Wall-Flow Filter Model

A pioneering ID model for the wall-flow DPF was originally presented in 1984 by Bissett [42]. A few years later, Konstandopoulos and Johnson developed a pressure 

A schematic of the side and front view of a filter channel is given in Fig. 13.10. The governing equations for the conservation of mass, momentum, energy, and species are given in the following subsections. 

The mass balance equation for the gas flowing in the inlet and outlet channels is 

Taking into account the mass loss/gain through the porous wall and the friction in the axial direction z, the momentum balance of exhaust gas can be formulated  

The temperature field in the filter is described by the equation of transient heat conduction with heat sources in axisymmetric coordinates  

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An exploratory study was carried out with respect to the performance of a copper fuel additive in combination with monolithic wall flow filters for the removal of soot firom diesel exhaust gas. Cordierite filters, copper coated cordierite filters, and silicon carbide filters were studied. Model experiments have been performed to investigate the influence of contact between soot and catalyst on the oxidation rate. 

In order to obtain more fundamental catalytic activity data of the catalytic materials of interest a number of model catalysts consisting of alkali metal and precious metal were prepared and tested for their ability to promote the reactions of water and carbon dioxide with solid carbon. These tests provide basic information about the ability of the catalysts to catalyse soot combustion with CO2, H2O and O2. Results are summarized in Table 2. Both alkali metal and precious metal (PM) doped supports were used. Two supports were used which can be categorised as an inert and a reducible oxide support. Clearly the presence of the alkali metal has a significant effect on catalysing the soot combustion as anticipated. The effect of the reducible oxide support is not significant. In addition to the experiments summarised in Table 2 two further samples of alkali metal supported on an alumina foam and cordierite wall flow filter were prepared and coated with soot in a similar manner to that described above. Measurement of the soot combustion characteristics of these samples in O2, CO2 and H2O were very similar to the powder samples. 

Filter collection efficiency was evaluated by comparing filter upstream and downstream particle concentrations measured by an SMPS (Scanning Mobility Particle Sizer) consisting of a long DMA (Differential Mobility Analyzer - Model 3080) and a U-CPC (Ultrafine Condensation Particle Counter - Model 3025). The cordierite wall-flow filters exhibited their well-known soot collection efficiency while the foam sample exhibited a lower collection efficiency. 

For the purposes of this study, a superimposition of the SCR chemistry and the soot reactivity is assumed. To account for NHa C/ reactions in the wall-flow filter the same kinetic model presented in Sect. 13.2 is used. Soot oxidation is modeled by two parallel reactions with O2 and NO2 [46, 47]. The respective rate expressions are also given below. 

Table 20.2 Model equations (ID) for a wall-flow filter adapted from [56] and with species conservation equations being added... 

In this section, we present a simulation study to compare the steady-state de-NO performance of catalytically coated DPF filters with integrated SCR capability with the respective flow-through SCR catalysts. The comparison is based on a theoretical basis, using the mathematical models presented in previous sections. Aim of the study is to quantify the effect of the mass transfer limitations in the case of the flow-through SCR catalyst, which are much less present in the case of the wall-flow SCRF filter. 

Bissett EJ (1984) Mathematical Model of the Thermal Regeneration of a Wall-Flow Monolith Diesel Paticulate Filter. Chemical Engineering Seienee 39 1233-1244... 

Fig. 20.10 Examples for the pressure drop of wall-flow particulate filter as function of the soot load. Lab pressure drop on 2" samples with Printex U soot. Filter with Fe-ZSM-5 model coating...

Bisset E J (1984) Mathematical model of the thermal regeneration of wall-flow monolith diesel particulate filter. Chem.Eng.Sci. 39 1233-1244... 

As mentioned in Chapters 2 and 4, peak distortion is caused by nonideal equipment not only outside the column but also inside the column. Although sophisticated measurements such as NMR (Tallarek, Bayer, and Guiochon, 1998) allow the investigation of the packed bed only, from a practical viewpoint the observable performance of a column always includes the effects of walls, internal distributors, and filters. Using the method described in this chapter, these are always contained in certain model parameters (e.g., in The column manufacturers have to ensure a proper bed packing and flow distribution (Chapter 4) and, thus, negative influence of imperfections on column performance, for example, on Dax, can be... 

The eaaest way to apply the flux with the shear model is to use Equation (10.23), where the wall shear stress can be obtained fi-om Equation (10.25). This model has been used to correlate data in both laminar and turbulent crossflows. If the deposit depth is agnificant, when filtering more concmtrated suspensions, the channel diameter open to flow must be deduced. This can be achieved but requires a more dialled knowledge of... 

In deep-bed filtration, very fine particles of uniform radius tp in suspension in water are deposited on the surface of the filter bed material as the water flows down. The porous medium of filter bed may be modeled as a bundle of straight capillaries of radius and length L through which water fiows vertically downward at a velocity vjj), considered parabolic. Figure 7.P.2 shows the limiting trajectory of a particle which enters the capillary (z = 0) at a radius r such that it is deposited on the capillary wall at z = L. Particles entering at a smaller r are not captured. 

In the CFD modelling of membrane filtration process, membranes are usually modelled as a porous wall while the flow within a membrane is usually solved using both Navier-Stokes and Darqr equations (Ghidossi et al, 2006). A porous media model is widely used for determining the pressure loss during flow through packed beds, filter papers, perforated plates, flow distributors and tube banks (ANSYS, 2010). A momentum source term is added to the governing momentum equations, which creates a pressure drop that is proportional to the fluid velocity ... 

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