Numerical research on cross-ventilation flow of a generic building in unsheltered and sheltered conditions impact of cross-section

. The performances of ventilation in the buildings with quadrate and cylindrical cross-sections are compared numerically. The incoming jet in the cylindrical unsheltered-building is more horizontal in comparison to the quadrate unsheltered-building. The dimensionless volume flow rates in the quadrate and cylindrical unsheltered-buildings are respectively 0.503 and 0.553. The incoming jet in the sheltered-buildings flows to the floors immediately. The velocity near the floor in the cylindrical sheltered-building is greater than that in the quadrate sheltered-building. The dimensionless volume flow rates in the quadrate and cylindrical sheltered-buildings are respectively 0.130 and 0.210.Comparing with the quadrate buildings, the ventilation rates in the cylindrical unsheltered and sheltered buildings increased by 10% and 61%.


Introduction
Cross-ventilation driven by wind pressure difference is an important ventilation method since it can provide a fast and effective way to remove large amounts of pollutants and internal heat from a building [1][2]. This is good for air-quality improvement and building energy reduction. The rate of the ventilation is the key factor in designing the cross-ventilation [3][4]. The ventilation rate of a building depends on the size and the position of the windows, the building roof and the airflow conditions around the building and so on [5][6][7]. The cross-section of the buildings influences the airflow around buildings significantly. However, the effects of the cross-section of the buildings on the crossventilation are rarely studied. In this paper, numerical study on the cross-ventilation flow of a generic cylindrical building in unsheltered and sheltered conditions is conducted.
An efficient hybrid turbulence numerical method based on the production-limited eddy simulation (PLES) proposed by us in the previous paper [8] is applied. The buildings are located within the atmospheric boundary layer.

Description of study cases
For analysing the cross-ventilation flow of a generic cylindrical building in unsheltered and sheltered conditions shown in Figs. 1 and 2, the results of the wind tunnel experiments conducted by Tominaga and Blocken [9] and Shirzadi et al. [10] are chosen as the referred for validation. Two conditions including a generic building unsheltered and sheltered shown in Fig.   1 are considered. The sheltered condition is the situation that the target building is surrounded with eight similar buildings without opening, which are arranged in a regular configuration with a planar area ratio of 0.25 displayed in Fig.1-(b). The wind speed at the unsheltered and the sheltered buildings` height were measured to be 4.3m/s [9] and 5.2m/s [10], yielding Reynolds numbers about 45 000 and 54 000.   The air is incompressible and Newtonian fluid. The continuity and momentum governing equations can be written in the Cartesian tensor form as follows.
(2) where ui and uj are the velocity components, ρ and p are the density and the pressure respectively, μ is the dynamic viscosity, and τij represents the Reynolds stresses . The overbar means ensemble-averaged. The underlying RANS model of the PLES model is the SST k-ω model [11], which works as the original kω model within the inner boundary layer and the standard k-ε model in the outer region. The modelled transport equations of the turbulence kinetic energy k and the specific dissipation rate ω are as follows.
The production term Pk is calculated as below.
The turbulent viscosity μt has the formula as follows.
The blending function F1 and F2, turbulent Prandtl numbers σk, σω, and model constants α, β are the same as those in the Ref. [11].

PLES model
In the PLES model, the production term of the k equation is substituted by the below formula.
where the shielding function fd is shown as follows. The wall-adapting local eddy-viscosity (WALE) model [12] is applied as the SGS eddy viscosity in the PLES model. The WALE turbulent viscosity is calculated by the equations (10-12).
where V is the cell volume.

Boundary conditions
The velocity and turbulent kinetic energy of the inlet boundary condition are the same as the wind tunnel experiments. The turbulence dissipation rate ε and the specific dissipation rate ω are calculated by below equations.
The symmetry boundary condition is set at the lateral and upper walls. The outflow boundary condition is used at the outlet. The building and ground surfaces are set to the wall boundary condition. The random 2D vortexes are generated on the plane away x/b=0.5 (b is the length of the side wall) from the inlet where modelled turbulence kinetic energy is converted into resolved energy using the vortex method [13].   Then, the performances of ventilation in the buildings with quadrate and cylindrical cross-sections are compared numerically. Figs. 5 and 6 give the profiles of the mean streamwise velocity for the quadrate and cylindrical unsheltered-buildings and shelteredbuildings respectively. The incoming jet in the centre of the cylindrical unsheltered-building is more horizontal in comparison to the quadrate unsheltered-building. And the mean streamwise velocity is gearter in the center of the cylindrical unsheltered-building, but smaller over the floor. The dimensionless volume flow rates in the quadrate and cylindrical unsheltered-buildings are respectively 0.503 and 0.553.

Model validation
The incoming jets in the sheltered-buildings flow to the floors immediately. The velocity near the floor in the cylindrical sheltered-building is greater than that in the quadrate sheltered-building. The dimensionless volume flow rates in the quadrate and cylindrical shelteredbuildings are respectively 0.130 and 0.210.   In summary, comparing with the quadrate buildings, the ventilation rates in the cylindrical unsheltered and sheltered buildings increased by 10% and 61%.
The performances of ventilation in the buildings with quadrate and cylindrical cross-sections are compared numerically. The incoming jet in the cylindrical unsheltered-building is more horizontal in comparison to the quadrate unsheltered-building. The mean streamwise velocity is gearter in the center of the cylindrical unsheltered-building. The dimensionless volume flow rates in the quadrate and cylindrical unsheltered-buildings are respectively 0.503 and 0.553.
The incoming jet in the sheltered-buildings flows to the floors immediately. The velocity near the floor in the cylindrical sheltered-building is greater than that in the quadrate sheltered-building. The dimensionless volume flow rates in the quadrate and cylindrical shelteredbuildings are respectively 0.130 and 0.210.
Comparing with the quadrate buildings, the ventilation rates in the cylindrical unsheltered and sheltered buildings increased by 10% and 61%.