# Analysis of Cyclone Spinning Effect with Different Guide Vane Heights
## 4 Analysis of Cyclone Spinning Effect
### Rotational Kinetic Energy  
The spiral flow generated by the cyclone is rotated around the axis of the tube. If the density of a homogeneous liquid is \(\rho\), the flow rate of the fluid passing through the tiny section \(dA\) is \(dQ\), and if the circumferential velocity of the fluid rotating relative to the axis of the pipe is \(u_{t}\), then the rotational kinetic energy \(E_{t}\) for the flow through the water section per unit time can be expressed as follows:  
\[E_{t}=\int\limits_{Q}\frac{1}{2}\rho u_{t}^{2}dQ=\int\limits_{A}\frac{1}{2} \rho u_{t}^{2}.u_{a}dA \tag{7}\]  
where \(E_{t}\) is the rotational kinetic energy value of the water flow passing through the water section along the way in the process of generating spiral flow in the cyclone, in J/s, as shown in Figure 8.  
Figure 8: Rotational kinetic energy \(E_{t}\) of water flowing through the cross-section inside the cyclone with different guide vane heights. (**a**) Re = 105,419; (**b**) Re = 140,559; (**c**) Re = 175,699; (**d**) Re = 210,838.  
As can be seen from Figure 8, (1) the rotational kinetic energy of the outlet section increases with the increase in the guide vane height, but the cyclone with the relative height of the guide vane H/R = 0.8 increases slightly compared with the cyclone with H/R = 0.7. Possible reasons could be that, for cyclones, in order to generate large circumferential flow velocity and thus sufficiently large rotational kinetic energy, the guide vanes must be of a certain height so that they can cut into the main flow zone. However, if the guide vane height is too high, the choke area will be increased, and resistance loss will be caused. For the cyclone with relative height H/R = 0.7 and H/R = 0.8, the increase in rotational kinetic energy caused by the increase in the height of the guide vane is slightly greater than the drag energy loss caused by this process, which is manifested as the increase in relative height, and the increase in rotational kinetic energy is small. (2) In the cross-sectional section along the guide vane section, the rotational kinetic energy in the straight section of the guide vane is almost unchanged and close to 0. When the position of the guide vane twist segment is the same, the cyclone with higher guide vane height has greater rotational kinetic energy, and the rotational kinetic energy increases more along the way. (3) From the end of the guide vane to the outlet section of the cyclone, the rotational kinetic energy of the outlet section of the cyclone decreases, the speed decreases the fastest near the downstream of the end of the guide vane, and the rotational kinetic energy decreases in this section because of the presence of the circumferential velocity of the fluid, which will make the friction generated by the side wall have a circular component, and the circumferential component of the friction force will reduce the circumferential velocity of the fluid and then make the rotational kinetic energy of the fluid decrease. (4) There is a peak value of rotational kinetic energy near the leading edge of the guide vane, but it is rapidly dissipated, which is related to the flow of water around the leading edge of the guide vane when the water flow enters the guide vane section of the cyclone, and the peak value increases with the increase in the height of the guide vane. (5) In the twisting section of the guide vane, the growth rate of rotational kinetic energy increases along the way, which is related to the increase in the twisting degree along the guide vane.