MATHEMATICAL SIMULATION OF TEMPERATURE AND MOISTURE FIELDS WITHIN A GRAIN KERNEL DURING DRYING

ABSTRACT

Non-linear partial differential equations are presented for two dimensional heat and mass transfer within a single grain kernel during drying. In this model, the moisture evaporation inside the kernel is considered. The moisture is assumed to diffuse to the outer boundary of the kernel in liquid form and evaporate on the surface of the kernel. The influence of temperature and moisture content on grain properties is also considered in the simulation. The Non-linear partial differential equations are solved using the finite element method and simulation data is verified on a thin layer dryer for wheat kernels. The comparison shows that the simulated results have a high accuracy with average relative error of about 5%. The results of the finite element analysis can be used for grain quality evaluation, drying simulation studies and stress analysis of grain kernel.     

MATHEMATICAL SIMULATION OF STRESSES WITHIN A CORN KERNEL DURING DRYING

ABSTRACT

Thermal stress and hydro stress within a single com kernel during drying are analysed with the mechanics of elasticity and material. The mathematical model of the stress within a single com kernel during drying is given. A finite element method is developed in details to simulate the maximum principal stress and shear stress within a single com at 75^°C and 50^°C drying air temperatures. The locations of the predicted maximum stresses are described and stress fields at different drying time are obtained. The result shows that the predicted locations of the maximum stresses agree with published materials on stress-crack or burst of com kernels.     

MATHEMATICAL SIMULATION OF STRESSES WITHIN A CORN KERNEL DURING DRYING

Thermal stress and hydro stress within a single com kernel during drying are analysed with the mechanics of elasticity and material. The mathematical model of the stress within a single com kernel during drying is given. A finite element method is developed in details to simulate the maximum principal stress and shear stress within a single com at 75^°C and 50^°C drying air temperatures. The locations of the predicted maximum stresses are described and stress fields at different drying time are obtained. The result shows that the predicted locations of the maximum stresses agree with published materials on stress-crack or burst of com kernels.     

SIMULATION OF THE HEAT AND MOISTURE TRANSFER PROCESS DURING DRYING IN DEEP GRAIN BEDS

Grain drying is a simultaneous heat and moisture transfer problem. The modelling of such a problem is of significance in understanding and controlling the drying process. In the present study, a mathematical model for coupled heat and moisture transfer problem is presented. The model consists of four partial differential equations for mass balance, heat balance, heat transfer and drying rate. A simple finite difference method is used to solve the equations. The method shows good flexibility in choosing time and space steps which enable the simulation of long term grain drying/cooling processes. A deep barley bed is used as an example of grain beds in the current simulation. The results are verified against experimental data taken from literature. The analysis of the effects of operating conditions on the temperature and moisture content within the bed is also carried out     

SIMULATION OF THE HEAT AND MOISTURE TRANSFER PROCESS DURING DRYING IN DEEP GRAIN BEDS

ABSTRACT

Grain drying is a simultaneous heat and moisture transfer problem. The modelling of such a problem is of significance in understanding and controlling the drying process. In the present study, a mathematical model for coupled heat and moisture transfer problem is presented. The model consists of four partial differential equations for mass balance, heat balance, heat transfer and drying rate. A simple finite difference method is used to solve the equations. The method shows good flexibility in choosing time and space steps which enable the simulation of long term grain drying/cooling processes. A deep barley bed is used as an example of grain beds in the current simulation. The results are verified against experimental data taken from literature. The analysis of the effects of operating conditions on the temperature and moisture content within the bed is also carried out     

TEMPERATURE AND MOISTURE CHANGES DURING MICROWAVE DRYING OF SLICED FOOD

Microwave drying characteristics of sliced foods were investigated using potatoes (Solarium tuberosum) as a test model. Sliced samples were dried to 7-10% moisture content at microwave power levels between 2.2 W/g and 3.6 W/g (raw material). Moisture and temperature changes during drying were monitored. Semi-empirical models were developed that followed temperature and moisture changes during microwave drying. Sliced potatoes experienced three distinct periods: a warming-up period with little removal of moisture; a constant temperature period in which most of the drying took place; and a heating up period in which the drying rate decreased and sample temperature increased rapidly, often causing partial charring. Product temperature during the second period of microwave drying increased with sample thickness and microwave power. Drying rates were not affected by slice thickness, but increased with the microwave power/mass ratio. Product charring towards the end of drying may be avoided by reducing microwave power and increasing ambient air velocity.     

TEMPERATURE AND MOISTURE CHANGES DURING MICROWAVE DRYING OF SLICED FOOD

ABSTRACT

Microwave drying characteristics of sliced foods were investigated using potatoes (Solarium tuberosum) as a test model. Sliced samples were dried to 7-10% moisture content at microwave power levels between 2.2 W/g and 3.6 W/g (raw material). Moisture and temperature changes during drying were monitored. Semi-empirical models were developed that followed temperature and moisture changes during microwave drying. Sliced potatoes experienced three distinct periods: a warming-up period with little removal of moisture; a constant temperature period in which most of the drying took place; and a heating up period in which the drying rate decreased and sample temperature increased rapidly, often causing partial charring. Product temperature during the second period of microwave drying increased with sample thickness and microwave power. Drying rates were not affected by slice thickness, but increased with the microwave power/mass ratio. Product charring towards the end of drying may be avoided by reducing microwave power and increasing ambient air velocity.     

EXPERIMENTAL MEASUREMENT OF TEMPERATURE AND MOISTURE PROFILES DURING APPLE DRYING

An experimental system has been designed and constructed to investigate the drying rate, temperature and moisture profiles developed within food materials during forced convective air drying. The moisture profile was determined by employing the technique of gamma ray densitometry, and embedded thermocouples were used to sense temperature at different locations. The overall drying rate was measured using an electronic balance. A microcomputer and a computer front end were implemented for data acquisition and experimental control. Sample temperature and moisture profiles measured during drying are presented as a function of both drying time and the distance to the surface of the specimen. Both profiles described the drying phenomena inside the sample. The evaporation front was observed in a narrow region of the apple specimen, this front moved into the sample as drying progressed. The amount of apple shrinkage was determined to be linearly related to the distance which the evaporation front had recededfrom the initial surface.     

EXPERIMENTAL MEASUREMENT OF TEMPERATURE AND MOISTURE PROFILES DURING APPLE DRYING

An experimental system has been designed and constructed to investigate the drying rate, temperature and moisture profiles developed within food materials during forced convective air drying. The moisture profile was determined by employing the technique of gamma ray densitometry, and embedded thermocouples were used to sense temperature at different locations. The overall drying rate was measured using an electronic balance. A microcomputer and a computer front end were implemented for data acquisition and experimental control. Sample temperature and moisture profiles measured during drying are presented as a function of both drying time and the distance to the surface of the specimen. Both profiles described the drying phenomena inside the sample. The evaporation front was observed in a narrow region of the apple specimen, this front moved into the sample as drying progressed. The amount of apple shrinkage was determined to be linearly related to the distance which the evaporation front had recededfrom the initial surface.     

A COMPREHENSIVE MATHEMATICAL AND NUMERICAL MODELING OF DEEP-BED GRAIN DRYING

This paper deals with comprehensive mathematical and numerical modeling of deep-bed grain drying. In order to build the process model, it is necessary to analyze the transport in both grain and gas phases. Experimental works were carried out for a layer of grain bed in order to validate the models. The models consider momentum, energy, and mass conservation within grain and drying air phase. The two-dimensional dynamic equations of energy and mass conservation are solved numerically by finite-difference method (FDM) and utilizing alternating direction implicit algorithm within grain and drying air phase, while momentum conservation are solved by finite difference method by utilizing Semi-Implicit Method for Pressure-Linked Equations (SIMPLE) algorithm. Furthermore, the models will be applied in consideration with developing and designing dryer in order to simulate humidity and temperature profiles of the drying gas together with moisture content and temperature of grain across dryer in term of the dryer performance. The simulations show that the models can be used to predict the dynamic drying characteristic profiles as well as the superficial velocity of drying air phase across dryer.     

A COMPREHENSIVE MATHEMATICAL AND NUMERICAL MODELING OF DEEP-BED GRAIN DRYING

ABSTRACT

This paper deals with comprehensive mathematical and numerical modeling of deep-bed grain drying. In order to build the process model, it is necessary to analyze the transport in both grain and gas phases. Experimental works were carried out for a layer of grain bed in order to validate the models. The models consider momentum, energy, and mass conservation within grain and drying air phase. The two-dimensional dynamic equations of energy and mass conservation are solved numerically by finite-difference method (FDM) and utilizing alternating direction implicit algorithm within grain and drying air phase, while momentum conservation are solved by finite difference method by utilizing Semi-Implicit Method for Pressure-Linked Equations (SIMPLE) algorithm. Furthermore, the models will be applied in consideration with developing and designing dryer in order to simulate humidity and temperature profiles of the drying gas together with moisture content and temperature of grain across dryer in term of the dryer performance. The simulations show that the models can be used to predict the dynamic drying characteristic profiles as well as the superficial velocity of drying air phase across dryer.     

EFFECTS OF HYBRID AND DAMAGE ON MOLD DEVELOPMENT DURING LOW TEMPERATURE DRYING AND STORAGE OF HIGH MOISTURE SHELLED CORN

Several corn hybrids either resistant or susceptible to storage mold were harvested with a combine and stored at high moistures (19 to 24% moisture, wet basis) in 0.81 m³ (23 bu) bins nd in “mini-bins” containing 1200 g (2.6 lbs). For several hybrids, two damage levels were achieved by adjusting combine cylinder speed. Storage conditions were the same as those found in a low temperature drying bin. Mold growth in the bins and “mini-bins” was monitored by determining number of propagules, percent seeds fine material was removed from all hybrids tested in 1986, whereas in 1985 it was not removed. This probably improved the storability of the 198 6 corn and reduced the differences in mold invasion. Furthermore, the sporulation and growth of mold were lower and differences may not have had time to develop.

Bin and small scale tests were consistent in differentiating the relative resistance of hybrids and they agreed with results of laboratory studies (Friday, 19,87). Some of the observed differences can be attributed to physical damage. However, there was an incremental decrease in storability above that which could be explained by damage, which the authors believe was caused by the hybrid effect. FRB73 × Mol7 was consistently more resistant to storage molds than the other hybrids tested. FRB73 × Mol7 and FR35 × FR20 displayed a higher level of mold resistance in all storage tests while P3707 and P3377 were consistently more susceptible. (Authors note: not all Pioneer hybrids are more susceptible to storage molds as some Pioneer hybrids have been found to store well in laboratory tests.)

The agreement of the bin, small scale, and laboratory studies suggests that hybrids can be screened for mold resistance in the laboratory. Hopefully, this will encourage plant breeders to begin such screening. This would be even more feasible if the laboratory procedures could be simplified and if the incubation time prior to evaluation for mold invasion could be reduced.     

EFFECTS OF HYBRID AND DAMAGE ON MOLD DEVELOPMENT DURING LOW TEMPERATURE DRYING AND STORAGE OF HIGH MOISTURE SHELLED CORN

Several corn hybrids either resistant or susceptible to storage mold were harvested with a combine and stored at high moistures (19 to 24% moisture, wet basis) in 0.81 m³ (23 bu) bins nd in “mini-bins” containing 1200 g (2.6 lbs). For several hybrids, two damage levels were achieved by adjusting combine cylinder speed. Storage conditions were the same as those found in a low temperature drying bin. Mold growth in the bins and “mini-bins” was monitored by determining number of propagules, percent seeds fine material was removed from all hybrids tested in 1986, whereas in 1985 it was not removed. This probably improved the storability of the 198 6 corn and reduced the differences in mold invasion. Furthermore, the sporulation and growth of mold were lower and differences may not have had time to develop.

Bin and small scale tests were consistent in differentiating the relative resistance of hybrids and they agreed with results of laboratory studies (Friday, 19,87). Some of the observed differences can be attributed to physical damage. However, there was an incremental decrease in storability above that which could be explained by damage, which the authors believe was caused by the hybrid effect. FRB73 × Mol7 was consistently more resistant to storage molds than the other hybrids tested. FRB73 × Mol7 and FR35 × FR20 displayed a higher level of mold resistance in all storage tests while P3707 and P3377 were consistently more susceptible. (Authors note: not all Pioneer hybrids are more susceptible to storage molds as some Pioneer hybrids have been found to store well in laboratory tests.)

The agreement of the bin, small scale, and laboratory studies suggests that hybrids can be screened for mold resistance in the laboratory. Hopefully, this will encourage plant breeders to begin such screening. This would be even more feasible if the laboratory procedures could be simplified and if the incubation time prior to evaluation for mold invasion could be reduced.     

A METHOD OF DETERMINATION OF THE DIFFUSION COEFFICIENT BASED ON KERNEL MOISTURE CONTENT AND ITS TEMPERATURE

Mathematical analysis of convection drying in the falling rate period was used to determine the overall coefficient of diffusion as a function of temperature and moisture content. The mass diffusion equation and its series solution was adopted for a single wheat kernel, assuming that it can be represented by a sphere as a model system. The results of the experimental data and the calculations are presented in the graphical form.     

污水污泥干燥过程中表观形态变化及水分析出特性

The drying mechanism is important to the drying technology of sewage sludge. Using dynamic electronic balance and image acquisition technique, the paper studies the change of surface configuration and characteristics of moisture transference for three kinds of sewage sludge during drying. In the meantime, the paper also analyses the influence of sludge shape on moisture transference and the change of sludge apparent volume and porosity in the course of drying.     

STOCHASTIC MODELING OF GRAIN TEMPERATURE IN NEAR-AMBENT DRYING

Stochastic analytical model was developed to describe the heat transfer in a thin layer of grain ventilated with ambient air. As an excitation to the drying system, a stochastic analytical model of ambient air temperature variations during the period of drying, based on a sine function, was used. Mean, correlation function, variance and the standard deviation were determined for air and grain temperature, both treated as random processes. The stochastic model of air temperature variation was fitted to the observed historical data. The effect of the standard deviation of air temperature of the three different climates (Canadian in Winnipeg, Polish in Poman and English in Weddington) on the standard deviation of grain temperature is shown.     

多孔介质对流干燥机理及其模型

在对现有的多孔介质对流干燥传热、传质模型归类分析的基础上,从介质内部热湿迁移机制出发,建立了能较完善、较准确地描述多孔介质在恒速段及降速段热质传递规律的“三耦合-六场量”混合理论模型.同时针对干燥问题数值模拟中的移动边界问题,提出了一种迭代修正的思想,并发展了相应的数值计算方法.对砖的干燥模拟计算结果表明,本文的模型较其他模型具有更好的精确性.     

DETERMINATION OF MOISTURE DIFFUSIVITY AND BEHAVIOR OF TOMATO CONCENTRATE DROPLETS DURING DRYING IN AIR

ABSTRACT

The drying mechanism and diffusion coefficient of water in spherical droplets (1.73 – 2.08 mm diameter) of tomato concentrates were successfully interpreted and modelled by using Fick's law. Solids content of the initial concentrate (5–15% w/w), and drying temperature (60^° – 100^° C) were varied but the drying air was kept at constant velocity and humidity.

The effective moisture diffusivity was estimated from the drying rate curves and expressed by an Arrhenius relation. Further, it was observed that case hardening has a large effect on the diffusion process causing the effective diffusional distance and the rate of moisture accumulation in the hardened crust to vary with the moisture content, according to a sorption controlled mechanism.     

TEMPERATURE,DISTRIBUTIONS AND HEAT TRANSFER DURING THE DRYING OF LUMBER

ABSTRACT

This paper describes techniques that have been developed for accurately measuring the surface temperature of drying lumber using a radiation thermometer, and interior temperatures at various depths using 30 gauge thermocouples. Methods for calculating heat transfer coefficients during the drying of lumber are also described. Experimental results, showing surface and interior temperatures, and moisture content, as functions of drying time are presented.     

AN APPLICATION OF GLASS TRANSITION TEMPERATURE TO EXPLAIN RICE KERNEL FISSURE OCCURRENCE DURING THE DRYING PROCESS *

Fissure formation during rice drying is a major cause of rice milling quality reduction. This work has applied principles of polymer science in studying thermal and hygroscopic properties of rice kernels, particularly the glass transition temperature (T_g). This data was used to develop a hypothesis that explains the occurrence of rice kernel fissuring as a result of drying. The drying process was mapped onto a state diagram to illustrate the changes in state that a kernel could incur through drying and tempering operations. An experiment was designed to validate the hypothesis in which the effect of the T_g on rice drying and tempering in terms of milling quality was determined. Results showed that drying air temperatures up to 60°C and high moisture removal rates could be used without reducing the milling quality, as long as sufficient tempering was allowed at a temperature above the T_g of the rice.