Simulating and Modeling Particulate Removal Processes by Elliptical Fibers

Figures & data

FIG. 1 Discrete velocities in D2Q9 model.

FIG. 2 Pressure drop ratio of elliptical to circular fiber vs. packing density.

FIG. 3 The correction factor C _E,F of dimensionless drag force between elliptical and circular fibers ((a): vs. ϵ; (b): vs. θ)v.

TABLE 1 Comparison of C _E,F and results of Kirsh (α = 25.5%)

Aspect ratio, ϵ	Orientation angle, θ	C E,F	Kirsh (2011)	Relative error
2	0	0.937	0.854	9.72%
2	π/6	0.984	0.973	1.13%
2	π/3	1.190	1.259	5.48%
2	π/2	1.397	1.427	2.10%

FIG. 4 Particle trajectories in different mechanisms: (a) diffusion; (b) interception; (c) inertial impaction; ϵ = 4, θ = π/3.

FIG. 5 Capture efficiency ratio of elliptical to circular fiber vs. packing density.

TABLE 2 Diffusional capture efficiency with different ϵ (η _E,D/η _0,D), where η _Raynor,D is the prediction of Regan and Raynor (2009)

Pe	ϵ	LB-CA	C E,D	ηRaynor,D/η0,D	Relative error
235	1.6	1.071	1.058	1.024	3.32%
235	4	1.221	1.216	1.167	4.20%
235	6	1.336	1.348	1.286	4.82%
700	1.6	1.054	1.058	1.025	3.22%
700	4	1.237	1.216	1.175	3.49%
700	6	1.344	1.348	1.300	3.69%

FIG. 6 Diffusional capture efficiency ratio (η _E,D/η _0,D).

FIG. 7 Interception capture efficiency ratio (η _E,R/η _0,R).

TABLE 3 Interception capture efficiency (η _E,R/η _0,R), where η _Raynor,E is the prediction of Raynor (2008)

ϵ	θ	LB-CA	C E,R	ηRaynor,E/η0,R
1.6	0	0.939	0.867	0.639
1.6	π/6	0.961	0.907	0.881
1.6	π/3	1.043	1.030	1.084
1.6	π/2	1.175	1.132	1.181
4	0	0.815	0.861	0.358
4	π/6	1.025	1.018	0.921
4	π/3	1.358	1.370	1.391
4	π/2	1.633	1.612	1.654

TABLE 4 Inertial impaction capture efficiency (η _E,I/η _0,I)

ϵ	θ	R = dp /df	LB-CA	C E,I	Relative error
1.6	0	0.09375	0.943	0.923	−2.00%
1.6	0	0.125	0.905	0.864	−4.40%
1.6	0	0.15625	0.853	0.789	−7.26%
1.6	π/6	0.09375	0.966	0.975	1.03%
1.6	π/6	0.125	0.966	0.964	−0.15%
1.6	π/6	0.15625	0.941	0.959	2.00%
1.6	π/3	0.09375	1.019	1.032	1.31%
1.6	π/3	0.125	1.053	1.076	2.21%
1.6	π/3	0.15625	1.089	1.159	6.45%
1.6	π/2	0.09375	1.132	1.066	−5.74%
1.6	π/2	0.125	1.178	1.147	−2.64%
1.6	π/2	0.15625	1.208	1.290	6.83%
4	0	0.09375	0.845	0.878	3.81%
4	0	0.125	0.684	0.729	6.71%
4	0	0.15625	0.545	0.541	−0.10%
4	π/6	0.09375	1.057	1.007	−4.75%
4	π/6	0.125	1.013	0.979	−3.42%
4	π/6	0.15625	0.941	0.966	2.71%
4	π/3	0.09375	1.132	1.147	1.39%
4	π/3	0.125	1.291	1.258	−2.60%
4	π/3	0.15625	1.485	1.465	−1.35%
4	π/2	0.09375	1.208	1.234	2.20%
4	π/2	0.125	1.392	1.434	3.02%
4	π/2	0.15625	1.842	1.793	−2.65%

FIG. 8 Inertial impaction capture efficiency ratio (η _E,I/η _0,I).

FIG. 9 Quality factor of elliptical fiber with different ϵ and θ when (a) Brownian diffusion, (b) interception, and (c) inertial impaction are dominated.

Kirsh , V. 2011 . Stokes Flow and Deposition of Aerosol Nanoparticles in Model Filters Composed of Elliptic Fibers . Colloid J. , 73 : 345 – 351 .

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Regan , B. D. and Raynor , P. C. 2009 . Single-Fiber Diffusion Efficiency for Elliptical Fibers . Aerosol Sci. Technol. , 43 : 533 – 543 .

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Raynor , P. C. 2008 . Single-Fiber Interception Efficiency for Elliptical Fibers . Aerosol Sci. Technol. , 42 : 357 – 368 .

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