A Three-Dimensional Simulation of a Spray Dryer Fitted with a Rotary Atomizer

Spray dryers fitted with rotary atomizers are commonly used in diverse industries to produce engineered powders on a large scale. Scale-up of such units is still largely empirical and based on prior experience and know-how. In the present study, a three-dimensional spray dryer with rotary atomizer is investigated numerically with a commercial CFD code. Continuous-phase, i.e., air, conservation equations are formulated in the Eulerian model while the droplet or particle equations are set up in the Lagrangian model. Two-way coupling between the continuous and dispersed phases is taken into account in the governing equations. The stochastic approach is used to predict the particle trajectories. The RNG k - ε turbulence model was used. Typical results, viz. air velocity, temperature, humidity profiles, and particle trajectories are presented and discussed. Compared with the pressure nozzle spray dryer, more volume of drying chamber is used effectively by the rotating disc type spray dryer. It is found that evaporation and drying take place mainly in the region and in the vicinity of first contact between air and spray. A parametric study is presented and, where appropriate, comparison is made with experimental data obtained with the simulated spray dryer.     

A Three-Dimensional Simulation of a Spray Dryer Fitted with a Rotary Atomizer

Abstract

Spray dryers fitted with rotary atomizers are commonly used in diverse industries to produce engineered powders on a large scale. Scale-up of such units is still largely empirical and based on prior experience and know-how. In the present study, a three-dimensional spray dryer with rotary atomizer is investigated numerically with a commercial CFD code. Continuous-phase, i.e., air, conservation equations are formulated in the Eulerian model while the droplet or particle equations are set up in the Lagrangian model. Two-way coupling between the continuous and dispersed phases is taken into account in the governing equations. The stochastic approach is used to predict the particle trajectories. The RNG k ? ? turbulence model was used. Typical results, viz. air velocity, temperature, humidity profiles, and particle trajectories are presented and discussed. Compared with the pressure nozzle spray dryer, more volume of drying chamber is used effectively by the rotating disc type spray dryer. It is found that evaporation and drying take place mainly in the region and in the vicinity of first contact between air and spray. A parametric study is presented and, where appropriate, comparison is made with experimental data obtained with the simulated spray dryer.     

Parallel and high resolution numerical solution of concentration and temperature distributions in fluidized beds

In this article higher order in time numerical schemes with efficient time stepping for the solution of concentration and temperature distributions in fluidized beds using parallel computers are presented. The mathematical model equations consist of strongly coupled and semi linear convection-diffusion-reaction equations. Invariant regions for the model are derived to check the solution bounds. The numerical discretization for the space using the finite element method is presented and the numerical treatment is enhanced by using adaptive and higher order linearly implicit Runge–Kutta methods for the time discretization. For different time stepping methods and different spatial grid sizes numerical results are obtained and compared. The methods used show a clear improvement for the problem under consideration compared to previously presented results (Nagaiah, Warnecke, Heinrich, & Peglow, 2008). Additionally, the higher order time stepping methods yield a good parallel efficiency, paving the way for the efficient study of more complex phenomena.     

Numerical simulations of ultrafine powder coating systems

Numerical simulations for gas–solid two-phase flows were conducted for an experimental coating booth and an industrial coating booth to study the effect of the coating powder size on the performance of the coating process. To optimize coating parameters, simulations were conducted for different coating parameters, such as the size of the coating part, the distance between the coating part and the spray gun, the air flow rate and particle flow rate from the spray gun, the position of the pattern adjust sleeve of the spray gun, and the electrostatic field, in order to increase the coating process efficiency and coating quality.

In numerical simulations, the air flow field is obtained by solving three-dimensional Navier–Stokes equations with standard κ– turbulence model and non-equilibrium wall function. The second phase, the coating powder, consists of spherical particles and is dispersed in the continuous phase, the air. In addition to solving transport equations for the air, the trajectories of the particles are calculated by solving the particle motion equations using Lagrangian method. It is assumed that the particle–particle interaction can be neglected due to low particle volume fraction in coating systems. The electrostatic field is predicted by solving the Laplace equation.     

喷雾冲击条件下液膜流动与传热模型

针对现有喷雾冷却计算模型的不足,以质量、动量、能量守恒方程为基础,建立喷雾冷却非沸腾区的液膜流动与传热方程,并采用数量级分析的方法对方程简化,最后运用数值方法对模型进行求解。给定液滴速度及液体温度,由模型计算液膜厚度、平均热通量与液体流出温度,与实验测试结果对照。结果显示,液膜厚度的计算结果与实验结果相差6%以内;平均热通量和液体离开待冷却表面的最终温度计算结果与实验结果相差10%以内,且超过60%的计算结果偏差小于5%。计算结果与实验结果的高度匹配证明该模型可较好地反映喷雾冷却过程的流动与换热。由模型可以获取不同位置处液膜厚度与温度,从而加深对喷雾冷却传热机理的理解。     

Numerical Study of the Effect of Particle Size on the Coating Efficiency and Uniformity of an Electrostatic Powder Coating Process

This paper reports on a research project that studies the effect of particle size on the coating efficiency and coating uniformity in a powder coating system using the computational fluid dynamics as a modelling tool. The numerical simulations are conducted for different particle sizes with different distances between the spray gun and the coating part and different positions of the powder spray gun pattern adjuster sleeve (PAS). This study can provide detailed information on air flow pattern and particle trajectories inside the powder coating booth, and the coating film thickness on the coated part as well as the particle transfer efficiency (PTE). In numerical simulations, the air flow field is obtained by solving three‐dimensional Navier‐Stokes equations with standard κ‐ϵ turbulence model and non‐equilibrium wall function. The second phase, the coating powder, consists of spherical particles that are dispersed in the continuous phase, the air. In addition to solving transport equations for the air, the trajectories of the particles are calculated by solving the particle motion equations using the Lagrangian method. It is assumed that particle‐particle interaction can be neglected. The electrostatic field is modelled by solving the Laplace equation.     

Numerical simulation of temperature and concentration distributions in fluidized beds with liquid injection

In this paper a numerical simulation study of dynamic behavior of a fluidized bed with liquid injection is presented. A continuum model has been developed taking into account the mass and energy balances of solid, gas as well as liquid to describe the temperature and concentration distributions in gas-solid-fluidized beds. The model considers the deposition efficiency of the liquid droplets as well as the influence of the spray nozzle region. For solving the non-linear partial differential equations with discrete boundary conditions a finite element method is used. Numerical computations have been done with two different schemes of time integration, a fully implicit and a semi implicit scheme. The complex correlations of mass and liquid flow rates, mass and heat transfer, drying, and transient two-dimensional air humidity, air temperature, particle wetting, liquid film temperature and particle temperature were simulated. The model was validated with transient measurements of the air temperature and air humidity at the outlet of a fluidized bed with water injection.     

Chebyshev配置点谱方法直接求解离散坐标辐射传递方程

针对三维长方形炉内具有吸收-发射介质的辐射换热,基于Chebyshev配置点谱方法和Schur分解开发了直接求解辐射离散坐标方程的求解器。针对离散后所得到的三维矩阵方程,分别用两种方法进行求解,一种是用张量积将三维转变成二维然后直接用Schur分解求解;另一种是自行开发三维Schur分解直接求解。数值实验表明,在相同的输入参数下,新求解器具有很好的精度,尤其相比于标准离散坐标法,新求解器能节省大量计算时间。特别是基于三维Schur分解的直接求解器,在相同的输入参数下,计算时间只有标准离散坐标法的10%～1%。     

Effects of uniform magnetic field on the interaction of side-by-side rising bubbles in a viscous liquid

Effects of uniform magnetic fields on the interaction and coalescence of side-by-side rising bubbles of dielectric fluids were not studied; so in the present research, effects of different strengths of uniform magnetic field on the interaction of two bubbles rising side by side in a viscous and initially stagnant liquid are studied, numerically. For numerical modeling of the problem, a full computer code was developed to solve the governing equations which are continuity, Navier-Stokes, magnetic field and interface capturing equations which are level set and re-initialization equations. The finite volume method is used for the discretization of the hydrodynamic equations where the finite difference method is used to discretization of the magnetic field equations. The results are compared with available numerical and experimental results which show a good agreement. It is found that the uniform magnetic field can be used for contactless control of side-by-side coalescence of bubbles.     

APPLICATION OF A k-ε TURBULENCE MODEL TO AN ENCLOSED BUOYANCY DRIVEN RECIRCULATING FLOW

A numerical study is performed of the turbulent two-dimensional air flow in a square enclosure where the vertical walls are held at different constant temperatures and horizontal walls have linear temperature distributions. The equations solved are for continuity, mean momentum and mean thermal energy. The turbulent shear stresses and heat fluxes in these equations are prescribed using a three-dimensional turbulence model involving the solution of two extra differential equations for k, the turbulent kinetic energy, and ε, its rate of dissipation. Buoyancy effects on the turbulence structure are also accounted for. Results have been obtained in the range of Grashof numbers of 107-108. Moreover, various model constants were tested and a sensitivity study was carried out in order to determine the effect of these constants on the results. A comparison with experimental data is given: the agreement is good.     

A Three Dimensional Model for Heat and Mass Transfer in Convective Wood Drying

A three-dimensional model is proposed to describe the heat and mass transport process in drying of wood. The model is based on conservation of mass and energy and uses constant parameters obtained by comparing experimental data with numerical results. The model uses parameter values from literature. Experimental results obtained for temperature profiles during drying of a block of beech wood are compared with the model results. Satisfactory agreement is obtained over a range of drying air temperatures and velocities.     

Three-Dimensional Simulation of the Non-Isothermal Cast Film Process of Polymer Melts

A modeling system is proposed to simulate the non-isothermal three-dimensional cast film process of viscous polymer melts. The finite element method (FEM) is used to solve the system and the numerical results are compared with the experimental measurements, including temperature, velocity fields, and final film shape. It is found from these results that the model is able to predict the film shape accurately under the steady-state processing conditions. The model considers the flow in the thickness direction, shear-thinning, non-isothermal effect, self-weight, and viscous dissipation, but it excludes die swell at the die exit, elasticity of materials, crystallization, and film sag. Using the model, the influence of temperature variation, draw ratio, and air gap length on the final film shape is also investigated.     

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.     

A Three-Dimensional Numerical Study of the Gas/Particle Interactions in an Industrial-Scale Spray Dryer for Milk Powder Production

Gas/particle interaction plays an important role in modern spray dryers and may have influences on wall deposition, agglomeration, powder degradation, etc. In the present study, the three-dimensional (3-D) transient multiphase flow in an industrial-scale spray dryer has been investigated using the CFD package FLUENT. The Eulerian–Lagrangian approach and two-way coupling method were used in the simulations. The reaction engineering approach (REA model) for milk particles has been implemented. Some new characteristics of the gas flow pattern and the particle behavior (e.g., temperature–time profiles) were identified from the numerical results; for example, the milk particles flow in such a way that makes the central jet oscillation more nonlinear. The discrete phase enhances the turbulence near the air/droplet inlet but damps it downstream. The transient turbulent flow causes significant uncertainties in the particle tracking, which presented some challenges in simulations. The study has highlighted the importance in performing 3-D transient simulations in order to understand the industrial-scale dryers.     

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

ABSTRACT

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.     

A Modified Eulerian-Lagrangian Approach Applied to a Compact Down-Hole Sub-Sea Gas-Liquid Separator

This article presents a modified Eulerian-Lagrangian approach for solving multi-phase flow applied to a laboratory-scale gas-liquid separator designed for high gas content. The separator consists of two concentric pipes with a swirl tube in the annular space between the pipes. The gas-liquid mixture comes from a tangential side inlet and the system works with a combination of gravity and centrifugal forces to achieve a high-efficient gas-liquid separation. In the modified Eulerian-Lagrangian method, gas flow is coupled with the spray and wall film models. The spray model involves multi-phase flow phenomena and requires the numerical solution of conservation equations for the gas and the liquid phase simultaneously. With respect to the liquids phase, the discrete-droplet method (DDM) is used. The droplet-gas momentum exchange, droplet coalesces and breaks-up, and the droplet-wall interaction with wall-film generation and entrainment of the water droplet back into the gas stream are taken into account in this investigation. To be consistent with the experiments the experimental air water mixture on the liquid carry over (LCO) curve is used for the numerical investigation. The standard k-? turbulence model is used for turbulence closure. The predicted results from the modified Eulerian-Lagrangian multi-phase model explain the complex flow behavior inside the separator and are in good agreement when compared with experiments.     

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.