Large-Eddy Simulation of Efficiency of Momentum Transport in Spatially Developing Urban Boundary Layer

1. Introduction

    Urban heat island phenomena and air pollution have become serious issues in urban spaces. To arrive at solutions to these problems, it is necessary to predict the urban climate accurately. However, the presently used numerical models for predicting the urban climate are not sufficiently accurate at the micro scale and meso scale. To improve the prediction accuracy of these models, it is necessary to investigate the contribution to transport and the mechanism of transport of turbulent structures in the flow fields of urban spaces and model transport of turbulent structures in the flow fields of urban spaces. The Reynolds Averaged Navier-Stokes Simulation (RANS), which facilitates the analysis of the average flow fields, is widely used to predict the flow fields for buildings and city blocks in urban spaces. However, turbulent structures in the flow fields of urban spaces affect the accuracy of RANS. A few studies have been conducted on the developing process of turbulent structures and the accuracy of RANS in the spatially developing urban boundary layer. It is necessary to investigate these topics using detailed data of the flow fields of urban spaces, obtained via Large-Eddy Simulations (LES).

2. Method

    Fig. 1 illustrates the urban model considered in this study. This model is set up with consideration of the wind tunnel experiment conducted by Uehara et al. (2000). Cubic building model blocks with dimensions of HxHxH (H = 100 mm) are arranged streamwise at H intervals and spanwise at 0.5H intervals. On the upwind side of the building model blocks, roughness blocks with dimensions of HxHx0.5H are arranged in a staggered configuration at H intervals streamwise as well as spanwise. In this study, to investigate the urban boundary layer with spatial development, the centers of the urban canyons in the fifth row (Point1), fifteenth row (Point2), and thirtieth row (Point3) are investigated. The numerical analysis is performed using OpenFOAM, an open source computational fluid dynamics analysis software. The subgrid scale model of the LES is a standard Smagorinsky model. The Smagorinsky constant (C_s) is 0.12. Table 1 lists the conditions of the numerical analysis and the boundary conditions in detail.

3. Result

3.1 The statistics of the flow field

    Fig. 2 shows the results of the LES for each point on the model. With the spatial development of the urban boundary layer, the gradient of the streamwise mean wind velocity reduces, which results in the reduction of the turbulent kinetic energy and the Reynolds stress.

3.2 Turbulent correlation coefficient of the momentum transport

    The turbulent correlation coefficient of the momentum transport, which is expressed by equation (1), is used to investigate the efficiency of the momentum transport in the spatially developing urban boundary layer. Fig. 3 shows the turbulent correlation coefficient of each point on the model. The efficiency of the momentum transport is found to not be affected by the spatial development of the urban boundary layer, however, for every point on the model, the efficiency of the momentum transport is the largest at the top of the urban canopy (z/H = 1.0). The efficiency of the momentum transport increases with the height except for the top of the urban canopy.

3.3 Evaluation of RANS accuracy

    To investigate the accuracy of RANS, the constant Cµ, which is used in the eddy diffusivity coefficient for momentum in the k-ƒÃ model, is evaluated. The constant Cµ indicates the efficiency of the momentum transport. The eddy diffusivity coefficient for momentum ƒË_t is expressed by equation (2), Cµ is expressed by equation (3). In the k-ƒÃ model, Cµ is 0.09. Fig. 4 shows the value of Cµ, calculated from the results of LES for each point on the model. At all the points on the model, Cµ reduces to less than 0.09 as the height increases from z/H = 1.0 to z/H = 2.5. The accuracy of the k-ƒÃ model decreases in the spatially developing urban boundary layer. Eddy diffusivity approximation, the eddy diffusivity coefficient for momentum, and local equilibrium are assumed to derive the equation (3). It is necessary to investigate the accuracies of these assumptions hereafter.

4. Conclusion

    LES is performed to investigate the efficiency of the momentum transport and evaluate the accuracy of RANS in a spatially developing urban boundary layer. The efficiency of the momentum transport is the largest at the top of the urban canopy and is found to increase with height, except for the top of the urban canopy. The constant Cµ, which is calculated from the results of LES, reduces to less than 0.09 as the height increases from z/H = 1.0 to z/H = 2.5. The accuracy of the k-ƒÃ model decreases in the spatially developing urban boundary layer.

                       (1)

                                (2)

                    (3)