Modelling and Simulation of Momentum, Heat, and Mass Transfer in a Deep-Bed Grain Dryer

This article concerns the modelling and simulation of a deep-bed grain dryer in a large diameter-column. Two-dimensional (2D) models of deep-bed grain dryers were built by considering simultaneously momentum, heat, and mass transfer in the drying phase together with coupled heat and mass balance in the grain phase. The dynamic equations are solved numerically by using finite difference method. The momentum equations are applied to simulate pressure drop and velocity field of the drying air across the bed. The mass and heat balance in the two phases determine the profile of temperature and moisture content in both phases. Further, drying rate curves for various temperature of inlet drying gas together with moisture content of grain were simulated. The simulated profiles are in close agreement with experimental data.     

CONVECTTVE HEAT AND MASS TRANSFER AND EVOLUTION OF THE MOISTURE DISTRIBUTION IN COMBINED CONVECTION AND RADIO FREQUENCY DRYING

ABSTRACT

In a previous study (Dostie and Navarri, 1994), experiments indicated that a non-uniform moisture distribution could develop in radio frequency drying depending on the applied power and initial conditions, making the design and scale-up of such a dryer a more difficult task. Consequently, a thorough study of the combined convection and RF drying process was undertaken. Experimental results have shown that the values of the neat and mass transfer coefficients decrease with an increase in evaporation rate caused by RF energy. This effect is adequately taken into account by the boundary layer theory. Furthermore, the usual analogy between heat and mass transfer has been verified to apply in RF drying. Experiments have also shown that a different mass transfer resistance on both sides of the product should not result in non-uniform drying. However, it appears that non-uniform drying is dependent upon the initial moisture distribution and the relative intensity of heal transfer by convection and RF- It was shown that the maximum drying rate occurs at a higher average water content and that the total drying time increases with non-uniformity of the initial moisture distribution.     

Coupling CFD and Diffusion Models for Analyzing the Convective Drying Behavior of a Single Rice Kernel

The drying behavior of a single rice kernel subjected to convective drying was analyzed numerically by solving heat and moisture transfer equations using a coupled computational fluid dynamics (CFD) and diffusion model. The transfer coefficients were computed simultaneously with the external flow field and the internal diffusive field of the grain. The model was validated using results of a thin-layer drying experiments from the literature. The effects of velocity and temperature of the drying air on the rice kernel were analyzed. It was found that the air temperature was the major variable that affected the drying rate of the rice kernel. The initial drying rates (in first 20 min) were 7, 12, and 19% per hour at inlet air temperatures of 30, 45, and 60 ^° C, respectively. Important temperature gradients within the grain existed only in the first few minutes of the drying process. The moisture content gradients reached a maximum value of 11.7% (db) mm ^?1 at approximately 45 min along the short axis in the thickness direction. The variation in the inlet air velocity showed a minor effect on the drying rate of the rice kernel. The heat and mass transfer coefficients varied from 16.57 to 203.46 W·m ^?2·K ^?1 and from 0.0160 to 0.1959 m·s ^?1, respectively. The importance of the computation of the transfer coefficients with the heat and mass transfer model is demonstrated.     

A COMPARTMENTAL MODEL OF THIN-LAYER DRYING KINETICS OF ROUGH RICE

Rough rice at about 21% (wet basis) was dried at various conditions of temperatures and evaporating capacities of air. The influence of both parameters on drying rate has been studied. At high temperatures, high drying rates can be achieved with low evaporating capacities. In addition, desorption isotherms of rough rice were measured at 35, 60 and 85°C and the experimental isotherms data were fitted using a modified Pfost equation.

A compartmental model was developed to simulate the grain moisture content. Heat and mass transfer coefficients were optimized using a Nelder & Mead method. Internal mass transfer coefficient was written as an exponential function of the average moisture content and temperature of the grain and the external mass transfer coefficient as a function of air temperature. The compartmental approach predicts very well the average moisture content with a mean error of about 5% in static and dynamic conditions.     

A COMPARTMENTAL MODEL OF THIN-LAYER DRYING KINETICS OF ROUGH RICE

ABSTRACT

Rough rice at about 21% (wet basis) was dried at various conditions of temperatures and evaporating capacities of air. The influence of both parameters on drying rate has been studied. At high temperatures, high drying rates can be achieved with low evaporating capacities. In addition, desorption isotherms of rough rice were measured at 35, 60 and 85°C and the experimental isotherms data were fitted using a modified Pfost equation.

A compartmental model was developed to simulate the grain moisture content. Heat and mass transfer coefficients were optimized using a Nelder & Mead method. Internal mass transfer coefficient was written as an exponential function of the average moisture content and temperature of the grain and the external mass transfer coefficient as a function of air temperature. The compartmental approach predicts very well the average moisture content with a mean error of about 5% in static and dynamic conditions.     

The Role of Nonuniformity in Convective Heat and Mass Transfer through Porous Media,Part 1

Through-air drying is commonly used in the drying of high-quality tissue and towel products. A representative elementary volume method was used to model the fluid flow and heat and mass transfer during through drying in heterogeneous porous biobased materials such as tissue and towel products. Results of flow both upstream and downstream of a modeled porous sheet allowed visualization of the effects of mixing at the top and bottom of the porous medium. The effect of initial nonuniformity on fluid flow and convective heat and mass transfer in heterogeneous porous media was studied. The effect of material nonhomogeneity and associated transport properties on moisture content of the porous material as a function of drying time was studied. Modeling results indicate that for the first time it is possible to simulate the effect of nonuniformity on fluid flow and convective heat and mass transfer in porous media during through-air drying of paper. Moisture and structural nonuniformity contributing to nonuniformity in air flow might contribute significantly to drying nonuniformity. Depending on the moisture regimes and degree of saturation of the convective medium, heat and mass transfer coefficients may have varying effects on the overall drying.     

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.     

Modeling of Moisture and Temperature Changes of Wheat during Drying in a Triangular Spouted Bed Dryer

A mathematical model of temperature and wheat moisture content distribution inside a triangular spouted bed dryer was developed. The model is based on analysis of heat and mass transfer inside the dryer. In addition to that, an empirical bulk density model has been developed for wheat and included in the drying simulation. A laboratory-scale triangular spouted bed (TSB) dryer was used to dry wheat grain to validate the model. The dryer was divided into three sections, namely spouting, downcomer, and fountain. A series of drying runs were conducted to record moisture and temperature profile. There were two distinct regions observed during wheat drying. A constant rate period was observed during the initial drying stage and the falling rate period took place at the later drying stage. Initial moisture content and operating drying temperature governed the timing of transition from constant rate period to falling rate period. The model can be used to accurately predict the moisture content of wheat during drying. The temperature prediction inside the TSB dryer was less accurate, especially at high temperatures due to heat losses in the experimental dryer. Further studies are needed to improve the accuracy of this model, especially with regard to the temperature prediction.     

Modeling of Moisture and Temperature Changes of Wheat during Drying in a Triangular Spouted Bed Dryer

A mathematical model of temperature and wheat moisture content distribution inside a triangular spouted bed dryer was developed. The model is based on analysis of heat and mass transfer inside the dryer. In addition to that, an empirical bulk density model has been developed for wheat and included in the drying simulation. A laboratory-scale triangular spouted bed (TSB) dryer was used to dry wheat grain to validate the model. The dryer was divided into three sections, namely spouting, downcomer, and fountain. A series of drying runs were conducted to record moisture and temperature profile. There were two distinct regions observed during wheat drying. A constant rate period was observed during the initial drying stage and the falling rate period took place at the later drying stage. Initial moisture content and operating drying temperature governed the timing of transition from constant rate period to falling rate period. The model can be used to accurately predict the moisture content of wheat during drying. The temperature prediction inside the TSB dryer was less accurate, especially at high temperatures due to heat losses in the experimental dryer. Further studies are needed to improve the accuracy of this model, especially with regard to the temperature prediction.     

Mass Transfer Coefficients and Drying Rates in Through Air Drying: Part II

In this study experimental results and analysis are given of convective heat and mass transfer in the drying of tissue and towel products (25 and 50 g/m² basis weight) under commercially realistic conditions under through flow. Parameter effects on drying rate include process variables such as refining, shaping, commercial forming, initial moisture content, and drying temperature. Drying rate curves display initial increase, plateau, and final decrease as the paper dries. Nondimensional Sherwood numbers (versus Peclet number) generally agreed with and augment the available dataset on through drying.     

Variability in Transport Properties Regarding Drying Behavior for Blackbutt Timber in New South Wales

ABSTRACT

Variability is a key issue in the processing of many biological materials, in this case the drying of hardwood timber. This article reports the measurements of variability of the diffusion coefficient (a transport property), the initial moisture content, and the basic density that are relevant to the drying of blackbutt, Eucalyptus pilularis Sm, from northern New South Wales in Australia. The diffusion coefficient was quantified using a mathematical model solving Fick's second law of diffusion for mass transfer, and Fourier's law for heat transfer. The initial moisture content and the basic density were measured using experimental procedures. Specifically, within-tree and between-tree variations are reported. The coefficients of variation of the initial moisture contents and final moisture contents are 0.24 and 0.19, respectively, for within-tree variability. A similar result was found for the amount of between-tree variability. Compensating differences in the diffusion coefficients of the timber boards were a significant reason for the small dispersion of final moisture contents, despite the large variation in initial moisture contents.

An analysis of variance showed that some timber properties were affected by the board positions within trees and between trees. Circumferential and radial effects were significant for the within-tree variability of most transport properties. Moreover, principal components analysis suggested that timber boards with low densities have high initial moisture contents and high diffusion coefficients. A potential reason is that if there is less wood material per unit volume (lower density), then there is more space to be occupied by water (higher initial moisture content), and there is also less resistance to the diffusive transport of moisture (higher diffusion coefficients).     

Multiscale and multilayer structural modeling and simulation on drying of grain packing porous media

ABSTRACT

Aiming at the problem of multilayer physical structure for the skeleton of porous media, a multiscale and multilayer structural model of heat and mass transfer processes for drying of grain packing porous media was established by applying the pore network method and multiscale theory. An experimental study on rice drying was conducted in order to validate this model. The simulation and experimental results indicated that the established model could explain the mechanical properties of rice drying well. The rate of heat transfer was faster than the rate of mass transfer and there was a higher moisture gradient inside the rice grain. The diffusion coefficient of rice embryo played an important role in the drying process, and whose effect on drying was larger than the diffusion coefficient of rice hull and chaff. The moisture was imprisoned effectively inside the rice when the diffusion coefficient of rice embryo was very small.     

Coupled Heat and Mass Transfer in a Solar Grain Dryer

This paper presents the analysis of a coupled heat and mass transfer process in a fixed-bed solar grain dryer. Measurements of moisture concentration and air humidity along with temperature measurements were carried out in a solar grain dryer located in Port Harcourt, Nigeria, at the latitude of 4.858°N and longitude of 8.372°E. The process was also modelled, mathematically, by a set of partial differential equations that were coupled within the grain and through the grain boundary with the hot drying air. A finite difference scheme was used to obtain the moisture concentration and air humidity, and temperature fields within the grain and drying air. There was good agreement between the theoretical and experimental results at specified Biot and Posnov numbers, and varying Fourier number. The effects of time, space, and key model parameters such as the Biot and Posnov numbers and the initial conditions of the grains and drying air were simulated and discussed. The results from this study can be used to specify the design parameters for solar grain dryers.     

DETERMINATION METHOD OF VARIABLE DIFFUSION COEFFICIENTS OF HYGROSCOPIC MATERIAL FROM DRYING RATE CURVES OF THE SINGLE PARTICLE

The concentration dependency of diffusion coefficients of hygroscopic materials can usually only be calculated by cumbersome experimental techniques.

Taking the diffusion rate in the fictious steady state with the same mean moisture concentration as in the regular regime of the drying process of a spherical hygroscopic particle (which means the drying period not influenced by initial moisture distributions) into account, a simple method is proposed to estimate the dependency of diffusion coefficients on the moisture concentration for hygroscopic materials from drying rate curves of the single particle.     

An Experimental Study of Wheat Drying in Thin Layer and Mathematical Simulation of a Fixed-Bed Convective Dryer

Drying of wheat (Algerian cultivar: Hadba03) in thin layers was studied and mass flux phenomenon was used to characterize the thin-layer drying process. Thin-layer drying of wheat was determined for drying air temperature range of 40–60°C, relative humidity of drying air from 10 to 30%, air velocity of 0.7 m/s, and initial grain moisture from 26 to 31% (dry basis). Equilibrium moisture content of wheat was determined using desorption isotherms obtained from the thin-layer drying data. An equilibrium model for a stationary deep bed with drying air moving vertically upward was developed using mass and energy balance between grain and drying air in the bed and drying air characteristics obtained from thin-layer drying experiments. The developed model was validated by drying wheat in a laboratory dryer using different drying air temperatures and initial moisture contents.     

PARAMETERS AFFECTING GRAIN DRYING BY IMMERSION IN A HOT PARTICULATE MEDIUM

High temperature particulate medium conduction grain drying is a very promising technique. However, lack of basic drying characteristic information has resulted in unsuccessful attempts to develop an efficient, economical, continuous flow dryer.

In this study, the effects of initial grain moisture content, initial medium temperature, medium particle size, medium to grain mass ratio, and contact time on the drying of shelled corn immersed in hot sand are evaluated.

Moisture losses ranged between 0.2 and 5.2 percentage points (wb).     

Modeling Superheated Steam Vacuum Drying of Wood

A two-dimensional mathematical model developed for vacuum-contact drying of wood was adapted to simulate superheated steam vacuum drying. The moisture and heat equations are based on the water potential concept whereas the pressure equation is formulated considering unsteady-state mass conservation of dry air. A drying test conducted on sugar maple sapwood in a laboratory vacuum kiln was used to infer the convective mass and heat transfer coefficients through a curve fitting technique. The average air velocity was 2.5 m s^-1 and the dry-bulb temperature varied between 60 and 66°C. The ambient pressure varied from 15 to 11 kPa. Simulation results indicate that heat and mass transfer coefficients are moisture content dependent. The simulated drying curve based on transfer coefficients calculated from boundary layer theory poorly fits experimental results. The functional relation for the relative permeability of wood to air is a key parameter in predicting the pressure evolution in wood in the course of drying. In the case of small vacuum kilns, radiant heat can contribute substantially to the total heat transfer to the evaporative surface at the early stages of drying. As for conventional drying, the air velocity could be reduced at the latter stage of drying with little or no change to the drying rate.     

DETERMINATION METHOD OF VARIABLE DIFFUSION COEFFICIENTS OF HYGROSCOPIC MATERIAL FROM DRYING RATE CURVES OF THE SINGLE PARTICLE

ABSTRACT

The concentration dependency of diffusion coefficients of hygroscopic materials can usually only be calculated by cumbersome experimental techniques.

Taking the diffusion rate in the fictious steady state with the same mean moisture concentration as in the regular regime of the drying process of a spherical hygroscopic particle (which means the drying period not influenced by initial moisture distributions) into account, a simple method is proposed to estimate the dependency of diffusion coefficients on the moisture concentration for hygroscopic materials from drying rate curves of the single particle.