Wall flow

In the previous section we discussed wall functions, which are used to reduce the number of cells. However, we must be aware that this is an approximation that, if the flow near the boundary is important, can be rather crude. In many internal flows—where all boundaries are either walls, symmetry planes, inlets, or outlets—the boundary layer may not be that important, as the flow field is often pressure determined. However, when we are predicting heat transfer, it is generally not a good idea to use wall functions, because the convective heat transfer at the walls may be inaccurately predicted. The reason is that convective heat transfer is extremely sensitive to the near-wall flow and temperature field. 

The first approach developed by Hsu (1962) is widely used to determine ONE in conventional size channels and in micro-channels (Sato and Matsumura 1964 Davis and Anderson 1966 Celata et al. 1997 Qu and Mudawar 2002 Ghiaasiaan and Chedester 2002 Li and Cheng 2004 Liu et al. 2005). These models consider the behavior of a single bubble by solving the one-dimensional heat conduction equation with constant wall temperature as a boundary condition. The temperature distribution inside the surrounding liquid is the same as in the undisturbed near-wall flow, and the temperature of the embryo tip corresponds to the saturation temperature in the bubble 7s,b- The vapor temperature in the bubble can be determined from the Young-Laplace equation and the Clausius-Clapeyron equation (assuming a spherical bubble) ... 

Scientists from Politecnico di Milano and Ineos Vinyls UK developed a tubular fixed-bed reactor comprising a metallic monolith [30]. The walls were coated with catalytically active material and the monolith pieces were loaded lengthwise. Corning, the world leader in ceramic structured supports, developed metallic supports with straight channels, zig-zag channels, and wall-flow channels. They were produced by extrusion of metal powders, for example, copper, fin, zinc, aluminum, iron, silver, nickel, and mixtures and alloys [31]. An alternative method is extrusion of softened bulk metal feed, for example, aluminum, copper, and their alloys. The metal surface can be covered with carbon, carbides, and alumina, using a CVD technique [32]. For metal monoliths, it is to be expected that the main resistance lies at the interface between reactor wall and monolith. Corning... 

HfCl2[N(SiMe3)2]2 was synthesized with the reaction of anhydrous HflCU and Na[N(SiMe3)] in toluene [5]. The films were grown in a cold-wall flow-type ALD reactor on (100) oriented p-Si substrates in the temperature range of 150-400 °C. Prior to deposition. Si substrate was etched in dilute HF solution to remove the native oxide and then rinsed in deionized water. The pressure in the reactor was fixed at about 0.5 torr. Argon (99.99995%) was used as a... 

The differential form of this equation is used in calculating the effective viscosity in the RNG k-s model. This method allows varying the effective viscosity with the effective Reynolds number to accurately extend the model to low-Reynolds-number and near-wall flows. 

At this stage it seemed clear that to improve near-wall heat transfer modeling would require better representation of the near-wall flow field, and how it was connected to bed structure and wall heat transfer rates. Our early models of full beds of spheres at N — 4 were too large for our computational capacity when meshed at the refinement that we anticipated to be necessary for the detailed flow fields that we wanted. We therefore developed the WS approach described above in Section II.B.3. 

For relating the wall heat flux and the near-wall flow patterns quantitatively the separate pieces of information had to be linked. Detailed information on the... 

Solidus Temperature, 13 487 Solid walls, flows near, 11 751-753 Solid waste(s)... 

Fig. 32. Path lines (spaced at intervals of equal flux) of the wall flow in different asymmetric shape cells in clean (left) and loaded (right) states. From the top, geometries a, b and c of Fig. 30 are shown.

Konstandopoulos, A. G., and lohnson, I. H. Wall-flow diesel particulate filters-their pressure drop and collection efficiency. SAE Technical Paper No. 890405, SAE Trans. 98 sec. 3 (I. Engines), pp. 625-647 (1989). 

Konstandopoulos, A. G., and Kladopoulou, E. The optimum cell density for wall-flow monolithic filters Effects of filter permeability, soot cake structure and ash loading. SAE Technical Paper No. 2004-01-1133 (2004). 

Konstandopoulos, A. G., Vlachos, N., Housiada, P., and Kostoglou, M. Simulation of triangularcell-shaped, fibrous wall-flow filters. SAE Technical Paper No. 2003-01-0844 (SP-1755) (2003). 

In the Roto-Louvre design of Figure 9.10(b) the gas enters at the wall, flows first through the bed of particles and subsequently through the shower of particles. Performance data are in Tables 9.10(b) and (c). 

Wall flow effects become large when DT/Dp falls below about 10. Packing diameter should be selected such that DT/Dp exceeds 10. 

A characteristic of micro channel reactors is their narrow residence-time distribution. This is important, for example, to obtain clean products. This property is not imaginable without the influence of dispersion. Just considering the laminar flow would deliver an extremely wide residence-time distribution. The near wall flow is close to stagnation because a fluid element at the wall of the channel is, by definition, fixed to the wall for an endlessly long time, in contrast to the fast core flow. The phenomenon that prevents such a behavior is the known dispersion effect and is demonstrated in Figure 3.88. 

They include a mass balance of particulate on the trap pore walls and a mass balance of the major gas phase compounds, such as CO, CO2, O2, and N2. A pseudohomoge-neous enthalpy balance with thermal conductivity of the trap is used to cover the description of temperature changes [57-64] or to calculate the thermal stress of a honeycomb-structured wall flow diesel particulate filter [65]. Haralampous et al. added a diffusion term to cover the effect of NO2 back-diffusion, which is responsible for higher reaction rates than expected at low temperatures [66]. 

Wad flow (66,67,140,141-149). The tendency of liquid to flow toward the walls of packed columns is a fundamental phenomenon associated with packed-column hydraulics. The development of wall flow is illustrated in Fig. 9.4 using typical measurements by Hoek (140) in a pilot-scale column. The column diameter was 20 in, and the outer distributor nozzle was located about 1.5 in from the wall. In these experiments, wall flow was defined as the flow in the outer ring of the column (with an area of 16 percent of the column cross section). 

Figure 9.4 shows little wall flow near the top of the bed. This is because the liquid distributor drip points stop short of the wall (the unirrigated ring at the top of the bed was 1 in wide in Hoek s measurements). With increasing depth below the top of the bed, liquid... 

The factors affecting the development of wall flow are the same as those that affect the liquid spread. These include height into the bed, packing type, packing size, and liquid flow rate (66,140). 

FIGURE 45 Continuous regenerating trap for soot abatement (734). In the monolith (in addition to the oxidation of CO and hydrocarbons), NO is oxidized to give NO2, which gasifies the soot deposited on the wall-flow filter. 

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