## 4 Results and Discussion
### The Effects of the Material and Riblet on Cavitation-Induced Erosion Morphology  
Figure 4 compares the captured optical microscope images, maps, and three-dimensional topographies of the damaged surfaces, obtained using a confocal microscope. This comparison provides the necessary analysis to identify the effects of material and surface morphology on cavitation-induced erosion caused by multiple single bubble collapses. Figure 4 shows the relevant microscopic images of the eroded surfaces of Al and brass side by side to provide sufficient conditions for comparing erosion intensity. The color map depicted on the right of this figure shows the color contours for the maps and the three-dimensional topographies of the damaged surfaces, which can be observed in Figure 4c-f,i-1. The optical microscope images are also indicated in Figure 4a,b,g,h. Figures 4a and 4b shows the optical microscope images of the eroded Al and brass surfaces without riblets, respectively. Based on these photos, it can be concluded that the cavitation-induced damage shape caused by bubble collapse resembles a rounded cone. Generally, the cross-section of erosion is circular because the water hammer front wave, formed subsequent to the water jet and the complete collapse of the bubble, provides a semi-spherical shape, and its two-dimensional map is circular on the surface. Therefore, the initial eroded area mimics a circular shape. More information regarding water hammer formation subsequent to the water jet and the complete collapse of the bubble can be found in detail elsewhere [9; 17; 22; 28]. This research focuses only on the damage caused by the water hammer on the surface. Creating a single bubble at the same position and repeatedly collapsing it leads to deep erosion growth, ultimately resulting in an erosion shape that mimics a rounded cone with a circular cross-section. The intercomparison of erosion shapes for Al and brass with riblets in Figures 4g and 4h, respectively, reveals a similar erosion morphology to that of surfaces without riblets. However, the erosion occurs between two riblet lines due to the initial experimental setup, and it seems that the erosion area and depth are decreased in comparison to those of flat surfaces. The similar shape of erosion originates from the similar collapse characteristics of the water hammer and jet in the presence and absence of riblets. Because the bubble collapse dynamics, formed water jet, and water hammer near the flat and ribleted surfaces are similar, the erosion shapes on flat and ribleted surfaces resemble rounded cones, with circular cross-sections. In contrast, the lower erosion depth and area on ribleted surfaces result from the effects of riblets on the bubble collapse time and the momentum of the water hammer and jet. Riblets can decrease the bubble collapse time and reduce the momentum carried by the water jet and hammer [9; 17; 29], resulting in a lower erosion depth and area. Maps of the damaged surfaces without riblets for Al and brass are depicted in Figure 4c,d to provide more evidence of erosion morphology and depth. Based on these figures, the erosion area can be divided into five regions. The first region, with a semi-circular shape, which is well-known as the cross-section of a cone, shows a depth between 0 to 100 \(\upmu\)m. The second region, with a lower cross-sectional area and yellow color, indicates a depth of approximately 150 \(\upmu\)m. The third and fourth regions, in green and blue colors, correspond to depths of 200 \(\upmu\)m and 300 \(\upmu\)m, respectively. Finally, the fifth region, with a navy blue color and a depth of 330-450 \(\upmu\)m, identifies the approximate depth of the erosion. In the case of Al and brass with riblets, as shown in Figure 4i,j, it is clear that the morphology of the erosion is similar to that of flat surfaces. However, in the fifth region, the depth of the erosion decreases to 315-416 \(\upmu\)m.  
Figures 4e and 4f compare the three-dimensional topography of the damaged Al and brass surfaces without riblets, respectively.