Analysis of Scoop System in a Mechanically Driven Gas Centrifuge.

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. 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 exhibit less decelerating moment and generates a reduced amount of secondary radial flow ((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. 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. 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.