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Thermal instability induced by solar radiation is the most common condition of urban atmosphere in daytime. Compared to researches under neutral conditions, only a few numerical works studied the unstable urban boundary layer and the effect of buoyancy force is unclear. In this paper, unstably stratified turbulent boundary layer flow over three-dimensional urban-like building arrays with ground heating is simulated. Large eddy simulation is applied to capture main turbulence structures and the effect of buoyancy force on turbulence can be investigated. Lagrangian dynamic subgrid scale model is used for complex flow together with a wall function, taking into account the large pressure gradient near buildings. The numerical model and method are verified with the results measured in wind tunnel experiment. The simulated results satisfy well with the experiment in mean velocity and temperature, as well as turbulent intensities. Mean flow structure inside canopy layer varies with thermal instability, while no large secondary vortex is observed. Turbulent intensities are enhanced, as buoyancy force contributes to the production of turbulent kinetic energy.

Global urbanization over the past decades has significantly changed the atmospheric environment of urban area. Urban environment problems caused by human activities arise and related researches become increasingly popular. Urban boundary layer (UBL) involves multiscale, multiphysics processes and thermal dynamics is one of the critical issues. Heterogeneous thermal distribution caused by solar radiation, anthropogenic heat, and building materials influences pedestrian comfort. Urban heat island [

Three-dimensional building arrays have been widely employed as models in studies of district-scale air flow and pollutant dispersion process. Compared with numerous experimental and numerical works on neutral flow over building arrays [

Numerical simulation provides a flexible and low-cost method for studies of urban atmospheric environment. So far, most of the numerical studies of thermal effect were conducted using Reynolds averaged Navier Stokes (RANS) simulation [

In this paper, a numerical model able to simulate thick boundary layer flow over three dimensional building arrays is established, which can be used in the study of the effect of buoyancy force on flow both within and above canopy layer. Large eddy simulation with dynamic subgrid scale model is employed. The mean flow and turbulence statistics presented in Uehara et al.’s experiment [

The aim of the present study is to simulate unstably stratified turbulent boundary layer flow over three-dimensional building array. Some researchers studying neutral turbulent flow over building arrays employ numerical models with shear-free and impermeable condition on the upper boundary and periodic condition in streamwise and spanwise directions [

Three-dimensional schematic of numerical model.

Configuration of the array considered in the present paper is the same as Uehara et al.’s scaled model [

Both neutral and thermally unstable cases are simulated to study the effect of buoyancy force. The free stream velocity ^{6}~10^{7}. It is difficult for laboratory experiment to reach such a high Reynolds number. In present paper Uehara et al.’s experiment is simulated, and investigation of real urban scale arrays is left for further studies.

Grid distribution is illustrated in Figure

Grid distribution in horizontal and vertical planes.

Horizontal plane

Vertical plane

For the filtered velocity

The subgrid scale stress and subgrid scale thermal flux are assumed to be in eddy viscosity and eddy diffusion form, which can be written as:

To take into account large pressure gradient induced by separation flow behind bluff bodies, wall function proposed by Wang and Moin [

Consider

Consider

Finite volume method (FVM) [

Cheng and Liu [

Uehara et al. measured mean flow at the center of the canyon where depth of boundary layer is about 7 times of the building height. In Figure

Vertical profiles of mean streamwise velocity normalized with free stream velocity

Neutral

Unstable

For both neutral and unstable cases, our LES results are in fine agreement with the experiment and slightly better than CLES both within and above canopy layer. Flow speed is reduced within the canopy and strong shear layer is observed at roof level for both thermal conditions. Difference between two conditions can be observed. Buoyancy force enhances vertical convection and high momentum fluid in the out flow is transferred to roof level, which results in stronger roof level shear layer in unstable case as seen in Figure

Spatial distribution of mean flow structure can be better viewed in Figure

Normalized velocity vector

Neutral

Unstable

Vertical profiles of root mean square of velocity fluctuation

Vertical profiles of streamwise turbulence intensity

Neutral

Unstable

Large gradient of

Figure

Contours of streamwise turbulence intensity

Neutral

Unstable

Similarly, rms of vertical velocity fluctuation

Vertical profiles of vertical turbulence intensity

Neutral

Unstable

Contours of vertical turbulence intensity

Neutral

Unstable

Turbulent kinetic energy

Distributions of temperature and heat flux are discussed in this subsection. Since CLES cannot provide mean temperature and temperature fluctuation, present LES results and measured results are compared in Figure

Contours of turbulence kinetic energy normalized with free stream velocity

Neutral

Unstable

Vertical profiles of mean temperature and turbulent intensity for temperature

Mean temperature

Temperature fluctuation

Contours of normalized mean temperature

Contours of normalized mean temperature

Temperature

Heat flux

Turbulent heat flux, which is in the form of second-order moment of velocity and temperature fluctuation

In this paper, flow field both within and above three dimensional array is investigated with large eddy simulation. Thermal instability is induced by ground heating and buoyancy force is taken into account using Boussinesq hypothesis. Subgrid scale model and wall function employed are suitable for heterogeneous flow with separation behind buildings. Both neutral and unstable cases are simulated to explore the effect of buoyancy force. Overall, the simulated results shows fine agreement with the experiment in both mean flow and turbulent intensities, and perform better than former LES study. Our numerical model is suitable for further studies of more complex flow cases.

It is shown that buoyancy force changes pattern of mean flow inside canopy layer while no secondary reverse circulation is observed, which coincides with wind tunnel experiment and field measurement. The effect of buoyancy force is overestimated by RANS simulations and LES is a better choice for unstably stratified turbulent flow. Moreover, buoyancy force contributes to the production of turbulent kinetic energy, and turbulent intensities are enhanced, especially the vertical component.

Thermal dynamics of high Reynolds number flow over urban-scale buildings with heterogeneous temperature distribution induced by solar radiation, shading, or nonuniform building layout, will be investigated in further studies.

The authors declare that there is no conflict of interests regarding the publication of this paper.

The authors thank the National Natural Science Foundation of China (Grants 11132005, 10925210, and 11002081), MOST-2011BAK07B01-03, and the National Laboratory for Information Science and Technology for the financial support.