Decay of Mechanically Driven Axial Counter-Current in a High Speed Rotating Cylinder Using DSMC Simulations

The decay of mechanically driven axial counter-current along the axial direction in a high speed rotating cylinder is studied for wall pressure P_w in the range 20 to 100 m-bar using two dimensional Direct Simulation Monte Carlo (DSMC) simulations. The shape & magnitude of the radial-profile of the axial mass flux is investigated quantitatively at various axial locations and the axial-decay is characterized by a universal exponential function with varying exponent & pre-exponential factor based on the wall pressure and hence the hold up. The analysis shows that as the wall pressure is increased from 20 to 100 m-bar, the shift in the inversion point (corresponds to zero axial mass flux) along the axial length is significant ((Pradhan & Kumaran, J. Fluid Mech., vol. 686, 2011, pp. 109-159); (Kumaran & Pradhan, J. Fluid Mech., vol. 753, 2014, pp. 307-359)). The analysis further indicates that the decay of axial counter-current influences both the flow profile efficiency (E_F) and the circulation efficiency (E_C) to a great extent, and plays an important role in deciding the separation performance of the gas centrifuge machine. The DSMC simulation results are compared with the analytical results for the decay length based on Dirac equation of high speed approximation ( Z_D = (1/ 2η) (1/(4.82 A⁶)) ((P_wall M_W)/(R_g T)) (V_θ R²_wall ) [ 1 + (((γ-1) M_W V_θ²)/(4 γ R_g T))² ] ^1/2 , and found good agreement (error within 15%). Here, Z_D is the decay length, η is the gas viscosity, A is the stratification parameter A= (M_W V_θ²/(2 R_g T))^1/2, P_wall is the wall pressure, M_W is the molecular weight, R_g is the universal gas constant, T is the uniform gas temperature, V_θ is the peripheral velocity, R_wall is the radius of the cylinder, γ is the specific heat ratio (C_P/C_V), and the parameter B = (((γ-1) M_W V_θ²)/(4 γ R_g T)) represents the ratio of adiabatic force to angular momentum force.