Comparison of Three Approaches to Model Particle Penetration Coefficient through a Single Straight Crack in a Building Envelope

Abstract

In this study, we present three approaches to predict particle penetration coefficients through a single straight crack in building envelops. The three approaches are an analytical approach, an Eulerian approach, and a Lagrangian approach, respectively. The particle penetration coefficient through an idealized straight crack (smooth inner surfaces) and a strand board crack (rough inner surfaces) were modeled by the three presented approaches. The calculated results were compared with the literature results. The comparison shows that for the idealized smooth crack, the modeled results by the Eulerian approach match the experiments best for the entire range of particle sizes studied among the three approaches. The predicted results by the analytical approach also match the experiments reasonable well. Results modeled by the Lagrangian approach are less satisfied for fine particles (d _p < 0.1 μm). Overall, all the three approaches agree well with the experiments for particle sizes ranging from 0.4–1.2 μm. For cracks with rough inner surfaces, the results agree better with the measurements for all the three approaches by adjusting the boundary conditions to incorporate the “intercept” effect of roughness on particle deposition in the cracks.

This work was sponsored by the National Natural Science Foundation of China (Grant No. 50908127) and partially supported by a grant from City University of Hong Kong (7002378).

Notes

^aThe computing time is based on the same personal computer with Intel® Core™ Duo CPU T2450 @ 2.00 GHz and RAM 1.0 GB DDR2.

^bAveraged error is defined as:

^cStandard deviation of the error is defined as: σ = √∑(R _p − )²/N _p

^b ,

^c The footnotes b and c are the same as shown in Table 2.