Mathematical Modeling of the Fluidized Bed Drying of Cubic Materials

The unsteady‐state simultaneous heat and mass transfer between gas and potato cubes during the drying process in a batch fluidized bed was described by a mathematical model. Mass transfer was considered to occur in three dimensions whereas heat transfer between the gas and dried material was assumed to be lumped. It was found that the model could describe the drying process with acceptable accuracy. The moisture profile inside the material at any cross‐section and at any time can be predicted by the model.     

Simulation of Drying Using a Kiln Model

A mathematical model was developed for simulating a convective batch lumber drying process. The model incorporates mass and heat transfer relationships within the lumber stack, as well as thermodynamic properties of the wood and drying air. It takes into account the change of air properties along the stack and its effect on the mass and heat transfer parameters. The model relies on a drying rate function that is an empirical correlation based on single-board tests. A drying rate function for western hemlock (Tsuga heterophylla) lumber was developed. The drying rate function was obtained based on experiment results from 500 small boards dried over a range of conditions used in commercial practice. The model was first validated against data available in the literature and then against large batches of hemlock dried in a laboratory kiln. In both cases, the model output was in good agreement with the average moisture content, the drying rates, and the temperatures measured in the larger batches.     

Gaseous Carbon Dioxide as the Heat and Mass Transfer Medium in Drying

Using available correlations for heat transfer, a comparative analysis of drying rates in CO₂ and in air was performed for several basic types of dryers. Higher heat transfer rates were found for dryers with active hydrodynamics, which translates into shorter drying time for materials dried in the first drying period. These results were validated by experiments on drying wheat kernels fluidized by air and by CO₂. Shorter drying times by about 20% were confirmed for CO₂, which offers energy savings of about 3% of the heat input to the dryer. Additional energy savings of 4% of the heat load can be expected for drying at temperatures below 100°C because of the lower wet-bulb temperature for CO₂ than that for air. The potential for CO₂ abatement was evaluated based on a case study for drying of distillers' spent grain.     

Dimensionless Formulation of Convective Heat Transfer in Fry‐Drying of Sewage Sludge

Fry‐drying is an alternative for heat and mass transfer intensification. The process reuses waste oil as a heating medium for drying by contact with the wet sludge. At the end of the process, a stable derived fuel is obtained, a granular solid composed of the dried indigenous sewage solid and the impregnated oil. The fry‐dried sludge is storable and transportable without any pathogen elements. Knowledge about heat and mass transfer rates during the frying process is essential in order to assess the quality of the final product such as calorific value, oil uptake, porosity changes, etc. The heat transfer properties including transfer by free convection between the solid and the frying oil are fundamental for the process design and manufacturing of the fry‐dried product. The convective heat coefficient by temperature measurement and overall energy balance calculation is determined. The heat flux is calculated from the fry‐drying kinetics including moisture loss and oil intake kinetics. Various hydrodynamic regimes for convective heat transfer during the frying process are discussed (non‐boiling, boiling, and low‐boiling regime). A dimensionless formulation for estimating the convective transfer is proposed.     

Gaseous Carbon Dioxide as the Heat and Mass Transfer Medium in Drying

Using available correlations for heat transfer, a comparative analysis of drying rates in CO₂ and in air was performed for several basic types of dryers. Higher heat transfer rates were found for dryers with active hydrodynamics, which translates into shorter drying time for materials dried in the first drying period. These results were validated by experiments on drying wheat kernels fluidized by air and by CO₂. Shorter drying times by about 20% were confirmed for CO₂, which offers energy savings of about 3% of the heat input to the dryer. Additional energy savings of 4% of the heat load can be expected for drying at temperatures below 100°C because of the lower wet-bulb temperature for CO₂ than that for air. The potential for CO₂ abatement was evaluated based on a case study for drying of distillers' spent grain.     

Mathematical Modeling of Kiln Drying of Softwood Timber: Model Development, Validation, and Practical Application

Mathematical modeling of wood drying is a powerful tool to better understand and quantify the effects of wood properties as well as the effects of drying and post-drying treatment conditions on drying and thus the wood drying models can be used to improve drying quality. The models that have been developed can be divided into three categories: models for drying a single board, models for drying a kiln-wide stack, and models for drying stress and deformation. The single-board drying model employs comprehensive heat and moisture mass transfer equations and can be used to investigate the influence of wood variability. The kiln-wide drying model, which is based on the transfer processes between wood and the drying medium, is able to examine the influence of drying schedules and wood properties. The stress model can predict stress development in drying and stress relief in final steam conditioning and post-kiln treatment. An integrated model can be used to optimize drying schedules and develop strategies for high-quality dried timber.     

Experimental study and simulation of vibrated fluidized bed drying

The paper addresses numerical simulation for the case of convective drying of seeds (fine-grained materials) in a vibrated fluidized bed, analyzing agreement between the numerical results and the results of corresponding experimental investigation. In the simulation model of unsteady simultaneous one-dimensional heat and mass transfer between gas phase and dried material during drying process it is assumed that the gas-solid interface is at thermodynamic equilibrium, while the drying rate (evaporated moisture flux) of the specific product is calculated by applying the concept of a “drying coefficient”. Mixing of the particles in the case of vibrated fluidized bed is taken into account by means of the diffusion term in the differential equations, using an effective particle diffusion coefficient. Model validation was done on the basis of the experimental data obtained with narrow fraction of poppy seeds characterized by mean equivalent particle diameter (d_S,d = 0.75 mm), re-wetted with required (calculated) amount of water up to the initial moisture content (X₀ = 0.54) for all experiments. Comparison of the drying kinetics, both experimental and numerical, has shown that higher gas (drying agent) temperatures, as well as velocities (flow-rates), induce faster drying. This effect is more pronounced for deeper beds, because of the larger amount of wet material to be dried using the same drying agent capacity. Bed temperature differences along the bed height, being significant inside the packed bed, are almost negligible in the vibrated fluidized bed, for the same drying conditions, due to mixing of particles. Residence time is shorter in the case of a vibrated fluidized bed drying compared to a packed bed drying.     

OPTIMAL CONTROL OF THE PRIMARY AND SECONDARY DRYING STAGES OF BULK SOLUTION FREEZE DRYING IN TRAYS

The problem of operating a tray freeze dryer to obtain a desired final bound water content in minimum time is formulated as an optimal control problem with the use of the rigorous unsteady state mathematical model of Sadikoglu and Liapis [9] that has been found to describe satisfactorily the experimental dynamic behavior of the primary and secondary drying stages of bulk solution freeze drying of pharmaceuticals in trays. The heat input to the material being dried and the drying chamber pressure are considered to be control variables. Constraints are placed on the system state variables by the melting and scorch temperatures during primary drying, and by the scorch temperature during secondary drying. Necessary conditions of optimality for both the primary and secondary drying stages are derived and presented, and an approach for constructing the optimal control policies that would minimize the drying times for both the primary and secondary drying stages, is presented. The theoretical approach presented in this work was applied in the freeze drying of skim milk, and significant reductions in the drying times of primary and secondary drying were obtained, when compared with the drying times obtained using the operational policies reported in the literature, by using the optimal control policies constructed from the theory presented in this work. Furthermore, it is shown that the optimal control policy leads to the desired in practice result of having at the end of secondary drying temperature and bound water concentration profiles (in the dried layer) whose gradients are very small. It is also shown that by using the optimal control policy and an excipient capable of increasing the melting temperature without affecting product quality, one can significantly reduce the drying time of the primary drying stage.     

Drying Behavior of Carrots Dried in a Spout–Fluidized Bed Dryer

The effect of water blanching treatment and the inlet air temperature on drying kinetics as well as the quality attributes of carrot cubes dried in a spout–fluidized bed dryer at 60, 70, 80, and 90°C were analyzed. The material shrinkage and the rehydration potential were calculated to assess the changes in quality of dried carrots. It was found that the value of the air velocity during the drying of carrot cubes in a spout–fluidized bed dryer should be related to the moisture content of the carrot particles. A high value of air velocity at the beginning of the drying cycle and a lower value for the later stages were also required. The linear equation was correlated to the data of shrinkage of raw and blanched carrots. Blanching significantly influenced the coefficients in the shrinkage model derived for drying of carrot cubes in a spout–fluidized bed dryer, while drying temperature did not influence the shrinkage of carrot particles. The intensity of heat and mass transfer during spout–fluidized drying of carrot cubes was dependent on the drying temperature. A correlation was developed to calculate the values of effective moisture diffusivity of dried carrot cubes as a function of the moisture content and temperature of the material. It was observed that for any given time of rehydration, both the moisture content and the rehydration ratio calculated for samples dried at 60°C were higher than for samples dried at temperatures of 60, 70, 80, and 90°C.     

Design and validation of an innovative soft-sensor for pharmaceuticals freeze-drying monitoring

The paper is focused on the development of a Kalman filter type observer for the monitoring of the primary drying phase of the freeze-drying of pharmaceutical products in vials. The proposed soft-sensor is able to estimate the evolution of temperature of the product, the duration of the primary drying phase, the value of the overall heat transfer coefficient between the heating shelf and the product, as well as the mass transfer resistance of the dried cake to vapor flow. Accurate results are obtained for various types of products, characterized by a different dependence of the mass transfer resistance on the dried cake thickness. Theoretical results are confirmed by experimental tests carried out in a pilot-scale freeze-dryer. Finally, the strength and the weakness of the proposed observer are pointed out.     

Drying Characteristics In Superheated Steam Drying at Reduced Pressure

The superheated steam drying at reduced pressure is performed, and the effects of operational conditions such as drying pressure and temperature on the drying characteristics are examined. In order to obtain the basic guideline for the design of the superheated steam dryer at reduced pressure, the heat flux to sample was calculated and the optimal conditions were estimated.

After the sample temperature reached at the boiling point, the temperature was maintained at the boiling point and the drying rate became almost constant. Once the sample was dried out, the temperature suddenly increased up to the drying gas temperature. From the calculation of combined heat flux, the followings were found. The contribution of radiative heat transfer to the combined heat flux became larger as the drying pressure was lower. The combined heat flux had a maximum value against the drying pressure. The optimum drying pressure, which gave the maximum heat flux, became lower as the drying gas temperature decreased. It was found that reduction in the drying pressure is effective for the enhancement in drying performance.     

A review of: “Developments in Drying,Vol. 2” Edited by A.S. Mujumdar and S. Suvachittanont Kasetsart University Press,Bangkok, Thailand 2000

Although pulse combustion devices exhibit a high thermal efficiency and low pollutant emission when used in a drying process, a broad application of these dryers has been limited because of a lack of understanding of the fundamental controlling heat and mass transfer. This paper reports the results of an experimental investigation of heat transfer between unsteady airflow and a brass sphere under various oscillating frequencies. In order to generate an unsteady flow, we constructed a gas-fired, water-cooled pulse burner. The burner is of a Helmholtz type and its operating frequency can be adjusted by changing the tailpipe length. The heat transfer coefficient between unsteady air outflow and brass was determined by the lumped capacity method. The effect of airflow oscillating frequency on heat transfer coefficient was investigated and their correlation was established. Refractory clay particles in the oscillating airflow were dried and the effect of the frequency on the drying process was predicted using the heat transfer coefficients obtained.     

Modellierung der Trocknungsdauer für die dynamische Gefriertrocknung

During dynamic freeze drying, the dry layer is permanently rubbed off, which results in an increase in drying performance. By means of the experimental determination of the heat transfer coefficients in dependence of some process parameters (rotational frequency, loading, drying temperature), the heat transfer coefficient can be interpolated by means of the presented model and from this the drying time can be determined. Milk spheres, milk pellets and starter culture of the strain Pediococcus pentosaceus were used as model systems.     

Drying Characteristics In Superheated Steam Drying at Reduced Pressure

Abstract

The superheated steam drying at reduced pressure is performed, and the effects of operational conditions such as drying pressure and temperature on the drying characteristics are examined. In order to obtain the basic guideline for the design of the superheated steam dryer at reduced pressure, the heat flux to sample was calculated and the optimal conditions were estimated.

After the sample temperature reached at the boiling point, the temperature was maintained at the boiling point and the drying rate became almost constant. Once the sample was dried out, the temperature suddenly increased up to the drying gas temperature. From the calculation of combined heat flux, the followings were found. The contribution of radiative heat transfer to the combined heat flux became larger as the drying pressure was lower. The combined heat flux had a maximum value against the drying pressure. The optimum drying pressure, which gave the maximum heat flux, became lower as the drying gas temperature decreased. It was found that reduction in the drying pressure is effective for the enhancement in drying performance.     

OPTIMAL CONTROL OF THE PRIMARY AND SECONDARY DRYING STAGES OF BULK SOLUTION FREEZE DRYING IN TRAYS

Abstract

The problem of operating a tray freeze dryer to obtain a desired final bound water content in minimum time is formulated as an optimal control problem with the use of the rigorous unsteady state mathematical model of Sadikoglu and Liapis [9] that has been found to describe satisfactorily the experimental dynamic behavior of the primary and secondary drying stages of bulk solution freeze drying of pharmaceuticals in trays. The heat input to the material being dried and the drying chamber pressure are considered to be control variables. Constraints are placed on the system state variables by the melting and scorch temperatures during primary drying, and by the scorch temperature during secondary drying. Necessary conditions of optimality for both the primary and secondary drying stages are derived and presented, and an approach for constructing the optimal control policies that would minimize the drying times for both the primary and secondary drying stages, is presented. The theoretical approach presented in this work was applied in the freeze drying of skim milk, and significant reductions in the drying times of primary and secondary drying were obtained, when compared with the drying times obtained using the operational policies reported in the literature, by using the optimal control policies constructed from the theory presented in this work. Furthermore, it is shown that the optimal control policy leads to the desired in practice result of having at the end of secondary drying temperature and bound water concentration profiles (in the dried layer) whose gradients are very small. It is also shown that by using the optimal control policy and an excipient capable of increasing the melting temperature without affecting product quality, one can significantly reduce the drying time of the primary drying stage.     

Low-Temperature Drying Using a Versatile Heat Pump Dehumidifier

A drying system incorporating a commercial 2.3 kW heat pump dehumidifier was designed and constructed. The HPD was equipped with an external water-cooled condenser that rejected excess heat out of the system. The design of the system allowed for conducting drying with recirculation of air as well as use of electrical heaters. In an open mode, the drying could be carried out simultaneously with room dehumidification and water heating in the secondary condenser. Drying experiments were conducted with apple and comparisons were made between HPD assisted drying (partial and complete) and hot air drying (at 45 and 65°C). The HPD dried fruit exhibited better rehydration properties than the hot air dried samples. Water activity of the HPD dried samples was noticeably lower than that of the hot air dried samples at the same water content, indicating that the residual moisture was probably held under higher tension in the former. In terms of energy consumption, the process of HPD assisted drying is more expensive as much of the energy input is rejected at the secondary condenser as excess heat.     

Effects of Drying Parameters on Heat Transfer during Drying of Fermented Ground Cassava in a Rotary Dryer

The effects of drying parameters on heat transfer during drying of fermented ground cassava in a rotary dryer were studied. The fermented ground cassava was dried in a bench-scale rotary dryer at different inlet air temperatures, inlet air velocities, relative humidities, feed rates, drum drive speeds, and feed drive speeds. It is shown that inlet air temperature, inlet air velocity, and feed rate have significant effects on the specific heat transfer coefficient and heat load in the material. Models that predict the specific heat transfer coefficient as a function of inlet air temperature and inlet air velocity and the heat load as a function of inlet air temperature, inlet air velocity, and feed rate are also presented. Predictions of the models are compared with experimental data and good agreement is obtained.     

Experimental Investigation and Practical Application of Superheated Steam Drying Technology for Softwood Timber

Due to several advantages, superheated steam drying of timber has attracted great attention. However, the technology is still restricted to some special cases, partly due to the lack of fully understanding of the drying process. In this work, experiments were conducted to dry radiata pine timber using superheated steam under vacuum and at pressure. In the first part of the experiments, softwood timber was dried in a superheated steam kiln with drying rates, steam temperature across the stack and wood temperature being measured during drying. In the second part of the work, experimental studies were performed to investigate potential applications of the superheated steam drying at ultra-high temperatures (UHT) and pressurized steam conditioning of kiln dried timber. Compared to normal drying temperatures, the UHT drying can reduce the drying time by a factor of 5 to 10 and it is also more energy efficient. The pressurized steam conditioning has been proven to be a promising technology to relieve drying stresses and to reduce twist of the dried timer.     

TRANSPORT PROPERTIES OF CELLULAR FOOD MATERIALS UNDERGOING FREEZE-DRYING

The samples of sliced and mashed apples were freeze-dried by controlling their surface temperatures over the usual pressure range of commercial operations. The surface of sliced samples could not be maintained at above 10°C in order to prevent the frozen layer from melting, while that of mashed samples was allowed to heat up to 70°C.

Thermal conductivities and permeabilities were determined by applying the uniformly-retreating-ice front model to the dried layer of the samples undergoing freeze-drying. The values of permeability for the mashed samples were found to depend on the ice-crystallization time during freezing. The results indicated that the drying rate of sliced samples was limited by the transfer rate of water vapor flowing through the dried layer. A cellular structural model is proposed for predicting the permeability of the dried layer, based on the resistance of the cell membrane to molecular transfer of water vapor.     

FUNDAMENTALS OF DRYING TECHNIQUES

The samples of sliced and mashed apples were freeze-dried by controlling their surface temperatures over the usual pressure range of commercial operations. The surface of sliced samples could not be maintained at above 10°C in order to prevent the frozen layer from melting, while that of mashed samples was allowed to heat up to 70°C.

Thermal conductivities and permeabilities were determined by applying the uniformly-retreating-ice front model to the dried layer of the samples undergoing freeze-drying. The values of permeability for the mashed samples were found to depend on the ice-crystallization time during freezing. The results indicated that the drying rate of sliced samples was limited by the transfer rate of water vapor flowing through the dried layer. A cellular structural model is proposed for predicting the permeability of the dried layer, based on the resistance of the cell membrane to molecular transfer of water vapor.