In this study, we develop and assess a new approach to modeling slip boundary conditions in gas mixtures with coupled state-to-state vibrational-chemical kinetics and surface physical and chemical processes: adsorption, desorption, vibrational energy transitions, and chemical reactions. Expressions for velocity slip, temperature jump, and mass fluxes of species are derived on the basis of the advanced kinetic boundary condition taking into account gain and loss of particles in surface processes; theoretical expressions for the mass fluxes obtained in the frame of various approaches are compared. The developed model is implemented to the fluid-dynamic solver for modeling dynamics and state-to-state air kinetics in the boundary layer near stagnation point. Several test cases corresponding to a various degree of gas rarefaction are considered. Recombination probabilities and effective reaction rates are calculated and compared to recent molecular-dynamic simulations; the proposed model yields the best agreement for the recombination rate coefficient. It is shown that temperature jump significantly affects fluid-dynamic parameters and surface heat flux; the role of heterogeneous reactions on the silica surface is weaker. In the surface heating, there is a competition between these two effects: whereas the temperature jump reduces the wall heat flux, surface reactions cause its increase, but to a lesser extent. It is concluded that the model proposed in this study describes self-consistently detailed vibrational kinetics, rarefaction effects, and surface reactions and can be applied both in continuum and slip flow regimes.

1.
J. N.
Moss
and
G. A.
Bird
, “
Direct simulation of transitional flow for hypersonic reentry conditions
,”
J. Spacecr. Rockets
40
,
830
843
(
2003
).
2.
D.
Bruno
,
M.
Capitelli
,
F.
Esposito
,
S.
Longo
, and
P.
Minelli
, “
Direct simulation of non-equilibrium kinetics under shock conditions in nitrogen
,”
Chem. Phys. Lett.
360
,
31
37
(
2002
).
3.
I.
Wysong
,
S.
Gimelshein
,
Y.
Bondar
, and
M.
Ivanov
, “
Comparison of direct simulation Monte Carlo chemistry and vibrational models applied to oxygen shock measurements
,”
Phys. Fluids
26
,
043101
(
2014
).
4.
S.
Gimelshein
and
I.
Wysong
, “
DSMC modeling of flows with recombination reactions
,”
Phys. Fluids
29
,
067106
(
2017
).
5.
H.
Luo
,
I. B.
Sebastião
,
A. A.
Alexeenko
, and
S. O.
Macheret
, “
Classical impulsive model for dissociation of diatomic molecules in direct simulation Monte Carlo
,”
Phys. Rev. Fluids
3
,
113401
(
2018
).
6.
H.
Chen
,
B.
Zhang
, and
H.
Liu
, “
Role of chemical reactions in the stagnation point heat flux of rarefied hypersonic cylinder flows
,”
Phys. Fluids
32
,
096105
(
2020
).
7.
E. V.
Kustova
and
E. A.
Nagnibeda
, “
Transport properties of a reacting gas mixture with strong vibrational and chemical nonequilibrium
,”
Chem. Phys.
233
,
57
75
(
1998
).
8.
E. V.
Kustova
, “
On the simplified state-to-state transport coefficients
,”
Chem. Phys.
270
,
177
195
(
2001
).
9.
E.
Nagnibeda
and
E. V.
Kustova
,
Nonequilibrium Reacting Gas Flows. Kinetic Theory of Transport and Relaxation Processes
(
Springer Verlag
,
Berlin, Heidelberg
,
2009
).
10.
S. F.
Gimelshein
,
I. J.
Wysong
,
A. J.
Fangman
,
D. A.
Andrienko
,
O. V.
Kunova
,
E. V.
Kustova
,
C.
Garbacz
,
M.
Fossati
, and
K.
Hanquist
, “
Kinetic and continuum modeling of high-temperature oxygen and nitrogen binary mixtures
,”
J. Thermophys. Heat Transfer
36
,
399
418
(
2022
).
11.
S. F.
Gimelshein
,
I. J.
Wysong
,
A. J.
Fangman
,
D. A.
Andrienko
,
O. V.
Kunova
,
E. V.
Kustova
,
F.
Morgado
,
C.
Garbacz
,
M.
Fossati
, and
K. M.
Hanquist
, “
Kinetic and continuum modeling of high-temperature air relaxation
,”
J. Thermophys. Heat Transfer
36
,
870
893
(
2022
).
12.
O. V.
Kunova
and
E. A.
Nagnibeda
, “
State-to-state description of reacting air flows behind shock waves
,”
Chem. Phys.
441
,
66
76
(
2014
).
13.
M.
Panesi
,
A.
Munafò
,
T. E.
Magin
, and
R. L.
Jaffe
, “
Nonequilibrium shock-heated nitrogen flows using a rovibrational state-to-state method
,”
Phys. Rev. E
90
,
013009
(
2014
).
14.
O.
Kunova
,
E.
Kustova
,
M.
Mekhonoshina
, and
E.
Nagnibeda
, “
Non-equilibrium kinetics, diffusion and heat transfer in shock heated flows of N2/N and O2/O mixtures
,”
Chem. Phys.
463
,
70
81
(
2015
).
15.
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
,
337
352
(
2018
).
16.
I. N.
Kadochnikov
and
I. V.
Arsentiev
, “
Kinetics of nonequilibrium processes in air plasma formed behind shock waves: State-to-state consideration
,”
J. Phys. D
51
,
374001
(
2018
).
17.
L.
Campoli
,
O.
Kunova
,
E.
Kustova
, and
M.
Melnik
, “
Models validation and code profiling in state-to-state simulations of shock heated air flows
,”
Acta Astronaut.
175
,
493
509
(
2020
).
18.
I.
Alekseev
and
E.
Kustova
, “
Extended continuum models for shock waves in CO2
,”
Phys. Fluids
33
,
096101
(
2021
).
19.
M. Y.
Melnik
and
E.
Kustova
, “
Impact of electronic excitation on the state-to-state vibrational-chemical co kinetics
,”
J. Phys.: Conf. Ser.
2308
,
012014
(
2022
).
20.
G.
Colonna
,
M.
Capitelli
,
M.
Tuttafesta
, and
D.
Giordano
, “
Non-Arrhenius NO formation rate in one-dimensional nozzle airflow
,”
J. Thermophys. Heat Transfer
13
,
372
375
(
1999
).
21.
E. V.
Kustova
,
E. A.
Nagnibeda
,
T. Y.
Alexandrova
, and
A.
Chikhaoui
, “
On the non-equilibrium kinetics and heat transfer in nozzle flows
,”
Chem. Phys.
276
,
139
154
(
2002
).
22.
G. V.
Candler
,
J.
Olejniczak
, and
B.
Harrold
, “
Detailed simulation of nitrogen dissociation in stagnation regions
,”
Phys. Fluids
9
,
2108
2117
(
1997
).
23.
I.
Armenise
,
M.
Capitelli
,
E.
Kustova
, and
E.
Nagnibeda
, “
The influence of nonequilibrium kinetics on the heat transfer and diffusion near re-entering body
,”
J. Thermophys. Heat Transfer
13
,
210
218
(
1999
).
24.
E.
Kustova
,
E.
Nagnibeda
,
I.
Armenise
, and
M.
Capitelli
, “
Non-equilibrium kinetics and heat transfer in O2/O mixtures near catalytic surfaces
,”
J. Thermophys. Heat Transfer
16
,
238
244
(
2002
).
25.
I.
Armenise
,
M.
Barbato
,
M.
Capitelli
, and
E.
Kustova
, “
State-to-state catalytic models, kinetics and transport in hypersonic boundary layers
,”
J. Thermophys. Heat Transfer
20
,
465
476
(
2006
).
26.
I.
Armenise
and
E.
Kustova
, “
On different contributions to the heat flux and diffusion in non-equilibrium flows
,”
Chem. Phys.
428
,
90
104
(
2014
).
27.
E.
Josyula
,
J. M.
Burt
,
E.
Kustova
, and
P.
Vedula
, “
State-to-state kinetic model for a viscous radiating hypersonic flow
,” AIAA Paper No. AIAA 2015-0475,
2015
).
28.
D.
Ninni
,
F.
Bonelli
,
G.
Colonna
, and
G.
Pascazio
, “
Unsteady behavior and thermochemical non equilibrium effects in hypersonic double-wedge flows
,”
Acta Astronaut.
191
,
178
192
(
2022
).
29.
D.
Ninni
,
F.
Bonelli
,
G.
Colonna
, and
G.
Pascazio
, “
On the influence of non equilibrium in the free stream conditions of high enthalpy oxygen flows around a double-cone
,”
Acta Astronaut.
201
,
247
258
(
2022
).
30.
R. G.
Lord
, “
Some extensions to the Cercignani–Lampis gas–surface scattering kernel
,”
Phys. Fluids A
3
,
706
710
(
1991
).
31.
R. G.
Lord
, “
Some further extensions of the Cercignani–Lampis gas–surface interaction model
,”
Phys. Fluids
7
,
1159
1161
(
1995
).
32.
D.
Bruno
,
M.
Cacciatore
,
S.
Longo
, and
M.
Rutigliano
, “
Gas-surface scattering models for particle fluid dynamics: A comparison between analytical approximate models and molecular dynamics calculations
,”
Chem. Phys. Lett.
320
,
245
254
(
2000
).
33.
K.
Yamamoto
,
H.
Takeuchi
, and
T.
Hyakutake
, “
Scattering properties and scattering kernel based on the molecular dynamics analysis of gas-wall interaction
,”
Phys. Fluids
19
,
087102
(
2007
).
34.
M.
Hossein Gorji
and
P.
Jenny
, “
A gas-surface interaction kernel for diatomic rarefied gas flows based on the Cercignani–Lampis–Lord model
,”
Phys. Fluids
26
,
122004
(
2014
).
35.
J.
Deng
,
J.
Zhang
,
T.
Liang
,
J.
Zhao
,
Z.
Li
, and
D.
Wen
, “
A modified Cercignani–Lampis model with independent momentum and thermal accommodation coefficients for gas molecules scattering on surfaces
,”
Phys. Fluids
34
,
107108
(
2022
).
36.
I.
Choquet
, “
A new approach to model and simulate numerically surface chemistry in rarefied flows
,”
Phys. Fluids
11
,
1650
1661
(
1999
).
37.
V. L.
Kovalev
,
V. Y.
Sazonenko
, and
A. N.
Yakunchikov
, “
Dynamic Monte Carlo simulation of surface recombination
,”
Moscow Univ. Mech. Bull.
62
,
53
58
(
2007
).
38.
A. N.
Molchanova
,
A. V.
Kashkovsky
, and
Y. A.
Bondar
, “
Surface recombination in the direct simulation Monte Carlo method
,”
Phys. Fluids
30
,
107105
(
2018
).
39.
L. P.
Pitaevskii
and
E.
Lifshitz
,
Course of Theoretical Physics: Physical Kinetics
(
Butterworth-Heinemann
,
2012
), Vol.
10
.
40.
S. K.
Dadzie
and
J. G.
Méolans
, “
Temperature jump and slip velocity calculations from an anisotropic scattering kernel
,”
Physica A
358
,
328
346
(
2005
).
41.
I.
Armenise
,
M.
Capitelli
, and
S.
Longo
, “
Fourier and diffusive heat transfer in hypersonic nitrogen flows: The state-to-state approach
,”
J. Thermophys. Heat Transfer
23
,
674
683
(
2009
).
42.
S.
Takata
,
S.
Yasuda
,
S.
Kosuge
, and
K.
Aoki
, “
Numerical analysis of thermal-slip and diffusion-slip flows of a binary mixture of hard-sphere molecular gases
,”
Phys. Fluids
15
,
3745
3766
(
2003
).
43.
C. E.
Siewert
, “
Viscous-slip, thermal-slip, and temperature-jump coefficients as defined by the linearized Boltzmann equation and the Cercignani–Lampis boundary condition
,”
Phys. Fluids
15
,
1696
1701
(
2003
).
44.
F.
Sharipov
and
D.
Kalempa
, “
Velocity slip and temperature jump coefficients for gaseous mixtures. I. Viscous slip coefficient
,”
Phys. Fluids
15
,
1800
1806
(
2003
).
45.
F.
Sharipov
and
D.
Kalempa
, “
Velocity slip and temperature jump coefficients for gaseous mixtures. II. Thermal slip coefficient
,”
Phys. Fluids
16
,
759
764
(
2004
).
46.
A.
Stepanenko
,
V.
Zaznoba
, and
V.
Zhdanov
, “
Boundary slip phenomena in multicomponent gas mixtures
,”
Phys. Fluids
31
,
062105
(
2019
).
47.
N. N.
Nguyen
,
I.
Graur
,
P.
Perrier
, and
S.
Lorenzani
, “
Variational derivation of thermal slip coefficients on the basis of the Boltzmann equation for hard-sphere molecules and Cercignani–Lampis boundary conditions: Comparison with experimental results
,”
Phys. Fluids
32
,
102011
(
2020
).
48.
R.
Li
and
Y.
Yang
, “
Slip and jump coefficients for general gas–surface interactions according to the moment method
,”
Phys. Fluids
35
,
032010
(
2023
).
49.
H.
Grad
, “
On the kinetic theory of rarefied gases
,”
Commun. Pure Appl. Math.
2
,
331
407
(
1949
).
50.
G. N.
Patterson
,
Molecular Flow of Gases
(
Wiley
,
New York
,
1956
).
51.
A.
Zade
,
M.
Renksizbulut
, and
J.
Friedman
, “
Slip/jump boundary conditions for rarefied reacting/non-reacting multi-component gaseous flows
,”
Int. J. Heat Mass Transfer
51
,
5063
5071
(
2008
).
52.
K.
Aoki
and
V.
Giovangigli
, “
Kinetic model of adsorption on crystal surfaces
,”
Phys. Rev. E
99
,
052137
(
2019
).
53.
K.
Aoki
and
V.
Giovangigli
, “
Kinetic theory of chemical reactions on crystal surfaces
,”
Physica A
565
,
125573
(
2021
).
54.
V. P.
Shidlovskiy
,
Introduction to Dynamics of Rarefied Gases
(
Elsevier
,
New York
,
1967
).
55.
L.
Shakurova
and
E.
Kustova
, “
State-specific boundary conditions for nonequilibrium gas flows in slip regime
,”
Phys. Rev. E
105
,
034126
(
2022
).
56.
L. A.
Shakurova
and
E. V.
Kustova
, “
Boundary conditions for fluid-dynamic parameters of a single-component gas flow with vibrational deactivation on a solid wall
,”
Vestnik St. Petersb. Univ. Math.
55
,
249
256
(
2022
).
57.
L.
Shakurova
and
E.
Kustova
, “
Slip boundary conditions for gas mixture flows with state-to-state vibrational-chemical kinetics
,”
AIP Conf. Proc.
(to be published).
58.
I.
Armenise
,
M.
Capitelli
,
C.
Gorse
,
M.
Cacciatore
, and
M.
Rutigliano
, “
Nonequilibrium vibrational kinetics of an O2/O mixture hitting a catalytic surface
,”
J. Spacecr. Rockets
37
,
318
323
(
2000
).
59.
E.
Kustova
,
E.
Nagnibeda
,
I.
Armenise
, and
M.
Capitelli
, “
Non–Equilibrium distributions and heat transfer near a catalytic surface of re-entering bodies
,”
AIP Conf. Proc.
663
,
497
504
(
2003
).
60.
I.
Armenise
and
F.
Esposito
, “
N+O2(v) collisions: Reactive, inelastic and dissociation rates for state-to-state vibrational kinetic models
,”
Chem. Phys.
551
,
111325
(
2021
).
61.
F.
Nasuti
,
M.
Barbato
, and
C.
Bruno
, “
Material-dependent recombination modeling for hypersonic flows
,”
J. Thermophys. Heat Transfer
10
,
131
136
(
1996
).
62.
M.
Barbato
,
S.
Reggiani
,
C.
Bruno
, and
J.
Muylaert
, “
Model for heterogeneous catalysis on metal surfaces with applications to hypersonic flows
,”
J. Thermophys. Heat Transfer
14
,
412
420
(
2000
).
63.
C.
Scott
, “
Wall boundary equations with slip and catalysis for multicomponent, nonequilibrium gas flows
,”
Technical Report No. NASA-TM-X-58111
(
NASA
,
1973
).
64.
R.
Gupta
,
C.
Scott
, and
J.
Moss
, “
Slip-boundary equations for multicomponent nonequilibrium airflow
,”
Report No. NASA-TP-2452
(NASA,
1985
).
65.
B.
Xu
and
Y.
Ju
, “
Theoretical and numerical studies of non-equilibrium slip effects on a catalytic surface
,”
Combust. Theory Modell.
10
,
961
979
(
2006
).
66.
Z.
Li
and
H.
Wang
, “
Gas-nanoparticle scattering: A molecular view of momentum accommodation function
,”
Phys. Rev. Lett.
95
,
014502
(
2005
).
67.
O.
Deutschmann
,
U.
Riedel
, and
J.
Warnatz
, “
Modeling of nitrogen and oxygen recombination on partial catalytic surfaces
,”
ASME. J. Heat Transfer
117
,
495
501
(
1995
).
68.
J.
Ferziger
and
H.
Kaper
,
Mathematical Theory of Transport Processes in Gases
(
North-Holland Publishing Co
.,
Amsterdam/London
,
1972
).
69.
V.
Kovalev
,
Heterogeneous Catalytic Processes in Aerothermodynamics
(
FIZMATLIT
,
Moscow
,
2002
).
70.
V.
Kovalev
and
A.
Kolesnikov
, “
Experimental and theoretical simulation of heterogeneous catalysis in aerothermochemistry (a review)
,”
Fluid Dyn.
40
,
669
693
(
2005
).
71.
J. D.
Anderson
,
Hypersonic and High-Temperature Gas Dynamics
, AIAA Education Series (
American Institute of Aeronautics and Astronautics
,
2006
).
72.
I.
Armenise
and
E.
Kustova
, “
State-to-state models for CO2 molecules: From the theory to an application to hypersonic boundary layers
,”
Chem. Phys.
415
,
269
281
(
2013
).
73.
V. M.
Doroshenko
,
N. N.
Kudryavtsev
,
S. S.
Novikov
, and
V. V.
Smetanin
, “
Dependence of heat transfer on the formation of vibrationally excited nitrogen molecules during the recombination of atoms in a boundary layer
,”
High Temp
28
,
70
76
(
1990
).
74.
G. D.
Billing
and
E. R.
Fisher
, “
VV and VT rate coefficients in N2 by a quantum-classical model
,”
Chem. Phys.
43
,
395
401
(
1979
).
75.
M.
Capitelli
,
C.
Gorse
, and
G.
Billing
, “
V–V pumping up in non-equilibrium nitrogen: Effects on the dissociation rate
,”
Chem. Phys.
52
,
299
304
(
1980
).
76.
G. D.
Billing
, “
Vibration-vibration and vibration-translation energy transfer, including multiquantum transitions in atom-diatom and diatom-diatom collisions
,” in
Nonequilibrium Vibrational Kinetics
, edited by
M.
Capitelli
(
Springer Berlin Heidelberg
,
Berlin, Heidelberg
,
1986
), pp.
85
112
.
77.
G.
Billing
and
R.
Kolesnick
, “
Vibrational relaxation of oxygen. state to state rate constants
,”
Chem. Phys. Lett.
200
,
382
386
(
1992
).
78.
I.
Armenise
and
M.
Capitelli
, “
State to state vibrational kinetics in the boundary layer of an entering body in earth atmosphere: Particle distributions and chemical kinetics
,”
Plasma Sources Sci. Technol
14
,
S9
(
2005
).
79.
I.
Armenise
and
F.
Esposito
, “
N2, O2, NO state-to-state vibrational kinetics in hypersonic boundary layers: The problem of rescaling rate coefficients to uniform vibrational ladders
,”
Chem. Phys.
446
,
30
46
(
2015
).
80.
F.
Esposito
,
I.
Armenise
, and
M.
Capitelli
, “
N–N2 state to state vibrational-relaxation and dissociation rates based on quasiclassical calculations
,”
Chem. Phys.
331
,
1
8
(
2006
).
81.
F.
Esposito
,
I.
Armenise
,
G.
Capitta
, and
M.
Capitelli
, “
O–O2 state-to-state vibrational relaxation and dissociation rates based on quasiclassical calculations
,”
Chem. Phys.
351
,
91
98
(
2008
).
82.
I.
Wysong
,
S.
Gimelshein
,
N.
Gimelshein
,
W.
McKeon
, and
F.
Esposito
, “
Reaction cross sections for two direct simulation Monte Carlo models: Accuracy and sensitivity analysis
,”
Phys. Fluids
24
,
042002
(
2012
).
83.
F.
Esposito
and
I.
Armenise
, “
Reactive, inelastic, and dissociation processes in collisions of atomic oxygen with molecular nitrogen
,”
J. Phys. Chem. A
121
,
6211
6219
(
2017
).
84.
M.
Cacciatore
,
M.
Rutigliano
, and
G.
Billing
, “
Eley–Rideal and Langmuir–Hinshelwood recombination coefficients for oxygen on silica surfaces
,”
J. Thermophys. Heat Transfer
13
,
195
203
(
1999
).
85.
I.
Armenise
,
M.
Rutigliano
,
M.
Cacciatore
, and
M.
Capitelli
, “
Hypersonic boundary layers: Oxygen recombination on SiO2 starting from ab initio coefficients
,”
J. Thermophys. Heat Transfer
25
,
627
632
(
2011
).
86.
M.
Rutigliano
,
A.
Palma
, and
N.
Sanna
, “
Vibrationally excited hydrogen molecules formation on a cesiated surface
,”
Plasma Sources Sci. Technol.
27
,
075014
(
2018
).
87.
M.
Rutigliano
,
M.
Cacciatore
, and
G. D.
Billing
, “
Hydrogen atom recombination on graphite at 10 K via the Eley–Rideal mechanism
,”
Chem. Phys. Lett.
340
,
13
20
(
2001
).
88.
M.
Rutigliano
and
M.
Cacciatore
, “
Recombination of oxygen atoms on silica surface: New and more accurate results
,”
J. Thermophys. Heat Transfer
30
,
247
250
(
2016
).
89.
J.
Shinn
,
J.
Moss
, and
A.
Simmonds
, “
Viscous-shock-layer heating analysis for the shuttle windward-symmetry plane with surface finite catalytic recombination rates
,” AIAA Paper No. AIAA 1982-0842,
1982
.
90.
A. A.
Kroupnov
and
M. J.
Pogosbekian
, “
Interaction of dissociated air with the surface of β-cristobalite material
,”
Acta Astronaut.
203
,
454
468
(
2023
).
91.
J.
Shinn
and
A.
Simmonds
, “
Comparison of viscous-shock-layer heating analysis with shuttle flight data in slip flow regime
,” AIAA Paper No. AIAA 1984-0226,
1984
.
92.
J. A.
Fay
and
F. R.
Riddell
, “
Theory of stagnation point heat transfer in dissociated air
,”
J. Aerosp. Sci.
25
,
73
85
(
1958
).
93.
R.
Goulard
, “
On catalytic recombination rates in hypersonic stagnation heat transfer
,”
J. Jet Propul.
28
,
737
745
(
1958
).
94.
S.
Lee
,
Y.
Yang
, and
J. G.
Kim
, “
Evaluation of Fay and Riddell formula under hypersonic flight conditions
,”
Int. J. Numer. Methods Heat Fluid Flow
33
,
14
41
(
2023
).
95.
S. J.
Fenster
, “
Stagnation-point heat transfer for a new binary air model including dissociation and ionization
,”
AIAA J.
3
,
2189
2196
(
1965
).
96.
K.
Sutton
and
R. A.
Graves
, Jr.
, “
A general stagnation-point convective heating equation for arbitrary gas mixtures
,” Technical Report No.
NASA-TR-R-376
(
NASA
,
1971
).
97.
I.
Armenise
,
M.
Barbato
,
M.
Capitelli
, and
C.
Gorse
, “
Surface recombination coefficients and boundary-layer hypersonic-flow calculations on different surfaces
,”
J. Spacecr. Rockets
41
,
310
313
(
2004
).
You do not currently have access to this content.