A Particle Resuspension Model in Ventilation Ducts

Figures & data

FIG. 1 Schematic diagram of a turbulent burst near the wall (Cleaver and Yates 1973).

Schematic diagram of turbulent burst distribution on the surface (Cleaver and Yates 1973).

Forces acting on a small aggregate in a viscous sublayer (Theerachaisupakjj et al. 2003).

FIG. 4 Critical jump-start air velocity versus particle diameter (with parameters in Table 1).

TABLE 1 Condition/parameters for critical jump-start air velocity calculation shown in Figure 4

Parameter	Value
A	2 × 10^−19 J
D	0.24 m
C	0.1 /Pa
k 0	2
ze	4 × 10^−10 m
z 0	5 × 10^−5 m
tanθ	0.3
ν f	1.55 × 10^−5 m^2/s
ρ f	1.18 kg/m^3
ρ p	2000 kg/m^3
φ	0.25

FIG. 5 Calculated α (with parameters in Table 1).

FIG. 6 Particle resuspension rate at time t = 100 s versus particle diameter.

FIG. 7 Particle resuspension rate at time t = 100 s versus average air speed in ducts.

FIG. 8 Particle resuspension rate of particle with diameter of 1 μm versus time.

TABLE 2 Parameters of Nicholson's experiment

Parameter	Value
A	2 × 10^−19 J
D	1 m
C	0.1 /Pa
k 0	2
ze	4 × 10^−10 m
z 0	3 × 10^−4 m (concrete) and 5 × 10^−3 m (grass)
tanθ	0.3
ν f	1.55 × 10^−5 m^2/s
ρ f	1.18 kg/m^3
ρ p	1000 kg/m^3
φ	0.25

FIG. 9 Comparison with the experimental data of Nicholson: Resuspension rate from a grass surface vs. particle diameter at time = 50 s.

FIG. 10 Comparison with the experimental data of Nicholson: Resuspension rate from a grass surface vs. air speed at time = 50 s.

FIG. 11 Comparison with the experimental data of Nicholson: resuspension rate versus time.

TABLE 3 Parameters of Giess et al.'s experiment

Parameter	Value
A	2 × 10^−19 J
D	1 m
C	0.1 /Pa
k 0	2
ze	4 × 10^−10 m
z 0	0.01 m (short grass) and 0.03 m (long grass)
tanθ	0.3
ν f	1.55 × 10^−5 m^2/s
ρ f	1.18 kg/m^3
ρ p	1000 kg/m^3
φ	0.25

FIG. 12 Comparison with the experimental data of Giess and others: resuspension rate versus air speed on short grass surfaces.

TABLE 4 Parameters for model calculation of Lengweiler's experimental case

Parameter	Value
A	5 × 10^−20 J
D	0.5 m
C	0.1 /Pa
k 0	2
ze	5 × 10^−9 m
z 0	5 × 10^−4 m
tanθ	0.3
ν f	1.57 × 10^−5 m^2/s
ρ f	1.165 kg/m^3
ρ p	2000 kg/m^3
φ	0.25

FIG. 13 Comparison with the experiment of Lengweiler: resuspension rate versus u _∞, comparison of model and experiment.

FIG. 14 Particle resuspension rate with revised K versus time with C′ = 0.01.

TABLE 5 Model sensitivity analysis results

Input parameter	Typical value of input parameter	Range of the input parameter	Range of R	Change in order
u ∞	5 m/s	1→10 m/s	5.38×10^−8→2.08×10^−4/s	3.9×10^3
Dp	5 μm	0.1→10 μm	5.16×10^−8→6.15×10^−5/s	1.2×10^3
	4×10^−10 m	4×10^−10→5×10^−9m	1.68×10^−5→1.34×10^−3/s	8.0×10^1
ρ f	1.18 kgm^3	0.085→1.9 kgm^3	9.77×10^−7→4.53×10^−5/s	4.5×10^1
k 0	2	1→5	5.42×10^−6→7.95×10^−5/s	1.5×10^1
z 0	5×10^−5 m	1×10^−5→1×10^−2m	2.05×10^−5→4.04×10^−5/s	2.0×10^0
ρ p	2000 kg/m^3	1000 → 4000 kg/m^3	1.27×10^−5→2.27×10^−5/s	1.8×10^0
A	2×10^−19J	4×10^−20→4×10^−19 J	8.30×10^−5→8.41×10^−6/s	1.0×10^−1
D	0.24 m	0.2→2.0 m	1.84×10^−5→5.81×10^−6/s	3.2×10^−1
φ	0.25	0.25→1	1.68×10^−5→5.42×10^−6/s	3.2×10^−1
ν f	1.55 × 10^−5 m^2/s	7.8 × 10^−6 → 1.0 × 10^−4 m^2/s	4.53×10^−5→9.77×10^−7/s	2.2×10^−2
t	100s	0→24h	3.36×10^−5→3.80×10^−8/s	1.1×10^−3

FIG. 15 Particle resuspension rate with revised K versus diameter with C′ = 0.01.

FIG. 16 Particle resuspension rate with revised K versus air speed with C′ = 0.01.

FIG. 17 Resuspension rate R versus the revised rate constant K (air speed u _∞ is 5 m/s, particle diameter D_p is 5 μm, and time is from 0 to 3600 s).

FIG. 18 Resuspension rate R versus particle load N(D_p ) at time t = 100 s (Since t is fixed, K remains constant), when air speed u _∞ is 5 m/s, particle diameter D_p ranges from 0.1 to 10 μm, the initial particle number load N ₀ is set to be 8×10¹⁰ per m².

TABLE 6 Resuspension rate change with unit change of input parameters at typical value

Input parameter	Typical value	Change of R (with unit change of parameter based on typical value)
ze	4×10^−10m	8.0×10^5
k 0	2	1.5×10^−5
u ∞	5 m/s	1.2×10^−5
φ	0.25	9.4×10^−6
Dp	5 μm	6.2×10^−6
ρ f	1.18 kg/m^3	4.2×10^−6
ρ p	2000 kg/m^3	3.5×10^−9
t	100 s	−8.4×10^−8
D	0.24 m	−3.5×10^−6
z 0	5×10^−5m	−3.6×10^−2
ν f	1.55 × 10^−5 m^2/s	−1.3×10^0
A	2×10^−19 J	−4.9×10^13

FIG. 19 Particle resuspension rate with different working fluids (Helium, Carbon Dioxide, Air, and Hydrogen).

Cleaver , J. W. and Yates , B. 1973 . Mechanism of Detachment of Colloidal Particles from a Flat Substrate in a Turbulent Flow . J. Colloid Interf. Sci. , 44 : 464 – 474 .

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