Diurnal variations of temperatures in the building walls and their effects on air flows around buildings

HOTMAC is a three-dimensional mesoscale model based on the Mellor-Yamada Level 2.5 second-moment turbulence-closure equations. We recently combined HOTMAC with CFD (Computational Fluid Dynamics) capabilities so that the terrain and building scale effects on air flows are seamlessly integrated by using a two-way nested grid algorithm.

Five primitive equations were solved for ensemble averaged variables: three wind components, potential temperature, and mixing ratio of water vapor. In addition, two primitive equations were solved for turbulence: one for turbulence kinetic energy and the other for a turbulence length scale.

Pressure variations are caused by the changes in wind speeds, and the resulted pressure gradients subsequently affect wind distributions. We adopted the HSMAC (Highly Simplified Marker and Cell) method for pressure computation because the method is simple yet efficient. The method is equivalent to solving a Poisson equation, which is commonly used in non-hydrostatic atmospheric models.

RAPTAD is a three-dimensional transport and diffusion model based on a Lagrangian random puff algorithm. RAPTAD uses wind and turbulence distributions predicted by HOTMAC.

The HOTMAC/RAPTAD modeling system can simulate air flows and transport and diffusion of airborne materials in wind tunnel and atmosphere. We successfully simulated separation, recirculation, and reattachment of air flows around model buildings placed in a wind tunnel.

In atmospheric applications, diurnal variations of temperatures in the building walls were computed by solving a heat conduction equation. The boundary conditions were the heat energy balance at the outer wall surfaces and room temperatures specified at the inner wall surfaces.

Two inner domains were nested in a large domain. The first domain was 6560 m x 8960 m with horizontal grid spacing of 160 m. The second domain was 1280 m x 1440 m with horizontal grid spacing of 40 m and the third domain was 360 m x 400 m with horizontal grid spacing of 10 m.

Domain 1 included topographic features such as the ocean, coastal area, plains, and hills. Domain 2 was a transition area between Domain 1 and Domain 3. Buildings were located in Domain 3.

Radiative heating and cooling of the building walls greatly influenced air flows around buildings, resulting in circulations that are quite different from those modeled without thermal effects of buildings. The results are presented visually by using animations.