Using a Lagrangian solver, thermochemical nonequilibrium simulations are performed for the entire range of practical operating conditions of expansion tubes to isolate the influence of nonequilibrium and identify key features in large-scale facilities. Particular attention is given not only to the influence of the nonequilibrium unsteady expansion but also to the influences of the nonequilibrium region behind the primary shock and non-ideal secondary diaphragm rupture. The nonequilibrium unsteady expansion is found to be the most influential process in the test flow—it can significantly influence the flow properties and cause significant temporal variations in the properties during the test time. The nonequilibrium unsteady expansion is also found to accelerate the secondary shock and contact surface. The non-ideal secondary diaphragm rupture is found to increase the amount of nonequilibrium in the test flow due to the generation of a reflected shock. The nonequilibrium region behind the primary shock may be considered negligible in most conditions. Regarding the creation of thermochemical equilibrium test conditions, important factors for achieving this include having a high acceleration tube fill pressure, large-scale facility, and high total enthalpy. The combined effects of viscosity and nonequilibrium are postulated, and the results are supported by experimental works that report consistent findings. To provide an idea of the sensitivity of the numerical configuration, simulations of fixed-volume reactors at various de-excitation conditions are performed using different nonequilibrium models.

1.
S.
Gu
and
H.
Olivier
, “
Capabilities and limitations of existing hypersonic facilities
,”
Prog. Aerosp. Sci.
113
,
100607
(
2020
).
2.
C.
Park
, “
Experimental aspects of nonequilibrium flow
,” in
Nonequilibrium Hypersonic Aerothermodynamics
(
Wiley
,
New York
,
1989
), Chap. 7, pp.
219
254
.
3.
A.
Paull
and
R.
Stalker
, “
Test flow disturbances in an expansion tube
,”
J. Fluid Mech.
245
,
493
521
(
1992
).
4.
D.
Gildfind
,
P.
Jacobs
,
R.
Morgan
,
W.
Chan
, and
R.
Gollan
, “
Scramjet test flow reconstruction for a large-scale expansion tube. II. Axisymmetric CFD analysis
,”
Shock Waves
28
(
4
),
899
918
(
2018
).
5.
L. N.
Connor
, Jr.
, “
Calculation of the centered one-dimensional unsteady expansion of a reacting gas mixture subject to vibrational and chemical nonequilibrium
,”
NASA Technical Report No. TN D-3851
, National Aeronautics and Space Administration, Langley Research Center,
1967
.
6.
L. N.
Connor
, Jr.
, “
The one-dimensional unsteady expansion of a reacting mixture of gases considering vibrational and chemical nonequilibrium
,” Ph.D. thesis
(North Carolina State University
,
1965
).
7.
J.
Ray
 et al, “
Estimation of inflow uncertainties in laminar hypersonic double-cone experiments
,”
AIAA J.
58
(
10
),
4461
4474
(
2020
).
8.
A.
Neely
and
R.
Morgan
, “
The superorbital expansion tube concept, experiment and analysis
,”
Aeronaut. J.
98
(
973
),
97
105
(
1994
).
9.
I.
Nompelis
,
G.
Candler
,
M.
Holden
, and
T.
Wadhams
, “
Numerical simulation of high-enthalpy experiments in the LENS X expansion tube facility
,” AIAA Paper No. 2004-1000,
2004
.
10.
I.
Nompelis
,
G. V.
Candler
, and
M. S.
Holden
, “
Effect of vibrational nonequilibrium on hypersonic double-cone experiments
,”
AIAA J.
41
(
11
),
2162
2169
(
2003
).
11.
F.
Liu
and
L.
Bao
, “
Peak heat flux prediction of hypersonic flow over compression ramp under vibrationally excited free-stream condition
,”
Phys. Fluids
35
,
016120
(
2023
).
12.
M.
MacLean
,
A.
Dufrene
,
T.
Wadhams
, and
M.
Holden
, “
Numerical and experimental characterization of high enthalpy flow in an expansion tunnel facility
,” AIAA Paper No. 2010-1562,
2010
.
13.
P.
Jacobs
,
T.
Silvester
,
R.
Morgan
,
M.
Scott
,
R.
Gollan
, and
T.
McIntyre
, “
Superorbital expansion tube operation: Estimates of flow conditions via numerical simulation
,” AIAA Paper No. 2005-694,
2005
.
14.
A. T.
Dufrene
,
M. S.
Holden
, and
M. J.
Ringuette
, “
Microwave shock-speed diagnostic development and analysis of expansion tunnel viscous effects
,”
AIAA J.
53
(
3
),
573
587
(
2015
).
15.
P.
Jacobs
, “
Quasi-one-dimensional modeling of a free-piston shock tunnel
,”
AIAA J.
32
(
1
),
137
145
(
1994
).
16.
P. A.
Jacobs
, “
Shock tube modelling with L1d
,”
Report No. 13/98
, The University of Queensland,
1998
.
17.
P. A.
Jacobs
, “
Approximate Riemann solver for hypervelocity flows
,”
AIAA J.
30
(
10
),
2558
2561
(
1992
).
18.
C.
Park
, “
Review of chemical-kinetic problems of future NASA missions. I. Earth entries
,”
J. Thermophys. Heat Transfer
7
(
3
),
385
398
(
1993
).
19.
J. W.
Rich
,
S. O.
Macheret
, and
I. V.
Adamovich
, “
Aerothermodynamics of vibrationally nonequilibrium gases
,”
Exp. Therm. Fluid Sci.
13
(
1
),
1
10
(
1996
).
20.
S.
Gu
,
H.
Olivier
,
C.-Y.
Wen
,
J.
Hao
, and
Q.
Wang
, “
Characterization of reflected shock tunnel air conditions using a simple method
,”
Phys. Fluids
34
(
5
),
056103
(
2022
).
21.
C.
Mundt
,
R.
Boyce
,
P.
Jacobs
, and
K.
Hannemann
, “
Validation study of numerical simulations by comparison to measurements in piston-driven shock-tunnels
,”
Aerosp. Sci. Technol.
11
(
2–3
),
100
109
(
2007
).
22.
D.
Gildfind
,
P.
Jacobs
,
R.
Morgan
,
W.
Chan
, and
R.
Gollan
, “
Scramjet test flow reconstruction for a large-scale expansion tube. I. Quasi-one-dimensional modelling
,”
Shock Waves
28
(
4
),
877
897
(
2018
).
23.
J.
Saavedra
,
G.
Grossir
,
O.
Chazot
, and
G.
Paniagua
, “
Start-up analysis of a hypersonic short-duration facility
,”
AIAA J.
60
(
4
),
2060
2074
(
2022
).
24.
G.
Grossir
,
Z.
Ilich
, and
O.
Chazot
, “
Modeling of the VKI longshot gun tunnel compression process using a quasi-1D approach
,” AIAA Paper No. 2017-3985,
2017
.
25.
R.
Ramani
,
J.
Reisner
, and
S.
Shkoller
, “
A space-time smooth artificial viscosity method with wavelet noise indicator and shock collision scheme I. The 1-D case
,”
J. Comput. Phys.
387
,
81
116
(
2019
).
26.
B.
Grossman
and
P.
Cinnella
, “
Flux-split algorithms for flows with non-equilibrium chemistry and vibrational relaxation
,”
J. Comput. Phys.
88
(
1
),
131
168
(
1990
).
27.
R.
Loubere
and
M. J.
Shashkov
, “
A subcell remapping method on staggered polygonal grids for arbitrary-Lagrangian–Eulerian methods
,”
J. Comput. Phys.
209
(
1
),
105
138
(
2005
).
28.
M. C.
Cline
,
J. K.
Dukowicz
, and
F.
Addessio
, “
CAVEAT-GT: A general topology version of the caveat code
,”
Technical Report No. LA-11812-MS
,
Los Alamos National Laboratory
,
1990
.
29.
M.
Di Renzo
,
L.
Fu
, and
J.
Urzay
, “
HTR solver: An open-source exascale-oriented task-based multi-GPU high-order code for hypersonic aerothermodynamics
,”
Comput. Phys. Commun.
255
,
107262
(
2020
).
30.
A.
Peyvan
,
K.
Shukla
,
J.
Chan
, and
G.
Karniadakis
, “
High-order methods for hypersonic flows with strong shocks and real chemistry
,” arXiv:2211.12635 (
2022
).
31.
L.
Sciacovelli
,
D.
Passiatore
,
P.
Cinnella
, and
G.
Pascazio
, “
Assessment of a high-order shock-capturing central-difference scheme for hypersonic turbulent flow simulations
,”
Comput. Fluids
230
,
105134
(
2021
).
32.
D. F.
Potter
, “
Modelling of radiating shock layers for atmospheric entry at Earth and Mars
,” Ph.D. thesis (
University of Queensland
,
2011
).
33.
J.
Shen
,
H.
Lu
,
R.
Li
,
X.
Chen
, and
H.
Ma
, “
The thermochemical non-equilibrium scale effects of the high enthalpy nozzle
,”
Adv. Aerodyn.
2
(
1
),
1
20
(
2020
).
34.
Z.
Jiang
,
J.
Li
,
Z.
Hu
,
Y.
Liu
, and
H.
Yu
, “
On theory and methods for advanced detonation-driven hypervelocity shock tunnels
,”
Nat. Sci. Rev.
7
(
7
),
1198
1207
(
2020
).
35.
S. J.
Stennett
,
D.
Gildfind
,
P.
Jacobs
,
R.
Morgan
,
C.
James
, and
P.
Toniato
, “
The X3R free-piston reflected shock tunnel: Australia's new large-scale
,” AIAA Paper No. 2020-2447,
2020
.
36.
D. E.
Gildfind
,
R. G.
Morgan
,
P. A.
Jacobs
, and
M.
McGilvray
, “
Production of high-Mach-number scramjet flow conditions in an expansion tube
,”
AIAA J.
52
(
1
),
162
177
(
2014
).
37.
C. M.
James
,
S. W.
Lewis
,
R. G.
Morgan
,
Y.
Liu
, and
A.
Lefevre
, “
Generating high-speed earth reentry test conditions in an expansion tube
,”
J. Spacecr. Rockets
58
(
2
),
345
362
(
2021
).
38.
M. P.
Scott
, “
Development and modelling of expansion tubes
,” Ph.D. thesis (
University of Queensland
,
2007
).
39.
E. J.
Fahy
, “
Superorbital re-entry shock layers: Flight and laboratory comparisons
,” Ph.D. thesis (
University of Queensland
,
2017
).
40.
V.
Wheatley
,
H.
Chiu
,
P. A.
Jacobs
,
M. N.
Macrossan
,
D. J.
Mee
, and
R. G.
Morgan
, “
Rarefied, superorbital flows in an expansion tube
,”
Int. J. Numer. Methods Heat Fluid Flow
14
(
4
),
512
537
(
2004
).
41.
D. E.
Gildfind
 et al, “
Flow characterization and modeling of the X2 and X3 expansion tubes
,” NATO STO Lecture Series, STO-AVT-352-VKI,
2018
.
42.
R. J.
Bakos
and
R. G.
Morgan
, “
Chemical recombination in an expansion tube
,”
AIAA J.
32
(
6
),
1316
1319
(
1994
).
43.
C.
James
,
D.
Gildfind
,
S.
Lewis
,
R.
Morgan
, and
F.
Zander
, “
Implementation of a state-to-state analytical framework for the calculation of expansion tube flow properties
,”
Shock Waves
28
,
349
377
(
2017
).
44.
S.
Gu
,
J.
Hao
, and
C.-Y.
Wen
, “
Air thermochemistry in the converging section of de Laval nozzles on hypersonic wind tunnels
,”
AIP Adv.
12
(
8
),
085320
(
2022
).
45.
T.
Furukawa
,
T.
Aochi
, and
A.
Sasoh
, “
Expansion tube operation with thin secondary diaphragm
,”
AIAA J.
45
(
1
),
214
217
(
2007
).
46.
A. E.
Nasser
and
J. W.
Cleaver
, “
Vibrational relaxation of carbon monoxide in an unsteady expansion wave
,”
Acta Astronaut.
4
(
3–4
),
357
373
(
1977
).
47.
V. A.
Miller
,
M.
Gamba
,
M. G.
Mungal
, and
R. K.
Hanson
, “
Secondary diaphragm thickness effects and improved pressure measurements in an expansion tube
,”
AIAA J.
52
(
2
),
451
456
(
2014
).
48.
G.
Wilson
, “
Time-dependent quasi-one-dimensional simulations of high enthalpy pulse facilities
,” AIAA Paper No. 1992-5096,
1992
.
49.
S.
Gu
, “
Mars entry afterbody radiative heating: An experimental study of nonequilibrium CO2 expanding flow
,” Ph.D. thesis
(University of Queensland
,
2018
).
50.
D. E.
Gildfind
,
D.
Smith
,
P. A.
Jacobs
,
R.
Kelly
,
A.
Lefevre
, and
T. J.
McIntyre
, “
Expansion tube test flow design for magnetohydrodynamic aerobraking
,”
AIAA J.
59
(
4
),
1328
1341
(
2021
).
51.
R.
Gollan
 et al, “
A simulation technique for radiating shock tube flows
,” in
26th International Symposium on Shock Waves, Göttingen, Germany
, edited by
K.
Hannemann
and
F.
Seiler
(
Springer
,
Berlin
,
2009
), pp.
465
470
.
52.
J. G.
Hall
and
C. E.
Treanor
, “
Nonequilibrium effects in supersonic-nozzle flows
,” AGARDograph No. 124,
1967
.
53.
C. M.
James
 et al, “
Improved test time evaluation in an expansion tube
,”
Exp. Fluids
59
(
87
),
87
(
2018
).
54.
A.
Sasoh
,
Y.
Ohnishi
,
D.
Ramjaun
,
K.
Takayama
,
H.
Otsu
, and
T.
Abe
, “
Effective test time evaluation in high-enthalpy expansion tube
,”
AIAA J.
39
(
11
),
2141
2147
(
2001
).
55.
T.
Schwartz
 et al, “
Characterization of the Caltech hypervelocity expansion tube via tunable diode laser absorption spectroscopy
,” AIAA Paper No. 2021-3524,
2021
.
56.
S.
Gu
,
J.
Hao
, and
C.-Y.
Wen
, “
State-specific study of air in the expansion tunnel nozzle and test section
,”
AIAA J.
60
(
7
),
4024
4038
(
2022
).
57.
C.
James
 et al, “
Using optically filtered high-speed imaging to characterise expansion tube operating conditions
,”
Shock Waves
30
(
5
),
523
544
(
2020
).
58.
C.
Park
, “
Thermochemical relaxation in shock tunnels
,”
J. Thermophys. Heat Transfer
20
(
4
),
689
698
(
2006
).
59.
C.
Wen
and
H.
Hornung
, “
Nonequilibrium recombination after a curved shock wave
,”
Prog. Aerosp. Sci.
46
(
2–3
),
132
139
(
2010
).
60.
M. N.
Macrossan
, “
Hypervelocity flow of dissociating nitrogen downstream of a blunt nose
,”
J. Fluid Mech.
217
,
167
202
(
1990
).
61.
M. E.
Holloway
,
R. S.
Chaudhry
, and
I. D.
Boyd
, “
Assessment of hypersonic double-cone experiments for validation of thermochemistry models
,”
J. Spacecr. Rockets
59
(
2
),
389
400
(
2022
).
62.
S.
Gu
,
J.
Hao
, and
C.-Y.
Wen
, “
On the vibrational state-specific modelling of radiating normal-shocks in air
,”
AIAA J.
60
(
6
),
3760
3774
(
2022
).
63.
J. D.
Schmisseur
, “
Hypersonics into the 21st century: A perspective on AFOSR-sponsored research in aerothermodynamics
,”
Prog. Aerosp. Sci.
72
,
3
16
(
2015
).
64.
T. I.
McLaren
and
J. P.
Appleton
, “
Vibrational relaxation measurements of carbon monoxide in a shock‐tube expansion wave
,”
J. Chem. Phys.
53
(
7
),
2850
2857
(
1970
).
65.
G. V.
Candler
, “
Nonequilibrium hypersonic flows and hypersonic nozzle flow modeling
,” NATO STO Lecture Series: Flow Characterization and Modeling of Hypersonic Wind Tunnels, STO-AVT-352-VKI,
2018
.
66.
M.
Lino da Silva
,
B.
Lopez
,
V.
Guerra
, and
J.
Loureiro
, “
A multiquantum state-to-state model for the fundamental states of air: The stellar database
,” in
Proceedings of 5th International Workshop on Radiation of High Temperature Gases in Atmospheric Entry
, Barcelona, Spain, 16–19 October
2012
, Vol.
714
.
67.
I. V.
Adamovich
,
S. O.
Macheret
,
J. W.
Rich
, and
C. E.
Treanor
, “
Vibrational energy transfer rates using a forced harmonic oscillator model
,”
J. Thermophys. Heat Transfer
12
(
1
),
57
65
(
1998
).
68.
F.
Esposito
and
M.
Capitelli
, “
The relaxation of vibrationally excited O2 molecules by atomic oxygen
,”
Chem. Phys. Lett.
443
(
4–6
),
222
226
(
2007
).
69.
W.
Su
,
D.
Bruno
, and
Y.
Babou
, “
State-specific modeling of vibrational relaxation and nitric oxide formation in shock-heated air
,”
J. Thermophys. Heat Transfer
32
(
2
),
337
352
(
2018
).
70.
J.
Hao
,
J.
Wang
, and
C.
Lee
, “
State-specific simulation of oxygen vibrational excitation and dissociation behind a normal shock
,”
Chem. Phys. Lett.
681
,
69
74
(
2017
).
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