# Analysis of Cyclone Spinning Effect with Different Guide Vane Heights
## 3 Numerical Calculations and Validation of Results
### The Simulation Results Are Validated by Experiments
Therefore, a standard deviation can be defined to represent this discrepancy, indicated below:  
\[\sigma_{ij}=\sqrt{\frac{\sum\limits_{i=1}^{n}\sum\limits_{j=1}^{m}\big{(}X_{ ij}\ -\ X_{SV}\big{)}}{(n-1)(m-1)}} \tag{5}\]  
where \(\sigma\) represents the standard deviation, \(i\) = 1, 2, \(\ldots\), \(n\) is the number of images, \(j\) = 1, 2,\(\ldots\), \(m\) is the number of points, \(X_{ij}\) represents the area of the sequence points, and \(X_{SV}\) represents the standard area of the image points. The standard deviation of this area is \(\sigma_{ij}\) = 2.79 \(\times\) 10\({}^{-2}\) mm\({}^{2}\), and the relative error for the first type of error is \(E_{1}\) = 0.66%. The second type of error is directly caused by the Dantec Dynamics Stereo PIV software. The original experimental data are processed through cross-correlation algorithms, and the assessment of uncertainty is conducted using coherence statistical methods. The maximum relative error in length is \(E_{2}\) = 0.74%. According to the research by [PERSON] et al., relative errors are considered to be independent of each other. The total relative error is calculated using Equation (6). The overall relative error is 1.2%, which is below the 5% threshold; thus, the uncertainty of the experimental results is deemed acceptable. \[E=\sqrt{E_{0}^{2}+E_{1}^{2}+E_{2}^{2}}=1.2\%<5\% \tag{6}\]  
The guide vane heights H = 20 mm, 30 mm, and 40 mm cyclones were selected for experimental validation under the condition of Re = 140,559, and Figure 7 shows the comparison of the results of the numerical simulation and the experiment. It can be found from Figure 8 that the maximum relative errors of axial flow velocity, radial flow velocity, and circumferential flow velocity are 3.52%, 4.57%, and 4.32%, respectively, and the simulation results are in good agreement with the experimental values. From the overall point of view of Figure 7, the axial velocity distribution of water flow along the diameter direction is approximately logarithmic distribution, and the axial velocity fluctuation degree of the main flow area increases with the increase in the height of the guide vane of the cyclone. The radial velocity distribution along the diameter direction of the water flow shows obvious extreme values, and with the increase in the height of the guide vanes, the absolute values of the extreme values on both sides show an increasing trend as a whole. The circumferential velocity distribution along the diameter direction of the water flow is large on both sides and gentle in the middle, and the circumferential velocity has an obvious negative value in the middle region. The numerical simulation results are consistent with the variation trend in the three-phase velocity along the diameter direction of the experimental value. The curves represent the simulated values, and the scatters represent the experimental values. Figure 7: Validation of simulation results: (**a**) H = 20 mm; (**b**) H = 30 mm; (**c**) H = 40 mm. The blue line represents the simulated values, and the dotted line represents the experimental values.