**1. Introduction**

330 Computational Simulations and Applications

M.J. Raw (1996). Robustness of Coupled Algebraic Multi-grid for the Navier Stokes

E. Williams (2004). A computational fluid dynamics study of unsteady flow theory

NV.

Canada.

Equation," AIAA 96-0297, 34th Aerospace and Sciences Meeting & Exhibit, Reno,

Coefficients for tube array fluidelastic instability, Master's thesis, New Brunswick,

In one of local-scale dispersion problems, we have an important issue in the accurate prediction of airborne contaminant dispersion from industrial or nuclear facilities for safety and consequence assessments of nuclear facilities. For evaluating radiological consequences of radioactive materials, it is need to predict not only the material concentration in the air at the evaluation point for internal dose but also on the three-dimensional distribution of the plume and surface deposition for external dose. In a flat terrain, time-averaged concentration of a plume can be easily predicted by a conventional Gaussian plume model. However, in Japan, most nuclear facilities are located in complex coastal terrain. Therefore, it is important to predict the spatial distribution of concentrations considering effects from terrain and buildings.

Another issue related to atmospheric dispersion in a local-scale is the potential problem that hazardous and flammable materials are accidentally or intentionally released into the atmosphere, either within or close to populated urban areas. For the assessment of human health hazards from such toxic substances, the existence of high concentration peaks in a plume should be considered because it is the instantaneous, not average, concentration that is fatal to humans. In such a situation, it is necessary to accurately predict the unsteady behavior of a plume, considering the effects of individual buildings. For the safety analysis of flammable gases, certain critical threshold levels should be evaluated. Therefore, in such a situation, not only the average levels but also instantaneous magnitudes of concentration should be accurately predicted.

There are various methods for predicting plume dispersion in atmospheric boundary layers, e.g. wind tunnel experiments and Computational Fluid Dynamics (CFD). It is well known that wind tunnel experiments are a rational tool for predicting plume dispersion behavior under local topography and/or building conditions. For the case of accidental or intentional release of contaminated materials within urban areas, many studies using a wind tunnel have been made to investigate the spatial extent of contaminated areas and the characteristics of mean and fluctuating concentrations around an individual building. In the safety assessment for the construction of nuclear facilities, prediction of the spatial distribution of radionuclide concentrations over complex terrain containing buildings is required by using a wind tunnel (*Meteorological Guide for Safety Analysis of Nuclear Power* 

Large-Eddy Simulation of Turbulent Flow and

**2. Numerical model** 

and

expression;

the Navier-Stokes equation,

Plume Dispersion in a Spatially-DevelopingTurbulent Boundary Layer Flow 333

The governing equations for LES of atmospheric flow are the filtered continuity equation,

0 *<sup>i</sup> i u x*

*u f t x xx x x x* 

*ij uu uu <sup>i</sup> <sup>j</sup> <sup>i</sup> <sup>j</sup>*

 

<sup>2</sup> <sup>1</sup> <sup>2</sup>

where *ui, t, p, ρ, ν, τιj* and *fi* are the wind velocity, time, pressure, density, kinematic viscosity, subgrid-scale Reynolds stress and external force term, respectively. The subscript *i* stands for coordinates (1, streamwise; 2, spanwise; and 3, vertical direction). Over bars, (¯) denote application of the spatial filter. *δij, νSGS, Cs* and *fs* are the Kronecker delta, the eddy viscosity coefficient, the model constant of the flow field and Van Driest damping function (Van Driest., 1956), respectively. denotes the grid-filter width. In this LES model, the external force term proposed by Goldstein *et al*., (1993) is applied because of its computational stability for turbulent flow around a bluff body. The force term, *fi* is incorporated into the Navier-Stokes equation to consider the building effects and can be assumed as the following

1

( ) ( ), 0, 0

 

(7)

*t*

*j ij i j ij ji j*

1 *<sup>j</sup> i i <sup>i</sup>*

*u u p u u*

 

0

*ii i f u t dt u t*

 

where *α* and *β* are negative constants. The stability limit is given by <sup>2</sup> <sup>2</sup> *<sup>k</sup>*

where *k* is a constant of order 1. The most commonly used sub-grid scale models are the standard and dynamic type Smagorinsky models (Smagorinsky., 1963; Germano *et al*., 1991; Lilly *et al*., 1992; Meneveau *et al*., 1996). Although *Cs* should be estimated depending on the flow type, the standard Smagorinsky model (Smagorinsky., 1963) with the Van Driest damping function is used instead in our LES model because of its simplicity and low

*t*

computational cost. *Cs* is set to 0.12 (Shirasawa *et al*., 2008).

3

 

, (1)

, (2)

 

, (3)

<sup>1</sup> <sup>2</sup>

/ 2 *S ux u x ij i j j i* , (5)

<sup>3</sup> *xyz* , (6)

*ij ij kk SGS ij SGS s s ij ij S Cf SS* , (4)

*Plant Reactor*, Nuclear Safety Commission of Japan, 1982). Although reliable data can be obtained on air flow and plume dispersion, wind tunnel experiments are time consuming, costly, and have limited availability for these applications. For example, in the safety assessment, experimental results are only used to derive the effective stack height, which is applied for long term assessment using a Gaussian plume model, and the effective stack height is usually determined lower height than the actual height considering terrain and building effects in a way that provides a conservative evaluation. On the other hand, recently the CFD technique has been proposed for use as an alternative to wind tunnel experiments (Sada *et al*., 2009) developed a numerical model for atmospheric diffusion analysis and evaluation of effective dose for safety analysis and showed its effectiveness in comparison with wind tunnel experiments.

The CFD technique has been recognized as a helpful tool with the rapid development of computational technology. The CFD technique uses computers to numerically predict fluid flow, heat transfer and mass transfer by solving the governing equations. In particular, there are two different approaches, the Reynolds-Averaged Navier-Stokes (RANS) and Large-Eddy Simulation (LES) models, which are both effective for predicting turbulent flows. In RANS, a mean wind flow is computed, delivering an ensemble- or time-averaged solution, and all turbulent motions are modeled with a turbulence model. The main advantage of the RANS model is its efficiency in computing a mean flow field with relatively low computational cost. Sada *et al*., (2009) designed a practical numerical model based on the RANS model.

Recently, LES has come to be regarded as an effective prediction method for environmental flows. LES resolves the large-scale turbulent motions and models only the smallest scale motions, which are usually more universal. Although the LES model requires larger computational costs than RANS model, it is no less useful the latter, considering the cost and limited availability of wind tunnels and the experimental time needed. Furthermore, LES can provide accurate predictions and detailed information about turbulence structures, and mean and fluctuating concentrations of a plume as well as wind tunnel experiments can provide them. Therefore, we have developed an LES dispersion model applicable to actual problems of atmospheric dispersion on a local scale. As a first step, we previously performed LES for turbulent flows and plume dispersion over a flat terrain (Nakayama & Nagai, 2009). When compared to experimental results of Fackrell & Robins., (1982), it was shown that turbulence structures, the characteristic mean and r.m.s. (root mean square) concentrations, turbulent concentration flux and peak concentration over a flat terrain are successfully simulated. These findings implied that our LES model could replace wind tunnel experiments for safety assessments of nuclear facilities and also provide detailed information for the consequence assessment of accidental and intentional releases of radioactive materials into the atmosphere.

For the second step, we apply our LES dispersion model to the complex behaviors of separated shear layers and large eddies in the near-wake of a building. First, we propose a scheme to generate a spatially-developing turbulent boundary layer flow with strong velocity fluctuations, which is applicable to various types of wind tunnel flows and perform an LES of plume dispersion around an isolated cubical building. Then, we examine basic performance of the model and scheme by comparing LES data of the turbulent structure and characteristics of mean and r.m.s. concentrations including peak concentration with experimental data.
