A COMPREHENSIVE MATHEMATICAL AND NUMERICAL MODELING OF DEEP-BED GRAIN DRYING

This paper deals with comprehensive mathematical and numerical modeling of deep-bed grain drying. In order to build the process model, it is necessary to analyze the transport in both grain and gas phases. Experimental works were carried out for a layer of grain bed in order to validate the models. The models consider momentum, energy, and mass conservation within grain and drying air phase. The two-dimensional dynamic equations of energy and mass conservation are solved numerically by finite-difference method (FDM) and utilizing alternating direction implicit algorithm within grain and drying air phase, while momentum conservation are solved by finite difference method by utilizing Semi-Implicit Method for Pressure-Linked Equations (SIMPLE) algorithm. Furthermore, the models will be applied in consideration with developing and designing dryer in order to simulate humidity and temperature profiles of the drying gas together with moisture content and temperature of grain across dryer in term of the dryer performance. The simulations show that the models can be used to predict the dynamic drying characteristic profiles as well as the superficial velocity of drying air phase across dryer.     

A COMPREHENSIVE MATHEMATICAL AND NUMERICAL MODELING OF DEEP-BED GRAIN DRYING

ABSTRACT

This paper deals with comprehensive mathematical and numerical modeling of deep-bed grain drying. In order to build the process model, it is necessary to analyze the transport in both grain and gas phases. Experimental works were carried out for a layer of grain bed in order to validate the models. The models consider momentum, energy, and mass conservation within grain and drying air phase. The two-dimensional dynamic equations of energy and mass conservation are solved numerically by finite-difference method (FDM) and utilizing alternating direction implicit algorithm within grain and drying air phase, while momentum conservation are solved by finite difference method by utilizing Semi-Implicit Method for Pressure-Linked Equations (SIMPLE) algorithm. Furthermore, the models will be applied in consideration with developing and designing dryer in order to simulate humidity and temperature profiles of the drying gas together with moisture content and temperature of grain across dryer in term of the dryer performance. The simulations show that the models can be used to predict the dynamic drying characteristic profiles as well as the superficial velocity of drying air phase across dryer.     

MODELING AND SIMULATION OF CROSSFLOW MOVING BED GRAIN DRYERS

ABSTRACT

The drying of grain in dryers of a crossflow moving bed type was theoretically and experimentally studied. Two different dryer configurations were analyzed, a dryer with central air distribution and another with multiple air duels. Experimental information was obtained in pilot-size dryers. A mathematical model to simulate the process was developed. Hindered drying was accounted for by using the concept of relative drying rate. An adjustable factor, specific to the dryers, was used to account for the uncertainties of the contact area and the transfer coefficients encountered in the literature. Agreement between experimental results and simulations was fairly good. Simulations showed that distance between inlet air and outlet devices, air to solid flow ratio and dryer height to cross section ratio have great influence on the process. The mathematical model may be a useful tool for process exploration and optimization of this type of dryers.     

MODELING AND SIMULATION OF CROSSFLOW MOVING BED GRAIN DRYERS

The drying of grain in dryers of a crossflow moving bed type was theoretically and experimentally studied. Two different dryer configurations were analyzed, a dryer with central air distribution and another with multiple air duels. Experimental information was obtained in pilot-size dryers. A mathematical model to simulate the process was developed. Hindered drying was accounted for by using the concept of relative drying rate. An adjustable factor, specific to the dryers, was used to account for the uncertainties of the contact area and the transfer coefficients encountered in the literature. Agreement between experimental results and simulations was fairly good. Simulations showed that distance between inlet air and outlet devices, air to solid flow ratio and dryer height to cross section ratio have great influence on the process. The mathematical model may be a useful tool for process exploration and optimization of this type of dryers.     

DYNAMICS AND CONTROL OF CROSS-FLOW GRAIN DRYERS I. MODEL DEVELOPMENT AND TESTING

A general dynamic model for a cross-flow dryer is developed from fundamental balance equations. Six dimensionless groups that govern the process are defined and the resulting dimensionless equations are solved with the method of lines, using the Advanced Continuous Simulation Language software package ACSL (1986). The mesh influence on the numerical solution is investigated, and the assumption of quasi-steady state for the air is discussed. Application of the model to rice-drying experiments shows good agreement, and the results underline the potential of the model and the numerical solution strategy in obtaining critical physical insight towards the operation of cross-flow rice dryers.     

SIMULATION AND SCALE-UP OF PNEUMATIC CONVEYING AND CASCADING ROTARY DRYERS

This paper presents a unified model for simulation of cocurrent and countercurrent dispersion-type dryers. The main industrial applications are to pneumatic conveying (flash) dryers and cascading (direct) rotary dryers. The basic model is a one-dimensional incremental (stepwise) simulation, which has been developed over a number of years Equations for particle motion, heat and mass transfer, heat and mass balances and local gas conditions are solved simultaneously over a small increment along the dryer. All workers have previously had considerable difficulty in obtaining a good fit between simulations and actual results from pilot-plants or large-scale industrial dryers. A new “fitting mode” calculation overcomes this by identifying the parameters which need to be adjusted, concentrating on those which cannot be measured accurately. Excellent agreement has been obtained between the model and experimental data by this method. The paper also presents revised formulations for particle motion and heat transfer in rotary dryers. The model has been incorporated into two computer programs for flash and rotary dryers respectively, and results from the former are shown for a case study.     

SIMULATION AND SCALE-UP OF PNEUMATIC CONVEYING AND CASCADING ROTARY DRYERS

ABSTRACT

This paper presents a unified model for simulation of cocurrent and countercurrent dispersion-type dryers. The main industrial applications are to pneumatic conveying (flash) dryers and cascading (direct) rotary dryers. The basic model is a one-dimensional incremental (stepwise) simulation, which has been developed over a number of years Equations for particle motion, heat and mass transfer, heat and mass balances and local gas conditions are solved simultaneously over a small increment along the dryer. All workers have previously had considerable difficulty in obtaining a good fit between simulations and actual results from pilot-plants or large-scale industrial dryers. A new “fitting mode” calculation overcomes this by identifying the parameters which need to be adjusted, concentrating on those which cannot be measured accurately. Excellent agreement has been obtained between the model and experimental data by this method. The paper also presents revised formulations for particle motion and heat transfer in rotary dryers. The model has been incorporated into two computer programs for flash and rotary dryers respectively, and results from the former are shown for a case study.     

MODELING AND MEASUREMENTS OF INFRARED DRYERS FOR COATED PAPER

We have developed models to determine the radiative heat transfer of infrared dryers. Using the models, the efficiencies of several IR constructions are calculated. The radiation properties of all parts of the IR dryer are measured with an IT-IR spectrometer using integrating sphere techniques. With these models and measured results, the total efficiencies of several dryer constructions are calculated for: an electric dryer with a pambolic mirror, an elecmc dryer with a flat ceramic mirror, and a gas-fired dryer. The effect of a back reflector on these dryers is also calculated. The efficiencies of all these dryers are compared to each other.     

OPTIMAL DESIGN OF WELL-MLXED FLUIDIZED BED DRYERS

ABSTRACT

In a recent article, Baker described a novel technique for estimating the energy consumption of well-mixed fluidized bed dryers based on the use of experimental drying curves. An integrated approach to performing sizing and energy consumption calculations for such dryers using this technique is described in the present paper. A computer program, which includes not only the dryer simulator but also a heat recovery module and an exhaust air recycle option, is used to evaluate the viability of different energy-conservation strategies. The effects of operating parameters such as bed temperature, solids loading and air velocity on energy consumption and bed area are also explored. The observed drying kinetics are shown to have a major effect on the optimal design and operation of the dryer.     

MODELING AND SIMULATION OF AIRFLOW IN SPOUTED BED DRYERS

ABSTRACT

This paper presents an axisymmetric three-dimensional semi-empirical model that describes the airflow in both the spout and annular regions. Both the pressure and air velocity distributions can be calculated at any point inside the dryer. Thus, the effect of the fluid dynamics on the heat and mass transfer coefficients and, consequently, on the drying process, can be evaluated. The finite element method was used to solve the model. Pressure distributions were measured for several conditions in which stable spouted bed flow regime was attained. Simulated pressure distributions agreed well with experimental data.     

SIMULATION OF TRANSPORT DYNAMICS IN FLUIDIZED-BED DRYERS

ABSTRACT

A mathematical model for predicting three-dimensional, two-phase flow, heat and mass transfer inside fluidized-bed dryers has been developed. The model consists of the full set of partial-differential equations that describe the conservation of mass, momentum and energy for both phases inside the dryer, and is coupled with correlations concerning interphase momentum-, heat-, and mass-transfer.

It is shown that the model can predict the most important engineering aspects of a fluidized-bed dryer including pressure drop, particle holdup, temperature distribution in both phases as well as drying efficiency all over the fluidized-bed. Plug-flow conditions are predicted for the gas phase, while back-mixing is predicted for the particles.

The effect of particle mass-flow-rate on fluidized-bed dryer performance is evaluated. It is shown that the lower the particle mass flow-rate, the more intense the horizontal moisture gradients, while the higher the particle rate the more uniform the moisture distribution throughout the bed.     

PREDICTING THE ENERGY CONSUMPTION OF CONTINUOUS WELL-MIXED FLUIDIZED BED DRYERS FROM DRYING KINETIC DATA

ABSTRACT

Previous work has shown that it is possible to predict the size of a continuous welt-mixed fluidized bed dryer from batch drying curve measurements. This approach has been extended in the present study to include energy consumption calculations. A computer code was written to simulate the performance of the dryer and to determine its specific energy consumption E_s. Starting in this case with an isothermal bed batch drying curve, the program first calculates the mean solids residence time required under specified operating conditions. Mass and energy balances are then used to calculate the heat duty and E_s. The bed temperature was found to have a significant effect on specific energy consumption in all cases. However, the influences of air flowrate and humidity, and of solids loading, were shown to depend on the solids drying characteristics.     

MODELING, SIMULATION AND CONTROL OF CRUDE TOWERS

Crude towers are one of the most energy consuming, complex distillation columns in a refinery. A mathematical model for the rigorous dynamic simulation of a crude tower is presented. Because of the large dimension, large stiffness and non-linearity of the model, dynamic simulation of a crude tower has proven to be very difficult. In this paper, the Sum of Rates algorithm is shown to be suitable for obtaining the steady states of a crude tower. Once a steady state is approached, the dynamic responses of a crude tower can be simulated by the Bubble Point algorithm. The dynamic simulation predicts strong, one-way interaction among the product streams. Through dynamic simulation, it is shown that the interaction can be eliminated by a decoupler.     

STOCHASTIC MODELING OF GRAIN TEMPERATURE IN NEAR-AMBENT DRYING

Stochastic analytical model was developed to describe the heat transfer in a thin layer of grain ventilated with ambient air. As an excitation to the drying system, a stochastic analytical model of ambient air temperature variations during the period of drying, based on a sine function, was used. Mean, correlation function, variance and the standard deviation were determined for air and grain temperature, both treated as random processes. The stochastic model of air temperature variation was fitted to the observed historical data. The effect of the standard deviation of air temperature of the three different climates (Canadian in Winnipeg, Polish in Poman and English in Weddington) on the standard deviation of grain temperature is shown.     

DYNAMICS AND CONTROL OF CROSS-FLOW GRAIN DRYERS 11. A FEEDFORWARD-FEEDBACK CONTROL STRATEGY

ABSTRACT

A feedforward-feedback control of a cross-flow dryer is developed based on a simple mass balance on the dryer. The feedforward action is based on a pseudo inlet moisture and adjusts the grain flow to correct for inlet moisture variations. The feedback loop accounts for possible process changes and model inaccuracies. Simulations of a rice dryer show good control of the outlet moisture for variations in the inlet moisture with or without simultaneous disturbances in air flowrate. Effect of the'feedforward algorithm on feedback control is also investigated and the suggested combination of feedforward and feedback controls is tested for variations in the inlet moisture when its measurements are biased.     

DYNAMICS AND CONTROL OF CROSS-FLOW GRAIN DRYERS 11. A FEEDFORWARD-FEEDBACK CONTROL STRATEGY

A feedforward-feedback control of a cross-flow dryer is developed based on a simple mass balance on the dryer. The feedforward action is based on a pseudo inlet moisture and adjusts the grain flow to correct for inlet moisture variations. The feedback loop accounts for possible process changes and model inaccuracies. Simulations of a rice dryer show good control of the outlet moisture for variations in the inlet moisture with or without simultaneous disturbances in air flowrate. Effect of the'feedforward algorithm on feedback control is also investigated and the suggested combination of feedforward and feedback controls is tested for variations in the inlet moisture when its measurements are biased.     

THE DESIGN AND PERFORMANCE OF CONTINUOUS WELL-MIXED FLUIDIZED BED DRYERS - AN ANALYTICAL APPROACH

In a previous study, a unified approach to the calculation of the size and energy consumption of well-mixed fluidized bed dryers was developed. A computer code was written and a parametric study undertaken to determine the effects of the principal operating variables. The results were shown to depend on the form of the drying kinetics. The present paper describes the formulation of an analytical model of a well-mixed fluidized bed dryer, which applies for materials that exhibit linear falling-rate drying. These materials are typified by small hygroscopic particles, which are frequently dried in such equipment. Equations are presented that enable the drying time, specific energy consumption, heater duty and bed area to be calculated. The predictions of these equations agreed well with previously published experimental findings and with the results of computer simulations for a typical solid (ion exchange resin) exhibiting the required drying characteristics.     

THE DESIGN AND PERFORMANCE OF CONTINUOUS WELL-MIXED FLUIDIZED BED DRYERS - AN ANALYTICAL APPROACH

Abstract

In a previous study, a unified approach to the calculation of the size and energy consumption of well-mixed fluidized bed dryers was developed. A computer code was written and a parametric study undertaken to determine the effects of the principal operating variables. The results were shown to depend on the form of the drying kinetics. The present paper describes the formulation of an analytical model of a well-mixed fluidized bed dryer, which applies for materials that exhibit linear falling-rate drying. These materials are typified by small hygroscopic particles, which are frequently dried in such equipment. Equations are presented that enable the drying time, specific energy consumption, heater duty and bed area to be calculated. The predictions of these equations agreed well with previously published experimental findings and with the results of computer simulations for a typical solid (ion exchange resin) exhibiting the required drying characteristics.     

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.     

MODELING AND SIMULATION OF BINARY APPROACH BY ENERGY CONSERVATION ANALYSIS

A new model for approach processes of two unequal or equal sized drops or bubbles is proposed based on a parallel film concept and energy conservation analysis. This model can estimate the interaction time and the maximum film area for an approach and the effects of Weber number, size ratio and curvature of film. It also gives a good explanation why the effective virtual mass coefficienl in the model of Chesters and Hofman (1982) changes with the size ratio of drops or bubbles.