**5.2 Turbulent flow field**

336 Computational Simulations and Applications

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

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

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,

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

**12 34 x/H**

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

**z/H**

**1**

**0 5**

**2**

**3**

 

is a damping function

inlet. *ui* is the averaged wind velocity in the horizontal plane.

respectively. A tripping fence has a height of 0.45H.

layer.

Figure 2.

Fig. 2. Coordinate system.

**5. Results** 

**5.1 Approach flow** 

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.

Fig. 4. Mean velocity vectors around a building.

Large-Eddy Simulation of Turbulent Flow and

satisfactorily results.

**5.3 Dispersion field** 

for the plume source.

the active turbulent motions.

Plume Dispersion in a Spatially-DevelopingTurbulent Boundary Layer Flow 339

building, x/H=3.5, the LES model results of both horizontal and vertical turbulence intensities around the building height are a little overestimated. Mochida *et al*., (1991) reported that the LES results of turbulence kinetic energy using the standard Smagorinsky model were overestimated around the upper edge of the recirculation zone of an obstacle in comparison with the wind tunnel experimental data. The overestimation of turbulence intensities of LES behind a building is due to the use of the standard Smagorinsky model. Although the standard Smagorinsky model has the above problems, the main characteristics are obtained in our simulation. They include a sharp peak behind the building due to the strong instability of separated shear layers and the formation of a uniform turbulent flow field with downstream distance due to the active turbulent motions almost the same as in the experimental data of Sada & Sato., (2002). The slight overestimation of the reattachment length has also been reported in other LES calculations (Murakami *et al*., 1986). Therefore, our LES model with the conventional Smagorinsky model shows reasonable accuracy and

Figure 7(a), (b) and (c) shows instantaneous plume dispersion fields around a building at times t\* (=tU∞/H) = 15, 45 and 90 after the plume release. The yellow areas on iso-surface indicate 0.01% of initial concentration. It shows that the plume is passed above the building roof at first, and then the plume is entrained into the wake region of a building. After enough time passing, the plume is found to be widely dispersed behind a building due to

Figure 8 shows a comparison of our LES model results and the wind tunnel experimental data (Sada & Sato., 2002) of the vertical profiles of mean (C) and r.m.s. (c') concentrations obtained downstream at x/H=1.5, 2.5, 3.5 and 5.0 in the near-wake region of the cubical building. The mean and r.m.s. concentrations are normalized by free-stream velocity, the building height and the source strength (Q). In both mean and r.m.s. concentration fields, the peak values of the LES model near the point source are about 50% smaller than the wind tunnel experimental results, while the model results are in good agreement with the experimental data, particularly at the position x/H=5.0, located away from the point source. These large discrepancies near the point source are possibly due to a coarse grid resolution

In our LES model, a plume source is provided in one grid-cell. Thus, the size of the point source is determined by the grid resolution. Michioka *et al*., (2003) examined the sensitivity of the grid resolution for the point source by LES of a plume dispersion released from the point sources corresponding to 1.0 and 10 times the real diameters of the point source. As a result, they found that the peak values of mean and r.m.s. concentrations near the point source in a coarse grid resolution were 80% smaller than the wind tunnel experimental data, while those in a fine grid resolution were consistent with the experimental data. The plume source diameter in our LES model is about 5.5 times that of the real one. Considering the discrepancy of the plume source diameter between the LES model and the wind tunnel experiments, our results have the same tendency to underestimate near the point source as the LES results by Michioka *et al*. Therefore, if the plume source size corresponding to the real one is properly set in our LES model, the model results near the point source should be improved. However, a fine grid resolution is not appropriate for our purpose and target scale considering its computational cost. Except for this discrepancy, the basic characteristics, such as a sharp peak just behind the cubical building and the formation of

Fig. 5. Streamwise variation of vertical profiles of mean wind velocity.

Fig. 6. Streamwise variation of turbulence intensities. (a) Horizontal turbulence intensity. (b) Vertical turbulence intensity.

Figure 6 shows a comparison of our LES model results with the wind tunnel experimental data of the vertical profiles of (a) horizontal and (b) vertical turbulence intensities normalized by free-stream velocity obtained downstream at x/H=0.0, 1.5, 2.5 and 3.5. Just above the roof of the building at x/H=0.0, the LES model results of both horizontal and vertical turbulence intensities are underestimated. At the position located away from the building, x/H=3.5, the LES model results of both horizontal and vertical turbulence intensities around the building height are a little overestimated. Mochida *et al*., (1991) reported that the LES results of turbulence kinetic energy using the standard Smagorinsky model were overestimated around the upper edge of the recirculation zone of an obstacle in comparison with the wind tunnel experimental data. The overestimation of turbulence intensities of LES behind a building is due to the use of the standard Smagorinsky model. Although the standard Smagorinsky model has the above problems, the main characteristics are obtained in our simulation. They include a sharp peak behind the building due to the strong instability of separated shear layers and the formation of a uniform turbulent flow field with downstream distance due to the active turbulent motions almost the same as in the experimental data of Sada & Sato., (2002). The slight overestimation of the reattachment

length has also been reported in other LES calculations (Murakami *et al*., 1986). Therefore, our LES model with the conventional Smagorinsky model shows reasonable accuracy and satisfactorily results.
