# Interdisciplinary Applied Mathematics

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2001).

Ahmed and Beskok (2002) studied gas flows through a microfilter array using p,Flow. Isothermal conditions for the filter surface were assumed. A schematic view of a rectangular microfilter array is shown in Figure 6.22. In their study the filter width (w) was significantly larger than the filter height (h), so that the flow was approximated as two-dimensional. Considering that the filter holes repeat in a periodic fashion, they simulated gas flow through only one hole by imposing periodicity conditions in the spanwise direction. (see Figure 6.22). In addition, h/t = 1.5 and в = h/L = 0.6 were used; these dimensions are labeled in Figure 6.22 (right). Using this fixed aspect ratio geometry, they varied the reference length scale (L), creating a series of geometrically similar filters ranging from L = 6 p,m to L =1 p,m (hence, h varied from 3.6 p,m to 0.6 p,m).

Figure 6.23    shows    a    comparison    of    numerical    results    with    the    scaling

laws of    (Yang    et    al.,    2001) and (Mott    et    al.,    2001).    The    results are pre

sented as a function of a new parameter К, which is defined in the figure. Significant scatter in the data is observed using Mott’s model, while a constant offset is observed using Yang’s model. Ahmed and Beskok’s numerical solutions have consistently shown smaller pressure drops than the values

FIGURE 6.23. Comparisons of simulations of Ahmed and Beskok (2002) with the empirical scaling laws developed by (Mott et al., 2001) indicated by M, and (Yang et al., 2001) indicated by Y.

reported in (Yang et    al.,    2001).    The    reason    for    this    was    attributed    to the

smoothened filter geometry shown in Figure 6.22. This filter model had finite radius of curvature at the inlet and exit sections. The smooth entrance and exit shape with finite radius of curvature (r/h = 0.1) reduced the pressure drop at these locations, resulting in a reduced pressure drop compared to the experiments and numerical calculations of (Yang et al., 2001). Strong dependence of the data on the side-wall shape has been demonstrated in (Yang et al., 2001), by comparisons of numerical simulations with the experimental data. In addition to the differences in the side-wall shapes, three-dimensional flow effects can also be a possible explanation for the differences between Yang’s model and results by (Ahmed and Beskok, 2002). Here    we    must    mention    that    the    inability    to match    Mott’s    scaling

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