## 3 Results and Discussion
### Airflow Rate  
The airflow rate per m\({}^{2}\) floor area (\(Q_{f}\)) was calculated using the ventilation rate divided by the area of the building. The \(Q_{f}\) of the NVD building increased with the increase of the external air velocity. Compared with the SM opening combination, the \(Q_{f}\) was 1.92, 1.57, 2.39, 2.41, 2.01, 1.66, and 2.45 times higher in SMT, SMB, SWC, SWFD, SWTD, SMBD, and SWCD opening combinations, respectively. Larger openings resulted in higher \(Q_{f}\) than smaller openings (Figure 12), which is in line with the study of [PERSON] et al. [22]. The \(Q_{f}\) of SMT is greater than SMB even though they have the same opening areas. However, the opening location of SMT is higher than SMB, which has larger air  
Figure 11: Effects of different opening combinations on air velocities in different locations away from the windward side at the middle of the barn (**a**) at the cow height and (**b**) close to the emission surface. R—Cov resting area, W—Cov walking area and FA—Feeding alley.  
velocities through the windward opening and thus a higher \(Q_{f}\). Door openings in gable walls also had some influences on the \(Q_{f}\) even though the wind direction was perpendicular to sidewall openings. For example, the \(Q_{f}\) of SWFD is 0.8% higher than SWC, which is caused by the door opening in the feeding alley. The \(Q_{f}\) of SWCD is 2.5% higher than SWC when all doors were open. The highest \(Q_{f}\) was obtained in SWCD case where generally the highest air velocities occurred at the animal height and near the emitting surface.  
Figure 13 shows the non-dimensional ventilation rate (\(Q^{*}\)) through different openings in different cases. The highest ventilation occurred through the windward sidewall opening, followed by the leeward opening in all cases. The roof opening and doors contributed to only a small part of the ventilation rate compared with sidewall openings. The perpendicular wind direction is the main reason for this phenomenon. The \(Q^{*}\) through the windward sidewall opening in SMT and SMTD opening configurations were obviously higher than the rest cases. It was partly caused by the boundary layer wind profile with higher air velocities occurring at a higher altitude.  
Figure 12: Airflow rate per unit floor area in different opening combinations.  
Figure 13: Non-dimensional airflow rate (\(Q^{*}\)) at the different openings of NVD building for (**a**) Case 1 to Case 8 with same reference velocity \(U_{ref}\) = 4.41 m\(\cdot\)s\({}^{-1}\) and (**b**) Case 9 to Case 18 for different inlet velocity (\(U\)) 1 to 10 m\(\cdot\)s\({}^{-1}\); where SO_WW—Side wall opening in windward side, SO_LW—Sidewall opening at leeward side, RO—Roof opening, DOF—Doors opening in the front gable wall, DOB—Doors opening in the back gable wall, FOF—Feeding alley opening in the front gable wall, and FOB—Feeding alley opening in the back gable wall. \(U\) value in the legend indicates inlet velocity in m\(\cdot\)s\({}^{-1}\).  
The presence of the bottom sidewall was another possible reason since it guided the air flow upwards which increased the air velocities through the windward opening. The results indicated that the control of the ventilation rate mainly depends on the control of sidewall openings, while the effects from the ridge opening and doors are minimal in the perpendicular wind direction and wind-driven ventilation conditions. In addition, it was found that when the inlet air velocity increased over 6 m\(\cdot\)s\({}^{-1}\), the \(Q^{*}\) through the leeward opening increased dramatically. Under this circumstance, the airflows tended to leave the building via the leeward opening than via the roof opening.