Mathematical model for simulating headspace and grain temperatures in grain bins

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