## 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....

## 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.,...

## 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)....

## 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...

## 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,...

## 1

P - v pk fk (p, T) (2.16) For ideal gases, it is possible to write component density, pk in terms of the molecular weight of component k, temperature, operating pressure and universal gas constant. For non-ideal fluids, one can use empirical correlations to represent variations of fluid density with temperature. The values of fluid viscosity, thermal conductivity and molecular diffusivity can be estimated using kinetic theory (Hirschfelder et al., 1964). Kinetic theory allows one to estimate...

## 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...

## 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...

## 2

For a computational cell is equivalent to the sum of local momentum transport rates of all the dispersed phase particles within that computational cell. In principle, local momentum transport rate for each dispersed phase particle (at its center of mass) must be distributed to all the surrounding nodes of the continuous phase (Fig. 7.14). Since the local values of continuous phase properties are obtained by the reverse procedure, this method will ensure momentum conservation rigorously (as...

## 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...