Mathematical Modelling of Grain Drying in Counter-flow Beds: Investigation of Crossover of Air and Grain Temperatures

Abstract

Under the conditions of low airflow and warm inlet grain, such as can occur within mixed-flow grain dryers, a mathematical model of a counter-flow drying bed predicted a depression of both air and grain temperatures below their inlet values and crossover i.e. a change of sign of the grain-to-air temperature difference. The counter-flow model comprised unsteady-state drying equations formulated for a bed of grain and solved by an Euler procedure, together with an algorithm to simulate the movement of the bed. As this behaviour was unexpected, two other counter-flow programmes were developed to test the predictions of the first. The second programme solved the unsteady-state equations with an improved Euler plus fourth-order Runge-Kutta method. The third used steady-state equations solved by finite difference with deferred correction allied to a Newton iteration, and with a continuation parameter applied to mass transfer rate or to the airflow. Both new programmes predicted the crossover effect, and the steady-state simulation programme developed had convergence properties better than those reported previously in the literature. Validation of the effect was performed in a bench-scale counter-flow dryer, under appropriate experimental conditions selected using the simulation model. Under conditions where convective heat transfer was low but a relatively large driving force existed for mass transfer from grain to air, the grain experienced rapid evaporative cooling. This caused a depression of the air temperature below the inlet grain temperature, which lead to crossover of the air and grain temperatures within the bed. The work has demonstrated that the predictions of the original routine, although by a simple numerical method, were substantially correct. Although the phenomenon was not thought to be of great practical significance, its resolution reinforced confidence in the ability of the models to predict grain temperature accurately for the purposes of calculating the effects of drying on grain quality.