## 2

FIGURE 10.30 Computational simulation of accumulation of gas behind impeller blades (black 0 white > 0.1) (from Ranade et al., 2001c). Reproduced in colour plate section between pages 210 and 211. FIGURE 10.30 Computational simulation of accumulation of gas behind impeller blades (black 0 white > 0.1) (from Ranade et al., 2001c). Reproduced in colour plate section between pages 210 and 211. it may be necessary to treat the three phases separately. For such systems, it is often necessary to...

## 0302

02 10 202 302 40 502 60 702 802 902 Impeller21egrees2 0.502 0.402 0.302 0.202 0.102 O.OOi -0.102 0.202 -0.302 02 10 202 302 402 502 602 702 802 902 Impeller21egrees2 FIGURE 10.19 Comparison of simulated and experimental results for pitched blade turbine (normalized radial velocity, Uradial Utip). r T (a) 0.118 (b) 0.171 (c) 0.197. Traces simulation results Schafer et al. (1998) data (from Ranade et al., 2001a). Figs 10.22-10.24 respectively. Experimental results corresponding to these flow...

## 102 Cfdbased Modeling Of Stirred Reactors

Flow in baffled stirred reactors has been modeled by employing several different approaches which can be classified into four types, and are shown schematically in Fig. 10.3. Most flow simulations of stirred vessels published before 1995 were based on steady-state analyses (reviewed by Ranade, 1995) using the black box approach. This approach requires boundary conditions (mean velocity and turbulence characteristics) on the impeller swept surface, which need to be determined experimentally....

## 36

Morsi and Alexander's (MA) correlation represents the single-particle drag curve accurately. Ma and Ahmadi's correlation predicts values comparable with the MA correlation. Molerus' correlation deviates from the MA correlation at higher Reynolds numbers. Patel's correlation is found to give a better fit with the MA correlation than Richardson's correlation. Dalla Ville's correlation overpredicts values of drag coefficient compared to the MA correlation. A4.2.2. Drag Coefficient for...

## 66 Summary

The finite volume method ensures integral conservation of mass, momentum and energy and is, therefore, attractive for reactor engineering applications. The steps in applying the finite volume method to solve transport equations are listed below. Select appropriate solution domain (and boundary conditions). Divide the selected domain into an adequate (which may be verified by examining the grid dependence of predicted results) number of computational cells. Obtain a set of discretized equations...

## 103 Computational Snapshot Approach

The flow generated by an impeller of any shape is governed mainly by pressure and centrifugal forces generated by impeller rotation and the corresponding rotating flows. The shape of the impeller blade controls the direction and characteristics of the impeller discharge stream via the generated pressure and centrifugal forces. Blade rotation causes suction of fluid at the rear side of the blades and equivalent ejection of fluid from the front side of the blades. This phenomenon of ejection and...

## References

Acrivos, A. and Goddard, J.D. (1965), Asymptotic expansions for laminar-forced convection heat and mass transfer, J. Fluid Mech., 23, 273-291. Ahmedi, G. (1987), On the mechanics of incompressible multiphase suspensions, Adv. Water Res., 10, 32. Allen, M.P. and Tildesley, D.J. (1990), Computer Simulations of Liquids, Oxford Science Publications, Oxford. Auton, T.R. (1983), The dynamic of bubbles, drops and particles in motion in liquids, PhD Thesis, University of Cambridge, UK. Balzer, G.,...

## A

Only aggregates intermix, no reaction occurs Mixing on molecular level, reaction occurs Only aggregates intermix, no reaction occurs FIGURE 5.1 Macrofluid and microfluid Idealizations (from Levenspiel, 1972). Two extremes of molecular mixing are traditionally known as microfluid and macrofluid. In microfluid, species are completely mixed on a molecular scale, while in macrofluid, there is no mixing on a molecular scale although the lumps of fluid are macroscopically well mixed. When miscible...

## 1

Where CD0 is the drag coefficient for a single particle of diameter dP and LP is the distance between the centers of the two spheres. Several correlations have been proposed to represent the influence of other particles on the drag coefficient (see a recent review by Enwald et al, 1996 and Appendix 4.2). More information about drag coefficient correlations is included in Part IV when discussing the modeling of different reactor types. For granular flows (fluid-solid flows), in which...

## 133 Other Reactors

One textbook reactor which also has several industrial applications, is a tubular reactor. For example, polymerization of ethylene is carried out in a tubular reactor. Although, a lot of information is available on global fluid dynamics of tubular reactors, when reactions and fluid dynamics are intimately connected via mixing, it is necessary to develop a comprehensive computational flow model including chemical reactions. Recently Kolhapure and Fox (1999) used such a computational flow model...

## 113 Application To Reactor Engineering

An overall procedure for reactor engineering is discussed in Chapter 1. Additional comments on the engineering of bubble column reactors are made in Section 11.1. Some of these are repeated here to emphasize their importance. As for any other reactor, conventional reaction engineering models are first used to evaluate the influence of various fluid dynamic characteristics (mixing, volume fraction, interfacial area, heat transfer coefficient and so on) on overall performance of a reactor. These...

## 075

FIGURE 12.17 Some simulation results for gas-solids flows in a riser. (a) Axial particle diameter profiles for different superficial gas velocities (Vsup ) (from Mathiesen et al., 2000). (b) Radial solid volume fraction profiles at 0.7 m from the bottom, Vsup 1.0ms-1 (from Mathiesen et al., 2000). (c) Radial solids volume fraction profiles at different heights solid line and circles 1.86 m short-dashed line and squares 4.18 m long-dashed line and diamonds 5.52 m (from Neri and Gidaspaw, 2000)....

## 85 Summary

The basic elements involved when using a computational flow model for reactor engineering or any other application, are (1) geometry modeling and grid generation (2) specification of system data and selection of mathematical models and boundary conditions (3) solution of model equations and (4) analysis and interpretation of simulation results. The tools required to carry out these elements are generally classified into three groups pre-processors, solvers and post-processors. Some of the...

## 03679

K-e model is that it overpredicts turbulence generation in regions where the mean flow is highly accelerated or decelerated. Kato and Launder (1993) proposed a modified k-e model to overcome this problem. It will not be possible to discuss all the proposed modifications of the k-e model here. Launder and Spalding (1972), Rodi (1984), Markatos (1986) and Nallaswamy (1987) discuss these modifications, among others. More discussion on the influence of compressibility and other issues can be found...

## Author Index

Abba, I.A. 400, 401 Abbott, D.E. 70, 82 Abou-Arab, T.W. 340 Acharya, S. 188 Acrivos, A. 115, 121 Afacan, A. 415, 417, 418 Ahmadi, G. 102, 106, 110, 115, 119, 120, 116, 333 Al -Dibouni, M.R. 115 Al-Dahhan, M.H. 416, 418 Alexander, A.J. 117, 119 Allen, M.P. 99, 115 Allia, K. 115 Almstedt, A.E. 115, 399, 401 Amano, R.S. 75, 82 Amsden, A.A. 102, 116 Anderson D.A. 43, 165, 188 Arastoopour, H. 400, 401 Arcilla, A.S. 24, 30, 219, 226 Aris, R. 4, 30, 243, 281 Arnstrong, R.C. 39 Atkinson, C.M. 339...

## 54 Ransbased Models Of Reactive Flow Processes

Reynolds-averaged equations for momentum transport, are already discussed in Chapter 3. For modeling reactive flow processes, in addition to the solution of overall mass conservation equation described in Chapter 3, it is necessary to solve conservation equations for individual species. Following the practices of Reynolds averaging, an instantaneous concentration of species k, Ck, can be written as the sum of time-averaged species concentration Ck and a fluctuation around the time average, C'k...

## G

Is being used as reactors in practice. Some of the commonly used types of reactor are shown in Fig. 1.2. Although the reactors included in this figure show contacting of two phases (gas-liquid or gas-solid), similar equipment can also be used to carry out reactions involving a single phase (homogeneous reactions) or more than two phases. Several different versions of these four major reactor types are used in practice. By looking at these configurations, one can imagine the complexities of the...

## 75 Summary

Modifications and enhancements in the basic finite volume method, necessary for simulations of complex multiphase or reactive flows, are discussed in this chapter. Approximations invoked in linearization of source terms and interpolation practices need to be examined carefully in light of their implications on convergence and accuracy. For most of the multiphase flow simulation methods, suitable modifications need to be incorporated in the discretized equations to avoid non-physical results....

## 72 Simulation Of Multiphase Flows

Mathematical models governing multiphase flows are discussed in Chapter 4. As mentioned earlier, multiphase flows may exhibit several different flow regimes, and different modeling approaches are used to simulate these different flow regimes. Three basic modeling approaches, namely (1) volume of fluid approach (VOF), (2) Eulerian-Lagrangian (EL), and (3) Eulerian-Eulerian (EE) and the corresponding basic transport equations governing multiphase flows were discussed in Chapter 4. Although the...

## 11 Chemical Reactor Engineering

Chemical reactor engineering activity is related to the engineering of chemical transformations. Chemical transformations or reactions can occur only if the reactant molecules are brought into molecular contact (mixed) under the appropriate environment (temperature and concentration fields, catalysts) for an adequate time. A process vessel which provides the necessary conditions to favor the desired reaction and allows for removal of products, is called a 'reactor'. A large variety of equipment

## 4

Bulk viscosity accounts for resistance of solid body to dilation and can be given as In the limit of maximum packing, granular flow becomes incompressible. Under such conditions, the kinetic contribution to viscosity is replaced by a friction contribution. Theories of soil mechanics may be used to estimate such friction contributions (Schaeffer, 1987). The granular temperature, 0s is obtained by solving its transport equation, which has the form Ts V Us -V (ke0s) - Ye + f + fas (4.43)

## C

If the gas velocity is higher than minimum fluidization velocity (Umb Umf ). With an increase in velocity beyond minimum bubbling velocity, large instabilities with bubbling and channeling of gas are observed. At high gas velocities, the movement of solids becomes more vigorous. Such a bed is called a bubbling bed or heterogeneous fluidized bed (Fig. 1.9). In this regime, gas bubbles generated at the distributor coalesce and grow as they rise through the bed. For deep beds of small diameter,...

## 3piCoP IUr

Where CDP is the average drag coefficient for a single particle in a suspension. In the frame of a kinetic theory, the particle-particle collision time can be written where 0s is the granular temperature and go is a distribution function defined in Section 4.2.2. Particle response time is defined as APPENDIX 4.2. CORRELATIONS FOR DRAG COEFFICIENT A4.2.1. Drag Coefficient for Single Particle

## 101 Engineering Of Stirred Reactors

Several types of stirred reactor are used in practice and several ways of classifying these exist. Some of the widely used types of stirred reactors are shown in Fig. 10.1. The stirred reactor shown in Fig. 10.1(a) is a typical multiphase reactor used for carrying out exothermic reactions such as hydrogenations and oxidations. Stirred reactors provide excellent heat and mass transfer characteristics and can handle multiphase systems effectively. Most industrial reactors of this type use more...

## 33 Modeling Approaches

Although the structural and deterministic approaches to characterizing turbulence have demonstrated promising results, a deductive approach based on solution of the basic governing equations of the flow processes is the most widely used approach for engineering applications. The basic premise in modeling turbulence is that it can be understood within the continuum assumption of fluid dynamics. There are some experimental facts which might shed doubt on the validity of the assumption. For...

## Preface

Industrial Flow Modeling Group, iFMg at National Chemical Laboratory undertakes contract research and consultancy projects in the general area of reactor engineering. We use computational flow modeling to carry out these industrial projects. Computational flow modeling is a powerful tool for the design and analysis of industrial flow processes. Though it is routinely used as a design tool in aerospace engineering, chemical engineers have started exploiting the power of computational flow...

## 10

FIGURE 12.23 Influence of gas distributor on particle and gas temperatures (simulations of ethylene polymerization, 14000 particles, u 3umf, t 6.25, from Kaneko et al., 1999). -1.0 -0.5 0.0 0.5 Radial distance, r R FIGURE 12.24 Comparison of simulation results with the experimental data of Bader et al., 1988 (from Gao et al., 1999). -1.0 -0.5 0.0 0.5 Radial distance, r R FIGURE 12.24 Comparison of simulation results with the experimental data of Bader et al., 1988 (from Gao et al., 1999). is...

## 131 Fixed Bed Reactors

In a fixed bed reactor, gas phase reactions are generally carried out using a stationary bed of solid catalyst. In a typical reactor, suitable screens support the bed of catalyst particles, through which the gas phase flows. Gaseous reactants adsorb on the catalyst surface, reactions occur on this surface and reaction products desorb back to the gas phase. Two major types of fixed bed reactor are the conventional axial flow fixed bed reactor and the radial flow fixed bed reactor. These types...

## 12 Computational Flow Modeling

As mentioned in the previous section, the equations of fluid mechanics are analytically solvable for only a limited number of flows. Though known solutions are extremely useful in providing an understanding of the fluid dynamics, these rarely can be used for engineering analysis and design. Although many key ideas for the numerical solution of partial differential equations were established more than a century ago, these were of little use before the advent of digital computers. The revolution...

## 1211 Gas Solid Flows in Fluidized Bed Reactors

When gas is passed through a bed of solid particles, various types of flow regime, ranging from fixed bed to pneumatic conveying, are observed. The prevailing flow regime and quality of fluidization depend on several factors. Operating conditions, solids flow rate (flux), gas flow rate (flux) and system configuration affect the prevailing flow regime. In addition, the properties of solid particles (size distribution, shape, density, and restitution coefficient) significantly affect the quality...

## 93 Example 2 Oxy Reactor For

Ethylene dichloride (EDC) is used to manufacture vinyl chloride monomer (VCM), which is one of the largest commodity chemicals produced in the world. EDC may be produced by the direct chlorination of ethylene or oxychlorination of ethylene in the presence of oxygen and hydrogen chloride. Pyrolysis of EDC produces VCM and an equal amount of hydrogen chloride as a co-product. This hydrogen chloride produced in the pyrolysis reactor is utilized by the oxychlorination process as one of the...

## 95 Example 4 Fcc Regenerator

Fluidized catalytic cracking FCC , which converts heavy oil to value added low boiling point products is an important process in refineries around the world. During cracking reactions, catalyst is deactivated rapidly owing to coke deposition. In industrial FCC units, the deactivated catalyst is continuously regenerated by employing a regenerator connected to the cracking reactor. Besides regenerating the catalyst by contacting it with air , the FCC regenerator also provides the heat required...

## 12

FIGURE 12.12 Comparison of simulation results with experimental data at low solids flux dp 54 xm, ps 1545 kg m-3, D 0.14 m, Ug 4.33 ms-1, Gs 10 kg m2 s-1 from Ranade, 1999 . FIGURE 12.13 Sensitivity of simulation results to model parameters dp 54 xm, ps 1545 kg m-3, D 0.14 m, Ug 4.33 ms-1, Gs 10 kg m-2s-1 from Ranade, 1999 . FIGURE 12.13 Sensitivity of simulation results to model parameters dp 54 xm, ps 1545 kg m-3, D 0.14 m, Ug 4.33 ms-1, Gs 10 kg m-2s-1 from Ranade, 1999 . predicted results...