Modelling ecosystems in ventilated conical bottomed farm grain silos

Grain silos that have conical shaped bases to promote their ease of emptying are ubiquitous. Conical bottomed silos are widely used in Australia and in North America by farmers wishing to store their produce for prolonged periods of time. Such silos may be aerated to cool the grains and prevent moisture migration. To date, the design of such silos has been largely ad hoc because thorough experimentation is expensive and limitations in readily available computing power have prevented detailed analysis of the ecosystem contained within such inherently three-dimensional structures. This paper presents the differential equations that govern distributions of velocity, moisture and temperature in conical bottomed silos that contain peaked bulks of grain. The equations are solved by transforming the shape of the silo into a right cylinder with a flat top and base. An orthogonal mesh in the computational domain is then readily implemented to express the equations in finite difference form. The temperatures on the outer surface of the silo are calculated by using solar radiation and other climatic data. The mathematical model incorporates biological phenomena such as the respiration of grain, the population dynamics of three species and a total of four strains of stored products Coleoptera and the loss of viability of seeds. Expressions that relate to the rate of decay of chemical pesticides are also incorporated into the ecosystem model. Results of the research show that aeration of a small farm silo with ambient air results in improved storage conditions compared with those that obtain in unaerated silos. The work indicates that conditions on the west facing portion of the wall, which is subject to high solar radiation loads, are somewhat less favourable to insect population growth compared with that portion of the wall facing away from the equator. Importantly, it is shown that the traditional placement of aeration ducts in farm silos results in a very uneven air flow distribution, and consequently a very uneven cooling of the grains.