## 3 Results and Discussion
### Effects of the Helix Angle of V-Shaped Hole Cleaning Device  
The swirl intensity decay law of spiral flow induced by the V-shaped hole cleaning device (\(\alpha\) = 0\({}^{\circ}\)) along the flow direction under four different helix angles is shown in Figure 10, and the decay equation is obtained by fitting and regression, as displayed in Table 5. It can be seen that when the helix angle increases from \(\alpha\) = 0\({}^{\circ}\) to \(\alpha\) = 30\({}^{\circ}\), the change in the initial swirl intensity \(S_{0}\) is not noticeable, which is concentrated in the range of \(S_{0}\) = 0.172\(\sim\)0.195. When the helix angle is near \(\alpha\) = 20\({}^{\circ}\), the blade has the most robust ability to induce spiral flow. The change of helix angle will deflect the flow direction of the local fluid. After the fluid flows through the blade, the flow is deflected by the deflection force of the rotational blade, so that the spiral flow with apparent circumferential velocity distribution is induced locally to improve the local hole cleaning effect.  
Figure 10: Decay law of swirl intensity of spiral flow induced by the hole cleaning device along the flow direction under different helix angles (numerical results).  
Figure 9: Annular cuttings concentration contour at different fluid consistency index conditions.  
When the rotational speed is 120 rpm, the time-averaged fluid's circumferential velocity distribution of the V-shaped blade under different helix angles is shown in Figure 11. It can be seen that with the increase in helix angle, the intensity and range of circumferential velocity induced by the V-shaped blade increase. The blade-induced ability was better when the helix angle was from about 10 to 20 degrees.  
The time-averaged vorticity and streamline distribution at the end cross-section of the V-shaped blade under different helix angles are shown in Figure 12. It can be seen that the ability of the V-shaped blade to induce swirl increases with the increase in helix angle and the influence range of tip leakage vortex gradually decreases. The area occupied by tip leakage vortex in the center of flow channel decreases gradually with the increase in helix angle, and spiral flow is dominant.  
The time-averaged annular cuttings concentration contour with different helix angle conditions is shown in Figure 13. The cuttings bed swings significantly in the circumferential direction, and the cuttings deposited on the low side of the annulus can transport from narrow gap to wide gap and transport to the wellhead driven by axial flowing drilling fluid, which significantly improves the hole cleaning performance in the annulus. However, with the increase in helix angle, the change in cuttings bed area in the annulus is not apparent. The hole cleaning performance is the strongest when the helix angle is near \(\alpha=20^{\circ}\), and the hole cleaning performance is the second strongest when \(\alpha=10^{\circ}\).  
Figure 11: Fluid circumferential velocity distribution at different cross sections of the blade under different helix angles.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Helix Angle Degree** & **Decay Equation** & \
\begin{tabular}{c} **Initial Swirl** \\ **Intensity \(S_{0}\)** \\ \end{tabular} &
\begin{tabular}{c} **Decay** \\ **Coefficient \(\beta\)** \\ \end{tabular} & \(\mathbf{R^{2}}\) \\ \hline
0 & \(S_{n}=0.172e^{-0.013L/D_{x}}\) & 0.172 & 0.013 & 0.982 \\
10 & \(S_{n}=0.192e^{-0.016L/D_{x}}\) & 0.192 & 0.016 & 0.976 \\
20 & \(S_{n}=0.195e^{-0.014L/D_{x}}\) & 0.195 & 0.014 & 0.999 \\
30 & \(S_{n}=0.178e^{-0.012L/D_{x}}\) & 0.178 & 0.012 & 0.984 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Decay equation of spiral flow induced by the hole cleaning device under different helix angles (numerical results).