Analysis of Feed Gas Expansion in a High-Speed Rotating Cylinder

In this study we investigate the expansion of the feed gas from the feed nozzle into a strongly rotating gas at the pure diffusive region of the inner core in a high-speed rotating cylinder with the characteristic radial length scale equal to (ξ /A²) for peripheral speed (V_wall) in the range 450 to 700 m/sec, feed nozzle radius (R_nozzle) in the range 3 to 8 mm, expansion pressure ratio (P_o/P_∞ ) in the range 10 to 10⁵ , and  for pure UF₆ as well as for a mixture of UF₆ and Hydrogen Fluoride (HF: acts as a light gas) with HF concentration up to 60 mole % ((Pradhan & Kumaran, J. Fluid Mech., vol. 686, 2011, pp. 109-159); (Kumaran & Pradhan, J. Fluid Mech., vol. 753, 2014, pp. 307-359)).The feed gas expansion into the vacuum core is characterized by the formation of a barrel shock, and the boundary layer type flow is developed on the surface of the barrel shock. The analysis of the jet boundary is carried out with the estimation of important parameters like angular dependency of mass flux (ρV), the pressure on the jet boundary (P_∞ ), the initial longitudinal radius of curvature (R_CO), the centerline Mach number distribution (Ma_CL), and the ratio of sonic radius to nozzle exit radius (r*/R_nozzle). The analysis indicates that as the feed nozzle radius is increased from 3 to 8 mm, the pressure on the jet boundary increases monotonically, whereas, with the increase of feed nozzle radius, the ratio (R_CO / R_nozzle) initially decreases and finally saturates at a constant value. The thickness of the shock layer is also studied for the peripheral speed in the range 450 to 700 m/sec, and the result shows that with the increase of peripheral speed the shock layer becomes more and more thinner. At  (P/P_S) = 10, the thickness of the shock layer has decreased from 0.40278 mm to 0.16645 mm. Here, P_S is the pressure behind the barrel shock. An important finding is that with the increase of peripheral speed from 450 to 700 m/sec , the rate of efflux from the boundary layer increases, and at (X/R_nozzle) = 20, its normalized value ( ρV_γ (∞)/ρ_SV_γ,S (∞)) has increased from 0.4751 to 0.7392. Here, ρ_SV_γ,S (∞) indicates the properties behind the barrel shock.  It is also seen that with the increase of Reynolds number from 10^-4 to 10^3, the rate of efflux from the boundary layer decreases, and at  (X/R_nozzle) = 20,  its normalized  value ( ρV_γ (∞)/ρ_SV_γ,S (∞)) has decreased from 633.59  at  Re = 10^-4   to  0.2003 at Re = 10^3.