This article studies the mechanics of the N2–N2 collision process at temperatures up to 2000 K through an extensive set of classical trajectory calculations of binary collisions. It is found that key postcollision characteristics, namely, the deflection angle and the rotational–translational energy exchange rate, are significantly affected by precollision values of the rotational energies of the molecules, which is not addressed in commonly used collision models. On the macroscopic scale, such a behavior will lead to viscosity collision cross section and relaxation rate becoming dependent on both translational and rotational temperatures, as well as on the form of the nonequilibrium rotational energy distribution.
REFERENCES
1.
P.
Valentini
and T. E.
Schwartzentruber
, “Large-scale molecular dynamics simulations of normal shock waves in dilute argon
,” Phys. Fluids
21
, 066101
(2009
).2.
P.
Valentini
, P. A.
Tump
, C.
Zhang
, and T. E.
Schwartzentruber
, “Molecular dynamics simulations of shock waves in mixtures of noble gases
,” J. Thermophys. Heat Transfer
27
, 226
–234
(2013
).3.
G. A.
Bird
and J.
Brady
, Molecular Gas Dynamics and the Direct Simulation of Gas Flows
(Clarendon Press
, Oxford
, 1994
), Vol. 5.4.
J.
Struckmeier
and K.
Steiner
, “A comparison of simulation methods for rarefied gas flows
,” Phys. Fluids
7
, 2876
–2885
(1995
).5.
E. S.
Oran
, C. K.
Oh
, and B. Z.
Cybyk
, “Direct simulation Monte Carlo: Recent advances and applications
,” Annu. Rev. Fluid Mech.
30
, 403
–441
(1998
).6.
J. N.
Moss
and G. A.
Bird
, “Direct simulation of transitional flow for hypersonic reentry conditions
,” J. Spacecr. Rockets
40
, 830
–843
(2003
).7.
P.
Prasanth
and J. K.
Kakkassery
, “Direct simulation Monte Carlo (DSMC): A numerical method for transition-regime flows-A review
,” J. Indian Inst. Sci.
86
, 169
(2006
).8.
C.
Coletti
and G. D.
Billing
, “Vibrational energy transfer in molecular oxygen collisions
,” Chem. Phys. Lett.
356
, 14
–22
(2002
).9.
E.
Nagnibeda
and E.
Kustova
, Kinetic Theory of Transport and Relaxation Processes in Nonequilibrium Reacting Flows
(Saint-Petersburg University Press
, Russia
, 2003
).10.
E.
Nagnibeda
and E.
Kustova
, Non-equilibrium Reacting Gas Flows: Kinetic Theory of Transport and Relaxation Processes
(Springer Science & Business Media
, 2009
).11.
I. D.
Boyd
and E.
Josyula
, “State resolved vibrational relaxation modeling for strongly nonequilibrium flows
,” Phys. Fluids
23
, 057101
(2011
).12.
E. V.
Kustova
, “On the simplified state-to-state transport coefficients
,” Chem. Phys.
270
, 177
–195
(2001
).13.
Z.
Chavis
and R. G.
Wilmoth
, “Plume modeling and application to Mars 2001 Odyssey aerobraking
,” J. Spacecr. Rockets
42
, 450
–456
(2005
).14.
J.
Zhong
, T.
Ozawa
, and D. A.
Levin
, “Modeling of stardust reentry ablation flows in the near-continuum flight regime
,” AIAA J.
46
, 2568
–2581
(2008
).15.
I. D.
Boyd
, K. A.
Trumble
, and M. J.
Wright
, “Modeling of stardust entry at high altitude, part 1: Flowfield analysis
,” J. Spacecr. Rockets
47
, 708
–717
(2010
).16.
I. D.
Boyd
and P.
Jenniskens
, “Modeling of stardust entry at high altitude, part 2: Radiation analysis
,” J. Spacecr. Rockets
47
, 901
–909
(2010
).17.
T. E.
Schwartzentruber
and I. D.
Boyd
, “Progress and future prospects for particle-based simulation of hypersonic flow
,” Prog. Aerosp. Sci.
72
, 66
–79
(2015
).18.
P. W.
Erdman
, E. C.
Zipf
, P.
Espy
, C. L.
Howlett
, D. A.
Levin
, R. J.
Collins
, and G. V.
Candler
, “Measurements of ultraviolet radiation from a 5-km/s bow shock
,” J. Thermophys. Heat Transfer
8
, 441
–446
(1994
).19.
A. A.
Shevyrin
, Y. A.
Bondar
, S. T.
Kalashnikov
, V. I.
Khlybov
et al., “Direct simulation of rarefied high-enthalpy flow around the RAM C-II capsule
,” High Temp.
54
, 383
–389
(2016
).20.
J. N.
Moss
and G. A.
Bird
, “Direct simulation Monte Carlo simulations of hypersonic flows with shock interactions
,” AIAA J.
43
, 2565
–2573
(2005
).21.
C. H.
Kruger
and W.
Vincenti
, Introduction to Physical Gas Dynamics
(John Wiley & Sons
, 1965
).22.
R. C.
Millikan
and D. R.
White
, “Systematics of vibrational relaxation
,” J. Chem. Phys.
39
, 3209
–3213
(1963
).23.
P.
Valentini
, C.
Zhang
, and T. E.
Schwartzentruber
, “Molecular dynamics simulation of rotational relaxation in nitrogen: Implications for rotational collision number models
,” Phys. Fluids
24
, 106101
(2012
).24.
P.
Norman
, P.
Valentini
, and T.
Schwartzentruber
, “GPU-accelerated classical trajectory calculation direct simulation Monte Carlo applied to shock waves
,” J. Comput. Phys.
247
, 153
–167
(2013
).25.
M.
Panesi
, R. L.
Jaffe
, D. W.
Schwenke
, and T. E.
Magin
, “Rovibrational internal energy transfer and dissociation of N2(1Σg+) − N(4Su) system in hypersonic flows
,” J. Chem. Phys.
138
, 044312
(2013
).26.
M.
Panesi
, A.
Munafò
, T.
Magin
, and R.
Jaffe
, “Nonequilibrium shock-heated nitrogen flows using a rovibrational state-to-state method
,” Phys. Rev. E
90
, 013009
(2014
).27.
A.
Broc
, S.
De Benedictis
, G.
Dilecce
, M.
Vigliotti
, R. G.
Sharafutdinov
, and P. A.
Skovorodko
, “Experimental and numerical investigation of an O2/NO supersonic free jet expansion
,” J. Fluid Mech.
500
, 211
–237
(2004
).28.
A.
Naß
and E.
Steffens
, “Direct simulation of low-pressure supersonic gas expansions and its experimental verification
,” Nucl. Instrum. Methods Phys. Res., Sect. A
598
, 653
–666
(2009
).29.
H.
Laribou
, C.
Fressengeas
, D.
Entemeyer
, V.
Jeanclaude
, R.
Pesci
, and A.
Tazibt
, “Effects of the impact of a low temperature nitrogen jet on metallic surfaces
,” Proc. R. Soc. A
468
, 3601
–3619
(2012
).30.
P.
Skovorodko
, A.
Ramos
, G.
Tejeda
, J.
Fernández
, and S.
Montero
, “Experimental and numerical study of supersonic jets of N2, H2, and N2+H2 mixtures
,” AIP Conf. Proc.
1501
, 1228
–1235
(2012
).31.
J.
Lengrand
, V.
Prikhodko
, P.
Skovorodko
, I.
Yarygin
, and V.
Yarygin
, “Outflow of gas from nozzle with screen into vacuum
,” AIP Conf. Proc.
1084
, 1158
–1163
(2008
).32.
C.
Xie
, “Characteristics of micronozzle gas flows
,” Phys. Fluids
19
, 037102
(2007
).33.
M.
Darbandi
and E.
Roohi
, “Study of subsonic–supersonic gas flow through micro/nanoscale nozzles using unstructured DSMC solver
,” Microfluid. Nanofluid.
10
, 321
–335
(2011
).34.
F.
La Torre
, S.
Kenjereš
, J.-L.
Moerel
, and C. R.
Kleijn
, “Hybrid simulations of rarefied supersonic gas flows in micro-nozzles
,” Comput. Fluids
49
, 312
–322
(2011
).35.
M. M. J.
Opgenoord
and P. C.
Caplan
, “Aerodynamic design of the hyperloop concept
,” AIAA J.
56
, 4261
–4270
(2018
).36.
J.
Braun
, J.
Sousa
, and C.
Pekardan
, “Aerodynamic design and analysis of the hyperloop
,” AIAA J.
55
, 4053
–4060
(2017
).37.
Y.
Ben-Ami
and A.
Manela
, “Nonlinear thermal effects in unsteady shear flows of a rarefied gas
,” Phys. Rev. E
98
, 033121
(2018
).38.
J.-S.
Oh
, T.
Kang
, S.
Ham
, K.-S.
Lee
, Y.-J.
Jang
, H.-S.
Ryou
, and J.
Ryu
, “Numerical analysis of aerodynamic characteristics of hyperloop system
,” Energies
12
, 518
(2019
).39.
P.
Zhou
, J.
Zhang
, T.
Li
, and W.
Zhang
, “Numerical study on wave phenomena produced by the super high-speed evacuated tube maglev train
,” J. Wind Eng. Ind. Aerodyn.
190
, 61
–70
(2019
).40.
R.
Hruschka
and D.
Klatt
, “In-pipe aerodynamic characteristics of a projectile in comparison with free flight for transonic Mach numbers
,” Shock Waves
29
, 297
–306
(2019
).41.
K.
van Goeverden
, D.
Milakis
, M.
Janic
, and R.
Konings
, “Analysis and modelling of performances of the HL (Hyperloop) transport system
,” Eur. Transp. Res. Rev.
10
, 41
(2018
).42.
See https://hyperloop-one.com/ for Hyperloop webpage; accessed 25-11-2019.
43.
J. K.
Haviland
and M. L.
Lavin
, “Application of the Monte Carlo method to heat transfer in a rarefied gas
,” Phys. Fluids
5
, 1399
–1405
(1962
).44.
G.
Bird
, “Monte-Carlo simulation in an engineering context
,” Prog. Astronaut. Aeronaut.
74
, 239
–255
(1981
).45.
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
).46.
K.
Koura
and H.
Matsumoto
, “Variable soft sphere molecular model for air species
,” Phys. Fluids A
4
, 1083
–1085
(1992
).47.
H. A.
Hassan
and D. B.
Hash
, “A generalized hard-sphere model for Monte Carlo simulation
,” Phys. Fluids A
5
, 738
–744
(1993
).48.
J.
Fan
, “A generalized soft-sphere model for Monte Carlo simulation
,” Phys. Fluids
14
, 4399
–4405
(2002
).49.
C.
Borgnakke
and P. S.
Larsen
, “Statistical collision model for Monte Carlo simulation of polyatomic gas mixture
,” J. Comput. Phys.
18
, 405
–420
(1975
).50.
B. K.
Annis
and A. P.
Malinauskas
, “Temperature dependence of rotational collision numbers from thermal transpiration
,” J. Chem. Phys.
54
, 4763
–4768
(1971
).51.
R. N.
Healy
and T. S.
Storvick
, “Rotational collision number and Eucken factors from thermal transpiration measurements
,” J. Chem. Phys.
50
, 1419
–1427
(1969
).52.
E. H.
Carnevale
, C.
Carey
, and G.
Larson
, “Ultrasonic determination of rotational collision numbers and vibrational relaxation times of polyatomic gases at high temperatures
,” J. Chem. Phys.
47
, 2829
–2835
(1967
).53.
T. G.
Winter
and G. L.
Hill
, “High-temperature ultrasonic measurements of rotational relaxation in hydrogen, deuterium, nitrogen, and oxygen
,” J. Acoust. Soc. Am.
42
, 848
–858
(1967
).54.
J. G.
Parker
, “Rotational and vibrational relaxation in diatomic gases
,” Phys. Fluids
2
, 449
–462
(1959
).55.
I. D.
Boyd
, “Analysis of rotational nonequilibrium in standing shock waves of nitrogen
,” AIAA J.
28
, 1997
–1999
(1990
).56.
I. D.
Boyd
, “Rotational-translational energy transfer in rarefied nonequilibrium flows
,” Phys. Fluids A
2
, 447
–452
(1990
).57.
I. D.
Boyd
, “Relaxation of discrete rotational energy distributions using a Monte Carlo method
,” Phys. Fluids A
5
, 2278
–2286
(1993
).58.
I. D.
Boyd
, “Temperature dependence of rotational relaxation in shock waves of nitrogen
,” J. Fluid Mech.
246
, 343
–360
(1993
).59.
J. A.
Lordi
and R. E.
Mates
, “Rotational relaxation in nonpolar diatomic gases
,” Phys. Fluids
13
, 291
–308
(1970
).60.
C. A.
Brau
and R. M.
Jonkman
, “Classical theory of rotational relaxation in diatomic gases
,” J. Chem. Phys.
52
, 477
–484
(1970
).61.
C.
Zhang
, P.
Valentini
, and T. E.
Schwartzentruber
, “Nonequilibrium-direction-dependent rotational energy model for use in continuum and stochastic molecular simulation
,” AIAA J.
52
, 604
–617
(2014
).62.
K.
Koura
, “Statistical inelastic cross-section model for the Monte Carlo simulation of molecules with discrete internal energy
,” Phys. Fluids A
4
, 1782
–1788
(1992
).63.
K.
Koura
, “Statistical inelastic cross-section model for the Monte Carlo simulation of molecules with continuous internal energy
,” Phys. Fluids A
5
, 778
–780
(1993
).64.
F.
Robben
and L.
Talbot
, “Experimental study of the rotational distribution function of nitrogen in a shock wave
,” Phys. Fluids
9
, 653
–662
(1966
).65.
R. B.
Smith
, “Electron-beam investigation of a hypersonic shock wave in nitrogen
,” Phys. Fluids
15
, 1010
–1017
(1972
).66.
T.
Tokumasu
and Y.
Matsumoto
, “Dynamic molecular collision (DMC) model for rarefied gas flow simulations by the DSMC method
,” Phys. Fluids
11
, 1907
–1920
(1999
).67.
J. I.
Steinfeld
, P.
Ruttenberg
, G.
Millot
, G.
Fanjoux
, and B.
Lavorel
, “Scaling laws for inelastic collision processes in diatomic molecules
,” J. Phys. Chem.
95
, 9638
–9647
(1991
).68.
I. J.
Wysong
and D. C.
Wadsworth
, “Assessment of direct simulation Monte Carlo phenomenological rotational relaxation models
,” Phys. Fluids
10
, 2983
–2994
(1998
).69.
V.
Kosyanchuk
, “Results of N2-N2 collisions simulated using Molecular Dynamics for temperature up to 2000 K
,” Harvard Dataverse, V1
(2019
).70.
A.
van der Avoird
, P. E. S.
Wormer
, and A. P. J.
Jansen
, “An improved intermolecular potential for nitrogen
,” J. Chem. Phys.
84
, 1629
–1635
(1986
).71.
D.
McQuarrie
and J.
Simon
, Physical Chemistry: A Molecular Approach
(University Science Books
, Sausalito, CA
, 1997
), Vol. 1.72.
D.
Frenkel
and B.
Smit
, Understanding Molecular Simulation: From Algorithms to Applications
(Elsevier
, 2001
), Vol. 1.73.
A.
Riganelli
, F. V.
Prudente
, and A. J. C.
Varandas
, “On the rovibrational partition function of molecular hydrogen at high temperatures
,” J. Phys. Chem. A
105
, 9518
–9521
(2001
).74.
P.
Valentini
, P.
Norman
, C.
Zhang
, and T. E.
Schwartzentruber
, “Rovibrational coupling in molecular nitrogen at high temperature: An atomic-level study
,” Phys. Fluids
26
, 056103
(2014
).75.
A.
Yakunchikov
, “Potential energy surface of interaction of two diatomic molecules for air flows simulation
,” Harvard Dataverse, V3
(2019
).76.
M. S. H.
Ling
and M.
Rigby
, “Towards an intermolecular potential for nitrogen
,” Mol. Phys.
51
, 855
–882
(1984
).77.
T. E.
Schwartzentruber
, M. S.
Grover
, and P.
Valentini
, “Direct molecular simulation of nonequilibrium dilute gases
,” J. Thermophys. Heat Transfer
32
, 892
–903
(2017
).78.
V. Y.
Rudyak
and E. V.
Lezhnev
, “Stochastic algorithm for simulating gas transport coefficients
,” J. Comput. Phys.
355
, 95
–103
(2018
).79.
M. H.
Karimi-Jafari
and M.
Ashouri
, “Quantifying the anisotropy of intermolecular potential energy surfaces: A critical assessment of available N2-N2 potentials
,” Phys. Chem. Chem. Phys.
13
, 9887
–9894
(2011
).80.
A.
Yakunchikov
, V.
Kosiantchouk
, A.
Kroupnov
, M.
Pogosbekian
, I.
Bryukhanov
, and A.
Iuldasheva
, “Potential energy surface of interaction of two diatomic molecules for air flows simulation at intermediate temperatures
,” Chem. Phys.
536
, 110850
(2020
).81.
E. V.
Kustova
and G. M.
Kremer
, “Effect of molecular diameters on state-to-state transport properties: The shear viscosity coefficient
,” Chem. Phys. Lett.
636
, 84
–89
(2015
).82.
A.
Yakunchikov
and V.
Kosyanchuk
, “Application of event-driven molecular dynamics approach to rarefied gas dynamics problems
,” Comput. Fluids
170
, 121
–127
(2018
).83.
A.
Donev
, A. L.
Garcia
, and B. J.
Alder
, “Stochastic event-driven molecular dynamics
,” J. Comput. Phys.
227
, 2644
–2665
(2008
).84.
P.
Valentini
and T. E.
Schwartzentruber
, “A combined event-driven/time-driven molecular dynamics algorithm for the simulation of shock waves in rarefied gases
,” J. Comput. Phys.
228
, 8766
–8778
(2009
).85.
F.
Sharipov
, L. M. G.
Cumin
, and D.
Kalempa
, “Heat flux between parallel plates through a binary gaseous mixture over the whole range of the knudsen number
,” Physica A
378
, 183
–193
(2007
).86.
F.
Sharipov
and V. J.
Benites
, “Transport coefficients of helium-neon mixtures at low density computed from ab initio potentials
,” J. Chem. Phys.
147
, 224302
(2017
).87.
V. V.
Voevodin
, A. S.
Antonov
, D. A.
Nikitenko
, P. A.
Shvets
, S. I.
Sobolev
, I. Y.
Sidorov
, K. S.
Stefanov
, V. V.
Voevodin
, and S. A.
Zhumatiy
, “Supercomputer Lomonosov-2: Large scale, deep monitoring and fine analytics for the user community
,” Supercomput. Front. Innovations
6
, 4
–11
(2019
).© 2020 Author(s).
2020
Author(s)
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