FINITE ELEMENT SIMULATION OF THE THERMO-HYDRO STRESSES IN A VISCOELASTIC SPHERE DURING DRYING

The objective of this study is the formulation of a finite element model that could be used to analyze the stress crack formation in a viscoelastic sphere resulting from temperature and moisture gradients during the drying process. Numerical solutions to the simultaneous moisture and heat diffusion equations describing moisture removal and heat intake process for the sphere are obtained. The distribution and gradients of temperature and moisture developed inside the sphere during drying are established. The calculated temperature and moisture gradients are used in a finite element analysis of the thermo-hydro viscoelastic boundary value problem to simulate the stresses in the body.

The model is used to solve a sample problem of drying a soybean kernel. The simulated drying curve for the soybean model is obtained and compared favorably with the experimental results reported in the literature. Tangential stress, as a criteria for failure, is shown to change from compressive to tensile stress as it approaches the surface. It reaches its peak value at the surface in one hour and then decays slowly. The effect of different drying conditions is studied and the results are discussed.     

a rview of: UNIFIED ANALYSIS AND SOLUTIONS OF HEAT AND MASS DIFFUSION

ABSTRACT

The objective of this study is the formulation of a finite element model that could be used to analyze the stress crack formation in a viscoelastic sphere resulting from temperature and moisture gradients during the drying process. Numerical solutions to the simultaneous moisture and heat diffusion equations describing moisture removal and heat intake process for the sphere are obtained. The distribution and gradients of temperature and moisture developed inside the sphere during drying are established. The calculated temperature and moisture gradients are used in a finite element analysis of the thermo-hydro viscoelastic boundary value problem to simulate the stresses in the body.

The model is used to solve a sample problem of drying a soybean kernel. The simulated drying curve for the soybean model is obtained and compared favorably with the experimental results reported in the literature. Tangential stress, as a criteria for failure, is shown to change from compressive to tensile stress as it approaches the surface. It reaches its peak value at the surface in one hour and then decays slowly. The effect of different drying conditions is studied and the results are discussed.     

A Numerical Study of Transient Deformation and Stress Behavior of a Clay Slab During Drying

A transient three-dimensional analysis was carried out on internal strain-stress as well as heat and the moisture transfer in a ceramic slab during drying. A model was developed to analyze viscoelastic behavior, heat conduction and moisture diffusion. The basic equations were solved by the finite element method. The effects of several dimensionless parameters are discussed to find an optimum drying process and a precise design of molds in ceramic production. The stress and the gradient of moisture content were influenced significantly by the Biot or Lewis number. When the moisture diffusion is enhanced or the drying is controlled well so as to form only gentle gradients of moisture content in the slab, the maximum tensile stress can be reduced. Nonuniform drying results in the develoment of warp and increase in the maximum tensile stress. The drying characteristics were not appreciably influenced by shrinkage.     

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

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 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.     

Non-structural cracking in RC walls: Part I. Finite element formulation

In this paper, a three-dimensional finite element model for the analysis of non-structural cracks occurring in reinforced concrete (RC) walls is introduced. The numerical model could take into account both time-dependent temperature variations due to hydration heat and non-uniform moisture distribution during drying, and the coupling effect between the heat transfer and the moisture diffusion. Calculation of the temperature and internal relative humidity variations of RC walls is followed by determination of stresses due to thermal gradients, differential drying shrinkage, and average drying shrinkage. The mechanical properties of early age concrete, determined from numerous experimental studies, are taken into consideration to improve the accuracy of the numerical results, and a discrete steel element derived using the equivalent nodal force concept is also used to simulate reinforcing steels embedded in a concrete matrix. The validity of the proposed procedure is verified by comparing the measured experimental data with the analytical results for RC walls.     

Mechanical Effects in Saturated Capillary-Porous Materials during Convective and Microwave Drying

The differences are analyzed in distribution and time evolution of the temperature, moisture content, and drying-induced stresses generated by convective and microwave drying. The theoretical analysis of the drying induced stresses and the deformations of dried materials is based on the elastic and viscoelastic constitutive models. The theoretical predictions are confronted with the experimental data obtained by the acoustic emission (AE) method, which enable monitoring on line the development of the drying induced stresses. The system of double coupled differential equations of the thermomechanical drying model is solved numerically using the finite element (FEM) and the finite difference (FDM) methods. A cylindrical sample made of kaolin was chosen to compare experimental data with the model solution. Essential differences were identified in the analyzed items for convective and microwave drying as well as a significant difference in stress distribution was noted for elastic and viscoelastic constitutive models.     

INFLUENCE OF THE DRYING MEDIUM PARAMETERS ON DRYING INDUCED STRESSES

A thermomechanical model of drying of capillary-porous materials whose material constants depend on moisture content and temperature is presented in the paper. The finite element method is used for the solution of two-dimensional problem of convective drying of a prismatic bar. The moisture distributions, temperature distributions, drying induced strains and stresses for various drying medium parameters are determined. The effect of these parameters on moisture distribution and in particular on drying induced stresses is discussed.     

Modeling heat and mass transfer–induced stresses in germinated brown rice kernels during fluidized bed drying

A study of stress distribution inside a germinated brown rice (GBR) kernel during drying is important to understand the fissure formation of GBR and hence control the drying process in order to improve the quality of GBR. In this study, a finite element method performed in three dimensions in conjunction with the heat and mass balance of the drying system was developed to describe moisture, temperature, and stress distributions inside GBR kernels during fluidized bed drying. The modeling was carried out using the coupling of heat and mass transfer and validated with experimental data at 90–150°C. The results of moisture and temperature predictions agreed well with the experiments. During drying, tensile stress occurred at the layers close to surface and compressive stress occurred at the inner portion of a kernel. The tensile and compressive stresses increased to the highest value at about 30 s of drying, corresponding to the highest moisture gradient, and then decreased afterwards. The tensile and compressive stresses were higher at a higher drying temperature. These stress prediction results corresponded to the experiments, which show more severe GBR fissuring at higher drying temperatures.     

INFLUENCE OF THE DRYING MEDIUM PARAMETERS ON DRYING INDUCED STRESSES

ABSTRACT

A thermomechanical model of drying of capillary-porous materials whose material constants depend on moisture content and temperature is presented in the paper. The finite element method is used for the solution of two-dimensional problem of convective drying of a prismatic bar. The moisture distributions, temperature distributions, drying induced strains and stresses for various drying medium parameters are determined. The effect of these parameters on moisture distribution and in particular on drying induced stresses is discussed.     

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     

Computer model of drying behaviour of ceramic green bodies with particular reference to moisture content dependent properties

A numerical model was developed to predict the drying behavior of ceramic green bodies. Resolution of the simultaneous heat and mass transfer equations involved finite elements and the Backward Euler method. Based on experimental data, the model uses equivalent moisture diffusivity, water activity, thermal conductivity and heat capacity as input parameters which depend on moisture content. In particular, the equivalent moisture diffusivity is a key parameter controlling water transport from the body interior to the surface. A simple method was used to estimate the effect of shrinkage on drying rate during the initial drying stage. Predictions of the internal moisture distribution, drying rate and surface temperature as a function of time gave good agreement to experiment for green bodies of alumina paste. External conditions of convection coefficient and relative humidity are shown to sensitively control drying rate and surface temperature evolution during the constant rate period.     

Modeling and On-line Measurement of Drying Stress of Pinus massoniana Board

A drying stress model was established by considering that the total shrinkage of wood is the sum of free shrinkage, instantaneous strain, viscoelastic strain, and mechanosorptive strain. From the stress model, the stress can be calculated once the actual wood shrinkage and moisture content gradient are known. Based on this theory, on-line measurement of the drying stress has been realized by measuring the moisture content (MC) gradient between the surface and the core layers, and the actual shrinkage of the board for Pinus massoniana.

A sensor for measuring wood shrinkage was developed based on electric resistance and strain relationship in a selected element material within the sensor. A resistance type of MC sensor was used for the MC gradient measurement. These sensors are reliable and can meet the requirement of the measurements in practical drying. The technique reported in this article for detecting drying stress from the on-line measurements of board shrinkage and MC gradient can be applied to develop optimized drying schedule in commercial drying.     

EFFECT OF INTERMITTENT HEATING ON DRYING-INDUCED STRAIN-STRESS OF MOLDED CLAY

Parametric analyses of the strain-stress in the drying process are performed to study the influence of the intermittent drying on the behaviors of drying-induced strain-stress and deformation as well as the drying characteristic. The transient three-dimensional problem of strain-stress and heat and moisture transfer in a slab is solved simultaneously by the finite element method. The dimensionless parameters are introduced to generalize the problem in the conservation equations of heat and moisture transfer. The intermittent drying is modeled by applying periodically smaller and larger Biot numbers to the boundary conditions. The maximum tensile and compressive stresses fluctuate, and fall remarkably during the smaller Biot number period when a slab is heated intermittently. The peak stress of the fluctuation exceeds beyond the case in the continuous healing where the overall drying rate is almost equivalent to that in the intermittent beating, but the reduction of the stresses takes place rapidly in the low heating period.     

Modeling and On-line Measurement of Drying Stress of Pinus massoniana Board

A drying stress model was established by considering that the total shrinkage of wood is the sum of free shrinkage, instantaneous strain, viscoelastic strain, and mechanosorptive strain. From the stress model, the stress can be calculated once the actual wood shrinkage and moisture content gradient are known. Based on this theory, on-line measurement of the drying stress has been realized by measuring the moisture content (MC) gradient between the surface and the core layers, and the actual shrinkage of the board for Pinus massoniana.

A sensor for measuring wood shrinkage was developed based on electric resistance and strain relationship in a selected element material within the sensor. A resistance type of MC sensor was used for the MC gradient measurement. These sensors are reliable and can meet the requirement of the measurements in practical drying. The technique reported in this article for detecting drying stress from the on-line measurements of board shrinkage and MC gradient can be applied to develop optimized drying schedule in commercial drying.     

Effect of Geometry of Rice Kernels on Drying Modeling Results

Geometry of rice grain is commonly represented by sphere, spheroid, or ellipsoid shapes in the drying models. Models using simpler shapes are easy to solve mathematically; however, deviation from the true grain shape might lead to large errors in predictions of drying characteristics such as moisture content (MC) and moisture gradients (MG). This research was undertaken to determine the impact of such shape considerations on prediction of drying characteristics. Impact of shrinkage of grains caused by drying was also investigated. Three separate mathematical models, each representing rice grain by sphere, spheroid, and ellipsoid shapes, were developed to describe the drying process. These models were solved by the finite element method using Comsol Multiphysics® simulation program. Drying simulations showed important differences in predictions of MC and MG in these three models. The sphere-shaped model predicted a slower drying than the spheroid- and ellipsoid-shaped models, whose MC predictions were similar. In all three models, maximum moisture gradients (MMG) were observed along the shortest axis in the bran region. During drying, MMG increases, reaches a peak, and then decreases. Magnitude and onset of peak of MMG were different in the three models. These differences in drying predictions among the three models make it important to use the appropriate shape to represent the rice grain in mathematical models. Ellipsoid shape, which closely resembles geometry of the rice grain, was found to be the most suitable. Reliable MG predictions from such ellipsoid-shaped models could be correlated to grain fissuring, which thereafter can be employed to optimize the drying process. The impact of shrinkage of rice grains during drying on model predictions is very small. In any drying simulation, maximum error due to neglecting shrinkage would be less than 5% of total moisture loss value.     

Stress and Failure Prediction for the Drying, Tempering, and Cooling of Extruded Durum Semolina

This work presents a method to predict the stress and breakage that is caused by the drying of hygros-copic materials. Stresses were predicted for a viscoclasic cylinder with the properties of extruded durum semolina, or pasta noodles. The stresses were calculated as functions of the transient moisture and tem-perature gradients in the material which were predicted for the combined processes of drying, tempering,and cooling. The time and radial position of failure were predicted based on failure data for extruded semolina.

Isotherm data for extruded durum semolina were obtained for temperatures from 40 to 60°C and for relative humidities from 75 to 95%. The results were fit with a modified form of Henderson's equation.Thermal conductivities were measured for temperatures from 30 to 50°C and a moisture range of 12 to 27% (dry basis).

A drying model based on the principles of irreversible thermodynamics; (Fortes, 1978; Fortes and Okos, 1981a, 1981b) was used to successfully predict drying curves for a range of experimental conditions. Transient moisture and temperature profiles were calculated numerically, and a receding evapora-tion front was predicted to exist. Drying was predicted to be a coupled liquid, vapor, and heat transport phenomena.

The drying data were used in a stress analysis of a Maxwell viscoelastic cylinder to predict trends in stress development under various contiitions of combined drying, tempering, and cooling. High temperature-high humidity drying, HTHH, (lOO°C, 65% RH) was compared with low temperature-low humidity drying, LTLH, (53°C, 13% RH). The HTHH drying offered definite advantages in terms of reduced product breakage susceptibility. The reasons for those advantages were increased failure strength and a decreased moisture gradient at the end of drying. In a five-stage drying process, the cooling stage was shown to have a significant impact on the predicted levels of stress and on the strength of the extruded material. Analysis of the model suggested that gradual temperature and humidity transitions from stage to stage in multistage processes were important to product quality.     

EFFECT OF INTERMITTENT HEATING ON DRYING-INDUCED STRAIN-STRESS OF MOLDED CLAY

ABSTRACT

Parametric analyses of the strain-stress in the drying process are performed to study the influence of the intermittent drying on the behaviors of drying-induced strain-stress and deformation as well as the drying characteristic. The transient three-dimensional problem of strain-stress and heat and moisture transfer in a slab is solved simultaneously by the finite element method. The dimensionless parameters are introduced to generalize the problem in the conservation equations of heat and moisture transfer. The intermittent drying is modeled by applying periodically smaller and larger Biot numbers to the boundary conditions. The maximum tensile and compressive stresses fluctuate, and fall remarkably during the smaller Biot number period when a slab is heated intermittently. The peak stress of the fluctuation exceeds beyond the case in the continuous healing where the overall drying rate is almost equivalent to that in the intermittent beating, but the reduction of the stresses takes place rapidly in the low heating period.     

I. THEORY AND FINITE ELEMENT FORMULATION

A theoretical basis for a nonlinear thermo-hydro viscoelastic boundary value problem was developed. An incremental finite element formulation was derlved using the principle of virtual work. The effects of non-uniform temparature and moisture gradients and solution dependent material property functions are outlined. An appropriate