Journal of Nuclear Science, Engineering and Technology (JONSAT)
In cooperation with the Iranian Nuclear Society

Investigation of hydrodynamic parameters inside a gas centrifuge rotor in the presence of hydrogen fluoride and air light gases using DSMC and Boltzmann distribution function

Document Type : Research Paper

Authors

M. Khajenoori 1
A. Haghighi Asl 1
J. Safdari 2
A. Norouzi 2

1 Faculty of Chemical, Gas and Petroleum Engineering, Semnan University, P.O.Box:35131-19111, Semnan - Iran

2 Advanced Technology Company of Iran, AEOI, P.O.Box:14399-55431, Tehran - Iran

https://doi.org/10.24200/nst.2021.1176
Abstract
The Boltzmann equation which describes binary collisions between molecules is a very important equation in physics and fluid dynamics. Direct Monte Carlo simulation is one of the methods to solve the Boltzmann equation. The moisture can leak to the fluid pipelines in the various places of cascades so many times through the enrichment operations since the pressure of the most enrichment process units is less than the atmospheric pressure. It causes the solid uranium precipitation on the inner surfaces of rotor and HF production upon the reaction with UF6. In the present work, the effect of concentration and total pressure inside a hypothetical centrifuge for binary component conditions (ZUF6=0.97, ZHF=0.03), (ZUF6=0.93, ZHF=0.07), (ZUF6=0.9, ZHF=0.1), (ZUF6=0.85, ZHF=0.15), and three component conditions (ZUF6=0.9, ZHF=0.05, ZAir=0.05) and (ZUF6=0.8, ZHF=0.1, ZAir=0.1) have been investigated. The results have been compared with those of the Boltzmann distribution function. Moreover, increment in the amount of light gas along with UF6 results in the decrement of ρνz.

Highlights

1. M. Khajenoori, et al, Modeling and simulating of feed flow in a gas centrifuge using the Monte Carlo method to calculate the maximum separation power, Journal of Molecular Modeling, 25 (11), 333 (2019).

 

2. J. Safdari, A. Noroozi, R. Toumari, Parameters optimization of a counter-current cascade based on using a real coded genetic algorithm, Separation Science and Technology, 52(18), 2855-2862 (2017).

 

3. V.D. Borisevich, et al, On ideal and optimum cascades of gas centrifuges with variable overall separation factors, Chemical Engineering Science, 116,  465–472 (2014).

 

4. M. Benedict, Nuclear Chemical Engineering, Mcgraw-Hill Book Company, Second Edition, chapter 14 (1981).

 

5. H.G. Wood, J.B. Morton, Onsager’s pancake approximation for the fluid dynamics of a gas centrifuge, J. Fluid Mech. 101, 1–31 (1980).

 

6. K. Cohen, The Theory of Isotope Separation as Applied to the Large Scale Production of U235, 103-125 (1951).

 

7. Soubbaramayer, Centrifugation, Applied Physics, 35, 183-244 (1979).

 

8. D.R. Olander, The theory of uranium enrichment by the gas centrifuge, Progress in Nuclear Energy, 8(1), 1-33 (1981).

 

9. M.D. Gunzburger, H.G. Wood, A finite element method for the Onsager pancake equation, Computer methods in applied mechanics and engineering, 31(1), 43–59 (1982).

 

10. W. Jin, J. Ruud Van Ommen, C.R. Kleijn, Simulation of atomic layer deposition on nanoparticle agglomerates, Physics of Fluids, 212(1), 146-151 (2017).

 

11. M. Pfeiffer, M.H. Gorji, Adaptive particle–cell algorithm for Fokker–Planck based rarefied gas flow simulations, Physics of Fluids, 213(1), 1-8 (2017).

 

12. S. Pradhan, V. Kumaran, The generalized Onsager model for the secondary flow in a high-speed rotating cylinder, Journal of Fluid Mechanics, 686(1), 109–159 (2011).

 

13. M. Khajenoori, et al, Modeling gas-granular flow in molecular using the DSMC method and continuum regions by Onsager’s pancake equation with mass sources and sinks in a rotating cylinder, Granular Matter, 21(3), 63 (2019).

 

14. C. Tantos, D. Valougeorgis, A. Frezzotti, Conductive heat transfer in rarefied polyatomic gases confined between parallel plates via various kinetic models and the DSMC method, Int. J. Heat Mass Transfer, 88, 636–651 (2015).

 

15. G.A. Bird, The DSMC method, The University of Sydney, 208-211 (2013).

 

16. K.C. Tseng, et al, Simulations of subsonic vortex-shedding flow past a 2D vertical plate in the near-continuum regime by the parallelized DSMC code, Comp. Phys. Comm, 183(8), 1596-1608 (2012).

 

17. P. Barletta, COOL: A code for dynamic Monte Carlo simulation of molecular dynamics, Physics of Fluids, 183(2), 438-439 (2012).

 

18. P.S. Prasanth, J.K. Kakkassery, Molecular models for simulation of rarefied gas flows using direct simulation Monte Carlo method, Fluid Dynamics Research, 40(4), 233-252 (2008).

 

19. M. Wang, Z. Li, Gas mixing in micro channels using the direct simulation Monte Carlo methods, International Journal of Heat and Mass Transfer, 49, 1696–1702 (2005).

 

20. J-S. Wu, K-C. Tseng, Fu-Y Wu, Parallel three-dimensional DSMC method using mesh refinement and variable time-step scheme, Physics of Fluids, 162(1), 166-187 (2004).

 

21. P. Roblin, F. Doneddu, Rarified gas dynamics: 22nd International Symposium, 169 -173 (2001).

 

22. G.A. Bird, Molecular gas dynamics and the direct simulation of gas flows, Oxford University Press, New York, (1994).

 

23. R.D. Bundy, E.B. Munday, The Oak Ridge K-25 Site is managed by Martin Marietta Energy Systems, Inc. for the U.S. Department of energy, (1991).

 

24. E.R. Elsharkawy, A. Abdien, E.F. Salem, Risk assessment due to postulated accidental releases of UF6 and emergency preparedness to mitigate its consequences, International Journal Of Modern Engineering Research (IJMER), 6(9), 58-64 (2016).

 

25. H. Makihara, T. ITO, Centrifugal separation of uranium isotopes in presence of light gas, Journal of nuclear science and technology, 26(11), 1023-1037 (1989).

 

26. S.R. Auvil, A General Analysis of Gas Centrifugation with Emphasis on the Countercurrent Production Centrifuge, (1974).

 

27. H.G, Wood, T.C. Mason, Multi-Isotope Separation in a Gas Centrifuge Using Onsager's Pancake Model, Separation and Science Technology, 31(9), 1185-1213 (1996).

 

28. C. Cercignani, The Boltzmann equation and its applications, Lectures series in mathematics. 68, Berlin, New York, (1988).

 

29. G.J.M. Hagelaar, L.C. Pitchford, Solving the Boltzmann equation to obtain electron transport coefficients and rate coefficients for fluid models, Plasma Sources Sci. Technol. 14, 722–733 (2005).

Keywords

Boltzmann equation
Hydrogen fluoride
Gas centrifuge
DSMC
1. M. Khajenoori, et al, Modeling and simulating of feed flow in a gas centrifuge using the Monte Carlo method to calculate the maximum separation power, Journal of Molecular Modeling, 25 (11), 333 (2019).
 
2. J. Safdari, A. Noroozi, R. Toumari, Parameters optimization of a counter-current cascade based on using a real coded genetic algorithm, Separation Science and Technology, 52(18), 2855-2862 (2017).
 
3. V.D. Borisevich, et al, On ideal and optimum cascades of gas centrifuges with variable overall separation factors, Chemical Engineering Science, 116,  465–472 (2014).
 
4. M. Benedict, Nuclear Chemical Engineering, Mcgraw-Hill Book Company, Second Edition, chapter 14 (1981).
 
5. H.G. Wood, J.B. Morton, Onsager’s pancake approximation for the fluid dynamics of a gas centrifuge, J. Fluid Mech. 101, 1–31 (1980).
 
6. K. Cohen, The Theory of Isotope Separation as Applied to the Large Scale Production of U235, 103-125 (1951).
 
7. Soubbaramayer, Centrifugation, Applied Physics, 35, 183-244 (1979).
 
8. D.R. Olander, The theory of uranium enrichment by the gas centrifuge, Progress in Nuclear Energy, 8(1), 1-33 (1981).
 
9. M.D. Gunzburger, H.G. Wood, A finite element method for the Onsager pancake equation, Computer methods in applied mechanics and engineering, 31(1), 43–59 (1982).
 
10. W. Jin, J. Ruud Van Ommen, C.R. Kleijn, Simulation of atomic layer deposition on nanoparticle agglomerates, Physics of Fluids, 212(1), 146-151 (2017).
 
11. M. Pfeiffer, M.H. Gorji, Adaptive particle–cell algorithm for Fokker–Planck based rarefied gas flow simulations, Physics of Fluids, 213(1), 1-8 (2017).
 
12. S. Pradhan, V. Kumaran, The generalized Onsager model for the secondary flow in a high-speed rotating cylinder, Journal of Fluid Mechanics, 686(1), 109–159 (2011).
 
13. M. Khajenoori, et al, Modeling gas-granular flow in molecular using the DSMC method and continuum regions by Onsager’s pancake equation with mass sources and sinks in a rotating cylinder, Granular Matter, 21(3), 63 (2019).
 
14. C. Tantos, D. Valougeorgis, A. Frezzotti, Conductive heat transfer in rarefied polyatomic gases confined between parallel plates via various kinetic models and the DSMC method, Int. J. Heat Mass Transfer, 88, 636–651 (2015).
 
15. G.A. Bird, The DSMC method, The University of Sydney, 208-211 (2013).
 
16. K.C. Tseng, et al, Simulations of subsonic vortex-shedding flow past a 2D vertical plate in the near-continuum regime by the parallelized DSMC code, Comp. Phys. Comm, 183(8), 1596-1608 (2012).
 
17. P. Barletta, COOL: A code for dynamic Monte Carlo simulation of molecular dynamics, Physics of Fluids, 183(2), 438-439 (2012).
 
18. P.S. Prasanth, J.K. Kakkassery, Molecular models for simulation of rarefied gas flows using direct simulation Monte Carlo method, Fluid Dynamics Research, 40(4), 233-252 (2008).
 
19. M. Wang, Z. Li, Gas mixing in micro channels using the direct simulation Monte Carlo methods, International Journal of Heat and Mass Transfer, 49, 1696–1702 (2005).
 
20. J-S. Wu, K-C. Tseng, Fu-Y Wu, Parallel three-dimensional DSMC method using mesh refinement and variable time-step scheme, Physics of Fluids, 162(1), 166-187 (2004).
 
21. P. Roblin, F. Doneddu, Rarified gas dynamics: 22nd International Symposium, 169 -173 (2001).
 
22. G.A. Bird, Molecular gas dynamics and the direct simulation of gas flows, Oxford University Press, New York, (1994).
 
23. R.D. Bundy, E.B. Munday, The Oak Ridge K-25 Site is managed by Martin Marietta Energy Systems, Inc. for the U.S. Department of energy, (1991).
 
24. E.R. Elsharkawy, A. Abdien, E.F. Salem, Risk assessment due to postulated accidental releases of UF6 and emergency preparedness to mitigate its consequences, International Journal Of Modern Engineering Research (IJMER), 6(9), 58-64 (2016).
 
25. H. Makihara, T. ITO, Centrifugal separation of uranium isotopes in presence of light gas, Journal of nuclear science and technology, 26(11), 1023-1037 (1989).
 
26. S.R. Auvil, A General Analysis of Gas Centrifugation with Emphasis on the Countercurrent Production Centrifuge, (1974).
 
27. H.G, Wood, T.C. Mason, Multi-Isotope Separation in a Gas Centrifuge Using Onsager's Pancake Model, Separation and Science Technology, 31(9), 1185-1213 (1996).
 
28. C. Cercignani, The Boltzmann equation and its applications, Lectures series in mathematics. 68, Berlin, New York, (1988).
 
29. G.J.M. Hagelaar, L.C. Pitchford, Solving the Boltzmann equation to obtain electron transport coefficients and rate coefficients for fluid models, Plasma Sources Sci. Technol. 14, 722–733 (2005).
Journal of Nuclear Science, Engineering and Technology (JONSAT)
Volume 41, Issue 4 - Serial Number 94
December 2020
Pages 118-127

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