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.     

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.     

Two-Fluid,Two-Dimensional Model for Pneumatic Drying

Abstract

Pneumatic drying is a widely used process in the chemical industries and includes simultaneous conveying and heat and mass transfer between the particles and the heat gas. The increase in the use of this unit operation requires reliable mathematical models to predict processes in the industrial facilities. In the present study a Two-Fluid model has been used for modeling the flow of particulate materials through pneumatic dryer. The model was solved for a two-dimensional steady-state condition and considering axial and radial profiles for the flow variables. A two-stage drying process was implemented. In the first drying stage, heat transfer controls evaporation from the saturated outer surface of the particle to the surrounding gas. At the second stage, the particles were assumed to have a wet core and a dry outer crust; the evaporation process of the liquid from a particle is assumed to be governed by diffusion through the particle crust and by convection into the gas medium. As evaporation proceeds, the wet core shrinks while the particle dries. The numerical procedure includes discretization of calculation domain into torus-shaped final volumes, solving conservation equations by implementation of the SIMPLE (Semi-Implicit Method for Pressure-Linked Equations) algorithm and controls over coupling of phases by IPSA (Interphase Slip Algorithm). The developed model was applied to simulate a drying process of wet PVC particles in a large-scale pneumatic dryer and to a drying process of wet sand in a laboratory-scale pneumatic dryer. The numerical solutions are compared successfully with the results of independent numerical and experimental investigations. Following the model validation, the two-dimensional distributions of the flow characteristics were examined.     

PNEUMATIC DRYING IN DILUTED PHASE: PARAMETRIC ANALYSIS OF TUBE DIAMETER AND MEAN PARTICLE DIAMETER

ABSTRACT

In previous work on pneumatic drying presented by the authors, a mathematical model based on the conservation equations of momentum, mass and energy was proposed. This model was developed taking into account axial and radial profiles for gas and solids velocities, pressure and porosity in the drying tube. These dynamic profiles influenced the behavior of temperature in the gas and particulate phases, gas humidity and solids moisture content. In this work, this model has been used to perform a parametric analysis of the tube and panicle diameters in the pneumatic drying process. These variables were analyzed here for fixed conditions of gas and solids flowrates and initial values of temperatures, humidity and moisture content. Factorial planning was applied to the numerical solution of the mathematical model. Experimental data obtained in a pilot scale pneumatic dryer were used as the initial conditions in the simulation to specify the levels of the variables analyzed. Results on the influence of tube diameter and particle diameter on the drying process were obtained by statistical analysis of the responses generated by the factorial planning.     

PSEUDO TWO-DIMENSIONAL MODEL FOR A PNEUMATIC DRYER

ABSTRACT

Pneumatic drying of chemical products has been frequently used in chemical industries. The increase in the use of this unit operation requires the knowledge of the dynamic of the gas-solid flow in tubes. The mathematical models of vertical pneumatic conveying found in the literature mostly consider the flow steady and one dimensional. However, experimental evidences suggest that radial profiles of the basic variables of the flow exist. In this work a model is proposed for vertical pneumatic conveying considering axial and radial profiles for gas and solids velocities, porosity and pressure. The conservation equations for energy and mass of water were written to extend the model to a pneumatic dryer. The equations of the model were solved using finite difference method and the results show the axial and radial variations of gas and solid temperatures, gas humidity and particle moisture content in the dryer.     

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.     

Two-Fluid, Two-Dimensional Model for Pneumatic Drying

Pneumatic drying is a widely used process in the chemical industries and includes simultaneous conveying and heat and mass transfer between the particles and the heat gas. The increase in the use of this unit operation requires reliable mathematical models to predict processes in the industrial facilities. In the present study a Two-Fluid model has been used for modeling the flow of particulate materials through pneumatic dryer. The model was solved for a two-dimensional steady-state condition and considering axial and radial profiles for the flow variables. A two-stage drying process was implemented. In the first drying stage, heat transfer controls evaporation from the saturated outer surface of the particle to the surrounding gas. At the second stage, the particles were assumed to have a wet core and a dry outer crust; the evaporation process of the liquid from a particle is assumed to be governed by diffusion through the particle crust and by convection into the gas medium. As evaporation proceeds, the wet core shrinks while the particle dries. The numerical procedure includes discretization of calculation domain into torus-shaped final volumes, solving conservation equations by implementation of the SIMPLE (Semi-Implicit Method for Pressure-Linked Equations) algorithm and controls over coupling of phases by IPSA (Interphase Slip Algorithm). The developed model was applied to simulate a drying process of wet PVC particles in a large-scale pneumatic dryer and to a drying process of wet sand in a laboratory-scale pneumatic dryer. The numerical solutions are compared successfully with the results of independent numerical and experimental investigations. Following the model validation, the two-dimensional distributions of the flow characteristics were examined.     

PNEUMATIC DRYING IN DILUTED PHASE: PARAMETRIC ANALYSIS OF TUBE DIAMETER AND MEAN PARTICLE DIAMETER

In previous work on pneumatic drying presented by the authors, a mathematical model based on the conservation equations of momentum, mass and energy was proposed. This model was developed taking into account axial and radial profiles for gas and solids velocities, pressure and porosity in the drying tube. These dynamic profiles influenced the behavior of temperature in the gas and particulate phases, gas humidity and solids moisture content. In this work, this model has been used to perform a parametric analysis of the tube and panicle diameters in the pneumatic drying process. These variables were analyzed here for fixed conditions of gas and solids flowrates and initial values of temperatures, humidity and moisture content. Factorial planning was applied to the numerical solution of the mathematical model. Experimental data obtained in a pilot scale pneumatic dryer were used as the initial conditions in the simulation to specify the levels of the variables analyzed. Results on the influence of tube diameter and particle diameter on the drying process were obtained by statistical analysis of the responses generated by the factorial planning.     

GRAIN DRYING OPTIMISATION AT LOW TEMPERATURES

ABSTRACT

The optimisation of grain drying systems was studied through the dynamic programming technique focusing on the minimisation of the energy consumption, lakingin account the conservation of the product quality and avoiding excessive humidity gradients in the bed at the end stages of drying. An algorithm was developed, where the input data were the initial conditions of the product and the climate data of the region. The operational conditions considered were: fan on or off, and different degrees of air heating (1 to 5 °C). The result obtained was an optimised management strategy for the operation of the dryer, specified for each stage of the process, in two situations: calculated from the mean climate dam of ten years, and corrected day by day with up to date climate data.     

COMPARISON OF SUPERHEATED STEAM AND AIR OPERATED SPRAY DRYERS USING COMPUTATIONAL FLUID DYNAMICS.

ABSTRACT

In this paper a numerical simulation of a spray dryer using the computational fluid dynamics (CFD) code Fluent is described. This simulation is based on a discrete droplet model and solve the partial differential equations of momentum, heat and mass conservation for both gas and dispersed phase.

The model is used to simulate the behaviour of a pilot scale spray dryer operated with two drying media : superheated steam and air Considering that there is no risk of powder ignition in superheated steam, we choosed a rather high inlet temperature (973 K). For the simulation, drop size spectrum is represented by 6 discrete droplets diameters, fitting to an experimental droplets size distribution and all droplets are injected at the same velocity, equal to the calculated velocity of the liquid sheet at the nozzle orifice.

It is showed that the model can evaluate the most important features of a spray dryer : temperature distribution inside the chamber, velocity of gas, droplets trajectories as well as deposits on the walls. The model predicts a fast down flowing core jet surrounded by a large recirculation zone. Using superheated steam or air as a drying medium shows only slight differences in flow patterns. Except for the recirculation which is tighter in steam.

The general behaviour of droplets in air or steam are quite the same : smallest droplets are entrained by the central core and largest ones are taken into the recirculation zone. In superheated steam, the droplets penetrate to a greater extent in the recirculation zone. Also, they evaporate faster. The contours of gas temperature reflect these differences as these two aspects are strongly coupled. In both air and steam there is a “cool” zone which is narrower in steam than in air. Finally, the panicle deposit problem seems to be more pronounced in air than in steam.

Adding to the inherent interest in using superheated steam as a drying medium, the model predicts attractive behaviour for spray drying with superheated steam. In particular. under the conditions tested with the model, a higher volumetric drying rate is obtained in superheated steam.     

Comparison of Moving Bed Dryers of Solids Operating in Parallel and Counterflow Modes

Abstract

The drying rates in moving bed dryers are compared. The gas and the solids to be dried are in parallel flow or counterflow. A new simplified method to simulate the drying in parallel and counterflow moving beds is developed. This model is based on the solution of arbitrary experimental or theoretical drying rate Equations of single solid particles (or thin-layer drying rate equation) coupled with heat and mass conservation Equations of the dryer. The solution is presented in an integral form of the drying equation showing the relation between time or location in the dryer and degree of drying. The method allows rapid calculation of the moisture, vapor mass fraction, and temperature distributions along the dryer in drying with moist air or steam. The model is demonstrated by using a result based on the receding front evaporation model as the specific thin-layer drying equation in the moving bed model. Wood chips are chosen as an example of the substance to be dried, but the method applies also for other medium, if the dependence of the drying rate on moisture and ambient temperature and humidity (thin layer drying rate) is known. The size of the dryer needed to reach the same degree of drying operating in the parallel mode is much greater than that of counterflow type, when the drying medium is air or flue gases. The reason for the poorer drying in parallel flow is mainly the unfavorable distribution of the evaporation temperature. In steam drying, the difference in the size is not so great, since the evaporation takes place approximately at constant temperature.     

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.     

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.     

COMPUTER ANALYSIS OF INDUSTRIAL BATCH DRYER AERODYNAMICS

ABSTRACT

One of the fundamental problems encountered in the batch dryer design field is the determination of appropriate equipment configuration that would ensure uniform distribution of air over the dryer trays. Such industrial batch dryer aerodynamics problems can be successfully investigated using computational fluid dynamics techniques. A mathematical model for predicting the two-dimensional air flow inside a typical industrial batch dryer equipment is developed and analyzed. The model consists of the full set of partial differential equations that describe the conservation of mass and momentum inside the dryer. The standard k-E model is used to describe turbulence in addition to the governing conservation equations. Distribution of drying air within the dryer is regulated using adjustable air blast blades in the entrance section of the drying chamber. An appropriate configuration of these flow adjusting devices is proposed so that an adequately uniform drying air distribution pattern inside the drying chamber is achieved. Finally, a characteristic design case is presented to demonstrate the effectiveness of the proposed approach.     

A Parametric Study of Spray Drying of a Solution in a Pulsating High-Temperature Turbulent Flow

Spray drying of a concentrated common salt (NaCl) solution carried out in the intense oscillating high-temperature turbulent flow field generated in the tailpipe of a pulse combustor was simulated. Simulation of such transport process problems is especially crucial since the environmental conditions are too hostile for detailed and reliable measurements. The momentum, heat, and mass transfer processes between the gas and droplet phases during drying were simulated using a computational fluid dynamic solver. The simulated profiles of flow field, temperature, and humidity of gaseous phase, and particle trajectories in a drying chamber are presented and discussed. The effects of gas temperature, pulse frequency and amplitude, and gas mass flow rate on the transient flow patterns, droplet trajectories, and overall dryer performance were investigated. Different turbulence models were also tested. Simulation results show that the flow field and droplet drying conditions vary widely during a single pulsating period. Very short drying times and very high drying rate characterize pulse combustion spray drying. Thus, pulse combustion drying can be applied to drying of fine droplets of highly heat-sensitive materials although the jet temperature initially is extremely high.     

One-dimensional phosphate flash dryer model for design application

The present paper studies the design of a bench scale flash dryer for phosphate particles using a one-dimensional steady-state model. The model was based on the two-fluid theory considering momentum, heat, and mass transfer between the solid and gas phases for a dilute gas–solid suspension flow and for which solid interactions were neglected. The set of coupled nonlinear differential equations of the model was solved using a Runge–Kutta method. A sensitivity analysis for inlet air and solid velocity, air temperature and pressure, air and solid moisture content, and for tube diameter and length was performed to design phosphate bench scale flash dryer to reduce the solid moisture content from 18 to 2%. An analysis of the results enabled choosing the appropriate conditions for experiments of phosphate drying for a hot air stream inlet of 200°C, in a flash dryer of 1.7?m length and 0.2?m internal diameter.     

A Parametric Study of Spray Drying of a Solution in a Pulsating High-Temperature Turbulent Flow

Spray drying of a concentrated common salt (NaCl) solution carried out in the intense oscillating high-temperature turbulent flow field generated in the tailpipe of a pulse combustor was simulated. Simulation of such transport process problems is especially crucial since the environmental conditions are too hostile for detailed and reliable measurements. The momentum, heat, and mass transfer processes between the gas and droplet phases during drying were simulated using a computational fluid dynamic solver. The simulated profiles of flow field, temperature, and humidity of gaseous phase, and particle trajectories in a drying chamber are presented and discussed. The effects of gas temperature, pulse frequency and amplitude, and gas mass flow rate on the transient flow patterns, droplet trajectories, and overall dryer performance were investigated. Different turbulence models were also tested. Simulation results show that the flow field and droplet drying conditions vary widely during a single pulsating period. Very short drying times and very high drying rate characterize pulse combustion spray drying. Thus, pulse combustion drying can be applied to drying of fine droplets of highly heat-sensitive materials although the jet temperature initially is extremely high.     

Modelling and Simulation of a Direct Contact Rotary Dryer

ABSTRACT

A mathematical model able to predict solid and drying gas temperature and moisture content axial profiles along a direct contact rotary dryer was developed. The study was focused on the drying kinetics based on phenomenological models. Two different drying mechanisms in the decreasing drying rate period were tested: proponional to the unbound moisture content and moisture diffusion inside the particle. Experimental data collected in a pilot-scale direct contact rotary dryer was used to validate the model. Soya and fish meals were used as drying material.     

COMPARISON OF SUPERHEATED STEAM AND AIR OPERATED SPRAY DRYERS USING COMPUTATIONAL FLUID DYNAMICS.

In this paper a numerical simulation of a spray dryer using the computational fluid dynamics (CFD) code Fluent is described. This simulation is based on a discrete droplet model and solve the partial differential equations of momentum, heat and mass conservation for both gas and dispersed phase.

The model is used to simulate the behaviour of a pilot scale spray dryer operated with two drying media : superheated steam and air Considering that there is no risk of powder ignition in superheated steam, we choosed a rather high inlet temperature (973 K). For the simulation, drop size spectrum is represented by 6 discrete droplets diameters, fitting to an experimental droplets size distribution and all droplets are injected at the same velocity, equal to the calculated velocity of the liquid sheet at the nozzle orifice.

It is showed that the model can evaluate the most important features of a spray dryer : temperature distribution inside the chamber, velocity of gas, droplets trajectories as well as deposits on the walls. The model predicts a fast down flowing core jet surrounded by a large recirculation zone. Using superheated steam or air as a drying medium shows only slight differences in flow patterns. Except for the recirculation which is tighter in steam.

The general behaviour of droplets in air or steam are quite the same : smallest droplets are entrained by the central core and largest ones are taken into the recirculation zone. In superheated steam, the droplets penetrate to a greater extent in the recirculation zone. Also, they evaporate faster. The contours of gas temperature reflect these differences as these two aspects are strongly coupled. In both air and steam there is a “cool” zone which is narrower in steam than in air. Finally, the panicle deposit problem seems to be more pronounced in air than in steam.

Adding to the inherent interest in using superheated steam as a drying medium, the model predicts attractive behaviour for spray drying with superheated steam. In particular. under the conditions tested with the model, a higher volumetric drying rate is obtained in superheated steam.     

Superheated Steam Drying of a Single Particle in an Impinging Stream Dryer

ABSTRACT

Impinging stream contactors provide a novel configuration for drying and/or chemical reactions of particulates, pastes or suspensions which can be dispersed in a flowing gas stream. Essentially they consist of one or more highly turbulent “impingement” zones formed by collision of two opposing jets (OJ) in a confied channel or duct. The objective of this paper is to present computational fluid dynamic predictions for two-dimensional turbulent opposing jets over a range of nozzle-to-nozzle separations and jet Reynolds numbers for the simulation of single particle drying in these systems using superheated steam. A number of different turbulence models were tested ( e.g. high Reynolds, Lam-Bremhorst, Launder and Sharma models etc.). Predictions are performed in two distinct parts. In the first part a power law, finite volume method based on the “SIMPLEC” algorithm is used to solve the momentum and energy conservation equations for air in OJ systems in order to gain insight into their