This study examines the collision dynamics of atom–atom, atom–molecule, and molecule–molecule interactions for O–O, N–N, O2–O, N2–N, O2–N, N2–O, O2–O2, N2–N2, and N2–O2 systems under thermal nonequilibrium conditions. Investigations are conducted from a molecular perspective using accurate O4, N4, and N2O2 ab initio potential energy surfaces and by performing Molecular Dynamics (MD) simulations. The scattering angle and collision cross sections for these systems are determined, forming the basis for better collision simulations. For molecular interactions, the effect of the vibrational energy on the collision cross section is shown to be significant, which in turn has a profound effect on nonequilibrium flows. In contrast, the effect of the rotational energy of the molecule is shown to have a negligible effect on the cross section. These MD-based cross sections provide a theoretically sound alternative to the existing collision models, which only consider the relative translational energy. The collision cross sections reported herein are used to calculate various transport properties, such as the viscosity coefficient, heat conductivity, and diffusion coefficients. The effect of internal energy on the collision cross sections reflects the dependence of these transport properties on the nonequilibrium degree. The Chapman–Enskog formulation is modified to calculate the transport properties as a function of the trans-rotational and vibrational temperatures, resulting in a two-temperature nonequilibrium model. The reported work is important for studying highly nonequilibrium flows, particularly hypersonic re-entry flows, using either particle methods or techniques based on the conservation laws.
REFERENCES
1.
S. K.
Stefanov
, “On the basic concepts of the direct simulation Monte Carlo method
,” Phys. Fluids
31
, 067104
(2019
).2.
R. S.
Myong
, A.
Karchani
, and O.
Ejtehadi
, “A review and perspective on a convergence analysis of the direct simulation Monte Carlo and solution verification
,” Phys. Fluids
31
, 066101
(2019
).3.
G. A.
Bird
, “Monte-Carlo simulation in an engineering context
,” Prog. Astronaut. Aeronaut.
74
, 239
–255
(1981
).4.
K.
Koura
and H.
Matsumoto
, “Variable soft sphere molecular model for inverse-power-law or Lennard-Jones potential
,” Phys. Fluids A
3
, 2459
–2465
(1991
).5.
H. A.
Hassan
and D. B.
Hash
, “A generalized hard-sphere model for Monte Carlo simulation
,” Phys. Fluids A
5
, 738
–744
(1993
).6.
J.
Fan
, “A generalized soft-sphere model for Monte Carlo simulation
,” Phys. Fluids
14
, 4399
–4405
(2002
).7.
H.
Matsumoto
and K.
Koura
, “Comparison of velocity distribution functions in an argon shock wave between experiments and Monte Carlo calculations for Lennard-Jones potential
,” Phys. Fluids A
3
, 3038
–3045
(1991
).8.
A.
Venkattraman
and A.
Alexeenko
, “DSMC collision model for the Lennard-Jones potential: Efficient algorithm and verification
,” in 42nd AIAA Thermophysics Conference
(AIAA
, 2011
), p. 3313
.9.
A.
Venkattraman
and A.
Alexeenko
, “Binary scattering model for Lennard-Jones potential: Transport coefficients and collision integrals for non-equilibrium gas flow simulations
,” Phys. Fluids
24
, 027101
(2012
).10.
F.
Sharipov
and J. L.
Strapasson
, “Direct simulation Monte Carlo method for an arbitrary intermolecular potential
,” Phys. Fluids
24
, 011703
(2012
).11.
F.
Sharipov
and F. C.
Dias
, “Ab initio simulation of planar shock waves
,” Comput. Fluids
150
, 115
–122
(2017
).12.
N.
Parsons
, D. A.
Levin
, A. C. T.
van Duin
, and T.
Zhu
, “Modeling of molecular nitrogen collisions and dissociation processes for direct simulation Monte Carlo
,” J. Chem. Phys.
141
, 234307
(2014
).13.
J. D.
Bender
, P.
Valentini
, I.
Nompelis
, Y.
Paukku
, Z.
Varga
, D. G.
Truhlar
, T.
Schwartzentruber
, and G. V.
Candler
, “An improved potential energy surface and multi-temperature quasiclassical trajectory calculations of N2 + N2 dissociation reactions
,” J. Chem. Phys.
143
, 054304
(2015
).14.
M.
Kulakhmetov
, M.
Gallis
, and A.
Alexeenko
, “Ab initio-informed maximum entropy modeling of rovibrational relaxation and state-specific dissociation with application to the O2 + O system
,” J. Chem. Phys.
144
, 174302
(2016
).15.
D. A.
Andrienko
and I. D.
Boyd
, “Rovibrational energy transfer and dissociation in O2-O collisions
,” J. Chem. Phys.
144
, 104301
(2016
).16.
W.
Lin
, R.
Meana-Pañeda
, Z.
Varga
, and D. G.
Truhlar
, “A quasiclassical trajectory study of the N2(X1Σ) + O(3P) → NO(X2Π) + N(4S) reaction
,” J. Chem. Phys.
144
, 234314
(2016
).17.
H.
Luo
, M.
Kulakhmetov
, and A.
Alexeenko
, “Ab initio state-specific N2 + O dissociation and exchange modeling for molecular simulations
,” J. Chem. Phys.
146
, 074303
(2017
).18.
J. G.
Kim
and I. D.
Boyd
, “Monte Carlo simulation of nitrogen dissociation based on state-resolved cross sections
,” Phys. Fluids
26
, 012006
(2014
).19.
E. V.
Kustova
and G. M.
Kremer
, “Influence of state-to-state vibrational distributions on transport coefficients of a single gas
,” AIP Conf. Proc.
1786
, 070002
(2016
).20.
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
).21.
H.
Luo
, A. A.
Alexeenko
, and S. O.
Macheret
, “Development of an impulsive model of dissociation in direct simulation Monte Carlo
,” Phys. Fluids
31
, 087105
(2019
).22.
T. K.
Mankodi
, U. V.
Bhandarkar
, and B. P.
Puranik
, “Dissociation cross sections for N2 + N → 3N and O2 + O → 3O using the QCT method
,” J. Chem. Phys.
146
, 204307
(2017
).23.
T. K.
Mankodi
, U. V.
Bhandarkar
, and B. P.
Puranik
, “Global potential energy surface of ground state singlet spin O4
,” J. Chem. Phys.
148
, 074305
(2018
).24.
T. K.
Mankodi
and R. S.
Myong
, “Quasi-classical trajectory-based non-equilibrium chemical reaction models for hypersonic air flows
,” Phys. Fluids
31
, 106102
(2019
).25.
T. K.
Mankodi
and R. S.
Myong
, “Erratum: Quasi-classical trajectory-based non-equilibrium chemical reaction models for hypersonic air flows [Phys. Fluids 31, 106102 (2019)]
,” Phys. Fluids
32
, 019901
(2020
).26.
J. H.
Chae
, T. K.
Mankodi
, S. M.
Choi
, and R. S.
Myong
, “Combined effects of thermal non-equilibrium and chemical reactions on hypersonic air flows around an orbital reentry vehicle
,” Int. J. Aeronaut. Space Sci.
(publishined online, 2019
).27.
R. M.
Berns
and A.
van der Avoird
, “N2-N2 interaction potential from ab initio calculations, with application to the structure of (N2)2
,” J. Chem. Phys.
72
, 6107
–6116
(1980
).28.
V.
Aquilanti
, M.
Bartolomei
, D.
Cappelletti
, E.
Carmona-Novillo
, and F.
Pirani
, “The N2-N2 system: An experimental potential energy surface and calculated rotovibrational levels of the molecular nitrogen dimer
,” J. Chem. Phys.
117
, 615
–627
(2002
).29.
R.
Hernández-Lamoneda
, M.
Bartolomei
, M. I.
Hernández
, J.
Campos-Martínez
, and F.
Dayou
, “Intermolecular potential of the O2–O2 dimer. An ab initio study and comparison with experiment
,” J. Phys. Chem. A
109
, 11587
–11595
(2005
).30.
A.
Scemama
, M.
Caffarel
, and A.
Ramírez-Solís
, “Bond breaking and bond making in tetraoxygen: Analysis of the O2(X3Σg−) + O2(X3Σg−) ⇆ O4 reaction using the electron pair localization function
,” J. Phys. Chem. A
113
, 9014
–9021
(2009
).31.
Y.
Paukku
, K. R.
Yang
, Z.
Varga
, G.
Song
, J. D.
Bender
, and D. G.
Truhlar
, “Potential energy surfaces of quintet and singlet O4
,” J. Chem. Phys.
147
, 034301
(2017
).32.
Y.
Paukku
, Z.
Varga
, and D. G.
Truhlar
, “Potential energy surface of triplet O4
,” J. Chem. Phys.
148
, 124314
(2018
).33.
Y.
Paukku
, K. R.
Yang
, Z.
Varga
, and D. G.
Truhlar
, “Global ab initio ground-state potential energy surface of N4
,” J. Chem. Phys.
139
, 044309
(2013
).34.
Z.
Varga
, R.
Meana-Pañeda
, G.
Song
, Y.
Paukku
, and D. G.
Truhlar
, “Potential energy surface of triplet N2O2
,” J. Chem. Phys.
144
, 024310
(2016
).35.
R. J.
Duchovic
, Y. L.
Volobuev
, G. C.
Lynch
, D. G.
Truhlar
, T. C.
Allison
, A. F.
Wagner
, B. C.
Garrett
, and J. C.
Corchado
, “POTLIB 2001: A potential energy surface library for chemical systems
,” Comput. Phys. Commun.
144
, 169
–187
(2002
).36.
M.
Karplus
, R. N.
Porter
, and R. D.
Sharma
, “Exchange reactions with activation energy. I. Simple barrier potential for (H, H2)
,” J. Chem. Phys.
43
, 3259
–3287
(1965
).37.
D. G.
Truhlar
and J. T.
Muckerman
, “Reactive scattering cross sections III: Quasiclassical and semiclassical methods
,” in Atom-Molecule Collision Theory: A Guide for the Experimentalist
, edited by R. B.
Bernstein
(Springer US
, Boston, MA
, 1979
), pp. 505
–566
.38.
W. G.
Vincenti
and C. H.
Kruger
, Introduction to Physical Gas Dynamics
(Wiley
, New York
, 1965
).39.
G. A.
Bird
, Molecular Gas Dynamics and the Direct Simulation of Gas Flows
(Clarendon
, 1994
).40.
R. A.
Svehla
, “Estimated viscosities and thermal conductivities of gases at high temperature
,” NASA Technical Report, R-132, 1962
.41.
T.
Ozawa
, “Improved chemistry models for DSMC simulations of ionized rarefied hypersonic flows
,” Ph.D. thesis, The Pennsylvania State University
, (2007
).42.
R. S.
Myong
, “A generalized hydrodynamic computational model for rarefied and microscale diatomic gas flows
,” J. Comput. Phys.
195
, 655
–676
(2004
).43.
S.
Singh
, A.
Karchani
, and R. S.
Myong
, “Non-equilibrium effects of diatomic and polyatomic gases on the shock-vortex interaction based on the second-order constitutive model of the Boltzmann-Curtiss equation
,” Phys. Fluids
30
, 016109
(2018
).44.
S.
Bhola
and T. K.
Sengupta
, “Roles of bulk viscosity on transonic shock-wave/boundary layer interaction
,” Phys. Fluids
31
, 096101
(2019
).45.
S.
Singh
, A.
Karchani
, K.
Sharma
, and R. S.
Myong
, “Topology of the second-order constitutive model based on the Boltzmann-Curtiss kinetic equation for diatomic and polyatomic gases
,” Phys. Fluids
32
, 026104
(2020
).46.
A.
Boushehri
, J.
Bzowski
, J.
Kestin
, and E.
Mason
, “Equilibrium and transport properties of eleven polyatomic gases at low density
,” J. Phys. Chem. Ref. Data
16
, 445
–466
(1987
).47.
C.
Wilke
, “A viscosity equation for gas mixtures
,” J. Chem. Phys.
18
, 517
–519
(1950
).48.
F. G.
Blottner
, M.
Johnson
, and M.
Ellis
, “Chemically reacting viscous flow program for multi-component gas mixtures
,” Technical Report SC-RR-70-754, Sandia National Laboratories
, Albuquerque, NM
, 1971
.49.
50.
G. V.
Candler
and I.
Nompelis
, “Computational fluid dynamics for atmospheric entry
,” Technical Report RTO-EN-AVT-162, Department of Aerospace Engineering and Mechanics, University of Minnesota
, Minneapolis
, 2009
.51.
B.
Armaly
and K.
Sutton
, “Viscosity of multicomponent partially ionized gas mixtures
,” in 15th Thermophysics Conference, Los Angeles, USA
(AIAA
, 1980
), p. 1495
.52.
G. E.
Palmer
and M. J.
Wright
, “Comparison of methods to compute high-temperature gas viscosity
,” J. Thermophys. Heat Transfer
17
, 232
–239
(2003
).53.
T.
Mankodi
, U.
Bhandarkar
, and B.
Puranik
, “Dissociation cross section for high energy O2–O2 collisions
,” J. Chem. Phys.
148
, 144305
(2018
).© 2020 Author(s).
2020
Author(s)
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