Computational fluid dynamic heat transfer

A suitable mesh for modeling fluid dynamics, heat transfer, mass transfer and current conservation using a 3D geometry would require very large computational resources. Some simplifications are usually necessary. 

Nevertheless, a number of problems remain in modelling both the physical processes (fluid dynamics, heat transfer), the complex chemistry and the coupling between them. There are major limitations on the applicability of computer models and in the accuracy which simulations can achieve. It is of the utmost importance for model users to be aware of the main sources of error blind belief in the output from models can be dangerous and expensive. In this chapter we consider the major source of uncertainty in chemical simulations, whether full or reduced mechanisms are used, namely the quality and quantity of the available kinetics data. 

Mass transfer processes are complicated, usually involving turbulent flow, heat transfer, multiple phases, chemical reactions, unsteady operation, as well as the influences from internal construction of the equipment and many other factors. To study such complicated system, we propose a novel scientific computing framework in which all the relevant equations on mass transfer, fluid-dynamics, heat transfer, chemical reactions, and all other influencing factors are involved and solved numerically. This is the main task and research methodology of computational mass transfer (CMT). 

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. 

Logtenberg, S. A., Nijemeisland, M., and Dixon, A. G., Computational fluid dynamics simulations of fluid flow and heat transfer at the wall-particle contact points in a fixed-bed reactor, Chem. Eng. Sci. 54, 2433-2439 (1999). 

In practice, the process regime will often be less transparent than suggested by Table 1.4. As an example, a process may neither be diffusion nor reaction-rate limited, rather some intermediate regime may prevail. In addition, solid heat transfer, entrance flow or axial dispersion effects, which were neglected in the present study, may be superposed. In the analysis presented here only the leading-order effects were taken into account. As a result, the dependence of the characteristic quantities listed in Table 1.5 on the channel diameter will be more complex. For a detailed study of such more complex scenarios, computational fluid dynamics, to be discussed in Section 2.3, offers powerful tools and methods. However, the present analysis serves the purpose to differentiate the potential inherent in decreasing the characteristic dimensions of process equipment and to identify some cornerstones to be considered when attempting process intensification via size reduction. 

Arana et al. have performed extensive modeling and thermal characterization experiments on their reactor design. They modeled their design consisting of two suspended SiN - tubes linked with slabs of silicon using two-dimensional computation fluid dynamics and a heat transfer model (Femlab, Comsol Inc.). The heat of reaction of the steam reforming or... 

Another important modeling aspect is the simulation of catalytic process parameters and reactor configurations. Such models are typically associated with process engineering, and involve computational fluid dynamics and heat- and mass-transfer calculations. They are essential in the process planning and scale-up. However, as this book deals primarily with the chemical aspects of catalysis, the reader is referred to the literature on industrial catalysis and process simulations for further information [49,56]. 

Dembele, S., Zhang, J., and Wen, J.X. Assessments of spectral narrow band and weighted-sum-of-gray-gases models for computational fluid dynamics simulations of pool fires. Numerical Heat Transfer Part B, 2005.48(3), 257-276. 

Egorov, Y., Menter, F., Kloeker, M., Kenig, E.Y. Hydrodynamik und Stofftransport in katalytischen Packungen detaillierte CFD Berechnung und Prozesssimulation. Proc. GVC-Conf. Heat and Mass Transfer" and CFD Computational Fluid Dynamics", Weimar, 2002. 

Logtenberg, A., Dixon, A.G. Computational Fluid Dynamics studies of fixed bed heat transfer. Chem. Eng. Process., Vol. 37, 7-21, 1998. 

Problem understanding In many cases, experiments can provide only reliable integral values. In the case of twin screw extruders, for example, these are the shaft torque and the pressure and the temperature at the extrusion nozzle. Computational fluid dynamics, however, provide local information about pressure, velocity, and temperature within the overall computational domain. The calculation of gradients provides additional information about the shear rate or the heat transfer coefficients. 

Mathematical models have been developed by considering classical flow models. At the same time, the capacity of computational fluid dynamics to be coupled with heat and mass transfer processes and with a reaction has been considered. 

Computational fluid dynamics involves the analysis of fluid flow and related phenomena such as heat and/or mass transfer, mixing, and chemical reaction using numerical solution methods. Usually the domain of interest is divided into a large number of control volumes (or computational cells or elements) which have a relatively small size in comparison with the macroscopic volume of the domain of interest. For each control volume a discrete representation of the relevant conservation equations is made after which an iterative solution procedure is invoked to obtain the solution of the nonlinear equations. Due to the advent of high-speed digital computers and the availability of powerful numerical algorithms the CFD approach has become feasible. CFD can be seen as a hybrid branch of mechanics and mathematics. CFD is based on the conservation laws for mass, momentum, and (thermal) energy, which can be expressed as follows ... 

Mampaey, F., and Xu, Z. A., An experimental and simulation study of mould filling combined with heat transfer. In Computational Fluid Dynamics 92, (C. Hirsch, J. Periaux and W. Kordulla, eds.), Elsevier, Amsterdam, 1992, Vol. 1,421. 

Takeuchi et al. 7 reported a membrane reactor as a reaction system that provides higher productivity and lower separation cost in chemical reaction processes. In this paper, packed bed catalytic membrane reactor with palladium membrane for SMR reaction has been discussed. The numerical model consists of a full set of partial differential equations derived from conservation of mass, momentum, heat, and chemical species, respectively, with chemical kinetics and appropriate boundary conditions for the problem. The solution of this system was obtained by computational fluid dynamics (CFD). To perform CFD calculations, a commercial solver FLUENT has been used, and the selective permeation through the membrane has been modeled by user-defined functions. The CFD simulation results exhibited the flow distribution in the reactor by inserting a membrane protection tube, in addition to the temperature and concentration distribution in the axial and radial directions in the reactor, as reported in the membrane reactor numerical simulation. On the basis of the simulation results, effects of the flow distribution, concentration polarization, and mass transfer in the packed bed have been evaluated to design a membrane reactor system. 

---