An improved SST k−ω model for pollutant dispersion simulations within an isothermal boundary layer

Journal of Wind Engineering & Industrial Aerodynamics 179 (2018) 369–384

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An improved SST k
ω model for pollutant dispersion simulations within an isothermal boundary layer K. An a, *, J.C.H. Fung a, b a b

Division of Environment and Sustainability, The Hong Kong University of Science and Technology, Hong Kong Department of Mathematics, The Hong Kong University of Science and Technology, Hong Kong

A R T I C L E I N F O

A B S T R A C T

Keywords: Pollutant dispersion CFD simulations Turbulence model Wind tunnel measurements Sensitivity study

The selection of turbulence models has always been one of the important aspects of computational fluid dynamics model simulations of wind flow and pollutant dispersion problems. The commonly industrially adopted steady Reynolds-averaged Navier–Stokes turbulence models are the realizable k
ε model and Menter's shear stress transport k
ω model. In this study, we demonstrated that the realizable k
ε model and Menter's SST k
ω model produced nonsatisfactory correlation results with the experimental data, in terms of the normalized pollutant concentration for a cuboid obstacle. Here, an improved formulation of Menter's SST k
ω turbulence model, particularly for the wind flow and pollutant dispersion simulations, is applied. The modifications have been added in a systematic manner which include the addition of damping functions in the closure equations, the inclusion of the turbulent cross-diffusion term in the omega equation, and the re-establishment of model constants and parameter profiles. Considerable improvement in the correlation between the prediction and the experimental data up to a value of 0.78 with matching wind and turbulent kinetic energy profiles was obtained by the proposed model. Significant reduction of more than 80% in NSME and a satisfactory FAC2 value of 0.54 are also achieved with the improved model.

1. Introduction Computational fluid dynamics (CFD), because of the rapid advancements in computer technologies in the recent decades, has been widely acknowledged as a useful tool in dealing with challenging problems within the fields not limited to engineering, biomedical, environmental, and geophysical sciences. In particular, in the field of environmental science, extensive environmental impact assessments (EIAs) have been carried out, aiming to assess and predict the effects of urbanization and renovation activities on the environment. One of the assessment aspects in EIA is air quality and wind ventilation. Ventilation and pollutant accumulation are closely related, and the problems of poor ventilation and deteriorated air quality are the inevitable outcomes of high-density living and urbanization in developing countries (Manning, 2011). Taking Hong Kong as an example, urbanization tends to increase the number of skyscrapers. The construction of these skyscrapers indirectly forms deep street canyons with limited air exchange. Complex and welldeveloped road networks interweave among them and the daily heavy

traffic flow releases a significant amount of passive pollution. Therefore, the fact that pedestrians suffer from poor air quality and deteriorated ventilation is not difficult to comprehend. In view of the urgency to explore an optimized architectural design that will mitigate the drawbacks of urban ventilation and facilitate pollutant dispersion, architects and town planners have been continuously proposing building designs and working in extensive cooperation with environmental scientists, who practice CFD model simulations on different building schemes, to further consolidate the effectiveness of these designs with respect to the alleviation of the problems related to urban pollution and ventilation. Turbulence leads to the formation of eddies with different length scales. These eddies continuously interact with each other, with larger eddies breaking down into smaller eddies through a transfer of turbulent kinetic energy (TKE), forming a hierarchy of eddies known as the turbulent energy cascade (Richardson, 1922). Turbulence fluctuations can be interpreted as three-dimensional eddies with different length scales that constantly interact with each other. In an urban canopy with numerous building developments and street canyons having different aspect ratios, eddies with relatively small length scales appear at

* Corresponding author. The Hong Kong University of Science and Technology, Division of Environment and Sustainability, Clear Water Bay, Hong Kong. E-mail address: [email protected] (K. An). https://doi.org/10.1016/j.jweia.2018.06.010 Received 5 December 2017; Received in revised form 23 May 2018; Accepted 18 June 2018 Available online 30 June 2018 0167-6105/© 2018 Elsevier Ltd. All rights reserved.

K. An, J.C.H. Fung

Journal of Wind Engineering & Industrial Aerodynamics 179 (2018) 369–384

situated within an isothermal boundary layer. Furthermore, sensitivity tests have been carried out through adjustments of influential model parameters to evaluate the changes in model performance. The model simulation results for the single block obstacle obtained using Menter's SST k
ω model before modification and the realizable k
ε model are also presented for reference. Furthermore, the procedures and methodologies documented in this paper should serve as another useful reference in addition to the existing guidelines for environmental scientists, modelers, and engineers during different stages of pollutant dispersion assessments by CFD modeling.

locations within the street canyons, while larger eddies appear in the main flow at the top of the street canyons. Understanding the flow characteristics before investigating the wind flow and pollutant dispersion phenomena in an urban area is of utmost importance. Therefore, numerical modeling of turbulence helps to understand the flow characteristics and plays a crucial role in providing wind fields which are necessary to predict transport and dispersion of passive pollutants within an urban city (Ehrhard et al., 2000). CFD simulations attempt to mimic the characteristics of turbulent flows via the adoption of appropriate turbulence models. A common application of CFD is the evaluation and mediation of air pollution and ventilation problems associated with the dispersion of harmful and odorous effluents. CFD has been proven to be a successful tool to simulate and investigate the wind environment in urban cities (Van Hooff and Blocken, 2010; Blocken and Persoon, 2009). This tool has also been applied to understand the external flow environment of cities to aid design processes (Blocken et al., 2010; Baskaran and Kashef, 1996). Because of the balance between accuracy and computational cost, Reynolds-averaged Navier–Stokes (RANS) k
ε turbulence models are still commonly being used for studying pollutant dispersion problems (Tominaga and Stathopoulos, 2017; Lateb et al., 2016; Pontiggia et al., 2010). Numerous studies have been conducted using RANS k
ε models focusing on pollutant transport in regular building array configurations and semi-idealized street canyons (Cheng et al., 2008; Chen et al., 2013; Di Sabatino et al., 2007b; Hang et al., 2012; Tominaga and Stathopoulos, 2012; Gromke and Blocken, 2015a; b; Thaker and Gokhale, 2016). Menter's shear stress transport (SST) k
ω model focuses mainly on aerodynamics applications including aero-foil and wind turbine designs (Menter, 1993; Douvi et al., 2012; Derakhshan and Tavaziani, 2015; Zhou and Wang, 2016), and is considered to be the preferred model because of its superiority in comparison with the k
ε models, in simulations of cross-ventilation pollutant dispersion (Ramponi and Blocken, 2012; Cao and Meyers, 2013). Validation and verification processes are essential for accurate CFD simulations (Meroney et al., 2016; Blocken et al., 2013) to assess the pollutant dispersion phenomenon. However, attention should be drawn to the limited wind tunnel experiment data for CFD validation. Although comparison of model simulation results with field measurement data might be another alternative for model validation, it is likely there would be observable differences between model predictions and the real situation for the pollutant concentration field due to factors not limited to geometric uncertainties, atmospheric conditions and model assumptions. Model simulations via CFD are capable of providing complete data for the flow and concentration field within the computational domain, and can be performed on both reduced and full scales. They are also efficient in carrying out parametric and sensitivity analyses. Meroney et al. (2016) pointed out that the protocols and regulations concerning the application of CFD to dispersion modeling are not uniform. However, the recent review paper published by Tominaga and Stathopoulos (2016) summarized several aspects of the CFD modeling of pollutant dispersion problems. The researchers pointed out that the robustness of the CFD approach in pollutant dispersion simulations considerably depends on the selection of turbulence models, modeled geometries, topographical factors, and model boundary/parameter settings (Tominaga and Stathopoulos, 2013). They highlighted the importance of the inflow atmospheric conditions and boundary conditions, which has also been reported by An et al. (2013). This paper puts forward an improved formulation of the Menter's SST k
ω model based on the modified k
ω model proposed by Peng et al. (1997), for the prediction of the wind flow and pollutant dispersion patterns around building blocks within an urban environment under isothermal conditions. The improved model has been validated in a systematic and stepwise manner against the data obtained from the wind tunnel experiment performed by Tanaka et al. (2006) at the Tokyo Polytechnic University around a single block obstacle, releasing a passive pollutant from a tiny source located on the leeward side of the obstacle

2. Formulation of an improved SST k
ω model for pollution dispersion 2.1. Menter's SST k
ω model Menter's SST k
ω turbulence model (Menter, 1993, 1994) is a two-equation eddy viscosity turbulence model which combines the merits of both the k
ε and the k
ω models by using Wilcox's k
ω model in the near-wall regions and switching to a k
ε formulation outside the boundary layer via blending functions depending on the turbulence length scale. The adoption of a k
ω formulation in the inner regimes of the boundary layer enables us to directly apply the model all the way down to the wall through the viscous sub-layer, while the adoption of the k
ε model in the outer regimes eliminates the disadvantage of sensitivity to the inlet free stream turbulence properties as observed in Wilcox's k
ω model. The conservation of mass and the conservation of momentum equations for an incompressible flow, in the Cartesian tensor notation, can be expressed as follows:

∂ui ¼0 ∂xi ρ

(1)

∂ui ∂ui ∂p ∂Sij þ ρuj ¼
þ 2μ ∂t ∂xj ∂xi ∂xj

(2a)

∂S

The last term 2μ ∂xijj in Equation (2a) is the viscous stress tensor, where Sij is the strain rate tensor defined as follows: 1 ∂ui ∂uj Sij ¼ þ 2 ∂xj ∂xi

! (2b)

Besides Equations (1) and (2), two other equations are required for the closure of the system. The first closure equation involves the TKE k, and the second equation involves the specific dissipation rate ω, which is the dissipation per unit of the TKE. The two closure equations can be expressed as follows: 

ρ

∂k ∂k ∂ þ ρuj ¼ Pk
ρβ ωk þ ∂t ∂xj ∂xj

ρ

∂ω ∂ω ∂ þ ρuj ¼ αPω
ρβω2 þ ∂t ∂xj ∂xj



μþ

μt ∂k σ k ∂xj





 (3) 

μt ∂ω σ ω ∂xj 1 ∂k ∂ω þ 2ρð1
FB Þ σ ωout ω ∂xj ∂xj μþ

(4)

The eddy viscosity μt in Menter's SST k
ω model can be defined as follows: 

k aω μt ¼ ρ min α* ; 1 ω SFE

 (5a)

where a1 ¼ 0:31 and α ¼ 1 in Menter's SST k
ω model, which is the coefficient describing the nonlinear transition of the flow regime from a laminar flow to a turbulent flow in which the relationship α* β* ¼ 0:09 is satisfied. FE in Equation (5a) is a blending function defined as follows: 370

K. An, J.C.H. Fung

Journal of Wind Engineering & Industrial Aerodynamics 179 (2018) 369–384

"

  pffiffiffi 2 k 500v ; 2 FE ¼ tanh max 2 β ωd d ω

Fμ ¼ 0:025 þ 1
exp

(5b)



Ret
200

with d being the distance of the cell to the nearest surface. The production of the TKE term Pk in Equation (3) is restricted by a production limiting term Pklimit ¼ 10ρβ kω for the prevention of turbulence built-up in the stagnation regions and the production of the specific dissipation rate Pω is related to the production of the TKE and eddy viscosity through the relationship in Equation (6b):   Pk ¼ min μt S2 ; 10ρβ k ω

(6a)

P

k a1 k min αω* k; SF E

(6b)

Pω ¼

 ρ where Dþ ω ¼ max 2 σ ω

∂k ∂ω ; 10
10 out ω ∂xj ∂xj

(8b)

The cross-diffusion terms arise during the transformation of the dissipation rate equation in the standard k
ε model to the specific dissipation rate equation ω for the k
ω model. Note that the turbulent cross-diffusion term (the last term on the right-hand side of Equation (9d)) neglected by Wilcox in his k
ω model in the specific dissipation rate equation has been brought back as suggested in Peng's k
ω model. The turbulent cross-diffusion terms neglected by Wilcox may play a nonnegligible role in the transport of the TKE and its specific dissipation rate in regions with turbulent recirculating flows. Another major role of the turbulent cross-diffusion term is to suppress the increase in the turbulence length scale in the near-wall region, with Cω controlling the degree of suppression. Peng et al. adopted a value of 0.75 for the coefficient Cω in front of the turbulent cross diffusion term in their proposed k
ω model which was found that the magnitude was too small to give satisfactory results for our particular application, therefore, the value of the coefficient Cω is increased to 1.5 and satisfies the relationship Cω < σ1k þ

(7a)

 is the positive portion of the cross-

diffusion term and F* ¼ 1, via the relationship: φ ¼ FB φin þ ð1
FB Þφout

2 )#

(  34 )# " Ret 0:001  0:975 þ
exp Ret 10

2.4. Turbulent cross diffusion term

pffiffiffiffiffiffiffiffiffiffiffiffi where S ¼ 2Sij Sij is the magnitude of the strain rate. The model constants α, β, σ k , and σ ω are blended across different regions through the blending function FB defined as follows:    pffiffiffi   4 k 500v 4ρk ; 2 FB ¼ tanh min max ; 2 F* β ωd d ω σ ωout Dþ ωd

(

in

1

σ ωin .

The argument for neglecting the viscous cross-diffusion term is that

where φin and φout are the corresponding constants for the inner and outer regions, respectively. In Equations (1)–(7), ui and xj denote the velocity and position, respectively, t represents the time, p is the pressure, ρ is the fluid density, μ is the molecular viscosity. The model parameters have constant values with β ¼ 0:09, σ kin ¼ 1:176, σ kout ¼ 1, σ ωin ¼ 2, and σ ωout ¼ 1:168.

the viscous cross-diffusion is far smaller than the turbulent crossdiffusion (i.e., μ ≪ μt ) and is not significant in fully turbulent regions. In addition, the inclusion of the viscous cross-diffusion terms might lead to the incorrect asymptotic behavior of the TKE (Speziale et al., 1992), which contradicts the realizable principle of turbulence modeling suggested by Lumley (1978). Therefore, the viscous cross-diffusion term is dropped, and the specific dissipation equation is modeled with a turbulent cross-diffusion term.

2.2. Improved SST k
ω model

2.5. Damping functions on k and ω equations

The main framework for developing the improvement model is the partial replacement of Wilcox's k
ω model by Peng et al.’s k
ω model as the inner-region model for the SST k
ω model. Peng et al. (1997) applied some empirical damping functions to the closure equations and the eddy viscosity definition of Wilcox's k
ω model, and improved the prediction of the reattachment length for the backward-facing step problem. As the accuracy of prediction of the reattachment length plays an important part in the robustness of the prediction of dispersion patterns, particularly on the leeward side of building obstacles, we expect the adoption of Peng's k
ω model as the inner-regime model for Menter's SST k
ω model with optimized damping function on the production term of the specific dissipation rate in the scale-determining equation and reestablished model parameters would serve the purpose to improve the prediction accuracy in pollutant dispersion applications around building obstacles.

The greatest amount of uncertainty lies in the specific dissipation rate equation. Wilcox's SST k
ω model is reported to have an underestimation of turbulent kinetic energy owing to the over prediction of the specific dissipation rate. This would result in an underestimation in the near-wall eddy viscosity. In addition, there is also inaccuracies in prediction of the reattachment length for the backwardfacing step problem by Wilcox's SST k
ω model. One of the improvement approach is to suppress the specific dissipation rate by reducing its production through constant α in the ω equation or by suppression of the turbulent kinetic energy destruction rate in the turbulent kinetic energy equation. This can be achieved by imposition of damping functions on the turbulent kinetic energy and the specific dissipation rate equations. The damping function Fk proposed by Peng's model as stated in Equation (9a), which is an increasing function of the turbulent Reynolds number, is capable to reduce down the turbulent kinetic energy destruction rate in regions with relatively low Reynolds number while its effect would be diminished in high turbulent Reynolds number regions, which usually appear in the upper boundary layer. For the damping function Fω stated in Equation (9b), in which its purpose is to limit the production of the specific dissipation rate, by maintaining the same equation form as Fk , computer optimization have been carried out by varying the coefficient before the exponential function and found that the value 0.9 would result in good fit of the simulation results to experimental data in the current case study. By imposition of these damping functions into the k and ω equations, consequently, the magnitude of the turbulent kinetic energy would be enhanced. The damping functions Fk and Fω in terms of the turbulent Reynolds number Ret ¼ k=ων are defined as follows:

(7b)

2.3. Eddy viscosity formulation The formulation of the eddy viscosity μt in the improved SST k
ω model with an extra damping function Fμ is same as in Peng's k
ω model as follows: 

μt ¼



ρk a1 ω min α Fμ ; ω SFE

(8a)

where α satisfies the relationship α β F ¼ 0:09. FE is the same blending function as that defined in Equation (5b) in Menter's SST k
ω model. The damping function Fμ is defined as follows: 371

K. An, J.C.H. Fung

Journal of Wind Engineering & Industrial Aerodynamics 179 (2018) 369–384

4 !



Ret Fk ¼ 1
0:722exp
10 " Fω ¼ 1
0:9 exp




Ret 2500





μt ∂k σ kin ∂xj

μþ 

ρ





  zþ 2:4 F* ¼ B1
B2 exp
400

βin ¼

ρ

∂ω ∂ω ∂ þ ρuj ¼ αin Fω Pω
ρβin ω2 þ þ ∂t ∂xj ∂xj



μt ∂k σ kin ∂xj



αin;out ¼



μt ∂ω μ ∂k ∂ω þ Cω t σ ωin ∂xj k ∂xj ∂xj



∂ω ∂ω ∂ þ ρuj ¼ αout Pω
ρβout ω2 þ þ ∂t ∂xj ∂xj

μt ∂k σ kout ∂xj



βin;out κ2 pffiffiffiffiffiffiffiffiffiffiffiffiffiffi
β* F* σ ωin;out α* F* β*

(13c)

TKE is related to the fluctuating velocity components u' , v' , and w' wherein k ¼ 12 ½ðu' Þ2 þ ðv' Þ2 þ ðw' Þ2 . In the near-wall regions, the fluctuating velocity components can be expanded by the Taylor series of y (the distance normal to the wall) as follows:

 (11c)

  u' ¼ Aðx; z; tÞy þ O y2

(14a)

μt ∂ω 2 ∂k ∂ω þρ σ ωout ∂xj ωσ ωout ∂xj ∂xj

  v' ¼ Bðx; z; tÞy2 þ O y3

(14b)

(11d)

  w' ¼ Cðx; z; tÞy þ O y2

(14c)



μþ

(13b)

2.7. Near-wall asymptotic behavior

The closure equations for the k and ω terms of the improved model in the outer region are as follows:

μþ

(13a)

The model constants for Menter's SST k
ω model and the reestablished model constants for the improved SST k
ω model are summarized in Table 1.

(11a)

(11b)





should be satisfied by Cε2 ¼ 1:92. Furthermore, Poroseva and Iaccarino (2001) emphasized the importance of turbulence diffusion in unbounded flows and suggested setting σ ε ¼ 1:5 for the k
ε model; thus, this constant of the outer region (i.e. σ kout ¼ σ ωout ¼ 1:5) was modified for the improved SST k
ω model. In addition, for zero-pressure-gradient local-equilibrium boundary layer flows, the model parameters αin and αout should satisfy the following relationship:





μþ

β  F 1:27

βout ¼ ðCε2
1Þβ F*

Here, the adjustable constants have values of B1 ¼ 0:61 and B2 ¼ 0:28. By applying the correction function on the model parameter β , the turbulent cross diffusion term and also the damping functions on k and ω equations, we obtain the following closure equations for the improved SST k
ω model for the inner regimes:

μþ



μt ∂ω σ ω ∂xj

For the value of βout in the outer region, the relationship:

(10)



μþ

The model constants α, β, σ k , and σ ω are blended across different regions through the blending function FB via the relation in Equation (7b). The definitions of the production of TKE Pk and the production of the specific dissipation rate Pω remain unchanged as in Equations (6a) and (6b). Based on the isotropic turbulence calibration, the value of βin in the inner region is selected to satisfy the following ratio:



As pointed out by Richards and Hoxey (1993), a smaller value of β has often been observed in the field measurements of atmospheric boundary flows. Grounded on the above modifications, Peng's SST k
ω model has been advanced by incorporation of a correction function that depends on the dimensionless distance zþ ¼ zuν in Equation (10) on the model constant β , where B1 and B2 are adjustable constants:

∂k ∂k ∂ þ ρuj ¼ Pk
ρFk F β ωk þ ∂t ∂xj ∂xj



(12b)

μ ∂ω μ ∂k ∂ω μþ t þ Cω t σ ωin ∂xj k ∂xj ∂xj

ρ

∂ω ∂ω ∂ þ ρuj ¼ ½αin Fω FB þ ð1
FB Þαout Pω
ρβω2 þ ∂t ∂xj ∂xj   μ 2ρ ∂k ∂ω þ Cω FB t þ ð1
FB Þ k ωσ ωout ∂xj ∂xj

(9c)

2.6. Reestablished model parameters

ρ



(9b)

(9d)

∂k ∂k ∂ þ ρuj ¼ Pk
ρF* β* ωk þ ∂t ∂xj ∂xj

μþ

(12a)

∂ω ∂ω ∂ ρ þ ρuj ¼ αin Fω Pω
ρβin ω2 þ ∂t ∂xj ∂xj

ρ



μt ∂k σ k ∂xj

The ω equation for the improved SST k
ω model can be expressed as follows:

4 #

∂k ∂k ∂ þ ρuj ¼ Pk
ρFk β ωk þ ∂t ∂xj ∂xj



(9a)

After the implementation of the damping functions, the new set of closure equations for the inner region of the improved SST k
ω model are as follows:

ρ

∂k ∂k ∂ þ ρuj ¼ Pk
ρF* β* ωk½FB Fk þ ð1
FB Þ þ ∂t ∂xj ∂xj

ρ



With respect to the blending function FB of Menter's SST k
ω model as stated in Equation (7a), we multiplied Equation (11a,b) by FB and Equation (11c,d) by 1
FB and summed up the two resulting equations. Thus, the k equation for the improved SST k
ω model can be expressed as follows:

From Equations (14a) and (14c) and the relationship of TKE k to the fluctuating velocities, we infer that k∝y 2 . For the turbulent dissipation ∂u' ∂u'i 0 ∂xk ∝y ,

rate ε ¼ ν∂xki

the specific dissipation rate ω, which is the

Table 1 Model constants for Menter's SST k
ω model and the improved SST k
ω model. Model constants

σ kin

σ kout

σ ωin

σ ωout

βin

βout

β

a1

κ

Modified values Default values

0.9 1.176

1.5 1

2.5 2

1.5 1.168

Depending on β 0.075

0.0828

0.09 0.09

0.31 0.31

0.4 0.4

372

K. An, J.C.H. Fung

Journal of Wind Engineering & Industrial Aerodynamics 179 (2018) 369–384

study, the temperature gradient effects and the buoyance and chemical reactions between pollutants were not considered. The continuity equation (Equation (1)), momentum equation (Equation (2)), the eddy viscosity definition (Equation (8a) and (8b)), TKE equation (Equation (12a)), specific dissipation rate equation (Equation (12b)) and the species transport equation (Equation (15a) and (15b)) form a closed system for the improved SST k
ω model to solve the pollutant dispersion problem.

reciprocal turbulent time scale, is related to the TKE k and the dissipation rate ε by ω  ε=k∝y
2 . Moreover,
u' v' ∝y 3 and near the wall, we assume that uþ ¼ yþ , thus achieving the relation ∂∂uy∝y 0 . This leads to the ! ! production of the TKE term Pk ¼
ρu'i u'j

∂ui ∂x j

¼ μt

∂ui ∂xj

∂u

þ ∂xji

∂ui 3 ∂xj ∝y

and

the turbulent Reynolds number Ret ∝y 4 as y → 0. Based on the production of TKE term, we concluded that the eddy viscosity should satisfy μt ∝ y 3 in the near-wall areas. The damping function Fμ in Equation (8b)   1 þ … ∝y
1 ; imposed on the eddy viscosity term satisfies Fμ  Re
0:25

3. Examination of modeling

t

3.1. Wind tunnel experiment

this relationship ensures the asymptotic consistency of the near-wall shear stresses. For the k
ω model, the asymptotic solution for the TKE k has the form of k → Cy n as y → 0, where C denotes a constant and  qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  n ¼ 12 1 þ 1 þ 24 F*ββin* Fk . For k∝y 2 , n should be equal to 2, requiring that

F* β* Fk βin

To validate the robustness of the simulation results of the improved SST k
ω model, a validation model was built, as shown in Fig. 1, and compared against the data obtained from an experiment of the flow and the tracer gas dispersion around a single block building conducted in a wind tunnel (cross section of the measurement part: 1.2 m  1.0 m) of Tokyo Polytechnic University (Tanaka et al., 2006). As illustrated in Fig. 1, the model building had the following dimensions: height of 0.2 m, width of 0.1 m, and depth of 0.1 m (H : W : D ¼ 2 : 1 : 1). The building was located in an isothermal turbulent boundary layer with a power law index of approximately 0.25. A small-area gas source was set on the floor 0:25H away from the leeward side of the model building releasing ethylene (C2H4) as a tracer gas at a volume flow rate (q) of 5:83  10
6 m3 =s. The Reynolds number based on the building height and the inflow velocity at the building height was approximately 56000. The wind velocity and the gas concentration were simultaneously measured using a split-film probe for the wind velocity and a fast-response flame ionization detector for the gas concentration. The sampling frequency was set at 1000 Hz, which provided 120; 000 data elements in 120 s.

¼ 13. The damping function is then Fk ¼ 1
0:722 exp


 4 ! Ret 10

∝y 0 and approaches the value of 0.278 as Ret → 0. With the

relationship in Equation (13a),

F* β* Fk βin

 13 and n  2, resulting in the

correct asymptotic behavior of the TKE in the near-wall region. The specific dissipation rate ω approaches the value βin6νy 2 as y → 0, in which it

fulfills ω∝y
2 . Furthermore, the damping function Fω imposed on the production term of the specific dissipation rate in Equation (12b) follows Fω ∝y 0 . As the production of the specific dissipation term follows the asymptotic behavior of Pω ∝y
1 , the addition of the term Fω ∝y 0 ensures the asymptotic consistency of the modeled production term in the ω equation as y → 0. Both the damping functions Fk and Fω are increasing functions of the turbulent Reynolds number. These damping functions have a value that tends to unity for the high turbulent Reynolds number regions, which usually appear in the upper boundary layer. The roles of the damping functions become more significant in regions with relatively low Reynolds number regimes, which usually appear in the near-obstacle and the wake regions. Within these regions, the TKE production is considerably greater than the turbulent dissipation. The damping function Fk in the TKE closure equation imposed on the TKE destruction term aims to reduce the rate of destruction of TKE. In contrast, another damping function Fω obtained through computer optimization is applied to the production term of the specific dissipation rate to slow down the production of the specific dissipation rate in the recirculation and nearobstacle regimes; however, its effect reduces in regions located away from the obstacle. As illustrated above, the introduction of the damping functions Fk ; Fω , and Fμ in the improved SST k
ω model equations preserves the correct asymptotic behavior for the near-wall turbulence.

3.2. CFD simulations CFD simulations for the cases were carried out using the baseline profiles (wind and TKE profiles shown in Fig. 3) obtained from the wind tunnel experiment (Tanaka et al., 2006) as the inflow conditions.

2.8. Modeling species transport To apply the improved SST k
ω model to the simulation of the dispersion phenomenon under isothermal conditions without chemical reactions, an additional equation for the mass fraction of pollutants is added to the system to account for the species transport behaviors. The species transport equation is as follows: !  ∂ðρMi Þ þ r ðρ! u Mi Þ ¼
r  J i ∂t

(15a)

  μ ! J i ¼
ρDi;m þ t rMi Sct

(15b)

The term on the right-hand side of Equation (15b) is responsible for the turbulence diffusion and mass diffusion, where Di;m is the mass diffusion coefficient and Sct is the turbulent Schmidt number. In this

Fig. 1. Illustrational diagram of the geometry tested and model parameters (figure adopted from Architectural Institute of Japan (AIJ) website). 373

K. An, J.C.H. Fung

Journal of Wind Engineering & Industrial Aerodynamics 179 (2018) 369–384

Fig. 2. Mesh grids (Basic Grid) and pollutant source location.

Fig. 3. Inflow profiles for the simulated cases.

influence of the side walls demarcating the lateral side can be reduced by using a sufficiently large computational domain (Li et al., 2006; Blocken et al., 2007). The size of the computational domain was set according to the CFD guidelines (Franke et al, 2011; Tominaga et al., 2008), which recommended that the lateral and top boundaries should be set at 5H or further from the target building, where H is the height of the tallest building. The outflow boundary should also be set at least 10H behind the target building (Mochida et al., 2002; Shirasawa et al., 2003). The size of the computational domain in this study extended 5H upwind of the obstacle, 5H in the lateral direction, 5H in the vertical direction, and 15H downwind of the obstacle. The boundary types of the computational domain were typical with the two lateral sides of the domain set as the symmetry boundary conditions; the top face was set with the velocity and turbulence quantities at the domain height. The obstacle walls and the ground were set as the no-slip wall boundary conditions. In addition, the outlet face was set as an outflow condition that assumed a zero gradient flow for all flow variables except pressure. Together with the inflow face set as the velocity inlet condition with the inflow profiles, as shown in Fig. 3, the outflow boundary condition ensured the mass balance and considered the exit flow to be close to that of a fully developed condition. Approximately 1.6 million structured mesh grid cells were created. In addition, the grid expansion ratio in both the horizontal and the vertical directions was at most 1.2 with yþ  1. The general settings of the CFD model are summarized in Table 2.

Sensitivity tests for various model parameters and correction functions for the improved SST k
ω model were carried out. The simulated wind velocity profiles and pollutant concentration data were then compared with the data obtained from the well-controlled wind tunnel experiment of Tanaka et al. (2006) for model validation. The data obtained from the wind tunnel experiment with respect to the mean velocities, normalized pollutant concentration, and the three normal stresses (summed together to obtain the TKE) were available at the data measurement locations (illustrated in Fig. 4). Therefore, throughout the investigated simulations discussed in this section of the paper, the mean velocity profiles, TKE profiles, and the scatter plots of the normalized pollutant concentration from the wind tunnel experiment against the CFD simulation are plotted to provide comparisons between the CFD simulation predictions and the data obtained from the wind tunnel experiment. The CFD code ANSYS FLUENT 14.5 (Fluent Inc., 2009) with the modified equations was used in this study to apply the finite volume method to solve three-dimensional, incompressible steady-state continuity and momentum equations. The mesh grids of the simulated cases are shown in Fig. 2. 3.3. Computational domain settings and boundary conditions The first task before performing a CFD simulation is to decide the size and shape of the computational domain and the corresponding boundary conditions imposed on the different faces of the domain. The 374

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Journal of Wind Engineering & Industrial Aerodynamics 179 (2018) 369–384

Table 2 Settings for the CFD simulations of the investigated cases. CFD model Computational domain size

Boundary conditions

Turbulence model Numerical scheme for pressure term and advection terms Convergence criteria Schmidt number

5H for inflow buffer and 5H for lateral region 15H for downstream region, 5H for vertical region Symmetry condition for two side boundaries Top specified stress Wall boundary condition for the ground Velocity inlet condition for inflow boundary Outflow condition for outlet boundary Improved SST k
ω model Second order for pressure term Second-order upwind schemes for advection terms Scaled residuals dropped to below 1  10
5 0.7–1.1

3.4. Test cases Model simulations of nine test cases in wind tunnel scale as tabulated in Table 3 were carried out and compared with each other in terms of the downwind wind profiles, TKE profiles, and the normalized pollutant concentration by applying both Menter's and improved SST k
ω models and the commonly adopted realizable k
ε model on the model geometry specified above. Test cases T1 and T2 were the simulation cases with Menter's SST k
ω model and the realizable k
ε model, respectively, with a Schmidt number of 0.7. Test cases T3 to T5 were designed in a manner attempting to gradually evaluate the effectiveness of the proposed modifications (i.e., (A) Impose empirical damping functions on the inner model equations of Menter's SST k
ω model. (B) Include the turbulent cross-diffusion term. (C) Impose a modification function F* to the model parameter β* .) in improving the robustness of the pollutant concentration prediction. The three cases T3 to T5 all had a Schmidt number of 0.9 with case T3 including only the potential improvement modification (A), case T4 including the potential improvement modifications (A) and (B), and case T5 including all the potential improvement modifications. Following the simulations of cases T3 to T5, we simulated cases T6 and T7 to test the sensitivity of the simulation solutions to the F* profiles. Case T6 adopted an F* profile with a 25% increment from that in case T5, while case T7 adopted an F* profile with a 50% increment from that in case T5. The other settings for cases T6 and T7 were consistent with those of case T5. After the sensitivity test for the F* profile modification, based on the settings of case T5, two other simulations (case T8 with Schmidt number ¼ 0.7 and case T9 with Schmidt number ¼ 1.1) were carried out aiming to test the sensitivity of the pollutant dispersion patterns to the Schmidt number. 3.5. Resolution of computational grid Grid-sensitivity test has been performed based on three types of grids: a coarse grid, a basic grid and a fine grid. The basic grid has 1559280 cells and the coarse grid has 767754 cells, in which its grid cell number is approximately half of the basic grid. The fine grid has 2751516 cells, in which the grid amount is approximately double of the basic grid. Menter's SST k
ω model was adopted as the turbulence model for grid sensitivity analysis. Fig. 5 illustrates the three types of grids. Fig. 6 depicts a comparison of the results for the velocity magnitude and turbulent kinetic energy based on the three grids. A small deviation for the simulation results is found among the three grids for the lines at x=H ¼ 0:125, x=H ¼ 0:25 and 0:5 behind the block obstacle, with relatively closer match in the simulation results between the three types of grid. No significant grid sensitivity has been identified, therefore, the resolution of the basic grid is considered sufficient and has been adopted for the simulations for the test cases in this study.

Fig. 4. Data extraction locations on different planes.

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Journal of Wind Engineering & Industrial Aerodynamics 179 (2018) 369–384

are used to quantify the agreement between the simulation and experimental results (Schatzmann et al., 2010) for pollutant concentration: the fraction of the prediction within a factor of 2 of the observations (FAC2) and normalized mean square error (NMSE). These metrics can be expressed as follows:

Table 3 F* profiles, Schmidt number, and various model constants used in different investigated cases for the improved SST k
ω model. Test cases

Case T1 (Menter's SST k
ω model) Case T2 (realizable k
ε model) Case T3 Case T4 Case T5 (optimal) Case T6 Case T7 Case T8 Case T9

Correction functions

Crossdiffusion term

Schmidt number

–

–

–

0.7

–

–

–

–

0.7

– – 0.61 0.76 0.92 0.61 0.61

– – 0.28 0.35 0.42 0.28 0.28

þ þ þ þ þ þ þ

– þ þ þ þ þ þ

0.9 0.9 0.9 0.9 0.9 0.7 1.1

F profile B1

B2

–

8 > > > <

Pi 1 for 0:5 2 N Mi 1 X FAC2 ¼ ni with ni ¼ 1 for M W and P W > i i N i¼1 > > : 0 else

NMSE ¼

ðPi
Mi Þ2 P  M

(16a)

(16b)

where Mi and Pi are measured and predicted values of a given variable for sample i, respectively; and N is the number of data points. The overbar denote the mean of the dataset. The allowed absolute difference W is set to 0.1 for FAC2. An ideal model would produce metrics value of 1.0 for FAC2 and 0 for NMSE. Previous studies suggested the following judgment criteria for these metrics for pollutant concentration is FAC2 > 0:5 and NMSE < 4 (Schatzmann et al., 2010; Hanna et al., 2004).

3.6. Performance metrics The following validation metrics in addition to the correlation value

Fig. 5. Illustrational diagrams showing Coarse, Basic and Fine Grids.

Fig. 6. Wind and TKE profiles at near downwind of obstacle under different types of grids. 376

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Journal of Wind Engineering & Industrial Aerodynamics 179 (2018) 369–384

3.7. Performance of Menter's SST k
ω model and realizable k
ε model (cases T1 and T2)

three test cases T3 to T5 were formulated. The imposition of the damping functions (Equation 9(a) and (9b)) on the turbulence closure equations of the inner SST k
ω model together with a modification in the eddy viscosity definition (Equation (8a) and (8b)) in case T3 was expected to bring about significant improvement in the prediction accuracy of Menter's SST k
ω model. Promising improvements with a closer match to the wind tunnel experiment data than the results of Menter's SST k
ω model and the realizable k
ε model are observed from the plots of the vertical downstream wind and the TKE profiles shown in Fig. 9. The roles of the correction functions become relatively significant at regions with relatively low Reynolds number regimes which appear near to the obstacle, which results in an increase in net production of TKE in these regimes for the improved SST k
ω model in case T3 compared to the default models in cases T1/T2. In general, the results indicate that the addition of the modification functions to reduce the dissipation of the TKE and limit the production of the specific dissipation rate is effective in improving the correlation between the CFD simulation results and the wind tunnel experiment data. The correlation of the normalized pollutant concentration between the wind tunnel experiment and the CFD simulation improved with an increase in the correlation values from R2  0:10 to R2  0:52. There are also improvements in both the FAC2 and NMSE values in Case T3 compared to the default model cases T1/T2. The FAC2 value improved from 0.36 in case T1 to 0.52 in case T3, while the NMSE value has an approximate reduction of 58%, indicating there is an observable improvement in the model prediction capability. However, Peng et al. (1996, 1997, 2007) reported, and as mentioned in the previous section of this paper, that Wilcox omitted the cross-diffusion terms, among which the turbulent cross-diffusion term probably played an important role in pollutant dispersion problems. Therefore, in addition to all the settings in case T3, the turbulent cross-diffusion term in Equation (9d) was included in the specific dissipation rate equation and tested out in case T4. With the addition of the turbulent cross-diffusion term, nonobservable improvements on the vertical wind velocity profiles were found as the prediction of these profiles had already reached a considerably satisfactory state after the addition of the damping functions in case T3. However, the vertical TKE profiles exhibited further improvements with a closer match to the wind tunnel data, as shown in Fig. 10.

The downstream vertical velocity profiles and the TKE profiles generated from Menter's SST k
ω model and the commonly adopted realizable k
ε model in FLUENT are plotted and compared with the wind tunnel experiment data in Fig. 7. As reported in Tanaka et al. (2006), the relative uncertainty of mean value of measurements is less than 10% for the wind tunnel experiment. The comparison revealed that the obtained profiles from both the simulations of these models have relatively large discrepancies as compared to the data obtained from the wind tunnel experiment. Menter's SST k
ω model tends to over-predict the vertical spreading of the wake on the near-downwind side of the obstacle and under-predict the velocity deficit recovery rate in the downstream area. Meanwhile, the realizable k
ε model produces relatively good predictions of wind profiles in the near-downwind region from the obstacle as compared to Menter's SST k
ω model with a more accurate prediction of the vertical spreading of the wake. However, as in the case of Menter's SST k
ω model, observable deviations from the experimental wind profile still appear at the downwind locations located further away from the obstacle. This finding suggests an over-prediction of the reattachment length behind the obstacle by both the models. In addition, as revealed in Fig. 8, the correlation between the simulation results and the experimental data with respect to the normalized pollutant concentration is relatively low with R2 values of around 0:10 and 0:20, respectively. Moreover, FAC2 value of 0.36 and a marginal FAC2 value (0.5) have been obtained for Menter's SST k
ω model and realizable k
ε model respectively with both models has NMSE values greater than 3 (NMSE ¼ 4:17 for Menter's SST k
ω model and NMSE ¼ 3:16 for realizable k
ε model). These results indicate that these two CFD turbulence models do not predict the pollutant dispersion patterns around the investigated bluff body well. This inference can also be explained by the under-prediction of TKE profiles by these two turbulence models as compared to the wind tunnel data, as shown in Fig. 7. 3.8. Performance of improved SST k
ω model (cases T3, T4, and T5) The three potential improvement modifications as discussed in Section 2 were added one at a time to Menter's SST k
ω model, and the

Fig. 7. (a) Wind tunnel experiment results against CFD simulation results for downwind vertical wind velocity profiles of cases T1 and T2. (b) Wind tunnel experiment results against CFD simulation results for the TKE profiles of cases T1 and T2. 377

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Journal of Wind Engineering & Industrial Aerodynamics 179 (2018) 369–384

Fig. 8. (a) Wind tunnel experiment results against CFD simulation results of case T1. (b) Wind tunnel experiment results against CFD simulation results of case T2.

Fig. 9. (a) Wind tunnel experiment results against CFD simulation results for downwind vertical wind velocity profiles of case T3. (b)Wind tunnel experiment results against CFD simulation results for TKE profiles of case T3.

case (Khurshudyan et al., 1981), we imposed the correction functions in the form of Equation (10) on the model parameter β . The corrected β profile (line with circles in Fig. 14) with an approximate value of 0.03 for the dimensionless distance zuν < 100 and a ceiling β value of 0.055 was adopted in case T5. This case resulted in the most optimal simulation results with a promising correlation value of approximately 0.78 (see Fig. 12(c)) with low NMSE value of 0.67 and satisfactory FAC2 value of 0.54. Best match in terms of both the vertical wind velocity and the TKE profiles with the wind tunnel experimental data has also been achieved. Moreover, the magnitude of the simulated normalized pollutant concentration scattered near the 20% lines, which can be considered relatively satisfactory

Moreover, the correlation between the CFD simulation results and the wind tunnel experiment data further improved to a R2 value of 0.60, as shown in Fig. 12(b). There is only slight improvement in the FAC2 value for case T4 in comparison with case T3. However, further reduction in NMSE value compared to case T3 is observed in this test case (NSME value reduced from 1.76 to 1.15). The default value of 0.09 for the model parameter β* has been reported to be large (Richards and Hoxey, 1993). The value of this model parameter has been corroborated by various experiments to be approximately 0.03. Maintaining the merits and the settings of cases T3 and T4, while taking this piece of information into account and referring to the experimental measurement profile data for β of the RUSHIL reference 378

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Journal of Wind Engineering & Industrial Aerodynamics 179 (2018) 369–384

Fig. 10. (a) Wind tunnel experiment results against CFD simulation results for downwind vertical wind velocity profiles of case T4. (b) Wind tunnel experiment results against CFD simulation results for TKE profiles of case T4.

Fig. 11. (a) Wind tunnel experiment results against CFD simulation results for downwind vertical wind velocity profiles of case T5. (b)Wind tunnel experiment results against CFD simulation results for TKE profiles of case T5.

The wind and the normalized pollutant concentration contours obtained from the different models are also provided in Fig. 13 for reference. Despite the fact that the improved SST k
ω model predicts relatively good vertical wind velocity within the near-wake region as compared to the regions slightly further away, with a little slower

when compared with the results from cases T1 to T4. The improved SST k
ω model produces downwind wind velocity profiles and TKE profiles consistent with the wind tunnel experiment data as shown in Fig. 11 and is concluded to be capable of providing accurate predictions of the wind field.

379

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Journal of Wind Engineering & Industrial Aerodynamics 179 (2018) 369–384

Fig. 12. Wind tunnel experiment results against CFD simulation results of cases (a) T3, (b) T4 and (c) T5.

respectively. The line with squares indicates a 25% increment in magnitude, while the line with crosses indicates a 50% increment in magnitude from the β* profile in case T5 (the line with circles). Moreover, note that the β* values should not exceed 0.09; β* values that deviate considerably from this default value lead to numerical convergence issues. Fig. 15, which shows a comparison between the simulation results and the wind tunnel experiment data for cases T6 and T7, reveals that a β* profile in which the magnitude deviates from the optimal profile in case T5 by þ25% in case T6 results in a correlation value approximately 10% (reduced from 0.78 to 0.70) lower than that of the optimum case, in addition, the NMSE value is also increased by around 19% (from 0.67 to 0.80). A further change in the β* profile's magnitude by a þ50% deviation from the optimum profile in case T7 further lowers the correlation value (from 0.70 to 0.64) at the same time increases the NSME value from 0.80 to 1.03. Nevertheless, comparable FAC2 values have been acquired in cases T6/T7 and the optimal case. In terms of the magnitude of the predicted normalized pollutant concentration, Fig. 15(b) shows that case T6 predicts a slight deviation of

10% to 15% when compared with case T5. With a further deviation of the β* profile in case T7, the deviation in the normalized pollutant

recovery rate from the velocity deficit of the CFD simulation than that in the wind tunnel experiment, the improved SST k
ω model with the modifications exhibited the best performance among the three models and is proposed to be a speedy and optimum turbulence model for solving the wind flow and pollutant dispersion problems around building obstacles via the CFD approach. 3.9. Sensitivity test of F* functions on model parameter β* (cases T6 and T7) Following test case T5, the sensitivity of the β* profiles was investigated in cases T6 and T7. Taking case T5 as a control base case, we adjusted the β* profiles in cases T6 and T7 with a consistent Schmidt number of 0.9 to investigate the sensitivity of the β* profiles to the predicted normalized pollutant concentration fields; the results are illustrated in Fig. 15. Fig. 14 illustrates the β* profiles for the various test cases. The line with circles denotes the β* profile in cases T5, T8, and T9; in these cases, this profile was found to provide optimal results when compared with the Tokyo Polytechnic University's wind tunnel experiment data for the tested single bluff body. The blue line with squares and the red line with crosses correspond to the β* profiles in cases T6 and T7, 380

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Journal of Wind Engineering & Industrial Aerodynamics 179 (2018) 369–384

Fig. 13. Wind (upper) and normalized pollutant concentration (lower) contours.

in the robustness of the results. 3.10. Sensitivity test of Schmidt number (cases T8 and T9) Tominaga and Stathopoulos (2007) investigated the effect of the turbulent Schmidt numbers using the CFD analysis for various types of flow fields and concluded that the selection of specific values of the Schmidt number had a significant effect on the predicted pollutant field results. Sensitivity tests of the Schmidt numbers were performed for cases T8 and T9 with the same β* profile but different Schmidt number values of 0.7 and 1.1, respectively. The mesh grids and the other model parameter settings for cases T8 and T9 were consistent with those for cases T5 to T7. As shown in Fig. 16, the change in Schmidt number would not result in a significant change in the correlation relationships between the CFD simulation results and the wind tunnel experiment data. The R2 value for the optimum case with a Schmidt number value of 0.9 was approximately 0.78; case T8 with a Schmidt number of 0.7 could maintain a similar R2 value of 0.79. For case T9 with a Schmidt number of 1.1, although the R2 value was 0.74, which is slightly lower than the R2 value (0.78) of the optimal case T5, the value is still satisfactory when compared with that in the other cases. In addition to the above, there is only slight increment in the NMSE values for cases T8 and T9 while comparable values of FAC2 are obtained when compared with the optimal case T5. The above results propose that the variation in Schmidt number resulted in differences in the predicted normalized pollutant concentration data, as shown in Fig. 16(b) and (d). Compared with the CFD simulation results of the normalized pollutant concentration from case T5, the smaller Schmidt number (0.7) in case T8 resulted in 10%–15% lower predicted normalized pollutant concentration. In contrast, an increase in the Schmidt number to 1.1 in case T9 resulted in 10%–15% higher magnitude of the normalized pollutant concentration. This result implies that the value of the Schmidt number can be slightly tuned depending on different case scenarios to achieve a better predicted value of the pollutant concentration.

Fig. 14. β* profiles for the cases investigated using the logarithmic scale.

concentration from case T5 increased with deviations within 20% at most of the test points, as shown in Fig. 15(d). The results clearly showed that the variation in the β* profiles affected the correlation between the simulation results and the wind tunnel experiment data for the normalized pollutant concentration when the improved SST k
ω model was used as the turbulence model. The change in the β* profiles also resulted in changes in the predicted magnitude of the pollutant concentration. The model parameter β* is a sensitive parameter and should be carefully chosen, and the default constant value of 0.09 is proven to be overestimated for the SST k
ω model if used to solve the pollutant dispersion problems. However, a 25% deviation in the magnitude of β* from the proposed β* profile is not likely to result in a significant change for both the predicted normalized pollutant concentration and the correlation between the model and the experimental data. However, any deviation greater than þ25% from the optimum β* profile would result in changes

4. Conclusion Compared with the data of the wind and pollutant concentration obtained under isothermal conditions in an experiment of a single obstacle carried out by Tokyo Polytechnic University, we discovered that neither the realizable k
ε turbulence model (commonly practiced turbulence model in air ventilation assessments) nor Menter's SST k
ω 381

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Journal of Wind Engineering & Industrial Aerodynamics 179 (2018) 369–384

Fig. 15. (a) Wind tunnel experiment results against CFD simulation results of case T6 (b) CFD simulation results of case T6 against case T5 (c) Wind tunnel experiment results against CFD simulation results of case T7 (d) CFD simulation results of case T7 against case T5.

turbulence model (model that combines the advantages of both the k
ε and the k
ω models) produced robust downwind vertical wind profiles and pollutant dispersion patterns with a satisfactory correlation between the CFD simulation results and the wind tunnel experiment data. One possible explanation of the non-satisfactory behavior of these models is their tendency to over-predict the reattachment length, and thus, they are not recommended for tackling the wind flow and pollutant dispersion problems within urban areas. Menter's SST k
ε model was modified to improve its prediction ability. Three improvement modifications have been identified: (A) replace the inner-region model of Menter's SST k
ω model with Peng et al.’s k
ω model; (B) add the turbulent cross-diffusion term to the specific dissipation rate equation and (C) modify the β* profile. The effectiveness of these improvement modifications was investigated by applying the modifications one at a time to Menter's SST k
ω model in a systematic manner. After the adoption of Peng et al.’s k
ω model as the inner model, the correlation of the pollutant concentration data from Menter's SST k
ω model with the wind tunnel experiment data was improved from 0.10 to 0.52 with a reduction in NMSE from 4.17 to 1.76. By further adding the turbulent cross-diffusion term to the specific dissipation rate equation along with a modified β* profile (the default empirical value of β* ¼ 0:09 is overestimated as pointed out in the

existing literature), we further improved the pollutant prediction capability with more robust simulation results, in which the pollutant concentration correlation value with the wind tunnel experimental data increased from 0.52 to 0.78 with the smallest NMSE value of 0.67 among the test cases. Furthermore, the improved SST k
ω model also achieved relatively matching downwind vertical velocity profiles and TKE profiles with the wind tunnel experiment as compared to the realizable k
ε model and Menter's SST k
ω model. The over-/under-prediction phenomenon of the pollutant concentration by steady-state CFD models has also been reported in previous studies (Gromke and Ruck, 2012; Yuan et al., 2014); this phenomenon can be mitigated by fine-tuning the Schmidt number depending on the different cases investigated. This study has proven that slight adjustments in the Schmidt number do not lead to significant changes in the correlation between the simulation results and the wind tunnel experiment data. This can also be reflected by the NMSE values for cases T8 and T9 in tabulated in Table 4 which summarize the NMSE, FAC2 and correlation values for different test cases. To summarize, the improved SST k
ω model is a better choice of turbulence model for environmental modelers and scientists to consider for pollutant dispersion studies in comparison with the baseline models. The improved model is capable to achieve a correlation value up to 0.78 382

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Journal of Wind Engineering & Industrial Aerodynamics 179 (2018) 369–384

Fig. 16. (a) Wind tunnel experiment results against CFD simulation results of case T8 (b)CFD simulation results of case T8 against case T5 (c)Wind tunnel experiment results against CFD simulation results of case T9 (d)CFD simulation results of case T9 against case T5.

many other factors including but not limited to changes in atmospheric conditions, geometric uncertainties and also assumptions in turbulence models.

Table 4 Summary table of NMSE, FAC2 and correlation values for different test cases. Test Cases Case T1 (Menter's SST k-ω model) Case T2 (realizable k-ε model) Case T3 Case T4 Case T5 (optimal) Case T6 Case T7 Case T8 Case T9

NMSE

FAC2

Correlation Value

4.17

0.36

0.10

Acknowledgement

3.16

0.50

0.20

1.76 1.15 0.67 0.80 1.03 0.71 0.73

0.52 0.56 0.54 0.55 0.56 0.54 0.52

0.52 0.60 0.78 0.70 0.64 0.79 0.74

This work was supported by NSFC Grant 41575106 and the RGC Grant 16300715. The authors would also like to thank the anonymous reviewers for their useful suggestions. References An, K., Fung, J.C.H., Yim, S.H.L., 2013. Sensitivity of inflow boundary conditions on downstream wind and turbulence profiles through building obstacles using a CFD approach. J. Wind Eng. Ind. Aerod. 115, 137–149. Baskaran, A., Kashef, A., 1996. Investigation of air flow around buildings using computational fluid dynamics techniques. Eng. Struct. 18, 861–873, 875. Blocken, B., Carmeliet, J., Stathopoulos, T., 2007. CFD evaluation of wind speed conditions in passages between parallel buildings-effect of wall-function roughness modifications for the atmospheric boundary layer flow. J. Wind Eng. Ind. Aerod. 95, 941–962. Blocken, B., Persoon, J., 2009. Pedestrian wind comfort around a large football stadium in an urban environment: CFD simulation, validation and application of the new Dutch wind nuisance standard. J. Wind Eng. Ind. Aerod. 97, 255–270.

between the predicted pollutant concentration data and the wind tunnel experiment data. In addition, the improved model is observed to reduce down the NSME value by more than 80% compared to the baseline model with achievement of satisfactory FAC2 value greater than 0.5. However, even though this model has improved prediction capabilities, there will be some locations with discrepancies in magnitude between the simulation results and the real-world situation, which could be attributed to 383

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