Dynamics of nonlinear concentration waves in fluidized beds: modelling, analysis and simulation
Fluidized beds; instabilities; waves; linear stability; numerical simulations
In this work, we investigate one-dimensional concentration waves that occur in fluidized beds, focusing mainly on liquid-solid beds. The full set of averaged equations of motion for the continuous phases is used, as well as closure relations for the stress tensors of the fluid and solid phases and the interaction force between the phases. A linear stability analysis in the wavenumber space is performed in order to obtain the dispersion relation and the growth rate of small disturbances to the state of homogeneous fluidization. The system of governing equations is numerically integrated. The temporal and spatial evolution of small amplitude sinusoidal instabilities is observed until they become fully nonlinear with large amplitudes. The simulations in short time are validated by comparing the wave amplitude with the values predicted by the linear stability analysis with the same physical parameters. A very good agreement is observed. The influence of the relevant physical parameters of the system such as the Froude and Reynolds numbers, the density ratio between the phases and the equilibrium concentration on the response of the bed to excitation is examined and discussed in this dissertation. Additionally, we identify with the present study several regimes of nonlinear concentration waves in a fluidized bed, such as steady state saturated waves, solitary waves and oscillation without any recognizable pattern, depending on the configuration of the system and the boundary conditions.