*3.3. Relative Velocity Distribution Near the Wall of Blade*

In order to analyze the near wall flow on the blade surfaces, the velocity vectors of the near-wall flow were projected onto the profiles of lpI-0.5, lpI-2, lsI-0.5, and lsI-2. The relative velocity was recorded as *W* and *W* = (*u*, *v*) · (cos α, cos β), where (*u*, *v*) is the velocity vector near the wall and (cos α, cos β) the directional derivative of the profiles. The direction from the blade inlet to the outlet was positive, and if there was a negative value, then there was countercurrent near the wall.

Figure 9 shows the relative velocity distributions of profiles at the distance of 0.5 mm from blades with Q = 13 m3/h, where the relative velocity of profiles at the distance of 0.5 mm from blade I is shown with a black solid line on the pressure side and with a black dotted line on the suction side, and the other relative velocity of profiles of blades II, III, IV, and V are shown with their respective colorful lines. The relative velocity distributions of the five blades were almost the same. The relative velocity on the pressure side was greater than that on the suction side in the range of radii from 20 mm to 68 mm, because the near-wall flow at the radius of 73 mm on the pressure side was the inner flow of the volute, the near-wall flow at the radius of 73 mm on the suction side was still in the blade channel 5, and the relative velocity on the pressure side was greater than that on the suction side. The relative velocity on the pressure side and suction side of blade I was slightly lower than that of other blades. Within the radius of 40 mm to 50 mm, the relative velocity on the pressure side appeared negative, which suggests the existence of a countercurrent. There was positive flow, deceleration flow, and acceleration flow, in turn, on the pressure sides. There was a maximum relative velocity in the range of radii from 30 mm to 40 mm in the inlet area on the suction side, and the relative velocity suddenly decreased in the range of radii from 40 mm to 50 mm.

**Figure 9.** Relative velocity distributions of profiles at the distance of 0.5 mm with Q = 13 m3/h.

Figure 10 shows the relative velocity distributions of profiles under different flow rates of blade I. Except at the outlet on the blade pressure side, the relative velocity on the suction side was larger than that on the pressure side in most areas. For Q = 7 m3/h, the relative velocity on the pressure side was positive as a whole. In the range of radii from 20 mm to 35 mm, the relative velocity of profiles lpI-0.5 and lpI-2 on the pressure side had a certain difference. When the radius was greater than 35 mm, the velocity difference was very small. In the range of radii from 20 mm to 32 mm, the relative velocity on the suction side was obviously greater than that on the pressure side, and for the radius of 32 mm, the relative velocity on the pressure side dropped suddenly to below that on the suction side and then rose slowly.

**Figure 10.** Relative velocity distributions of profiles with different flow rates.

For Q = 13 m3/h, the relative velocity on the suction side and the pressure side showed an obvious difference, and the relative velocity on the suction side was generally positive. In the range of radii from 35 mm to 55 mm, the relative velocity of profiles lpI-0.5 and lpI-2 showed some differences. In the range of radii from 40 mm to 50 mm, there was an extent of negative relative velocity of the profiles on the pressure side where the countercurrent zone existed. When the radius was greater than 55 mm, the relative velocity on the pressure side rose rapidly, and in the area near the outlet of the blade, the relative velocity amplitude on the pressure side rose rapidly to the same order as that on the suction side.

The difference between the relative velocity on the suction side and the pressure side when Q = 20 m3/h was larger than that when Q = 13 m3/h, and the maximum relative velocity on the suction side was close to 13 m/s when Q = 20 m3/h. Within the range of radii from 30 mm to 55 mm, there was a certain difference between the relative velocity of profiles lpI-0.5 and lpI-2 on the suction side. Within the range of radii from 40 mm to 50 mm, there was an extent of negative relative velocity of the profiles on the pressure side, and when the radius was greater than 55 mm, the relative velocity on the pressure side rose rapidly. In the region near the blade outlet, the relative velocity amplitude on the pressure side rose rapidly to even larger than that on the suction side. It was also found by Wang et al. that there is a clockwise relative flow vortex in the flow channel of a low specific speed impeller with counterclockwise rotation, thus a positive relative velocity forms on the suction surface of blades, and a negative relative velocity may form on the pressure surface of the blades, and the center of the vortex is about one third of the position from the inlet to the outlet of the blades [13].
