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.     

A Simulation Model for Heat Pump Dryer Plants for Fruits and Roots.

Dryer design requires food properties, drying rate and mass-heat transfer coefficients. These values change continuously during drying due to changes in food fractions, particularly the water fraction. The high energy demand and costs allied to inefficient devices, creates a great need for new processing equipment. Along these guide-lines, several heat pump drying research projects were established at the Norwegian University of Science and Technology. The heat pump dryer provides high quality final product as its drying conditions can be controlled. Its efficiency and non-polluting operation come from closed air-refrigerant circuits and from its ability to fully recover the latent heat of moist air as it exits the drying chamber. Most of the above features are quite the opposite of the conventional dryer characteristics. Several experiments were made on heat pump drying of fruits and roots at temperatures from -22.5 to 40°C to obtain data and correlations on thermophysical properties, specific enthalpy and rehydration. Also, tests were done on drying rate, moisture content, drying constant, effective mass diffusivity and heat and mass transfer equations. The next important phase is the development of a simulation model to predict the performance and characteristics of the heat pump dryer plant. The objectives of the present work are to develop and lo test a heat pump dryer simulation model. The simulation provides results on the characteristics of both plant and components which are integrated by heat and mass transfer equations. The program has menus with click-on icons, input and output pop-up dialogue boxes. The usual commands such as, file-open, file-save, edit-delete are available in this program simply called Hpdryer. The model contains moist air psychrometric. natural and conventional refrigerant property libraries. Ammonia is a time-tested, self-alarming and natural refrigerant. It has been used extensively in the past, and it has better thermodynamic and transport properties than halocarbons. Safety is easily attained by design and its restrictive standards have helped increase its use in several countries. There are 36 ammonia installations in Norway and in the United Kingdom, including a drying plant. Ammonia has zero Odp, zero Gwp and the recent R&D has led to viable small-sale heat pump plants. Ammonia and dichlarodifluoromethane refrigerants were used in the test cases simulated by Hpdryer madel.     

A Simulation Model for Heat Pump Dryer Plants for Fruits and Roots.

ABSTRACT

Dryer design requires food properties, drying rate and mass-heat transfer coefficients. These values change continuously during drying due to changes in food fractions, particularly the water fraction. The high energy demand and costs allied to inefficient devices, creates a great need for new processing equipment. Along these guide-lines, several heat pump drying research projects were established at the Norwegian University of Science and Technology. The heat pump dryer provides high quality final product as its drying conditions can be controlled. Its efficiency and non-polluting operation come from closed air-refrigerant circuits and from its ability to fully recover the latent heat of moist air as it exits the drying chamber. Most of the above features are quite the opposite of the conventional dryer characteristics. Several experiments were made on heat pump drying of fruits and roots at temperatures from -22.5 to 40°C to obtain data and correlations on thermophysical properties, specific enthalpy and rehydration. Also, tests were done on drying rate, moisture content, drying constant, effective mass diffusivity and heat and mass transfer equations. The next important phase is the development of a simulation model to predict the performance and characteristics of the heat pump dryer plant. The objectives of the present work are to develop and lo test a heat pump dryer simulation model. The simulation provides results on the characteristics of both plant and components which are integrated by heat and mass transfer equations. The program has menus with click-on icons, input and output pop-up dialogue boxes. The usual commands such as, file-open, file-save, edit-delete are available in this program simply called Hpdryer. The model contains moist air psychrometric. natural and conventional refrigerant property libraries. Ammonia is a time-tested, self-alarming and natural refrigerant. It has been used extensively in the past, and it has better thermodynamic and transport properties than halocarbons. Safety is easily attained by design and its restrictive standards have helped increase its use in several countries. There are 36 ammonia installations in Norway and in the United Kingdom, including a drying plant. Ammonia has zero Odp, zero Gwp and the recent R&D has led to viable small-sale heat pump plants. Ammonia and dichlarodifluoromethane refrigerants were used in the test cases simulated by Hpdryer madel.     

Modelling Diffusion-Limited Drying Behaviour in a Batch Fluidized Bed Dryer

Fluidized bed dryers are often used to extract water from granular materials. When the drying process is mainly limited by the resistance against water transport inside the particle the drying behaviour is said to be diffusion-limited. In the literature there are several models that predict this drying process with very diverging results. In this study a model is set up to arrive at a better prediction for this drying process. The heat and mass transfer in the granular material and the drying air is described. The resulting equations are solved numerically. The model must be extended to incorporate the heat capacity of the dryer.     

Modelling Diffusion-Limited Drying Behaviour in a Batch Fluidized Bed Dryer

ABSTRACT

Fluidized bed dryers are often used to extract water from granular materials. When the drying process is mainly limited by the resistance against water transport inside the particle the drying behaviour is said to be diffusion-limited. In the literature there are several models that predict this drying process with very diverging results. In this study a model is set up to arrive at a better prediction for this drying process. The heat and mass transfer in the granular material and the drying air is described. The resulting equations are solved numerically. The model must be extended to incorporate the heat capacity of the dryer.     

ANALYSIS OF HEAT AND MASS TRANSFER DURING COMBINED MICROWAVE CONVECTIVE SPOUTED-BED DRYING

Heat and mass transfer phenomena during the combined microwave-convective batch spouted bed drying are analyzed. Wheat was chosen as a test material. The governing equations, including consideration of internal heat generation and thermodiffusion are formulated and solved using the numerical method of lines. The model allowed variable material transport and dielectric properties. The parameters investigated include electric field strength, electromagnetic field frequency, inlet air temperature, and superficial air velocity. Representative drying and temperature curves as well as moisture and temperature profiles are presented and discussed.     

ANALYSIS OF HEAT AND MASS TRANSFER DURING COMBINED MICROWAVE CONVECTIVE SPOUTED-BED DRYING

Heat and mass transfer phenomena during the combined microwave-convective batch spouted bed drying are analyzed. Wheat was chosen as a test material. The governing equations, including consideration of internal heat generation and thermodiffusion are formulated and solved using the numerical method of lines. The model allowed variable material transport and dielectric properties. The parameters investigated include electric field strength, electromagnetic field frequency, inlet air temperature, and superficial air velocity. Representative drying and temperature curves as well as moisture and temperature profiles are presented and discussed.     

Drying of soybean seeds in a crossflow moving bed

The aim of this work was to investigate simultaneous heat and mass transfer between air and soybean seeds in a crossflow moving bed dryer. A model was developed from mass and energy conservation applied to the fluid and particulate phases. The equilibrium, heat transfer and mass transfer equations were taken from studies published earlier. Equations for drying kinetics were obtained from a thin layer study, and the equilibrium equation was chosen from rival model discrimination based on nonlinearity measures. The experimental part of this work involved the determination of air temperature distribution, grain moisture through the bed and air humidity at the bed outlet. The model equations were discretized by orthogonal collocation in the air flow direction. The resulting differential-algebraic equations were solved using a method based on backward differential formulas. Simulation results showed good agreement with experimental data.     

Numerical Simulation of Vacuum Drying by Luikov's Equations

A two-dimensional mathematical model was developed to simulate coupled heat and mass transfer in apple under vacuum drying. Luikov's equations are the governing equations in analyzing heat and mass diffusion problems for capillary-porous bodies. The model considers temperature- and moisture-dependent material properties. The aim of this study is to analyze the influence of some of the most important operating variables, in particular, pressure and temperature of drying air, on the drying of apple. The resulting system of unsteady-state partial differential equations has been solved by a commercial finite element method (FEM) package called FEMLAB (COMSOL AB, Stockholm, Sweden). Simulations, carried out in different drying conditions, showed that temperature is more effective than air pressure in determining the drying rate. A parametric study was also carried out to determine the effects of heat and mass transfer coefficients on temperature and moisture content distributions inside apple during vacuum drying. A comparison between the theoretical predictions and a set of experimental results reported in the literature showed very good agreement, especially during the first 4,200 s, when experimental data and theoretical predictions overlapped and relative errors never exceeded 2%.     

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.     

RADIO FREQUENCY VACUUM DRYING OF WOOD. I. MATHEMATICAL MODEL

A one-dimensional mathematical model to describe the transport phenomena during continuous radio frequency/vacuum (RF/V) drying of thick lumber was developed from general conservation equations. When drying at temperatures near the boiling point, as in RF/V drying, the effect of the gas phase pressure gradient on moisture transfer within the solid can be very important. The controlling resistances and transport mechanisms are discussed in detail. In addition, capillary transport in RF/V drying is discussed and its effect is compared with convective drying. The model provides a relatively fast and efficient way to simulate vacuum drying behavior assisted by dielectric heating. As an example, the governing heat and mass transfer equations, including consideration of internal heat generation and the effect of gas phase pressure gradient, are derived and solved in a one-dimensional system using a finite volume method. The effect of changes of the most important parameters on the predictions of the model is also presented.     

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.     

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.     

气流干燥过程的数学模拟

针对颗粒和空气在干燥管内的相互作用和传质传热机理,首先建立了直管式气流干燥数学模型,然后通过分析脉冲式气流干燥器的结构特点,求出了管径变化的微分方程,将其和直管式气流干燥的五个常微分方程耦合在一起,构成了脉冲式气流干燥的传质传热数学模型。根据模型方程的特点,运用四阶龙格-库塔法对其进行了数值求解。通过实验结果验证,该模型正确可靠。     

Dynamic Modeling and a Parametric Study of an Indirect Solar Cabinet Dryer

A dynamic mathematical model for drying of agricultural products in an indirect cabinet solar dryer is presented. This model describes the heat and mass transfer in the drying chamber and also considers the heat transfer and temperature distribution in a solar collector under transient conditions. For this purpose, using conservation laws of heat and mass transfer and considering the physical phenomena occurring in a solar dryer, the governing equations are derived and solved numerically. The model solution provides an effective tool to study the variation of temperature and humidity of the drying air, drying material temperature, and its moisture content on each tray. The predicted results are compared with available experimental data. It is shown that the model can predict the performance of the cabinet solar dryer in unsteady-state operating conditions well. Furthermore, the effect of some operating parameters on the performance and efficiency of dryer is investigated and compared with selected published data.     

CONJUGATE ANALYSIS OF NATURAL CONVECTIVE DRYING OF BIOLOGICAL MATERIALS

This paper presents a numerical analysis of heat and mass transport during natural convective drying of an extruded com meal plate. The conjugate problem of drying and natural convection boundary layer Is modeled. The finite volume technique was used to discretize and solve the highly nonlinear system of coupled differential equations governing the transport inside the plate. The boundary layer solution was obtained by means of a finite difference software package that utilizes Runge-Kutta's 5th order method to solve the inherent transport equations. A methodology for evaluating the heat and mass transfer coefficients during the numerical simulation was developed and successfully implemented. The results showed that there is no analogy between heat and mass transfer coefficients for this type of problem.     

SOME CRITERIA OF SPRAY DRYER DESIGN FOR FOOD LIQUID

Spray drying has many applications for a wide variety of dried food powders. The quality of spray dried food is quite dependent on the atomization characteristics and the heat and mass transfer on drops inside the spray dryer. This paper deals with some design criteria of the spray dryer such as the atomizer, the drop trajectory and the heat/mass transfer between the drop and the drying air.     

Spatial reaction engineering approach as an alternative for nonequilibrium multiphase mass‐transfer model for drying of food and biological materials

Drying is a complex process which involves simultaneous heat and mass transfer. Complicated structure and heterogeneity of food and biological materials add to the complexity of drying. Drying models are important for improving dryer design and for evaluating dryer performance. The lumped reaction engineering approach (L‐REA) has been shown to be an accurate and robust alternative for cost‐effective simulations of challenging drying systems. However, more insightful physics has to be shown spatially. In this study, the REA is coupled with the standard mechanistic drying models to yield the spatial‐REA (S‐REA) as nonequilibrium multiphase mass‐transfer model. The S‐REA consists of a system of equations of conservation with the REA representing the local evaporation and wetting rate. Results of the modeling using the S‐REA match well with the experimental data reported previously. This is the first comprehensive REA approach to model the profiles of water vapor concentration during drying of food and biological materials. This study indicates that the S‐REA can be an accurate nonequilibrium multiphase mass‐transfer model with appropriate account of the local evaporation rate. The overall REA concept is expected to contribute substantially for better and cost‐effective representation of transport phenomena of drying process. © 2012 American Institute of Chemical Engineers AIChE J, 59: 55–67, 2013     

COMPUTATIONAL FLUID DYNAMICS OF INDUSTRIAL BATCH DRYERS OF FRUITS

An industrial batch-type, tray air dryer constructed for drying of several fruits, was investigated. Momentum, heat and mass transfer regarding both gaseous and solid phases was simulated using computational fluid dynamics. A mathematical model of the dryer for predicting the turbulent, three-dimensional transfer phenomena inside the industrial batch dryer equipment was developed and analyzed. The model consists of the full set of partial differential equations that describe the conservation of mass, momentum and heat inside the dryer. The standard k-ε model was used to describe turbulence in addition to the governing conservation equations. The simulated profiles of flow field, temperature and humidity of the air phase revealed a lack of spatial homogeneity of air conditions above the product. The situation was found to greatly influence the distribution of material moisture content of the dried product for the various stages of drying. The investigation was carried out for the representative case of sultana raisins.