Disodyum oktaborat kurutulan püskürtmeli kurutucunun modellenmesi
Stokiometrik oranlarda borik asit ve borakstan hazırlanan çözeltiden suyun püskürtmeli kurutucuda uzaklaştırılması ile üretilen hidrate disodyum oktoboratın kuruma davranışının belirlenmesi için gerçekleştirilen matematiksel modelleme çalışmalarında en az varsayımın yapıldığı en üst düzey kabul edilen hesaplamalı akışkanlar dinamiği modeli uygulanmıştır. Modellemede, sürekli faza ait kütle, momentum ve enerji korunum eşitlikleri ile dispers faza ait temel korunum eşitlikleri ve türbülans büyüklüklerini içeren diferansiyel denklem setlerinin çözümü için sonlu hacimler metodu ile çalışan STAR-CD yazılımı kullanılmıştır. Damlacıkların kurutulması esnasında aynı anda iki süreç gerçekleşmektedir. Bunlardan birincisi damlacıklara dışarıdan transfer edilen enerji ile yüzeydeki suyun hava akımı içerisine buharlaştırılması, ikinci süreç ise suyun yüzeyden buharlaşmaya başlaması ile aynı zamanda damlacığın iç kısımlarındaki nemin sıvı veya buhar halinde yüzeye transferidir. Parti-kül içerisindeki nem taşınımı kararsız hal difüzyon eşitliği ile ifade edilerek, lokal nem içeriği ve sıcaklığa bağlı difüzyon katsayısı hesaplanmış literatürden elde edilen matematiksel eşitliğe uyarlanmıştır. Ayrıca, iki farklı sıcaklıkta ve bağıl nem 0.1 - 0.9 aralığında su buharı desorpsiyon izotermleri oluşturularak denge nem oranları hesaplanmıştır. Difüzyon eşitliğine ait katsayılar, damlacık boyut dağılımı, damlacıkların ilk hızları, türbülans model katsayıları, kurutma havası ve besleme çözeltisi özellikleri yazılımın ön işlemcisinde tanımlanarak, kurutucu içerisinde sürekli faza ait hız, yörünge, sıcaklık ve nem değerleri ile dispers fazda, damlacık kuruma hızları ve kurutucuda kalma süreleri belirlenmiştir. Püskürtmeli kurutucunın üç seviyesinde her seviye için altı noktada nem ve sıcaklık değerleri ölçülerek, elde edilen model sonuçları ile deneysel ölçümler karşılaştırılmış, model sonuçları ile deney sonuçlarının birbirine uyum gösterdiği saptanmıştır.
Modelling of disodium octaborate drying in a spray dryer
Spray drying is one-step continuous unit processing operation for transformation of feed from a liquid form to a dry powder. The feedstock prepared by aqueous solution of borax and boric acid mixtures was atomized into a drying chamber where the resulting spray mixes with hot gas, which evaporates the liquid component of the droplets. The spray dried powders have the appropriate composition of disodium octaborate tetrahydrate.A computational fluid dynamic study was carried out to investigate airflow pattern, temperature, and humidity profile at different levels in the drying chamber. The effects of operating and boundary conditions on the gas flow pattern, droplet trajectories, and overall dryer performance also were investigated. Results are presented and discussed in terms of the gas velocity, temperature, and humidity profiles within the chambers.The analysis were performed on spray dryer fitted with rotary atomizer using STAR-CD code by Euler - Lagrange approaches in which the conservation equations of mass, momentum and energy for the gas flow in the dryer are expressed in the Eulerian form and the droplets in the Lagrangian. In the case of turbulent flow, the conservation equations were solved to obtain time - averaged equations. Additional terms in these equations represent the transport of momentum, heat and mass solved by RNG k -e turbulence model. The droplets temperature, mass and velocity were determined at every location of their trajectories from the local time-averaged solution for the gas. -In order to describe the internal mass transfer, one-dimensional diffusion equation was solved to model the internal distribution and diffusion of water moisture inside the particle which is assumed as spherical shaped. The diffusion coefficient was determined as function of moisture content and temperature. The partial water pressure at the droplet surface is related to the surface moisture content and droplet temperature by desorption isotherms which mathematically represented with three-parameter Guggenheim - Anderson - De Boer (GAB) equation that represents a kinetic model based on multilayer and condensation. Atomization from a rotating disc was modeled by putting 100 injection points along the peripheral of the size of the atomizer. The total feed rate was distributed evenly. between the injection points. Foreach injection, the initial droplet size distribution was back calculated from the size of particles collected from the drying experiments. This back-calculation method assumes uniform shrinkage of the droplet and that there is no inhibition to shrinkage due to the sudden reduction in moisture. In actual condition, depending on the operating parameters, a crust may form from the sudden initial removal of moisture, preventing further shrinkage of the droplet. Since such mechanism is difficult to quantify in an actual dryer, the shrinkage model used as a simplifying assumption. The volume of product changes with the moisture content can be calculated from the actual density of the product and actual particle weight.For carrying out a simulation, first of all the geometry of the dryer was required to be able to make the mesh for the CFD calculations. A calculation grid of the drying chamber was generated with the help of the grid generator. During the calculations the CFD model interacts with the material property database. The gas flow solver calculates the gas conditions, such as temperature, moisture, velocity and degree of turbulence, in each cell of the grid. The particle tracker reads in these data in order to calculate the trajectories and the drying behavior. When the particles pass a cell of the grid the amounts of energy, mass and momentum transferred to the gas are calculated. In the next iteration program uses these transfer terms for a new calculation. The calculation loop is repeated until sufficient convergence is achieved.Accuracy of the drying models is largely affected by the prediction of the airflow within patterns in the drying chamber. The coupling effects from the transfer of mass and energy through the droplet-air interface which will further affect the properties of the air. A simple case study was used to illustrate the ability of CFD in performing optimization analysis. The model was validated by experimental tests on a pilot scale dryer on the base of temperature and water vapor concentration field measurements. The results showed that, this model is potentially usable for spray dryer chamber design for optimization, deposit prevention and scale up.
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