ADAPTIVE AND STOCHASTIC FINITE ELEMENT ANALYSIS IN DRYING

The focus of this paper is on the use of new advances in the finite element method to model and analyze drying problems, with emphasis on biological, food and grain materials. It presents the current status of the use of numerical analysis for such process, and emphasizes the need and advantages of incorporating adaptive and stochastic strategies into the finite element analysts. The existing literature on the application of the adaptive and stochastic finite elements is reviewed in conjunction with the relevant advances in this area. A new perturbation-based stochastic methodology far nonlinear and transient drying problems is formulated and presented in detail. The specific application of this new methodology to drying is under development. In conclusion, tracks for future research in this field are proposed.     

An Adaptive Approach to Finite Element Modeling of Drying Problems

ABSTRACT

This study presents me development of an efficient adaptive finite element methodology for the analysis of drying problems. The propsed technique first uses an unified error estimator to assess the accuracy and reliability of the finite element solution. It then employs an automatic and adaptive finite element refinement strategy to reduce the errors to acceptable values. A new adaptive strategy applied to transient problems is also presented. The performance of the proposed methodology is evaluated by applying it to timber and clay brick drying problems. The estimated error agreed with the expected behavior: greater in regions of steeper gradients and lower in regions of smaller gradients. In addition, the proposed new adaptive strategy avoids unnecessary remeshing, i.e., remeshing when the error is decreasing with time at a reasonable rate.     

An Adaptive Approach to Finite Element Modeling of Drying Problems

This study presents me development of an efficient adaptive finite element methodology for the analysis of drying problems. The propsed technique first uses an unified error estimator to assess the accuracy and reliability of the finite element solution. It then employs an automatic and adaptive finite element refinement strategy to reduce the errors to acceptable values. A new adaptive strategy applied to transient problems is also presented. The performance of the proposed methodology is evaluated by applying it to timber and clay brick drying problems. The estimated error agreed with the expected behavior: greater in regions of steeper gradients and lower in regions of smaller gradients. In addition, the proposed new adaptive strategy avoids unnecessary remeshing, i.e., remeshing when the error is decreasing with time at a reasonable rate.     

Adaptive Finite Element Analysis of Air Flow Inside Grain Dryers

ABSTRACT

This paper presents a simulation study of air flow inside dryers. An adaptive finite element methodology for two-dimensional problems was developed. This study is the first application of nadaptive techniques to such tupe of problems. The formultion is generic and can be easily extended to three-dimensional analysis. Several dryer configurations were studied in order to verify the efficiency and accuracy of the proposed methodology. Results agreed well with experimental data and show significant imporvements when compared to the conventional finite elements analysis.     

Three‐Dimensional Simulation of Moisture Diffusion in Polymer Composite Materials

Abstract

This article presents a three‐dimensional Galerkin finite element methodology (GFEM) for simulating Fickian diffusion with temperature‐dependent diffusion coefficients, with particular application to moisture diffusion in composite materials. The coupled thermal and moisture diffusion problems are solved by using three‐dimensional finite element method with orthotropic diffusion coefficients and an implicit time‐stepping procedure. Both Frontal and Jacobi conjugate gradient (JCG) solution techniques are used. Numerical examples are presented to illustrate the methodology and include orthotropic diffusivities and multiple material regions. Moisture diffusion within a periodic unit cell of a typical composite material is also considered. The results show that the iterative JCG method is effective and computationally inexpensive to analyze diffusion three‐dimensional diffusion problems with multiple materials.     

CONJUGATE HEAT AND MASS TRANSFER IN CONVECTIVE DRYING OF MULTIPARTICLE SYSTEMS PART II: SOYBEAN DRYING

Abstract

This is the second of two papers concerning conjugate transport in convective drying of multiparticle systems. In the first paper (part 1), a solution methodology for conjugate transport problems was porposed and successfully tested for assemblages of spheres. This paper deals with the application of the proposed methodology to a soybean drying problem. The analysis in this study allowed certain phenomena, that are usually not present in single-kernel and deep-bed drying analyses, to be captured by the drying rate curves. The results presented here reinforce the need to take into account particle interactions when studying the drying mechanisms of multiparticle systems.     

A Two-Dimensional Finite Element Model for Kiln-Drying of Refractory Concrete

ABSTRACT

A two-dimensional finite element model is developed for kiln-drying of refractory concrete. Using this model simulations are carried out for refractory concrete castings of different thicknesses to investigate the effects of drying schedules on pore steam pressure and moisture removal. Simulation results from both one- and two-dimensional models are compared and discussed. On the basis of the simulation results new realistic drying schedules are suggested.     

TRANSPORE : A GENERIC HEAT AND MASS TRANSFER COMPUTATIONAL MODEL FOR UNDERSTANDING AND VISUALISING THE DRYING OF POROUS MEDIA

ABSTRACT

In this work a sophisticated numerical model is presented that describes the drying of porous media. This model, which is known as TransPore, has evolved over the years through the direct inputs of both authors. Nowadays, TransPore can be used to analyse the drying of media that are of completely arbitrary shape and size, under a variety of drying conditions. The engine of the computational model uses a number of state-of-the-art numerical methods that ensure the simulation results describe the particular drying process accurately, whilst guaranteeing the most efficient and effective usage of computer resources. For example, the numerical discretisation method is based on a completely conservative hybrid finite element control volume technique that uses a finite element mesh for its background gradient interpolation. Furthermore, flux limiting is used to reduce numerical dispersion in the drying kinetics and the generated non-linear system is resolved using the full Newton method for the outer iteration coupled together with a preconditioned conjugate gradient technique for the inner iteration. A graphical interface has been linked to the model to enable online visualisation of the drying process. The mathematical model allows both homogeneous and heterogeneous porous media to be simulated. The resultant software is an extremely powerful and effective tool for investigating existing dryer designs and for proposing new and innovative drying schedules that provide optimal drying quality in minimal drying time.     

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.     

OPTIMISATION OF HARDWOOD DRYING SCHEDULES ALLOWING FOR BIOLOGICAL VARIABILITY

ABSTRACT

The amount of biological variability in timber creates considerable problems in producing timber of adequate and reproducible quality with a predictable amount of variability in final moisture contents. The development of optimised drying schedules for addressing these problems is therefore desirable. Previous methods (largely of a stochastic type) are reviewed in this work and their limitations assessed. The physical parameters which have the greatest impact on the stress levels (and hence quality) of the timber have been assessed using a diffusion model for the drying of Australian hardwood timber. This deterministic model is then used, together with statistical methods for quantifying the confidence regions for the variability in the physical parameters with the greatest impact, in a systematic technique to develop a new optimised schedule for grey ironbark timber (Eucalyptus paniculaia). This new schedule is then compared with a previous optimised schedule, which did not take this variability into account. The productivity (amount of good quality timber divided by drying time) appears to be maximised when the schedule is such that 90% of the timber produced is good quality.     

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.     

Adaptive Finite Element Analysis of Air Flow Inside Grain Dryers

This paper presents a simulation study of air flow inside dryers. An adaptive finite element methodology for two-dimensional problems was developed. This study is the first application of nadaptive techniques to such tupe of problems. The formultion is generic and can be easily extended to three-dimensional analysis. Several dryer configurations were studied in order to verify the efficiency and accuracy of the proposed methodology. Results agreed well with experimental data and show significant imporvements when compared to the conventional finite elements analysis.     

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.     

DEFORMATION AND SlRESS ANALYSIS OF POROUS CAPILLARY BODIES DURING INTERMITTENT VOLUMERIC THERMAL DRYING

ABSTRACT

lntermittent heating in a thermal drying is one way to improve energy utilization and to enhance the quality for some products. Using the finite element method and Luikov's theory. the temperature, moisture and stress distributions at different instances of intermittent drying were obtained. Several examples were analyzed using this method. The numerical results are compared with prior experimental and theoretical results. This numerical simulation method could be used to devise an intermittent drying process schedule optimal operation.     

A Preliminary Study on Strategies for Optimal Fluid-Bed Drying

ABSTRACT

The degradation of product quality during convective drying depends on the temperature and water concentration history of the panicles and drying time. For improving product quality in combination with acceptable operation costs, optimal control of the operation variables is required.

In this preliminary study the relevance of dynamic optimal operations for batch-wise fluid-bed drying is explored by simulation. Optimal trajectories of operation variables were calculated for a pilot-plant installation by using a model which concerned the drying history of the panicles and the product quality (inactivation of biological active components). The applied objective function was based on an economic criterion combining product quality and operation costs.

Although the advances for the chosen pilot-plant application are moderate, in future studies the potentials and relevance of dynamic optimal operations for drying will be quantified for installations on industrial scale.     

On-Line Determination of Water Activity at the Lean Surface of Meat Products During Drying and Its Relationship with the Crusting Development

Abstract

One of the main problems in drying of meat products is the surface hardening or crusting. The crusted surface layer is harder and less permeable than the inner part of the product. A dramatic increase of hardness during drying in dry-cured meat products has been found when the water content reaches a critical value. The water content can be related with the water activity by sorption isotherms. Therefore, an on-line measurement of the water activity at the surface (a_ws) could be used by the control system in order to avoid the crusting problem. The aim of this study was to evaluate a methodology for the on-line water activity determination at the lean surface of raw or salted meat during drying and relate this determination with the crusting development. Water activity at the surface was estimated from the heat balance (a_ws ^h) in salted meat slices and in unsalted and in salted loin samples. The proposed methodology was able to monitor the a_ws in both products. The estimated a_ws ^h was related with the crusting development in loin samples, showing its potential application in control systems for avoiding the crusting development during the drying of meat products.     

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.     

CONJUGATE ANALYSIS OF NATURAL CONVECTIVE DRYING OF BIOLOGICAL MATERIALS

ABSTRACT

This paper presents a numerical analysis of heat and mass transport during natural convective drying of an extruded com meal plate. The conjugate problem of drying and natural convection boundary layer Is modeled. The finite volume technique was used to discretize and solve the highly nonlinear system of coupled differential equations governing the transport inside the plate. The boundary layer solution was obtained by means of a finite difference software package that utilizes Runge-Kutta's 5th order method to solve the inherent transport equations. A methodology for evaluating the heat and mass transfer coefficients during the numerical simulation was developed and successfully implemented. The results showed that there is no analogy between heat and mass transfer coefficients for this type of problem.     

Modelling of Fish Drying Kinetics Using a Combination of Surface Response Methodology and Diffusional Models

ABSTRACT

Drying is a common fish preservation technique used in developing countries. Analysis of process factors involved in controlled fish drying permits process optimization and assists in design of suitable dryers. Various methodologies, with models of different complexities (analytical, semi–empirical and empirical models), have been used to investigate fish drying kinetics. The original feature of this study is the combined use of surface response methodology and diffusional models. In a limited number of experimetns, this combination allowed development of a predictive tool for assessing fish drying mechanisms and drying time.