Linear stability and numerical analysis of vertical dense particulate flows in hydraulic conveying

We investigate the concentration instabilities that arise in vertical dense particulate flows during hydraulic conveying, where the widely used two-fluid model is employed. Results show that the system exhibits instability across a broad spectrum of controlling parameters. We also obtain a fully nonlinear transient numerical solution for the system by using the finite difference method. It is found that small disturbances transform into saturation waves with finite amplitudes when the nonlinear effect becomes dominant, which corresponds to plug flow or slug flow.