Analysis of Internal Flow Phenomena in a High Speed Rotating Cylinder Using Double Parabolic Axial Flow Model

In this study we investigate the internal flow phenomena in a high speed rotating cylinder using double parabolic axial flow model for wall pressure in the range 20 to 100 m-bar. These includes the quantitative estimation of the important process parameters L₀, L, m, and (F/L).Here, L₀ is the internal circulation rate at total reflux, L is the actual internal circulation rate, m = L/ L₀ is the internal circulation parameter, (F/L) is the internal reflux ratio, and F is the external feed flow rate. The radial profile of axial mass flux  (ρv_z) is specified as a function of radial scale height  ξ   ( ξ = A² (1 - ( r² / R_w² )),  A is the stratification parameter,  A = (( M_w V_θ ²) / (2 R_g T))^1/2, M_w is the molecular weight, V_θ   is the peripheral speed of the cylinder, R_g is the universal gas constant, and T is the uniform gas temperature)  by two parabolas. One parabola represents the flow downward in the region near the rotor wall, and the second one representing the upflow adjacent to the downflow. The feed gas introduced into the rotating cylinder is considered to be associated with the upflowing stream ((Pradhan & Kumaran, J. Fluid Mech., vol. 686, 2011, pp. 109-159); (Kumaran & Pradhan, J. Fluid Mech., vol. 753, 2014, pp. 307-359)). An important finding is that as the wall pressure is increased from 20 to 100 m-bar, there is a increase in L₀, L, and m. However, there are important differences. L₀ initially increases at a faster rate and then saturates at high wall pressure. On the other hand the parameters L and m increases monotonically with the wall pressure. The effect of feed flow rate on the parameters L₀, L, and m is also studied and the analysis indicates that as the feed flow rate is increased, the parameters L₀, L, and m increases, and the effect is significant at high wall pressure. The analysis also shows that as the average gas temperature is increased, the parameters L₀, L, and m increases, and the effect is more pronounced at high wall pressure. However, with the increase of wall pressure, the internal reflux ratio (F/L) decreases, initially at faster rate and then become constant at high wall pressure, which indicates that there is a strong coupling between the process parameters  L₀, L,  m, and (F/L), and the result also reveals that at high wall pressure (hence at high holdup) the separation process takes place under improved equilibrium condition.