Parallel channel models

Modeling manifold physics is an essential element for defining all geometry elements required to provide sufficient flow distribution to many thousands of parallel channels. No manifold can ever be perfect, and thus the idealized goal of uniform flow distribution will remain elusive. In some cases, tailored rather... 

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. 

The simple water charmel models can explain the ionomer peak and the small-angle upturn in the scattering data of fhe unoriented samples as well as of the oriented films. Interestingly, the helical structure of backbone segments is responsible for fhe sfabilify of fhe long cylindrical charmels. The self-diffusion behavior of wafer and protons in Nation is well described by the water channel model. The existence of parallel wide channels af high wafer uptake favors large hydrodynamic confributions to electro-osmotic water transport and hydraulic permeation. 

In many situations, the monolith reactor can be represented by a single channel. This assumption is correct for the isothermal or adiabatic reactor with uniform inlet flow distribution. If the actual conditions in the reactor are significantly different, more parallel channels with heat exchange have to be simulated (cf., e.g. Chen et al., 1988 Jahn et al., 1997, 2001 Tischer and Deutschmann, 2005 Wanker et al., 2000 Young and Finlayson, 1976). In this section we will further discuss effective single channel models. 

We have seen how the screw extruder pump is synthesized from a simple building block of two parallel plates in relative motion. We have also seen how the analysis of the screw extruder leads in first approximation back to the shallow channel parallel plate model. We carried out the analysis for isothermal flow of a Newtonian fluid, reaching a model (Eq. 6.3-27) that is satisfactory for gaining a deeper insight into the pressurization and flow mechanisms in the screw extruder, and also for first-order approximations of the pumping performance of screw extruders. 

Partially Filled Screw Channel The accompanying figure below shows a partially filled screw channel. Using the single-screw Newtonian parallel plate model show that the free boundary profile is given by19... 

The intra-pebble coolant flow is simplified such that the flow occurs at equal speed in parallel channels (Seker, 2005). The side reflector control rods are modelled as concentrations of boron in a concentric cylinder (Seker, 2005). 

Flow in a thin rectangular channel (Figure 4.2), such as that used in field-flow fractionation, can be treated in a manner similar to that used for cylindrical capillary tubes. If the drag at the edges of the channel is neglected (infinite parallel plate model), then the force balance expression (corresponding to Eq. 4.5 for capillary tubes) becomes... 

The channel model This model attributes packed-column pressure drop to the resistance to flow in a multitude of parallel channels. The channels may have bends in them or may have contractions and enlargements. Liquid flows down the walls of the channel, thus consuming some of the available cross-section area. This in turn increases the pressure drop. The channel model has been applied both for random and structured packings (e.g., 3,62,736,78,91,92,93a), A popular application of this model is the Bravo et al. (91) correlation for structured-packing pressure drop ... 

Alternative models. Stichlmair and Stemmer (146,151) model the column as a large number of parallel channels, each operated at a differ-... 

We shall develop next a single-channel model that captures the key features of a catalytic combustor. The catalytic materials are deposited on the walls of a monolithic structure comprising a bundle of identical parallel tubes. The combustor includes a fuel distributor providing a uniform fuel/air composition and temperature over the cross section of the combustor. Natural gas, typically >98% methane, is the fuel of choice for gas turbines. Therefore, we will neglect reactions of minor components and treat the system as a methane combustion reactor. The fuel/air mixture is lean, typically 1/25 molar, which corresponds to an adiabatic temperature rise of about 950°C and to a maximum outlet temperature of 1300°C for typical compressor discharge temperatures ( 350°C). Oxygen is present in large stoichiometric excess and thus only methane mass balances are needed to solve this problem. 

With the average velocity and channel size now expressed in terms of the measurable parameters Vq, Dp, and e, thp channel model can be used to predict the form of the correlation for pressure drop. For flow at very low Reynolds numbers, the pressure drop should vary with the first power of the velocity and inversely with the square of the channel size, in accordance with the Hagen-Poiseuille equation for laminar flow in straight tubes, Eq. (5.16). The equations for V and ), are used in Eq. (5.16), and a correction factor Aj is added to account for the fact that the channels are actually tortuous and not straight and parallel ... 

Quaresima et al. used a single TCSPC channel and a multianode PMT to record sequences of time-of-flight curves in eight parallel channels [421]. The acquisition time per step of the sequence was 166 ms. The data of five steps were averaged. Values of p s and Pa were calculated from the averaged data by using a standard model of diffusion theory. 

The energy disposal and effective upper state lifetimes have been reproduced using classical trajectory calculations a quasi-diatomic assumption was made to determine the slope of the section through the upper potential energy surface along the N—a bond from the shape of the u.v. absorption profile. The only adjustable parameter was the assumption of a parallel transition in the quasi-diatomic molecule. In contrast, a statistical adiabatic channel model which assumed dissociation via unimolecular decomposition out of vibrationally and rotationally excited level in the ground electronic state (following internal con-... 

Two model fuel cell reactors, the stirred tank reactor- polymer electrolyte membrane fuel cell and the segmented anode parallel channel fuel cell, have been shown to be effective in the study of PEM fuel cell dynamics. Simplified... 

The geometrical stmctures of packed beds are too complex for simple mathematical description. Therefore, the real bed stmctures are replaced by model stmctures, for instance by a system of parallel channels or a system of dispersed particles. The model stmctures should have the same interfacial area a and the same porosity s as the packed bed. From both conditions follows the hydraulic diameter df, of the channel model stmcture ... 

Fig. 6.4 Inverted micelles model by Gierke (top left), polymer bundles model (top right), and parallel water-channel model (bottom) (Reproduced from Refs. [16, 20] with pmnissiffli of the American Chemical Society (copyright 2004) and Nature Publishing Group)...

To account easily for the velocity distribution influence, a very simple model is adopted. It consists in a set of parallel channels (see figure 12). Each channel corresponds to a flow trajectory. All the independent lengths of these trajectories i.e. the lengths between two intersection points are assumed to be equal to a mean channel length L. Using this model, Carbonell (198I) derived an approximate expression for the area and time-averaged value of the axial dispersion coefficient... 

Beginning with fundamentals of fluid dynamics, correlations for the pressure loss in channel elements are presented, which are concatenated to fluidic networks to distribute fluid homogeneously over a certain area. Computational fluid dynamic (CFD) simulations of single elements are exploited for analytical pressure loss correlations. These are employed in lumped element modeling of networks and manifolds, which are too complex for direct simulations. Design strategies and methods are presented for charmel networks, manifolds for parallel channels on a plate and headers for stacked-plate devices. 

---