Comparison of quasi-steady-state and unsteady-state formulations in a freeze dryer modeling

An unsteady-state model is developed for primary and secondary stages of freeze drying process of skim milk. The results are compared with those obtained from a quasi-steady-state (QSS) formulation. The QSS formulation is not valid where the applied heat load is high. The applied heat load affects on the drying time the most compared to other parameters like chamber pressure and the radiation surface temperature.     

Experimental study and modeling of particle drying in a continuously-operated horizontal fluidized bed

Multistage fluidized beds are frequently used for product drying in industry. One advantage of these fluidized beds is that they can achieve a high throughput, when operated continuously. In this study, γ-Al₂O₃ particles were dried in a pilot-scale horizontal fluidized bed, without considering any comminution effects. For each experiment, the particle moisture content distribution and residence time distribution were determined. To take into account particle back mixing in our experiments, a one-dimensional population balance model that considers particle residence time was introduced into a fluidized bed-drying model. Experimental particle residence time distributions were reproduced using a tank-in-series model. Subsequently, the moisture content distribution was implemented, as a second dimension to the population balance in this model. These two-dimensional simulations were able to describe the experimental data, especially the spread in the residual particle moisture distribution, much more accurately than one-dimensional simulations. Using this novel two-dimensional model, the effects of different operating parameters (process gas temperature, solid feed rate, superficial air velocity) on the particle moisture content distribution were systematically studied.     

Convective drying analysis of three-dimensional porous solid by mass lumping finite element technique

A numerical analysis of convective drying of a 3D porous solid of brick material is carried out using the finite element method and mass lumping technique. The energy equation and moisture transport equations for the porous solid are derived based on continuum approach following Whitaker’s theory of drying. The governing equations are solved using the Galerkin’s weighted residual method, which convert the governing equations into discretized form of matrix equations. The resulting capacitance matrices are made diagonal matrices by following the classical row-sum mass lumping technique. Hence with the use of the Eulerian time marching scheme, the final equations are reduced to simple algebraic equations, which can be solved directly without using an equation solver. The proposed numerical scheme is initially validated with experimental results for 1D drying problem and then tested by application to convective drying of 3D porous solid of brick material for four different aspect ratios obtained by varying the cross section of the solid. The mass lumping technique could correctly predict the wet bulb temperature of the solid under evaporative drying conditions. A parametric study carried out for three different values of convective heat transfer coefficients, 15, 30 and 45 W/m² K shows an increased drying rate with increase in area of cross section and convective heat transfer coefficient. The proposed numerical scheme could correctly predict the drying behavior shown in the form of temperature and moisture evolutions.     

Sweep numerical method and mass transport analysis in atmospheric freeze drying of protein particles

This work covers heat pump drying of protein with high quality and low cost. It consists of atmospheric freeze drying to keep product quality followed by evaporation to reduce time. A sweep numerical method was applied to predict the mass transport from the porous particle to gas. The maximum deviation between predictions and mass transfer data was below 4% indicating that the method well describes mass transport during protein drying.     

Influence of zone formation on stability of continuous fluidized bed layering granulation with external product classification

Continuous fluidized bed layering granulation with external product classification and a sieve-mill cycle can show instability in the form of self-sustained nonlinear oscillations of the particle size distribution. In the present study, the stability and bifurcation analysis of this process is presented. The underlying process models explicitly account for compartmentalization of the fluidized bed into a granulation and a drying zone, which is an important feature of many technical processes. Implications for plant operations are discussed with the help of stability diagrams as a function of zone size, residence time within different zones, the addition of external seeds and particular properties of the sieve-mill cycle.     

Flow characteristics of mixed particles with a simulated cold state in moving bed reactor

The funnel flow of high-temperature circulating ash and coal in moving bed with height restrictions directly influences the efficiency of coal pyrolysis and scale-up design of reactor. It is one of the technical bottlenecks in the use of moving bed. In order to provide data support for the particle flow and pyrolysis model close to the actual working conditions in the future, this study describes the flow characteristics of solid–solid mixed particles in a cold two-dimensional moving bed. The results indicate that flow characteristics of mixed particles in the quartz sand–coal system are better than those in the cold circulating ash–coal system. The optimized conditions were obtained, the insert half angle is 20° and a heat carrier to coal ratio of 6:1. As the mixture progressed downstream, secondary separation of the heat carrier and coal become apparent. Furthermore, mixture residence time has been investigated to explore the relationship between regional residence time and to predict accurately the actual pyrolysis progress in pyrolyzer.     

Heat and mass transfer in unsaturated porous media at a hot boundary: I. One-dimensional analytical model

We present a model of heat and mass transfer in an unsaturated zone of sand and silty clay soils, taking into account the effects of temperature gradients on the advective flux, and of the enhancement of thermal conduction by the process of latent heat transfer through vapor flow. The motivation for this study is to supply information for the planned storage of thermal energy in unsaturated soils and for hot waste storage. Information is required on the possibility of significant drying at a hot boundary, as this would reduce the thermal conductivity of a layer adjacent to the boundary and, thus, prevent effective heat transfer to the soil. This study indicates the possibility that the considered system may be unstable, with respect to the drying conditions, with the occurrence of drying depending on the initial and the boundary conditions. An analysis performed for certain boundary conditions of heat transfer and for given soil properties, disregarding the advective flux of energy, indicated that there are initial conditions of water content for which heating will not cause significant drying. Under these conditions, fine soils may be better suited for heat transfer at the hot boundary, due to their higher field capacity, although their heat conduction coefficients at saturation are lower than those of sandy soils. At present, these conclusions are limited to the range of 50–80°C. Potential effects of solute concentration at the hot boundary are indicated.     

A rigorous analysis of simultaneous heat and mass transfer in the pasta drying process

This study presents a two dimensional analysis of coupled heat and mass transfer during the process of pasta drying. Velocity and temperature distributions of air flowing around the pasta are predicted in steady state condition. Using these profiles and the similarity between heat and mass boundary layers, local convective heat and mass transfer coefficients were determined on different points of pasta surface. By employing these values, the solution of coupled heat and mass transfer equations within the pasta object in unsteady state condition was obtained. Furthermore the effects of operating conditions such as velocity, temperature and relative humidity of air flow on drying rate of pasta were studied. Sensitivity analysis results show that the effects of air temperature and relative humidity on the rate of drying are more important than the effect of air velocity. Finally, the results obtained from this analysis were compared with the experimental data reported in the literatures and a good agreement was observed while, no adjustable parameter is used in the presented model.     

Theoretical study of combined heat and mass transfer process during paper drying

Theoretical and experimental study of the paper drying process are presented. A mathematical model developed for combined heat ad mass transfer analysis of paper drying is given for both impinging air jets and through air drying methods. In this model, it is simply assumed that during the drying period of the paper has porous media and on the drying surface the vapour pressure of the evaporating liquid remains at a quasi-saturated value corresponding to the temperature of the liquid. The calculated transient paper temperatures in both methods agree well with the experimental results.     

Internal Heating Effect and Enhancement of Drying of Ceramics by Microwave Heating with Dynamic Control

The effectiveness of internal heating for enhancing the drying of molded ceramics is evaluated by both modeling and experiments. In the theoretical analysis, three dimensional drying-induced strain–stress are modeled, and the numerical solutions show that the internal heating generates lower internal stress than continuous convective heating or intermittent convective heating. Microwave drying is examined experimentally to study the effect of internal heating on the drying behavior of a wet sample of a kaolin slab. The drying behavior is compared among three modes: microwave heating, hot air heating and radiation heating. The transient behavior of temperatures in microwave drying is quite different from conventional drying by external heating. In particular, the temperature of the slab drops once in the progress of drying. This phenomenon cannot be predicted adequately by a simple model of one-dimensional heat conduction and moisture diffusion accompanied with an internal heat generation rate given as a linear function of the moisture content. It should be noted that the temperature behavior takes place due to the combined interactions with internal evaporation of moisture by rise in internal vapor pressure and shift of impedance or interference in the applicator. Microwave heating with a constant power above 100 W results in sample breakage due to the internal vapor pressure. However, if the power is dynamically controlled so as to maintain the temperature less than the boiling point of water, the drying succeeds without any crack generation until completion with a significantly faster drying rate than drying in convective heating or in the oven.     

Diffusion properties of aqueous slurries in evaporative spray drying of copper (II) chloride dihydrate

This study examines the evaporative heat transfer and diffusive mass transfer of a droplet of CuCl₂ solution. The validation of a new predictive model involves comparisons with experimental data from previous studies of different fluids based on non-dimensional analysis. The study provides new insight about the effects of different concentrations of water on the CuCl₂ slurry drying at low to moderate air temperatures. Predictive correlations of heat and mass transfer are developed for the aqueous solution, subject to various drying conditions. The analysis is performed for moist air in contact with a sprayed aqueous solution of copper (II) chloride dihydrate [CuCl₂·(2H₂O)]. Results are presented and discussed for the drying processes.     

Heat transfer in an inner loop reactor

General expressions for evaluating heat transfer in reactors with a draft tube have been derived. Theoretical results show that heat transfer can be enhanced for flow pattern (A) compared with that in an open duct whenK ₁ is not departed from 0.5. The competition of the residence time and the volumetric flow rate of the fluids in the annulus and in the draft tube may be used to explain the fluid behaviors. For flow patterns (B) and (C) as in a loop reactor, introduce of recycling can augment the heat transfer rate for large Graetz number, especially whenK ₁,K ₂ orR increases. The competition between the premixing and the residence time effects of the fluid may be used to describe the fluid behaviors. Moreover, asymptotic solutions for all flow patterns were also derived.     

Moisture transport in initially fully saturated concrete during drying

Moisture content changes during drying were investigated in the present work. Particular emphasis was placed on the initial stage of drying of saturated concrete, where moisture contents are high. For this stage of drying, experimental data are lacking, and no comprehensive theory exists to describe it. The present investigation was performed experimentally and numerically for drying of cylinders with one exposed end, made of normal weight and lightweight concrete with varying water to cement ratio (w/c). The gravimetric technique was employed to obtain the spatial distribution of moisture content. The experimental results obtained indicate that drying of concrete becomes diffusion controlled when the average moisture content decreases below 70 to 80% of the initial saturation. Typical drying rates are in the order of magnitude of 0.18 kg/day/m² and 0.02 kg/day/m² for the first and the second stage of drying, respectively. The lightweight concrete cylinders as compared to those made of normal weight concrete exhibited higher levels of moisture content throughout the process. At high w/c ratios, the moisture profiles for both types of cylinders, as expected, show steeper changes with time. Large, constant drying rates were observed both experimentally and numerically in the beginning of the drying. The numerical model developed is based on a generalized mathematical formulation for mass and heat transfer in porous media, and its predictions are in agreement with the experimental data within the uncertainty range of the input data.     

Numerical and experimental investigation of convective drying in unsaturated porous media with bound water

The heat and mass transfer in an unsaturated wet cylindrical porous bed packed with quartz particles was investigated theoretically for relatively low convective drying rates. Local thermodynamic equilibrium was assumed in the mathematical model describing the multi-phase flow in the unsaturated porous media using the energy and mass conservation equations to describe the heat and mass transfer during the drying. The drying model included convection and capillary transport of the free water, diffusion of bound water, and convection and diffusion of the gas. The numerical results indicated that the drying process could be divided into three periods, the temperature rise period, the constant drying rate period and the decreasing drying rate period. The numerical results agreed well with the experimental data verifying that the mathematical model can evaluate the drying performance of porous media for low drying rates. The effects of drying conditions such as the ambient temperature, the relative humidity, and the velocity of the drying air, on the drying process were evaluated by numerical solution.     

Conjugate mixed convection heat and mass transfer in brick drying

 In this study, a numerical methodology for the solution of conjugate heat and mass transfer problem is presented. Fluid flow, heat and mass transfer over a rectangular brick due to transient laminar mixed convection has been numerically simulated. The coupled non-linear partial differential equations, for both gas phase and solid are solved using finite element procedure. Flow is assumed to be incompressible, two-dimensional, laminar. Analysis has been carried out at a Reynolds number of 200 with Pr = 0.71. The effect of buoyancy on the brick drying has been investigated. Velocity vectors, streamlines in the flow field and temperature and moisture contours and temperature distribution along the solid surface are presented. It is observed that there is considerable effect of buoyancy during drying. The results indicate a non-uniform drying of the brick with the leading edge drying faster than the rest of the brick. Received on 9 December 1998     

Stress Generated During Drying of Saturated Porous Media

The article is a contribution for the modelling of heat and mass transfers coupled to strain–stress equations during drying of deformable two-phase media. Both unidirectional and bidirectional configurations are examined. In order to compare the results, one assumes the material of a convectively dried clay slab in two configurations. Numerical calculations of the temperature, drying curves variations and the spatio-temporal distributions of moisture, temperature and drying induced stresses are evaluated. A significant difference was observed between the results obtained for both configurations particularly in intensity of the shear stress that caused cracking.     

Drying of suspensions and solutions on inert particle surface in mechanically spouted bed dryer

To eliminate some disadvantages of the conventional spouted bed dryers the mechanically spouted bed （MSB） system was developed. This dryer type is convenient to use inert particles providing an increased surface area for drying of materials of high-moisture content and heat sensitive materials. On three different drying tasks are demonstrated the experimental optimization of process parameters to obtain products of demanded quality. The main object was at drying of AIO（OH） suspension to preserve the particle size under 2.5μm and to obtain product with a moisture content of about 0.05 kg/kg （d.b.）. For this reason a very thin particle coating and intensive abrasion had to be assured. At drying of tomato concentrates the thermoplasticity makes the process very difficult. To jump over the deliquescent and sticky state developed at the critical temperature-moisture content values a very short drying time （8-10 s） must be provided. The third task was to form powder-like product from bovine serum albumin （BSA） solution having very low solid content （2-4%）. The selected process parameters given in this paper resulted in a mean particle size of less than 20 μm while the soluble oreserved orotein content was higher than 90%.     

Optimization of Fine Solid Drying in Bubble Fluidized Bed

A commonly used method to dry fine solid particles is drying in a fluidized bed. This paper presents the optimization problem of fluidized drying of fine solids. A drying process proceeding in a three-stage cascade of fluidized cross-current dryers was considered. Solid flows from stage to stage, and fresh gas is introduced to each stage of the cascade. The hydrodynamics of bubble fluidized bed and kinetics of heat and mass transfer are taken into account. The bed hydrodynamics is described by a two-phase model. The drying process considered proceeds in the second period of drying. To optimize this problem a generalized version of a discrete algorithm with constant Hamiltonian was used. The optimization procedure is presented in the paper. In optimization calculations, gas parameters (temperature, humidity and flow rate) minimizing total process cost are sought. The results of calculation are presented as graphs. The results obtained and the conclusions drawn are discussed.     

A Non-isothermal Pore Network Drying Model with Gravity Effect

The concept of immiscible displacement as an invasion percolation (IP) process driven by heat and mass transfer is used in a pore network model for convective drying of capillary porous media. The coupling between heat and mass transfer occurs at the liquid–gas interface through temperature-dependent equilibrium vapor pressure and surface tension as well as the phase change enthalpy (in evaporation and condensation). The interfacial effects due to capillary forces and gravity are combined in an invasion potential; viscous forces are neglected. Simulation results show stabilized invasion patterns and finite drying front width by the influence of gravity.     

DEM simulation of particle percolation in a packed bed

The phenomenon of spontaneous particle percolation under gravity is investigated by means of the discrete element method. Percolation behaviors such as percolation velocity,residence time distribution and radial dispersion are examined under various conditions. It is shown that the vertical velocity of a percolating particle moving down through a packing of larger particles decreases with increasing the restitution coefficient between particles and diameter ratio of the percolating to packing particles. With the increase of the restitution coefficient,the residence time and radial dispersion of the percolating particles increase. The packing height affects the residence time and radial dispersion. But,the effect can be eliminated in the analysis of the residence time and radial dispersion when they are normalized by the average residence time and the product of the packing height and packing particle diameter,respectively.In addition,the percolation velocity is shown to be related to the vertical acceleration of the percolating particle when an extra constant vertical force is applied. Increasing the feeding rate of percolating particles decreases the dispersion coefficient.