New scheme for dry deposition of aerosols Rostislav D. Kouznetsov - - PowerPoint PPT Presentation

Intro New Scheme Smooth Rough Examples Conclusion

New scheme for dry deposition of aerosols

Rostislav D. Kouznetsov and Mikhail A. Sofiev

Intro New Scheme Smooth Rough Examples Conclusion

The problem

Given concentration at some height above ground find the steady-state flux. Deposition velocity: vd(z1) = J/C(z1) Approaches:

◮ Fixed or size-dependant deposition velocity ◮ Resistance analogy (aerodynamic + quasi-laminar

sub-layers etc. . . )

◮ Something more fancy. . .

Intro New Scheme Smooth Rough Examples Conclusion

On the resistance analogy

For gases – straightforward resistance analogy: steady-state flux over any layer is proportional to the difference of concentrations. For particles: J(z) = −K(z)∂C ∂z + v(z)C. Resistance analogy does not apply for finite layers.

Intro New Scheme Smooth Rough Examples Conclusion

Evolution of Resistance approaches

Slinn 1980:

◮ Concepts of ra, rb and correction.

vd = 1 ra + rb + vsrarb + vs

◮ Suggested for water surfaces. ◮ Rcommended by SP1998 for all surfaces. ◮ Very easy to implement, widely accepted.

Zhang 2001:

◮ Surface dependent rb ◮ 4 parameters, 15 LUC, 5 seasons ◮ Rcommended by SP2006

Petroff and Zhang 2010:

◮ “Exponential” form for

aerodynamic layer

◮ 10 parameters, 15 LUC, 5 seasons ◮ Finally fits the data

Intro New Scheme Smooth Rough Examples Conclusion

The scheme

J1 C2 Zobs Zobs Z2 Z1 C1 Smooth V1 V1 Rough Vint Vdif Vs Vimp Va Za

◮ “Exponential” scheme

for finite layers

◮ Separate treatment of

smooth and rough surfaces

◮ Rigorously derived

scheme for smooth surfaces

◮ Small amount of

parameters for rough surfaces

Intro New Scheme Smooth Rough Examples Conclusion

“Exponential” scheme

Steady-state particle flux equation below z1: J(z) = −K(z)∂C ∂z + v(z)C = const if v(z) = vs = const and C(0) = 0: J(z1) = C(z1) 1 − exp(−vsr)vs, r = z1 dz K(z) r is the resistance of the layer below z1. Can be also solved if v(z) = const and for C(0) = 0. The layer can be split at any point to evaluate corresponding concentration.

Intro New Scheme Smooth Rough Examples Conclusion

Smooth surfaces

10-3 10-2 10-1 100 101 102 1 10 100 νT

+

DNS Zhao&Wu (2006) This study 10-2 10-1 100 1 10 100 w+ 101 102 1 10 100 τL

+ = νT + / w+2

z+

◮ 1D problem ◮ Universal

turbulence profiles (normalized by ν,u∗ )

◮ Well studied ◮ Can be fit with

rational functions

◮ Of interest:

νt, w2, τL

Intro New Scheme Smooth Rough Examples Conclusion

Smooth surfaces

Steady-flux equation above smooth surface J = −(D + νp(z))∂C(z) ∂z + (Vt(z) − vs)C(z), where D and νp are Brownian and (vertical) eddy diffusivity of particles, and Vt is turbophoretic velocity: Vt = −τp dw2

p

dz , where w2

p is the mean square vertical velocity of a particle due to

turbulence. The profiles of turbulence over smooth surfaces are universal and can be approximated with rational functions.

Intro New Scheme Smooth Rough Examples Conclusion

Smooth surfaces: verification

Floor:

10−5 10−4 10−3 10−2 10−1 100 10−8 10−7 10−6 10−5 10−4 vd

+

Particle diameter, m u*=0.14 m/s 10−5 10−4 10−3 10−2 10−1 100 10−8 10−7 10−6 10−5 10−4 Particle diameter, m u*=0.4 m/s 10−5 10−4 10−3 10−2 10−1 100 10−8 10−7 10−6 10−5 10−4 Particle diameter, m u*=1 m/s This study, z = 30 cm Z01, inland water S80 Sippola & Nazaroff (2004), smooth floor Sehmel & Sutter (1974), water surface Möller & Schumann (1970), water surface Caffrey et al (1998), natural lake vd = 5⋅10−4 m/s

Wall:

10−5 10−4 10−3 10−2 10−1 100 10−7 10−6 10−5 10−4 vd

+

u*=0.14 m/s 10−5 10−4 10−3 10−2 10−1 100 10−7 10−6 10−5 10−4 u*=0.4 m/s 10−5 10−4 10−3 10−2 10−1 100 10−7 10−6 10−5 10−4 u*=1 m/s This study, z = 30 cm This study, z = 1 cm Sippola & Nazaroff (2004), smooth wall same, smooth ceiling Wells & Chamberlain (1967) Liu & Agarwal (1974) El−Shobokshy (1983)

Intro New Scheme Smooth Rough Examples Conclusion

Rough surfaces

Simple thoughts:

◮ Air moves in a canopy consisting of collectors ◮ Same collectors absorb momentum and matter ◮ Momentum flux is (more or less) well studied ◮ Ratio of corresponding cross-sections gives ratio of

deposition velocities Flow-collector interaction:

◮ Rec = Udc/ν

Particle-collector interaction:

◮ Diffusion Sc = ν/D ◮ Interception dp/dc ◮ Impaction St = 2τpUtop dc

Intro New Scheme Smooth Rough Examples Conclusion

Rough surfaces (starting points)

◮ Correlations for deposition on rough surfaces (FdlM&F, 1982):

Π = dp dc Re1/2

c

Sc1/3 Y = dp(Vd − vs) D Parameters: dp/dc, Rec = Udc/ν, Sc = ν/D. Y ∼ Π in the diffusion range (small Π) and Y ∼ Π3 in the interception range (large Π).

◮ Single-element efficiency for spheres and cylinders (P&F,

1984): dp dc RecSc · η = dpU D η = AΠ + BΠ3, A ≃ 2 and B ≃ 1 slightly depend on the collector shape.

◮ If u∗ and z0 are used as velocity and size, the correlation holds

with different coefficients for each surface (Schack, 1985).

Intro New Scheme Smooth Rough Examples Conclusion

Rough surfaces (continued)

◮ Relevant velocity scale Utop ≃ 3u∗. ◮ Collection scale

a = u∗ Utop dc

◮ Ratio u∗/Utop does not appear in

Π = dp a Re1/2

∗

Sc1/3

◮ Reynolds number

Re∗ = u∗a ν

◮ Once fitted for the dataset of Chamberlain (grass in wind

tunnel, dc = 5 mm), the correlation Y = 2Π + 80Π3 fits other datasets with a single fitting parameter a.

Intro New Scheme Smooth Rough Examples Conclusion

Rough surfaces (continued)

Π-Y correlation. “Learning” and “Control” datasets.

10-8 10-6 10-4 10-2 100 102 104 106 108 10-7 10-6 10-5 10-4 10-3 10-2 10-1 100 101 102 dp vd / D dp/dc Re1/2Sc1/3 Aerosol, grass a=2mm Aerosol, plastic grass a=2mm Thorium, grass a=2mm Thorium, short grass a=3mm Thorium, plastic grass a=2mm Thorium, toweling a=4mm Thorium, glass a=10mm Water, grass a=2mm Water, toweling a=4mm This study Single-element 10-2 100 102 104 106 10-3 10-2 10-1 100 101 102 dp vd / D dp/dc Re1/2Sc1/3 Sehmel & Sutter (1974), gravel, a=0.5mm Clough (1975), moss, a=0.5mm Sippola & Nazaroff (2003), insulated floor, a=0.5mm same, insulated wall, a=0.5mm This study Single-element

◮ “Learning” – given a, adjusted coefficients ◮ “Control” – fixed coefficients, adjusted a

Intro New Scheme Smooth Rough Examples Conclusion

Impaction

10-5 10-4 10-3 10-2 10-1 100 0.01 0.1 1 10 Efficiency Stokes number St = 2τpU/dc (a) Re=20 Re=100 Re=421 Re=1685 10-5 10-4 10-3 10-2 10-1 100 0.01 0.1 1 10 Efficiency St - Re-1/2 (b) Approximation

Stokes number can be expressed through the same scale: St = 2τpUtop dc = 2τpu∗ a Effective stokes number (accounting for viscous layer): Ste = St − Re

− 1

2

c

= St − u∗ Utop Re

− 1

2

∗ ,

The efficiency of impaction is approximated: ηimp(Ste) =

• exp
• −0.1

Ste−0.15 − 1 √Ste−0.15

• if Ste > 0.15,

if Ste ≤ 0.15.

Intro New Scheme Smooth Rough Examples Conclusion

Rough surfaces summary

Deposition velocity within in-canopy layer: Vd(z0) = vdif + vint + vimp + vs, vdif = u∗ · 2Re−1/2

∗

Sc−2/3, vint = u∗ · 80 dp a 2 Re1/2

∗

, vimp = u∗ 2u∗ Utop · ηimp (Ste) . Aerodynamic layer is accounted with exponential scheme: 1 Vd(z1) = 1 Vd(z0) exp(−vsra) + 1 vs (1 − exp(−vsra)) .

Intro New Scheme Smooth Rough Examples Conclusion

Overall scheme

J1 C2 Zobs Zobs Z2 Z1 C1 Smooth V1 V1 Rough Vint Vdif Vs Vimp Va Za

Smooth or rough is decided from roughness Reynolds number. Transition occurs: 2 < u∗z0/ν < 4

Intro New Scheme Smooth Rough Examples Conclusion

Illustration: “grass” and “snow”

10-4 10-3 10-2 10-1 10-8 10-7 10-6 10-5 10-4 vd

+

Particle diameter, m u*=0.35 m/s 10-4 10-3 10-2 10-1 10-8 10-7 10-6 10-5 10-4 Particle diameter, m u*=0.7 m/s 10-4 10-3 10-2 10-1 10-8 10-7 10-6 10-5 10-4 Particle diameter, m u*=1.4 m/s This study, smooth Z01, grass S80 This study, a=2mm Same, no impaction Grass Sticky grass 10-4 10-3 10-2 10-1 10-8 10-7 10-6 10-5 10-4 vd

+

Particle diameter, m u*=0.16 m/s 10-4 10-3 10-2 10-1 10-8 10-7 10-6 10-5 10-4 Particle diameter, m u*=0.37 m/s 10-4 10-3 10-2 10-1 10-8 10-7 10-6 10-5 10-4 Particle diameter, m u*=0.63 m/s This study, smooth Z01, snow S80 This study, a=0.5mm Same, no impaction Sippola & Nazaroff (2003), insulated floor

Intro New Scheme Smooth Rough Examples Conclusion

Account for the thermophoresis

◮ Thermophoresis: particles move to cooler regions

vTF = α(Kn) · ν dT/dz T = α(Kn) · PrFT T

◮ The order of magnitude: 1 mm/s per kW/m2. ◮ Is important in the laminar layer for sub-micro range. ◮ Easy to estimate when TF enhances deposition (heat flux

towards the surface) and/or when the surface is homogeneous

◮ Can block deposition to water surfaces for sub-micro

particles

Intro New Scheme Smooth Rough Examples Conclusion

Collector size from WT: trees/branches

0.01 0.1 1 10 0.01 0.1 1 Collection efficiency measured (%) Collection efficiency fit (%) Freer-Smith (2004), 1µm: A.Gultinosa, 7mm F.Excelsior, 5mm A.pseudoplatanus, 10mm P.menziezii, 1.7mm E.globulus, 22mm F.nitida, 12mm Q.petraea, 2mm Reinap (2009), 1.7µm:

• Q. robur, 130 mm

Beckett et al. (2000), 1.3µm: P.nigra, 2.5mm C.leylandii 3mm A.campestre 10mm S.intermedia 4.3mm P.deltoides x trihocarpa, 7 mm Courtesy of Walter Obermayer

Quercus Robur & Quercus petraea

Problems:

◮ Few studies ◮ Wide and uncertain particle

size spectra

◮ Experiments are done by

botanists/ecologists. . .

Intro New Scheme Smooth Rough Examples Conclusion

Outdoor experiments

10-2 10-1 100 101 102 10-4 10-3 10-2 10-1 100 dp vd / D dp/dc Re1/2Sc1/3 Nemitz et al. (2002), moorland, a=0.5mm Gallagher et al. (1997) forest, a=7mm same with a=0.1mm This study Single-element Aerodynamic limit, moorland

Intro New Scheme Smooth Rough Examples Conclusion

High vegetation

10-5 10-4 10-3 10-2 10-1 10-7 10-6 10-5 vd, m/s dp, m Joutsenoja (1992) Gallagher et al. (1997) Gallagher et al. (1992) Grosch & Schmidt (1992) Bewsick et al. (1991) Lorenz & Murphy (1989) Waranghai & Gravenhorst (1989) Reinap & Wiman (2009) + vs Z01, broadleaf forest S80 This study, a=7mm This study, a=0.5mm This study, a=0.05mm Settling, vs

Probable causes of discrepancies:

◮ Electricity?

◮ Boltzmann charging:

no sharp size dependence

◮ Dipole charging: 10

• rders of magnitude

weaker

◮ Wrong measured size? ◮ Complex particle shapes? ◮ Humidity? ◮ Something else?

Intro New Scheme Smooth Rough Examples Conclusion

Conclusions

◮ The new scheme is developed ◮ No fitting parameters for smooth-surfaces ◮ Universal empirical relationship and two scales for rough

surfaces (z0 and a)

◮ Does not fit outdoor experiments, esp. for high vegetation

(as all other mechanistic models)

◮ The collection scales for natural surfaces are needed. . . ◮ Implemented into SILAM model

• R. Kouznetsov, M. Sofiev 2012: J. Geophys. Res. 117,

D01202 DOI: 10.1029/2011JD016366