K. Alagusundaram

THREE-DIMENSIONAL, FINITE ELEMENT, HEAT TRANSFER MODEL OF TEMPERATURE DISTRIBUTION IN GRAIN STORAGE BINS

ABSTRACT A three-dimensional, heat conduction problem in cartesian coordinate system was solved using the finite element method for predicting the temperature distribution in grain storage bins. The program can handle linear and quadratic hexahedron elements with 1, 2, or 3 point Gauss quadrature in each plane. The model can simulate the temperatures in filled grain bins of any shape and at any location, if the hourly weather data (solar radiation, wind velocity, and ambient air temperature) for the location and the grain temperatures at the start of simulation are available. Other input data required for the model include the three dimensional grid data of a linear or quadratic hexahedron element, and the thermal properties of grain, bin wall material, soil and air. Temperatures predicted by the model were in very good agreement with the measured temperatures in two 5.56 m diameter bins containing rapeseed and barley, respectively, located near Winnipeg. Temperatures predicted by the model in 3.0 m and 4.0 m tall rapeseed bulks of various diameters were compared with the temperatures predicted by 2D finite difference and 3D finite difference models. The temperatures predicted by the 3D finite element model and the 3D finite difference model were nearly identical for different locations in the grain bulks. Three dimensional finite element model predicted higher temperatures by about 5 K to 15 K towards the south side of the bin than the north side, whereas 2D model predicted equal temperatures at these locations.

Thermal conductivity of bulk barley, lentils, and peas

ABSTRACT Thermal conductivities of bulk barley, lentils, and peas were determined using the line heat-source method. For each seed type, five moisture contents ranging from 9 to 23% and five temperatures ranging from -28 to +29** C were used. The thermal conductivities ranged from 0.169 to 0.232 W/(m*K) for barley, from 0.187 to 0.249 W/(m*K) for lentils, and from 0.187 to 0.257 W/(m»K) for peas. The thermal conductivities of all three seed types increased as the moisture content or temperature increased. Due to the formation of ice, the effects of moisture content and temperature on the thermal conductivities of high moisture seeds (>18%) at temperatures below 0** C were less than at other temperatures. The need for a standard procedure for calculating thermal conductivities of agricultural grains, using the line heat-source method, is demonstrated.

A THREE-DIMENSIONAL, ASYMMETRIC, AND TRANSIENT MODEL TO PREDICT GRAIN TEMPERATURES IN GRAIN STORAGE BINS

A three-dimensional, transient, combined model (headspace model + soil model + conduction model in bulk grain) was developed to predict grain temperatures in a granary. Different meshes (mesh refinement in the whole domain or at the boundary) including linear and hybrid (linear and quadratic) elements were used to simulate grain temperatures. Prediction accuracies of temperatures produced by the different meshes were compared, and the model was validated using measured temperatures in two flat bottom bins (3.76 m diameter and 5.5 m high filled with wheat up to 3 m) located side by side in the north-south orientation near Winnipeg, Manitoba. Grain temperatures predicted by the model were in close agreement with the measured temperatures throughout a 21-month test in the two bins. By using a hybrid element mesh (mesh refinement at the boundary), the mean, standard error, and maximum of the absolute difference between the measured and predicted temperatures in the south bin were 2.2°C, 0.4°C, and 7.0°C, respectively. The mean, standard error, and maximum of the absolute difference predicted by a linear element model (88 linear elements each layer) in the south bin were 2.1°C, 0.3°C, and 6.3°C, respectively. Including a headspace model improved the prediction accuracy of the conduction model at the top of the grain bulk. Mesh refinement only at the boundary produced a homogeneous distribution of errors in the whole domain; however, mesh refinement in the whole domain gave higher errors at the walls than at the center of the bins. Considering the increased computer time and slightly improved accuracy by mesh refinement at the boundary, a uniform mesh with mesh refinement in the whole domain was preferable for predicting grain temperatures in an entire grain bin.

Convective-diffusive Transport of Carbon Dioxide Through Stored-grain Bulks

A finite element model was developed to predict the convective-diffusive transport of introduced carbon dioxide (CO2) through stored-grain bulks. The CO2 concentrations predicted by the developed convective-diffusive model were compared with measured CO2 concentrations from three wheat-filled 1.42-m-diameter ¥ 1.37-m-tall bins. The bins were equipped with three different partially perforated floor openings (circular near the center, rectangular, and circular near the wall) to simulate true three-dimensional movement of CO2. Dry ice was used to create high CO2 concentrations in the wheat bulks. In the model, effective diffusivities in the longitudinal and lateral directions were used in place of a diffusion coefficient during the dry ice sublimation period and a diffusion coefficient was used thereafter. The effective diffusivities incorporated the effects of both the bulk movement caused by the dry ice sublimation and the diffusion caused by the concentration gradient. The predicted concentrations were close to the measured concentrations at 12 h and thereafter. In the initial sampling times, however, the errors were high (mean relative percent errors ranged from 30 to 60% in all the experiments). The need for additional data on the flow characteristics of CO2 through wheat bulks, CO2 sorption by wheat at low initial concentrations, and the effect of including the gravity term in the governing differential equation for accurate model predictions is discussed.

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.

Distribution of Introduced Carbon Dioxide Through Wheat Bulks Contained in Bolted-metal Bins

The distribution and maintenance of introduced carbon dioxide (CO2) gas were studied in three empty or wheat-filled bins of 5.56 m diameter. One bin had a 0.46-m-diameter ¥ 4.7-m-long circular aeration duct on the concrete floor, the second bin had a fully perforated floor, and the third bin had a concrete floor. The effects on CO2 distribution and maintenance of sealing various portions of the bin, the point of application, the amount and frequency of application, the mode of application of dry ice, and the grain surface left open or covered with polyvinylidene chloride (PVDC) sheet were determined. Irrespective of the point of application, the CO2 concentrations were greater in the bottom than the top portions of the grain bulk. Introducing dry ice on the grain surface resulted in greater CO2 concentrations in the top portions of the grain bulk than introducing it near the bottom. Placing insulated boxes filled with dry ice blocks on the grain surface was less labor intensive and maintained high levels of CO2 in the grain bulk for long durations. A new method of estimating retention efficiency (hr) is demonstrated. Due to uncontrollable leaks in the bin the hr was generally low.

Airflow Patterns Through Wheat, Barley, and Canola in Bins with Partially Perforated Floors— An Experimental Investigation

Experiments were conducted to study the airflow patterns during drying through wheat, barley, and canola stored in a 4.2-m diameter (13.6 ft) cylindrical steel bin with a fully perforated floor that was modified to give three different partially perforated floors (straight, cross, and square floor openings). To show the airflow patterns through the grains, iso-pressure and iso-traverse time lines were drawn across two different cross-sections of the bulk for each floor type. The zones of poor ventilation were the portions of the grain near the lower corners of the bin farthest from the floor opening in all three cases. The shapes of the ventilation fronts through wheat, barley, and Canola were almost the same across any given cross-section of the bulk and floor type. Based on the traverse time, calculated using the airflow resistance data from the literature, drying or cooling rates through barley were faster than through wheat and the drying or cooling rates through wheat were faster than canola.

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.

MEASUREMENT OF THERMAL PROPERTIES OF MUNG BEAN (VIGNA RADIATA)

The thermal properties of mung bean (Vigna radiata) are essential for designing postharvest handling equipment for mung bean processing. The specific heat, thermal conductivity, and thermal diffusivity of mung bean were determined as a function of moisture content and temperature. The specific heat and thermal conductivity were quantified using a specially built vacuum flask calorimeter and thermal conductivity probe, respectively. The specific heat was determined by mixing hot water with a sample maintained at lower temperature and incorporating graphical temperature-correction into the calculation. The thermal conductivity was determined by measuring the temperature response of the sample when heated with a line heat source. The thermal diffusivity was directly calculated from the specific heat and thermal conductivity data. The specific heat and thermal conductivity of mung bean increased linearly from 1.63 to 2.45 kJ kg-1 K-1 and from 0.092 to 0.141 W m-1 K-1, respectively, with the corresponding increase in moisture content from 9.9% to 18.3% w.b. and temperature from 10°C to 50°C. The thermal diffusivity of mung bean changed from 0.659 × 10-7 to 0.752 × 10-7 m2 s-1 with increase in moisture content and temperature. The thermal diffusivity increased with increase in moisture content and decreased with increase in temperature.