Impellers computational fluid dynamics

In solid-liquid mixing design problems, the main features to be determined are the flow patterns in the vessel, the impeller power draw, and the solid concentration profile versus the solid concentration. In principle, they could be readily obtained by resorting to the CFD (computational fluid dynamics) resolution of the appropriate multiphase fluid mechanics equations. Historically, simplified methods have first been proposed in the literature, which do not use numerical intensive computation. The most common approach is the dispersion-sedimentation phenomenological model. It postulates equilibrium between the particle flux due to sedimentation and the particle flux resuspended by the turbulent diffusion created by the rotating impeller. 

The use of computer generated solutions to problems and computational fluid dynamics is also another approach of comparing impellers and process results. There are software packages available. It is very helpful to have data obtained from a laser velocity meter on the fluid mechanics of the impeller flow and other characteristics to put in the boundary conditions for these computer programs. 

Since, as discussed above, it is impossible to achieve dynamic similarity between laboratory and full scale, the predictive capability of empirical modeling of crystallization is limited. Mathematical modeling also has its shortcomings. Suspension flows in crystallizers are turbulent, two and perhaps even three phase (for boiling crystallizers), the particle size is distributed, and the geometry is complicated with perhaps multiple moving parts (impellers). This is of course beyond the possibility of analytical solution of the equations of motion, so we must turn to computational fluid dynamics (CFD). However, even CFD is not capable of successfully dealing with all of these features. Successful computational models of crystallizers to date are limited to very specific limited problems. 

One method is to solve the population balance equation (Equation 64.6) and to take into account the empirical expression for the nucleation rate (Equation 64.10), which is modified in such a way that the expression includes the impeller tip speed raised to an experimental power. In addition, the experimental value, pertinent to each ch ical, is required for the power of the crystal growth rate in the nncleation rate. Besides, the effect of snspension density on the nucleation rate needs to be known. Fnrthermore, an indnstrial suspension crystallizer does not operate in the fully mixed state, so a simplified model, such as Equation 64.6, reqnires still another experimental coefficient that modifies the CSD and depends on the mixing conditions and the eqnipment type. If the necessary experimental data are available, the method enables the prediction of CSD and the prodnction rate as dependent on the dimensions of the tank and on the operating conditions. One such method is that developed by Toyokura [23] and discussed and modified by Palosaari et al. [24]. However, this method deals with the CTystaUization tank in average and does not distinguish what happens at various locations in the tank. The more fundamental and potentially far more accurate simulation of the process can be obtained by the application of the computational fluid dynamics (CFD). It will be discussed in the following section. 

FIGU RE 12.7 Typical velocity pattern for a three-dimensional model using computational fluid dynamics for an axial flow impeller (A310). 

INTRODUCTION, 297 Computational Fluid Dynamics, 298 Stirred Tanks, 298 Impeller Modeling, 299... 

Accurate CFD (computational fluid dynamic) simulation of the flow in stirred tanks requires correct specification of both the geometry and the physical conditions of the flow. While specification of the geometry, the gridding, and the solution algorithm is relatively straightforward, some other issues remain difficult. The most challenging problem is definition of a physically accurate, computationally tractable impeller or impeller model which incorporates the effect of the tank geometry. This... 

In the literature, blade impellers have been experimentally and theoretically studied. Several experimental pieces of equipment have been used to study the flow structure generated by two-blade impellers [5-9]. Most studies show that, for a low impeller speed, the flow is essentially tangential. Hiraoka et al. [10] and Bertrand and Couderc [11] studied the 2D flow of viscous Newtonian and non-Newtonian fluids generated by two-blade impellers and paddle agitators, using computation fluid dynamics (CFD). For some years, some new CFD studies concerning the flows... 

The heart of the eompander is the design of the impellers. A high performance aerodynamic shape for eaeh expander and compressor impeller is defined using Computational Fluid Dynamics (CFD). Finite Element Analysis (FEA) verified acceptable stresses due to speed and blade loading, and defined an operating zone free from destructive natural frequencies. This work was verified by outside consultants. 

Masel R.I. Chemical Kinetics and Catalysis. Wiley-VCH Publisher, 2001, ISBN No. 978-0-471-24197-3. Masoud R., Aso K., Ammar D., Abdul-Aziz A. Experimental and computational fluid dynamics (CFD) studies on mixing characteristics of a modified helical ribbon impeller. Korean. Chem. Eng., 2010 27(4) 1150-1158. 

Mixer and Impeller Design—Modem approaches employ the use of computational fluid dynamics (CFD) modelling to improve designs of mixer boxes, baffles, and impellers (Giralico et al. 2003 Gigas and Giralico 2002). The choice of whether or not to use mixer-settlers or columns can also influence the efficiencies achievable (Fox et al. 1998). 

If similarity theory is applied correctly, the dimensionless numbers and characteristics that are determined are independent of the scale. This makes it possible, by using appropriate scale-up rules, to specify the operating parameters for industrial-scale systems from the results of tests carried out on models. Computational fluid dynamics (CFD) can be used to visualize the impeller system at its full scale, thus contributing to solving scale-up problems. 

Shear rate, with reciprocal time as the unit, can be viewed as a time constant. If a process has a shear rate of 1000 s the events in the flow occur on the order of 1 ms. Such high shear rates are generated in the immediate vicinity of the impeller. However, the volume of this region is relatively small and, therefore, a very small amount of the material experiences these shear rates. The conditions in the vortices are similar, with high shear rate but small volume. The overall mixing process is defined by the combination of shear rate and the volume. Detailed information on the distribution of shear rates and respective volumes is difficult to obtain experimentally. Computational fluid dynamics can be used to extract such information for given mixing conditions. 

Multiple impellers can be used as shown in Figure 22-12. The configuration shown in this computational fluid dynamics (CFD) simulation uses three high solidity, up-pumping axial flow impellers. The simulation shows the flow pattern by depicting the flow of neutral density particles (Weetman, 1998a). Other impeller types are discussed in Chapter 6. 

Figure 22-12 Computational fluid dynamics plots of multiple up-pumping Lightnin A340 impeUCTs Np = 0.75 for each impeller.

Concluding, it is essential to represent complex, real-life flow situations by computationally tractable models that retain adequate details. As an example, a computational snapshot approach that simulates the flow in stirred reactors or other vessels for any arbitrary impeller has been developed [5]. This approach lets the engineer simulate the detailed fluid dynamics around the impeller blades with much less computations that would otherwise be required. Improvements in CFD technique are likely to encourage further work along these lines. 

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