Journal of Molecular Modeling

, 25:333 | Cite as

Modeling and simulating of feed flow in a gas centrifuge using the Monte Carlo method to calculate the maximum separation power

  • Masoud Khajenoori
  • Ali Haghighi Asl
  • Jaber Safdari
  • Ali NorouziEmail author
Original Paper


Most of the gas enters into a small portion of the rotating cylinder by increasing the rotational speed in a rotating cylinder. Navier-Stokes equations were used to evaluate gas behavior in this area. In this paper, the mass source calculated by the DSMC method at the boundary of the two regions has been used in the Onsager-Pancake equation and finite difference method was used to solve this equation. One of the assumed flow functions taking into account the effects of the scoop and thermal driving is the Olander’s flow function. By combining the flow function that resulted from the Onsager-Pancake equation and the Olander’s flow function, a new flow function is suggested, that in addition to applying the effect of thermal and mechanical driving, the feed driving added to it with the DSMC method. The results obtained using this new flow function in the modified diffusion equation by Onsager-Cohen, showing the resulted optimal separation power from that in comparison to the Olander’s function occurs in a state where thermal driving is insignificant and scoop driving has increased. The effects of scoop drive have increased by increasing the feed value with the new flow function. Furthermore, the diffusion equations have been solved for 235UF6 and 238UF6 using the new flow function and it has been calculated the separation parameters.


Mass source Onsager-Pancake equation Flow function DSMC 



  1. 1.
    Cohen KP (1951) The theory of isotope separation as applied to large scale production of U235. McGraw-Hill, New YorkGoogle Scholar
  2. 2.
    Soubbaramayer BJ (1980) A numerical method for optimizing the gas flow in a centrifuge. Comput. Methods Appl. Mech. Eng. 24:165–185CrossRefGoogle Scholar
  3. 3.
    Cloutman LD, Gentry RA (1981) Numerical simulation of the countercurrent flow in a gas centrifuge. Los Alamos Scientific Laboratory Rep. LA-UR-81-1821, Los Alamos, NM.Google Scholar
  4. 4.
    Wood HG, Morton JB (1980) Onsager’s pancake approximation for the fluid dynamics of a gas centrifuge. J. Fluid Mech. 101:1–31CrossRefGoogle Scholar
  5. 5.
    Carrier GF, Maslen SH (1962) Flow phenomena in rapidly rotating systems. USAEC Rep. TID-18065Google Scholar
  6. 6.
    Wood HG (1983) Sanders G. Rotating compressible flows with internal sources and sinks. J Fluid Mech 127:299–313CrossRefGoogle Scholar
  7. 7.
    Gunzburger MD, Wood HG, Jordan JA (1984) A finite element method for gas centrifuge flow problems. J Sci Stat Comput 5(1):78–94CrossRefGoogle Scholar
  8. 8.
    Wood HG (1995) Analysis of feed effects on a single-stage gas centrifuge cascade. Sep. Sci. Technol. 30(13):2631–2657CrossRefGoogle Scholar
  9. 9.
    Zeng S, Wood HG (2015) Analytical solution of Onsager’s Pancake equation with mass sources and sinks. Sep. Sci. Technol. 50(4):611–617CrossRefGoogle Scholar
  10. 10.
    Kumaran V, Pradhan S (2014) The generalized Onsager model for a binary gas mixture. J. Fluid Mech. 753(1):307–359CrossRefGoogle Scholar
  11. 11.
    Bird GA (1994) Molecular gas dynamics and the direct simulation of gas flows. Clarendon, OxfordGoogle Scholar
  12. 12.
    Mohammadzadeh AR, Struchtrup H (2015) Velocity dependent Maxwell boundary conditions in DSMC. Int. J. Heat Mass Transf. 87(1):151–160CrossRefGoogle Scholar
  13. 13.
    Nanbu K (1980) Direct simulation scheme derived from the Boltzmann equation. I. Monocomponent gases. J. Phys. Soc. Jpn. 49(1):2042–2049CrossRefGoogle Scholar
  14. 14.
    Koura K (1990) A sensitive test for accuracy in evaluation of molecular collision number in the direct simulation Monte Carlo method. Phys. Fluids A 2(7):1287–1289CrossRefGoogle Scholar
  15. 15.
    Kulakarni NK, Shterev K, Stefanov SK (2015) Effects of finite distance between a pair of opposite transversal dimensions in microchannel configurations: DSMC analysis in transitional regime. Int. J. Heat Mass Transf. 85:568–576CrossRefGoogle Scholar
  16. 16.
    Tantos C, Valougeorgis D, Frezzotti A (2015) Conductive heat transfer in rarefied polyatomic gases confined between parallel plates via various kinetic models and the DSMC method. Int. J. Heat Mass Transf. 88:636–651CrossRefGoogle Scholar
  17. 17.
    Qazi Zade A, Ahmadzadegan A, Renksizbulut M (2012) A detailed comparison between Navier–Stokes and DSMC simulations of multicomponent gaseous flow in micro channels. Int. J. Heat Mass Transf. 55:4673–4681CrossRefGoogle Scholar
  18. 18.
    Tzeng PY, Liu MH (2005) Influence of number of simulated particles on DSMC modeling of micro-scale Rayleigh–Benard flows. Int. J. Heat Mass Transf. 48:2841–2855CrossRefGoogle Scholar
  19. 19.
    Wang M, Li Z (2006) Gas mixing in micro channels using the direct simulation Monte Carlo method. Int. J. Heat Mass Transf. 49:1696–1702CrossRefGoogle Scholar
  20. 20.
    Roblin P, Doneddu F (2001) Direct Monte-Carlo simulations in a gas centrifuge. Department des Precedes d’ Enrichissement.:196–170Google Scholar
  21. 21.
    Pradhan S, Kumaran V (2011) The generalized Onsager model for the secondary flow in a high-speed rotating cylinder. J. Fluid Mech. 686:140–142CrossRefGoogle Scholar
  22. 22.
    Olander DR (1981) The theory of uranium enrichment by the gas centrifuge. Prog. In Nucl. Ener. 8:1–33CrossRefGoogle Scholar
  23. 23.
    Wood HG, Mason TC, Soubbaramayer (1996) Multi-Isotope separation in a gas centrifuge using Onsager’s Pancake model. Sep. Sci. Technol. 31(9):1185–1213CrossRefGoogle Scholar
  24. 24.
    Olander DR (1972) Technical basis of the gas centrifuge. Adv. Nucl. Sci. Technol. 6:105–174CrossRefGoogle Scholar
  25. 25.
    Gunzburger MD, Wood HG (1982) A finite element method for the Onsager pancake equation. Comput. Methods Appl. Mech. Eng. 31(1):43–59CrossRefGoogle Scholar
  26. 26.
    Furry WH, Jones RC, Onsager L (1939) On the theory of isotope separation by thermal diffusion. Phys. Rev. 55(11):1083–1095CrossRefGoogle Scholar
  27. 27.
    Ursu I, Bogdan M, Balibanu F, Fitori P, Mihailescu G, Demco DE (1987) Intermolecular potentials from nuclear spin lattice relaxation in pure gases with octahedral symmetry. Mol. Phys. 60(6):1357–1366CrossRefGoogle Scholar
  28. 28.
    Gray CG (1968) On the theory of multipole interactions. Can. J. Phys. 46(2):135–139CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Masoud Khajenoori
    • 1
  • Ali Haghighi Asl
    • 1
  • Jaber Safdari
    • 2
  • Ali Norouzi
    • 2
    Email author
  1. 1.Faculty of Chemical, Gas and Petroleum EngineeringSemnan UniversitySemnanIran
  2. 2.Materials and Nuclear Fuel Research SchoolNuclear Science and Technology Research InstituteTehranIran

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