Modeling of heat and mass transfer during gas adsorption by aerosol particles in air pollution plumes T. Elperin1, A. Fominykh1, I. Katra2, and B. Krasovitov1 1Department of Mechanical Engineering, The Pearlstone Center for Aeronautical Engineering Studies, Ben-Gurion University of the Negev, P.O.B. 653, 8410501, Israel 2Department of Geography and Environmental Development, Ben-Gurion University of the Negev, P.O.B. 653, 8410501, Israel

Motivation and goals Power plant (Ashquelon, Israel) Scavenging of air pollutions by cloud and rain droplets Ne'ot Hovav chemical factory (Northern Negev, Israel) Power plant (Ashquelon, Israel) Ben-Gurion University of the Negev CHT-17, Napoli, Italy, 28 May - 02 June 2017 2

Gaussian plume model Gaussian Plume model Scavenging of air pollutions by cloud and rain droplets Gaussian Plume model Ben-Gurion University of the Negev CHT-17, Napoli, Italy, 28 May - 02 June 2017 3

Pasquill-Gifford dispersion parameters Pasquill-Gifford stability categories Gradient Richardson number reads where q is potential temperature that can be calculated as follows Γ is the adiabatic lapse rate ( K/m over the distance to the mixing depth) Ben-Gurion University of the Negev CHT-17, Napoli, Italy, 28 May - 02 June 2017 4

Pasquill-Gifford dispersion parameters Pasquill-Gifford horizontal dispersion parameters Ben-Gurion University of the Negev CHT-17, Napoli, Italy, 28 May - 02 June 2017 5

Pasquill-Gifford dispersion parameters Pasquill-Gifford vertical dispersion parameters Ben-Gurion University of the Negev CHT-17, Napoli, Italy, 28 May - 02 June 2017 6

Turbulent diffusion of active gas in ABL Scavenging of air pollutions by cloud and rain droplets Mass transfer of gaseous adsorbent in atmospheric boundary layer (ABL) can be described using advection diffusion equation that reads (1) where is the mean concentration of gaseous adsorbent, are the components of mean wind velocity, are components of turbulent fluxes, is the rate of gas adsorption. Hereafter we adopted the turbulence closure based on the hypothesis of the gradient transport (K-theory) (2) where are the diagonal components of eddy diffusivity. Ben-Gurion University of the Negev CHT-17, Napoli, Italy, 28 May - 02 June 2017 7

Turbulent diffusion of active gas in ABL Governing equation Boundary conditions Scavenging of air pollutions by cloud and rain droplets at (4) (3) at - rate of loss of active gas due to adsorption by aerosol particles - height of ABL For stable boundary layer (SBL) coefficient reads (Blackadar, 1979): (5) where l is the turbulent mixing length, zm = 200 m, k = 0.4, RiC = 0.25 Ben-Gurion University of the Negev CHT-17, Napoli, Italy, 28 May - 02 June 2017 8

Turbulent diffusion of active gas in ABL Gas adsorption by PM Scavenging of air pollutions by cloud and rain droplets Time derivative of the radius-average concentration of the adsorbed gas in a porous particle reads: (6) Henry’s constant of adsorption specific surface area of a particle For an ensemble-average concentration field (7) Ben-Gurion University of the Negev CHT-17, Napoli, Italy, 28 May - 02 June 2017 9

Turbulent diffusion of active gas in ABL Gas adsorption by PM Scavenging of air pollutions by cloud and rain droplets from Eqs. (17) and (16) we obtain: (8) solution of Eq. (8) reads: (9) Consequently (10) Ben-Gurion University of the Negev CHT-17, Napoli, Italy, 28 May - 02 June 2017 10

Gas adsorption by aerosol particles expression for scavenging coefficient is the following: Scavenging of air pollutions by cloud and rain droplets (11) m - Henry’s adsorption constant DG - coefficient of molecular diffusion - volume fraction of particles - scavenging coefficient Ben-Gurion University of the Negev CHT-17, Napoli, Italy, 28 May - 02 June 2017 11

Gas adsorption by aerosol particles Table 1. Henry’s law constant of adsorption of active gases NO2, HNO3 and I-131 by carbon-based aerosols at temperature T = 298 K Scavenging of air pollutions by cloud and rain droplets aKalberer et al. (1999); bSeinfeld & Pandis (2016); cMunoz et al. (2002) dNoguchi et al. (1988) or - linear form of isotherm of adsorption U - adsorbed amount of active gas Ben-Gurion University of the Negev CHT-17, Napoli, Italy, 28 May - 02 June 2017 12 - volume fraction of particles

Gas adsorption by aerosol particles Scavenging of air pollutions by cloud and rain droplets Fig. 4. Dependence of adsorbed amount of iodine vs. time ( , , ) Fig. 3. Dependence of adsorbed amount of iodine vs. time ( , , ) Ben-Gurion University of the Negev CHT-17, Napoli, Italy, 28 May - 02 June 2017 13

Mean wind velocity profile In ABL the wind profile can be described by the logarithmic law Scavenging of air pollutions by cloud and rain droplets (6) - friction velocity - shear stress at the surface level - air density - aerodynamic surface roughness length that is 1/30 of the field roughness elements σ - standard deviation of velocity fluctuations Ben-Gurion University of the Negev CHT-17, Napoli, Italy, 28 May - 02 June 2017 14

Measurements of mean wind velocity profile Scavenging of air pollutions by cloud and rain droplets Fig. 6. A cup anemometer Measuring range 0 – 50 m/s Accuracy  0.49 m/s Fig. 5. A 10-m wind mast Ben-Gurion University of the Negev CHT-17, Napoli, Italy, 28 May - 02 June 2017 15

Measurements of mean wind velocity profile Scavenging of air pollutions by cloud and rain droplets For each height the average wind velocity was calculated as follows Ben-Gurion University of the Negev CHT-17, Napoli, Italy, 28 May - 02 June 2017 16

Governing equation and boundary conditions Scavenging of air pollutions by cloud and rain droplets at (4) (3) at - rate of loss of active gas due to adsorption by aerosol particles - height of ABL For stable boundary layer (SBL) coefficient reads (Blackadar, 1979): (5) where l is the turbulent mixing length, zm = 200 m, k = 0.4, RiC = 0.25 Ben-Gurion University of the Negev CHT-17, Napoli, Italy, 28 May - 02 June 2017 17

Numerical solution - Parabolic partial differential Eq. (3) was solved using the method of lines developed by Sincovec and Madsen [1975]. Scavenging of air pollutions by cloud and rain droplets - Spatial discretization on a three-point stencil with uniformly distributed mesh points was used in order to reduce partial differential equation (3) to the approximating system of coupled ordinary differential equations. - The resulting system of ordinary differential equations was solved using a backward differentiation method. Sincovec, R.F., Madsen, N.K. [1975] Software for nonlinear partial differential equations. ACM T. Math. Software, Vol. 1, pp. 232–260. Ben-Gurion University of the Negev CHT-17, Napoli, Italy, 28 May - 02 June 2017 18

Results and discussion NO2 HNO3 Scavenging of air pollutions by cloud and rain droplets Fig. 7. Concentration distributions in the XZ-plane, evaluated at Y=0. Ben-Gurion University of the Negev CHT-17, Napoli, Italy, 28 May - 02 June 2017 19

Conclusions The model is based on an application of theory of turbulent diffusion in the atmospheric boundary layer (ABL) in conjunction with plume dispersion model and model of gas adsorption by porous solid particles. The wind velocity profiles used in the simulations were fitted from data obtained in field measurements conducted in the Northern Negev (Israel) using the experimental wind mast. The adsorbate concentration distributions are calculated for the particulate matter PM2.5-10, which is typical for industrial emissions. It is shown that the concentration of the gases adsorbed by aerosol plume strongly depends on the level of atmospheric turbulence. The results of present study can be useful in the analysis of different atmospheric pollution models including gas adsorption by aerosol plumes emitted from industrial sources. Ben-Gurion University of the Negev CHT-17, Napoli, Italy, 28 May - 02 June 2017