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Aerothermodynamics of a sphere in a monatomic gas based on ab initio interatomic potentials over a wide range of gas rarefaction: subsonic flows

Published online by Cambridge University Press:  03 December 2024

Felix Sharipov Open the ORCID record for Felix Sharipov [Opens in a new window]  and
Alexey N. Volkov
Felix Sharipov*
Affiliation:
Departamento de Física, Universidade Federal do Paraná, Caixa Postal 19044, Curitiba 81531-980, Brazil
Alexey N. Volkov
Affiliation:
Department of Mechanical Engineering, University of Alabama, 7th Avenue, Tuscaloosa, AL 35487, USA
*
†Email address for correspondence: [email protected]
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Abstract

Aerothermodynamic characteristics of a sphere in a subsonic flow are calculated over a broad range of gas rarefaction by the direct simulation Monte Carlo method based on ab initio interatomic potentials and Cercignani–Lampis surface scattering kernel. Calculations of the drag and average energy transfer coefficients are performed for various noble gases in the range of Mach number from 0.1 to 1. The obtained results point out that the influence of the interatomic potential is weak in subsonic flows. A comparison of the present results with a linear theory shows that the numerical solutions at Mach number equal to 0.1 are close to those obtained from the linearized kinetic equation in the transitional and free-molecular regimes. In the near-continuum flow regime, the difference between the present solution and the linear theory is significant. To reveal the effects of the gas–surface accommodation, a few sets of the tangential momentum and normal energy accommodation coefficients are considered in simulations. It is shown that the effect of the accommodation coefficients on the sphere drag is not trivial, and, for non-diffuse scattering, the drag coefficient can be either larger or smaller than that for diffuse scattering. The effect of the sphere temperature is also investigated and the calculated values of the average energy transfer coefficient are used to find the Stanton number, recovery factor and adiabatic surface temperature. The numerical results for the sphere drag and energy transfer are compared with the semi-empirical fitting equations known from the literature.

JFM classification

Rarefied Gas Flow: Rarefied Gas Flow Aerodynamics: Aerodynamics Low-Reynolds-number flows: Low-Reynolds-number flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 1000 , 10 December 2024 , A78
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Copyright
© The Author(s), 2024. Published by Cambridge University Press

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References

Aleksandrov, V.Y. & Fridlender, O.G. 2008 Slow gas motions and the negative drag of a strongly heated spherical particle. Fluid Dyn. 43 (3), 485–492.CrossRefGoogle Scholar
Aoki, K. & Sone, Y. 1987 Temperature field induced around a sphere in a uniform flow of a rarefied gas. Phys. Fluids 30 (7), 2286–2288.CrossRefGoogle Scholar
Aziz, R.A., Janzen, A.R. & Moldover, M.R. 1995 Ab-initio calculations for helium: a standard for transport property measurements. Phys. Rev. Lett. 74 (9), 1586–1589.CrossRefGoogle ScholarPubMed
Bailey, A.B. 1974 Sphere drag coefficient for subsonic speeds in continuum and free-molecule. J. Fluid Mech. 65, 401–410.CrossRefGoogle Scholar
Bailey, A.B. & Hiatt, J. 1971 Free-flight measurements of sphere drag at subsonic, transonic, supersonic, and hypersonic speeds for continuum, transition, and near-free-molecular flow conditions. Tech. Rep. AEDC-TR-70-291. Arnold Engineering Development Center Report.Google Scholar
Beresnev, S.A., Chernyak, V.G. & Fomyagin, G.A. 1990 Motion of a spherical-particle in a rarefied-gas. Part 2. Drag and thermal polarization. J. Fluid Mech. 219, 405–421.CrossRefGoogle Scholar
Bird, G.A. 1994 Molecular Gas Dynamics and the Direct Simulation of Gas Flows. Oxford University Press.CrossRefGoogle Scholar
Carlson, D.J. & Hoglund, R.F. 1964 Particle drag and heat transfer in rocket nozzles. AIAA J. 2, 1980–1984.CrossRefGoogle Scholar
Cencek, W., Przybytek, M., Komasa, J., Mehl, J.B., Jeziorski, B. & Szalewicz, K. 2012 Effects of adiabatic, relativistic, and quantum electrodynamics interactions on the pair potencial and thermophysical properties of helium. J. Chem. Phys. 136 (22), 224303.CrossRefGoogle Scholar
Cercignani, C. & Lampis, M. 1971 Kinetic model for gas-surface interaction. Transp. Theory Stat. Phys. 1, 101–114.CrossRefGoogle Scholar
Cercignani, C. & Lampis, M. 1972 Free molecular flow past a flat plate in the presence of a nontrivial gas-surface interaction. Z. Angew. Math. Phys. 23, 713–728.CrossRefGoogle Scholar
Cercignani, C., Pagani, C.D. & Bassanini, P. 1968 Flow of a rarefied gas past an axisymmetrical body. II. Case of a sphere. Phys. Fluids 11 (7), 1399–1403.CrossRefGoogle Scholar
Chen, B., Wang, B., Mao, F., Ke, B., Wen, J., Tian, R. & Lu, C. 2020 Review on separation mechanism of corrugated plate separator. Ann. Nucl. Energy 144, 107548.CrossRefGoogle Scholar
Davis, E.J. 1997 A history of single aerosol particle levitation. Aerosol Sci. Technol. 26, 212–254.CrossRefGoogle Scholar
Eckert, E.R.T. & Drake, R.W. 1959 Heat and Mass Transfer, 2nd edn. McGraw-Hill.Google Scholar
Filippov, A.V. & Rosner, D.E. 2000 Energy transfer between an aerosol particle and gas at high temperature ratios in the Knudesn transition regime. Intl J. Heat Mass Transfer 43, 127–138.CrossRefGoogle Scholar
Galkin, V.S., Kogan, M.N. & Fridlender, O.G. 1972 Flow past a strongly heated sphere by a gas with low Reynolds numbers. Z. Angew. Math. Mech. 36 (5), 829–833.CrossRefGoogle Scholar
Hellmann, R., Bich, E. & Vogel, E. 2008 Ab initio potential energy curve for the neon atom pair and thermophysical properties of the dilute neon gas. I. Neon-neon interatomic potential and rovibrational spectra. Mol. Phys. 106 (1), 133–140.CrossRefGoogle Scholar
Henderson, C.B. 1976 Drag coefficients of spheres in continuum and rarefied flows. AIAA J. 14 (6), 707–708.CrossRefGoogle Scholar
Jäger, B., Hellmann, R., Bich, E. & Vogel, E. 2016 State-of-the-art ab initio potential energy curve for the krypton atom pair and thermophysical properties of dilute krypton gas. J. Chem. Phys. 144, 114304.CrossRefGoogle ScholarPubMed
Joachain, J. 1975 Quantum Collision Theory. North-Holland.Google Scholar
Kalempa, D. & Sharipov, F. 2020 Drag and thermophoresis on a sphere in a rarefied gas based on the Cercignani-Lampis scattering model of gas-surface interaction. J. Fluid Mech. 900, A37.CrossRefGoogle Scholar
Kalempa, D. & Sharipov, F. 2022 Thermophoretic force on a sphere of arbitrary thermal conductivity in a rarefied gas. Vacuum 201, 111062.CrossRefGoogle Scholar
Kavanau, L.L. 1955 Heat transfer from spheres to a rarefied gas in subsonic flow. Trans. ASME 77, 617–623.Google Scholar
Kayang, K.W., Volkov, A.N., Zhilyaev, P.A. & Sharipov, F. 2023 The ab initio potential energy curves of atom pairs and transport properties of high-temperature vapors of Cu and Si and their mixtures with He, Ar, and Xe gases. Phys. Chem. Chem. Phys. 25, 4872–4898.CrossRefGoogle Scholar
Kim, Y.W. & Yoo, J.Y. 2012 Transport of solid particles in microfluidic channels. Opt. Lasers Engng 50 (1, SI), 87–98.CrossRefGoogle Scholar
Koshmarov, Y.A. & Svirshevskii, S.B. 1993 Aero- and Hydromechanics. Mashinostroenie.Google Scholar
Lima Bernardo, B.L., Moraes, F. & Rosas, A. 2013 Drag force experienced by a body moving through a rarefied gas. Chinese J. Phys. 51, 189–199.Google Scholar
Liu, F., Daun, K.J., Snelling, D.R. & Smallwood, G.J. 2006 Heat conduction from a spherical nano-particle: status of modeling heat conduction in laser-induced incandescence. Appl. Phys. B 88, 355–382.CrossRefGoogle Scholar
Loth, E., Tyler Daspit, J., Jeong, M., Nagata, T. & Nonomura, T. 2021 Supersonic and hypersonic drag coefficients for a sphere. AIAA J. 59 (8), 3261–3274.CrossRefGoogle Scholar
Loyalka, S.K. 1992 Motion of a sphere in a gas: numerical solution of the linearized Boltzmann equation. Phys. Fluids 4 (5), 1049–1056.CrossRefGoogle Scholar
Millikan, R.A. 1910 The isolation of an ion, a precision measurement of its charge, and the correction of stokes's law. Science 32, 436–448.CrossRefGoogle Scholar
Nelson, H.F. & Fields, J.C. 1996 Heat transfer in two-phase solid-rocket plumes. J. Spacecr. Rockets 33, 494–500.CrossRefGoogle Scholar
Oseen, C.W. 1910 Ueber die Stokessche Formel und die verwandte Aufgabe in der Hydrodynamik. Ark. Mat. Astron. Fys. 6 (29), 1–20.Google Scholar
Oseen, C.W. 1913 Uber den Giiltigkeitsbereich der Stokesschen Widerstandsformel. Ark. Mat., Astron. Fys. 9 (16), 1–15.Google Scholar
Roos, F.W. & Willmarth, W.W. 1971 Some experimental results on sphere and disk drag. AIAA J. 9, 285–291.CrossRefGoogle Scholar
Shakhov, E.M. 1968 Generalization of the Krook kinetic relaxation equation. Fluid Dyn. 3 (5), 95–96.CrossRefGoogle Scholar
Sharipov, F. 2012 a Benchmark problems in rarefied gas dynamics. Vacuum 86, SI (11), 1697–1700.CrossRefGoogle Scholar
Sharipov, F. 2012 b Power series expansion of the Boltzmann equation and reciprocal relations for non-linear irreversible phenomena. Phys. Rev. E 84 (6), 061137.CrossRefGoogle Scholar
Sharipov, F. 2016 Rarefied Gas Dynamics. Fundamentals for Research and Practice. Wiley-VCH.CrossRefGoogle Scholar
Sharipov, F. 2022 Direct simulation Monte Carlo method based on ab initio potential: recovery of transport coefficients of multi-component mixtures of noble gases. Phys. Fluids 34, 097114.CrossRefGoogle Scholar
Sharipov, F. & Bertoldo, G. 2006 Heat transfer through a rarefied gas confined between two coaxial cylinders with high radius ratio. J. Vac. Sci. Technol. A 24 (6), 2087–2093.CrossRefGoogle Scholar
Sharipov, F. & Moldover, M. 2016 Energy accommodation coefficient extracted from acoustic resonator experiments. J. Vac. Sci. Technol. A 34 (6), 061604.CrossRefGoogle ScholarPubMed
Sharipov, F. & Strapasson, J.L. 2012 Ab initio simulation of transport phenomena in rarefied gases. Phys. Rev. E 86 (3), 031130.CrossRefGoogle ScholarPubMed
Sharipov, F. & Volkov, A.N. 2022 Aerothermodynamics of a sphere in a monatomic gas based on ab initio interatomic potentials over a wide range of gas rarefaction: transonic, supersonic and hypersonic flows. J. Fluid Mech. 942, A17.CrossRefGoogle Scholar
Stokes, G.G. 1845 On the theories of the internal friction of fluids in motion and of the equilibrium and motion of elastic solids. Trans. Camb. Phil. Soc. 8, 287–319.Google Scholar
Stokes, G.G. 1851 On the effect of internal friction of fluids on the motion of pedulums. Trans. Camb. Phil. Soc. 9, 8–106.Google Scholar
Stokes, M.A., Khairallah, S.A., Volkov, A.N. & Rubenchik, A.M. 2022 Fundamental physics effects of background gas species and pressure on vapor plume structure and spatter entrainment in laser melting. Additive Manuf. 55, 102819.CrossRefGoogle Scholar
Taguchi, S. & Tsuji, T. 2022 Inversion of the transverse force on a spinning sphere moving in a rarefied gas. J. Fluid Mech. 933, A37.CrossRefGoogle Scholar
Takata, S., Sone, Y. & Aoki, K. 1993 Numerical analysis of a uniform flow of a rarefied gas past a sphere on the basis of the Boltzmann equation for hard-sphere molecules. Phys. Fluids A 5 (3), 716–737.CrossRefGoogle Scholar
Trott, W.M., Castaneda, J.N., Torczynski, J.R., Gallis, M.A. & Rader, D.J. 2011 An experimental assembly for precise measurement of thermal accommodation coefficients. Rev. Sci. Instrum. 82 (3), 035120.CrossRefGoogle ScholarPubMed
Volkov, A.N. 2009 Aerodynamic coefficients of a spinning sphere in rarefied-gas flow. Fluid Dyn. 44, 141–157.CrossRefGoogle Scholar
Volkov, A.N. 2011 Transitional flow of a rarefied gas over a spinning sphere. J. Fluid Mech. 683, 320–345.CrossRefGoogle Scholar
Volkov, A.N. & O'Conner, G.M. 2011 Parallel direct simulation Monte Carlo of two-phase gas-droplet laser plume expansion from the bottom of a cylindrical cavity into an ambient gas. In Computational Fluid Dynamics 2010 (ed. A. Kuzmin), pp. 105–112. Springer.CrossRefGoogle Scholar
Volkov, A.N. & Sharipov, F. 2017 Flow of a monatomic rarefied gas over a circular cylinder: calculations based on the ab initio potential method. Intl J. Heat Mass Transfer 114, 47–61.CrossRefGoogle Scholar
Volkov, A.N. & Stokes, M.A. 2024 Effects of nanoparticles on plasma shielding at pulsed laser ablation of metal targets. In Proc. of SPIE, Vol. 12939 (ed. C.R. Phipps & V.E. Gruzdev), p. 1293904. Society of Photo-Optical Instrumentation Engineers.CrossRefGoogle Scholar
Volkov, A.N., Tsirkunov, Y.M. & Oesterlé, B. 2005 Numerical simulation of a supersonic gas-solid flow over a blunt body: the role of inter-particle collisions and two-way coupling effects. Intl J. Multiphase Flow 31, 1244–1275.CrossRefGoogle Scholar
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