Assessment of RANS-type turbulence models for CFD simulations of horizontal axis wind turbines at moderate Reynolds numbers

Abstract

Nowadays, numerical simulations of wind turbines based on the Reynolds-averaged Navier–Stokes (RANS) formulation are becoming, in terms of computational cost, increasingly more viable tools for geometry optimization and design. Nevertheless, a judicious use of RANS-type methods is still required to guarantee acceptable accuracy at manageable computational cost. Here, we assess the accuracy and cost of several well-known turbulence models (Spalart–Allmaras, $k-\varepsilon$, $k-\omega$ SST, along with transitional modelling) with and without a zigzag tape modelling for a representative horizontal axis wind turbine within a range of moderate Reynolds numbers ($\textrm{Re} \approx 3 \times 10^5$ to $8 \times 10^5$). This range allowed for the assessment of turbulence models under various complex flow conditions. Significant differences in performance have been found and, for a notable portion of the test cases, the $k-\varepsilon$ model was able to deliver good results (similar to $k-\omega$ SST results) with a considerably coarser mesh. This suggests that $k-\varepsilon$, although often recognized as less accurate than $k-\omega$ SST, might actually be more efficient for wind turbine simulations. Also, although the best results came only with a coupled transition model which required a higher computational cost, this increase in cost is not exceedingly high and might allow for this model’s usage in later design stages. Accordingly, the present study is a valuable source for future wind turbine simulations and design and we hope that it fosters further developments in the field.

Appendices

Appendix: A ${\mathcal {L}}^2$-norm of the residual values

The residual values of the velocity components, turbulent kinetic energy, dissipation rate, eddy viscosity, intermittency and transition onset Reynolds number at the converged condition of each simulation without the zigzag tape modelling are presented in Table 12 for repeatability purposes.

Table 12 ${\mathcal {L}}^2$-norm of velocity components, turbulent kinetic energy, dissipation rate and eddy viscosity at the convergence condition

Appendix B: Zigzag tape modelling’s results

The results of zigzag tape modelling are presented only for the $k-\omega$ SST coupled with the $\gamma -\textrm{Re}_{\theta t}$ model in Table 13 because it is the model that presented the better agreements with the experimental results, whereas the other studied cases actually worsened the accuracy as already shown in Sect. 5.2.

Table 13 Results for $k-\omega$ SST coupled with $\gamma - \textrm{Re}_{\theta t}$

Appendix C: Pressure coefficient distributions

Figures 10 and 11 show, respectively, the pressure coefficient distributions for $U_\infty =10.05$ m/s and $U_\infty =15.06$ m/s, both at the same five radial positions presented in Fig. 7. One can see good agreements at $r/R = 0.60$, 0.82 and 0.92 for both wind speeds. This is related to the fact that the local pressure sensors’ ranges are not sufficient to resolve the actual physics at low wind speeds [23, 39, 90]. In addition, less accuracy is found for the suction side, besides the greatest discrepancies at $r/R = 0.25$ and 0.35, and $U_\infty = 10.05$ m/s. From this figures, one could conclude that the torque and thrust calculated by the simulations with any of the three turbulence models would have very similar values, which is misleading due to what Sect. 5.1 showed.

Fig. 10

Pressure coefficient distribution along the (normalized) chord-wise direction at five sections (from $r/R = 0.25$ to 0.92) for case $U_{\infty } = 10.05$ m/s. Experimental data from [18]. For interpretation of the colours in the figure, the reader is referred to the digital version of this paper

Fig. 11

Pressure coefficient distribution along the (normalized) chord-wise direction at five sections (from $r/R = 0.25$ to 0.92) for case $U_{\infty } = 15.06$ m/s. Experimental data from [18]. For interpretation of the colours in the figure, the reader is referred to the digital version of this paper