*3.5. Shear Stress Distribution*

Shear stress is caused by viscous friction on the wall, which represents the spatial variation rate of the relative velocity near the wall. It is also the main cause of viscous dissipation and power loss. The study of the distribution of shear stress provides a guiding value for further optimization design. Figure 12 shows the distribution of the shear stress on the impeller walls for Q = 13 m3/h. Figure 12a shows that the shear stress on the suction sides of blades was greater than that on the pressure sides, which is consistent with the results that the relative velocity on suction sides was greater than that on the pressure side, as shown in Figures 8 and 9, where relatively large shear stress at the outlet of the

pressure surface existed locally. Figure 12b,c shows that the distribution of shear stress around different blades along the circumferential direction was generally similar, and the location of a larger shear stress distribution around the front and rear cover plates was generally consistent, which indirectly indicated that the three-dimensional characteristics of flow in the low specific speed impeller were not obvious. However, the shear stress on the front cover was slightly larger than that on the back cover.

**Figure 12.** Shear stress distribution on the impeller wall, Q = 13 m3/h.

#### *3.6. Turbulent Kinetic Energy*

The turbulent kinetic energy is related to the velocity fluctuation and turbulent dissipation, and it is a measure of the intensity of turbulence. Usually, the turbulent kinetic energy is estimated from the formula, *k* = 3(*u* · *I*) 2 /2, where *u* is the average velocity and *I* the intensity of turbulence. The larger the average velocity and intensity of turbulence are, the larger the turbulent kinetic energy is.

Figure 13 shows the turbulent kinetic energy distribution of profiles on blade I. In the range of radii from 25 mm to 30 mm, the amplitude of the turbulent kinetic energy was small, especially at a relatively low level on the pressure side. Affected by the rotor–static transition, the turbulent kinetic energy rose sharply at the outlet of the blade on pressure side, and the larger the flow rate was, the greater the turbulent kinetic energy on the pressure side was. The turbulent kinetic energy on the suction side was generally larger than that on the pressure side, and the larger the flow rate was, the larger the turbulent kinetic energy on the suction side was. The closer the profile was to the blade surface on the pressure side, the smaller the turbulent kinetic energy was; on the contrary, the closer the profile was to the blade surface on the suction side, the greater the turbulent kinetic energy was.

**Figure 13.** Turbulent kinetic energy distributions.
