Experimental Investigation of the Effect of Surface Roughness on the Shape and Region of Stability of Polygonal Hydraulic Jumps

The size and number of corners of a polygonal hydraulic jump depend on various parameters, including the fluid flow rate, the jet diameter, the obstacle height, and the physical properties of fluid. In other words, the size and shape of the polygonal hydraulic jump depend on the Reynolds number, the Weber number, and the Bond numbers. This study investigates the effect of the surface roughness on the shape and region of stability of polygonal hydraulic jumps. Sandpapers of different degrees of roughness are glued on the surface of the target plate to make it rough. The study reveals that, in addition to the Reynolds and Weber dimensionless numbers, the surface roughness of the target plate affects the stability of polygonal hydraulic jump. Based on the conditions of this study, including the thin-film flow, surface roughness leads to flow slip on the surface and, consequently, leads to a higher mean velocity and flow momentum. This study demonstrates that, in general, at given values of the Reynolds and Weber numbers, a rougher surface leads to a greater number of corners in the polygonal hydraulic jump. Furthermore, the rougher the surface, the smaller the extent of the region of stability of polygonal hydraulic jumps. At last, the Taguchi method is used to derive relations for estimating the number of corners of polygonal hydraulic jumps with respect to the jet diameter, the flow rate, the height of downstream obstacle, and the roughness of the target plate for both modes of increasing and decreasing flow rates.