Airflow through beds of cereal grains

Abstract

The equations used to model the flow of air through beds of cereal grains become nonlinear when the resistance to flow is a function of the velocity of the air. An analytic solution to this problem is obtained for the case where the flow is predominantly in one direction. The problem is defined in terms of a parameter ε which for typical cereal grains has values in the range 0.02–1.0. A perturbation expansion in terms of ε is used to obtain a weakly nonlinear solution to the flow problem. The solution is valid for small ε and this corresponds to small grains and low air velocity. The solution is used to study the effect of the nonlinearity on the flow pattern. A numerical method is used to extend the solution to larger values of ε, and this confirms the general effect of the nonlinear term on the airflow pattern which was determined by the analytic solution.