CFD Modeling of Aerosol Transport and Deposition Using a Drift-Flux Model

Abstract

Aerosol transport and deposition are important processes in modeling of accident scenarios for a small modular reactor. An aerosol drift-flux model is attractive because it is computationally less expensive than Lagrangian particle tracking. It must be determined, however, how well it performs when implemented in a commercial computational fluid dynamics (CFD) code. This work presents results of modeling aerosol transport and deposition using a full Eulerian three-dimensional drift-flux model implemented in the commercial CFD code STAR-CCM+. The forces due to gravity and thermophoresis are included in the present drift-flux model along with Brownian motion and turbulent diffusion. The forces are added as a source term to a passive scalar transport equation. In addition, a drift velocity representing the forces is used in a built-in electrochemical species transport equation. The results of these two approaches are compared. An appropriate deposition velocity is used to calculate the aerosol concentration deposited on surfaces. The semiempirical relation proposed by Lai and Nazaroff (2000) is used to compute the deposition velocity due to gravitational settling, and the present results are compared with the experimental and numerical data obtained from the work of Chen et al. (2006). It was found that the concentration profile obtained from the present drift-flux model showed reasonable agreement with the literature data. A thermophoresis model showed good agreement when compared with the analytical solution of Nazaroff and Cass (1987). In addition to the particle concentration results, this work presents details of the drift-flux model implementation and the bulk flows. These extra details will enable comparisons by others developing similar models.

Keywords:

• Aerosol modeling
• drift-flux method
• validation and verification
• small modular reactors
• computational fluid dynamics

Nomenclature

$\mathit{A}$ =	=	area (${\mathrm{m}}^2$)
$\mathcal{C}$ =	=	aerosol general concentration notation
$C^{\ast }$ =	=	normalized aerosol concentration
$C_p$ =	=	specific heat ($\mathrm{J}/\mathrm{kg}\cdot \mathrm{K}$)
$C_{\mu }$ =	=	Cunningham slip factor
$\mathit{D}$ =	=	diffusion coefficient (${\mathrm{m}}^2$)
$d_p$ =	=	particle diameter (m)
$\mathit{F}$ =	=	Faraday constant
$f_b$ =	=	body force ($\mathrm{N}/{\mathrm{m}}^3$)
$\mathit{g}$ =	=	gravitational acceleration ($\mathrm{m}/{\mathrm{s}}^2$)
$\mathit{H}$ =	=	H factor in $k_{\mathit{th}}$ equation
$\mathit{I}$ =	=	integral in Ref. [11]
$\mathit{J}$ =	=	deposition velocity ($\mathrm{kg}/{\mathrm{m}}^2\cdot \mathrm{s}$)
$\mathit{k}$ =	=	thermal conductivity ($\mathrm{W}/\mathrm{m}\cdot \mathrm{K}$)
$k_B$ =	=	Boltzmann constant $(1.380649\$\times {10}^{-23}\$\mathit{J}/\mathit{K})$
$k_{\mathit{th}}$ =	=	thermophetic force coefficient
$\mathit{M}$ =	=	migration (m/s)
$\mathit{P}$ =	=	pressure (Pa)
$\mathrm{R}{\mathrm{a}}_L$ =	=	Rayleigh number, ${\rho }^2{C}_p\mathit{g\beta }\Delta \mathit{T}{L}^3/(\mathit{\mu k})$
$\mathit{S}$ =	=	source term
$\mathrm{Sc}$ =	=	Schmidt number
$\mathit{T}$ =	=	temperature (K)
$\mathit{t}$ =	=	time (s)
$\mathit{U}$ =	=	fluid velocity (m/s)
$u^{\ast }$ =	=	friction velocity (m/s)
$\mathit{V}$ =	=	volume (${\mathrm{m}}^3$)
$V_d$ =	=	deposition velocity (m/s)
$\mathit{v}$ =	=	slip velocity (m/s)
$\mathit{W}$ =	=	aerosol mass concentration (mass fraction)
$\mathit{x}$, $\mathit{y}$, $\mathit{z}$ =	=	Cartesian coordinates (m)
${\mathit{z}}_{\mathit{e}}$ =	=	charge number

Greek symbols

${\alpha }_s$ =	=	relaxation factor
$\mathit{\beta }$ =	=	thermal expansion coefficient (1/K)
${\mathrm{\Delta }}_{\mathit{S},\mathrm{rel}}$ =	=	source term relative change
$\mathit{ϵ}$ =	=	ECS migration error
$\mathit{\eta }$ =	=	dimensionless coordinate
$\mathit{\lambda }$ =	=	mean free path (m)
$\mathit{\mu }$ =	=	dynamic viscosity ($\mathrm{Pa}\cdot \mathrm{s}$)
${\mathit{\mu }}_{\mathit{e}}$ =	=	charge mobility
$\mathit{\rho }$ =	=	density ($\mathrm{kg}/{\mathrm{m}}^3$)
${\rho }_{ϵ}$ =	=	electromotive force density
$\mathit{\sigma }$ =	=	electrical conductivity
${\tau }_p$ =	=	particle relaxation time (s)

Subscripts

$\mathit{B}$ =	=	Brownian
diff =	=	drift
eff =	=	effective
gs =	=	gravitational settling
$\mathit{p}$ =	=	particle
ref =	=	reference value
surf =	=	surface orientation, surf = $\mathit{c}$, $\mathit{f}$, or $\mathit{v}$
$\mathit{t}$ =	=	turbulent
th =	=	thermophoresis
$\mathrm{\infty }$ =	=	bulk (free stream)

Acknowledgments

The financial support of the Natural Sciences and Engineering Research Council of Canada (NSERC Alliance Grant ALLRP 561213-20), Canadian Nuclear Laboratories, and the Univeristy of Manitoba is gratefully acknowledged. The authors are grateful to Bin Zhao of Tsinghua University for his discussions on implementing a drift-flux model.

Disclosure Statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the Natural Sciences and Engineering Research Council of Canada [ALLRP 561213-20]; Canadian Nuclear Laboratories; University of Manitoba.