A Review of Drying Models Including Shrinkage Effects

ABSTRACT

This article presents a review of the different strategies used in the literature to model drying processes in which material shrinkage occurs. An analysis is provided of the different drying theories, the different approaches to deal with the shrinkage phenomenon, and the numerical methods used. It is common practice to directly apply the transfer models applicable for non-shrinking situations to the shrinking cases and to adopt a separate procedure to account for shrinkage. In addition, the use of effective transfer coefficients also abounds in the literature. Thus, coupling between the transfer processes and mechanical interactions is rarely considered.     

A Review of Drying Models Including Shrinkage Effects

This article presents a review of the different strategies used in the literature to model drying processes in which material shrinkage occurs. An analysis is provided of the different drying theories, the different approaches to deal with the shrinkage phenomenon, and the numerical methods used. It is common practice to directly apply the transfer models applicable for non-shrinking situations to the shrinking cases and to adopt a separate procedure to account for shrinkage. In addition, the use of effective transfer coefficients also abounds in the literature. Thus, coupling between the transfer processes and mechanical interactions is rarely considered.     

Modeling and Numerical Analysis of an Atypical Convective Coal Drying Process

This work presents modeling and numerical simulation of batch convective coal drying in a deep packed bed after a high-pressure steam treatment (a part of the Fleissner coal drying process). The process is atypical, because ambient air is used to dry and cool hot particles, while usually, e.g., in the deep packed bed drying of biomaterials, hot air is contacting cold particles. Product-specific data (intraparticle mass transfer, gas-solids moisture equilibrium) for coal (here lignite) are taken over from literature. Available data on coal drying in packed beds of medium height are used for model validation. Then, the model is applied to the considered industrial process. The design point of the process is critically reviewed, and alternatives are developed by systematically simulating the influence of inlet air conditions (temperature, humidity, flow-rate) and coal particle size. This type of analysis is necessary for efficiently scheduling plant dryers, since coal particle size may change, and air inlet temperature and humidity are changing with the ambient conditions.     

A Simulation Study on Convection and Microwave Drying of Different Food Products

It is now well recognized that matching the external drying condition with the drying kinetics of a material can lead to substantial savings of energy and in the case of heat-sensitive products, even to higher quality product. In this work, the effect of convection and microwave heat input and other product parameters on the batch drying characteristics of model materials, potato and carrot slabs, whose thermo-physical data are readily available in the literature, was modeled using a one dimensional liquid diffusion model. The influence of various thermo-physical properties of the product in drying of heat-sensitive materials was quantitatively assessed. Heat of wetting, temperature and moisture dependent effective diffusivity and thermal conductivity are considered in this model. The effect of moisture diffusivity on drying using convection and a microwave field is simulated in view of the interest in predicting the drying performance by simplified method. Conditions under which the drying rate is controlled by the external drying conditions and the internal thermo-physical properties of the product are computed and discussed.     

A Simulation Study on Convection and Microwave Drying of Different Food Products

Abstract

It is now well recognized that matching the external drying condition with the drying kinetics of a material can lead to substantial savings of energy and in the case of heat-sensitive products, even to higher quality product. In this work, the effect of convection and microwave heat input and other product parameters on the batch drying characteristics of model materials, potato and carrot slabs, whose thermo-physical data are readily available in the literature, was modeled using a one dimensional liquid diffusion model. The influence of various thermo-physical properties of the product in drying of heat-sensitive materials was quantitatively assessed. Heat of wetting, temperature and moisture dependent effective diffusivity and thermal conductivity are considered in this model. The effect of moisture diffusivity on drying using convection and a microwave field is simulated in view of the interest in predicting the drying performance by simplified method. Conditions under which the drying rate is controlled by the external drying conditions and the internal thermo-physical properties of the product are computed and discussed.     

A Combined Experimental and Theoretical Approach to Study Temperature and Moisture Dynamic Characteristics of Intermittent Paddy Rice Drying

Intermittent drying of paddy rice is fully investigated both theoretically and experimentally. A model is developed to describe simultaneous heat and mass transfer for the drying stages and mass transfer for the tempering ones. The model is considered for both cylindrical and spherical geometries. The model excels in considering non-constant paddy rice and air physical properties as well as surface vaporization and convection. The consequent equations are numerically solved with finite-difference method of line using implicit Runge–Kutta. Furthermore, a set of experiments is conducted in a laboratory-scale fluidized bed dryer to estimate the moisture diffusivity of rice and evaluate the effects of different parameters. Two correlations for moisture diffusivity are derived for each geometry based on the experimental results. It is noteworthy that the geometry choice leads to significantly different moisture diffusivities. As a result, the diffusivity values obtained for spherical presentation is 2.64 times greater than that of cylinder. Moreover, the cylindrical model fits the experimental results more precisely, especially for tempering stage (AARD_cyl = 1.03%; AARD_sph = 1.53%). Model results reveal that thermal equilibrium is quickly reached within the first 2 min. Air velocity shows no influential effect on drying upon establishment of fluidized condition. In addition, drying rate is drastically improved after applying the tempering stage. A definition for tempering stage efficiency is also proposed which shows that 3 h tempering will be 80% efficient for the studied case. Rising temperature significantly improves the drying rate, while it does not contribute much in the tempering efficiency.     

Diffusion Models to Describe the Drying Process of Peeled Bananas: Optimization and Simulation

This article aims to study the mass transient diffusion in solids with a cylindrical shape. To this end, the one-dimensional diffusion equation was discretized using the finite volume method with a fully implicit formulation. The solution can be used to simulate diffusive processes and to determine thermophysical parameters via optimization techniques. The computational package developed was applied to study the thin-layer drying of peeled bananas. Three models were used to describe the drying process: (1) the volume V and the effective mass diffusivity D are considered constant; (2) variable V and constant D; (3) V and D are considered variable. For all models, the convective mass transfer coefficient h is considered constant. The statistical indicators show that for the two cases analyzed (low and high temperature), model 3 describes the drying process better than the other models.     

Drying of Lentil Including Shrinkage: A Numerical Simulation

This article presents a theoretical study about drying of lentil including shrinkage. The two-dimensional unsteady-state diffusion modeling written in the oblate spheroidal coordinates system considers the volume variation effect, convective boundary condition at the surface of the solid, and variable thermo-physical properties. The governing equation was discretized using the finite-volume method and the linear equations system was solved by Gauss-Siedel iterative method. To validate the model, numerical results of the average moisture content were compared with experimental data from eight experiments and a good agreement was obtained. The diffusion coefficients for all drying experiments are determined using the least square error technique.     

Drying of Lentil Including Shrinkage: A Numerical Simulation

Abstract

This article presents a theoretical study about drying of lentil including shrinkage. The two-dimensional unsteady-state diffusion modeling written in the oblate spheroidal coordinates system considers the volume variation effect, convective boundary condition at the surface of the solid, and variable thermo-physical properties. The governing equation was discretized using the finite-volume method and the linear equations system was solved by Gauss-Siedel iterative method. To validate the model, numerical results of the average moisture content were compared with experimental data from eight experiments and a good agreement was obtained. The diffusion coefficients for all drying experiments are determined using the least square error technique.     

Numerical Modeling of Moisture and Temperature Distribution within a Rectangular Bagasse Layer Undergoing Drying

In this work, a numerical two-dimensional model using the finite volume method, which predicts the temperature and moisture distribution of the moist rectangular bagasse layer undergoing drying, is developed. During the drying process, variable heat and mass transfer coefficients are considered. The flow fields are numerically predicted using a commercial CFD package, Fluent. The temperature and moisture distributions under transient conditions are obtained, which determine both heat and moisture transport inside the material. The validation of the model is carried out by comparing the predicted mean moisture content values with those obtained experimentally. The comparison of the numerical and experimental result shows good agreement up to 8%.     

Convective Drying Analysis of a Single Wheat Kernel Based on an Irreversible Thermodynamics Model

The application of irreversible thermodynamics offers a formal treatment for drying analysis that allows the evaluation of intra-particle or intra-medium temperature and moisture profiles, and enthalpy, liquid, and vapor fluxes. However, researchers have claimed that its implementation is complex. This work presents a simple methodology for modeling, solving, and validating the drying equations, as applied to wheat kernels, and for obtaining the inherent and usually unavailable transport coefficients. To clarify and simplify the ensuing physical analysis, a spherical shape and isotropy were assumed. Additionally, solutions obtained with both Dirichlet and convective boundary conditions were analyzed and compared against experimental data. The thermal and hydro-stresses depend heavily on internal vapor and liquid fluxes and on the respective drying evaporation fronts, all of which were evaluated and compared.     

An Experimental Study and Mathematical Simulation of Wheat Drying

Abstract

A fixed-bed dryer was designed and constructed and drying experiments with fixed beds of wheat were carried out under various conditions of drying air with wheat of several initial moisture contents. The air temperature and moisture content of wheat at various levels within the beds were measured periodically. A computer program based on energy and mass balances was developed to simulate the deep bed drying process. Experimental data from the dryer were compared with the results from this program. The results showed that there was good agreement between the simulated drying rates between the layers and those experimentally observed. In addition, there was a good agreement with respect to the shapes of the drying air temperature profiles.     

An Experimental Study and Mathematical Simulation of Wheat Drying

A fixed-bed dryer was designed and constructed and drying experiments with fixed beds of wheat were carried out under various conditions of drying air with wheat of several initial moisture contents. The air temperature and moisture content of wheat at various levels within the beds were measured periodically. A computer program based on energy and mass balances was developed to simulate the deep bed drying process. Experimental data from the dryer were compared with the results from this program. The results showed that there was good agreement between the simulated drying rates between the layers and those experimentally observed. In addition, there was a good agreement with respect to the shapes of the drying air temperature profiles.     

Experimental and Numerical Investigation of the Heat and Mass Transfer for Cut Tobacco During Two-Stage Convective Drying

In this article, a two-stage convective drying strategy was presented for dehydration of flue-cured tobacco. In order to develop the multistage drying method of tobacco, two-stage drying as well as traditional single-stage drying of cut tobacco was experimentally evaluated and accurately simulated by proposed heat and mass transfer models. The experiments were performed in a dual fixed bed dryer. Different air temperature combinations of 120°C/90°C, 110°C/80°C, and 100°C/70°C were employed during two-stage drying. The drying rate and temperature variations of cut tobacco were investigated. The results showed that the average drying rates during two-stage drying were nearly 50% higher than those obtained from lower-temperature single-stage drying. On the other hand, the two-stage drying method, which used high air temperature for the early period and low temperature for the late period, could reduce the exposure of tobacco to high temperature due to the low final temperature of the dried sample. The temperature and moisture evolution of cut tobacco at different air temperature combinations were consistent with simulation results by developed heat and mass transfer models. This indicated that the models had a good prediction precision for two-stage drying of cut tobacco. The model predictions can be useful for the design of a feasible two-stage drying process for flue-cured tobacco.     

A Binary Gas Transport Model Improves the Prediction of Mass Transfer in Freeze Drying

Monitoring partial vapor pressure in the freeze-drying chamber is a cheap, global, and non-intrusive way to assess the end of the primary drying stage. Most existing dynamic freeze-drying models which predict this partial pressure describe mass transfer between the product and the condenser via a mass transfer resistance or a mass transfer coefficient. Experimental evidence suggests that such models can be significantly in error for some values of the sublimation flux, leading to physically inconsistent predictions and possibly incorrect assessment of primary drying termination, with potential risk of product damage if moving to secondary drying and increasing shelf temperature while some ice is still present. Assuming a binary gas transport model for vapor and inert gas leads to improved and consistent predictions and explains the apparent variation of the mass transfer resistance with total pressure, shelf temperature, and product sublimation area.     

Vacuum Contact Drying Kinetics: An Experimental Parametric Study

Abstract

Vacuum contact drying kinetics of a model system consisting of nonporous glass beads and water has been experimentally measured on a laboratory scale. A methodology for determination of drying curves from experimental data in a statistically robust way has been developed. The effects of jacket temperature, head-space pressure, particle bed depth, vessel diameter, and particle size on drying rate during constant and falling rate periods have been studied. It was found that in the range of parameters investigated, drying rate does not depend on the means of realization of the driving force (by temperature or pressure); drying rate in the constant-rate period decreases with increasing bed depth while the overall heat-transfer rate increases due to increased surface area. A very strong dependence of drying rate and regime on particle size was observed; the constant-rate period disappeared for small particles.     

Vacuum Contact Drying Kinetics: An Experimental Parametric Study

Vacuum contact drying kinetics of a model system consisting of nonporous glass beads and water has been experimentally measured on a laboratory scale. A methodology for determination of drying curves from experimental data in a statistically robust way has been developed. The effects of jacket temperature, head-space pressure, particle bed depth, vessel diameter, and particle size on drying rate during constant and falling rate periods have been studied. It was found that in the range of parameters investigated, drying rate does not depend on the means of realization of the driving force (by temperature or pressure); drying rate in the constant-rate period decreases with increasing bed depth while the overall heat-transfer rate increases due to increased surface area. A very strong dependence of drying rate and regime on particle size was observed; the constant-rate period disappeared for small particles.     

A Parametric Study of the Gas Flow Patterns and Drying Performance of Co-current Spray Dryer: Results of a Computational Fluid Dynamics Study

Abstract

A computational fluid dynamic study was carried out to investigate airflow pattern, temperature, and humidity profile at different levels in the drying chamber. Good agreement was obtained with published experimental data. The effects of operating pressure, heat loss from the chamber wall and inlet air conditions on the gas flow pattern, droplet trajectories, and overall dryer performance also were investigated. Results are presented and discussed in terms of the gas velocity, temperature, and humidity profiles within the chambers. The volumetric evaporation values, heat transfer intensity, and thermal energy consumption per unit evaporation rate were computed and compared for drying of a 42.5% solids solution in a spray chamber 2.215 m in diameter with a cylindrical top section 2.005 m high and a bottom cone 1.725 m high. Wall regions subject to formation of undesirable deposits are also identified.     

A Parametric Study of the Gas Flow Patterns and Drying Performance of Co-current Spray Dryer: Results of a Computational Fluid Dynamics Study

A computational fluid dynamic study was carried out to investigate airflow pattern, temperature, and humidity profile at different levels in the drying chamber. Good agreement was obtained with published experimental data. The effects of operating pressure, heat loss from the chamber wall and inlet air conditions on the gas flow pattern, droplet trajectories, and overall dryer performance also were investigated. Results are presented and discussed in terms of the gas velocity, temperature, and humidity profiles within the chambers. The volumetric evaporation values, heat transfer intensity, and thermal energy consumption per unit evaporation rate were computed and compared for drying of a 42.5% solids solution in a spray chamber 2.215 m in diameter with a cylindrical top section 2.005 m high and a bottom cone 1.725 m high. Wall regions subject to formation of undesirable deposits are also identified.