various Driver Gases ........ 15 Figure 8. Reynolds Number vs. Mach Number in Air for Various Driver Gases 15 Figure 9. Stagnation Enthalpy vs. Test Time in Air for Various Driver Gases .... 17 Figure 10. Test Time Contours with Respect to Mach Number and Stagnation
Enthalpy in Air.................................................................................................................. 18 Figure 11. Reynolds Number vs. Flow Length in Air Various Driver Gases....... 18 Figure 12. Stagnation Enthalpy Number vs. Flow Length in Air for Various
Driver Gases...................................................................................................................... 19 Figure 13. Stagnation Enthalpy vs. Primary Interface Sound Speed Ratio in Air
for Various Driver Gases .................................................................................................. 19 Figure 14. Reynolds Number vs. Stagnation Enthalpy with and without Sound
Speed Ratio Limitation ..................................................................................................... 20 viii
Figure 15. Reynolds Number vs. Stagnation Enthalpy in Air for Helium and Air
Expansion Gases ............................................................................................................... 22 Figure 16. Mach Number vs. Stagnation Enthalpy for Helium and Air Expansion
Gases ................................................................................................................................. 23 Figure 17. Reynolds Number vs. Stagnation Enthalpy in an Assortment of Test
Gases ................................................................................................................................. 23 Figure 18. Density vs. Stagnation Enthalpy in an Assortment of Test Gases ...... 24 Figure 19. Secondary Shock Speed vs. Initial Expansion Gas Pressure in Air .... 24 Figure 20. Four-chamber Configuration for Higher Velocity/Stagnation Enthalpy
Testing............................................................................................................................... 25 Figure 21. Example Pitot Pressure Measurements from 11-44 MJ/kg ................. 26 Figure 22. Comparison of Schlieren and CFD Density Gradient at 25 MJ/kg in Air
........................................................................................................................................... 27 Figure 23. Comparison of Aerothermal Measurements and CFD at 25 MJ/kg in
Air ..................................................................................................................................... 28 Figure 24. Non-Dimensional Heat Transfer with Reference Temperature
Correction Normalized with Reynolds Number Based on Laminar Boundary Layer
Exponent vs. Position for LENS XX Runs Including One Moderate Enthalpy 67CH
LENS I Run....................................................................................................................... 29 Figure 25. Schematic of Original Microwave Measurement System for
Determining Shock Speed in LENS XX........................................................................... 33 Figure 26. Theoretical Detected Signal from Microwave Shock Speed
Measurement and Corresponding Shock Speed Derived based on Signal Period ............ 37 ix
Figure 27. Theoretical Detected Signal from Microwave Shock Speed
Measurement and Corresponding FFT to Determine Shock Speed.................................. 38 Figure 28. Voltage Reflection Coefficients from a Plasma Slab .......................... 39 Figure 29. Shock Speed vs. Electron Density in Various Initial Pressures of Air 41 Figure 30. Shock Speed vs. Electron Density in Various Gases at 100 Pa........... 41 Figure 31. Pictures of Log-Periodic Antenna Used for Shock Speed
Measurements ................................................................................................................... 43 Figure 32. Post-Test Picture of Antenna Shield After High-Pressure Run with
Thick Secondary Mylar Diaphragm.................................................................................. 43 Figure 33. Example of Typical Post-test Expansion Tunnel Damage After One
Run (MSL Testing in Prototype LENS X Facility) .......................................................... 44 Figure 34. Schematic of Upgraded Microwave Measurement System for
Determining Shock Speed in LENS XX........................................................................... 45 Figure 35. Reflection and Transmission Characteristics With and Without Tuning
........................................................................................................................................... 47 Figure 36. ElectroDynamic Applications Planar Resonance Probe for LENS XX
Testing............................................................................................................................... 51 Figure 37. ANSYS HFSS Electric Field Contour Plots of Planar Resonance Probe
........................................................................................................................................... 52 Figure 38. Computational Fluid Dynamic Simulation of Extruded Capsule at
7km/s in Air ...................................................................................................................... 54 Figure 39. RF Resonance Probe Reflection Coefficient Comparisons on Backward
Face of Extruded Capsule Model ...................................................................................... 56 x
Figure 40. CFD Solution for Run 05 Showing Electron Density and Collision
Frequency Distribution from the Bow Shock to the Model Surface ................................ 56 Figure 41. CFD Solution for Run 09 Showing Electron Density and Collision
Frequency Distribution from the Bow Shock to the Model Surface ................................ 57 Figure 42. Electron Density Comparison of CFD Simulations for Run 05 and Run
09....................................................................................................................................... 57 Figure 43. RF Resonance Probe Reflection Coefficient Comparisons in Stagnation
Configuration .................................................................................................................... 59 Figure 44. Normalized Electron Density Comparison between Equilibrium
Estimate and Resonance Probe Measurement .................................................................. 59 Figure 45. Picture of Langmuir Probe for Demonstration Testing in Shock Layer
of 3-in. Hemisphere .......................................................................................................... 61 Figure 46. Langmuir Probe Scan from 3-in. Hemisphere Demonstration Testing
(91-CH Run 6) .................................................................................................................. 62 Figure 47. 3 in. Hemisphere CFD Simulations for Air at 25 MJ/kg in LENS XX
........................................................................................................................................... 63 Figure 48. Microwave Measurement of Primary and Secondary Shock Speeds
(Run 75) ............................................................................................................................ 66 Figure 49. Microwave Measurement of Primary and Secondary Shock Speeds
(Run 76) ............................................................................................................................ 66 Figure 50. Microwave Measurement of Primary and Secondary Shock Speeds
(Run 77) ............................................................................................................................ 67 xi
Figure 51.
Time-Frequency Analysis of Run 75 using the Pseudo-Wigner
Distribution ....................................................................................................................... 68 Figure 52. Effect of Boundary Layer Growth due to Viscous Effects in an
Expansion Tunnel ............................................................................................................. 68 Figure 53. Mirels’s Laminar Boundary Layer Calculations for Langley Tunnel
(C1-C20 Conditions are Listed in Appendix B) ............................................................... 72 Figure 54. Mirels’s Turbulent Boundary Layer Calculations for Langley Tunnel
(C1-C20 Conditions are Listed in Appendix B) ............................................................... 72 Figure 55. Langley Expansion Tunnel Velocity Contour x-t Diagram for C11
Condition (Contact Surfaces Shown in White, Shocks Identified by Stark Boundaries,
Expansion Waves Identified by Smooth Transitions) ...................................................... 74 Figure 56. LENS XX Expansion Tube Velocity Contour x-t Diagram for C11
Condition........................................................................................................................... 75 Figure 57. LENS XX Expansion Tunnel Velocity Contour x-t Diagram for C11
Condition including Steady Nozzle Expansion ................................................................ 75 Figure 58.
Test Gas Velocity vs. Time Assuming Mirel’s Displacement
Thickness for Small-scale and Large-scale Expansion Tunnels ....................................... 77 Figure 59.
Attenuating secondary shock speed comparison between Laney
Microwave Data and Jaguar 1D simulation including Mirels displacement thickness .... 78 Figure 60. Reflected Microwave Signal with Cycle Peaks Identified (Nozzle
Calibration Run 5)............................................................................................................. 79 Figure 61. Microwave Measurement of Primary and Secondary Shock Speeds
(Nozzle Calibration Run 5) ............................................................................................... 80 xii
Figure 62. Sample Standard TOA Measurements from Low Density MURI Run
07....................................................................................................................................... 82 Figure 63. Microwave Measurement of Test Gas Velocity (MURI Run 7) ........ 83 Figure 64. Microwave Measurement of Shock Speed (MURI Run 10) .............. 84 Figure 65. Residual Gas Analyzer Results for Low Density MURI Runs .......... 85 Figure 66. Langley Expansion Tube Data with Various Test Gases .................... 92 xiii
List of Symbols
A
Power detected from standing wave shock speed measurement
c
Speed of light (m/s), or sound speed (m/s)
Ch
Stanton number
d
Distance to target (m)
e
Electron charge
f
Frequency (Hz)
me
Electron mass
p
Pressure (Pa)
Re
Reynolds Number
u
Velocity (m/s)
V
Standing wave signal
γ
Magnitude of reflection coefficient, or Ratio of specific heat constants
ε0
Permittivity of free space
λ
Wavelength
θ
Phase of traveling wave (radians)
ρ
Density (kg/m3)
φ
Phase shift coefficient of reflection (radians)
ω
Radial frequency
xiv
Subscripts
g
Guide (referring to the waveguide standing wave frequency/wavelength)
k
Target/Shock wave location
p
Plasma
T
Transmitted or traveling wave
R
Reflected wave
xv
Abstract
The focus of this research is the development of non-intrusive microwave diagnostics for
characterization of expansion tunnels. The main objectives of this research are to accurately
characterize the LENS XX expansion tunnel facility, develop non-intrusive RF diagnostics that
will work in short-duration expansion tunnel testing, and to determine plasma properties and
other information that might otherwise be unknown, less accurate, intrusive, or more difficult to
determine through conventional methods. Testing was completed in LENS XX, a new largescale expansion tunnel facility at CUBRC, Inc. This facility is the largest known expansion
tunnel in the world with an inner diameter of 24 inches, a 96 inch test section, and an end-to-end
length of more than 240 ft. Expansion tunnels are currently the only facilities capable of
generating high-enthalpy test conditions with minimal or no freestream dissociation or
ionization. However, short test times and freestream noise at some conditions have limited
development of these facilities.
To characterize the LENS XX facility, the first step is to evaluate the facility pressure,
vacuum, temperature, and other mechanical restrictions to derive a theoretical testing parameter
space. Test condition maps are presented for a variety of parameters and gases based on 1D
perfect gas dynamics. Test conditions well beyond 10 km/s or 50 MJ/kg are identified with
minimum test times of 200 μs. Additionally, a four-chamber expansion tube configuration is
considered for extending the stagnation enthalpy range of the facility even further.
A microwave shock speed diagnostic measures primary and secondary shock speeds
accurately every 30 in. down the entire length of the facility resulting in a more accurate
determination of freestream conditions required for computational comparisons. The high
xvi
resolution of this measurement is used to assess shock speed attenuation as well as secondary
diaphragm performance. Negligible shock attenuation is reported over a large range of test
conditions and gases, and this is attributed to the large diameter of the LENS XX driven and
expansion tubes. Shock tube boundary layer growth solutions based on Mirels’s theory confirm
LENS XX test conditions should not be adversely affected by viscous effects. Mirels’s theory is
applied to both large- and small-scale expansion tube facilities to determine displacement
thicknesses, and quasi one-dimensional solutions show how viscous effects become significant in
long, smaller diameter facilities.
In collaboration with ElectroDynamic Applications, Inc., (EDA) plasma frequency
measurements are made in two different configurations using a swept microwave frequency
power reflection measurement. Electric field characteristics of EDA’s probe are presented and
show current probe design is ideal for measuring properties of shock layers that are 1-2 cm thick.
Electron density and radio frequency communication characteristics through a shock layer on the
lee side of a capsule up to 8.9 km/s and in a stagnation configuration up to 5.4 km/s in air are
reported.
xvii
1.
Introduction
Hypervelocity ground test facilities are essential to the development and advancement of
hypersonic propulsion systems, high-speed cruise or strike vehicles, and reentry vehicles. An
overview of existing hypervelocity ground test facilities can be found in Dufrene et al.[1]
LENS XX was designed to extend ground test capabilities as a well-characterized, high-enthalpy
(10-50+ MJ/kg) facility and provide a capability for larger-scale hypervelocity testing.
1.1.
Historical Background
Hypervelocity simply refers to a high-enthalpy (high-velocity) hypersonic flow. This
regime of hypersonics is distinctly different in that it is characterized by chemical
nonequilibrium, kinetic (vibrational excitation) and radiation effects, as well as the fluid dynamic
nature of the gas.[2] These effects play an important role in the aerodynamic behavior of vehicles
and engines operating in that regime, and further research is required to provide a more in-depth
understanding. There are many types of supersonic and hypersonic facilities, but few that capture
the high-temperature effects discussed above.[3] For a more complete historical background of
hypersonic facilities, see Ref. [4].
Shock tunnels have been the standard high-enthalpy test facility since their inception in
the 1950s. A driver system initiates the flow, and several variations exist, including piston
drivers, electric-arc drivers, static high-pressure drivers, and detonation drivers. All have the
same purpose, which is to transmit a strong shock into the driven section, or test gas, accelerating
it and heating it at the same time. This strong shock then reflects off an end-wall with a small
throat, stagnating the test gas and heating it even further. This high-pressure, high-temperature
gas expands through the small throat into a nozzle that accelerates the flow. For moderate
1 / 100
enthalpies, up to ~10-20 MJ/kg, this approach has worked fairly well using air as a test gas, but
begins to fail at enthalpies as low as 5 MJ/kg for a CO2 test gas.[5] For reference, stagnation
enthalpy is roughly equivalent to the square of the velocity divided by two.
Figure 1 shows the dissociation and ionization temperatures of air at 1 atm (reproduced
from Ref. [6]). The maximum test gas temperature of two identical test conditions generated by a
shock tunnel and an expansion tunnel at 10 MJ/kg are compared in this figure. The shock tunnel
condition generates a temperature of 6,250 K, which is almost a factor of three higher than what
is generated in an expansion tunnel for the same condition. Furthermore, the shock tunnel
stagnation conditions are at a much higher pressure which also enhances dissociation reactions.
In addition to dissociated freestream conditions, shock tunnels have physical limitations of
approximately 20 MJ/kg before nozzle throats can no longer survive at the high stagnation
temperatures required.[7]
Expansion tunnels date to the early 1960s, but never became common research tools due
to short test times (<1/10th shock tunnels) and noisy test conditions that were not well understood
until recently.[8, 9] Expansion tunnel research began again, starting with the University of
Queensland facility and the revived NASA HYPULSE facility at GASL.[10, 11] An expansion
tunnel never stagnates the freestream gas; rather, the gas is accelerated by an unsteady expansion
wave instead of a nozzle as with a shock tunnel. The first two sections of an expansion tunnel are
the same as a shock tunnel. The unsteady expansion wave is generated by the addition of a third
low-pressure tube generally referred to as the accelerator tube. The major benefit of this unsteady
expansion process is that the test gas is never heated to the point that excessive dissociation or
ionization occurs, resulting in well-characterized freestream conditions ideal for direct
comparisons with computations and to flight tests. The penalty associated with this type of test
2 / 100
gas acceleration is the limited test times, which are typically 1/10th of shock tunnel test time, or
on the order of 100 μs. Fortunately, the large-scale size LENS XX tends to yield test times closer
to 500-1,000 μs or more for all but the most extreme enthalpies. A full description of the gas
dynamic processes involved in expansion tunnel operation can be found in References [1],
R ang e of dis s oc iation R ang e of ioniz ation
[9],and [12].
Maximum T es t G as T emperature for 10 MJ /kg T es t C ondition
N Æ N + + e ‐
O Æ O + + e ‐
S hock T unnel: 6,250K
E xpans ion T unnel: 2,260K
9000 K
N 2 almos t completely dis s ociated; ionization begins
N 2 Æ 2N
4000 K
2500 K
N 2 begins to dis s ociate; O 2 is almos t completely dis s ociated O 2 Æ 2O
O 2 begins to dis s ociate
No R eactions
800 K
Vibrational
excitation
0 K
Figure 1. Dissociation and ionization in air for shock/expansion tunnel comparison at
10 MJ/kg condition [6]
1.2.
Motivation for Current Work
To some extent, the current work is a continuation of the author’s Master’s thesis, [13]
which was the design and characterization of a smaller-scale expansion tunnel at the University
of Illinois. The principles and lessons learned are applied to the LENS XX expansion tunnel
facility. Standard Pitot pressure and time-of-arrival measurements are of value, but the objective
of the present work is to develop a non-intrusive diagnostic that could provide more information
3 / 100
about how the tunnel is actually performing, namely, the variation of shock speeds, viscous
effects, and diaphragm rupture processes. Here a microwave shock speed measurement first
made by NASA in the early 1970s [14] is adopted to work in the larger LENS XX facility. When
the NASA expansion tunnels were closed down, the development of this useful microwave
measurement was not continued. It is ideally suited for expansion tunnels, because there is no
small throat that would otherwise block the radio frequency (RF) energy.
Other non-intrusive microwave diagnostics are also considered for plasma measurements.
An RF resonance probe designed by ElectroDynamic Applications, Inc. (EDA) is identified as a
good candidate for testing in LENS XX testing, and demonstration testing is reported on two
different test configurations. EDA’s probe is used as a frequency domain reflectometer to
measure local plasma frequencies, which correspond directly to the electron density and cutoff
RF transmit/receive frequency.
The purpose of this research is to develop nonintrusive microwave/radio frequency
instrumentation for expansion tunnel characterization. Better characterization of expansion
tunnels and their flow fields is required to exploit their full potential for high-enthalpy studies of
radiation effects, plasma diagnostics, real-gas chemistry, and ablating surfaces. These
measurements provide more accurate freestream boundary conditions for comparisons with
computations in these areas.
4 / 100
2.
LENS XX Facility Description
The LENS XX facility at CUBRC is a large-scale expansion tunnel. Figure 2 shows a
picture of LENS XX taken from the test section looking upstream towards the red nozzle and the
stainless steel tubes. This expansion tunnel was designed as a stand-alone facility after the
successful prototype testing of LENS X.[15] The tubes have an internal diameter of 61 cm with a
nozzle expanding into a 244 cm test section, and an end-to-end length of more than 73 m. A
simple schematic of the facility is shown in Fig. 3. It highlights the fact that the driver is
electrically heated and that there are two test sections. The primary test section has a 244 cm
diameter for expansion tunnel operation, but the facility also has a 61 cm. test section prior to the
nozzle divergence for expansion tube operation. The 61 cm test section is more ideal for higher
Reynolds number testing because there is no steady expansion through the nozzle, or very low
Reynolds number testing because this is a much smaller volume that can be evacuated to a few
orders of magnitude lower than the large test section and ballast tank. The smaller test section is
also useful for non-intrusive measurements or shock radiance measurements as well. The larger
test section is better suited for the majority of applications and offers cooler test gas conditions,
accommodation of larger models, and most importantly significantly-reduced particulate in the
post test gas flow. The size of this facility offers significant advantages, namely the ability to test
large, heavily-instrumented models for longer run times.
The expansion tube concept is not new,[9] but the LENS XX facility is unique in its large
size and development as both a research facility and a production wind tunnel. The LENS XX
facility offers four unique advantages which no other facility in the world can match. The first is
a long test time, which will is on the order of one millisecond for most conditions and up to eight
milliseconds for very low enthalpy flows (most other expansion tubes measure test time in tens
5 / 100
of microseconds). This yields several advantages, such as improved signal-to-noise for spectral,
visual, or integrated measurements, time to stabilize separated regions, subsonic regions, or
wakes, and improved data filtering options for measurements such as heat transfer or forces and
moments. Second, the LENS XX facility is unique in that it employs a moderately-heated
hydrogen driver and emission comes only from the shock layer. Other high-enthalpy facilities
use piston-driven, arc heated, or combustion drivers,[16-18] which are often as hot as the shocklayer gas itself so a spectrometer at the stagnation point of a model will be unable to distinguish
between the emission that it sees from the shock layer and that from the driver. Third, the
increased size of the facility provides a very large inviscid core flow to test models either in the
61 cm (24”) tube test section or the larger 240 cm (96”) test section. Finally, we test our models
out of the line-of-sight of the expansion tube. This is critical because extensive damage can occur
from the metal diaphragms used in the driver; most other facilities cannot employ the sensitive
and accurate measurement techniques that CUBRC utilizes without sacrificing the model on each
and every run.
Construction of LENS XX was completed in the spring of 2009, at which point
preliminary testing began. During the preliminary testing, safety and operational procedures
were finalized and documented, the driver pressure and temperature were ramped up to the levels
needed for current testing, vacuum systems and gas fill systems were checked out, primary and
secondary diaphragms were evaluated and optimized, and additional instrumentation was
brought online as we began to reach target conditions. Initial testing focused on shock radiance
measurements as discussed in Ref. [19]. Aerothermal and radiation measurements on blunt
bodies began in the late spring of 2010 with simple cylindrical and hemispherical models in both
expansion tube and expansion tunnel operation modes.[20] Testing of heavily instrumented
6 / 100
models began
b
first in the sum
mmer of 20011 with measurements
m
s on an Appollo/Orion heat
shield.[21] Now thatt facility chaaracterizationn has matureed, testing of
o complex models
m
conttinues
at an accelerated pace.
Figure 2. LENS XX
X - 61- cm. laarge-scale exxpansion tu
unnel at CU
UBRC
Primary
Diaphragm
Electrically
Heatted Driver
D
Driven
Tube
Secondary
Diaphragm
Acc
celeration Tube
24” Test
Section
96” Test
Section
Large Optical
O
Ports
Figure 3. Sch
hematic of LENS
L
XX
2.1.
L
LENS
XX Design an
nd Expansion Tunneel Gas Dyn
namics
T LENS XX
The
X expansionn tunnel faccility generattes test flow
ws in a mannner very diffferent
from thee reflected shock
s
tunnell facilities. Reflected shhock tunnells operate by
b driving strong
incident and reflected shocks through
t
thee test gas which
w
resultts in a highh-pressure, hightemperatuure, stagnan
nt reservoir which
w
can be
b expandedd through a converging//diverging nozzle
n
like a bloowdown faccility. Expannsion tunnelss never stagnnate the testt gas before it flows oveer the
7 / 100
test article. Instead, the test gas is set into motion by a single shock of only weak to moderate
strength, and the bulk of the energy in the flow is added to kinetic energy directly by using an
unsteady acceleration to increase the velocity. A wave diagram of the basic states of the
expansion tunnel is given in Fig. 4. In this figure, position is plotted schematically along the
horizontal axis and time is plotted qualitatively along the vertical axis. The three test chambers
are filled to different pressures and initially separated by diaphragms, where the primary
diaphragm between the driver and test gas sections is broken at a time designated as zero. The
waves in the diagram are shocks (red), contact surfaces (dotted grey) or isentropic expansion
fans (green), where the thermodynamic state and/or composition of the gases change across any
of the waves. Important thermodynamic states of the gases are numbered and the label is colored
by the gas composition.
The driver gas (State 4) is a very high-pressure, heated, low molecular weight gas
(typically hydrogen or helium) that causes a primary shock of moderate strength to move through
the test gas when the primary diaphragm is broken. This shock raises the pressure in the test gas
just sufficiently to break the secondary diaphragm, and causes an initial velocity toward the right
in the schematic (State 2). The peak temperature of the test gas during the entire excitation
process occurs at State 2, which is typically on the order of 2,000 – 3,000 K or approximately an
order of magnitude lower than a comparable freestream condition in a reflected shock tunnel.
The moving test gas then accelerates into a much lower pressure acceleration segment that is
typically at nearly vacuum (State 10). The unsteady expansion causes the test gas to cool and
accelerate to very high velocities, given by State 5; this is the freestream state of the test gas at
the end of the tube. The freestream velocity obtained is primarily dependent on the molecular
weight of the driver gas, the pressure of the driver gas, and the vacuum level of the acceleration
8 / 100
segment. Test time available for experiments begins at the contact surface between States 20 and
5 and lasts until either the tail of the left-running expansion between States 2 and 5 reaches the
test station or until the reflected head of the same wave reaches the test station.[1] The
freestream state of the gas typically has a translational temperature near 300 K with a very high
velocity. The relative strengths of the primary shock (State 1 to State 2) and the unsteady
expansion (State 2 to State 5) can be utilized to generate different Mach numbers and test
conditions for a given total pressure ratio (P4/P10), which provides a significant degree of
flexibility for the facility. Additional details about the LENS XX facility may be found in the
prevous work of the author et al.[22, 23]
Notional maps of the duplication capability of the LENS XX facility for air and carbon
dioxide test gases are shown in Fig. 5(a) and (b). In each case, several trajectories of interest
from recent NASA exploration activities are shown for reference to demonstrate that LENS XX
can duplicate a relevant range of conditions. In general, the facility can run any pure gas or
mixture of test gases including: air, nitrogen, oxygen, carbon dioxide, methane, argon, neon, etc.
Although the facility is relatively new, calibration and validation has been ongoing since
late 2010. This calibration process made basic characterization measurements such as profiles of
Pitot pressure in the test section plane as well as measurements on building-block models such as
wedge, hemisphere, and cylinder shapes, along with comparisons to CFD using freestream
conditions determined from the techniques outlined by MacLean et al. [24]
9 / 100
(5)
Time
(20)
(3)
(2)
(4)
(10)
(1)
Primary
Diaphragm
DRIVER
Secondary
Diaphragm
TEST GAS
Distance
ACCELERATION GAS
Figure 4. X-t Wave Diagram of an Expansion Tunnel
(a) Air (Earth entry)
10 / 100
Test Time
(b) CO2 (M
Mars/Venuss entry)
Figurre 5. Capabiility of LEN
NS XX to Du
uplicate Hyp
personic Coonditions in Air and CO
O2
2.2.
D
Determina
tion of Teest Conditiion
T conditions for each run in the LENS
Test
L
XX faacility are coomputed usinng the CHEE
ETAh
code outtlined by MacLean,
M
et al. [24] CHEETAh
C
soolves the prrimary and secondary wave
systems, shown in
n Fig. 4, by incorpoorating opttions for equilibrium
e
chemistry and
meters in the facility to annchor
thermodyynamics. This code makkes use of meeasured operrating param
the calcuulation of freeestream connditions. In the primaryy system (connsisting of States
S
1, 2, 3,
3 4),
the initiaal test gas sttate (State 1),
1 the driveer gas tempeerature (Statte 4), and thhe primary shock
s
speed are measured quantities. The effectivve driver gaas pressure is computed to accounnt for
pressure losses incurrred by non--ideal breakiing of the laarge, steel diaphragms.
d
In the seconndary
system (cconsisting of States 2, 5,
5 20, 10), thhe computedd test gas staate (State 2), the accelerration
gas tempperature (Statte 10), and the secondarry shock speeed are measuured quantitiies. The effeective
accelerattion gas prressure is calculated due to thee difficulty in makingg very acccurate
measurem
ments of vaccuum level pressures.
p
N
Non-ideal
seccondary diapphragm breaaking is also an importannt issue in exxpansion tunnnels.
This effeect can be accounted for
f by definning a State 2s, which modifies Sttate 2 throuugh a
travelingg wave at thee point of secondary diapphragm breaak. CHEETA
Ah can accouunt for this effect
e
11 / 100
empirically by specifying measured pressures located on the wall of the facility just upstream
and just downstream of the secondary diaphragm. Conditions that use little Mylar at this station
tend to break in a nearly ideal fashion while conditions with thick Mylar tend to show a
correction.
The expansion process in the test section is anchored with a measured Pitot pressure at or
near the location of the model. The effective area ratio of the expanding nozzle is different from
the geometric area ratio of the nozzle because of viscous boundary layer growth, both on the
expansion tube walls and the surface of the nozzle itself, which are extremely difficult to
characterize accurately.
Lastly, viscous effects in expansion tubes can significantly alter the test gas velocity and
other thermodynamic properties. Mirels describes how the shock speed decreases and test gas
speed increases as the boundary layer grows behind a shock wave.[25] This boundary layer
growth issue has been evaluated experimentally for specific conditions in small-scale expansion
tunnel facilities.[26-28] However, the present large-scale tunnel research will improve
understanding of viscous effects through high-resolution, accurate shock speed attenuation
measurements.
2.3.
LENS XX Capabilities
LENS XX is an extremely flexible facility that operates over a vast range of test
conditions. In order to characterize LENS XX, the first step is to evaluate the facility pressure,
vacuum, temperature, and other mechanical restrictions to derive a theoretical testing parameter
space. Figures 6 through 18 show the theoretical parameter space of LENS XX. An iterative
solver is utilized that was written in Matlab and varied the initial gas properties based on realistic
LENS XX design parameters. The code is based on the 1D, perfect gas relations described in
12 / 100
Ref. [1], and Sutherland’s law is used to determine viscosity for the Reynolds number
calculation. Newton’s method type solvers were used for fast convergence as opposed to
Matlab’s symbolic solver which can find exact solutions, but take a large amount of
computational time. The parameter space maps shown in this section comprise more than
100,000 individual solutions.
At higher enthalpies, perfect gas assumptions become less accurate. In particular, they
over-predict the temperature significantly, causing errors in other properties and the unsteady
wave dynamics. More advanced numerical tools, which include thermodynamic equilibrium
along with vibrational and electronic state equilibrium, were developed by MacLean to predict
and validate actual LENS XX test conditions.[24] For the purpose of mapping out a design
space, however, these simplified equations are adequate and illustrative. Figures 6 through 14
were generated using air as both the test gas and the accelerator gas. At hypervelocity conditions
stagnation enthalpy is equivalent to the square of the velocity divided by two, so no test gas
velocity charts are presented to avoid redundancy.
Figures 6 and 7 outline the range of conditions for Reynolds number and density vs.
stagnation enthalpy, respectively, using various driver gases. The overprediction of temperature
results in an underprediction of Reynolds number by not only decreasing density, but by
increasing viscosity, so all of the parameter space maps should have a maximum Reynolds
number easily an order of magnitude higher than what is predicted from perfect gas assumptions.
Likewise, maximum density values could easily be five times greater than what is shown, and
even larger if restrictions on initial driven gas pressure are relaxed due to current maximum
secondary diaphragm capabilities. Additionally, conservative limitations were placed on initial
13 / 100
vacuum levels in the accelerator section, so it is possible to extend the operational range down to
lower densities as well.
Figure 8 shows Reynolds number vs. Mach number in air. The Mach number parameter
space can easily be extended by relaxing the secondary Mylar constraints and increasing the
initial driven pressure; however, stagnation enthalpy or velocity are generally more important
testing parameters, so they are given more attention. Another way to extend the Mach number
parameter space is to introduce a lighter accelerator gas which will be discussed later.
Figure 6. Reynolds Number vs. Stagnation Enthalpy in Air for Various Driver Gases
14 / 100
Figure 7. Density vs. Stagnation Enthalpy in Air for Various Driver Gases
Figure 8. Reynolds Number vs. Mach Number in Air for Various Driver Gases
15 / 100
Test time is either limited by the arrival of the tail of the secondary expansion, or by the
reflected head of the secondary expansion wave. Since the location of the secondary diaphragm
can be moved to optimize test time, this optimized time is selected as that presented in the
figures. Test time versus stagnation enthalpy in air is plotted in Fig. 9 for various driver gases.
An argon driver yields very long test times in excess of 8 ms, but at fairly low enthalpies. Test
time appears to approach a minimum value, such that even at very high enthalpies there is still
over 200 μs of test time. Figure 10 represents test time contours for a given Mach number and
stagnation enthalpy using a hydrogen driver gas. In most instances, there are several ways to
generate a given condition, so values of test time presented in the contour plot may not represent
the maximum test time for the given properties. Due to limitations in the test condition database,
there are some high and low values of test time that are not consistent with the trend of the chart,
but, in general, as Mach number and stagnation enthalpy are increased, test time is decreased. In
order to size models, steady-state flow lengths is often more useful than test time. Flow length is
simply the product of test time and test gas velocity. In Figs. 11 and Figure 12, flow lengths in
air are compared to Reynolds number and stagnation enthalpy, respectively. As test time
decreases, velocity increases such that the flow length size remains almost constant. In fact, at
the maximum stagnation enthalpy of 90 MJ/kg, there is still up to 6 m of flow length which is
sufficient for very large models.
In addition to secondary diaphragm limitations and minimum and maximum pressure
limitations, test gas disturbances have proven to be another practical limitation of expansion
tunnels as mentioned above.[29] These test gas disturbances have been attributed to the driver
gas and have been shown to be damped by operating with a primary sound speed ratio less than
unity. The primary sound speed ratio is the ratio of driver sound speed to test gas sound speed
16 / 100
across the primary contact surface ( ⁄
1, see Fig. 2). Figure 13 shows the sound speed ratio
versus stagnation enthalpy in air for various driver gases. An argon driver results in extremely
low sound speed ratios, but severely restricts potential stagnation enthalpy. High sound speed
ratios are more prevalent at lower enthalpies, but it unclear from Fig. 13 how much this condition
restricts the design space. In Fig. 14, we return to the Reynolds number versus stagnation
enthalpy in air with a hydrogen driver gas. The blue plot underneath is the same as what is
shown in Fig. 6; however, all conditions with a sound speed ratio greater than or equal to unity
were removed to generate the yellow plot. The two overlap almost completely, resulting in only
a small limitation on the very low end of stagnation enthalpy. If low stagnation enthalpies are
required, however, the driver gas can simply be changed to argon or an argon-helium mixture.
Figure 9. Stagnation Enthalpy vs. Test Time in Air for Various Driver Gases
17 / 100
26
0.5
24
0.45
22
0.4
0.35
18
0.3
16
0.25
14
0.2
12
0.15
10
8
0.1
6
0.05
4
Test Time (ms)
Mach Number
20
10
20
30
40
50
60
Stagnation Enthalpy (MJ/kg)
70
80
90
0
Figure 10. Test Time Contours with Respect to Mach Number and Stagnation Enthalpy in
Air
Figure 11. Reynolds Number vs. Flow Length in Air Various Driver Gases
18 / 100
Figure 12. Stagnation Enthalpy Number vs. Flow Length in Air for Various Driver Gases
Figure 13. Stagnation Enthalpy vs. Primary Interface Sound Speed Ratio in Air for
Various Driver Gases
19 / 100
Figure 14. Reynolds Number vs. Stagnation Enthalpy with and without Sound Speed Ratio
Limitation
Another way of extending the operation space on an expansion tunnel is to vary the
accelerator gas. Figures 15 and Figure 16 were generated using a hydrogen driver gas and air as
the test gas with both helium and air as the expansion gas. Reynolds number versus stagnation
enthalpy is plotted in Fig. 15, and it is clear that the maximum stagnation enthalpy can be
extended by selecting helium as the accelerator gas. Figure 16 shows Mach number versus
stagnation enthalpy, and indicates that helium widens the parameter space significantly,
extending both Mach number and stagnation enthalpy ranges. From an operational standpoint,
using helium complicates the test setup procedure slightly by adding another chamber to purge
and fill. It is also more demanding on the vacuum system requiring lower ultimate vacuum
capabilities, and the chamber must be essentially leak free to avoid air contamination to ensure
repeatable test conditions.
Another major benefit of expansion tunnels is the ability to test in any desired freestream
gas. Simply varying the driven gas composition allows for testing in any simulated atmosphere.
20 / 100
Figures 17 and Figure 18 were generated using a hydrogen driver gas and air as the expansion
gas. Various atmospheres were simulated using the following compositions: Jovian – 90% H2,
10% He, Martian – 96% CO2, 4% N2, Titan – 98% N2, 2% CH4. Both Reynolds number and
density are plotted versus stagnation enthalpy in Figs. 17 and Figure 18, respectively. Earth,
Martian and Titan atmospheres all have very similar parameter spaces due to their similar
molecular weights and specific heat ratios; however, the Jovian atmosphere has a much larger
parameter space with the exception that the maximum density is lower. Again, density is
underpredicted with the perfect gas calculation, but, nonetheless, the trends are correct.
Testing conditions thus far have focused on freestream conditions behind the secondary
contact surface shown in Fig. 4 as state 5, however, the extremely fast shock waves generated are
also of interest. Shock radiance measurements similar to those done in Ref. [30] are used to
validate non-equilibrium shock radiation models. These studies are necessary to understand
radiative heating loads associated with planetary entry. Figure 19 shows the parameter space for
this type of testing with shock speed versus initial acceleration tube pressure. Unlike electric arc
shock tubes or other small-scale expansion tubes, the contact surface is up to 200 μs behind the
shock ensuring the quality of the pure air test gas and allowing ample time to study the postshock
relaxation dynamics.
The large scale of LENS XX produces test times that are significantly longer than other
smaller-scale expansion tunnels. Long test times are particularly useful for testing large, heavily
instrumented models or when making force measurements. However, it is not always necessary
to have long test times. The availability of high-speed data acquisition systems and sensors
paired with proper model scaling can allow useful testing to be completed in the shorter steadystate test times generated in typical expansion tunnels. LENS XX can be configured in a four-
21 / 100
chamber mode shown in Fig. 20, which would accelerate the leading shock and test gas even
further resulting in stagnation enthalpies potentially greater than 100 MJ/kg and shock speeds
over 17 km/s. Lapygin et al. describe a similar concept for a multi-chambered shock tunnel to
generate a high velocity test gas.[31] The test gas would be in what is referred to as Driven
Tube 2 in the figure. There is a penalty to the test time on the order of one-third that predicted in
the typical expansion tunnel configuration. Test times, therefore, would be reduced to ~100 μs at
the extremely high enthalpy cases, but this corresponds to two or three meters of flow length
which is more than adequate for testing reasonably sized blunt body models.
Figure 15. Reynolds Number vs. Stagnation Enthalpy in Air for Helium and Air Expansion
Gases
22 / 100
Figure 16. Mach Number vs. Stagnation Enthalpy for Helium and Air Expansion Gases
Figure 17. Reynolds Number vs. Stagnation Enthalpy in an Assortment of Test Gases
23 / 100
Figure 18. Density vs. Stagnation Enthalpy in an Assortment of Test Gases
Figure 19. Secondary Shock Speed vs. Initial Expansion Gas Pressure in Air
24 / 100
Time
Distance
Primary
Diaphragm
Electrically
Heated Driver
Secondary
Diaphragm
Driven
Tube 1
Tertiary
Diaphragm
Driven
Tube 2
Acceleration
Tube
24” Test
Section
96” Test Section
Figure 20. Four-chamber Configuration for Higher Velocity/Stagnation Enthalpy Testing
2.4.
Typical Measurements in LENS XX
LENS XX was designed to generate well-characterized, high-enthalpy test conditions.
Traditionally, shock tunnel and expansion tunnel testing are completed to make aerothermal
measurements which primarily include pressure and heat transfer measurements, as well as
Schlieren photography to examine shock structure and other areas with large density gradients.
The remainder of this work will focus on a microwave shock speed measurement and plasma
diagnostics; however a brief review of traditional measurements in XX is useful to put the
facility capabilities in context. Examples of two Pitot traces are shown in Fig. 21 at 11 and
44 MJ/kg. In general, the lower the velocity the longer the test time; however, the two examples
selected show roughly 500 μs of steady-state test time. Test time for the 11 MJ/kg case could
have been maximized by moving the secondary diaphragm further downstream, because this
25 / 100
condition was limited by the arrival of the reflected expansion head. Since the test condition was
acceptable, and 500 μs is sufficient test time, the run condition was not modified.
9
8
7
Pressure (psi)
Pressure (psi)
100
90
80
70
60
50
40
30
20
10
0
Test Gas
Accel
Gas
6
5
3
2
11 MJ/kg
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3
Time (ms)
Test Gas
4
1
Accel
Gas
44 MJ/kg
0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1
Time (ms)
a. Pitot pressure at 11 MJ/kg
b. Pitot pressure at 44 MJ/kg
Figure 21. Example Pitot Pressure Measurements from 11-44 MJ/kg
Measurements were made on an Orion heat shield model to demonstrate the capability of
the LENS XX facility to make high-quality measurements of heat transfer distributions at flow
velocities from 3 km/s (h0 = 5 MJ/kg) to 8.4 km/s (h0 = 36 MJ/kg). [21] Thirty-nine heat transfer
gauges, including both thin-film and thermocouple instruments, as well as four pressure gauges,
and high-speed Schlieren were used to assess the aerothermal environment on the capsule heat
shield. Complete results can be found in Ref. [21], but results from Run 03 (25 MJ/kg in air) are
included here in Figs. 22 and 23 to highlight the more traditional measurements. A Schlieren
image from a Phantom 710 CMOS camera and corresponding CFD comparison of a bow shock
in front of a capsule at 25 MJ/kg is shown in Fig. 22. Quality Schlieren photography at these
high-velocity conditions is complicated by the intensity of the glowing shock layer. Pulsed
monochromatic laser light is used a light source, because this allows the use of optical filters to
block most of the broadband light emission from the shock layer. Additionally, by syncing the
camera with the light source precisely, the shutter speed can be reduced to one microsecond, so
26 / 100
less stray light is collected by the imager. A comparison of the aerothermal measurements and
CFD solutions are shown in Fig. 23. PCB 113B28 high-frequency pressures gauges were used in
this experiment, and are the standard pressure gauge of choice in LENS XX, although other
types and models are used where necessary. The heat flux measurements are made with a
combination of thin-film gauges made by CUBRC and Medtherm coaxial thermocouples.
Excellent agreement between CFD and experiment are observed for shock shapes comparisons
and aerothermal measurements.
(a) Flow Image
(b) CFD and Tare
(c) CFD and Flow
Figure 22. Comparison of Schlieren and CFD Density Gradient at 25 MJ/kg in Air
27 / 100
a. Surface pressure
b. Surface heat flux
Figure 23. Comparison of Aerothermal Measurements and CFD at 25 MJ/kg in Air
A non-dimensional analysis was completed based on the Stanton number (Ch)-Reynolds
(Re) number scaling typically used in lower enthalpy shock tunnel programs. Where noted, a
reference temperature correction based on the estimated boundary layer temperature from
Cheng[32] was used to compute Ch* and Re* values. Figure 24 shows the normalized, nondimensional heat transfer for all 91CH and 113CH 7” capsule runs, including one moderate
enthalpy (5 MJ/kg) run on a 14” capsule in LENS I under 67CH. In an attempt to collapse all the
run datan the data were normalized with Reynolds number based on the laminar boundary layer
exponent of 0.5 and the reference temperature correction was applied. In addition to the
reference temperature correction, LENS I heat transfer rates were scaled up based on the ratio of
the square root of the diameters of the models used. The non-dimensional collapse is quite nice
over a huge range of conditions (5-36 MJ/kg), two different nozzles in XX and the 5 MJ/kg run
in LENS I. It is also important to note that Runs 22-31 were transitional, so for these runs heat
transfer values after y/R = 0.25 were removed, so that we are only comparing laminar values
over all of these runs. It is very interesting that indeed all of these program runs do collapse so
28 / 100
well. It is not obvious, at this point, if the reference temperature correction is physically
meaningful across this large range of conditions involving complex shock layer chemistry, or if
it is a fortuitous result related to some other phenomenon. However, it indicates that results are
consistent which is positive.
Heat Transfer (Ch* Re*1/2)
12
10
8
6
4
2
0
1.000
0.500
0.000
‐0.500
y/R
‐1.000
Run 1
Run 2
Run 3
Run 5
Run 6
Run 7
Run 13
Run 19
Run 21
Run 22
Run 24
Run 27
Run 29
Run 30
Run 31
Run 18 ‐ LENS I
Figure 24. Non-Dimensional Heat Transfer with Reference Temperature Correction
Normalized with Reynolds Number Based on Laminar Boundary Layer Exponent vs.
Position for LENS XX Runs Including One Moderate Enthalpy 67CH LENS I Run
2.5.
Expansion Tunnel Test Gas Disturbances
The source of expansion tunnel test gas disturbances has been the subject of many
research studies. NASA Langley[33], University of Queensland [29], and the University of
Illnois[28], have all systematically tested a range of test parameters to determine a range of
acceptable test conditions for their facilities for different disturbances. Paull and Stalker showed
that some disturbances come from acoustic waves generated in the driver transmitted through the
expansion wave, but they also showed how the these disturbances could be minimized by
29 / 100
reducing the driver gas to test gas sound speed ratio across the primary contact surface.[29]
These same disturbances were also confirmed by Dufrene at the University of Illinois.[13]
Miller’s[33] test data for a variety of test and accelerator gases shows another type of
disturbance that manifests itself as a large dip in pitot pressure followed by a highly unsteady
trace. These data are reproduced along with a qualitative assessment of the noise levels and
calculation of the test conditions in Appendix B, note that all values are in standard metric units.
Test conditions are correlated with the qualitative noise assessment in Table VIII in the same
appendix, and the only correlations of any significance relate to the initial fill pressure or density
of the accelerator gas. This indicates that viscous effects generate large disturbances or the large
dip in Pitot pressure at the higher velocity conditions attempted in the Langley facility. A similar
finding was reported by Jacobs [34], but test conditions, correlation factors, and Pitot traces have
not previously been presented together.
Sharma completed a series of tests with various test gases and accelerator gases as well.
[28] In Sharma’s test series, all but one run had a suitable driver gas to test gas ratio to avoid the
frequency focusing disturbances discovered by Paull and Stalker; however, large, high-frequency
noise fluctuations were identified at several conditions. In an attempt to correlate facility noise
with test conditions, Sharma suggested using D=us(ρ1c1+ ρ
10c10)
as a qualitative correlation
parameter, where D is the total characteristic acoustic impedance factor, c is sound speed, us is
primary shock speed, and ρ is density. Subscripts correspond to the states in the wave diagram
shown above in Fig. 4. Test conditions and correlations were made to the reported Pitot pressure
standard deviation in Table IX of Appendix B. There is a strong correlation with this D
parameter, but the acoustic impedance ratio across the secondary contact surface, and various
test gas parameters also showed strong correlations. A high acoustic impedance ratio at the
30 / 100
secondary contact surface would not allow any disturbances to propagate into the accelerator gas,
so disturbances would be focused in the test gas. Acoustic impedances clearly contribute to test
gas noise, but further investigation is required to determine the magnitude and potential remedy
for these test gas disturbances.
Another major source of disturbances not mentioned above is the non-ideal rupturing of
the secondary diaphragm station. The rupture process of these thin diaphragms has been studied
experimentally.[35, 36] Results show that the secondary rupture process often generates reflected
shocks or standing waves. Furthermore, the diaphragm ruptures initially around the peripheral
and travels a short distance downstream. As it travels downstream, it begins to disintegrate and
then fragments lag the contact surface. An inertial diaphragm model and a holding time model
have been developed to attempt to account for the non-ideal rupture.[17] A related source of
noise can come from the reflected head from the secondary expansion wave. Depending on the
rupture process and the wave speeds, it is possible for the reflected head to arrive in the test
section early resulting in high-frequency, large fluctuations during the test time.[34] Expansion
tubes/tunnels offer test condition possibilities not attainable in any other type of facility, but
proper selection of test conditions and diaphragms is critical in obtaining low-noise, high-quality
test conditions.
31 / 100
3.
Development of Microwave Shock Speed Measurement
for LENS XX
The development of a shock speed measurement based on microwave standing wave
reflection is presented. Accurate shock speed measurements are critical in determining
freestream conditions. Uncertainties associated with non-ideal diaphragm opening processes and
measuring vacuum pressures are avoided by using the experimentally measured shock speeds to
determine freestream conditions.[24] There are several methods to measure shock speed, but
most require individual time-of-arrival (TOA) gauges located at known positions along the
length of the facility. Simply dividing the distance between gauges by the shock arrival time
between gauges yields the shock speed between the two points. Shock waves emit light and have
a large pressure, density, and temperature rise behind them, so the arrival of a shock wave is
fairly easy to identify from a variety of optical, pressure and temperature gauges. The problem
with TOA methods is that accuracy and resolution are dependent on the number of gauges used.
There are practical limitations such as the costs of machining ports and the cost of the gauges
themselves, as well as data acquisition limitations. That is why a microwave measurement
similar what Laney reported is used here.[14]
3.1.
Details of Microwave Shock Speed Measurement
A microwave shock speed measurement system uses only one data acquisition channel
for the simple in-phase analysis demonstrated below (or two for in-phase (I) and quadrature
phase (Q) complex signal analysis) and one antenna. Moreover, it accurately measures primary
and secondary shock speed down the entire length of the facility. This method is ideally suited
for expansion tubes because there is no small nozzle throat to reflect the radio waves as in a
32 / 100
shock tunnel. A microwave shock speed measurement system was described and used by Laney
in one of the original NASA expansion tube facilities.[14] The measurement can be thought of as
a radar measurement to track shock wave position versus time, and therefore velocity, utilizing a
standing wave as opposed to a pulse or spread spectrum radar. A schematic of the system
designed for LENS XX is found in Fig. 25. A single antenna is placed in the test section and set
to a specific frequency to generate a standing wave in the driven and expansion tubes. As a highspeed shock travels through the stationary standing wave, the electrons immediately behind the
shock act as the target reflecting the signal back. The reflected signal received by the antenna is
mixed with the input signal and passed through a detector into the data acquisition system. The
reflected signal appears as a sinusoidal-like waveform whose frequency is directly proportional
to shock speed. Flexible coaxial microwave cable was used for coupling to the antenna, but the
majority of the components were connected directly with rigid couplers or extremely short
flexible coaxial cables. A complete list of the RF equipment used is found in Appendix A.
Moving Reflective Surface
Antenna Voltage Standing Wave A/D Convertor & Data Acquisition Computer
U
Shock Wave 30 in.
Mixer
~
Microwave Source (350 MHz)
RF
Circulator
IF
Detector
LO
Figure 25. Schematic of Original Microwave Measurement System for Determining Shock
Speed in LENS XX
The standing wave frequency in a circular waveguide is directly proportional to the
diameter of the tube or facility in this case. The required frequency must be higher than the
33 / 100
cutoff frequency for the fundamental mode and lower than the cutoff frequency for the next
higher mode to generate a stationary standing wave in the tube. The lower cutoff limit for a
circular waveguide is 2.61 times the radius (here 288 MHz) and the higher cutoff frequency is
3.412 times the radius (here 377 MHz). Biasing the microwave source towards the higher cutoff
frequency will result in a shorter wavelength standing wave, and, therefore, a slightly more
accurate measurement, so a target frequency of 350 MHz was selected. Equation 1 can be used to
determine the standing wave properties, where λ is wavelength, and the subscripts g and c,
represent free space wavelength and higher mode cutoff wavelength, respectively. Equation 2
gives the standing wave frequency in the tunnel.
λg =
λ
1− ( )
λ 2
λc
fg =
, λg 2 = 75.5 cm (29.7 in.)
c
λg
= 198.5 MHz
Eq. 1
Eq. 2
Shock speed can easily be resolved along the tunnel almost every tube diameter or the
half wavelength (λg/2) of the standing wave. More sophisticated time–frequency waveform
analysis could result in higher resolution shock speed measurements. Additionally, the accuracy
of the measurement is based in part on how accurately the transmission frequency is known.
Originally, a voltage controlled oscillator was used as the microwave source, but the frequency
drifted with time, so the microwave source was replaced with a stable fixed frequency crystal
oscillator with a transmission frequency of 349,995,150 Hz. The frequency is checked
periodically with a microwave frequency counter and has not drifted more than 25 Hz over
several months. A stable transmission frequency can be measured to the hertz level, so the
uncertainty due to this drift is negligible. The inner diameter of the LENS XX tubes was honed
34 / 100
to within five thousands of an inch, so variation in standing wave frequency associated with the
tube diameter is also negligible. Lastly, the standing wave frequency was verified experimentally
by pulling a reflective metallic disc through the tunnel and counting the number of cycles over
the length of the tunnel.
Ref. [37] derives the wave equations for a radar distance/velocity measurement utilizing a
standing wave, which is directly applicable to this shock speed measurement. To determine
shock wave position and relative velocity, consider the transmitted wave and the reflected wave
components of the standing wave separately. The equations for a stationary target are given in
Eqs. 3 and 4 for the transmitted wave and reflected wave, respectively, where d represents
distance to the target, c is light speed, and γ and φ are coefficients expressing magnitude and
phase of the reflection off the target, respectively.
VT ( f , x ) = e
j 2π f g
c
VR ( f , x ) = γe ⋅ e
jφ
x
j 2π f g
c
(2 d − x )
Eq. 3
Eq. 4
Relative velocity can now be determined by slightly modifying the above equations.
Considering the location of the target at t=tk as dk, θ as the phase of transmitted wave, and the
velocity as v, the updated components of the standing wave become the expressions in Eqs. 5 and
6. The sum of VT and VR given in Eq. 7 describe the standing wave with respect to a moving
target. The phase of the transmitted wave is constant and can be considered zero. The power
spectrum of Eq. 7 is represented by A, and the power of a standing wave detected at a fixed
location of x=0 is found in Eq. 8.
VT ( f , x, t ) = e
j 2π f g ( t −tk + cx ) + jθ
35 / 100
Eq. 5
VR ( f , x, t ) = γe ⋅ e
jφ
(
j 2π f g t − t k +
2 ( d k + v ( t −tk )) − x
c
)+ jθ
d + v ( t −t ) − x
j 2π f g (2 k c k ) ⎤ j 2π f g (t − t k + cx )+ jθ
jφ
⎡
VT + VR = 1 + γe ⋅ e
e
⎢⎣
⎥⎦
(
A( f ,0, t ) = VT + VR = 1 + γ 2 + 2γ cos
2
4π f g
c
{dk + v(t − tk )}+ φ )
Eq. 6
Eq. 7
Eq. 8
Equation 8 is the mathematical expression for the power of the wave that is measured
from the detector shown in Fig. 25. Since γ and φ are constants associated with the properties
behind the shock wave, fg is the fixed frequency of the standing wave in the tube, and dk is
related to the target velocity history, Eq. 8 reduces to a single variable, v(t). Every cycle of the
measured periodic waveform, A, corresponds to target or shockwave movement of half the
waveguide wavelength (λg/2). Since the waveguide wavelength is well defined, the target or
shockwave velocity is simply found by dividing λg/2 by the cycle time.
The first method of determining cycle times is based on identifying local maxima of the
waveform and determining the peak-to-peak time differences. Figure 26a shows the
theoretically-predicted waveform based on Eq. 8 and a constant target or shock velocity of
6,000 m/s. This waveform was generated using a sample frequency corresponding to 100 kHz,
which was the original data acquisition frequency used in this experiment. Local peaks are
identified by the red diamonds, and the time between these peaks is used to determine the shock
velocity shown in Fig. 26b. The velocity accuracy is limited primarily by the sample frequency,
and this is apparent in the oscillations shown in Fig. 26b. The shock speed and sample frequency
used in this example are representative of the original configuration, and in this example single
cycle error was 233 m/s or 3.9%, but the average velocity error was only 11 m/s or 0.18%. Even
36 / 100
with a relatively low sample rate and high shock speeds the measurement is quite accurate. TOA
type measurements typically have uncertainties of two to three percent over ten times this cycle
length, so accuracy and resolution are essentially improved by an order of magnitude assuming
the same sample rate.
7,000
Shock Speed (m/s)
2.5
Voltage (V)
2
1.5
1
0.5
6,000
5,000
4,000
3,000
2,000
1,000
0
0
0.0005
0.001
0.0015
0
0.002
0
5
10
15
20
25
30
Distance (m)
Time (s)
a. Profile of theoretical reflected signal with
cycle peaks identified for v = 6,000 m/s
b. Reduced velocity based on peak-to-peak
time cycle time
Figure 26. Theoretical Detected Signal from Microwave Shock Speed Measurement and
Corresponding Shock Speed Derived based on Signal Period
A more elegant and faster method for determining the average shock speed is to
transform signal A to frequency space with a Fourier transform. Figure 27a shows the same
theoretically predicted waveform used in Fig. 26a with the same resolution or sample rate and
half the total number of samples. The Fast Fourier Transform (FFT) of that signal is given in
Fig. 27b and clearly shows a dominant frequency of 7,959 Hz. An average shock velocity of
6,010 m/s (0.17% error) is found by simply multiplying the dominant frequency by the standing
wave half wavelength (λg/2). Higher data acquisition speeds result in much more accurate
velocity determination for both data reduction methods, but the initial goals were to determine
the viability of the measurement and to compare average shock speeds to standard time-ofarrival shock speed measurements.
37 / 100
2.5
Magnitude of FFT
Amplitude
2
1.5
1
0.5
0
0
0.0002
0.0004
0.0006
0.0008
500
450
400
350
300
250
200
150
100
50
0
0
0.001
5000
10000
15000
20000
Frequency (Hz)
Time (s)
a. Profile of theoretical reflected signal
b. FFT of theoretical signal (Peak of 7959 Hz
corresponds to velocity of 6010 m/s)
Figure 27. Theoretical Detected Signal from Microwave Shock Speed Measurement and
Corresponding FFT to Determine Shock Speed
Another possible source of error comes from the magnitude and phase coefficients
associated with the reflection from the target or shock wave. Since the magnitude coefficient, γ,
is multiplied by the cosine function in Eq. 8, it effectively only controls the signal-to-noise ratio
that is measured at the power detector. The phase coefficient, φ, provides a constant phase shift
to the signal, so this value is of little importance when determining shock speed, except near the
location of the secondary diaphragm. These voltage reflection coefficients can be calculated
assuming reflection from a plasma slab of known properties.[38] Plots of the reflection
coefficients versus electron density are shown below in Fig. 28 for various collision frequencies
between 108 and 1012; similar calculations were described by Laney[14] with regards to the
original NASA measurement. Note that coefficients used in Eq. 8 and Fig. 28 are analogous.
Since there is a rapid change in the shock speed and the post shock conditions, this phase
coefficient can change between the primary and secondary shocks resulting in higher uncertainty
of the shock speed nearest the secondary diaphragm location. The region nearest the diaphragm
is never used when determining test conditions, so the higher uncertainty in those one or two
38 / 100
incremental velocity measurements is acceptable. Furthermore, it is possible to measure the
phase shift and theoretically reduce the shock speed measurement uncertainty in this region by
measuring the in-phase and quadrature phase of the signal as discussed in Section 3.3.
1
v=10⁸
v=10¹⁰
v=10¹²
ψ Γ (deg)
0.8
Γp
0.6
0.4
0.2
0
1.E+09
1.E+11
Ne
1.E+13
1.E+15
180
160
140
120
100
80
60
40
20
0
1.E+09
v=10⁸
v=10¹⁰
v=10¹²
1.E+11
Ne
, electrons/cm‐3
a. Power reflection coefficient vs. electron
density
1.E+13
1.E+15
, electrons/cm‐3
b. Phase reflection coefficient vs. electron
density
Figure 28. Voltage Reflection Coefficients from a Plasma Slab
Thus far, the microwave shock speed measurement has been framed from an
electromagnetic standpoint, and it has been shown that it is possible to accurately track the
velocity of a moving target through a standing wave in a circular waveguide or tube. The target
that is tracked in this case is the shock, and it can only be tracked if electron density behind the
shock is sufficiently high to reflect the standing wave. Electron density is a function of the
plasma frequency which is shown in Eqs. 9 and 10, where fp is the plasma frequency, ωp is the
radial plasma frequency, ε0 is permittivity of free space, me is electron mass, and e is electron
charge.[14, 38] The minimum electron density required to reflect the standing wave is
determined by substituting the transmission frequency of antenna, which is nominally 350 MHz,
for the plasma frequency and plugging in the plasma constants (ε0, me, e) , and the result is found
in Eq. 11.
39 / 100
ωp
2π
fp =
ωp =
N e e2
ε 0 me
Eq. 9
Eq. 10
2
⎛ 350 × 106 ⎞
−
⎟ = 1.52 × 109 e cm3
N e = ⎜⎜
3⎟
⎝ 8.97 × 10 ⎠
Eq. 11
The minimum required shock speed is dependent on gas composition and pressure levels.
Figure 29 shows shock speed versus electron density for various initial pressures in air. The data
for this figure were calculated using MacLean’s CHEETAh[24] code and NASA’s CEA
code[39] assuming equilibrium chemistry, and including electronic and vibrational energy. An
approximate 2.5 km/s value is valid in air at most pressures of interest. Figure 30 shows shock
speed versus electron density for various gases at a fixed initial pressure of 100 Pa. Argon
readily ionizes at very low shock speeds, while helium requires extremely high shock speeds
before sufficient ionization will occur behind the shock to reflect the standing wave. Hydrogen
must dissociate before it can ionize, and it was determined that no shock speeds of interest can be
measured in hydrogen, so it does not appear in Fig. 30, even though hydrogen is used
occasionally as the accelerator gas in LENS XX. Carbon dioxide ionizes at a similar rate to that
of air for a given shock speed, although it requires more energy to drive stronger shocks into
carbon dioxide.
40 / 100
Electron Density (e‐/cm3)
1.E+18
1.E+16
1.E+14
1.E+12
1.E+10
Nemin 1 Pa
100 Pa
10,000 Pa
1.E+08
1.E+06
2000
4000
6000
8000
10000
Shock Speed (m/s)
Electron Density (e‐/cm3)
Figure 29. Shock Speed vs. Electron Density in Various Initial Pressures of Air
1.E+18
Ar
Air
CO2
He
1.E+16
1.E+14
1.E+12
1.E+10
1.E+08
1.E+06
2000
Nemin 4000
6000
8000
10000
Shock Speed (m/s)
Figure 30. Shock Speed vs. Electron Density in Various Gases at 100 Pa
3.2.
Antenna Selection and Shield Design
The shock speed measurement utilizes an AX-31CMX Planar Log-Periodic Antenna
from WiNRADiO, located in the test section away from the model sting support. This style
antenna was selected for two main reasons: it has good directionality and a compact form factor.
Log-periodic antennas use alternating staggered dipoles located along a central transmission line.
41 / 100
The spacing and the length of these elements increases logarithmically along the transmission
line. These antennas are typically used where directionality is required to improve signal quality
and they operate over a broadband, so typical applications include VHF/UHF signal transmission
and reception. In this case, the operation frequency is known well, so the broadband capability of
the AX-31CMX is not utilized, but it meets the other requirements and is commercially
available. Laney[14] used a simple monopole antenna which radiates energy in 360-deg, but the
LENS XX nozzle is proportionally smaller and its ballast tank is much larger than the one used
in NASA tests, so a large percentage of the RF energy would be wasted unless a directional
antenna was selected. A waveguide would have the best coupling with the tube, or experience
the least amount of loss, but would be much larger. The AX-31CMX antenna is 30 cm x 25 cm x
2.5 cm, while a standard waveguide designed for 350 MHz would have been approximately
twice the thickness and almost three times as long. A large antenna would be more difficult to
work around in the test section and would be more difficult to shield from the extreme tunnel
environment.
Post-test flows in expansion tunnels are extremely harsh with stagnation pressures ten to
twenty times higher than the test conditions. Additionally, diaphragm fragments are often present
in the flow which can cause significant damage at high velocities. For these reasons, the lowprofile log-periodic antenna was selected and a shield was designed to protect the antenna from
the main flow. It was constructed with a high-strength phenolic covering pinned together with
carbon fiber rods, and had a replaceable fiberglass 90-deg angle on the forward leading edge of
the shield. Composite materials were used so that the RF energy could propagate down the
tunnel and form the standing wave necessary for the measurement. Pictures of the antenna and
the shielded antenna mounted in the LENS XX test section are shown in Fig. 31. A post-test
42 / 100
picture of the replaceable fiberglass shield is given in Fig. 32, clearly showing the necessity for a
disposable shield due to the significant damage incurred. Another example of a post-test picture
is given in Fig. 33 which illustrates how severe the tunnel environment can be for even metallic
models. Again, LENS XX test articles are located out of the line-of-site of the tube, so model
damage is negligible, but antenna placement could not interfere with standard model
measurements, so it was necessary to place it in the “destruction zone” of the tunnel.
a. AX-31CMX Antenna
b. Phenolic shielded antenna
Figure 31. Pictures of Log-Periodic Antenna Used for Shock Speed Measurements
Figure 32. Post-Test Picture of Antenna Shield After High-Pressure Run with Thick
Secondary Mylar Diaphragm
43 / 100
Figure 33. Example of Typical Post-test Expansion Tunnel Damage After One Run
(MSL Testing in Prototype LENS X Facility)
In addition to the severe loads and the high-velocity debris, the tunnel also moves up to
three inches after the test. The original SMA coaxial connector on the antenna was a press-on
connector, so post test this connector could lose connectivity and the measurement would be lost
for the subsequent runs if the problem was not immediately identified. The fix was relatively
straightforward and required replacing the press-on connector on the antenna board with a
threaded SMA connection. The threaded connections are torqued to an appropriate level to
minimize periodic loosening. Additionally, a check that the antenna is radiating energy before
every test is now completed, which simply requires someone to wave their hand or walk in front
of the antenna while another person is watching the scope to verify a significant change in the
signal.
3.3.
Shock Speed Measurement Upgrades
The original microwave shock speed measurements were sufficient to obtain accurate
shock speeds with improved resolution, but several upgrades were identified to improve the
measurement. The first upgrade, mentioned in Section 3.1, was to replace the variable voltage
controlled oscillator with a fixed-frequency crystal oscillator. This reduced transmission
44 / 100
frequency drift from 1-2 MHz down to 25 Hz. Next a quadrature hybrid and a triple tuning stub
was incorporated into the system with the upgraded configuration shown in Fig. 34.
Moving Reflective
Surface
Antenna
Voltage Standing
Wave
A/D Convertor & Data
Acquisition Computer
U
Shock Wave
~30 in.
Tuning Stub
Quadrature
Hybrid
IN
Circulator
~
~
Microwave Source
50Ω
0º
ISO 90º
I
Mixer
RF
Q
Detectors
IF
LO
RF
IF
LO
Mixer
(350 MHz)
Figure 34. Schematic of Upgraded Microwave Measurement System for Determining
Shock Speed in LENS XX
The quadrature hybrid separates the I and Q components of the signal allowing a more
rigorous analysis of the reflected wave. Analysis of the I and Q components yields phase shift
information which relates to properties behind the shock discussed in Section 3.1. Additionally,
the quadrature phase cycle-to-cycle shock speed measurement serves as a redundant backup to
the in-phase measurement.
The triple stub tuner enables cancelation of static reflections associated with the metallic
test section. Un-tuned signals show DC offsets and a phase shift component that inhibits I and Q
analysis. The triple stub tuner was adjusted looking at both S11 and S21 parameters with a
network analyzer. A reflective boundary was setup at the end of the driven tube, because it was
not possible to set up a good open or microwave absorbing boundary. Tuning results are shown
below in Fig. 35. Typically, when tuning an antenna, one minimizes the reflection parameter, but
in this case S11 is maximized, which ensures good signal coupling in the tube. Figure 35a shows
the reflection coefficient measurement for just the antenna and the tuner, and Fig. 35b shows the
45 / 100
same measurement with the excitation frequency ran through the circulator. The design of the
circulator ensures that the excitation port is isolated from the reflected signal, so a 27 dB drop is
measured when the circulator is included. SEI, the circulator manufacturer, quotes 25dB
isolation, and additional losses are expected within the circulator and, of course, transmission
into the tunnel. Another interesting result from Fig. 35a is, that despite model changes and two
months of potential environmental changes, the antenna tuning originally applied still was a
significant improvement over the baseline without the tuner. Retuning was easily resolved by
moving one of the tuning stubs roughly a centimeter. In this case, the transmitting and receiving
antenna are one in the same, so the S21 measurement is redundant, but Fig. 35c is good
confirmation that a majority of the energy inserted into the circulator is returned through the
antenna to the circulator exit port. Again, small losses associated with the circulator and tunnel
coupling are expected, so the 0.6 dB loss measured after tuning is considered good. Tuning with
the network analyzer in this reflected mode is not sufficient alone, because similar results could
be obtained by placing a reflective box around the antenna. It was necessary to repeat the
calibration where a reflector is pulled through the tube again. Results indicated that a standing
wave of the expected wavelength was setup inside the tube. Additionally, the DC offset of the I
and Q signals was negligible and the phase shift of the two signals was within five degrees of the
nominal ninety degrees that should be expected. Without the tuner, the phase shift between the
signals was less than five degrees, so the addition of the triple stub tuner made a significant
improvement.
The last upgrade involved the acquisition of the detected signals. Originally, the analog
signals were acquired on the same 100 kHz data system that all the other model and facility data
was recorded on. This system was adequate, but increased sample rates and signal gain options
46 / 100
were realized by switching to a dedicated high-speed oscilloscope. A Tektronix DPO3014 scope
with a 100 MHz bandwidth and a 2.5 GHz sampling rate is now used. The voltage input range
and gain options also exceed what was possible on the original data system, so signal-to-noise
ratio was improved.
0
S11 (dB)
‐5
‐10
‐15
‐20
No Tuner
Tuned
Tuned 2 Months Prior
‐25
‐30
340
345
350
355
360
Frequency (MHz)
a. S11 coefficient of antenna only
0
‐10
‐5
‐20
S21 (dB)
S11 (dB)
0
No Tuner
Tuned
‐30
‐40
‐10
‐15
‐20
‐50
‐25
‐60
‐30
345
347.5
350
352.5
345
355
347.5
350
352.5
355
Frequency (MHz)
Frequency (MHz)
b. S11 coefficient of antenna and circulator
No Tuner
Tuned
c. S21 coefficient of antenna and circulator
Figure 35. Reflection and Transmission Characteristics With and Without Tuning
47 / 100
4.
Development of Plasma Diagnostics for Expansion
Tunnels
Plasma layer or plasma sheath measurements are of interest to the hypersonics
community for fundamental reasons to help characterize these complex flow fields, and for more
practical reasons to evaluate RF signal propagation through the plasma layer for communication
or GPS tracking of hypersonic vehicles. Jones[40] recently presented the expert panel
recommendations for research efforts associated with the communication blackout problem. The
highest priority was given to validating existing models, which requires quality ground test data
at duplicated hypervelocity conditions of interest.
Very little data are currently available to support model validation in the hypersonic
flight environment;[40] in fact, a single flight test (RAM C-II) is almost exclusively cited as the
plasma validation dataset for hypersonic modeling. NASA’s Radio Attenuation Measurement
(RAM C) experiments had a sphere cone geometry with peak velocities of approximately
7.5 km/s, and the tests were completed from 1967-1970. Ref. [41] has a collection of several
associated papers. RAM C-II was constructed with a non-ablating beryllium nosetip and there
was no water or electrophilic injection from the nosetip, as in the other tests, so it is generally
regarded as the best validation case. These test articles were heavily instrumented with multiple
frequency microwave reflectometers[42] and various types of Langmuir probes[43] to
characterize the plasma sheath throughout the trajectory. One other Air Force flight test of a
smaller, but similarly shaped vehicle called Trailblazer II, is sometimes cited as a validation case
too for conditions around 5 km/s.[44] Microwave interferometry and Langmuir probe plasma
diagnostics have both been successfully used in shock tunnels in the past.[45] However, as
48 / 100
discussed in Section 1.1 freestream dissociation at the higher velocities of interest is very
significant and shock tunnels are not capable of reaching the high velocities of RAM C.
LENS XX is uniquely positioned to generate well characterized flows at hypervelocity
conditions of interest where little or no plasma validation data exists so several types of
instrumentation were considered. Multiple fixed frequency reflectometers could be used at the
same time to determine plasma layer location, thickness, and average electron density. This
approach requires many probes, but originally it was thought that test times were too short for
typical swept frequency measurements. Fixed frequency reflectometers were used in the RAM-C
flight tests to calculate electron density based on the slope of the phase change as the steady-state
plasma sheath set up over the vehicle.[42] NASA developed a microwave reflectometer
ionization sensor (MRIS) for a canceled flight test program that could be used as a more elegant
solution to the RAM-C approach.[46, 47] The MRIS sensors use four different high-frequency
(10-200 GHz) transmitters and receivers located near one another, and electron density
measurements are based on the phase shift measured at the most relevant frequency. Several
frequencies are used for a wide range of operating conditions. This time domain reflectometry
type measurement employed by the MRIS should work in the expansion tunnel, but these sensors
are not commercially available, and redevelopment of this type of sensor is beyond the scope of
the current project. An ultra-short short broadband pulse time-domain reflectometer (TDR) could
potentially yield the same information as the swept frequency measurement during the short test
times available,[48] but in order to resolve centimeter-sized shock or plasma layers the pulse
width would have to be extremely narrow and the data acquisition system requirements exceed
the current state-of-the-art. Another interesting RF probe was developed for the Trailblazer II
flight tests. The Trailblazer II probe was referred to as the microstrip plasma probe, and it was a
49 / 100
simple probe that could be easily constructed and operated in a lab and rugged enough for a
flight test.[49, 50] The microstrip probe operated at a fixed frequency and relied on the simple
reflection coefficient measurement to describe the medium adjacent to the probe.
More recently, diagnostic probes have been developed by ElectroDynamic, Applications,
Inc. (EDA) to examine the likely problem of GPS blackout at hypervelocity flight
conditions.[51] They employ swept frequency reflection coefficient measurement using a simple
coaxial resonance probe and a vector network analyzer (VNA). EDA’s instrument is similar in
concept to the Trailblazer microstrip probe, but it utilizes the swept frequency measurement to
yield more information about the local plasma and has operability over a much larger range of
electron densities. The measurement range and resolution is limited by the VNA that is used to
make the measurement. A VNA capable of frequency sweeps in the sub millisecond range was
identified as a good candidate for measurements in LENS XX, so this measurement was selected
as the most likely to succeed. Details of EDA’s resonance probe are reported in the following
section. In addition to identifying a possible non-intrusive microwave diagnostic for evaluating
communication characteristics and plasma properties of a shock layer, traditional intrusive
Langmuir probes were also considered form comparison. The swept voltage Langmuir probes
that were tested are described in detail in Section 4.3.
4.1.
Microwave Frequency Domain Reflectometry Measurements
A schematic of the planar resonance probe designed by EDA is shown below in Fig. 36.
The probe has a threaded SMA connection on the backside and consists of a brass center core
conductor and an outer brass ground plane isolated with a boron nitride insulator. This resonance
probe is 1.5 in. in diameter can be mounted in a model with a flat face or normal to the flow as a
stagnation probe, and results from both of these configurations are reported in Section 4.2.
50 / 100
Ø 0.047
0.125 thick
Ø 0.300
Figure 36. ElectroDynamic Applications Planar Resonance Probe for LENS XX Testing
EDA’s experience with probe design and plasma vacuum testing was relied upon when
sizing the probe for use in LENS XX, but radiation characterization of the probe was not
completed until a later date by the author. ANSYS HFSS (originally called High-Frequency
Structural Simulator) is a finite element method solver for 3-D full-wave electromagnetic field
simulation. HFSS version 12 was used to simulate the EDA probe shown in Fig. 36 in a vacuum
environment. This analysis was used to evaluate the size of the electric field generated by the
probe and determine its propagation characteristics over the wide range of relevant frequencies.
The electron density measurement is effectively averaged over the electric field generated by the
probe, so it is important to understand how large this zone is to compare results with
computational fluid dynamic (CFD) solutions. A driven modal solution type was used along with
wave port excitation to avoid modeling of the SMA connectors. Material properties for brass and
boron nitride were used in a vacuum environment for the simulation, and the electric field
solutions were scaled independently. Figure 37 shows section views of the planar resonance
51 / 100
probe and the electric field contour plots at various frequencies. In general, our measurements
were made between 0.5 and 6.0 GHz, but a 10 GHz solution was also included. The radiation
pattern has a frequency dependence, but the higher strength electric field area seems be roughly
two to three times the size of the radiating plane or 1.5-2.0 cm in this case. Shock standoff
distances for most conditions and most models of interest would be on the order of 1-2 cm, so it
turns out that the probe is well suited for plasma layer measurements in LENS XX.
0.5 GHz
1 GHz
2 GHz
3 GHz
5 GHz
6 GHz
10 GHz
1 cm
4 GHz
Figure 37. ANSYS HFSS Electric Field Contour Plots of Planar Resonance Probe
The theory behind the resonance probe measurement is discussed in more detail in Refs.
[51-53], but a brief overview is given here. The resonance probe radiates the microwave energy
outwardly and its impedance depends on the average dielectric properties of the near field. In a
vacuum environment, all of the energy returns to the probe, but if plasma is present, the
dielectric properties of that plasma affect the impedance of the probe. As the probe frequency
approaches the characteristic plasma frequency the impedance magnitude resonates. The plasma
frequency is controlled by the ion-electron interaction. Ion masses are significantly greater than
52 / 100
electrons, so the electron resonance frequencies dominate the high frequency RF excitation. EDA
developed a model to determine detailed plasma properties from a swept frequency reflection
coefficient measurement based on the open ended coaxial sensor from Ref. [54]. In general, the
plasma density determines the location in frequency of the dip, the collision frequency the width
of the dip, and the plasma capacitance of the magnitude of the dip.[52] The plasma frequency
relation to electron density was given above in Eq. 10 from Section 3.1, so a reasonably good
estimate of electron density can be made by simply identifying the resonance peak from the
frequency domain reflectometer measurement. LENS XX steady-state run times are on the order
of 0.5-1.5 ms typically, so the frequency sweep of a high-speed VNA is limited to a resolution of
10-20 steps, but electron densities and the RF communication threshold are still determined
accurately. The uncertainty can be calculated for each run, but is dependent on the bandwidth of
the measurement, number of frequency steps, and plasma conditions.
4.2.
Results from Resonance Probe Reflection Measurements
Results for the resonance probe discussed in Section 4 are reported for two different
configurations. The probe was first installed on the back windward face of a 2D extruded capsule
model shown in Fig. 38. The model was designed for NASA to generate 2D flow in highenthalpy low-density conditions, to assess surface catalysis effects of different materials.
However, the back face of this model was large, flat, and un-instrumented, so it was a perfect
candidate for this piggy-back experiment. In the second configuration, the probe was used as a
stagnation probe with the flat circular face normal to the flow. The probe was supported off of a
rod approximately one-third its diameter, and tested alongside a 5.08 cm diameter cylinder.
Again this was considered a piggy-back test, where the primary test objective was to measure
UV spectral emission from a shock layer in front of a cylinder at approximately 5 km/s and
53 / 100
density corresponding to an altitude of 75 km. Both tests were completed in LENS XX; however,
the extruded capsule was tested in the 244 cm test section in expansion tunnel mode, while the
stagnation probe was mounted in the 61 cm test section in expansion tube mode.
RF Resonance Probe Location
Figure 38. Computational Fluid Dynamic Simulation of Extruded Capsule at 7km/s in Air
An Agilent Technologies E5071C vector network analyzer was used for all resonance
probe S11 reflection coefficient measurements. This instrument has a frequency range of 9 kHz 8.5 GHz, and depending on the range it can scan eight points in approximately 0.5 ms, or 15
points in approximately 1.0 ms. All reflected power plots for both probe configurations were
normalized with the free-space probe response, and connecting cables between the probe and the
VNA were also calibrated out.
The extruded capsule test series consisted of nine runs, and the two relevant test
conditions are reported below in Table I . Settings on the first several runs were chosen with long
scan times with the goals of simply acquiring a signal, becoming more familiar with the
measurement and triggering system properly. These runs were successful, but no useful
quantitative information was obtained, because the test condition velocity was changing by a
factor of two over the 4 ms scans. After this initial success, it was obvious that a short-duration
54 / 100
scan during the test time was possible, so the scan range was narrowed and the number of points
reduced to 15 for a sweep time of 1 ms. A number of runs had calibration issues, trigger timing
problems, or too narrow of a sweep range, but Fig. 39 shows two reasonably good measurements
at two different conditions. Extruded capsule Run 5 was at 7.9 km/s, and Run 9 was at 8.9 km/s,
and as expected the Run 9 shows a higher frequency resonance corresponding to a higher
electron density. The resonance frequency identified in Runs 5 and 9 correspond to an electron
density of 1.52x1017 /m3 and 2.41x1017 /m3, respectively. CFD solutions of the extruded capsule
shock layer for each run, generated by Matt MacLean using DPLR[55], are given in Figs. 40 and
41. Electron density and collision frequency are plotted from the model surface out just beyond
the shock at 2 cm. The bow shock boundary is clearly identified by the sharp reduction of
electron density to zero in the freestream.
A representative image of a CFD solution is shown above in Fig. 38. Note that the
solutions were run principally to make heat shield comparisons for the primary test objective,
and the grid actually stops prior to the resonance probe location on the backshell. This is
somewhat unfortunate, but the solutions shown in Figs. 40 and 41 are taken from the edge of the
grid and are still very illustrative for making qualitative comparisons. Additionally, the CFD grid
could be extended and solutions reran if more precise comparisons were ever needed, but that is
beyond the scope of this work. Figure 42 shows the comparison of electron density distributions
for the two runs. Absolute electron density measurements do not match well, since the CFD
solution is not taken at the probe location, but it is useful to non-dimensionalize the data by
looking at the ratio of Run 5 to Run 9. Assuming a probe electric field propagation distance of
1.5 cm, the CFD predicted electron density ratio between the runs is 0.56, where the measured
ratio based on resonance frequencies is 0.63. Given that these two ratios are close, it suggests
55 / 100
that the resonance
r
prrobe is indeeed proportioonally measuuring plasmaa properties in the expannsion
tunnel coorrectly.
psule Modeel
Table I. Freestrream Condiitions for Exxtruded Cap
Frrequency (G
GHz)
3.0
S11 (dB)
2.5
0
‐
‐2
‐
‐4
‐
‐6
‐
‐8
‐1
10
‐1
12
‐1
14
‐1
16
‐1
18
3
3.5
4.0
4.5
5.0
Ru
un 05, 7.9 km/ss
Ru
un 09, 8.9 km/ss
5E+19
4.5E+19
4E+19
3.5E+19
3E+19
2.5E+19
2E+19
1.5E+19
1E+19
5E+18
0
1E+10
9E+09
8E+09
7E+09
6E+09
5E+09
4E+09
3E+09
2E+09
1E+09
0
Electron Density
Collision Freequency
0
0.5
1
Distance (cm))
1.5
Collision Frequency (Hz)
Electron Density (1/m3)
Figure 39.
3 RF Reso
onance Prob
be Reflectioon Coefficien
nt Compariisons on Bacckward Facce of
Extruded
d Capsule Model
M
2
Figuree 40. CFD Solution for Run 05 Shoowing Electrron Densityy and Collisiion Frequen
ncy
Distribution
D
from the Bow
B Shock to the Model Surface
56 / 100
Electron Density
1.4E+10
1.2E+20
Collision Frequency
1.2E+10
1E+20
1E+10
8E+19
8E+09
6E+19
6E+09
4E+19
4E+09
2E+19
2E+09
Collision Frequency (Hz)
Electron Density (1/m3)
1.4E+20
0
0
0
0.5
1
Distance (cm)
1.5
2
Electron Density (1/m3)
Figure 41. CFD Solution for Run 09 Showing Electron Density and Collision Frequency
Distribution from the Bow Shock to the Model Surface
1.4E+20
Run 05
1.2E+20
Run 09
1E+20
8E+19
6E+19
4E+19
2E+19
0
0
0.5
1
Distance (cm)
1.5
2
Figure 42. Electron Density Comparison of CFD Simulations for Run 05 and Run 09
After the success of the first resonance probe installation, a second stagnation
configuration was considered at similar densities, but much lower velocities. The MURI run
conditions targeted 5 km/s, but exact conditions were reported above in Table VI. Since the
probe orientation changed, expected electron densities were still on the same order of magnitude
despite the lower velocity. These measurements were completed over a frequency range of
0.5-6 GHz, with only eight points to reduce the sweep time to approximately 0.5 ms. In addition
57 / 100
to running in shock tube mode for these tests, the first driven tube was converted to the driver
tube which reduced the steady-state test time by a factor of two, because the newly defined
driven and expansion tubes were roughly half as long. Power reflection measurements for MURI
Runs 2 through 7 in air are given in Fig. 43. Measurements in this test series were complicated
by the fact that the test time was much shorter than normal, and pressures and temperatures were
much lower than typical as well, so precise trigger became somewhat of an issue. Some of the
runs were triggered slightly early or slightly late, that is why there are some differences in the
pre-resonance spike measurement, but in general the resonance spike was clearly measured for
all runs in air. Run 1 had no facility trigger signal, so no data were recorded on any system, and
Run 6 was triggered late enough that the test velocity had already started to slow down due to the
arrival of the unsteady expansion waves. Normalized electron density measurements based on
the resonance frequencies measured are compared to the equilibrium electron density values
predicted by CHEETAh are shown in Fig. 44. Work with EDA still needs to be completed to
make the measurements fully quantitative, but in general the trends measured by the probe are
expected based on run conditions. Runs 2 and 7 deviate from expectations the most, but still lie
within acceptable limits based on the higher uncertainty of the run condition at these low
densities, and increased uncertainty from the course frequency sweep required for these test
times.
58 / 100
Frequency (GHz)
S11 (dB)
1.0
2.0
3.0
4.0
5.0
0
‐2
‐4
‐6
‐8
‐10
‐12
‐14
‐16
‐18
6.0
Run 02
Run 03
Run 04
Run 05
Run 06
Run 07
Normalized Electron Density
Figure 43. RF Resonance Probe Reflection Coefficient Comparisons in Stagnation
Configuration
10
9
8
7
6
5
4
3
2
1
0
Equilibrium Estimate
Resonance Probe
Run 2
Run 3
Run 4
Run 5
Run 7
Figure 44. Normalized Electron Density Comparison between Equilibrium Estimate and
Resonance Probe Measurement
These results were exploratory in nature and exceed any expectations going into the tests.
A frequency domain reflectometry measurement was successfully made in two configurations at
several conditions to characterize near field plasma properties in the LENS XX expansion tunnel.
Further improvements would lead to a more quantitative measurement, but clearly the goal
59 / 100
identifying a measurement technique and demonstrating a measurement to determine electron
density and examine RF communication frequencies through a shock layer at hypervelocity
conditions has been realized.
4.3.
Langmuir Probe Development
In order to develop non-intrusive measurements, it is useful to have reliable intrusive
measurements to compare to, so a Langmuir probe system is used. Swept-voltage Langmuir
probes have been used successfully in shock tunnel testing,[45, 56] but short test times has
precluded their use in expansion tunnels until now. Swept-voltage probes consist of a single
small-diameter wire. They can be placed on the surface of a model in a flush configuration, or
they can be used to probe the flow of a shock layer for instance. Since the voltage sweep takes
some finite time, the time resolution of this style of probe is limited to the sweep and data
acquisition electronics, but if steady-state test times are long enough, these probes yield the most
information about the plasma properties. Goekce et al.[57] demonstrated the use of a triple
Langmuir probe in the University of Queensland X2 expansion tunnel. A triple probe uses three
electrodes, as the name suggests, one with a positive bias, another with a negative bias and the
third is floating. The triple probe has good time resolution, but much worse spatial resolution
since three electrodes must be placed in the region of interest; therefore, this configuration
cannot readily be used to probe the flow around a model. Lastly, the I-V characteristic curve of
swept-voltage probes yields redundant information and often more accurate plasma properties.
A Langmuir probe tip for the swept-voltage probe was constructed from a 260 μm
diameter tungsten wire with a length of 2.35mm. The probe was placed in the shock layer of a 3”
hemisphere (shown in Fig. 45). The probe tip is indicated with a bracket and an arrow in the
figure, because it is very difficult to see on the model scale. An insulating ceramic holder is
60 / 100
graduallyy tapered up
p to a metalllic holder. A commerciaal swept-volttage Langm
muir probe syystem
was usedd to demonsstrate the ability to makke electron density
d
meassurements inn a plasma layer.
l
The ALP
P SystemTM by
b Impedanss is sufficienntly fast to determine
d
plasma param
meters in the short
test times of LENS XX.
X Impedaans software is used to extract
e
electtron temperaature and nuumber
density from
f
the meaasured curreent-voltage (I-V)
(
charactteristic curvee using Lafrramboise[58] and
Allen-Booyd-Reynold
ds (ABR)[599] theories, depending on the plaasma sheathh properties. The
collisionlless assumpttion of Lafraamboise is not
n always applicable,
a
s Rousseau et al. providde an
so
analyticaal expression
n to determiine which thheory to appply based onn the number of ion neeutral
collisionss in the sheaath. [59]
Figure 45. Picturee of Langmu
uir Probe foor Demonstrration Testiing in Shock
k Layer of 3-in.
3
Heemisphere
A Langmuir probe was tested in thhe plasma layer
l
of a 3”
3 hemispheere at freesttream
stagnatioon enthalpy of
o 25 MJ/kg in air (91-C
CH Run 6). Figure
F
46 shhows the meeasured Langgmuir
probe chharacteristic curve andd first and second derrivatives useed to calcuulate the pllasma
propertiees. This partticular scan was made from
f
-15 to +10V with 0.5 V steps. The steadyy test
time at 25MJ/kg is ro
oughly 1 ms, so the Langmuir probee scan was trriggered earlly in the testt time
and limitted to 400 μs.
μ Eighty daata samples were averagged at each step to get the
t smooth curve
c
61 / 100
shown below. Key points
p
on thhe plot incluude the floaating potentiial and the plasma poteential
which are required to
o determine electron tem
mperature annd electron density.
d
The floating poteential
m
cuurrent switchhes from neggative to possitive,
is identiffied on the I--V characterristic where measured
which occcurs at -3.6V for this caase. The plaasma potentiial is identifi
fied as the innflection poiint on
the I-V curve,
c
so it iss useful to loook at the firrst and seconnd derivativees which inddicate 8 V. Inn this
case the sweep is sto
opped prior to ion saturaation, so thee electron deensity is deteermined from
m the
electron-dominated region
r
usingg the theoriees referencedd above. Meeasured elecctron temperrature
68 eV and 77.5x1017 m-3, respectivelyy. Dunn[56]] provides a good discuussion
and denssity were 2.6
on the deetails of dataa reduction and use of Laangmuir probbes in shockk tunnels.
1st and 2nd derrivative of th
he I-V curvee
I-V charracteristic cu
urve
Figure 46. Langm
muir Probe Scan
S
from 3-in.
3
Hemisp
phere Demoonstration Testing
T
(91-C
CH
Run 6)
T primary production CFD tool ussed for LEN
The
NS facility design,
d
desiggn-of-experim
ment,
and data validation is
i the Data-P
Parallel Linee-Relaxationn (DPLR) coode licensed by NASA Ames
A
RC).[55] MaacLean perfoormed a simuulation of thhe 3” hemispphere at 25M
MJ/kg
Researchh Center (AR
to compaare to the Laangmuir proobe measurements, and details of thhe hemisphere simulatioons in
LENS XX
X are found
d in Ref. [600]. Results of
o this simullation are presented beloow in Fig. 47a-d,
4
showing the Mach number,
n
presssure, temperature, and electron
e
dennsity fields, respectively
r
. The
62 / 100
middle of the Langmuir probe tip is indicated in each of the figures, and the corresponding
electron density is 8.45x1017 m-3 which agrees well with experiment.
Mach Number field
Pressure field
Temperature field
Electron density field
Figure 47. 3 in. Hemisphere CFD Simulations for Air at 25 MJ/kg in LENS XX
63 / 100
5.
Results from Microwave Shock Speed Measurements
LENS XX has just recently completed its 140th run. The microwave shock speed
measurement was originally brought online around Run 75 in March of 2011. Since that time the
measurement has been active for approximately half of those runs, and going forward, there is no
reason to believe it will not be active for almost all future runs. Various issues, upgrades, or
schedule pressures have limited its use in certain programs, but the technique has repeatedly
proven its usefulness as a high-resolution shock speed measurement for improved facility
characterization of LENS XX. Now that the design has matured, it requires little effort between
runs to maintain and the system can be left alone between test programs, so it is more or less
always ready for testing. A few surprise results have also strengthened the value of this
measurement. In one instance, a triggering problem resulted in a loss of all standard TOA data,
so the only way to calculate the test conditions was from microwave measurement. Additionally,
TOA measurements for the latest low-density air measurements had much higher than typical
uncertainty due to low signal values, but the microwave measurement worked well. Furthermore,
the microwave system turned out to be measuring accelerator gas and test gas velocity at these
low-density conditions which was unexpected, but a very useful result. Detailed results are
presented in the subsequent subsections.
5.1.
Measuring Primary and Secondary Shock Speeds
Microwave shock speed results from facility Run 75 are given in Fig. 48. Figure 48a
shows the raw reflected signal that was recorded during the run with the cycle peaks identified
by the red diamonds. The amplitude of the signal shown in Fig. 48a drops by a factor of two for
the secondary shock. Recall from Section 3.1, that the magnitude of this signal is a function of
64 / 100
electron density and collision frequency. Even though the shock is traveling faster, the density is
so much less that the magnitude reflection coefficient is less for this particular case. Figure 48b
shows shock speed versus distance plot based on the half-wavelength of the standing wave
divided by cycle time between the identified peaks. Shock speed attenuation is very slight for
this condition. Another interesting feature is that it appears the shock speed increases faster than
expected after the secondary diaphragm station. At this point it is unclear why this occurs, but
the same phenomenon was reported by Laney.[14] Average shock speeds based on the standard
time-of-arrival (TOA) pressure and temperature sensors is compared to the microwave
measurement in Table II, and results are very encouraging with agreement of approximately
0.5 percent. Results from Run 76 are given in Fig. 49. Shock speeds are a little slower for this
condition, but the most notable difference is the fact that the primary shock speed is below the
cutoff frequency identified in Fig. 29, so no strong periodic reflected signal is received. The
electron density behind the primary shock was too low to determine its speed from the
microwave measurement, as expected. LENS XX is typically used to explore higher-velocity
conditions, so both shock speeds are typically recorded.
Table III shows the comparison between the average TOA and microwave measurements
again with very good agreement.
Figure 50 shows the microwave shock speed results from Run 77. Run 77 had similar
shock speeds to Run 76, but the accelerator gas density is roughly one tenth. Results between
these two runs are very similar. Primary shock speed is not measured, as expected, but secondary
shock speed is measured accurately and shown to be relatively constant. From Table IV, we
observe that the average values match TOA measures extremely well again. Figure 50a shows a
cut-away to a zoomed-in section of the waveform to highlight its sinusoidal nature.
65 / 100
12,000
0
200
10,000
0
Shock Speed (m/s)
Voltage (mV)
300
100
0
‐100
‐200
8,000
0
6,000
0
4,000
0
2,000
0
‐300
0
0.5
1
1.5
2
2.5
3
3.5
5
4
4.5
5
5
5.5
0
0
Time (ms)
5
10
15
20
25
30
Distance (m
m)
a.. Reflected miccrowave stand
ding wave
b. Shock
k speed vs. disttance
Figuree 48. Microw
wave Measu
urement of Primary an
nd Secondarry Shock Sp
peeds (Run 75)
7
Tablee II. Averag
ge Shock Speeed Comparison Betweeen Standarrd TOAs an
nd Microwavve
Measurement (Run
n 75)
Standard TTOAs Microwave % Difff
Primarry Shock Spe
eed (m/s)
3629
0
0.6%
3651
Second
dary Shock SSpeed (m/s)
7226
0
0.4%
7252
a.. Reflected miccrowave stand
ding wave
b. Shock
k speed vs. disttance
Figuree 49. Microw
wave Measu
urement of Primary an
nd Secondarry Shock Sp
peeds (Run 76)
7
Table III. Averag
ge Shock Sp
peed Compaarison betweeen Standarrd TOAs an
nd Microwaave
Measurement (Run
n 76)
Standard TTOAs Microw
wave
Primaary Shock Spe
eed (m/s)
2336
N/A
A
4727
Secon
ndary Shock SSpeed (m/s)
4727
7
66 / 100
% Difff
0.01%
%
a.. Reflected miccrowave stand
ding wave
b. Shock
k speed vs. disttance
Figuree 50. Microw
wave Measu
urement of Primary an
nd Secondarry Shock Sp
peeds (Run 77)
7
Tablee IV. Averag
ge Shock Sp
peed Compaarison betweeen Standarrd TOAs an
nd Microwaave
Measurement (Run
n 77)
Primaary Shock Spe
eed (m/s)
Secon
ndary Shock Speed (m/s)
Standard TOAs Microw
wave
1951
N/A
A
4826
4859
9
% Diff
0.69%
T time-freq
The
quency anallysis shown in Fig. 51 was compleeted using a pseudo-W
Wigner
distributiion (PWD). The pseudoo-Wigner disstribution is defined as the Fourier transform of
o the
unaveragged instantaaneous autoocorrelation function.[661] Figure 51 shows that the PWD
P
successfuully identifiees the prim
mary and seccondary shock frequenccies of 4,7600 and 9,6700 Hz,
respectivvely, but the resolution is
i not as higgh as desired and cross components show up in
i the
spectrogrram making
g the plot more difficultt to interpret. The Wignner distributtion was selected
because it
i is generally regarded as giving thhe best time--frequency resolution,
r
but other metthods
should bee explored in
n the future to
t remove crross componnents for an improved
i
sppectrogram.
67 / 100
Figure 51. Time-Frequency Analysis of Run 75 using the Pseudo-Wigner Distribution
5.2.
Shock Speed Attenuation
Viscous effects are present in the form of a boundary layer whenever a fluid passes over a
surface such as a wing or in this case through a tube. As mentioned in the introduction, a shock
wave initially accelerates the flow in an expansion tube, so the boundary layer actually develops
behind the shock wave as shown in Fig. 52. Boundary layer growth is not a problem in shock
tunnels, because the test gas is immediately behind the shock wave. Expansion tunnels, however,
do not use the gas behind the shock as the test gas due to its extremely high temperature, so the
boundary layer can grow to a significant portion of the tube as indicated in the figure.
Test Gas
Core Flow
Boundary Layer Growth
Shock
Wave
Figure 52. Effect of Boundary Layer Growth due to Viscous Effects in an Expansion
Tunnel
68 / 100
Hypersonic boundary layers are quite large compared to lower speed flows. Expansion
tubes need to be long to have sufficient test times, which has the unfortunate result that the
boundary layer can consume a majority of the core flow. Core flow is the uniform section of the
tube where test models are placed, so maximizing core flow whenever possible is desirable. The
analytical approach to investigating viscous effects will begin with implementation of Mirels’s
boundary layer theory.[25] Mirels’s theory compares boundary layer growth to a leaky piston
where mass is lost to the boundary layer. Therefore, the effective pressure driving the shock is
less, resulting in a slower shock.
Mirels’s calculations use a shock-fixed reference frame to develop the analytical
expressions, so instead of calculating an updated shock velocity, that velocity is held constant
while the contact surface speeds up approaching the shock velocity. Experimentally we measure
shock speed, so for qualitative comparisons to the analytical calculation, we compare measured
shock attenuation to predicted contact surface velocity growth. Mirels’s theory was used to
analyze the three shock speed measurements presented and results are reported in Table V.
Laminar boundary layer solutions are presented in the table, because the velocity correction
assuming turbulent boundary layers was negligible. Turbulent boundary layer growth is faster,
but the predicted shock attenuation is less. It is likely that the boundary layer will transition at
some point behind the shock,[62] but initial Reynolds numbers are small based on the separation
distance between the shock front and the contact surface, so the laminar assumption is
reasonable. Average shock velocities just after the secondary diaphragm and just prior to the test
section were compared. The percent difference is reported in the table as the measured shock
attenuation. The region of highest velocity near the secondary diaphragm for Run 75 was not
included in determining the attenuation for that run, because this overshoot is likely caused from
69 / 100
a combination a phase shift in the reflection coefficient and a non-ideal secondary diaphragm
rupture. Regardless of the cause, the overshoot exceeds the maximum velocity expected from 1D
unsteady calculation, so it is unlikely that viscous effects are influencing the overshoot region..
Minimal viscous effects are predicted from Mirels’s theory, and this appears to be collaborated
by the minimal shock attenuation measured down the length of the acceleration tube.
Table V. Microwave Shock Speed Attenuation Compared to Mirels’s Boundary Layer
Theory
Run 75
Run 76
Run 77
Average Secondary Predicted Boundary Predicted Contact Measured Shock Shock Speed (m/s)
Layer Size (in.)
Surface Velocity Growth
Attenuation
7252
2.0
2.0%
2.1%
4727
1.7
2.5%
1.8%
4826
4.0
5.5%
2.8%
High-resolution shock speed data over a variety of test conditions in smaller-scale
facilities is not readily available for comparisons. It is, however, useful to consider the NASA
Langley data described in Section 2.5 that covered freestream noise. The previously discussion
led to the conclusion that boundary layer growth or viscous effects were the primary cause of the
dip and large unsteadiness in Pitot pressure measurements reported by Miller.[33] Again, Pitot
pressures and freestream conditions are given in Appendix B Conditions and labeled C1-C20,
and Mirels’s boundary layer calculation was completed for all cases with both fully-laminar and
fully-turbulent assumptions. The laminar boundary layer calculations are shown below in
Fig. 53. Cases with a helium accelerator have the largest boundary layer growth, which can be
seen in Fig. 53a. The Langley tube inner diameter was six inches, and accelerator tube length
was variable but a fixed length of approximately 17 meters was used for these conditions.
Mirels’s contact surface growth, or acceleration, ratio is plotted in Fig. 53b. Again, Mirels’s
calculation is done in a shock-fixed frame in order to find an analytical solution, but this factor
would manifest itself in shock attenuation. Fully turbulent boundary layer predictions are shown
70 / 100
in Fig. 54. The turbulent predictions rise much faster for the helium accelerator gas cases, and
actually exceed the centerline of the tube, but predictions for the air and carbon dioxide
accelerator gas cases are not that much different from the laminar solutions. There is no strong
correlation between the size of the predicted boundary layer and the Pitot pressure freestream
noise measured. The poor correlation could be explained if the dip in pressure and enhanced
noise were related to turbulent boundary layer transition in the tubes. There could be some
intermediate acceleration tube pressure levels that facilitate transition and the noisy flow
conditions observed, while at lower pressures/densities the Reynolds number of the accelerator
and test gases would be sufficiently low to prohibit transition.
Refs. [27, 63] discuss these observations as well and attribute the dip in pressure to
boundary layer transition on the facility wall. McGilvray[63] simulated the expansion tube flow
field with a 2D CFD solver MB_CNS[64] and showed that a dip in Pitot pressure could occur
with fully turbulent solutions at some conditions. An algebraic turbulence model based on the
Baldwin-Lomax eddy-viscosity model was used in these simulations and severity of the dip was
reduced with finer grids. The computational results show a fairly constant velocity through the
test time, with an increase in freestream temperature and a corresponding decrease in density and
pitot pressure. Despite potential weaknesses in the modeling, the experimentally measured
phenomenon appears to be captured through this simulation, and the argument that transition
explains this particular type of disturbance is convincing.
71 / 100
C1_lam
C2_lam
C3_lam
C4_lam
C5_lam
C6_lam
C7_lam
C8_lam
C9_lam
C10_lam
C11_lam
C12_lam
C13_lam
C14_lam
C15_lam
C16_lam
C17_lam
C18_lam
C19_lam
C20_lam
2
1.5
1
0.5
0
0
5
10
15
Distance (m)
1.5
Contact Surface Acceleration Ratio
Boundary Layer Thickness (in.)
2.5
1.45
1.4
1.35
1.3
1.25
1.2
1.15
1.1
1.05
1
0
5
10
15
Distance (m)
a. Boudnary layer thickness vs. distance
C1_lam
C2_lam
C3_lam
C4_lam
C5_lam
C6_lam
C7_lam
C8_lam
C9_lam
C10_lam
C11_lam
C12_lam
C13_lam
C14_lam
C15_lam
C16_lam
C17_lam
C18_lam
C19_lam
C20_lam
b. Contact surface acceleration ratio
Figure 53. Mirels’s Laminar Boundary Layer Calculations for Langley Tunnel (C1-C20
Conditions are Listed in Appendix B)
4.5
Boundary Layer Thickness (in.)
4
3.5
3
2.5
2
1.5
1
0.5
0
0
5
10
Distance (m)
15
C1_turb
C2_turb
C3_turb
C4_turb
C5_turb
C6_turb
C7_turb
C8_turb
C9_turb
C10_turb
C11_turb
C12_turb
C13_turb
C14_turb
C15_turb
C16_turb
C17_turb
C18_turb
C19_turb
C20_turb
Figure 54. Mirels’s Turbulent Boundary Layer Calculations for Langley Tunnel (C1-C20
Conditions are Listed in Appendix B)
72 / 100
In order to investigate shock attenuation, displacement thicknesses for condition C11
were taken from Mirels’s boundary layer prediction calculation to be used in Jaguar. Jaguar is
the quasi one-dimensional LaGrangian CFD code for shock/expansion tube simulation was
created by Maclean.[24] The quasi one-dimensional simulation includes area changes based on
the predicted displacement thickness to determine shock attenuation and corresponding test gas
conditions down the length of the NASA Langley facility. Condition C11 was chosen because it
is a moderate enthalpy condition, approximately 9 MJ/kg, and uses both air as the accelerator
and test gases. C11 conditions overlap the higher velocity capabilities of shock tunnels, but the
freestream is quite cool, so this would be a test condition of primary interest; however, the
Langley tunnel showed an unacceptably noisy Pitot measurement. The Jaguar simulation for the
Langley tunnel is given in Fig. 55, showing velocity contours in the typical x-t (time vs.
distance) space used for evaluating expansion tunnel conditions. Only perfect gas Jaguar
solutions are considered in this work. The dark blue fields represent zero velocity and the
maximum velocity shown in red corresponds to 4,440 m/s. Contact surfaces are shown in white,
while shocks are simply indicated by the sharp contrast boundary from either blue to green for
the primary shock or blue to red/orange for the secondary shock, and expansion waves appear as
a gradual changes from blue to green and green to red. Close examination of Fig. 55 shows that
the secondary shock wave and contact surface is curving up, indicating that it is slowing down.
Additionally and perhaps more readily observable, the velocity behind the shock changes from
red to yellow-orange indicating that the test gas is also attenuating significantly. A more
quantitative assessment of velocity versus time will be discussed shortly. The same C11
condition is considered for LENS XX. First the displacement thicknesses were calculated from
Mirels’s theory, and then appropriate area changes were included along with LENS XX facility
73 / 100
dimensions to create the simulation shown in Fig. 56. Shock and contact surface curvature is
significantly less in the LENS XX expansion tube simulation, and accelerator gas/test gas
velocity appears to be almost constant with only a small change from red to red-orange. Lastly,
the same conditions are run for the LENS XX expansion tunnel mode, where the nozzle area
change is included at the end of the accelerator tube. Figure 57 shows a zoomed-in view of the
expansion tunnel simulation. As expected, the area change over this small distance alters the
accelerator gas properties, but test gas conditions behind the contact surface changes very little.
Nearest the contact surface there may be a region of higher-velocity test gas, but the increase is
Time
7.2 ms
not large and represents only a small fraction of the steady-state test time.
Distance
25 m
Figure 55. Langley Expansion Tunnel Velocity Contour x-t Diagram for C11 Condition
(Contact Surfaces Shown in White, Shocks Identified by Stark Boundaries, Expansion
Waves Identified by Smooth Transitions)
74 / 100
12.6 ms
Time
0
Distance
44 m
7.7 ms
Time
14.2 ms
Figure 56. LENS XX Expansion Tube Velocity Contour x-t Diagram for C11 Condition
26.3 m
Distance
48.6 m
Figure 57. LENS XX Expansion Tunnel Velocity Contour x-t Diagram for C11 Condition
including Steady Nozzle Expansion
75 / 100
These analyses seem to contradict the simplified Mirels analytical model, where the
contact surface velocity increases until it comes into equilibrium with the fixed shock velocity.
Over short distances and relatively large area changes (compared to displacement thickness
losses), shock attenuation and contact surface acceleration is appropriate as indicated in Fig. 57,
but shock attenuation over the length of a long facility likely corresponds to an attenuated test
gas velocity as well. Figure 58 shows test gas velocity versus time for all three cases mentioned
above. The test gas cell that is tracked is near the contact surface, so the initial plateau around
2,000 m/s corresponds to the state 2 velocity behind the primary shock. A time shift was applied
to the Langley tunnel trace so that all curves could be plotted together. Peak test gas velocities of
approximately 4,200 m/s are shown for all cases. Test gas velocity near the Langley test section
drops 17% down to 3,500 m/s. LENS XX expansion tube mode test gas velocity drops
approximately 3%, and expansion tunnel mode velocity appears to recover that lost velocity
through the steady nozzle expansion. LENS XX tube diameters are four times as large as the
Langley facility, so it is not surprising that the predicted viscous effects are so substantial. This
analysis highlights the need to understand facility wave dynamics accurately with higher
resolution. Typically as-run conditions are calculated based on shock speeds nearest the test
section, and to first order this is likely still sufficient. The high-resolution RF shock speed
measurement, however, offers improved facility characterization with reduced test condition
uncertainties and better prediction capabilities. Shock attenuation is negligible for most
conditions in LENS XX, but it is important to confirm this, and smaller facilities with more
attenuation could benefit from this measurement.
76 / 100
Test Gas Velocity (m/s)
4,500
4,000
3,500
3,000
2,500
2,000
1,500
Langley Tunnel
1,000
LENS XX
500
LENS XX with Nozzle
0
4
6
8
10
12
14
Time (ms)
Figure 58. Test Gas Velocity vs. Time Assuming Mirel’s Displacement Thickness for
Small-scale and Large-scale Expansion Tunnels
Lastly, it is useful to return to one of the only high resolution shock speed measurements
available in a smaller scale facility. Laney provided one sample measurement along with the
description of the microwave shock speed measurement.[14] Laney’s data is reproduced in
Fig. 59 and compared to the Jaguar 1D simulation including Mirels displacement thickness.
Mirels’s predicted contact surface acceleration is 12% and measured shock attenuation was
10.5%. A test gas velocity of 4,000 m/s is predicted from perfect gas relations based on the final
shock speed of 5,140 m/s, while a test gas velocity of 5,455 m/s is predicted from the original
shock speed and Mirels’s 12% acceleration. An average test gas velocity of 4,700 m/s is found
from the Jaguar simulation with Mirels’s displacement thickness included. Mirels’s theory is
often cited in justifying a predicted test gas velocity that is the same as the shock speed, which is
the limiting case but can be quite inaccurate, especially if the acceleration gas is different from
the test gas. Shocks propagate into light gases much faster than the velocity they induce, so for
cases such as this one where a helium accelerator gas is used with air as the test gas, it is not
77 / 100
appropriate to assume the test gas is the same speed as the secondary shock. This example
highlights the potential uncertainties in determining expansion tube/tunnel test conditions, where
possible test gas velocities vary ±16% depending on the method used. As shock attenuation is
Shock Speed (m/s)
reduced, this large uncertainty band is reduced proportionally.
6,000
5,800
5,600
5,400
5,200
5,000
4,800
4,600
4,400
4,200
4,000
Jaguar Calc w/ Mirels Disp. Thickness
Laney Incremental Shock Speed Data
4
4.25
4.5
4.75
5
5.25
5.5
5.75
Time (ms)
Figure 59. Attenuating secondary shock speed comparison between Laney Microwave
Data and Jaguar 1D simulation including Mirels displacement thickness
5.3.
Effects of Secondary Diaphragm
Effects of secondary diaphragm rupture process were discussed in Section 2.5 with
regards to freestream disturbances. Since Mylar is transparent to radio waves, one of the benefits
of RF shock speed measurement is that it can measure both primary and secondary shock speeds
assuming they are both fast enough to sufficiently ionize the gas behind the shocks. Assessments
of the rupture process are possible with this measurement, but a potential phase shift associated
with changing plasma properties behind the shocks restricts these assessments to purely
qualitative in nature. A typical method to assess rupture behavior is to use an upstream pressure
78 / 100
gauge located as close to diaphragm as possible. Such a gauge yields the speed and strength of
any reflected waves. Additionally, measuring freestream pressure on the tube wall far down
stream is sensitive to this condition. If the acceleration tube freestream pressure is elevated, it is
likely due to a reflection at the Mylar station.
Two examples of cases where both shock speeds are successfully recorded are shown in
Fig. 48 (Section 5.1) and Figs. 60 and 61 below. A velocity overshoot after the diaphragm station
was measured in Fig. 48; however, in most cases including the one shown in Fig. 61, no
overshoot is recorded. Laney’s sample shock speed measurement[14] shows an overshoot as
well, perhaps indicating a less than ideal diaphragm rupture for these cases. If the overshoot only
exists over one cycle, it could be a manifestation of a phase shift associated with changing
plasma properties, but if overshoot persists over several cycles as in Fig. 48 and in the Laney
data, then it likely is a real phenomenon associated with the Mylar rupture process. More
detailed pressure measurements around the diaphragm station, or ideally optical measurements
through a translucent diaphragm station would improve understanding of the process and how
the standing wave measurement responds.
Voltage (V)
3
2.5
2
1.5
1
0.5
0
‐0.5
‐1
‐1.5
‐2
‐0.5
Secondary Shock Reflection
Primary Shock Reflection
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
5.5
6
6.5
7
7.5
8
8.5
9
Time (ms)
Figure 60. Reflected Microwave Signal with Cycle Peaks Identified (Nozzle Calibration
Run 5)
79 / 100
Shock Speed (m/s)
6,000
5,000
4,000
3,000
2,000
1,000
0
4
9
14
19
24
29
34
39
Distance (m)
Figure 61. Microwave Measurement of Primary and Secondary Shock Speeds (Nozzle
Calibration Run 5)
5.4.
Low Density Microwave Shock Speed Measurements
A series of low-density expansion tube runs were made in air as part of a Multi
University Research Initiative (MURI) in collaboration with the University of Minnesota and
Penn State. Conditions required for these tests utilized pressures much lower than those typical
of expansion tube testing with hydrogen driver pressures of approximately 200 kPa, driven
tube/test gas pressures of 500 Pa, and acceleration tube pressures ranging from 0.01 to 0.1 Pa.
The target test condition was 5 km/s at densities corresponding to an altitudes of 75-90 km to
replicate the BSUV conditions.[65] As run test conditions are reported below in Table VI. An
altitude of 75 km corresponds to a density of approximately 4x10-5 kg/m3, so Run 4 most closely
matches the target test conditions. In addition to the air runs associated with the MURI project, a
carbon dioxide run was included as the final run.
80 / 100
Table VI. Equilibrium Freestream and Stagnation Properties from Low Density MURI
Runs
Freestream Properties
pressure (Pa)
temperature (K)
density (kg/m3)
velocity (m/s)
Mach
relative enthalpy (MJ/kg)
Reynolds Number (/m)
mole fraction
N2
O2
NO
N
O
e‐
NO+
Stagnation Properties
pitot pressure (Pa)
temperature (K)
mole fraction
N2
O2
NO
N
O
e‐
NO+
Run 2
Run 3
Run 4
Run 5
Run 6
Run 7
Run 10
8.9
252
1.22E‐04
4843
15.18
11.69
36447
13.4
292
1.60E‐04
4845
14.12
11.74
42797
2.2
176
4.38E‐05
5259
19.73
13.71
18965
9.7
261
1.29E‐04
4842
14.94
11.69
37796
3.6
215
5.86E‐05
5380
18.29
14.39
22095
39.1
413
3.29E‐04
4680
11.49
11.08
66371
155.9
2042
3.74E‐04
4532
6.75
13.40
24822
0.788
0.212
0.000
0.000
0.000
0.000
0.000
0.788
0.212
0.000
0.000
0.000
0.000
0.000
0.788
0.212
0.000
0.000
0.000
0.000
0.000
0.788
0.212
0.000
0.000
0.000
0.000
0.000
0.788
0.212
0.000
0.000
0.000
0.000
0.000
0.788
0.212
0.000
0.000
0.000
0.000
0.000
2750
4832
3609
4883
1171
4919
2923
4842
1639
5041
6928
4873
0.565
0.000
0.003
0.102
0.329
0.00007
0.00007
0.566
0.000
0.004
0.101
0.329
0.00008
0.00008
0.500
0.000
0.002
0.182
0.316
0.00010
0.00010
0.566
0.000
0.003
0.102
0.329
0.00007
0.00007
0.483
0.000
0.002
0.202
0.313
0.00012
0.00012
0.589
0.000
0.005
0.073
0.332
0.00006
0.00006
O2
O
CO2
CO
0.068
0.006
0.784
0.142
7656
3140
O2
O
CO2
CO
0.138
0.244
0.098
0.520
These low-density conditions are well outside the normal operating range of the
expansion tunnel, so extra care is required when determining the test conditions. The first issue is
that the signal-to-noise ratio of the standard TOA instrumentation becomes poor, so shock speed
uncertainty can be as high as plus or minus four percent. Three TOA temperature measurements
are shown in Fig. 62 from Run 7. TOA3 is gained by an additional factor of two over TOA1 and
TOA2, and it saturates with a signal just three times greater than the noise level. TOA1 and
TOA2 do not saturate as quickly due to the lower gain, but determination of shock arrival is
more open to interpretation than usual. The TOA measured shock speed is 5030 m/s with a plus
or minus 200 m/s uncertainty.
81 / 100
0.35
0 .1 4
0.25
Amplitude
0 .0 9
0.15
0 .0 4
0.05
TOA3
TOA2
TOA1
‐0.05
‐0.15
‐0 .0 1
‐0 .0 6
5
6
7
8
9
10
TIme (ms)
Figure 62. Sample Standard TOA Measurements from Low Density MURI Run 07
Results from the microwave measurement for Run 7 are given in Fig. 63. The average
velocity upstream of the model is 4,680 m/s with a standard deviation of 80 m/s. This measured
speed is clearly slower than the measured TOA shock speed. Run 7 is typical of all the air runs
(MURI Runs 2-7), which exhibit this discrepancy. Fortunately, for these runs a heavy Mylar
diaphragm was installed at the nozzle joint, so a sharp discontinuity is measured in the
microwave signal when the flow hits this heavy Mylar. Working upstream from this location it is
possible to identify the target location all the way up to the first measured peak. The target
tracking result is shown in Fig. 63b, where position zero corresponds to the secondary Mylar
location. The first peak is not identified until 1.1 meters downstream of this thin Mylar location,
indicating either the reflecting target takes significantly longer to setup than normal, or the target
does not have a thin sharp boundary, or some combination of the two. The target is also shown to
lag the arrival of the shock at the first TOA location. If the electron density behind the shock is
near the cutoff value for wave reflection, it is theoretically possible that the reflection is
generated as an integrated effect through the ionized accelerator gas or a thick plasma slab. The
accelerator gas, contact surface and test gas should all have roughly the same speed based on 1D
82 / 100
gas dynamics. Post-shock properties are reported in Table VII, and the equilibrium electron
density values predicted are extremely close to the cutoff of 1.52x109 e-/cm3 found in Eq. 11
0.15
6,000
0.125
5,000
0.1
0.05
0.025
0
‐0.025
4,000
Model Location
0.075
3,000
1st Accel Tube TOA
Speed (m/s)
Voltage (V)
above.
2,000
1,000
‐0.05
5
5.5
6
6.5
7
7.5
8
8.5
9
9.5
0
0
Time (ms)
5
10
15
Distance (m)
a. Reflected microwave standing wave
b. Speed vs. distance
Figure 63. Microwave Measurement of Test Gas Velocity (MURI Run 7)
Table VII. Secondary Shock Properties from the Low-Density MURI Runs
Secondary Shock Speed
Run 3
5186
Pressure (Pa)
Temperature (K)
Density (kg/m3)
Electron Density (e‐/m3)
13.4
4111
8.11E‐06
1.04E+10
Run 4
Run 5
5580
5180
Post Shock Equilibrium Conditions
2.2
9.7
4002
4067
1.31E‐06
5.92E‐06
1.89E+09
7.22E+09
Run 6
5700
Run 7
5030
Run 10
4900
3.6
4145
2.10E‐06
3.91E+09
39.1
4290
2.38E‐05
3.68E+10
155.9
4400
9.36E‐05
1.38E+11
All indications point to the fact that the microwave system is measuring accelerator gas,
and, therefore, test gas velocity at these low density conditions. Further evidence is found to
support this conclusion by examining the RF measurement for Run 10 which used carbon
dioxide as the test gas. Secondary shock speeds were similar on the order of 5 km/s, and
accelerator gas was air in both cases, but the post-shock conditions are considerably different due
to the matching requirements at the CO2/Air interface. Table VII shows predicted electron
densities one to two orders of magnitude higher for Run 10 than those with air as the test gas.
Figure 64 shows the shock speed measurement for Run 10, which shows an average shock speed
of 4,900 m/s with a standard deviation of 120 m/s, which compares well with the TOA shock
83 / 100
speed of 4,860 m/s with the same 200 m/s uncertainty as before. The next item to note is that
Fig. 64 has a full extra cycle measured over the same distance, which corresponds the target
developing within 15 cm of the thin secondary Mylar location. This behavior is more consistent
0.25
6,000
0.2
5,000
0.1
0.05
0
‐0.05
4,000
Model Location
0.15
3,000
1st Accel Tube TOA
Shock Speed (m/s)
Voltage (V)
with theory, as well as with previous microwave shock speed measurements.
2,000
1,000
‐0.1
4.8
5.3
5.8
6.3
6.8
7.3
7.8
8.3
8.8
0
0
Time (ms)
5
10
15
Distance (m)
a. Reflected microwave standing wave
b. Shock speed vs. distance
Figure 64. Microwave Measurement of Shock Speed (MURI Run 10)
Significant uncertainty in calculated test conditions can come from assuming improper
accelerator gas composition. At vacuum pressures below 1 Pascal, water vapor can be the
dominant gas. Predicted test gas velocities with a water-based accelerator gas are significantly
slower than with an air-dominated accelerator gas. Gas composition matters even more if helium
or hydrogen is used as the accelerator gas. To ameliorate the assumption of accelerator gas
composition, a residual gas analyzer (RGA) was installed on the accelerator tube. Residual gas
analyzers do not work well at the relatively high pressures the facility is operated at, so a small
turbo pump was installed in-line with the RGA and a needle valve was used to control the flow
rate from the tube to the RGA for maximum sensitivity. Figure 65 gives the RGA results over the
last several runs. Unfortunately, the RGA was not online for the first few runs. These results
show that indeed a large percentage of the gas composition is water (molecular weight 18)
relative to nitrogen or oxygen. Small spikes near molecular weights of two are associated
84 / 100
hydrogen from the presence of water. In all cases, the acceleration tube was pumped on
overnight with a turbo pump and base pressures reached approximately 0.001 Pa. The tube is
isolated from the turbo pump approximately two minutes before the test to ensure the safety of
the turbo pump and to avoid problems with potential false triggers. During this isolation time, the
tubes leak up in pressure. The leaked-in gas is assumed to be air, because at this point the gas
analyzer must be isolated. The accelerator gas composition is determined based on the RGA
levels before the test, and the pressure of the accelerator tube when the tube was fired.
H2 O
H2
N2
O2
Ar
Figure 65. Residual Gas Analyzer Results for Low Density MURI Runs
5.5.
Summary of Microwave Standing Wave Measurements
The microwave standing wave measurement was primarily selected to make accurate,
high-resolution shock speed measurements in an expansion tunnel and, in that regard, it was a
great success. FFT analysis yields quick and very accurate average shock speeds. Peak-to-peak
85 / 100
waveform analysis yields high-resolution shock speeds that can be used to qualitatively assess
viscous effects and the secondary diaphragm rupture process.
Another goal was to use an accelerator gas such as helium to measure the contact surface,
or test gas velocity, as described by Laney.[14]
After further investigation, however, the
equilibrium temperature of helium behind a 7 km/s shock is only 4,700 K and the air temperature
on the other side of the interface is approximately 2,000 K. Even with a small amount of mixing
it is unlikely that sufficient ionization would occur at the interface to reflect the microwave
signal. It is more likely that there was air contamination in the accelerator tube that ionized and
shock speed was actually measured. Furthermore, evidence of air in the accelerator tube comes
from the fact that the reported acceleration tube pressure is much lower than what would be
required to obtain the secondary shock speeds measured in 100% helium. Reported pressures
indicate air contamination on the order of 25-30%, or alternatively a combination of water and
air contamination. Understanding the accelerator gas composition is extremely important in
determining test conditions, since velocity is matched across the accelerator gas-to-test-gas
contact surface. For instance, producing a shock into 100% pure helium will result in gas
velocities at approximately 70-80% of the shock speed, whereas a shock into air accelerates the
gas to approximately 85-95% of the shock velocity. Correspondingly, the test gas velocity
assuming 30% air contamination would result in a gas velocity at approximately 85% of the
shock velocity. Laney’s data seemed to suggest that the standard photo-detector TOA
measurements measured shock speeds 1.5% higher than that of the microwave measurement, so
the microwave measurement was likely tracking the contact surface or test gas velocity. Laney
also had ionization detectors used to track what was thought to be the interface velocity, but
since it appears significant accelerator gas contamination existed, these detectors were also
86 / 100
essentially tracking shock speed, albeit perhaps with some small delay. The ionization detectors
matched more closely with the microwave speed measurement, but both are far too fast to be
measurements of the test gas or interface velocity, so these data are likely shock speed
measurements.
Contact surface velocity cannot be tracked simply by using a helium accelerator gas.
However, if the electron density behind the shock is very near the cutoff threshold of standing
wave reflection, it is possible to measure accelerator gas velocity, and therefore, test gas velocity.
Low-density measurements in air successfully tracked the accelerator gas velocity on several
runs. Theoretically, one could contrive accelerator gas mixtures with nitrogen and helium that
meet this near cutoff threshold for most conditions of interest, and test gas velocity could be
tracked.
One weakness of the measurement is that, the standing wave is designed for the tube
diameter, so there is not a reliable measurement through the nozzle where the area is rapidly
changing. A more traditional radar measurement could likely track the shock through the nozzle
as well, albeit with less accuracy than what is achieved in the tube, but it can be considered for
future work. Since standard TOA gauges are already installed in the LENS XX nozzle, and
shock attenuation through the nozzle does not alter test gas conditions according to 1D unsteady
analysis, the high-resolution shock speed measurement in the tube is considered sufficient, and
actually far superior to having just standard time-of-arrival instrumentation alone.
87 / 100
6.
Conclusions
6.1.
Summary of Completed Work
This work focuses on the characterization of a large-scale expansion tunnel and the
development of non-intrusive microwave diagnostics to improve the characterization. A highresolution, accurate microwave shock speed measurement was developed to characterize
LENS XX performance. A second swept frequency microwave reflection measurement was used
for the first time in an expansion tunnel to make plasma measurements on test articles in highenthalpy flows.
The microwave shock speed measurement measures primary and secondary shock speeds
accurately every 30 in. down the entire length of the facility resulting in a more accurate
determination of freestream conditions required for computational comparisons. The high
resolution of this measurement is used to assess shock speed attenuation as well as secondary
diaphragm performance. Negligible shock attenuation is reported over a large range of test
conditions and gases, and this is attributed to the large diameter of the LENS XX driven and
expansion tubes. Shock tube boundary layer growth solutions based on Mirels’s theory confirm
that negligible viscous effects. Another significant finding from this measurement is that when
post-shock electron density levels are near the cutoff required for standing wave reflection, test
gas velocities are measured. Test gas is usually derived from the measured shock speeds and
pressures in the facility, so a direct measurement reduces any uncertainty determining conditions
for computational comparisons. Theoretically acceleration gas composition could be tuned using
combinations of helium or hydrogen and nitrogen to meet this low electron density required for
the test gas velocity.
88 / 100
In collaboration with ElectroDynamic Applications, Inc., (EDA) plasma frequency
measurements are made in two different configurations using a swept microwave frequency
power reflection measurement. Electric field characteristics of EDA’s probe are presented and
show current probe design is ideal for measuring properties of shock layers that are 1-2 cm thick.
Electron density and radio frequency communication characteristics through a shock layer on the
lee side of a capsule up to 8.9 km/s and in a stagnation configuration up to 5.4 km/s in air are
reported.
6.2.
Future Work
The microwave shock speed will continue to stay online and aid in development of as-run
test conditions. Since the microwave measurement is incapable of regularly measuring the
interface velocity, other means of measuring freestream velocity would reduce uncertainty
associated with determining run conditions. Possible methods include Doppler shift associated
laser absorption features or acoustics, or spark source across a pre-ionized path from an e-beam.
Additional microwave plasma sheath measurements along with complimentary Langmuir probes
to describe plasma layers should be made in the expansion tunnel. These measurements should
also be made in a shock tunnel to determine differences based on altered freestream chemistry.
Now that LENS XX facility and test conditions are well characterized and discrete highresolution aerothermal loads are accurately measured, more advanced diagnostics can be
considered. Measurements associated with transitional and turbulent flows as well as catalytic
heating measurements in high-enthalpy flows are of primary interest, and have already begun.
Other diagnostics such as IR thermography, near-surface or shock-layer spectral measurements,
laser absorption measurements to understand shock layer chemistry, or even aerodynamic force
measurements should be considered for development.
89 / 100
Appendix A List of Microwave Components
Microwave frequency counter
EIP 548A
Vector Network Analyzer (VNA)
Agilent Technologies E5071C 9 kHz - 8.5 GHz
Voltage Controlled Oscillator
Mini-Circuits ZX95-400+
Crystal Oscillator
Trak Microwave Corp. 5042-1057, 350 MHz
(actual frequency 349,995,150 Hz, +/-100Hz)
Amplifier
Mini-Circuits ZFL-1000LN+
Splitter
Mini-Circuits ZFSC-2-5-S(+)
Mixer
Mini-Circuits ZLW-5
Quadrature Hybrid Coupler
NARDA 4030B (3dB,250-500 MHz, SMA)
Circulator
SEI model TH0301A (330-360 MHz)
Tuner
FXR/Microlab S3-02N Triple Stub Tuner, 2001000 MHz
SMA cable
Times Microwave LMR-200 Coaxial Cable
Crystal Detector
Hewlett-Packard Mode 432A
Antenna
AX-31CMX (log periodic antenna)
90 / 100
Appendix B HET and Langley Expansion Tube Data and
Noise Correlations
91 / 100
a. CO2-CO2, various accel pressures
b. Air-Air, various accel pressures
c. Air-Air, various accel pressures
d. Air-He, various accel pressures
Figure 66. Langley Expansion Tube Data with Various Test Gases
92 / 100
Table VIII. Miller’s Test Conditions and Correlation with Noise
C1
C2
C3
C4
C5
C6
C7
C8
C9
C10
C11
C12
C13
C14
C15
C16
C17
C18
C19
C20
Correlation with Observed Noise
Qualitative Observations
Noise Actual Test Test Time Rating
Time
Comparisons
1
200
‐49%
1
300
‐32%
3
100
‐80%
4
50
‐90%
5
25
‐96%
2
100
‐71%
2
150
‐65%
1
300
‐37%
2
300
‐42%
4
40
‐93%
4
40
‐94%
2
300
‐22%
2
300
‐35%
2
200
‐61%
3
100
‐82%
3
100
‐84%
4
20
‐97%
2
300
‐19%
2
200
‐43%
4
150
‐55%
P4
34464286
34464286
34464286
34464286
34464286
34464286
34464286
34464286
34464286
34464286
34464286
34464286
34464286
34464286
34464286
34464286
34464286
34464286
34464286
34464286
P1
3446.429
3446.429
3446.429
3446.429
3446.429
3446.429
3446.429
3446.429
3446.429
3446.429
3446.429
3446.429
3446.429
3446.429
3446.429
3446.429
3446.429
13785.71
27571.43
68928.57
P10
1.866513
3.199737
4.932928
6.666118
8.932599
1.733191
3.999671
5.999507
7.999342
11.99901
23.99803
15.06543
30.26418
43.99638
59.72842
87.99276
177.3188
3.199737
3.199737
3.199737
Driver Driven Accel Gas Gas Gas
He
CO2 CO2
He
CO2 CO2
He
CO2 CO2
He
CO2 CO2
He
CO2 CO2
He
Air
Air
He
Air
Air
He
Air
Air
He
Air
Air
He
Air
Air
He
Air
Air
He
Air
He
He
Air
He
He
Air
He
He
Air
He
He
Air
He
He
Air
He
He
CO2 CO2
He
CO2 CO2
He
CO2 CO2
1.00
Us
2245
2245
2245
2245
2245
2427
2427
2427
2427
2427
2427
2427
2427
2427
2427
2427
2427
1920
1743
1501
Ut
5851
5604
5402
5260
5120
5709
5428
5283
5177
5022
4744
7052
6725
6541
6387
6187
5810
5173
4898
4445
c3/c2
0.55
0.55
0.55
0.55
0.55
0.40
0.40
0.40
0.40
0.40
0.40
0.40
0.40
0.40
0.40
0.40
0.40
0.77
0.92
1.18
‐0.10 ‐0.36 0.12
(rho3c3)/ (rho5c5)/ Rel. Mach Test Time c5/c20 (rho2c2) (rho20c20) Enthalpy Number
(ms)
Pitot Pre
0.30
2.74
3.47
1.51E+07 9.3
0.39
9171
0.32
2.74
3.22
1.41E+07 8.7
0.44
14577
0.34
2.74
3.03
1.33E+07 8.2
0.49
20924
0.36
2.74
2.90
1.28E+07 7.9
0.53
26801
0.37
2.74
2.78
1.23E+07 7.6
0.56
34005
0.34
3.38
3.57
1.46E+07 10.3
0.34
8904
0.38
3.38
3.17
1.33E+07 8.9
0.43
17057
0.40
3.38
2.99
1.26E+07 8.3
0.48
23204
0.42
3.38
2.86
1.21E+07 7.9
0.52
28781
0.44
3.38
2.70
1.15E+07 7.3
0.58
38835
0.48
3.38
2.42
1.04E+07 6.4
0.72
64273
0.13
3.38
6.08
1.39E+07 9.5
0.38
2685
0.15
3.38
5.35
1.28E+07 8.4
0.46
4866
0.16
3.38
4.99
1.22E+07 7.9
0.51
6660
0.17
3.38
4.72
1.17E+07 7.5
0.56
8583
0.18
3.38
4.39
1.11E+07 7.0
0.63
11788
0.21
3.38
3.85
1.00E+07 6.1
0.79
20671
0.26
1.89
4.20
1.13E+07 10.9
0.37
12446
0.23
1.56
4.73
9.91E+06 12.0
0.35
11138
0.19
1.21
5.39
7.98E+06 13.7
0.34
9099
0.13
‐0.08
‐0.19
‐0.55
‐0.26
0.56
0.53
CHEETAh Derived Test Conditions
s
u5
5248
5026
4844
4716
4590
5329
5038
4889
4780
4621
4339
5181
4930
4790
4671
4517
4227
4638
4390
3982
rho5
0.004
0.006
0.008
0.010
0.012
0.003
0.005
0.007
0.009
0.011
0.017
0.004
0.007
0.008
0.010
0.013
0.020
0.009
0.011
0.015
T5
1449
1540
1613
1664
1712
681
825
903
961
1046
1205
754
881
955
1019
1104
1270
805
582
353
P5
1037
1631
2337
2994
3802
628
1304
1848
2360
3322
5895
919
1679
2309
2988
4128
7332
1390
1246
1027
‐0.67 0.73 0.26 0.64
g5
1.16036
1.15387
1.14779
1.1433
1.13889
1.36499
1.34958
1.34236
1.33741
1.33065
1.31993
1.35698
1.34432
1.33785
1.33272
1.32651
1.31596
1.19248
1.21565
1.2665
c5
564
580
592
600
608
518
567
591
608
633
677
543
584
607
626
650
694
426
366
291
rho20
3.27E‐04
5.60E‐04
8.63E‐04
1.16E‐03
1.56E‐03
3.10E‐04
6.62E‐04
9.55E‐04
1.24E‐03
1.79E‐03
3.35E‐03
9.33E‐05
1.86E‐04
2.70E‐04
3.65E‐04
5.36E‐04
1.07E‐03
5.59E‐04
5.58E‐04
5.55E‐04
‐0.12
0.17
0.56
T20
6169
6067
5992
5932
5859
4986
5006
4999
4986
4949
4818
4744
4337
4117
3938
3710
3302
5738
5499
4869
P20
1037
1631
2337
2994
3802
628
1304
1848
2360
3322
5895
919
1679
2309
2988
4128
7332
1390
1246
1027
g20
1.12
1.11
1.11
1.11
1.11
1.11
1.11
1.12
1.12
1.13
1.15
1.67
1.67
1.67
1.67
1.67
1.67
1.10
1.11
1.21
c20
1883
1798
1733
1688
1645
1501
1482
1471
1462
1449
1422
4053
3875
3775
3692
3584
3381
1658
1573
1495
u2‐3
1995
1995
1995
1995
1995
2068
2068
2068
2068
2068
2068
2068
2068
2068
2068
2068
2068
1699
1538
1315
rho2
0.56
0.56
0.56
0.56
0.56
0.28
0.28
0.28
0.28
0.28
0.28
0.28
0.28
0.28
0.28
0.28
0.28
2.16
4.22
10.06
T2
2538
2538
2538
2538
2538
2611
2611
2611
2611
2611
2611
2611
2611
2611
2611
2611
2611
2013
1708
1329
‐0.18 0.64 0.04 ‐0.06 ‐0.11 0.19 ‐0.10
P2
282371
282371
282371
282371
282371
208357
208357
208357
208357
208357
208357
208357
208357
208357
208357
208357
208357
826160
1362810
2526380
0.16
g2
1.11
1.11
1.11
1.11
1.11
1.22
1.22
1.22
1.22
1.22
1.22
1.22
1.22
1.22
1.22
1.22
1.22
1.14
1.16
1.17
c2 rho3 T3
748 2.77 49
748 2.77 49
748 2.77 49
748 2.77 49
748 2.77 49
961 2.31 43
961 2.31 43
961 2.31 43
961 2.31 43
961 2.31 43
961 2.31 43
961 2.31 43
961 2.31 43
961 2.31 43
961 2.31 43
961 2.31 43
961 2.31 43
660 5.28 75
612 7.13 92
542 10.33 118
‐0.06 ‐0.09 0.13 0.12
93 / 100
P3
282371
282371
282371
282371
282371
208357
208357
208357
208357
208357
208357
208357
208357
208357
208357
208357
208357
826160
1362810
2526380
0.16
g3
1.67
1.67
1.67
1.67
1.67
1.67
1.67
1.67
1.67
1.67
1.67
1.67
1.67
1.67
1.67
1.67
1.67
1.67
1.67
1.67
c3
412
412
412
412
412
388
388
388
388
388
388
388
388
388
388
388
388
511
564
639
rho1
0.062
0.062
0.062
0.062
0.062
0.041
0.041
0.041
0.041
0.041
0.041
0.041
0.041
0.041
0.041
0.041
0.041
0.249
0.498
1.245
c1
267
267
267
267
267
344
344
344
344
344
344
344
344
344
344
344
344
267
267
267
0.00 0.11 0.19 ‐0.07
rho10
3.37E‐05
5.78E‐05
8.91E‐05
1.20E‐04
1.61E‐04
2.06E‐05
4.75E‐05
7.13E‐05
9.51E‐05
1.43E‐04
2.85E‐04
2.48E‐05
4.97E‐05
7.23E‐05
9.81E‐05
1.45E‐04
2.91E‐04
5.78E‐05
5.78E‐05
5.78E‐05
c10
267
267
267
267
267
343
343
343
343
343
343
1007
1007
1007
1007
1007
1007
267
267
267
0.68
0.00
MW10
44
44
44
44
44
28.97
28.97
28.97
28.97
28.97
28.97
4
4
4
4
4
4
44
44
44
g10
1.29
1.29
1.29
1.29
1.29
1.40
1.40
1.40
1.40
1.40
1.40
1.67
1.67
1.67
1.67
1.67
1.67
1.29
1.29
1.29
0.02 ‐0.02
D
37,391
37,406
37,425
37,444
37,468
34,064
34,087
34,107
34,126
34,166
34,285
34,108
34,169
34,224
34,287
34,401
34,759
127,849
232,151
499,561
0.18
Table IX. HET Test Conditions and Correlation with Noise
HET Noise 1
HET Noise 2
HET Noise 3
HET Noise 4
HET Noise 5
HET Noise 6
HET Noise 7
HET Noise 8
Pitot Noise (Standard Deviation)
1.86
2.52
5.84
1.81
8.98
25.78
8.02
4.62
Correlation with Pitot Noise
1.00
P4
3.00E+06
3.00E+06
3.00E+06
3.00E+06
3.00E+06
3.00E+06
3.00E+06
3.00E+06
P1
1200
1200
1200
1200
6000
6000
6000
1500
Driver Driven Accel P10 Gas Gas Gas
20.0 He
CO2 CO2
24.0 He
CO2 Air
140.0 He
CO2 He
18.0 He
CO2
Ar
213.3 He
CO2 He
213.3 He
Ar
He
213.3 He
Air
He
23.3 He
Air
He
0.72 0.71
c5
526.339
520.019
521.989
525.039
391.686
459.956
483.605
536.755
rho20
3.20E‐03
2.41E+06
7.81E‐04
1.22E‐03
1.15E‐03
1.17E‐03
1.17E‐03
2.67E‐04
T20
3.29E+03
2.32E+06
1.99E+03
1.34E+04
1.66E+03
1.76E+03
1.83E+03
2.96E+03
P20
3.62E+03
6.21E+06
3.22E+03
3.50E+03
3.99E+03
4.27E+03
4.47E+03
1.07E+03
‐0.53
‐0.25
‐0.25
‐0.25
g20
1.14
1.15
1.67
1.49
1.67
1.67
1.67
1.49
Us
1832
1832
1832
1832
1443
1716
1638
1977
Ut
3421
3454
4375
4000
3950
4087
4177
4767
c3/c2
0.74
0.74
0.74
0.74
1.12
0.59
0.75
0.54
(rho3c3)/ (rho5c5)/ Rel. Mach c5/c20 (rho2c2) (rho20c20) Enthalpy Number Pitot Pres u5 rho5 T5
P5
g5
0.46
1.98
2.22
5.74E+06 5.8
140436 3053 0.015 1252 3623 1.17098
0.48
1.98
2.13
5.93E+06 6.0
127307 3129 0.013 1221 3053 1.17203
0.20
1.98
3.53
5.87E+06 5.9
131293 3105 0.014 1231 3221 1.1717
0.25
1.98
3.10
5.78E+06 5.8
137654 3068 0.015 1246 3498 1.17119
0.16
1.27
4.43
4.20E+06 7.1
233532 2767 0.031 674 3990 1.20423
0.19
1.69
5.37
4.30E+06 6.3
247417 2876 0.034 610 4275 1.66667
0.19
1.70
4.30
4.65E+06 6.1
218753 2948 0.026 590 4469 1.37539
0.22
2.40
4.14
7.36E+06 6.9
67192 3715 0.005 736 1069 1.35888
‐0.36 0.19 ‐0.17 ‐0.50
c20
1134
1088
2621
2068
2401
2471
2518
2444
u2‐3
1619
1619
1619
1619
1262
1242
1335
1647
rho2
0.18
0.18
0.18
0.18
0.85
0.35
0.38
0.10
T2
1850
1850
1850
1850
1245
2910
1459
1936
0.55 0.47 ‐0.77 0.33 0.67
P2
64598
64598
64598
64598
200671
212655
159248
58521
0.80
g2
1.14
1.14
1.14
1.14
1.17
1.67
1.31
1.28
c2
633
633
633
633
525
1005
741
844
‐0.42
rho3
0.49
0.49
0.49
0.49
0.97
1.01
0.86
0.46
0.94 0.73 0.79
94 / 100
0.81
T3
63.11
63.11
63.11
63.11
99.31
101.65
89.61
60.67
P3
64598
64598
64598
64598
200671
212655
159248
58521
0.79
0.80
‐0.61
g3
1.67
1.67
1.67
1.67
1.67
1.67
1.67
1.67
0.21
c3
467.41
467.41
467.41
467.41
2401
593
557
458
0.14
rho1
0.021
0.021
0.021
0.021
0.107
0.097
0.070
0.018
0.70
c1
269
269
269
269
269
321
346
346
0.74 0.39
‐0.39 0.74 ‐0.65 0.41
rho10
3.45E‐04
2.80E‐04
2.27E‐04
2.84E‐04
3.46E‐04
3.46E‐04
3.46E‐04
5.91E‐05
0.30
c10
274
346
1014
321
1014
1014
1014
802
MW10
42.6
28.9
4.0
38.9
4.0
4.0
4.0
6.3
g10
1.30
1.40
1.67
1.63
1.67
1.67
1.67
1.63
0.90
D
10,706
10,710
10,954
10,699
41,992
54,037
40,296
12,077
0.62 ‐0.57 0.46 0.85
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