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     

Modelling and Simulation of Momentum, Heat, and Mass Transfer in a Deep-Bed Grain Dryer

This article concerns the modelling and simulation of a deep-bed grain dryer in a large diameter-column. Two-dimensional (2D) models of deep-bed grain dryers were built by considering simultaneously momentum, heat, and mass transfer in the drying phase together with coupled heat and mass balance in the grain phase. The dynamic equations are solved numerically by using finite difference method. The momentum equations are applied to simulate pressure drop and velocity field of the drying air across the bed. The mass and heat balance in the two phases determine the profile of temperature and moisture content in both phases. Further, drying rate curves for various temperature of inlet drying gas together with moisture content of grain were simulated. The simulated profiles are in close agreement with experimental data.     

流化床氛围下多孔物料干燥传热传质的数值模拟

用有限差分法数值求解一个热、质传递耦合模型,理论研究多孔物料流化床干燥过程。方程离散采用全隐格式的控制容积方法,三对角矩阵法（TDMA）用来求解线性方程组。选用球形的苹果丁作为多孔物料。在典型操作条件下,通过分析温度、饱和度和压力的分布侧形,讨论了物料内部的热、质传递机理。在对比条件下,考察了气体入口温度、气速和床面积因子对干燥过程的影响。结果表明：干燥过程受气、固相间的耦合传热传质的影响十分明显,干燥时间随气体入口温度和气速的提高而减少;随床面积因子的增大而增加。     

MODELING AND SIMULATION OF DEEP-BED GRAIN DRYERS

This paper concerns with heterogeneous modeling of deep-bed grain dryers based on two-phase model by taking into account coupled heat and mass transfer within grains. This model also consider axial mass and heat dispersion in the fluid phase. The dynamic two-phase equations are solved numerically by finite difference with alternating direction implicit method algorithm, and then applied to simulate humidity and temperature profile of drying gas across dryers together with moisture content and temperature of grains. The capabilities of these models were compared with experimental data obtained from available literatures, under drying conditions such as temperature and absolute humidity of drying gas and moisture content of grains. The simulation results show that the dynamic of corn drying within the bed is well predicted by the two-phase model.     

MATHEMATICAL SIMULATION OF TEMPERATURE AND MOISTURE FIELDS WITHIN A GRAIN KERNEL DURING DRYING

Non-linear partial differential equations are presented for two dimensional heat and mass transfer within a single grain kernel during drying. In this model, the moisture evaporation inside the kernel is considered. The moisture is assumed to diffuse to the outer boundary of the kernel in liquid form and evaporate on the surface of the kernel. The influence of temperature and moisture content on grain properties is also considered in the simulation. The Non-linear partial differential equations are solved using the finite element method and simulation data is verified on a thin layer dryer for wheat kernels. The comparison shows that the simulated results have a high accuracy with average relative error of about 5%. The results of the finite element analysis can be used for grain quality evaluation, drying simulation studies and stress analysis of grain kernel.     

CONVECTIVE DRYING OF THIN AND DEEP BEDS OF GRAIN

The object of this paper is the experimental and theoretical investigation of heat and mass transfer during drying of packed beds of grain. A deep bed of grain was regarded as a series of thin beds. Analytical expressions for the thin bed drying rate were obtained by defining the air parameters at the grain surface in the falling rate period of drying and using the results of drying experiments. The paper also contains a simulation model for drying deep beds of grain, consisting of four partial differential equations based on energy and mass balances in a bed element. The system of equations was solved using finite difference techniques and a digital computer. A comparison between numerical solutions and experimental results is illustrated.     

CONVECTIVE DRYING OF THIN AND DEEP BEDS OF GRAIN

The object of this paper is the experimental and theoretical investigation of heat and mass transfer during drying of packed beds of grain. A deep bed of grain was regarded as a series of thin beds. Analytical expressions for the thin bed drying rate were obtained by defining the air parameters at the grain surface in the falling rate period of drying and using the results of drying experiments. The paper also contains a simulation model for drying deep beds of grain, consisting of four partial differential equations based on energy and mass balances in a bed element. The system of equations was solved using finite difference techniques and a digital computer. A comparison between numerical solutions and experimental results is illustrated.     

MATHEMATICAL SIMULATION OF TEMPERATURE AND MOISTURE FIELDS WITHIN A GRAIN KERNEL DURING DRYING

ABSTRACT

Non-linear partial differential equations are presented for two dimensional heat and mass transfer within a single grain kernel during drying. In this model, the moisture evaporation inside the kernel is considered. The moisture is assumed to diffuse to the outer boundary of the kernel in liquid form and evaporate on the surface of the kernel. The influence of temperature and moisture content on grain properties is also considered in the simulation. The Non-linear partial differential equations are solved using the finite element method and simulation data is verified on a thin layer dryer for wheat kernels. The comparison shows that the simulated results have a high accuracy with average relative error of about 5%. The results of the finite element analysis can be used for grain quality evaluation, drying simulation studies and stress analysis of grain kernel.     

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.     

Simulation and Validation of Microwave-Assisted Fluidized Bed Drying of Soybeans

A general mathematical model of heat and mass transfer was developed to simulate the microwave-assisted fluidized bed drying of bulk grain. The model was solved using the well-known Runge-Kutta-Gill method. The model is capable of predicting the moisture content of soybean as well as the drying air parameters (i.e., drying air temperature and moisture content) during drying. The values of mean relative deviation (MRD) were less than 8 and 10% for prediction of grain moisture content and outlet air parameters, respectively, which reflects an acceptable accuracy. In comparison with conventional fluidized bed drying of soybean, microwave-assisted fluidized bed drying led to 83.39–98.07% savings in drying time and 82.07–95.22% savings in specific energy consumption when reducing soybean moisture content from 18.32 to 12% (db).     

Modeling of Moisture and Temperature Changes of Wheat during Drying in a Triangular Spouted Bed Dryer

A mathematical model of temperature and wheat moisture content distribution inside a triangular spouted bed dryer was developed. The model is based on analysis of heat and mass transfer inside the dryer. In addition to that, an empirical bulk density model has been developed for wheat and included in the drying simulation. A laboratory-scale triangular spouted bed (TSB) dryer was used to dry wheat grain to validate the model. The dryer was divided into three sections, namely spouting, downcomer, and fountain. A series of drying runs were conducted to record moisture and temperature profile. There were two distinct regions observed during wheat drying. A constant rate period was observed during the initial drying stage and the falling rate period took place at the later drying stage. Initial moisture content and operating drying temperature governed the timing of transition from constant rate period to falling rate period. The model can be used to accurately predict the moisture content of wheat during drying. The temperature prediction inside the TSB dryer was less accurate, especially at high temperatures due to heat losses in the experimental dryer. Further studies are needed to improve the accuracy of this model, especially with regard to the temperature prediction.     

Modeling of Moisture and Temperature Changes of Wheat during Drying in a Triangular Spouted Bed Dryer

A mathematical model of temperature and wheat moisture content distribution inside a triangular spouted bed dryer was developed. The model is based on analysis of heat and mass transfer inside the dryer. In addition to that, an empirical bulk density model has been developed for wheat and included in the drying simulation. A laboratory-scale triangular spouted bed (TSB) dryer was used to dry wheat grain to validate the model. The dryer was divided into three sections, namely spouting, downcomer, and fountain. A series of drying runs were conducted to record moisture and temperature profile. There were two distinct regions observed during wheat drying. A constant rate period was observed during the initial drying stage and the falling rate period took place at the later drying stage. Initial moisture content and operating drying temperature governed the timing of transition from constant rate period to falling rate period. The model can be used to accurately predict the moisture content of wheat during drying. The temperature prediction inside the TSB dryer was less accurate, especially at high temperatures due to heat losses in the experimental dryer. Further studies are needed to improve the accuracy of this model, especially with regard to the temperature prediction.     

HEAT AND MASS TRANSFER DURING DRYING OF GRANULAR PRODUCTS BY COMBINED CONVECTION AND CONDUCTION

Numerical simulation of grain drying in a vertical cylindrical bed has been carried out with an imposed hot air flow and a conductive heat flux at the wall.

The model equations are numerically solved using a finite volume method. The numerical simulation gives the time and space evolution of temperature when the lateral area of the cylinder is heated by a constant density flux and a constant temperature. The influence of different parameters (essentially the ratio of heat flux to the heat capacity of flow, and the dryer geometry) on the relative moisture content and the drying time is examined.     

Cross-Flow Drying of Wheat. A Simulation Program with a Diffusion-Based Deep-Bed Model and a Kinetic Equation for Viability Loss Estimations.

ABSTRACT

A mathematical model of heat and mass transfer for fixed beds was developed according to the modern theory of process simulation and standard laws of thermodynamics and transport phenomena. The mass transfer grain-air was predicted with simplified diffusional expressions together with an equation for the static equilibrium moisture content. Four differential equations were obtained for a grain layer and they were integrated along the bed depth and time with second and a fourth-order methods, respectively. The model was validated by comparing drying time predictions with experimental values, being the average error of 6%. The model was extended into a program for continuous cross-flow drying-cooling     

Multiscale and multilayer structural modeling and simulation on drying of grain packing porous media

ABSTRACT

Aiming at the problem of multilayer physical structure for the skeleton of porous media, a multiscale and multilayer structural model of heat and mass transfer processes for drying of grain packing porous media was established by applying the pore network method and multiscale theory. An experimental study on rice drying was conducted in order to validate this model. The simulation and experimental results indicated that the established model could explain the mechanical properties of rice drying well. The rate of heat transfer was faster than the rate of mass transfer and there was a higher moisture gradient inside the rice grain. The diffusion coefficient of rice embryo played an important role in the drying process, and whose effect on drying was larger than the diffusion coefficient of rice hull and chaff. The moisture was imprisoned effectively inside the rice when the diffusion coefficient of rice embryo was very small.     

HEAT AND MASS TRANSFER DURING DRYING OF GRANULAR PRODUCTS BY COMBINED CONVECTION AND CONDUCTION

Abstract

Numerical simulation of grain drying in a vertical cylindrical bed has been carried out with an imposed hot air flow and a conductive heat flux at the wall.

The model equations are numerically solved using a finite volume method. The numerical simulation gives the time and space evolution of temperature when the lateral area of the cylinder is heated by a constant density flux and a constant temperature. The influence of different parameters (essentially the ratio of heat flux to the heat capacity of flow, and the dryer geometry) on the relative moisture content and the drying time is examined.     

Intergranular Air Movement and Grain Drying in Silos with Fully, Partially and Slanted Perforated Floor

Intergranular air movement and its relation with moving drying fmnt in a grain bulk were investigated experimentally. An improved computer simulation model was developed to analyze the drying or cooling process in a bed of grain with non-parallel airflow from a partially or slanted perforated floor. The model first simulates the airflow, then calc lates the heat and mass transfer between air and grain along the airflow streamlines. The results were compared with the simulated and experimental results from a fully perforated floor configuration. The degree of agreement between the computed and the experimental moisture contents depended upon the floor configuration. The model was not capable of predicting the temperatures to the accuracy of the predicted moisture contents, especially when airflow stream lines were not parallel to each other. For further improvement of the drying simulation model, an improved airflow model and computer program is required. Comparison of the simulated results with experimental data also     

SIMULATION OF DEEP BED DRYING OF HAZELNUTS

The deep bed drying modelling of hazelnut (Corylus avellana L.) have been studied by considering the deep bed as a series of thin layers. A partial differential equations model has been developed to simulate heat and mass transfer in fixed deep bed hazelnut dryers. The computer program developed permits the calculation of temperature and moisture content profiles along the dryer. As a process of validation of the model, the predicted and experimental results of average moisture content of the whole bed were compared. It has been observed that the simulation results agreed quite well with experimental data.     

Dynamic modeling of the steam supply system for a paper drying cylinder

A dynamic model describing the principles of a steam supply system for a paper drying cylinder used in paper production plants was developed based on the mass and heat balances around the cylinder. The balance equations consist of sets of differential equations describing heat and mass transfer around the canvas, the web and the drying cylinder. The effects of the steam valve adjustment on steam pressure, temperature and moisture content were investigated based on the model developed. It was found that application of simple model predictive control to the operation of steam supply system is enough to achieve satisfactory drying performance in a single paper drying cylinder.     

Cross-Flow Drying of Wheat: A Simulation Program with A Diffusion-Based Deep-Bed Model and A Kinetic Equation for Viability Loss Estimation

A mathematical model of heat and mass transfer for fixed beds was developed according to the modern theory of process simulation and standard laws of thermodynamics and transportphenomena. The mass transfer grain-air was predicted with simplified diffusional expressions together with an equation for the static equilibrium moisture content. Four differential equations were obtained for a grain layer and they were integrated along the bed depth and time with second