MODELING VACUUM-CONTACT DRYING OF WOOD: THE WATER POTENTIAL APPROACH

A two-dimensional mathematical model for vacuum-contact drying of wood is presented. The moisture and heat equations are based on the water potential concept whereas the pressure equation is formulated considering unsteady state conservation equation of dry air. Most of the model parameters were determined during independent experiments. The set of equations is then solved in a coupled form using the finite element method. The validation of the model is performed using experimental results obtained during vacuum-contact drying of sugar maple sapwood. The experimental and calculated data are in good agreement. Nevertheless, some discrepancies are observed which can be attributed to the boundary conditions used and to the fact that heat transfer by convection was neglected.     

Modeling Superheated Steam Vacuum Drying of Wood

Abstract

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.     

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.     

Conjugate heat and mass transfer model for predicting thin-layer drying uniformity in a compact,crossflow dehydrator

Abstract

A conjugate heat and mass transfer model was implemented into a commercial CFD code to analyze the convective drying of corn. The Navier–Stokes equations for drying air flow were coupled to diffusion equations for heat and moisture transport in a corn kernel during drying. Model formulation and implementation in the commercial software is discussed. Validation simulations were conducted to compare numerical results to experimental, thin-layer drying data. The model was then used to analyze drying performance for a compact, crossflow dehydrator. At low inlet air temperatures, the drying rate in the compact dehydrator matched the thin-layer drying rate. At higher temperatures, heat losses through the external walls resulted in temperature and moisture variations across the dehydrator.     

Drying Characteristics of Oil Palm Kernels

ABSTRACT

The drying characteristics of a single oil palm kernel suspended in a drying tunnel is studied. Luikov's unsteady state simultaneous heat and mass transpon equations are proposed as the governing equations. The model is simulated using the explicit and modified implicit Crank Nicholson finite difference algorithms. The desorption isotherms of the kernel warj determined using an environmental chamber and the data generated was found to fit the Hasley's and Henderson's equations well. The mass diffusion coefficient was determined by using a distributed system parameter identification technique where a weighted least square criterion between model and experimental average moisture content and temperature profiles is optimized using the Lagrangian algorithm within the constraints of the governing equations. The simulated parameter estimated drying characteristics were found to be in good agreement with experimental values.     

A MATHEMATICAL MODEL FOR DRYING OF SHRINKING MATERIALS

ABSTRACT

A mathematical model has been developed to describe heat and mass transfer within materials undergoing shrinkage during drying. Both heat and mass transfer equations are solved simultaneously using a numerical technique A beat pump dryer has been used to conduct experiments to validate the model. Several samples were placed in the drver and after the commencement of each drying test one sample was taken oat at rceular time interval: The bone-dry mass of each piece was also determined. This enables to determine moisture distribution within the materials. Temperatures at different locations of the material were measured with thermocouples. The predicted temperature and moisture distribution within the material agreed fairly well with the experimental results.     

NUMERICAL SIMULATION OF DRYING IN A CYCLONE

ABSTRACT

This work presents a complete improved mathematical model of drying in cyclone. The slip condition of the particles on the wall, the heat transfer wall-panicle and the shrinkage of the panicles during the drying process were considered. The mathematical model considers a two-dimensional turbulent gas-particle flow where the panicle phase is treated as a continuum. The momentum equations of both particle and gas phases were written in cylindrical coordinates. The discretized equations were solved by the SIMPLE algorithm. Considering the slip condition to the panicle phase and the shrinkage of the material during the drying process it was revealed a better fitness between numerical and experimental results than the previous model.     

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.     

SIMULATION OF THE HEAT AND MOISTURE TRANSFER PROCESS DURING DRYING IN DEEP GRAIN BEDS

ABSTRACT

Grain drying is a simultaneous heat and moisture transfer problem. The modelling of such a problem is of significance in understanding and controlling the drying process. In the present study, a mathematical model for coupled heat and moisture transfer problem is presented. The model consists of four partial differential equations for mass balance, heat balance, heat transfer and drying rate. A simple finite difference method is used to solve the equations. The method shows good flexibility in choosing time and space steps which enable the simulation of long term grain drying/cooling processes. A deep barley bed is used as an example of grain beds in the current simulation. The results are verified against experimental data taken from literature. The analysis of the effects of operating conditions on the temperature and moisture content within the bed is also carried out     

INVESTIGATION ON THE INCIPIENT FLUIDIZATION AND HEAT TRANSFER IN A CENTRIFUGAL FLUIDIZED BED DRYER

Abstract

Based on the continuum theory, a physical model of gas-solid two phase flow in a centrifugal fluidized bed has been proposed. A set of governing equations to describe the fluidization state are obtained and solved numerically after some simplifying. The quantitative experimental study on the characteristics of the incipient fluidization in the centrifugal fluidized bed is performed to examine the proposed model. Gas-solid two phase heat transfer in CFB during a drying process is also conducted. The influences of bed thickness, particle diameter, physical properties of particle, rotating speed of the bed and the gas superficial velocity on heat transfer characteristics are examined. A correlation that can be used to calculate the heat transfer coefficients in the drying process in CFB is obtained.     

Vacuum Drying of Oak Wood

ABSTRACT

Vacuum drying, j,e drying under absolute gas pressure of about 10? Pa. is an efficient means of reducing the process period and of producing good quality wood. We will examine here continuous vacuum drying where the plank surfaces are kept at a constant temperature, which remains above the boiling point, and moisture flowing to the surface is extracted from the kiln.

We have carried out an experimental study of oak drying under such conditions. The drying rate and moisture content profile of the sample (40 mm thick) are recorded during the whole drying period.

A model of continuous drying is established from general conservation equations with the main approximation that the air is rapidly extracted. The two constitutive equations of the model which describe temperature and water content fields are of a diffusive type and coupled through coefficients. The adequate boundary equation is not a convective one, but expresses a hygroscopic equilibrium between the vapour in the chamber and the wood surface. The mass diffusive coefficient can be adjusted to the drying rates through capillary pressure and bound water diffusion functions. The wood heterogeneity (seasonal growth) is the main factor of discrepancy in these functions. The simulated drying rates correspond with the experimental ones.     

Thermophysical Characteristics of Potatoes,Vegetables and Fruits

ABSTRACT

The main objective in this work is to study and deduce a governing equation for net mass transfer in moist air and turbulent flow. Development of simple and reliable steady state models for turbulent moist air-drying has been considered to be quite well covered in literature. However, the lack of necessary background information concerning classical drying models is now being rectified through research carried out with new approaches, which are initiated by advancement in laboratory equipment.

The known and trusted models are combined with coupled momentum, heat and mass transfer equations creating a reliable governing mass transfer equation for use in turbulent moist air drying processes, i.e. the advanced drying model (ADM). The ADM is a relatively user friendly and robust model, and it is well-suited for identifying transfer coefficients from boundary layer measurements, for example in modem high intensity paper drying machines.

The advanced drying model is analysed and verified with the specially designed experimental apparatus described in this article. The deduced mass transfer equation is then presented and experimentally verified to clarify why the use of Stefan's diffusion equation should be avoided when calculating high drying intensities in turbulent flow.

Finally, when applied to a wide drying range, the classical drying models require parameters which have been experimentally verified. Therefore, a comprehensive knowledge of governing mass transfer mechanisms will also reduce the large number of necessary drying experiments. The advanced drying model, which includes variable physical properties and transport coefficients, allows the simulation of many geometrical shapes and drying configurations and therefore provides a tool for optimising drying processes in a new manner.     

A DISTRIBUTED PARAMETER APPROACH TO THE DYNAMICS OF ROTARY DRYING PROCESSES

ABSTRACT

A nonequilibrium distributed parameter model for rotary drying and cooling processes described by a set of partial differitial equations with nonlinear algebraic constraints is developed in this work. These equations arise from the multi–phase heat and mass balances on a typical rotary dryer. A computational algorithm is devekped by employing a polynonial approximation ( orthogonal collocation) with a glotal splinc technique leading to a differential–algebraic equation ( DAE) system. The numerical solution is carried out by using a standard DAE solver.

The two– phase–flow heat transfer coelficient is computed by introducing a correction factor to the commonly accepted correlations. Since interaction between the falling particles are considered in the correction factor,the results are more reliable than those computed by assuming that heat transfer between a single falling particle and the drying air is unaffected by other particles. The heat transfer computations can be further justified via a study on the analogies between heat and mass transfer.

The general model devloped in this work is mathematically more ritorous yet more flexible that the lumped parameter models established by one of the authors (Douglas et al., (1993)). The three major assumptions of an equilibrium operation, perfect mixing and constant drying raic, are removed in the distributed parameter model.

The simulation results are compared with the operational data from an industrial sugar dryer and predictions from earlier models. The model and algorithm successfully predict the steady state behaviour of rotary dryers and collers. The generalized model can be applied to fertilizer drying processes in which the assumption of constant drying rate is no longer valid and the existing dynamic models are not applicable.     

ANALYSIS OF HEAT AND MASS TRANSFER DURING DRYING OF PAPER/BOARD

ABSTRACT

A mathematical model has been successfully developed to study the heat and mass transfer process during paper drying. This model takes into account the consective transfer of vapor and liquid apart from the known transport mechanisms of capillary flow of liquid, diffusion, vaporization-condensation, and heat conduction. The partial differential equations describing temperature, saturation and pressure change within the web during drying with associated boimdary conditions and initial conditions were solved using finite difference method. The model predictions show that during the drying process the web can be conveniently divided into three different zones, namely dry zone, wet zone and an intermediate zone. The movement of liquid and vapor in opposite directions in the intermediate zone is similar to the action of a heat pipe. Also, as drying proceeds the location of the intermediate zone and hence the heat pipe advances progressively through the thickness of the web.     

IMPROVED HEAT AND MASS TRANSFER MODELS TO PREDICT GRAIN QUALITY

ABSTRACT

This paper reviews a recent development in the heat and moisture transfer modeling for drying single layes of agricultural grains. A diffusion model with time-varying boundary condition predicts the complex shape of the drying curve well. A conduction model with evaporating boundary condition, when used with the Gamson correlation for convective heat transfer coefficient, accurately predicts experimental grain surface temperature. The new modewls were tested experimentally, drying wheat and barley in a thin-layer dryer useing 40 to 175 c air and the initial moisture ranging from 0.20 to 0.40 (decimal dry basis). It is shown that grain temperatures calculated by the conduction heat equation, when used in conjunction with a probit-type germination loss model, predict germination values different from those predicted by the lump heat equation.     

DETERMINATION OF MASS DIFFUSIVITY COEFFICIENT OF SWEET POTATO

Abstract

Using Luikov's heat and mass transfer equations and a finite element formulation, the drying process of an anisotropic biological product (sweet potato) was investigated. The model was used to determine the coefficients of heat and mass transfer, the mass diffusivity normal and parallel to the fibers of sweet potato samples. These parameters were estimated by minimizing the deviation of experimental data and numerical predictions.

Laboratory experiments with three different configurations were conducted to measure the temperature and moisture content of sweet potato samples during drying. Numerical simulation showed good agreement with the measured values.     

On The Drying of Food Products in a Tunnel Dryer

ABSTRACT

We present a dryer model for simulating the drying of hygroscopic-porous food products in a tunnel dryer. The model employs an improved receding-front formulation by taking into consideration the material volumetric shrinkage and the variation of the heat and mass transfer coefficient during drying. Predicted results show close agreement when compared with experimental data. We report a parametric analysis using the dryer model to study the drying transient and the need to cascade the drying process so as to maximise the drying potential of the air stream.     

Surface Stickiness of Drops of Carbohydrate and Organic Acid Solutions During Convective Drying: Experiments and Modeling

Abstract

Drying kinetics of low molecular weight sugars such as fructose, glucose, sucrose and organic acid such as citric acid and high molecular weight carbohydrate such as maltodextrin (DE 6) were determined experimentally using single drop drying experiments as well as predicted numerically by solving the mass and heat transfer equations. The predicted moisture and temperature histories agreed with the experimental ones within 6% average relative (absolute) error and average difference of ± 1°C, respectively. The stickiness histories of these drops were determined experimentally and predicted numerically based on the glass transition temperature (T _g ) of surface layer. The model predicted the experimental observations with good accuracy. A nonsticky regime for these materials during spray drying is proposed by simulating a drop, initially 120 µm in diameter, in a spray drying environment.     

Modeling and simulation of the drying process of natural gas pipeline using vacuum drying method

Abstract

Vacuum drying is one of the most effective methods to protect submarine natural gas pipes from blockage caused by hydrate and internal corrosion. This article presents a model for analyzing the mass, momentum, and energy transfer processes in pipeline drying with vacuum drying method. Model of the evaporation rate of liquid water is derived from Hertz–Knudsen–Schrage equation. Finite volume method is employed to discretize the governing equations with an upwind implicit scheme in present work, and 2nd order upwind scheme for energy equation is adopted to weaken numerical dissipation. Non-linear algebraic equations after discretization are solved by Newton-Raphson method. Reliability and accuracy of this model are validated via three experimental cases. Numerical results coincide well with the experimental data, and the relative errors of the calculated drying time are 1.7% in Case 1, 1.2% in Case 2, and 5.5% in Case 3. Finally, the dynamic characteristics of the vacuum drying process are analyzed such as dynamic distributions of pressure, temperature, mass flow rate, and liquid holdup. Mathematical model and algorithm developed in present work provide understanding and insights of the vacuum drying process, which aids in determining cost-effective pipeline drying scheme.     

Predicting Thermal Efficiency in Timber Radio Frequency Vacuum Drying

Abstract

In this work, the efficiency of transforming dielectric energy into evaporated water is analyzed for the case of timber radio frequency vacuum drying. Based on well-known heat and mass transfer equations, a simplified mathematical model is proposed that estimates the drying efficacy in regards to the thermo-physical properties of wood. Although not exact, the theoretical results are close to the experimental observations and elucidate some phenomena like the tendency of the timber to dry from inside to outside, and the drying rate increase with the rise of the timber gas permeability. The theoretical efficiency model also predicts a range of wood permeability values for which the drying efficiency changes from 100 to 0%, thus providing a quantitative scale for classifying the spectrum of “difficult-to-dry” all the way to “easy-to-dry” wood species when using radio frequency vacuum technology.