Numerical study of fluid flow and particle dispersion and deposition around two inline buildings

Journal of Wind Engineering & Industrial Aerodynamics 179 (2018) 385–406

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Numerical study of fluid flow and particle dispersion and deposition around two inline buildings H.R. Haghighifard a, M.M. Tavakol a, *, G. Ahmadi b a b

Department of Mechanical Engineering, Shiraz Branch, Islamic Azad University, Shiraz, Iran Department of Mechanical and Aeronautical Engineering, Clarkson University, Potsdam, NY, USA

A R T I C L E I N F O

A B S T R A C T

Keywords: Supported buildings CFD Turbulent flow Surface roughness Deposition fraction Lagrangian tracking

In the present study, turbulent airflows and particle deposition around two inline buildings were investigated numerically. A computational modeling approach including the RNG k-ε and Realizable k-ε turbulence models were used for these simulations. The Lagrangian particle tracking approach was implemented for evaluating dispersion and deposition of spherical dust particles. For simulation of turbulence fluctuations, an improved discrete random walk (DRW) model that includes the near wall correction was implemented into several userdefined functions (UDFs) that were linked to the ANSYS-Fluent code. It was shown that the new improved DRW stochastic model led to results that are more accurate compared to the standard model. The improved DRW model was then used for simulating turbulent deposition and dispersion of dust around building models. The presented results showed that putting buildings on elevated supports reduces dusts deposition from downstream of single and inline buildings at short distances, particularly for small particles of about 1 μm. It is also shown that particle deposition fractions around buildings on rough ground are higher than those for smooth ground. Deposition fractions were also predicted by the improved model for faces of single and inline buildings.

1. Introduction Scientists and engineers have been concerned with particle deposition in internal and external flows due to their significant industrial and environmental applications. Recently, there has been considerable interest in the dust transport and deposition processes in HVAC ducts and around buildings due to their importance in environmental air pollution and the associated health issues. In last three decades, there have been several studies on dust transport and deposition processes over smooth and rough flat plates (Sehmel, 1971; Wedding and Stukel, 1974; Clough, 1975; Paz et al., 2013). Experimental measurements of particle deposition in duct flows were reported by Friedlander and Johnstone (1957), Rosinski and Langer, 1967 and Liu and Agarwal (1974) among others. They found that particle deposition rate increases with airflow speed. Wood (1981), Hinds (1984) and Papavergos and Hedley (1984) provided extensive reviews of theoretical and experimental studies of transport and deposition of particles in turbulent flows. McLaughlin (1989), Ounis et al. (1993), Zhang and Ahmadi (2000), and Li et al. (2016) studied turbulent flows and particle deposition in duct flows using the direct numerical simulation (DNS). Understanding the features of flow and pollutant transport near

building models has also attracted considerable attention in the recent years. An earlier experimental study on dispersion of plume near cubical building model was reported by Robins and Castro (1977). Pesava et al. (1999) discussed the nature of separated flows and sub-micron aerosol deposition on a cube in cross winds. They observed that the deposition rates on various cube faces are different. Liu and Ahmadi (2006) investigated helium gas and particle transport and deposition around a building model. Flow field simulations were performed with the RSTM turbulence model and particle tracking was done by use of the Lagrangian approach. Their results indicated large particle are deposited mainly by impaction on the side of the building facing the wind, but the smaller particle deposition rate are more uniform. They noted that gravity effects are significant for particles larger than 10 μm, and Brownian motion was important for aerosol particles smaller than 0.1 μm. Nazridoust and Ahmadi (2006) simulated the flow and pollutant transport in street canyons. They used the Langrangian approach for evaluating the solid particle dispersion and deposition. In investigation of pollutant dispersion around an urban building model, Zhang et al. (2015) found that concentration of haze fog is not relevant to position of emission. Ai and Mak (2014) and Yu et al. (2017) investigated particle dispersion around multistory building models at different angle of wind

* Corresponding author. E-mail address: [email protected] (M.M. Tavakol). https://doi.org/10.1016/j.jweia.2018.06.018 Received 5 April 2018; Received in revised form 25 June 2018; Accepted 26 June 2018 0167-6105/© 2018 Elsevier Ltd. All rights reserved.

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Journal of Wind Engineering & Industrial Aerodynamics 179 (2018) 385–406

the standard building model height. Selecting proper boundary conditions are critical to the accuracy of Computational Fluid Dynamic (CFD) results. In recent years, certain guidelines for selection of boundary conditions for simulation of flow around buildings and urban areas were recommended in the literature (Franke et al., 2007; Tominaga et al., 2008). In the present study, the Working Group of the Architectural Institute of Japan (AIJ) guidelines (Tominaga et al., 2008) are used for appropriately modeling the flow field around single and inline buildings. The AIJ guideline suggests use of atmospheric boundary layer velocity profile for inlet wind flow, generation of appropriate computational domain to avoid blockage and side way interference and developing proper meshing of the computational domain around building. In addition, recommendations are provided for improving convergence of the numerical solutions and use of proper turbulence models. The developed computational domain is shown in Fig. 1 and the imposed boundary conditions at different planes are listed in Table 1. The developed computational grids consisted of 1.6 million hexahedral grid cells for the single building models. Grid quality assessment shows that the maximum aspect ratios for standard and supported building models were, respectively, about 8 and 10. For the inline buildings, the computational grids were in the range of 2–2.2 million cells. Number of grids for length (x direction), width (y direction) and height (z direction) around the single building models were 152
72
60 for the single building models. Fine grids were generated around the buildings and near wall. Fig. 2-a and 2-b show sample computational grid sections around inline standard surface-mounted and supported building models at the symmetry plane (Y/H ¼ 0) for separation distance of S¼H. Structure of grids around supports is shown in Fig. 2-c. Grid sensitivity tests were performed and the results are discussed in Section 7. The AIJ guideline was used and proper velocity distribution, turbulence kinetic energy and dissipation rate profiles at the inlet of compu-

incident. Moshfegh et al. (2010) studied particle deposition and dispersion around two inline 2D cylinders numerically. Particles were released from various source and the corresponding deposition efficiencies were evaluated. Wevers and Hoffer (2012) investigated particle dispersion around two buildings. Comparison between their numerical simulations and experiments showed that the prediction of particle concentration behind isolated building is overestimated, however, the concentration at the back of building with an open hall is underestimated. Tominaga and Stathopoulos (2017) compared steady Reynolds Average Navier-Stokes simulations (SRANS) and unsteady RANS (URANS) models for predicting flow field and pollution concentration around a cubic building model. They reported that URANS was more successful than SRANS model for prediction of concentration when the release source was located at the back of the building model. In the present study, the flow field and particle deposition around single supported and inline standard (non-supported) and supported lowrise buildings for three streamwise distances were studied. The results for single standard building were also presented for comparison. The simulated airflow fields around single and inline buildings were validated by comparison with the available experimental data. The predicted micronsize particle deposition fraction on the ground around single and inline buildings was validated by calculation of deposition velocity over smooth and rough flat plates and comparing them with the experimental results. In addition, the deposition fractions on various faces of standard and supported building models were investigated and compared with earlier experimental and numerical results and available theories. Then, the effect of surface roughness on the velocity distribution and deposition fraction of particles on the ground around buildings was evaluated and discussed. 2. Geometry and boundary conditions In this paper, airflow and particle dispersion and deposition around scaled models of single supported building and two inline buildings were simulated numerically. The cases of standard surface-mounted buildings, and when the buildings were supported on open frames were considered. Here a scale factor of 0.01 with respect to the full-scale buildings was used. With this scale factor, for a standard building, a 10 cm long, 10 cm wide and 3 cm height cube was considered. The supported building model had the same dimensions, but was mounted on four 0.4 cm
0.4 cm
1 cm supports. Inline building models were positioned at different streamwise distances of S¼H, 2H and 5H with H ¼ 3 cm was

Table 1 Boundary conditions used. Planes in Fig. 1

Boundary condition

abcd, a'b'c'd' efgh, e'f'g'h' abfe,a'b'f'e' cghd, c'g'h'd' adhe,a'd'h'e' bcgf, b'c'g'f'

Velocity inlet Pressure outlet Wall Symmetry Symmetry Symmetry

Fig. 1. Computational domain for inline buildings, a) Standard buildings, b) Supported buildings. 386

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0.14 Experiment (Motalebi et al., 2012) Power law(n=0.125) Power law(n=0.26) Logarithmic-Law

0.12 0.1 z(m )

0.08 0.06 0.04 0.02 0 0

2

4

6

8

10

12

U(m s -1) Fig. 3. Comparison of the experimental inlet velocity distribution with the power law formulas and logarithmic formula.

law for smooth (desert area) case and data of power law for rough wall are close to data of logarithmic law. In this work, power law profile with n ¼ 0.26 was adopted for the rough wall condition. As stated before, the inlet turbulence kinetic energy was estimated from the measured RMS velocities in the wind tunnel (Motalebi et al., 2012) and the AIJ guideline (Tominaga et al., 2008). The AIJ assumes that mean squares of spanwise and vertical velocity fluctuations are half of mean square of streamwise velocity fluctuation, and turbulence dissipation rate, ε, was derived from AIJ guideline. These are: k ¼ ðurms Þ2

ε ¼ Cμ1=2 kðzÞ

(1) dUðzÞ dz

(2)

where k and urms are, respectively, the turbulence kinetic energy and root mean square of streamwise fluctuation velocity. In Eq. (2) Cμ ¼ 0.09 is a constant and UðzÞ is the stream-wise velocity as a function of vertical distance from the wall, z. The wall boundary condition were considered for all faces of building models and supports and in order to model the flow near the walls, the standard wall function boundary condition was used for both smooth and rough walls. Turbulence kinetic energy was evaluated from the measured RMS velocities as reported by Motalebi et al. (2012) and turbulence dissipation rate was obtained from the AIJ guideline, and the results are shown in Fig. 4. Eqs. (1) and (2) with the fitted curves to data from were used in the user defined functions to provide the inlet boundary condition at abcd and a'b'c'd' sample planes of the computational domain.

Fig. 2. Computational grid for two inline buildings with S¼H, a) Standard building, b) Supported building, c) Surface grid around support.

tational domain were obtained from the experimental data of Motalebi et al. (2012). Fig. 3 compares the measured velocity profile in the wind tunnel as reported by Motalebi et al. (2012) with the power law formula
n UðzÞ y with n ¼ 0.125 and the rough logarithmic law of the wall URef ¼ δ   0 UðzÞ ¼ uκ * ln zþz with the power law formula with n ¼ 0.26. Here URef z0

3. Governing equations 3.1. Flow field equations In the present study, the air is treated as an incompressible fluid. The governing conservation equations for the time averaged threedimensional incompressible flow with constant properties can be expressed as:

is the free stream velocity and u* ¼ 0.21 m/s, κ ¼ 0.4 and z0 ¼ 0.00051 m are, respectively, the friction velocity, the von Karman constant and the roughness length. In Fig. 3, velocity profiles with two power law exponents with n ¼ 0.125 appropriate for desert areas and n ¼ 0.26 suitable for small towns (urban areas) were used (White, 1996). For both velocity profiles, the free stream velocity at the edge of boundary layer was 10 m/s. For the desert area case, a smooth ground surface was assumed, whereas, for the small town case a rough surface was considered. For the rough wall case, the roughness height, ks , roughness length, z0 , and roughness 0 (Blocken et al., 2007). Here, constant, Cs , are related, as kS ¼ 9:793z Cs

∂ Ui ¼0 ∂xi

(3)  

ρU j



∂U i ∂P ∂ ∂U i ∂U j ¼ þ μ þ  ρui uj ∂xj ∂xi ∂xj ∂xj ∂xi

 (4)

Here Ui and P are, respectively, the mean velocity and the mean pressure, ui is the fluctuation velocity, ui uj is the Reynolds stress tensor, and μ is the fluid viscosity.

ks ¼ 0.005 m, z0 ¼ 0.000510 m and Cs ¼ 1 are assumed and boundary layer height for both cases (rough and smooth) was 0.12 m. Fig. 3 shows that the inlet data used are in agreement with the power 387

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wherewith closure constants: Cμ ¼ 0:0845; σ k ¼ 0:7194; σ ε ¼ 0:7194; Cε1 ¼ 1:42 and Cε2 ¼ 1:68:Here μ and μt denote, respectively, the fluid dynamic viscosity and turbulent (eddy) viscosity, and Sij is the rate of deformation tensor. Gk and Yk are production and dissipation terms of turbulent kinetic energy respectively. Eqs.(8) and (9) list the expression of the coefficients and values of constants of the RNG k-ε model. The transport equations of the Realizable k- ε, which satisfies mathematical constraint of the Reynolds stresses, are given as (Shih et al., 1995):

∂ ∂ ðρkui Þ ¼ ∂xi ∂xi ∂ ∂ ðρεui Þ ¼ ∂xi ∂xi



μþ 

μþ





μt ∂k þ Gk  Yk σ k ∂xi 

(10)



μt ∂ε þ Gε  Yε σ ε ∂xi

(11)

with: Cμ ¼

  pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 1 ∂ui ∂uj and U ¼ S S þ Ω Ω ¼  ; Ω ij ij ij ij ij 2 ∂xj ∂xi A0 þ As kU ε

Where A0 ¼ 4:04; As ¼

pffiffiffi pffiffiffi 6cos ϕ; ϕ ¼ 13cos1 6W and W ¼

Gε ¼ ρC1 Sε andYε ¼ ρC2

ε2 kþ

pffiffiffiffiffi

νε

(12) 



Sij Sik Ski S3

(13)

    η ; η ¼ S kε where C1 ¼ max 0:43; ηþ5 Here closure constants are C2 ¼ 1:9; σε ¼ 1:2 and σ k ¼ 1:0

(14)

Gε and Yε represent production and dissipation of dissipation rate. Closure coefficients of Realizable k- ε are listed in Eq. (14). Fig. 4. Comparison of the experimental data for a) turbulence kinetic energy and b) turbulence dissipation rate used at the inlet with the fitted curves.

3.2. Particle motion Modeling particle dispersion and deposition in turbulent flows has attracted considerable interest due to its importance in numerous industrial and environmental applications. While Eulerian methods for predicting dust dispersion around buildings were used in the past (Lateb et al., 2010; Gousseau et al., 2012; Shen et al., 2015), the use of Lagrangian particle trajectory analysis is preferred. This is due to simplicity of boundary condition at particle-wall contacts and its ability of the approach to track each particle in the computational domain. In the present study, the airflow was evaluated using the Eulerian approach and the Lagrangian method was used to track particles. The particle equation of motion including the drag force and the gravity force is given as:

For turbulence modeling the RNG k-ε (Yakhot et al., 1992) and the Realizable k-ε (Shih et al., 1995) models were employed for numerical simulations. For these two-equation turbulence models, the Boussinesq eddy viscosity assumption was used. Therefore, the turbulence (Reynolds) stress tensor can be expressed as: 2 ui uj ¼ 2νt Sij  kδij 3

(5)

Here νt and Sij are, respectively, the kinematic eddy viscosity and the rate of deformation tensor, δij is the Kronecker delta. The RNG k-ε model was developed by renormalization of NavierStokes equations that account for various scales of turbulent motion. The correspond transport equations are given as (Yakhot et al., 1992):

∂ ∂ ðρkui Þ ¼ Gk  Yk þ ∂xi ∂xj





μþ

μt ∂k σ k ∂xj

∂ ε ε2 ∂ ðρεui Þ ¼ Cε1 Gk  Cε2;RNG ρ þ ∂xi k k ∂xj

dupi CD Rep ðui  upi Þ þ gi ¼ dt 24τ



Where ui and upi are, respectively, the fluid and particle velocities; CD and Rep denote the drag coefficient and the particle Reynolds number, while τ and gi are the particle relaxation time and the gravity acceleration, respectively. The location of particle is evaluated by integrating its velocity. That is,

(6)





μþ

μt ∂ε σ ε ∂x j

 (7)

Here: Yk ¼ ρε and; S ¼

Cε2;RNG ¼ Cε2 þ

  pffiffiffiffiffiffiffiffiffiffiffiffi 1 ∂ui ∂uj 2Sij Sij ; Gk ¼ S2 μt ; Sij ¼ þ 2 ∂xj ∂xi


 Cμ η3 1  ηη 0

1 þ β η3



η ¼ 2Sij Sij

12 k

ε

; η0 ¼ 4:377; β ¼ 0:012

(15)

(8)

dxi ¼ upi dt

(9)

Here ui and upi are, respectively, the instantaneous fluid and particle velocities, and xi is the particle position. In this work, the Saffman lift force, thermophoresis effects and Brownian force were neglected.

388

(16)

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3.2.1. Turbulence fluctuations RANS models provide the mean flow velocity fields as well the kinetic energy of turbulence and the turbulence dissipation rate. While the small particles are transported by the fluid mean motion, they are dispersed by the small eddies of turbulence. Therefore, appropriate modeling of instantaneous velocity fluctuations is needed for accurate simulation of particle dispersion and deposition in turbulent flows. Typically, stochastic models like the discrete random walk (DRW) model are used for generating the instantaneous turbulence fluctuations. In this study, both conventional discrete random walk model and an improved DRW model that includes the near wall corrections are used in the simulations. The DRW model equation for generating the instantaneous flow fluctuations in ANSYS-Fluent code can be expressed as (Ansys FLUENT, 2016): 0

ui ¼ ξurms;i 0

wall was discussed by Tian and Ahmadi (2007), Ghahramani et al. (2014) and Dehbi (2008). As noted before, the near wall corrections given by Eqs. (19)–(21) were obtained from the DNS simulation of channel flows. Earlier these equations were successfully used for ribbed channel flows (Lecrivain et al., 2014; Lu and Lu, 2015). Here, these are used to model the airflow turbulence near the ground and the near wall flows on the faces of single and inline building models. In these cases, the zþ are distances perpendicular the surface in wall units. Note also that these equations are used for all values of zþ and for both smooth and rough surfaces. In the modified model, the turbulence integral time scale in wall unit is given as (Kallio and Reeks, 1989; Matida et al., 2000):

(17) 0

τe ¼ 2TL where TL ¼ CL

wþ rms ¼

k

ε

0:19ðzþ Þ

TLþ ¼

0:203ðzþ Þ

z ¼z

ν

and

uþ rms

urms ¼ * where u* ¼ u

ν

; and εþ ¼

1 4:529 þ 0:0116ðzþ Þ1:75 þ 0:768ðzþ Þ0:5

(26)

(27)

In this study, ks and H for the scaled models were, respectively, 0.005 m and 0.03 m, and ks and H for physical wind flow around buildings were, respectively, 0.5 m and 3 m. Therefore, the requirement given by Eq. (27) is satisfied. In the presence of surface roughness, flow field should be appropriately simulated when the surface is aerodynamically rough. Therefore, the roughness Reynolds number must be greater than 2.5 (Sutton, 1955). In this study, based on friction velocity (u* ¼ 0.21 m/s), length of

rffiffiffiffiffi

τω ρ

TL u*2

    ks ks ¼ H Model H FullScale

þ

Here z and u are, respectively, the distance from wall and the root mean square velocity fluctuation in wall units defined as, u*

(25)

Satisfying scaling requirements such as fluid flow Reynolds number, surface roughness, and particle Stokes number are crucial for relating the real flow and particle transport around bluff bodies to those of the scaled model studies (White, 1996). In this study, an isothermal condition is assumed and the buoyancy effects were ignored. In the previous studies, it has been suggested that the dynamic similarity for flow field around sharp edge bluff bodies could be established between scaled simulation and real flow field if the Reynolds number is greater than 10000 (Gesellschaft and Niemann, 1994; Larose and Dauteuil, 2006). In the present study, the flow Reynolds number based on cube (standard building model) height and free stream velocity is 17000; hence, a dynamic similarity is expected. Surface roughness can be characterized by equivalent roughness height. In order to maintain the dynamic similarity of the wind flow field over buildings in various areas to the model study, the ratio of roughness height to building height should be matched (White, 1996). That is,

(21)

þ 0:00140ðzþ Þ2:421

for zþ > 200

4. Scaling requirements for flow field

2

0:0116ðzþ Þ

εþ

2

Here TLþ and εþ are dimensionless integral time scale and turbulence dissipation rate. Eqs. (23) and (24) were adopted based on Kallio and Reeks (1989) and suggestion of Matida et al. (2000) for calculation of integral time scale. For zþ >200 Eq. (25) is used. The DRW with appropriate shape functions given by Eqs. (19)–(21) and the integral time scale given by Eqs. (23)–(25) form the basis of the present improved DRW model. Dehbi (2008) suggested the use of shape function given by (19)–(21) in a continuous random walk (CRW) mode but without the adjustment for the integral time scale in the core region, zþ >200.

(20)

1 þ 0:0361ðzþ Þ1:322

wþ rms

where

(19)

1 þ 0:0239ðzþ Þ1:496

þ

þ

(24)



(18)

0:4ðzþ Þ

1þ



2 TLþ ¼ 7:122 þ 0:5731 zþ  0:00129 zþ for 5 < zþ < 200 TLþ ¼

Here TL denotes fluid integral time scale, CL is a constant, which is equal to 0.15 for the k-ε models. While the DRW model has been commonly used in the past, it is known that it may leads to considerable overestimation of particle deposition especially for small particles (Tian and Ahmadi, 2007; Zhang and Chen, 2009). This is because the isotropic eddy viscosity models do not account for anisotropy of the near wall turbulence fluctuations. In addition, the correct variation of normal fluctuation velocity (in this study, w' ) with distance from the wall is not properly predicted. As a result, the overactive turbophoresis effects transport too many particles from regions with high turbulence kinetic energy to the near wall region and significantly overestimate the particle deposition rate (He and Ahmadi, 1999). To improve the model predictions, the velocity fluctuations and integral time scale are calculated with near wall corrections (in the region with zþ<200) based on direct numerical simulations (DNS) for a turbulent channel flow (Dreeben and Pope, 1997; Dehbi, 2008). Accordingly:

vþ rms ¼

(23)

0

where u , v and w are instantaneous turbulent fluctuation velocity and urms , vrms and wrms are root mean square turbulent fluctuation velocity components, and ξ is a zero mean unit variance Gaussian random number. In the DRW model, a new random number for each velocity component is selected discretely after the eddy lifetime τe and the corresponding new fluctuation velocity components are calculated. Thus, the random velocity fluctuation components remain unchanged during the eddy lifetime. The eddy lifetime is given as,

uþ rms ¼

TLþ ¼ 10 for zþ < 5

(22)

Here z is the vertical distance from the wall, u* is the shear velocity parallel to the wall and ν is the fluid kinematic viscosity. In Eq. (22), τω and ρ are the wall shear stress and the fluid density. The importance of anisotropy and quadratic variation of fluctuation velocity normal to the 389

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roughness (z0 ¼ 0.000510 m) and fluid kinematic viscosity (υ ¼ 1.7647
105 m2/s) the roughness Reynolds number is about 7.

7. Results and discussion 7.1. Grid sensitivity study

5. Boundary conditions of flow and particle deposition for rough and smooth cases

For grid sensitivity study, different computational grids for flow around single standard and supported building models, which contained 0.8, 1.6 and 2.5 million cells, were considered. Using the RNG k-ε model, Fig. 6 compares the predicted mean velocity and stream-wise turbulence intensity profiles as evaluated by these computational grids at a section on the plane of symmetry (Y/H ¼ 0) of the buildings. It is seen that the mean velocity and turbulence intensity profiles for grids with 1.6 and 2.5 million cells are almost the same. Thus, it is assumed that the grid independent results are achieved and the mesh with 1.6 million cells is used for flow simulation around single buildings. In addition, in order to investigate grid independency for two inline buildings, three different computational grids with 1.5 million cells, 2 million cells and 3 million cells were tested. It was found that a grid with 2 million cells was sufficient for generating grid independent solution. Therefore, the grid with 2 million cells was selected for subsequent numerical simulations. The grid independency results for two inline buildings, however, are not shown here for brevity.

In this section, the boundary conditions for flow and particle deposition on smooth and rough ground are described. For smooth ground, it is assumed that the velocity distribution in the incoming atmospheric boundary layer is given by the power law formula with n ¼ 0.125 and surface roughness height is zero (ks ¼0). For rough ground, the power law formula with n ¼ 0.26 was used and the equivalent roughness height and roughness constant were, respectively, ks ¼ 0.005 m and CS ¼ 1. All faces of standard and supported buildings (including roof and lower surface of the supported-building) for both smooth and rough ground were assumed to be smooth; therefore, the equivalent roughness height for these surfaces is zero (ks ¼0). The criteria for particle deposition on smooth and rough surfaces are (Fan and Ahmadi, 1993): 8 dp > > For smooth  wall < ; 2 zc ¼ > > : dp þ ks þ σ k  e; For rough  wall 2

(28) 7.2. Validation In this section, validations of airflow field around single and inline buildings are carried out by comparing the simulated stream-wise velocity and turbulence intensity and streamlines with the experimental data. The particle transport model is validated by comparing the predicted deposition velocity of spherical particles on smooth plate, rough flat plate and the deposition fraction of particles on the back and front faces of standard building with the literature data.

Here zc denotes the capture distance. Eq. (28) implies that, for smooth surface when the particle centroid reaches to zc it is assumed it is deposited on the wall. Here dp and ks are the particle diameter and the equivalent roughness height. Hence, for a smooth wall zc is equal to the particle radius. The relevant parameters for particle deposition on a rough wall are shown in Fig. 5. According to Browne (1974) for rough wall, the origin of velocity profile is at e ¼ 0.53ks and the standard deviation of the roughness elements is σ k ¼ 0.17ks . The capture distance for rough walls is then given by the second line in Equation (28).

7.2.1. Flow field around buildings Motalebi et al. (2012) performed wind tunnel studies of airflow field around scaled single standard and supported buildings. The scaled standard building model was a 10 cm
10 cm
3 cm cube and the supported building model had the same dimensions with supports dimensions of 0.4 cm
0.4 cm
1 cm. These are identical to the scaled models used in the present simulations. Flow Reynolds number based on building heights and free stream velocity was 17000. The stream-wise velocity and turbulence intensity profiles around the buildings were simulated by the RNG k-ε and the Realizable k-ε models and the model predictions at the symmetry plane (Y/H ¼ 0) are compared with the wind tunnel data of Motalebi et al. (2012) in Fig. 7. This figure shows that the model predictions for velocity and turbulence intensity are in good agreement with the experimental data. A careful examination of the results in Fig. 7-a and 7-b shows that the RNG k-ε model predictions for stream-wise velocity on the roof of the standard building are in somewhat better agreement with the experimental data, whereas the Realizable k-ε more accurately predicted the velocity profiles on the roof and behind the supported building. The turbulence intensity profiles at three sections around the standard and supported buildings are shown, respectively, in Fig. 7-c and 7-d. It is seen that the predictions of both RNG k-ε and Realizable k-ε models generally agree well with the wind tunnel measurements; however, the Realizable k-ε model had a more accurate overall predictions. Based on the presented results, the Realizable k-ε model was selected for the subsequent

6. Solution settings In this study, a desktop computer with 2 parallel processors, 2.6 GHz CPU and 8 GB RAM was used for performing the required numerical simulations. In order to solve the governing equations, the ANSYS-Fluent (17.2) code, which uses the finite volume method, was used. For treating pressure-velocity coupling, the SIMPLE algorithm of the code was activated, and the QUICK method was used to discretize continuity, momentum and diffusion terms. A converged solution was assumed when the relative residual for continuity and momentum equations reduced to 106. Tracking individual particles was accomplished by ANSYS-Fluent discrete phase model. In order to simulate particle dispersion and deposition with reasonable statistical accuracy, typically, 500,000 uniform size spherical particles were released from the inlet plane of the computational domain. Different particle diameters from 1 to 50 μm were studied. Density of air was 1.225 kg/m3 and ratio of particle to fluid density was 2000. For the dilute particle concentration in airflow, a oneway coupling approach was used. That is, the airflow transports the particles, but the effect of particles on the flow, which is negligible, is ignored. It is also assumed that, when a particle touches a surface it will deposit.

Fig. 5. Introducing rough wall parameters. 390

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Fig. 6. Grid independency test for mean velocity profiles for a) standard building and b) supported building. Turbulence intensity profiles for c) standard building and d) supported building. All profiles are for a section in the plane of symmetry (Y/H ¼ 0), (Re ¼ 17000).

measurements of Kubilay et al. (2017). For Line a, Fig. 8-a shows that the LES had a better prediction near the ground, however, the Realizable k-ε model predicted more successfully than LES for height above 60 mm. For line b, however, Fig. 8-b shows that the LES had a better agreement with the experiment compared to the Realizable k-ε model. The hit rate (q) was, respectively, 0.78 and 0.84 for line (a) and line (b) for stream-wise velocity shown in Fig. 8. In Fig. 9, the simulated flow around two inline cubes, which resemble two inline building models, were compared with the experimental results of Martinuzzi and Havel (2004) for model validation and test of accuracy. Dimension of cubes here was H ¼ 4 cm and flow Reynolds number based on cube height and free stream velocity of 8.8 m/s was 22000. The inline cubes were placed on the ground level at a distance of S ¼ 2H. The computational domain consisted of 1.145 million rectangular grids and the Realizable k-ε turbulence model with standard wall function was used for the simulation of airflow field around the inline cubes. In these simulations a polynomial was fitted to the inlet velocity profile data and the inlet intensity and turbulence length scale were assumed, respectively, as 1.5% and 0.0028 m (thickness of boundary layer according to experiment). For other boundaries of computational domain, the boundary conditions were the same as those listed in Table 1. In Fig. 9,

simulations. In order to quantify differences between experimental and numerical results, validation metrics are presented in Table 2. The definitions related to these validation metrics were presented by Franke et al. (2007), Schatzmann et al. (2010) and Gousseau et al. (2013). The ideal values of hit rate (q) and FAC2 (factor of two of observations) are 1.0 and 0 for FB (fractional bias) and NMSE (normalized mean square error) for a perfect agreement. It is seen that the Realizable k-ε model had a better performance for simulating the mean stream-wise velocity profile and the RNG k-ε model had a better agreement with the data for turbulence intensity profile. In order to validate the model prediction for airflow field around inline buildings the airflow around three inline surface mounted cubes was numerically simulated using the Realizable k-ε model. The 5 cm
5 cm
5 cm cubes was placed on a wall with a distance of 5 cm between them. Flow Reynolds number based on cube height and free stream velocity of 2 m/s was 5618. For validation of the computational model, the predicted velocity profiles at two sections on the symmetry plane (Y ¼ 0) are compared with experimental data and LES simulation of Kubilay et al. (2017) in Fig. 8. It is seen that the predictions of the Realizable k-ε model are in good agreement with the wind tunnel

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Fig. 7. Comparison of predicted stream-wise velocity and turbulence intensity profiles at the symmetry plane with the experiment data, a) and c) Standard building, b) and d) Supported building (Re ¼ 17000).

7.2.2. Particle deposition over flat plates In this section, turbulent particle depositions on horizontal smooth and rough flat plates were simulated using the Lagrangian approach where the standard and the improved DRW models were used for generation of instantaneous turbulence fluctuations. Performance of the improved model with near wall corrections as given by Eqs. (19)–(26) is assessed by calculating the deposition velocity for a range of particle diameters and the results are compared with the standard model and the available experimental data. For both smooth and rough flat plate cases, the standard wall function boundary condition was used near the walls. For inlet, outlet and side planes of computational domain, respectively, velocity inlet, and pressure outlet and symmetry boundary condition were selected. The wall boundary condition was assumed for the flat plates where a roughness height of 0.5 mm for the rough plate was considered. As noted before, the boundary condition given by Eq. (28) was used for particle deposition on

Table 2 Validation metrics (hit rate q, factor of two of observations FAC2, fractional bias FB and normalized mean square error NMSE). Turbulence model

Realizable k-ε (Standard) RNG k-ε (Standard) Realizable k-ε (Supported) RNG k-ε (Supported)

U/U Ref

Intensity

q

FAC2

q

0.93 0.96 0.92 0.83

1 1 1 1

1 1 0.99 1

FB

NMSE

0.04 0.04 0.09 0.09

0.01 0.01 0.06 0.04

FAC2 1 1 1 1

the simulated flow pattern was compared with the experimental observation of Martinuzzi and Havel (2004). It is seen that the horseshoe vortex in front of the first cube, recirculation region between the first and second cubes and in the back of second cube are reasonably reproduced by the numerical simulation.

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Fig. 8. Comparison of predicted velocity profiles on the symmetry plane (Y/H ¼ 0) at the mid-section between the inline cubes with the experimental data and LES simulations, a) Line a, b) Line b, (Re ¼ 5618).

Fig. 9. a) Flow streamlines from experiments of Martinuzzi and Havel (2004), b) Simulated flow streamlines near the ground.

distributed. In practice Nd =tdþ is evaluated when the particles deposition rate reaches to a stable state. For studying particle deposition velocity on a smooth flat plate, a series of simulations were performed. Here the computational domain of 0.9144 m
0.30 m
0.15 m, which was constructed based on the wind tunnel dimension of Lane and Stukel (1978). The plate was assumed to be at the half height of the tunnel. Here a computational grid of 263, 900 cells was used with appropriate grid refinement near the wall. A power law velocity profile with n ¼ 0.125 was used for the inlet velocity profile. The inlet turbulence kinetic energy, k, and dissipation rate, ε, were computed as:

rough plate (Fan and Ahmadi, 1993). The dimensionless relaxation time and the deposition velocity in wall units are given as (Zhang, and Ahmadi, 2000):

τþ ¼

Cc Sdp2 u*2 18ν2

(29)

uþ d ¼

 ud Nd tdþ  ¼ u* N0 hþ 0

(30)

where hþ 0 ¼ h0

u*

ν

and tdþ ¼ td

u*2

ν

3 k ¼ ðI:UðzÞÞ2 2

(31)

Here Nd and N0 are, respectively, the number of deposited particles on surface and the total number of initially released particles, td is the time duration and h0 is distance from the wall that the particles at the inlet are

ε¼

393

u*3 κz

(32)

(33)

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computational grid included 104,000 rectangular cells and an appropriate growth rate near the wall. Roughness length was 0.03 mm and the equivalent roughness height was assumed to be 0.5 mm. For inlet velocity profile, the logarithmic law with free stream velocity of 11 m/s was used. The corresponding friction velocity was u* ¼ 0.54 m/s. At the inlet, the turbulence dissipation rate was evaluated using Eq. (33) and the turbulence kinetic energy was computed using,

Here a turbulence intensity of I ¼ 0.8% is assumed, κ ¼ 0.4 is the von Karman constant, and z is the vertical distance from wall. In Eq. (32), U(z) is mean velocity computed by the power-law formula with a freestream velocity of 4.572 m/s. The shear velocity u* was assumed to be 0.22 m/s. Note that the inlet turbulence dissipation rate, ε, as given by Eq. (32) is appropriate for an atmospheric boundary layer flow (Richards and Hoxey, 1993). Particles were injected at the inlet plane of computational domain with a uniform distribution. The plate was at a distance of 0.1524 m from the inlet. To obtain deposition data, 40,000 spherical particles with diameters of 3.5, 5, 8.5 and 10 μm were released at the inlet plane. The particle to fluid density ratio was kept fixed at 2000. Fig. 10-a shows particle dimensionless deposition velocity versus dimensionless relaxation time over a smooth flat plate. Prediction of the standard DRW and the improved model are compared with the experimental data of Lane and Stukel (1978). It is observed that the standard application of DRW (with isotropic turbulence fluctuation) leads to significant overestimation of the deposition velocity for dimensionless relaxation time less than 3 (for 3.5 and 5 μm particles). When the near wall anisotropic variations are included, the improved model agrees well with the experimental data for the entire range of particle sizes. Fig. 10-a shows that the predictions of standard and improved models for large particle sizes of the order of 10 μm are roughly same. For studying particle deposition on a rough flat plate, a computational domain with 8 m long, 1.3 m wide and 0.4 m height was used. The

u*2 k ¼ pffiffiffiffiffiffi Cμ

(34)

For the rough flat plate deposition study, 40,000 spherical particles were released from the inlet plane at the height of 0.2–0.4 m. This injection area was identical to that used in the experimental study of Zhang et al. (2014). Here, spherical particles with diameter of 1, 2.25, 4, 7.5, 22.5 and 40 μm were studied and the particle to fluid density ratio was 1796. The simulation results for deposition velocity on a rough plate versus particle relaxation time as predicted by the standard and improved models are shown in Fig. 10-b. The experimental data (Zhang et al., 2014) are reproduced in this figure for comparison. It is seen that the DRW model with the standard isotropic eddy viscosity model considerably overestimates the particle deposition velocity compared to the improved model. This is particularly the case for particles with small relaxation time less than 0.1 (1 and 2.25 μm). For particles with non-dimensional relaxation time larger than 1 (22.5 and 40 μm particles), the particle inertia and gravitational sedimentation effects dominate and the effect of near wall turbulence fluctuations becomes small. In this case, the predictions of the corrected and standard models become comparable. In summary, it is concluded that the DRW model with the isotropic fluctuation velocity components near the wall markedly overestimates the deposition velocity of small particles on smooth and rough surfaces. The improved model with correct anisotropic turbulence fluctuations, however, appropriately predicts particle deposition rate for all particle sizes. For large particles, the gravitational and inertia effects dominated and the standard and improved models lead to similar particle deposition velocities. 7.2.3. Particle deposition on faces of building model In this section, particle deposition (capture efficiency) on front face and back face of standard building model were simulated by the standard and improved models. Here the capture efficiency (deposition fraction) is evaluated versus Stokes number for a range of particle sizes and flow conditions. Simulation results are compared with the available experiment data and earlier models. Deposition fraction is defined as,

η¼

Nd Ni

(35)

Where Nd and Ni are number of particles deposited on surface and number of particles injected from inlet plane respectively. The Stokes number is defined as, Stk ¼

Sdp2 U∞ 18H ν

(36)

Here S, dp and U∞ are, respectively, the ratio of particle to fluid densities, the particle diameter and the freestream velocity. The characteristic flow length scale and the air kinematic viscosity are denoted by H and ν. For validation of the predicted deposition fractions on various faces of buildings, the condition of wind tunnel experiments of Motalebi et al. (2012) described in section 7.2.1 for flows and particle deposition around building models was simulated. Geometry and inlet airflow boundary condition was the same as the standard building model in the experiment (Motalebi et al., 2012). The Realizable k-ε turbulence model was used to model airflow field around the standard building model. For

Fig. 10. Comparison of dimensionless deposition velocity versus dimensionless relaxation time as predicted by the standard and improved with the experimental data, a) Smooth flat plate, b) Rough flat plate. 394

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different particle sizes in the range of 2–17 μm (0:008  Stk  0:60), ensembles of 40,000 spherical particles are injected at the inlet. The particle to fluid density ratio was S ¼ 2000 and injection plane had 10 cm width and 3 cm height (same as standard building model). The simulation results for particle deposition fractions on various faces of the building are evaluated and the results are presented in Fig. 11. Fig. 11-a compares the numerical result for deposition fraction on the back face of the standard building model predicted by the DRW and isotropic turbulence fluctuation and improved anisotropic model with the experimental data of Vincent and Humphries (1978) and the numerical results of Li et al. (1994). Note that experimental data was for deposition fraction of particle-laden turbulent flows on the back face of a circular disc. It is seen that the predictions of standard and improved models for particle deposition fractions are comparable with the earlier numerical predictions and the experimental data. Nevertheless, the improved model shows a generally better agreement with the experimental data compared with the standard DRW model. Fig. 11-b compares the predicted deposition fraction on the front face of standard building model. It is seen that the standard and improved model lead to similar particle deposition fraction for all particle sizes (2μm to 17μm). This is because the impaction process is dominated for deposition on the front face of the block. The predicted results by two models are in qualitative agreement with the experimental data of Vincent and Humphries (1978) and earlier simulations of Li et al. (1994). For small particle sizes between 2μm to 5μm(Stk  0:1) the model predictions are in reasonable agreement with the experimental data. For 5μm to 17μm particles (Stk  0:1), the simulations are consistent with the theoretical model of Longmuir and Blodgett (Fuchs, 1964), for particle deposition on a long ribbon using a potential airflow model. The DRW and the improved model predictions are close to the earlier numerical

results of Li et al. (1994), except for largest particle Stokes number (Stk ¼ 0.6) where these model predictions are closer to the Longmuir and Blodgett theory (Fuchs, 1964). 7.3. Flow field around buildings In this section velocity distributions, turbulence kinetic energy, and flow streamlines around buildings are present and discussed. Accurate evaluation of flow parameters critically influences particle dispersion and deposition around bluff bodies. Fig. 12 shows the schematic of flow reattachments and recirculation regions around a rectangular building model. The lengths of reattachment and recirculation zones for the standard and supported buildings as predicted by the CFD simulation (with the use of Realizable k-ε model) are listed in Table 2. The experimental data of Motalebi et al. (2012) are also shown in this table for comparison. It is seen that there is no recirculation zone and separation point in the front of supported building model. It is also observed that there is 16 percent difference between experimental data and numerical results for the length of recirculation region in front of the standard building model. There are reattachment points on the roof of standard and supported building model. The distance of the reattachment point on the roof of supported building is more than twice that of the standard building model. The corresponding discrepancies between experimental data and CFD results for standard and supported building models are, respectively, 68 and 40 percent. The reattachment point of the recirculation regions behind the standard building model is more than that for the supported building model. The numerical prediction for the reattachment point of standard building underestimates the experimental data by 4.5 percent, while the predictions for the supported building overestimate the experimental data by 46 percent. Fig. 13 illustrates several velocity profiles at different section along single standard and supported buildings in desert areas with smooth inlet boundary layer profile (ks ¼ 0) and in urban areas with rough boundary layer profile (ks ¼ 0.005 m) at the symmetry plane (Y ¼ 0). Smooth wall boundary condition was used for all single and inline building faces. For single standard buildings, only slight differences in the velocity distributions are observed. For the supported building comparison of the velocity profiles under the building for smooth and rough inlet profiles shows higher velocity near ground for smooth inlet profile and ground boundary conditions due to its higher momentum. Fig. 14 shows velocity vector plots around standard and supported building models at the symmetry planes of these buildings. Fig. 14-a shows that there are two small recirculation zones at the front and on the edge of roof of standard building model due to flow separation. A rather large recirculation region is also observed at the back of the building. Fig. 14-b indicates there is no recirculation zone in the front of supported building model. Similar to the standard building model, there is a flow separation at the edge of roof of supported building model. The large

Fig. 11. Comparison of deposition fractions as predicted by the standard and the improved models with the literature data, a) Back face of standard building, b) Front face of standard building.

Fig. 12. Schematic of location of separation and reattachment points. 395

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Fig. 13. Sample streamwise velocity profiles around single standard and supported buildings on symmetry plane (Y ¼ 0), a) Single standard building, b) Single supported building.

Fig. 14. Velocity vector plots around (a) standard and (b) supported buildings (Re ¼ 17000).

Fig. 15 shows sample velocity profiles at several sections along the inline building models for rough and smooth grounds. For inline standard building models, velocity distribution around buildings for both smooth and rough grounds are almost the same. But for supported buildings there is a positive velocity gradient near the surface downstream of second building for distance of (S¼H and S ¼ 2H) for both velocity distribution. However, for distance of (S ¼ 5H) there is a lower velocity gradient at this area for smooth boundary layer and for rough boundary layer reversed flow is detected. For smooth ground cases, contours of streamwise velocity distribution overlaying streamlines for single standard and supported buildings are shown in Fig. 16. It is seen that there are region of low velocity magnitude around the building models particularly in the wake behind the building. Fig. 16-a shows that there are two recirculation zones at the sides of the building due to flow separation at the leading edges of

Table 3 Length of separation and reattachment points for single standard and supported buildings. Building type Single-standard Single-supported

CFD Exp (Motalebi et al., 2012) CFD Exp (Motalebi et al., 2012)

XC/H

XRT/H

XRB/H

1.16 1 – –

0.9 0.533 1.93 1.37

2.33 2.44 2.1 1.43

recirculation flow region at the back of supported building model has two counter rotating vortices. It is also seen that the length of recirculation zone for the supported building is shorter compared to that of the standard building model. This observation is consistent with numerical and experimental data shown in Table 3. 396

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Fig. 15. Sample streamwise velocity profiles around inline buildings, a) Inline standard buildings (S¼H), b) Inline supported buildings (S¼H), c) Inline standard buildings (S ¼ 2H), d) Inline supported buildings (S ¼ 2H), e) Inline standard buildings (S ¼ 5H), f) Inline supported buildings (S ¼ 5H).

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Fig. 16. Mean streamwise velocity contours around single (a) standard and (b) supported building models at plane (Z/H ¼ 0.5).

Fig. 17. Mean streamwise velocity contours around inline building models at the plane (Z/H ¼ 0.5), a) standard buildings with S¼H, b) supported buildings with S¼H, c) standard buildings with S ¼ 2H, d) supported buildings with S¼H, e) standard buildings with S ¼ 5H, f) supported buildings with S ¼ 5H.

distribution overlaying streamlines for inline standard and support buildings are shown in Fig. 17. It is seen that there is a low velocity areas around the builds particularly in the wakes behind the buildings. Fig. 17a shows that there are flow separation at leading edge of sides of first building leading to the creation of recirculation zones on the side of the building. There are also recirculation regions between the standard building models and at the back of the second building. There are some reversed flow regions on the sides of upstream (first) building; however, there are no recirculation regions and negative velocity magnitude on the sides of downstream (second) building. There are strong reverse flow regions in the wake of the standard buildings. The maximum velocity magnitude occurs at some distances from the sides of upstream (first) building. Fig. 17-b shows that there are recirculation regions between the inline supported buildings and also in the wake of the downstream

standard building model. The wake at the back of standard building contains two symmetric recirculation regions. Maximum airflow velocity is seen at some distance away from the sides of the building model. The main reversed flow velocity occurs in wake of building model with some reversed flows seen at the recirculation regions on the side of the building model. For supported building model, Fig. 16-b shows that the low velocity region around the building is slightly weaker than that seen around the standard building. There is little if any negative velocity magnitude at the sides of building (no reversed flow). At the leeward side of supported building, there is a recirculation zone, which is much weaker than that of the standard building. A region with reversed flow is observed in the wake of supported building that is much smaller than that seen for the standard building. For smooth ground cases, contours of streamwise velocity 398

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models. For the supported buildings, however, slight differences are observed in the region above and below the buildings. This figure suggests that the non-dimensional velocity profile around the inline buildings are insensitive to the variation of Reynolds number for the range of parameters studied. Fig. 19 shows the TKE contours on the symmetry plane (Y/H ¼ 0) around single and inline standard and supported buildings. Fig. 19-a indicates that the TKE at the top of the roof and downstream of building in the shear layer region has the highest magnitude. Fig. 19-b shows that magnitude of TKE in the top recirculation region of the supported building is somewhat higher than that of the standard building. However, the TKE in the shear layer at the back of the supported building is lower than that of the standard building model. It is also seen that, the TKE has a peak in the gap beneath the supported building. Fig. 19-c shows that, the TKE at the roofs of the front building and part of the second building as well as in the shear layer downstream of the second building is highest. Fig. 19-d indicates that, the TKE upstream of the first supported building is somewhat higher than that of the standard building. Maximum TKE appears on top of the upstream building. The TKE downstream of the second supported building and in the gap beneath the second building is comparatively low perhaps due the wake effects of the first building. Fig. 19-e and 19-g show that increasing the space between two standard buildings leads to higher TKEs. Fig. 19-g and 19-h show that increasing the distance between supported inline buildings does not change the TKE significantly. From Fig. 19, it is observed that TKE downstream of single and inline buildings decrease when the buildings are on supports.

building. However, there are no recirculation zones on the sides of upstream (first) and downstream (second) supported buildings. Similar to the case of standard building, the maximum velocity magnitude occurs as some distance away from the sides of upstream (first) building. Fig. 17-c shows that recirculation zones for the inline standard buildings that are S ¼ 2H apart are similar to those for the standard buildings with S¼H. The main difference is that the strength of the recirculating region and reverse flow observed between the buildings is much stronger than that compared to the case of S¼H. However, the recirculation zones in the wake of the downstream building and the rest of the flow structure for S ¼ 2H are quite similar to those for standard building with S¼H. Similar to the case of standard buildings, Fig. 17-d shows that, there is a stronger recirculation zone between the supported inline buildings with S ¼ 2H compared to supported buildings with S¼H. Negative velocity (reverse flow) between the buildings, however, is slightly weaker than that for the supported building with S¼H. The structure of the wake and the recirculation zone is behind the downstream building for S ¼ 2H, however, is quite similar to that for the case of inline supported buildings with S¼H. Fig. 17-e indicates that, there is a much larger recirculation zone between the standard buildings which are S ¼ 5H apart comparison with those seen for the standard buildings with S¼H and S ¼ 2H. The recirculation zone in the wake behind the downstream building, however, is roughly the same as those for the standard buildings with S¼H and S ¼ 2H. Fig. 17-f shows that, flow pattern between and behind downstream inline supported building models with S ¼ 5H is quite different from those for supported buildings with S¼H and S ¼ 2H. There are more complex wake structures and recirculation region in the leeward side of downstream building for S ¼ 5H compared to the inline supported buildings with S¼H and S ¼ 2H. Negative velocity area in the back of upstream supported building is comparable to that of for S ¼ 2H but its amplitude is smaller than that see for the S¼H case. There are also two separated area with reverse flow velocity in the wake of the downstream supported building for S ¼ 5H. To investigate the influence of flow Reynolds number, sample velocity profiles along inline standard and supported buildings that are a distance of S¼H apart for two flow Reynolds numbers, Re ¼ 17000 and Re ¼ 170000 are evaluated and the results are shown in Fig. 18. It is seen that the non-dimensional velocity profiles for the two Reynolds numbers studied are roughly the same, particularly for the standard building

7.4. Deposition fraction at the ground level and faces of buildings 7.4.1. Deposition fraction on the smooth ground around buildings In this section, particle deposition around single and inline standard and supported buildings are investigated using the Lagrangian particle tracking method. As noted before, the Realizable k-ε model with the standard wall function boundary conditions are used for predicting the airflow field around the buildings. The improved DRW model was employed for evaluating the turbulence fluctuation field and the corresponding particle dispersion and deposition were evaluated.

Fig. 18. Sample streamwise normalized velocity profiles at symmetry plane (Y ¼ 0) along inline standard and supported buildings for Re ¼ 17000 and Re ¼ 170000, a) Inline standard buildings (S¼H), b) Inline supported buildings (S¼H). 399

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Fig. 19. Turbulence kinetic energy contours around single and inline standard and supported buildings on the symmetry plane (Y/H ¼ 0), a) Single standard, b) Single supported, c) Inline standard (S¼H), d) Inline supported (S¼H), e) Inline standard (S ¼ 2H), f) Inline supported (S ¼ 2H), g) Inline standard (S ¼ 5H), h) Inline supported (S ¼ 5H).

Comparison of particle deposition fraction for standard single and inline buildings is shown in Fig. 20-a. For improved model, the capture efficiencies (deposition fractions) of inline buildings are generally higher than those single buildings especially for particle sizes with 0:02  Stk  0:1. However, the DRW model predicts roughly the same capture efficiencies for all buildings. Deposition fraction around building models at the ground level slightly increases when the distance between inline buildings increases for medium-size particles. For large particles, the magnitude of deposition fraction stays roughly the same. Fig. 20-b compares the particle deposition fractions for supported single and inline buildings. It is observed that, using the improved model, the presence of downstream building causes an increase of particle deposition fraction for particles smaller than 10μm, but increasing the spacing between the buildings does not noticeably affect the particle capture efficiency of the ground. Fig. 21 compares the particle deposition fraction for standard and supported buildings in smooth ground cases. It is seen that the deposition of particles with 0:02  Stk  0:1 on the ground for supported buildings is slightly higher than that for the standard buildings. That is in part due to the inclusion of the ground under the supported building in the overall capture efficiency evaluation. In addition, the capture efficiency of 10–20 μm particles with 0:2  Stk  0:8 for supported building models is slightly more than that of the standard building models. The deposition

Figs. 20 and 21 show the capture efficiency (deposition fraction) of the smooth ground surface around the buildings versus Stokes number for single and two inline standard and supported buildings for different distances (S¼H, 2H and S ¼ 5H). For supported buildings the ground surface included the area under the building as well. In order to evaluate particle deposition both DRW and improved DRW models were employed and deposition fraction (capture efficiency) was computed for 1 μm–50 μm particles according to Eq. (35). For these particles sizes, the correspondingly Stokes numbers (Stk) is approximately between 0.002 and 5.25. For this range of Stokes number for particles smaller than 10μm, the airflow characteristics such as velocity, streamlines and turbulence kinetic energy are important factors affecting the particle deposition and dispersion processes. For Stokes number greater than 0.1 (particles larger than 10μm) the gravitational sedimentation and particle inertia effects are dominant. Fig. 20 shows that for smooth ground cases, both the standard DRW and the improved models predict that the particle deposition fraction increases with Stokes number. The standard DRW, however, overestimates the depositing fraction of particle with Stk<0.2. The improved DRW with corrected anisotropic turbulence fluctuations shows a sharp decrease of deposition fraction as particle size decreases. For large particles with Stk  0:2, the differences of prediction of DRW model and the improved model are diminished due to the domination of gravitational and inertia effects.

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Fig. 22. Deposition fraction on faces of (a) single and (b) inline buildings (with S¼H) versus Stokes number. Fig. 20. Comparison of capture efficiency versus Stokes number as predicted by the DRW and improved DRW models for smooth ground cases, a) Standard buildings, b) Supported buildings.

buildings at distance of S¼H are evaluated by and the corresponding deposition fraction (capture efficiency) are plotted versus Stokes number. The deposition fraction was evaluated using Eq. (35). Here the deposition fractions are predicted using the improved DRW model. The most important point perceived from Fig. 22-a is that, particle deposited on the front faces of standard and supported single building models increases with Stokes number. Deposition fraction of front faces of standard and supported buildings slightly increase until about Stk ¼ 0.1, whereas, there is a sharp increase for Stokes number larger than 0.1. Particle deposited on the front face of single supported building is more than that of for standard building model. On the other hand, particle deposition on other faces (back, left, right and roof) of single building models are much fewer than front face of models and they decrease with Stokes number. Number of deposited particles for these faces for Stokes numbers larger than 1 (inertial regime) stays the same. Minimum number of small particles (Stk ¼ 0.002) deposited on the back face of standard building and maximum deposition fraction of small particles (Stk ¼ 0.002) belongs to roof of single supported building model. Fig. 22-b shows that particle deposition on the front faces of standard and supported inline buildings with (S¼H) for the upstream (first) building is much greater than the downstream (second) building. Deposition fraction of front faces of first standard and supported buildings increase with Stokes number and for front faces of second standard and supported buildings decrease with Stokes number. Maximum difference for particle deposited on fist front face and second front face of

Fig. 21. Comparison of dimensionless deposition fraction versus Stokes number for standard and supported buildings for smooth ground cases.

fraction for other sizes remains roughly the same. 7.4.2. Deposition fraction on the faces of buildings In this section, particle deposition on faces of single and two inline

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Fig. 23. Typical deposition patterns of 1 μm dust particles on ground around single buildings, a) Improved model, standard building, b) Improved model, supported building c) Standard DRW model, standard building, d) Standard DRW model, supported building.

7.6. Effect of ground roughness on particle deposition

standard and supported building models occurs for the largest particle size (Stk ¼ 5.25). Deposition fraction for other spaces between buildings (S ¼ 2H and 5H) are similar and is not presented here in avoid to repetition.

The influence of surface roughness on particle deposition on ground is studied in this section. As noted before, a roughness height of k s ¼ 0.005 m is an appropriate choice for small towns areas. In addition, a realistic ground boundary condition given by Eq. (28) for particle deposition on rough surfaces was applied. Fig. 25-a shows that, for single and inline standard buildings the ground roughness significantly increases the particle deposition fraction compared to that of the smooth ground (desert areas). In particular, for small particles with 0:001  Stk  0:1 the amount of increase is the order of 160% or more. For larger particles with Stk  0:1, however, the influence of gravitational and particle inertia become important and the incremental effect of roughness on capture efficiency is smaller (or the order of 50%). Fig. 25-b shows a similar trend, however, the deposition fraction of smallest particle size (Stk ¼ 0.002) for single supported building for smooth and rough ground is about the same. This maybe because of weaker recirculation zone around supported buildings and highest velocity gradients near the ground around this type of buildings as are seen Figs. 13, 14 and 16. Greatest increase in the deposition fraction due to roughness is seen for medium particle sizes with 0.05 < Stk<0.1 for all single and inline standard and supported building models. Comparison of Fig. 25-a and 25-b indicates that the influence of surface roughness on increasing the ground deposition fraction for standard single and inline buildings is more than that of for the supported buildings. For rough ground surface, Fig. 26 compares the deposition fractions versus Stokes number for standard and supported buildings. It is seen that particle deposition on the ground for standard buildings is more than that of for the supported buildings. For supported buildings with rough ground, the deposition fraction of small and medium-size particles with Stk<0.1 increases from single building to inline buildings with S¼H, S ¼ 2H and S ¼ 5H. For standard buildings, however, the capture efficiencies for single and all inline buildings with different spacing are approximately the same.

7.5. Particle deposition patterns on the ground around buildings Particle deposition patterns on the smooth ground around buildings were studied in this section. Figs. 23 and 24 illustrate typical location of deposited 1 μm particles on the ground around single and inline standard and supported buildings predicted by the standard DRW and the improved DRW models. These figures show that the standard DRW without the corrected turbulence RMS fluctuations highly overestimates the deposition rate (Fig. 23-c and 23-d). In addition, the concentration of deposited 1 μm particles on the ground increases in the areas just ahead of the building and in the building wake. Fig. 23-a, 23b and 24 show that particle deposition on the ground near the back of supported single and inline buildings are less than those for the standard buildings and the concentration of deposited particles near the front side increases. Fig. 24 indicates that, when the distance between standard buildings increases from H to 2H, there is no significant difference in number of deposited particles on the ground behind the buildings. However, when the buildings are 5H apart, particles deposition behind the building models increases compared to the case of inline building at a distance of H. In addition, for supported buildings, when downstream building is located at the distance H or 2H from the upstream building, the distribution of deposited particles around buildings is not significantly affected. On the other hand, particle deposition in the region between inline-supported buildings at the distance of 5H is much higher than those for the cases when S¼H and 2H. It should be emphasized that, the use of improved model not only corrects the particle deposition fraction, but also modifies the particle deposition patterns around the standard and supported buildings. 402

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Fig. 24. Typical deposition pattern of 1 μm dust particles on ground as predicted by the improved model for two inline buildings, a) Inline standard buildings with S¼H, b) Inline supported buildings with S¼H, c) Inline standard buildings with S ¼ 2H, d) Inline supported buildings with S ¼ 2H, e) Inline standard buildings with S ¼ 5H, f) Inline supported buildings with S ¼ 5H.

Fig. 28 shows the patterns of deposited 1 μm particles on the rough ground for single and inline buildings. Fig. 28-a shows that, for rough ground (urban areas), most particles deposited on the side and wake of the building model. Some particles are trapped in recirculation zone behind the building model. Fig. 28-c and 28-g, show a similar pattern for inline standard buildings. In addition, it is seen that the number of deposited particles on the ground for different spacing between buildings (S¼H, S ¼ 2H and S ¼ 5H) is approximately the same. For a single supported building, Fig. 28-b shows that, the majority of deposited particles are in the front of building model and a few are deposited beneath and in the wake of the building model. Fig. 28-d and 28-h show that, the patterns of deposited aerosols around inline-supported buildings are roughly the same. However, the number of deposited particles increases with spacing between buildings. Comparing Fig. 28 with Fig. 23, it is seen that the number of particles deposited on the rough ground downstream of standard and supported buildings are more than those for smooth ground. This is because roughness elements enhances the deposition rate and causes a marked increase in the deposition of particles (Fan and Ahmadi, 1993). In addition, surface roughness increases the turbulence kinetic energy and enhances turbulence effect on particle deposition.

Fig. 27 compares the deposition fractions predicted by the standard and improved DRW models for standard and supported building models for the rough ground condition. Similar to the smooth ground case, the deposition of particles in the size range of 1μm to 50μm corresponding to the Stokes of 0.002–5.25 are studied. It is seen that the deposition fraction increases with particle size (Stk), however, there are considerable differences of particle deposition fractions predicted by the DRW and the improved DRW models for rough ground surfaces. Comparing Fig. 27 with Fig. 20 indicates that these differences decrease slightly for rough surfaces in urban areas compared to smooth ground in desert areas. For both cases for Stk0.2, the standard model significantly overestimates the deposition fraction compared to the improved model that accounts for the near wall effect and anisotropy of turbulence. For larger Stokes numbers, the predictions of the standard DRW model comparable with the improved model. This is because the gravitational sedimentation effects become important and the influence of turbulence becomes comparatively small. Comparing the predicted ground deposition fractions for standard and supported buildings as shown in Fig. 27-a and 27-b, shows that, the predictions of the standard DRW are roughly the same as those of the improved model. Predictions of the improved DRW model for standard and supported buildings, however, are quite different for Stk0.2. In this range, the ground deposition fractions for supported buildings are less than those of standard buildings. This is particularly the case for single and inline buildings that distance H apart.

8. Conclusions In this paper, the airflow and dust transport and deposition around

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Fig. 27. Comparison of deposition fraction versus Stokes number as predicted by the standard and improved DRW models for rough ground surface condition, a) Standard buildings, b) Supported buildings.

Fig. 25. Comparison of deposition fraction versus Stokes number for smooth and rough surfaces predicted by the improved model, a) Standard buildings, b) Supported buildings.

1. The recirculation region behind the supported buildings is smaller compared to the standard building. In addition, the turbulence kinetic energy downstream of supported buildings is lower than standard ones. These factors reduce number of deposited dust particles behind supported buildings compared to the standard ones. 2. The non-dimensional velocity profiles for inline standard building are Reynolds number independent, however, for supported buildings slight Re-dependence is observed in the regions above and below the buildings. 3. Compared to the standard DRW model, the improved DRW model provides more accurate predictions for particle deposition on the ground and on the buildings models, as well as, on smooth and rough flat plates. This is because the improved model accounts for anisotropy of turbulence and corrects for the near the wall variation of fluctuating velocities and turbulence integral time scale. 4. The improved DRW model correctly predicts both particle deposition fraction and deposition patterns around the standard and supported buildings. 5. Simulation results indicate that particle deposition on the front face of single supported building is more than that for standard building. For inline standard and supported buildings, the particle deposition in front of upstream building is much higher than the downstream building. 6. Simulations for the rough ground cases showed that the particle deposition fraction increases significantly in comparison to the smooth ground conditions.

Fig. 26. Comparison of ground deposition fraction versus Stokes number of standard and supported buildings for rough surface.

single and inline standard and supported building models were studied. The airflows were simulated using a RANS model. Lagrangian particle tracking was employed to analyze dust dispersion and deposition. For this purpose, and improved DRW model that accounts for the anisotropy and near wall behavior of turbulence fluctuation was developed and its accuracy was verified. Particle deposition and distribution around low rise single and inline standard and supported buildings were evaluated using the standard and improved DRW models. The factors influencing particle deposition were discussed. Major conclusions of the study are:

The influence of staggered arrangements standard and supported buildings, use of more advances turbulence model such as LES, in

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Fig. 28. Typical deposition pattern of 1 μm dust particles on rough ground as predicted by the improved model for two inline buildings, a) Inline standard buildings with S¼H, b) Inline supported buildings with S¼H, c) Inline standard buildings with S ¼ 2H, d) Inline supported buildings with S ¼ 2H, e) Inline standard buildings with S ¼ 5H, f) Inline supported buildings with S ¼ 5H.

addition to analysis of deposition of non-spherical particles on building faces, as well as, rebound effect are left for future studies.

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