Downstream development of characteristic length scales

Figure 5.8.: Centerline evolution of the varianceσ²downstream turbine 1 (purple *), turbine 2 mid (turquoise x) and turbine 2 side (green +). TheY-coordinate is with respect to the turbine center.

extrema and changes in the evolution can be found for different quantities in table 5.3. Thus, the existence of the before identified wake regions is confirmed.

(c) (b) (a)

Figure 5.9.: Evolution of the integral length downstream turbine 1 (a), turbine 2 mid (b) and turbine 2 side (c).

Figure 5.10.: Profile comparison of the integral length downstream turbine 1 (purple *), turbine 2 mid (turquoise x) and turbine 2 side (green +). TheY-coordinate is with respect to the turbine center.

Figure 5.11.: Centerline evolution of the integral length downstream turbine 1 (purple *), turbine 2 mid (turquoise x) and turbine 2 side (green +). TheY-coordinate is with respect to the turbine center.

was found in case of lowly turbulent inflow, andL_A,HT ≈0.72D in case of highly turbulent inflow. They concluded that the integral length is determined by large flow structures from the inflow. The results from the previous chapter allow for this interpretation, too. However, the results obtained in this chapter also allow for a different interpretation, i.e. that the integral length is higher at the same downstream position in highly turbulent inflow because the fixed measurement region is assigned to a different wake region. This interpretation has consequences for wake research as the wake region may not be fixed during different experiments, and thus, results obtained from different turbulence regions within the wake are compared. Therefore, knowledge of the region downstream the WGT is of importance.

Taylor length

The evolution of the Taylor length is visualized as contour plot in figure 5.12 for the three scenarios in the wake region. Very high Taylor length values that occur naturally in the laminar flow are masked. Downstream the turbine, the Taylor length increases fromλ_T ≈3−4 mm under the nacelle’s lee toλ_T ≈10 mm at the end of the scanned plane. As the wake expands, the Taylor length is calculated for more span-wise positions. The highest values are found in the shear layer of the wake at the farthest measured downstream positions. Downstream turbine 2 side, the evolution is asymmetric due to the asymmetric inflow conditions.

The profiles in figure 5.13 show how the Taylor length evolves differently downstream turbine 1 and 2, and how the profiles of turbine 2 mid and side almost collapse downstream atX/D≈8 despite the different inflows at this rotor area.

A direct comparison of the evolution of the Taylor length at centerline for the three scenarios is given in figure 5.14. Downstream turbine 1, the Taylor length evolves similarly to the previous experiments, overall increasing but with a decrease between 4.34D−6.41D. While this development is also seen in case of turbine 2 mid, but closer to the rotor, the Taylor length only increases downstream turbine 2 side. Far downstream, the Taylor length isλ_T ≈9 mm.

Overall, compared to the results in the preceding chapter (cf. figure 4.14(b)), the evolution is similar in case of turbine 1 and turbine 2 mid, although the Taylor length is about 50% higher in these scenarios.

Integral length over Taylor length and Taylor Reynolds number

The centerline evolution ofL/λ_T is plotted in figure 5.15 for the three scenarios. Downstream turbine 1,L/λ_T is constantlyL/λ_T ≈5 up toX/D≈4 in the near wake. Then,L/λ_T increases in the transition and turbulence decay region and saturates toL/λ_T ≈14 atX/D≈8 in the far wake.

Downstream turbine 2, the first region with constantL/λ_T is not found, butL/λ_T increases to

(c) (b) (a)

Figure 5.12.: Evolution of the taylor length downstream turbine 1 (a), turbine 2 mid (b) and turbine 2 side (c). Positions that are still influenced strongly by the ambient flow and do thus have extremely large Taylor length scales are masked to emphasize the influence of the model on the flow.

Figure 5.13.: Comparison of profiles of the Taylor length downstream turbine 1 (purple *), turbine 2 mid (turquoise x) and turbine 2 side (green +). Positions that are still influenced strongly by the ambient flow and do thus have extremely large Taylor length scales are masked to emphasize the influence of the model on the flow. TheY-coordinate is with respect to the turbine center.

Figure 5.14.: Centerline evolution of the Taylor length downstream turbine 1 (purple *), turbine 2 mid (turquoise x) and turbine 2 side (green +). TheY-coordinate is with respect to the turbine center.

Figure 5.15.: Centerline evolution ofL/λ_T downstream turbine 1 (purple *), turbine 2 mid (turquoise x) and turbine 2 side (green +). TheY-coordinate is with respect to the turbine center.

L/λ_T ≈15 atX/D≈4 and saturates from there. The increase indicates that turbulence expands and evolves as large flow structures are brought into the wake as described briefly in chapter 4. The saturation indicates that the scales within the turbulence range are preserved in the far wake in an extended area even though the turbulence decays. The evolution ofL/λ_T becomes independent ofX/D, as indicated in the previous chapter. A dependence on the inflow velocity and thus the global Reynolds number is not visible.

In figure 5.16, the centerline evolution of the Taylor Reynolds numberRe_λ is plotted. For all scenarios, Re_λ increases first and then saturates. While for turbine 1 and turbine 2 mid, the curves collapse toRe_λ ≈320 atX/D≈8 andX/D≈2, respectively, downstream turbine 2 side, Re_λ ≈450 fromX/D≈4. These values indicate fully developed turbulent flows. The results are in accordance with the results from the preceding chapter whereRe_λ also increased in a region and was constant with similar values forRe_λ further downstream. The wake regions can be distinguished in a similar manner as in the preceding chapter, although the transition region and the turbulence decay region melt together between the clearly identifiable near and far wake.

In the far wake,L/λ_T ≈const.andRe_λ ≈const. This is again an indication for the validity of the Richardson-Kolmogorov phenomenology in that area. However, in the region where both quantities change, the conditions are not fulfilled, and this will be object to further study outside of this work. In addition, it can be noted that both for active grid generated inflow and in the sheared inflow of turbine 2, the highest Taylor Reynolds numbers are reached, and thus, the inflow turbulence does affect the wake turbulence in the far wake.

Figure 5.16.: Centerline evolution of the Taylor Reynolds number downstream turbine 1 (purple *), turbine 2 mid (turquoise x) and turbine 2 side (green +). The Y-coordinate is with respect to the turbine center.

5.2. Investigation of the wake with extended