Crystallizers turbulence

In the Sulser-MWB process the naphthalene fractions produced by the crystallisation process are stored in tanks and fed alternately into the crystalliser. The crystalliser contains around 1100 cooling tubes of 25-mm diameter, through which the naphthalene fraction passes downward in turbulent flow and pardy crystallises out on the tube walls. The residual melt is recycled and pumped into a storage tank at the end of the crystallisation process. The crystals that have been deposited on the tube walls are then pardy melted for further purification. Following the removal of the drained Hquid, the purified naphthalene is melted. Four to six crystallisation stages are required to obtain refined naphthalene with a crystallisation point of 80°C, depending on the quaHty of the feedstock. The yield is typically between 88 and 94%, depending on the concentration of the feedstock fraction. 

Production of potassium permanganate in the CIS is beheved to be from potassium manganate. Electrolysis of potassium manganate in a continuous-flow electrolytic cell with turbulent electrolyte flow and continuous crystallization has been reported (72). 

Rielly and Marquis (2001) present a review of crystallizer fluid mechanics and draw attention to the inconsistency between the dependence of crystallization kinetic rates on local mean and turbulent velocity fields and the averaging assumptions of conventional well-mixed crystallizer models. 

Cate etal. (2001) propose a method for the calculation of crystal-crystal collisions in the turbulent flow field of an industrial crystallizer. It consists of simulating the internal flow of the crystallizer as a whole and of simulating the motion of individual particles suspended in the turbulent flow in a small subdomain (box) of the crystallizer. 

Computational fluid dynamics (CFD) is the numerical analysis of systems involving transport processes and solution by computer simulation. An early application of CFD (FLUENT) to predict flow within cooling crystallizers was made by Brown and Boysan (1987). Elementary equations that describe the conservation of mass, momentum and energy for fluid flow or heat transfer are solved for a number of sub regions of the flow field (Versteeg and Malalase-kera, 1995). Various commercial concerns provide ready-to-use CFD codes to perform this task and usually offer a choice of solution methods, model equations (for example turbulence models of turbulent flow) and visualization tools, as reviewed by Zauner (1999) below. 

Thus the turbulent break-up of parent crystals will depend on ... 

A dependence of both crystal and impeller material properties as well as the probability of crystal-impeller collision on fine particle generation rate has also been demonstrated. Thus the relative effects of impact, drag and shear forces responsible for crystal attrition have been identified. The contribution of shear forces to the turbulent component is predicted to be most significant when the parent particle size is smaller than a 200 pm while drag forces mainly affect larger crystals, the latter being consistent with the observations of Synowiec etal. (1993). 

The product of the collision energy E(L) and collision frequency f L) is integrated over all crystals in the distribution to obtain the total rate of energy transfer. Different approaches have been used to estimate E(L) and f L), both for particle impacts and turbulent fluid induced attrition. 

The dynamics of reactor flow is also important for its effect on the crystal agglomeration, since the intensity of turbulent shear dominates the orthoki-netic mechanism for both processes of aggregation and disruption. The mean shear rate is estimated as (see Harnby etai, 1992)... 

Wojcik, J. and Jones, A.G., 1998b. Particle disruption of precipitated CaC03 crystal agglomerates in turbulently agitated suspensions. Chemical Engineering Science, 53, 1097-1101. 

The extension of generic CA systems to two dimensions is significant for two reasons first, the extension brings with it the appearance of many new phenomena involving behaviors of the boundaries of, and interfaces between, two-dimensional patterns that have no simple analogs in one-dimension. Secondly, two-dimensional dynamics permits easier (sometimes direct) comparison to real physical systems. As we shall see in later sections, models for dendritic crystal growth, chemical reaction-diffusion systems and a direct simulation of turbulent fluid flow patterns are in fact specific instances of 2D CA rules and lattices. 

Almost all flows in chemical reactors are turbulent and traditionally turbulence is seen as random fluctuations in velocity. A better view is to recognize the structure of turbulence. The large turbulent eddies are about the size of the width of the impeller blades in a stirred tank reactor and about 1/10 of the pipe diameter in pipe flows. These large turbulent eddies have a lifetime of some tens of milliseconds. Use of averaged turbulent properties is only valid for linear processes while all nonlinear phenomena are sensitive to the details in the process. Mixing coupled with fast chemical reactions, coalescence and breakup of bubbles and drops, and nucleation in crystallization is a phenomenon that is affected by the turbulent structure. Either a resolution of the turbulent fluctuations or some measure of the distribution of the turbulent properties is required in order to obtain accurate predictions. 

Such spatial variations in, e.g., mixing rate, bubble size, drop size, or crystal size usually are the direct or indirect result of spatial variations in the turbulence parameters across the flow domain. Stirred vessels are notorious indeed, due to the wide spread in turbulence intensity as a result of the action of the revolving impeller. Scale-up is still an important issue in the field of mixing, for at least two good reasons first, usually it is not just a single nondimensional number that should be kept constant, and, secondly, average values for specific parameters such as the specific power input do not reflect the wide spread in turbulent conditions within the vessel and the nonlinear interactions between flow and process. Colenbrander (2000) reported experimental data on the steady drop size distributions of liquid-liquid dispersions in stirred vessels of different sizes and on the response of the drop size distribution to a sudden change in stirred speed. 

In view of secondary nucleation in crystallizers, Ten Cate et al. (2004) were interested in finding out locally about the frequencies of particle collisions in a suspension under the action of the turbulence of the liquid. To this end, they performed a DNS of a particle suspension in a periodic box subject to forced turbulent-flow conditions. In their DNS, the flow field around and between the interacting and colliding particles is fully resolved, while the particles are allowed to rotate in response to the surrounding turbulent-flow field. 

The second step in Ten Cate s two-step approach was to focus on crystal-crystal interaction by means of an explicit two-phase DNS of the turbulent suspension that completely resolves the translational and rotational motions and collisions of the spherical particles plus the turbulence of the liquid between the particles. The particle motions are driven by the turbulent flow and the particles affect the turbulent flow of the liquid in between. When particles approach one another down to a distance smaller than the grid spacing, lubrication theory is exploited to bridge the gap between them. 

Ten Cate, A., Turbulence and particle dynamics in dense crystal slurries—a numerical study by means of lattice-Boltzmann simulations , Ph.D. Thesis, Delft University of Technology, Delft, Netherlands (2002). 

The last two assumptions may not be true under actual well conditions, where instantaneous boiling and turbulent flow in the pipe occur. However, these conditions do not allow certain calcite crystals to deposit immediately and fractions may be removed by the fluid. 

Because the rate of growth depends, in a complex way, on temperature, supersaturation, size, habit, system turbulence and so on, there is no simple was of expressing the rate of crystal growth, although, under carefully defined conditions, growth may be expressed as an overall mass deposition rate, RG (kg/m2 s), an overall linear growth rate, Gd(= Ad./At) (m/s) or as a mean linear velocity, // (= Ar/At) (m/s). Here d is some characteristic size of the crystal such as the equivalent aperture size, and r is the radius corresponding to the... 

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