# PIV Measurements of Turbulent Airflow in a Channel with Trapezoidal Ribs on One Wall
## 3 Results and Discussion
### Average Values of Velocity Components  
The presented below average values of the velocity field are the result of averaging out 1200 instantaneous velocity fields. The spatial scale was divided by the height of the rib k = 0.002 m and the calculated velocity values by the average velocity over the rib U\({}_{\rm r}\) = 29 m/s. The results of the measurements were presented between two adjacent ribs within the height range from 0 to 4k.  
Figure 5 presents averaged streamlines. The flow detaching along the top edge of the rib forms a zone consisting of two minor vortices with identical rotation direction in the cavity. The center of the vortex is located at x/k = 1.9, y/k = 0.6 distance at the windward rib and at x/k = 3.9, y/k = 0.4 distance at the leeward rib.  
Figure 4: Distribution of the normalized streamwise velocity component: (**a**) and turbulence kinetic energy; (**b**) at distances x/H = 18.6, x/H = 20.6, x/H = 27.6, x/H = 41.6 and x/H = 49.6 from the first rib.  
Figure 6 presents scalar maps and profiles of streamwise U and transverse V velocity components at x/k distances equal to 0, 1, 2.5, 4 and 5. The profiles of the U velocity component obtained over the ribs at x/k = 0 and x/k = 5 are almost identical. Due to the presence of vortices in the cavity, the U component between the ribs has a negative value for x/k = 1 at the height y/k = 0.7, for x/k = 2.5 at the height y/k = 0.5 and for x/k = 4 at the height y/k = 0.35. The presence of the recirculation zone is also visible in the distribution of the V transverse component. A shearing layer and local acceleration occur over the rib.  
Figure 5: Average streamlines in the cavity.  
Figure 6: Average normalized U (**a**); and V (**b**) velocity components.  
Figures 7 and 8 present statistical values that accompany the turbulence, such as Reynolds stress and turbulence kinetic energy. The results in the direct vicinity of the edge carry a significant uncertainty. Figure 7 presents rms (root mean square) velocity values (U\({}_{\rm rms}\) and V\({}_{\rm rms}\)). Except at the top of the ribs, the maximum U\({}_{\rm rms}\) values occurred near the middle of the distance between the ribs at the height y/k = 1.2. Similar results were obtained through simulations by [PERSON] et al. [8] with the maximum U\({}_{\rm rms}\) value identified closer to the leeward rib. The maximum V\({}_{\rm rms}\) values were obtained for x/k equal to 3.2 at the height y/k = 0.75. The results of U\({}_{\rm rms}\) and V\({}_{\rm rms}\) components are qualitatively consistent with the results obtained by [PERSON] et al. [12].  
Figure 8 presents average, normalized, turbulent shear stress \(-\)u\({}^{\prime}\)v\({}^{\prime}\) and the turbulence kinetic energy (TKE). The shearing layer forming over the rough elements is clearly visible (the red area) on the outline of the \(-\)u\({}^{\prime}\)v\({}^{\prime}\) shear stress. The maximum values of turbulent shear stress were obtained at the x/k distance equal to 3.5. The zone of high values of turbulence kinetic energy overlaps to a large extent with high values of turbulent shear stress. Mass and momentum transfer occurs between the cavity and the zone present over the roughness, with the highest intensity for x/k ranging from 2 to 4.