Modelling juice flow in a shredded cane bed

摘要

A diffuser is essentially a porous bed of shredded sugarcane through which juice flows. Theory based on the equations attributed to Darcy for saturated flow and Richards for unsaturated flow predicts that the velocity of the flow through the bed depends on the distribution of the permeability in the bed. At steady state, a pressure profile is established within the bed so that the friction pressure loss exactly matches the gravitational pressure head. If the permeability in the bed is uniform then the theory predicts that the static pressure in the bed will be constant throughout the bed and will be equal to atmospheric pressure. A rectangular glass model diff user in which the lateral dispersion of the juice could be observed with a static cane bed was used to map the pressure distribution and flow through a bed. The results from pressure and flow distribution measurements were compared to theoretically derived results. The steady state pressure distribution that was measured verified the theoretical prediction that the static pressure would essentially be equal to atmospheric pressure. These results can form the basis for more complex models to predict the flow distribution within a full scale diffuser.