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

Investigation of concentration variation of the components of a three-component gas mixtures in the radial and axial direction of a gas centrifuge machine under “total reflux flow” conditions by using the DSMC method

Document Type : Research Paper

Authors

S Yousefi Nasab
J Karimi- Sabet
J Safdari
A Norouzi
E Amini
https://doi.org/10.24200/nst.2019.1028
Abstract
In this paper, using a new combinatory meshing technique in the axisymmetric coordinate, a MCC-DSMC solver is introduced. Using this solver, the flow and the concentration variation inside a centrifuge machine in a rigid body rotation mode with the DSMC method for a variable hard sphere and a variable soft sphere models and for the mixing hydrogen, argon, and krypton gases are investigated. Our results are compared with the analytical solution. The results indicate that the two collision models are totally in agreement with each other, but the results have some differences with the analytical results obtained from the Boltzmann distribution function. The results show that the presence of the several gases with different molecular weights in a centrifuge shaped a multi-layered radial flow of gas inside the rotor, so that the heaviest gas in the area of the side wall of the rotor, the lightest gas in the region near the axis of the rotor and gases with the medium molecular mass were placed in a layer between them. Furthermore, the variation of the concentration for each component of the mixing gas in the axial direction is also investigated by the DSMC method, otherwise, that it is impossible to investigate it using the analytical solution of the Boltzmann distribution function.

Highlights

 

 

1. J. Safdari, A. Noroozi, R. Toumari,Parameters optimization of a counter-current cascade based on using a real coded genetic algorithm, J. Sep. Scie. Tech. 515, 44 (2017).

2. H. G, Wood, J. B. Morton, Onsager’s pancake approximation for the fluid dynamics of a gas centrifuge, J. Fluid Mech, 20, 299 (1980).

3. K. Cohen, The Theory of Isotope Seperation as Applied to the Large Scale Production of UTM, J. Sep. Scie. and Tech. 18, 103 (1951).

4. L. Soubbaramayer, centrifugation, J. App. Phys. 35,183 (1979).

5. W. Wagner, A  convergence  proof  for  Bird’s  direct  simulation  Monte Carlo  method for the Boltzmann equation, J. Stat. Phys. 66, 1011 (1992). 

6. G. A. Bird, Molecular Gas Dynamics and the Direct Simulation of Gas Flows, 2nd ed. (Clarendon, Oxford, 1994).

7. P. Roblin, F. Doneddu, in: AIP Conference Procceeding, Direct Monte-Carlo Simulations in a Gas Centrifuge (American Institute of Physics, 2001), pp.169-175.

8. M. Wang, Z. Li, Gas mixing in micro channels using the direct simulation Monte Carlo methods, Int. J. Heat and Mass Trans. 49, 1696 (2005).

9. N. Pourmahmoud, Rarefied Gas Flow Modeling inside Rotating Circular Cylinder,  American J. of Eng. Appl. Sci. 1 (1) 62 (2008).

10. G. A, Bird, The DSMC method, 1nd ed. (The University of Sydney, 2013).

11. J. Khadem, A. Abotalebi, Investigation of internal flow of mixture gases inside a rotating cylinder by direct simulation monte carlo, J. Inst. Mech. 51, 270 (2015).

12. S. Pradhan, V. Kumaran, The generalized Onsager model for the secondary flow in a high-speed rotating cylinder, J. Fluid Mech. 686, 140 )2011(.

13. S. Pradhan, in: Conference of Annual Meeting, The generalized Onsager model and DSMC simulations of high-speed rotating flow in a multiply connected domain, (San Francisco, 2016), pp. 1021-1068.

14. S.R. Auvil, A General Analysis of Gas Centrifugation with Emphasis on the Countercurrent Production Centrifuge, PhD Thesis, Chemical Engineering, Michigan State University, 1974.

15. M. Benedict, Nuclear Chemical Engineering, 2nd ed. (Mcgraw-Hill Book Company 1981).

Keywords

Multi-component gases
Gas centrifuge
Total reflux
DSMC method
 
 
1. J. Safdari, A. Noroozi, R. Toumari,Parameters optimization of a counter-current cascade based on using a real coded genetic algorithm, J. Sep. Scie. Tech. 515, 44 (2017).
2. H. G, Wood, J. B. Morton, Onsager’s pancake approximation for the fluid dynamics of a gas centrifuge, J. Fluid Mech, 20, 299 (1980).
3. K. Cohen, The Theory of Isotope Seperation as Applied to the Large Scale Production of UTM, J. Sep. Scie. and Tech. 18, 103 (1951).
4. L. Soubbaramayer, centrifugation, J. App. Phys. 35,183 (1979).
5. W. Wagner, A  convergence  proof  for  Bird’s  direct  simulation  Monte Carlo  method for the Boltzmann equation, J. Stat. Phys. 66, 1011 (1992). 
6. G. A. Bird, Molecular Gas Dynamics and the Direct Simulation of Gas Flows, 2nd ed. (Clarendon, Oxford, 1994).
7. P. Roblin, F. Doneddu, in: AIP Conference Procceeding, Direct Monte-Carlo Simulations in a Gas Centrifuge (American Institute of Physics, 2001), pp.169-175.
8. M. Wang, Z. Li, Gas mixing in micro channels using the direct simulation Monte Carlo methods, Int. J. Heat and Mass Trans. 49, 1696 (2005).
9. N. Pourmahmoud, Rarefied Gas Flow Modeling inside Rotating Circular Cylinder,  American J. of Eng. Appl. Sci. 1 (1) 62 (2008).
10. G. A, Bird, The DSMC method, 1nd ed. (The University of Sydney, 2013).
11. J. Khadem, A. Abotalebi, Investigation of internal flow of mixture gases inside a rotating cylinder by direct simulation monte carlo, J. Inst. Mech. 51, 270 (2015).
12. S. Pradhan, V. Kumaran, The generalized Onsager model for the secondary flow in a high-speed rotating cylinder, J. Fluid Mech. 686, 140 )2011(.
13. S. Pradhan, in: Conference of Annual Meeting, The generalized Onsager model and DSMC simulations of high-speed rotating flow in a multiply connected domain, (San Francisco, 2016), pp. 1021-1068.
14. S.R. Auvil, A General Analysis of Gas Centrifugation with Emphasis on the Countercurrent Production Centrifuge, PhD Thesis, Chemical Engineering, Michigan State University, 1974.
15. M. Benedict, Nuclear Chemical Engineering, 2nd ed. (Mcgraw-Hill Book Company 1981).

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