Geodesic
Verification of software codes for simulation of unsteady flows in a gas centrifuge
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 53 (2013) no. 6, pp. 970-978 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

A simple semi-analytical solution is proposed for the problem of an unsteady gas flow in a gas centrifuge. The circulation in the centrifuge is driven by a source/sink of energy and by an external force (deceleration/acceleration of the gas rotation) acting on the gas at a given frequency. In the semi-analytical solution, the rotor is infinite, while the given forces vary harmonically with a given wave-length along the axial coordinate. As a result, the unsteady flow problem is reduced to a system of ordinary differential equations, which can be quickly solved to any prescribed accuracy. This problem is proposed for verifying numerical codes designed for the simulation of unsteady processes in gas centrifuges. A similar unsteady problem is solved numerically, in which case the cylinder is finite with the rotor length equal to the wavelength of the external force along the axis of rotation. The periodicity of the solution is set at end faces of the cylinder. As an example, the semi-analytical solution is compared with the numerical one obtained with these boundary conditions. The comparison confirms that the problem formulations are equivalent in both cases. 
@article{ZVMMF_2013_53_6_a10,
     author = {V. A. Abramov and S. V. Bogovalov and V. D. Borisevich and V. D. Borman and V. A. Kislov and V. N. Tronin and I. V. Tronin and S. V. Yupatov},
     title = {Verification of software codes for simulation of unsteady flows in a gas centrifuge},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {970--978},
     year = {2013},
     volume = {53},
     number = {6},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2013_53_6_a10/}
}
TY  - JOUR
AU  - V. A. Abramov
AU  - S. V. Bogovalov
AU  - V. D. Borisevich
AU  - V. D. Borman
AU  - V. A. Kislov
AU  - V. N. Tronin
AU  - I. V. Tronin
AU  - S. V. Yupatov
TI  - Verification of software codes for simulation of unsteady flows in a gas centrifuge
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2013
SP  - 970
EP  - 978
VL  - 53
IS  - 6
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2013_53_6_a10/
LA  - ru
ID  - ZVMMF_2013_53_6_a10
ER  - 
%0 Journal Article
%A V. A. Abramov
%A S. V. Bogovalov
%A V. D. Borisevich
%A V. D. Borman
%A V. A. Kislov
%A V. N. Tronin
%A I. V. Tronin
%A S. V. Yupatov
%T Verification of software codes for simulation of unsteady flows in a gas centrifuge
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2013
%P 970-978
%V 53
%N 6
%U http://geodesic.mathdoc.fr/item/ZVMMF_2013_53_6_a10/
%G ru
%F ZVMMF_2013_53_6_a10
V. A. Abramov; S. V. Bogovalov; V. D. Borisevich; V. D. Borman; V. A. Kislov; V. N. Tronin; I. V. Tronin; S. V. Yupatov. Verification of software codes for simulation of unsteady flows in a gas centrifuge. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 53 (2013) no. 6, pp. 970-978. http://geodesic.mathdoc.fr/item/ZVMMF_2013_53_6_a10/

[1] Borisevich V. D., Borman V. D., Sulaberidze G. A. i dr., Fizicheskie osnovy razdeleniya izotopov v gazovoi tsentrifuge, Izdatelskii dom MEI, 2011

[2] Wood H. G., Morton J. B., “Onsager pancake approximation for the fluid dynamics of a gas centrifuge”, J. Fluid Mech., 101 (1980), 1–31 | DOI | MR | Zbl

[3] Kai T., “Basic characteristics of centrifuges. IV: Analysis of separation performance of centrifuges”, J. Nucl. Sci. Technol., 14:7 (1977) | DOI

[4] Cloutman L. D., Gentry R. A., Numerical simulation of the countercurrent flow in a gas centrifuge, LA'8972' MC(UC22), DE83-013323, 1983

[5] Belotserkovskii O. M., Betelin V. B., Borisevich V. D. i dr., “K teorii protivotoka vo vraschayuschemsya vyazkom teploprovodnom gaze”, Zh. vychisl. matem. i matem. fiz., 51:2 (2011), 222–250 | Zbl

[6] Bogovalov S. V., Borisevich V. D., Borman V. D. et al., “Numerical simulation of an outflow through a 3D orifice in a rotating environment”, Proc. 11th Workshop on Separation Phenomena in Liquids and Gases (S.-Petersburg, June 13–18, 2010), 150–156

[7] Matsuda T., Sakurai T., Takeda H., “Source'sink flow in a gas centrifuge”, J. Fluid Mech., 69:01 (1975), 197–208 | DOI | Zbl

[8] Von Halle E., Wood H. G., Lowry R. A., “The effect of vacuum core boundary condition on separation in the gas centrifuge”, Nucl. Technol., 62 (1983), 325–334

[9] Landau L. D., Livshits E. M., Teoreticheskaya fizika, Uch. posob. dlya vuzov, V 10 t., v. 6, Gidrodinamika, Izd. 5-e, Fizmatlit, M., 2001

[10] C. Schwab, N. A. S. Rodrigues, H. G. Wood (eds.), Proceedings of the fifth workshop on separation phenomena in liquids and Gases (Iguassu Falls, Brazil, 1996)