Estimation of opening discharge coefficient of naturally ventilated dairy buildings by response surface methodology

Abstract

The discharge coefficient (Cd) is a characteristic parameter of an opening, which represents the effect of flow contraction and frictional losses when the flow goes across the opening. It is an important parameter for the ventilation rate determination when using the orifice equation method. The objectives of this study were to investigate the relationship between Cd and its potential influencing factors, i.e. opening ratio (r), building length to width ratio (α), wind speed (U), and wind direction (θ), and to evaluate the sensitivity of each factor on the Cd for naturally ventilated dairy buildings (NVDBs). The investigations were performed using the response surface methodology together with Box-Behnken Design and Computational Fluid Dynamics simulation methods. A second-order polynomial response surface model for the estimation of the discharge coefficient was developed and verified. The results showed that the Cd was significantly affected by the individual factors of r and θ, with more sensitivity to r when r > 42.5%. By contrast, the effects from the individual factors of α and U on Cd were insignificant. In addition, the interaction effects between r and θ, and between α and θ on Cd were also identified. It was concluded that the effects from both individual factors and interactions are required to be considered in the estimation of the opening discharge coefficient for NVDBs.