(363g) Analysis of Scoop System in a Mechanically Driven Gas Centrifuge

Author : Dr. Sahadev Pradhan

Affiliation : Chemical Technology Division, Bhabha Atomic Research Centre, Mumbai-400 085, India.

ABSTRACT:

In this study we investigate the performance of a stationary scoop system (scoop tip and its arm) in a mechanically driven gas centrifuge at wall Mach number Ma_wall in the range 4 to 8, wall pressure P_wall in the range 20 to 100 m-bar, scoop arm radius of curvature (extremity radius) R_roc in the range 5 to 30 mm, scoop wall gap d_wall in the range 5 to 20 mm, and slenderness ratio (major to minor axis) of the elliptic scoop in the range 1.2 to 6 [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]. The analytical model is formulated based on the steady state assumption where the accelerating moment exerted by the rotating wall and bottom end cap on the rotating gas contained in it, is balanced by the decelerating moment due to the aerodynamic resistance of the scoop tip and its arm, which allow us to evaluate the scoop plane Mach number as a function of wall Mach number with the parameter A Kn_axis. Here, Kn_axis is the Knudsen number at the axis of the rotating cylinder, and the factor “A”, characterized a particular scoop system (shape and size of the scoop tip and its arm). In a high speed rotating field we examine the stagnation to axis pressure ratio as a function of wall Mach number for different scoop systems and the result indicates that scoop system having smaller dimension exhibit higher pressure recovery with modest slow-down of the circumferential velocity of the rotating gas. An important finding is that the scoop arm with higher radius of curvature (tending towards more circular shape) exhibit less decelerating moment and generates a reduced amount of secondary radial flow. Therefore, in order to enhance the secondary radial flow towards the axis, which further excites the secondary axial flow, which could be very important for the centrifugal gas separation processes, scoop arm with lower radius of curvature (extremity radius) is preferred ((Pradhan & Kumaran, J. Fluid Mech., vol. 686, 2011, pp. 109-159); (Kumaran & Pradhan, J. Fluid Mech., vol. 753, 2014, pp. 307-359)). The analysis shows that with the increase of wall pressure from 20 to 100 m-bar the decelerating moment of the scoop-tip and its arm increases, which results more slow-down of the circumferential velocity of the rotating gas at the scoop plane. The analysis also indicates that at a given wall Mach number, scoop tip exhibit more decelerating moment compared to the scoop-arm having same dimensions, and with the increase of wall pressure the difference between them reduces. Therefore, the required magnitude of deceleration can be achieved at a given wall pressure through proper combination of the scoop tip and its arm dimension. The effective scoop arm length that provides most of the scoop arm deceleration, is estimated with respect to the total arm length, and the result shows that arm-profile of the effective length portion with various winged shape is an important design aspect while operating at high wall pressure.

Keywords: High-speed rotating flow, Scoop system, Analytical model, Accelerating and decelerating moments, Scoop plane Mach number.

References:

[1] PRADHAN, S. & KUMARAN, V. 2011 The generalized Onsager model for the secondary flow in a high-speed rotating cylinder. J. Fluid Mech. 686, 109.

[2] KUMARAN, V & PRADHAN, S. 2014 The generalized Onsager model for a binary gas mixture. J. Fluid Mech. 753, 307.

[3] WOOD, H.G. & MORTON, J.B. 1980 Onsager’s pancake approximation for the fluid dynamics of a gas centrifuge. J. Fluid Mech. 101, 1.

[4] WOOD, H. G. & SANDERS, G. 1983 Rotating compressible flows with internal sources and sinks. J. Fluid Mech. 127, 299.

[5] WOOD, H. G. & BABARSKY, R. J. 1992 Analysis of a rapidly rotating gas in a pie-shaped cylinder. J. Fluid Mech. 239, 249.

[6] OLANDER, D. R. 1981 The theory of uranium enrichment by the gas centrifuge. Prog. Nucl. Energy 8, 1.

[7] ZIPPE G. 1960 The development of short bowl ultracentrifuges, University of Virginia, Report no: EP-4420-101-600.

[8] Napolitano L. G., Monti R., Losito U.,Studio del sistema di estrazione del gas di un'ultracentrifuga, L'Aerotecnica Missili e Spazio n. 3, 1973.

[9] VINCENTI. 1967 Introduction to Physical Gas Dynamics. Wiley, New York.

[10] CHAPMAN, S. & COWLING, T. G. 1970 The Mathematical Theory of Non-Uniform Gases, 2nd edition. Cambridge, Cambridge University Press.