Modified ‘closure’ constants of the Standard k–ε turbulence model for the prediction of wind-induced natural ventilation

Abstract

In this study, wind-driven natural ventilation in buildings is investigated by means of computational fluid dynamics. The airflow in and around three pilot buildings, which correspond to the most common natural-ventilation designs, i.e. cross-, windward-and leeward-single-sided ventilation, is simulated by applying both the Standard and a modified k-" turbulence model. The latter represents a Prandtl number-modified version of the Standard k-" model, based on the flow-variable (velocity and turbulence variables) distributions and on the atmospheric boundary layer (ABL) assumptions. Numerical results of streamwise and vertical velocity components, as well as of pressure coefficients at the facades, obtained by both turbulence models are compared with available wind tunnel experimental data found in literature. It is concluded that both models applied are in acceptable agreement with measurements, especially for the mean streamwise velocity component, while the proposed modified model is more accurate as far as flow within the windward and the internal parts (i.e. within the building) of the domain is concerned. Practical application: This study focuses on the development of a modified k-" turbulence model for the prediction of wind-driven natural ventilation. The analysis described represents a methodology to produce 'closure' parameters, such as Prandtl numbers, compatible with the incoming wind characteristics (ABL). It was found that for all ventilation cases studied, i.e. cross-and single-sided ventilation, the proposed modified model is more accurate compared with the Standard k-" model, and it accounts for the dumping effect near the walls and for kinetic energy reduction in the impinging region adequately. It is satisfying that the modified k-" model leads to acceptable engineering results within relatively practical computer resources. NomenclatureA Cintegration constants C 1 , C 2 , C empirical constants in k and " equations H b building height (m) k turbulence kinetic energy (m 2 =s 2 ) k f free-stream kinetic energy (m 2 =s 2 ) NEL total number of experimental locations n ! normal-to-surface vector P pressure (Pa) P H b pressure value at the building height (Pa) P k kinetic-energy production rate (Pa=s) Downloaded from RMSE root-mean-squared error RMSE weighted-average value of RMSE RMSE pos RMSE value along the vertical origin located at the position pos S mean rate of strain S " dissipation-rate source term S k kinetic-energy source term S ' source term in the conservation equation u velocity magnitude (m=s) u ! velocity vector u 0 fluctuating velocity (m=s) u à friction-velocity magnitude (m=s) u H b wind speed at the building height (m=s) u i velocity component in i direction (m=s) u j velocity component in j direction (m=s) u x , u y , u z velocity components in Cartesian coordinates (m=s) u ref reference velocity (m=s) w pos1 À w pos10 interest factors (weights) participating in the RMSE equation x i spatial component in i direction x j spatial component in j direction y þ dimensionless distance o...

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