# PIV Measurements of Turbulent Airflow in a Channel with Trapezoidal Ribs on One Wall
###### Abstract  
This paper presents the results of PIV measurements of turbulent airflow in a channel with a single ribbed wall. The rough elements had the form of evenly spaced trapezoids. The ratio of the height of a single rib to the height of the measurement channel was 0.1. The ratio of the distance between adjacent ribs to the height of a single rib (i.e., the w/k ratio) was 5, which suggests a transitional region within the airflow structure between the d- and k- types. The measurements were carried out for the inlet velocity, at which the Reynolds number (Re) was equal to 32,500. The distance to the first rib, at which the turbulent velocity profile is fully developed, was determined. The distribution of the average velocity components, the velocity fluctuation components, turbulent shear stress, as well as the turbulence kinetic energy between two adjacent ribs was presented. The analysis of average streamlines indicated the existence of two vortex structures between the ribs. turbulent flow; trapezoidal ribs; PIV; surface roughness +
Footnote †: journal: Physics Letters B  
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phenomena as recirculation, detachment, and reattachment of the stream, the range of which only depended on the Re number to a minor extent. [PERSON] et al. [10] performed PIV measurements in a ribbed channel for Re = 22,000. The flow structure near the rib was identified. A probability density function (PDF) analysis of velocity fluctuation was carried out, which demonstrated the existence of two modes in the shearing layer. Additionally, the vortex topology was determined. [PERSON] et al. [11] performed numerical calculations using the direct numerical simulation (DNS) method in a channel with a single ribbed wall (with square-shaped ribs). Simulations were conducted for the conditions of a fully developed turbulent flow for the 8800-20,800 Re number range. Analyses were carried out for Re = 8800. The authors analyzed the w/k ratio in several configurations from 0.33 to 19. Two vortices with the opposite rotation direction appeared in the cavity between the ribs for the w/k ratio below 4. When the w/k ratio was equal to or greater than 7, the flow was reattached on the bottom wall. The problem of turbulent flow near square rough elements was examined by [PERSON] et al. in [12]. The authors performed numerical calculations using the LES method for two flow regimes: of the k-type (w/k = 9) and a transitional one between the d- and the k-type (w/k = 4.5). They observed differences in the flow structure between the two regimes despite the fact that in both regimes water flowed into and out of the cavity between the ribs, and despite the fact that there was a recirculation zone present in the cavity. The calculations performed using the LES method yielded similar results to the measurements carried out by [PERSON] et al. [7] as well as the numerical calculations performed using the DNS method by [PERSON] et al. [11]. Square-shaped ribs are the most common rough elements described in the literature. However, the problem of flow in a channel with a trapezoidal rib has only been described in a few studies. Using the PIV and liquid crystal thermography (LCT) methods, [PERSON] et al. [13] determined the effect the acute angle of the right-angled trapezoid on the flow structure and the distribution of heat downstream the rib for four Reynolds numbers within the 9400-61,480 range. For Re = 9400, the range of the recirculation zone is independent of the angle. For the remaining Re numbers, the recirculation zone increases in size with the increase in the angle of the trapezoid. In their publication, [PERSON] and [PERSON] [5] presented the results of measurements and numerical simulations of an airflow near a side wall of a mining longwall working with supports, the elements of which resembled trapezoidal ribs.