## 4 Results  
The three methods were compared in this article in the following way: calculation of torque on the turbine was carried out with the mixing plane and frozen rotor methods in a steady state, while the sliding mesh approach was in an unsteady state (Figure 15). The  
Figure 14: Velocity distribution near the rotors with the frozen rotor technique (0\({}^{\circ}\) position). Figure 12: The visualization of the adaptive mesh refinement\({}^{\prime}\)s criteria (position 0\({}^{\circ}\), iteration number = 2500). Figure 13: Y+ distribution on the turbines. obtained data were compared to see how much the results obtained from the mixing plane and the frozen rotor approaches deviated if they were compared with the unsteady sliding mesh method. In the case of the mixing plane method, the torque on the first turbine was \(-0.00145003\) Nm, while on the second turbine, \(0.000941719\) Nm. The average torque with the frozen rotor technique was \(-0.001471612\) Nm on the first turbine and \(0.000946494\) Nm on the second turbine. The average torque in the case of the sliding mesh method, between the fifth and the sixth revolutions, was \(-0.001707654\) Nm and \(0.001102037\) Nm on the first and the second turbine, respectively. When the torque obtained from the mixing plane and frozen rotor methods was compared to the averaged torque obtained from the sliding mesh method, then it can be seen that the steady-state solutions are 14-15% lower (Table 1). Based on the results, several conclusions have been made. First of all, it was expected that a higher difference would appear between the frozen rotor and the mixing plane methods since the second rotor behaved as a stator. Therefore, the impact of a stagnant rotor in the modeling was smaller than expected. Second of all, it was also hypothesized that the frozen rotor method would yield similar results to the sliding mesh method, with the second turbine showing a sinusoidal (or other periodic) change; however, this phenomenon did not appear in the solution of the frozen rotor. It must also be mentioned that the difference between the torque with the mixing plane method and the average torque with the frozen rotor method was 1.47% \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Method**} & \multirow{2}{*}{**Torque (Nm)**} & \multicolumn{2}{c}{**Percentage Difference**} \\  & & **Between Steady and** \\  & & **Unsteady Torque (-)** \\ \hline Sliding mesh first rotor & \(-0.001707654\) & - \\ Sliding mesh second rotor & \(0.001102037\) & - \\ Mixing plane first rotor & \(-0.001450030\) & 15.09\% \\ Mixing plane second rotor & \(0.000941719\) & 14.55\% \\ Frozen rotor first rotor & \(-0.001471612\) & 13.82\% \\ Frozen rotor second rotor & \(0.000946494\) & 14.11\% \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Average torque on the rotors and their differences compared with the average of the transient result. Figure 15: Functions of torque during a complete rotation. and 0.50% on the first and second turbines, respectively. Consequently, the two methods provide closely identical solutions if similar engineering objects and phenomena (no tower and no ground) are modeled. Therefore, it is advisable to use the computationally cheaper method for these types of simulations. Thirdly, the difference between the transient and steady-state results was higher than the difference between the steady-state results alone, with a difference of approx. 14-15% (using the average values as previously mentioned). The reason for this difference could be attributed to the different time domains (RANS vs. URANS) and the different rotating motion techniques (sliding mesh in a URANS simulation and steady rotating motion methods in a RANS simulation). In addition to the conclusions, several important features, such as the streamlines or the turbulence-related vorticity, were also investigated.