**4. Computational settings**

334 Computational Simulations and Applications

The LES of plume dispersion is also computed by using the standard Smagorinsky model.

*c c*

*j*

*s*

building height and wind speed at the building height is almost 5,000.

with the wind tunnel experimental data of Sada & Sato., (2002).

**3. Wind tunnel experiments for evaluating the model performance** 

*j j j j*

, (8)

*jj j s uc uc* (9)

, (10)

*u s txx* 

*SGS*

where *sj* is the subgrid-scale scalar flux which is also parameterized by an eddy viscosity model. The model constant, *ScSGS*, is the turbulent Schmidt number and it is set to a constant

The coupling algorithm of the velocity and pressure fields is based on the Marker and Cell (Harlow & Welch, 1965) method with the Adams-Bashforth scheme for time integration. The Poisson equation is solved by the Successive Over-Relaxation method that is an iterative method for solving a Poisson equation for pressure. For the spatial discretization in the governing equation of flow and the tracer transport, a second-order accurate central difference is used. For only the advection term in the dispersion field, the Cubic Interpolated Pseudo-particle (CIP) method (Takewaki *et al*., 1985; Yabe & Takei., 1988) is imposed in order to prevent a numerical instability. The CIP is a very stable scheme that can solve generalized hyperbolic equations in space. The Reynolds number based on the cubical

Over the past few decades many wind tunnel experiments have been conducted on the dispersion characteristics of a plume in the near-wake of a cubical building. For example, Sada & Sato., (2002) conducted experiments under neutral atmospheric stratification in the wind tunnel of Central Research Institute of Electric Power Industry. The wind tunnel test section was 20m long, 3m wide and 1.5m high. An approaching flow with strong velocity fluctuations was generated using roughness elements with L-shaped cross sections placed on the floor at the entrance of the wind tunnel. It was shown that spanwise and vertical spreads of a plume corresponded to the Pasquill-Gifford stability class D. A plume was released from an elevated point source located upstream from the cubical building and concentration of the plume is measured by a fast-response flame ionization detector. The vertical profiles of mean wind velocity, turbulence intensity, mean and r.m.s. concentrations and peak concentration in the near-wake region of the cubical building were all obtained from the experiments. In this wind tunnel experiment, the building Reynolds numbers based on the cubical building height and wind speed at the building height is about 13,000. In the present paper, in order to evaluate the model performance, we compare our LES results of turbulent flow and plume dispersion in the near-wake region of a cubical building

*Sc x* 

*SGS j*

*c*

The spatially filtered scalar conservation equations are presented by

and

value of 0.5 (Sada & Sato., 2002).

In wind tunnel experiments, a neutral atmospheric turbulent boundary layer is simulated mainly using various types of obstacle, such as spires, tripping fences and roughness blocks. Therefore, various wind tunnel flows that have different turbulence characteristics can be obtained depending on the wind tunnel facility. In an LES study of turbulent flow in the atmosphere, an approach flow with turbulent fluctuations as the inlet boundary condition of the model domain should be generated depending on the target wind tunnel flow by a certain method.

In our LES model, the driver region for generating a spatially-developing turbulent boundary layer flow and the main region for simulating of plume dispersion around a cubical building immersed in a fully-developed turbulent boundary layer are set up. In this scheme, first a thick turbulent boundary layer flow is generated by incorporating the existing inflow turbulence generation method, that is, the method of Kataoka & Mizuno., (2002) into an upstream small fraction of the driver region as shown in Figure 1(a). Then, a strong wind velocity fluctuation is produced by a tripping fence placed downstream from the recycle station as shown in Figure 1(b).

Fig. 1. Schematic of numerical model. (a) Driver region for generating turbulent boundary layer flow. (b) Main region for turbulent flow and plume dispersion around a cubical building.

In the method of Kataoka & Mizuno., (2002), the fluctuating part of the velocity at the recycle station is recycled and added to the specified mean wind velocity at each time interval by assuming that boundary layer thickness is constant within the driver section. This method requires a driver section with a length of about 1.0*δ*. The formulation of the method of Kataoka & Mizuno., (2002) is as follows.

$$
\mu\_{inlt}(y, z, t) = \left< u \right>\_{inlt}(z) + \phi(\theta) \left< u\_{recy}(y, z, t) - \left[ u \right](z) \right> \tag{11}
$$

$$
\psi\_{inlt} \left( y, z, t \right) = \phi \left( \theta \right) \psi\_{rcy} \left( y, z, t \right), \tag{12}
$$

$$w\_{inlt}\left(y,z,t\right) = \phi\left(\theta\right)\left\{w\_{rey}\left(y,z,t\right) - \left[w\right](z)\right\},\tag{13}$$

$$\phi(\theta) = \frac{1}{2} \left\{ 1 - \tanh \left[ \frac{a(\theta - b)}{(1 - 2b)\theta + b} \right] \Bigg/ \tanh a \right\},\tag{14}$$

Large-Eddy Simulation of Turbulent Flow and

model is also in good agreement with the experimental data.

Fig. 3. Turbulence characteristics of approach flow.

0

0.5

z/δ

1

1.5

Fig. 4. Mean velocity vectors around a building.

**5.2 Turbulent flow field** 

0.00 0.50 1.00 1.50

WT (Sada, 2002) LES

U/U∞

0

0.5

z/δ

1

1.5

Plume Dispersion in a Spatially-DevelopingTurbulent Boundary Layer Flow 337

intensities (u', v', w') and Reynolds stress in the driver region. The turbulence statistics is normalized by a free-stream velocity (U∞). We see that the mean wind velocity profile obtained by our LES model is consistent with the experimental data. Strong turbulent fluctuations are produced from the ground surface to the upper part of the boundary layer and each component of the LES-generated turbulent intensity profiles is found to be in good agreement with the experimental data. The Reynolds stress profile obtained by our LES

Figure 4 shows mean velocity vectors by LES around a building. The reattachment lengths of recirculating flow behind the building normalized by the building height of the experiments and the LES model is L/H=1.2 and 1.35 (L: reattachment length), respectively; the latter is slightly larger. Figure 5 shows a comparison of our LES model results with the experimental data (Sada & Sato., 2002) of the vertical profiles of mean wind velocity obtained downstream at x/H=0.0, 1.5, 2.5 and 3.5. The LES model results of mean wind velocity are consistent with the wind tunnel experimental data at each downwind position.

0.00 0.05 0.10 0.15 0.20

u', v', w'/U∞

0

0.000 0.005 0.010

WT (Sada, 2002) LES


0.5

z/δ

1

1.5

WT\_σu (Sada, 2002) WT\_σv (Sada, 2002) WT\_σw (Sada, 2002) LES\_σu LES\_σv LES\_σw

Here, *uinlt* and *urecy* are the instantaneous wind velocity at the inlet and the downstream position (the recycle station), respectively. *inlt u* is the specified mean wind velocity at the inlet. *ui* is the averaged wind velocity in the horizontal plane. is a damping function to control the transport of turbulent fluctuation into the free stream. *a* and *b* are constants.

Calculations of both driver and main regions are done by the same model with different computational settings. As boundary conditions, the Sommerfeld radiation condition (Gresho., 1992) is imposed at the exit, a free-slip condition for streamwise and spanwise velocity components is imposed and the vertical velocity component is 0 at the top, a periodic condition is imposed at the side, and a non-slip condition for each velocity component is imposed at the ground surface. Here, in our LES model, we do not use wall functions as the boundary condition of the ground surface. Therefore, the resolution of a vertically stretched grid above the ground surface is set to 1.7 in order to resolve the viscous layer.

The size and the number of grid points for the driver region is 32.8H×10.0H×9.5H (H: height of the cubical building) and 410×120×70 in streamwise, spanwise and vertical directions, respectively. A tripping fence has a height of 0.45H.

The size and number of grid points for the main region are 18.9H×10.0H×9.5H and 400×120×70 in streamwise, spanwise and vertical directions, respectively. The cubical building is resolved by 20×20×30 grids in the streamwise, spanwise and vertical directions, respectively. According to numerical experiments of Xie *et al*., (2006) and Santiago *et al*., (2008), a building should be resolved by at least 15-20 grid points in each dimension in order to capture complex turbulent behaviors. The mesh number of the building set up in our LES model is enough to accurately simulate turbulent flows around a building. At the inlet of the main region, the inflow turbulence data obtained near the exit of the driver region is imposed at each time interval. In a concentration field, zero gradient is imposed at all the boundaries. The release point of a tracer gas is located 1.5H upstream from the center of the building and elevated at height, H. According to the above-mentioned coordinates, the location of the release point of a plume corresponds to x/H=0.0 and z/H=1.0 as seen in Figure 2.

Fig. 2. Coordinate system.

#### **5. Results**

#### **5.1 Approach flow**

Figure 3 compares the LES model results with wind tunnel experimental data (Sada & Sato., 2002) of the vertical profiles of mean wind velocity (U), each component of turbulence intensities (u', v', w') and Reynolds stress in the driver region. The turbulence statistics is normalized by a free-stream velocity (U∞). We see that the mean wind velocity profile obtained by our LES model is consistent with the experimental data. Strong turbulent fluctuations are produced from the ground surface to the upper part of the boundary layer and each component of the LES-generated turbulent intensity profiles is found to be in good agreement with the experimental data. The Reynolds stress profile obtained by our LES model is also in good agreement with the experimental data.

Fig. 3. Turbulence characteristics of approach flow.
