Pressure and velocity of air during drying and storage of cereal grains

Abstract

A common method of drying cereal grains is to ventilate a large static mass of grain with an even flow of air at near ambient temperature. After the grain has been dried it is often stored in the same container and kept cool by aeration with a lower velocity of air than is used in drying. To analyse the airflow through this mass of grain a nonlinear momentum equation for flow through porous media is used where the resistance to flow is a + b ¦ν¦. This equation, together with the assumption that the air is incompressible, defines the problem which is solved numerically, using the finite element method, and the results compared with experimental values. The small parameter e = bν r /a, where ν r is the velocity scale, is used in a perturbation analysis to examine the nonlinear effects of the resistance on the airflow. When e = 0 the equations reduce to those for potential flow, while for small values of e there are first-order corrections to the pressure p1 and the stream function χ1. The nonlinear problem is simplified by changing to curvilinear coordinates (s, t) where s is constant on the potential flow isobars while t is constant on the streamlines. General conclusions are derived for p1 and χ1, for example that they depend on the curvature of the potential flow solution with a large curvature of the isobars leading to larger values of p1 and similarly for the streamlines. The potential flow solution p0 and the first order solution p0 + ep1 are close to the solution of the full nonlinear problem when e is small. To illustrate this for a typical grain storage problem, the solution p0 is shown to be very close to the finite element solution (with a difference of less than 1%) when e < 0.03 while for the first order solution p0 + ep1 the difference is less than 1% when e < 0.1.