E.A. Smith

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

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 ε = bνr/a, where νr is the velocity scale, is used in a perturbation analysis to examine the nonlinear effects of the resistance on the airflow. When ε = 0 the equations reduce to those for potential flow, while for small values of ε 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 + εp1 are close to the solution of the full nonlinear problem when ε 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 ε < 0.03 while for the first order solution p0 + εp1 the difference is less than 1% when ε < 0.1.

Modelling the Flow of Carbon Dioxide Through Beds of Cereal Grains

The insect population in grain stores can be kept under control by maintaining a high concentration of CO2 gas (greater than 35%) throughout the grain bed. In this paper the initial phase of this process is considered, where the gas is introduced into the bed. The flow of CO2 through the grain bulk is modelled as fluid flow in a porous medium and the effect of advection, dispersion, sorption and curvilinear isobars and streamlines are considered. An analytic solution to this problem is developed using perturbation expansions and the analysis is restricted to the dominant term in each expansion. In curvilinear flow, a useful variable is the traverse time; the time taken for the gas to travel from the inlet duct. It is shown that lines of constant traverse time are also lines of constant CO2 concentration throughout the grain bed except in the narrow region called the front, where the concentration gradient is large. For most grain stores the isobars have a negative curvature and in these situations the front moves more slowly than in uniform flow and the width of the front increases more rapidly as it travels through the grain bed. It is shown that sorption has an effect on the CO2 concentration in the air for some grains such as canola but not for others such as wheat.

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 e which for typical cereal grains has values in the range 0.02–1.0. A perturbation expansion in terms of e is used to obtain a weakly nonlinear solution to the flow problem. The solution is valid for small e 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 e, and this confirms the general effect of the nonlinear term on the airflow pattern which was determined by the analytic solution.

Simulation of Grain Drying in Bins with Partially Perforated Floors Part I: Isotraverse Lines

When grain is dried in storage bins, the drying front will be a curved surface if only part of the floor is perforated. A method is developed for simulating the drying of grain, in these three dimensional situations, when the drying air is at near-ambient temperatures. In this first part of this article, the hypothesis that the lines of constant air traverse time are the lines of constant moisture content is examined. It is shown that these lines are equal when the air and grain are close to thermal and moisture equilibrium. For near-ambient drying, much of the grain bed is close to equilibrium so the isotraverse lines will be the lines of constant moisture content. Inside the drying front, however, the grain is not in equilibrium with the air so the result is not valid there. But it is shown experimentally that the leading and trailing edges of the drying front are lines of constant traverse time.

Modeling the movement of fumigant gas within grain beds

The insect population in grain stores can be kept under control by maintaining a high concentration of CO2 gas throughout the grain bed. A method of calculating the distribution of the fumigant gas is useful for the design and management of grain storage systems. The equations that can be used to calculate this distribution are given, and they describe how the CO2 gas moves through a grain bin as a result of diffusion, gravity, and sorption. The equations are solved numerically, and the results are compared with experimental values. An analytic solution is given of a simplified version of the equations, and this is used to describe how the gas moves through the grain bed. It is shown that diffusion is the main process for most of the time that the gas is in the bin, and this can be used to estimate how the CO2 concentration changes with time.

Simulation of Grain Drying in Bins with Partially Perforated Floors Part II: Calculation of Moisture Content

It was shown in the first part of this article that lines of constant air traverse time indicate the approximate position of the drying front as the grain bed dries. This determines the position of the front but not the values of moisture content as the drying proceeds. In the second part, a method is developed for calculating the moisture content and temperature of the grain during drying. It is shown that the heat and mass transport along the streamlines dominates the drying process, with transport across the streamlines being negligible. Thus, drying can be simulated along individual streamlines and then the moisture content profile of the grain bed can be determined using isotraverse lines as lines of constant moisture content. The results of the simulation are compared with experimental results in which the air flow and moisture content are fully three dimensional.

CALCULATION AND LIMITATIONS OF TRAVERSE TIME IN DESIGNING FORCED VENTILATION SYSTEMS

Traverse time is the time taken for air (or a fumigant gas) to travel through a grain bed from the inlet to any point in the bed. This article analyzes the importance of traverse time in processes where gases are transported mainly by forced convection such as drying, heating, or cooling or where fumigants are initially dispersed by aeration. Traverse time gives insight into these processes; for example, in areas of the grain bin where the streamlines are straight, the grain temperature and the fumigant densities during aeration are constant along the lines of constant traverse time. Another result derived in this article is that transport across streamlines, by conduction or diffusion, is influenced by the curvature of the streamlines. If the streamlines are straight, then there is no such transport across streamlines, but the rate of transport across streamlines is larger in areas where the curvature is larger. It has been shown previously that lines of constant traverse time have the same shape as the drying front, but it is shown in this article that this is only true in areas where the curvature of the streamlines is not too large. The article also gives some insight into how lines of constant traverse time can be used in the design of systems that are dominated by forced convection.

Airflow and temperature distribution in two-dimensional drying bins

The design of a drying or cooling store aims to provide an even airflow distribution, when aerated, for preservation purposes. The airflow in some curved bottom bins are studied in this paper. The flow is modelled, using Darcys law. A generalized Schwarz-Christoffel transformation is employed to reduce the problem of computing streamlines and isobars of airflow to solving a single nonlinear equation for the flow angle along the wall. Corresponding to different bin shapes, a few computed streamlines and isobars of airflow are presented, showing the effect of changing bottom geometries on the air flow. Heat transfer in such bins is also investigated. Based on an analysis of the far field of airflow, finite-height bins are considered. Analytical solutions of the heat conduction equation in terms of streamlines and isobars are obtained.