The generation of aerosols of fine particles

A one-dimensional numerical model for a detergent slurry drying process in a counter-current spray drying tower is developed for the prediction of the gas and droplet/particle temperature profiles within the tower. The model accommodates droplets/particles over a range of sizes. A semi-empirical slurry droplet drying model is integrated with a counter-current tower simulation based on mass, energy and particulate phase momentum balances in order to calculate the drying rate and the particle residence time within the tower. The coupled first order ordinary differential equations for the two phases are solved numerically using the iterative shooting method in an algorithm developed within MATLAB. The predictions of the numerical model are compared with industrial pilot plant data. The results are found to vary significantly with the specified size distribution of the droplets. Despite the simplicity of the model in ignoring the coalescence, agglomeration, wall deposition and re-entrainment, the model gives reasonable agreement with the experimental data.

A one-dimensional plug-flow model of a counter-current spray drying tower

A steady-state, three-dimensional, multiphase computational fluid dynamics (CFD) modeling of a pilot-plant countercurrent spray drying tower is carried out to study the drying behavior of detergent slurry droplets. The software package ANSYS Fluent is employed to solve the heat, mass, and momentum transfer between the hot gas and the polydispersed droplets/particles using the Eulerian–Lagrangian approach. The continuous-phase turbulence is modeled using the differential Reynolds stress model. The drying kinetics is modeled using a single-droplet drying model, which is incorporated into the CFD code using user-defined functions (UDFs). Heat loss from the insulated tower wall to the surrounding is modeled by considering thermal resistances due to deposits on the inside surface, wall, insulation, and outside convective film. For the particle–wall interaction, the restitution coefficient is specified as a constant value as well as a function of particle moisture content. It is found that the variation...

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CFD modelling of a pilot-scale counter-current spray drying tower for the manufacture of detergent powder

Spray drying of atomised solutions or slurries is one of the most common methods for
the production of a wide variety of particulate products in the chemical, food, personal
care products and pharmaceutical industries. The modelling of a spray drying process
for the manufacture of detergent powder in a counter-current tower is carried out using
two different approaches: a simple one-dimensional multiphase plug-flow modelling
and a more rigorous CFD modelling approach. Both approaches are coupled with an
existing semi-empirical slurry droplet drying model. The plug-flow model considers
heat, mass and momentum transfer between the polydispersed droplets/particles and gas
phase, along the tower height. In the CFD model, based on the Eulerian-Lagargian
method, the three-dimensional turbulent swirling gas flow is fully coupled with the
droplets/particles motion along with particle-wall interactions via the heat, mass and
momentum exchanges. The simulation results are compared with the experimental data
collected from a large scale pilot-plant spray drying tower and a reasonable agreement
with the measured powder outlet temperature, moisture content, and exhaust gas
temperature is obtained, considering the complexity of the process and the accuracy of
the measured data. The plug-flow model gives similar qualitative trends compared to
the CFD model and can be a useful supplement for quick determination of operating
conditions for pilot-plant trials that would enable more extensive and accurate
optimisation of the process. The more computationally expensive CFD model can be
used for tackling operational and product quality issues including wall deposition and
thermal degradation. The gas flow and temperature profiles, and droplet/particle
trajectories obtained from the CFD modelling results are used to propose a zonal
modelling approach to model spray tower in a computationally efficient manner. This
approach can be used to develop models for process optimisation of counter-current
spray drying towers, as reliably as the CFD model.

Numerical modelling of a counter-current spray drying tower

https://lib.dr.iastate.edu/cgi/viewcontent.cgi?article=5475&context=rtd

Effect of fluid properties and nozzle parameters on drop size distribution from fan spray nozzles

Methods for expressing, measuring, and correlating drop-size distribution data for centrifugal spray nozzles are discussed.

A method for collecting spray droplets in liquid nitrogen is described which is rapid and efficient for most sprayed liquids which freeze above —20°C. Comprehensive correlations for drop-size distributions are reported based on 114 runs performed with the liquid nitogen method.

Size distribution of droplets from centrifugal spray nozzles

This paper presents a method for the dynamic optimization of a chemical process, applicable whether or not the uncontrolled system is stable at the desired operating conditions. The system has several advantages over other methods of dynamic optimization: (1) Dimensionality is not a limitation; (2) Inequality constraints are handled directly; (3) A two-point boundary value problem is not encountered; and (4) Control is designed around a stability criterion. Numerical results on a second order stirred-tank reactor system are presented in order to verily the practicality of the proposed method.

Dynamic optimisation: An extension of the direct method of lyapunov

The design of a continuous stirred-tank reactor, used in the formation of allyl chloride from chlorine and propylene, was optimized by a gradient method. Four process variables were considered: Reaction temperature, pressure, feed composition, and “pseudo” residence time (ratio of reactor volume to molar feed rate). In addition to the primary reaction, a secondary and a consecutive reaction were included in the process model.



Sensitivity analyses revealed that 5% errors in the reaction rate constants produced only very slight changes in the optimal design. In addition, it was found that the profit from the operating reactor was a strong function of feed composition and reaction temperature and a relatively weak function of pressure and “pseudo” residence time.



A program was developed for the IBM 709 computer by which the machine made all appropriate decisions and calculations in finding the optimal design and carrying out the sensitivity analyses.



La conception optimale, par la methode des gradients, d'un reacteur avec agitation continue utilisee pour la preparation du chlorure d'allyl a partir de chlore et de propylene est presentee. Quatre variables du procede sont considerees: temperature de reaction, pression, composition de l'alimentation et temps de residence fictif (volume du reacteur/taux d'alimentation molaire). Les reactions secondaire et consecutive sont aussi incluses dans le procede.



L'analyse revele que des erreurs de 5% dans la constante des reactions ne produisent que de faibles changements dans la conception ultime. De plus, le profit obtenu avec le reacteur est fortement affecte par la composition et la temperature de reaction mais peu affecte par la pression et le temps de residence fictif.



Un programme developpe pour le calculateur IBM 709 permet a ce dernier de prendre toutes les decisions opportunes et de proceder aux calculs necessaires pour realiser la conception optimale ainsi que les analyses requises.

William F. Stevens

Papers

Size distribution of droplets from centrifugal spray nozzles

Dynamic optimisation: An extension of the direct method of lyapunov

Optimal design of a continuous stirred-tank reactor by a gradient method