Abstracts:Time-average velocity distribution in steady and uniform channel flows is important for fundamental research and practical application as it is always three-dimensional (3D), regardless of channel geometry. However, its determination has predominantly been carried out by using complex numerical software, even for the simplest geometry such as rectangular channels. The log-law was developed initially for circular pipe flows, where a single shear velocity is used to normalize the velocity (u⁺) and its distance (y⁺). Tracy and Lester found that the performance of the log-law can be extended to express velocity profiles in rectangular channels when the global shear velocities (gRS)^0.5 and (ghS)^0.5 are used to normalize the measured velocity u and its distance y. This study extends this discovery from the channel central line to the corner regions, and its general form of log-law was found to be valid even in trapezoidal or triangular open channels or closed ducts. This modified log-law can produce good agreement with the measured velocity with an average error of less than 5%. Therefore, this study provides a simple and reliable tool for engineers and researchers to estimate the velocity contours in straight and smooth channel flows.

Abstracts:A series of experiments were conducted to investigate the effect of the inclination angle of the cylinders on the wake flow characteristics for flow past two and three side-by-side inclined cylinders using the particle image velocimetry (PIV). Depending on the inclination angles, purely deflected gap flow, no-deflection gap flow, and flip-flop gap flow patterns are identified for both two and three cylinder cases. In both two and three cylinder cases, the flows through the gaps are found to be in purely deflected flow pattern at small inclination angles and flip-flop pattern at large inclination angles. For the three-cylinder case with flip-flop gap flow pattern, gap flows are predominantly in the outward deflection pattern (toward the two side cylinders) and are occasionally deflected inward (toward the middle cylinder). The gap flow deflection angles for all the tested inclination angles of the cylinders are quantified through statistical analysis, in addition to identifying the flow patterns. The deflection angle is found to decrease with increasing inclination angle for both two- and three-cylinder cases, and the outward deflection angle for the three cylinder cases is greater than the deflection angle of the two-cylinder case. The probability density distributions of the deflection angles approximately follow normal distribution. In the two-cylinder case, the mean flow field is asymmetrical about the x-axis when the possibility of the flow deflection toward one side of the gap is greater than that toward the other side.