MATHEMATICAL MODEL FOR SIMULATING HEADSPACE AND GRAIN TEMPERATURES IN GRAIN BINS

Abstract

A computer simulation model for predicting temperatures of headspace air and the top meter of grain under bothnaturally and mechanically ventilated grain bin conditions is presented. Headspace air temperature was estimated usingenergy balances for the bin roof, exposed wall in the headspace, and headspace air exchange as a result of both natural andmechanical ventilation. Sub-models for estimating radiation (solar, sky, earth, and re-radiation) on bin roof and wall, andnatural ventilation of the headspace due to wind and thermal buoyancy forces were involved in the headspace air temperatureprediction model. Grain temperature was modeled by considering heat transfer due to conduction, natural convection causedby temperature differences between grain and ambient air, and convection due to forced air movement through grain duringaeration or mechanical ventilation of the headspace. The accuracy and validity of the model are discussed. Simulations wereconducted using 30 years of weather data for Minneapolis-St. Paul, Minnesota, and Lexington, Kentucky, for winter andsummer conditions. Sensitivity analyses for the effect of bin surface conditions (new and weathered galvanized steel, andblack- and white-colored steel bin surfaces) on the headspace air and grain temperatures were conducted. Headspace airchanges per hour and headspace air temperatures were calculated for 10 and 20 m diameter bins with various sizes of eavegap and roof vents, and for two bin surface conditions (new galvanized steel and white-colored bin surfaces). Regressionmodels to predict the number of air changes per hour in the headspace as a function of the ratio of headspace open area toheadspace volume were developed. For galvanized steel bin surfaces, increasing openings in the headspace to increasenatural ventilation reduced headspace air and grain temperatures. For white-colored bin surfaces, minimizing naturalventilation reduced headspace air and grain temperatures.