Channel fluid dynamics

In this work, the MeOH kinetic model of Lee et al. [9] is adopted for the micro-channel fluid dynamics analysis. Pressure and concentration distributions are investigated and represented to provide the physico-chemical insight on the transport phenomena in the microscale flow chamber. The mass, momentum, and species equations were employed with kinetic equations that describe the chemical reaction characteristics to solve flow-field, methanol conversion rate, and species concentration variations along the micro-reformer channel. 

A numerical study of the effect of area ratio on the flow distribution in parallel flow manifolds used in a Hquid cooling module for electronic packaging demonstrate the useflilness of such a computational fluid dynamic code. The manifolds have rectangular headers and channels divided with thin baffles, as shown in Figure 12. Because the flow is laminar in small heat exchangers designed for electronic packaging or biochemical process, the inlet Reynolds numbers of 5, 50, and 250 were used for three different area ratio cases, ie, AR = 4, 8, and 16. 

Equation 6-108 is also a good approximation for a fluidized bed reactor up to the minimum fluidizing condition. However, beyond this range, fluid dynamic factors are more complex than for the packed bed reactor. Among the parameters that influence the AP in a fluidized bed reactor are the different types of two-phase flow, smooth fluidization, slugging or channeling, the particle size distribution, and the... 

Celata GP, Cumo M, McPhail S, Zummo G (2006) Characterization of fluid dynamics behavior and channel wall effects in micro-tube. Int J Heat Fluid Flow 27 135-143... 

The subject of the book is fluid dynamics and heat transfer in micro-channels. This problem is important for understanding the complex phenomena associated with single- and two-phase flows in heated micro-channels. 

Correspondingly all calculations are finite element method (FEM)-based. Furthermore, the flow channel calculations are based on computer fluid dynamics (CFD) research test for the optimization of the mbber flow. 

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. 

The present book is devoted to both the experimentally tested micro reactors and micro reaction systems described in current scientific literature as well as the corresponding processes. It will become apparent that many micro reactors at first sight simply consist of a multitude of parallel channels. However, a closer look reveals that the details of fluid dynamics or heat and mass transfer often determine their performance. For this reason, besides the description of the equipment and processes referred to above, this book contains a separate chapter on modeling and simulation of transport phenomena in micro reactors. 

Van Reis et al. [92] reported the scale-up of a HF system for the recovery of human tissue plasminogen activator (t-PA) produced by recombinant CHO cells from the 2.5-m to the 180-m scale. A robust and reproducible process was achieved by combining hnear scale-up principles, control of fluid dynamic parameters and experimentally defined limits of product retention, which meant maintaining channel length, wall shear rate and flux constant. 

The up-scaling from microreactor to small monoliths principally deals with the change of geometry (from powdered to honeycomb catalyst) and fluid dynamics (from turbulent flow in packed-bed to laminar flow in monolith channels). In this respect, it involves therefore moving closer to the conditions prevailing in the real full-scale monolithic converter, while still operating, however, under well controlled laboratory conditions, involving, e.g. the use of synthetic gas mixtures. 

The success of the ID fluid dynamic model to describe the flow field in the DPF channel (Konstandopoulos and Johnson, 1989 Konstandopoulos et al., 1999, 2003) is an indication for the existence of a (nearly) self-similar flow field. A necessary condition for the application of the ID model for the heat transfer problem as well, is that the wall velocity ww variation must be small along the characteristic channel length required for establishment of a steady heat transfer pattern (i.e. a length of a2ftz/y.lh). In transferring the above to the case of flow and heat transfer in a DPF channel we may formally write the heat balance as... 

The equations implemented are those defined in Sections 3.2-3.4, i.e. in a partial differential form, for each cell component. This approach is also referred to as Computational Fluid Dynamic (CFD). In order to illustrate the capabilities of the model, in terms of assessment of particular phenomena taking place within the fuel cell, one particular problem is analyzed for each geometry. In particular, for the disk-shaped cell, emphasis is put on the effect of the gas channel configuration on the gas distribution, and, ultimately, on the resulting performance. For the tubular geometry, three different options for the current collector layouts are analyzed. 

Table 7.3 Boundary conditions used in the fluid-dynamic model of the air channel of Figure 7.11.

Fluid dynamics in a tubular fuel cell has significant effects on different other phenomena such as the electrochemical reactions, which need species to be transported to the reaction site, and mass and heat transfer. In the porous structures, an equation that accounts for the fluid flowing in the pores - such as Brinkman s or Darcy s equations (Equation (3.4)) - must be used usually the velocities are low. Fluid-dynamic is modelled through Navier-Stokes equation in the channels (Equation (3.3)). 

The analysis of the conditions within a gas channel can also be assumed to be onedimensional given that the changes in properties in the direction transverse to the streamwise direction are relatively small in comparison to the changes in the stream-wise direction. In this section, we examine the transport in a fixed cross-sectional area gas channel. The principle conserved quantities needed in fuel cell performance modeling are energy and mass. A dynamic equation for the conservation of momentum is not often of interest given the relatively low pressure drops seen in fuel cell operation, and the relatively slow fluid dynamics employed. Hence, momentum, if of interest, is normally given by a quasi-steady model,... 

In macroscopic reactors, knowledge of the velocity profile in the channel cross-section is a necessary and sufficient prerequisite to describe the material transport. In microscopic dimensions down to a few micrometers, diffusion also has to be considered. In fact, without the influence of diffusion, extremely broad residence time distributions would be found because of the laminar flow conditions. Superposition of convection and diffusion is called dispersion. Taylor [91] was among the first to notice this strong dominating effect in laminar flow. It is possible to transfer his deduction to rectangular channels. A complete fluid dynamic description has been given of the flow, including effects such as the influence of the wall, the aspect ratio and a chemical wall reaction on the concentration field in the cross-section [37]. 

Numerical simulations were conveniently used to describe complex fluid dynamic behavior in micro structures [36,101], Van der Linde et al. [101] solved the coupled diffusion equations for reacting species and compared the results with data from the oxidation of CO on alumina-supported Cr using the step-response method. Transient periodical concentration changes in micro channels were numerically calculated by various authors [34, 88, 124],... 

One reason to use micro structured reaction chambers is certainly the possibility of describing the fluid dynamic behavior in these structures due to the laminar flow regime. With the following calculations the reactive gas flow in a square micro structure with coated catalytically active walls will be studied in detail. The task was to find a channel arrangement and to calculate the residence time distribution of this arrangement numerically (Figure 4.93). 

As Fig. 12.1 indicates, the manifold cross section may be bead shaped and not circular. Thus, pressure flow in an elliptical cross-section channel may be more appropriate for the solution of the manifold flow. Such a problem, for Newtonian incompressible fluids, has been solved analytically. (J. G. Knudsen and D. L. Katz, Fluid Dynamics and Heat Transfer, McGraw-Hill, New York, 1958). See also, Table 12.4 and Fig. 12.51. 

Computational fluid dynamics simulations were used by Li et al. [68] to determine mass transfer coefficients and power consumption in channels filled with non woven net spacers. The geometric parameters of a non woven spacer were found to have a great influence on the performance of a spacer in terms of mass transfer enhancement and power consumption. The results from the CFD simulations indicated that an optimal spacer geometry exists. 

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