4. Results 1: Comparison of a disc and a turbine wake 33
4.1.1. Downstream development of the normalized mean velocity
Figure 4.1 shows the evolution of the normalized mean velocityu/u0downstream the disc and the turbine for the three inflow conditions (cf. page 33) as interpolated contour plots. u0is the respective inflow velocity (cf. table 3.2).
Directly downstream the disc (plots (a.i)), the flow shows a strong velocity drop due to the local blockage. Beyond this velocity drop, the actual wake evolves. In the center of the wake, the velocity recovers after a local minimum aroundX/D≈1.5. The decrease of the normalized velocity outside the rotor plane with increasing downstream position indicates the wake expansion. An influence of the inflow conditions on the wake evolution downstream the disc is not visible.
Downstream the turbine (plots (b.i)), a strong decrease of the velocity is visible directly behind the rotor blades, while the velocity is not as much reduced under the nacelle’s lee. The wake
evolves from there: First, the velocity decreases in the center of the wake. Then, the wake recovery starts around X/D≈2. The wake expansion can be identified by the decrease in velocity outside the rotor plane with increasing distance from the turbine. An influence of the inflow conditions is visible, although the overall behavior of the wake evolution is comparable for the different inflow conditions.
For a better direct comparison, figure 4.2 shows wake profiles at distances X/D = 1.07,2.10,2.97,4.00 for the disc (a) and turbine (b). Downstream the disc, a strong profile evolves that flattens downstream. As already expected from the contour plots, the profiles downstream the disc show no dependence on the inflow condition.
In the wake of the turbine at X/D=1.07, the influence of the nacelle is visible. A profile develops only farther downstream, and it flattens downstream. An influence of the inflow on the wake development is visible, although the qualitative evolution is comparable. With regard to laminar inflow, the average difference across the rotor varies between 7% atX/D=1.07 and 29% atX/D=2.10 for regular grid inflow, and between 12% atX/D=1.07 and 19% at X/D=2.97 for active grid inflow.
The centerline evolution of the normalized mean velocity is considered for all inflows in figure 4.3 for the disc (a) and turbine (b).
Looking at the development of the normalized mean velocity downstream the disc confirms its independence on the inflow condition. Quantitatively, the local minimum ofu/u0≈0.19 at X/D=1.59 can be seen as the start of the wake recovery. This point will be namedXa.iu, and the results are also summarized in table 4.1. AtX/D=4.69, the wake has recovered tou/u0≈0.63.
In the wake of the turbine, differences due to the inflow conditions can be seen, although the overall behavior is comparable for the different inflow conditions. The wake recovery defined by the minimum velocity starts depending on the inflow at aroundX/D≈2, where the normalized centerline velocity is betweenu/u0≈0.1 andu/u0≈0.2. The precise positionsXb.iu can be found in tables 4.1 and also E.1. At the end of the test field, the wake has recovered to u/u0≈0.53. The difference between laminar inflow and inflow generated by a regular grid is 18%, and it is 1% in case of inflow generated by an active grid.
For a direct comparison of the wakes of the two WGTs, the average evolution of the normalized mean velocity downstream the disc is indicated in figure 4.3(b) where the centerline evolution of the normalized mean velocity downstream the turbine is shown.
In figures 4.1 and 4.2, a comparison of the wakes between disc and turbine shows that on the one side, the flow field looks differently in proximity to the WGT. On the other side, the flow fields look similar far downstream except for the slightly lower velocity downstream the turbine. The normalized velocity profiles and the centerline evolution of the normalized velocity pronounce both the different development of the wake close to the respective WGT and the wakes’ adaption far away. The high downstream resolution of measurement points allows for a
(b.3) (b.2) (b.1)
(a.3) (a.2) (a.1)
Figure 4.1.: Evolution of normalized mean velocityu/u0: Surface plots downstream the disc (a.i) and the turbine (b.i) for laminar (x.1), regular grid (x.2) and active grid (x.3) inflow.
(a) (b)
Figure 4.2.: Profiles of the normalized mean velocity downstream the disc (a) and the turbine (b) atX/D=1.07,2.10,2.97,4.00 for different inflow conditions. Error bars are included but may be within the symbols.
(a) (b)
Figure 4.3.: Development of the normalized mean velocity downstream the disc (a) and the turbine (b) on the centerline for different inflow conditions. Error bars are included but may be within the symbols. In (b), the downstream evolution of the mean velocity averaged over all inflow conditions is plotted for comparison.
detailed investigation of the evolution of the mean velocity, and the downstream position where the wake recovery begins can be identified.
To summarize, the evolution of the mean velocity downstream the disc and the turbine shows the expected behavior. From the direct comparison of the centerline evolution of the mean velocity in figure 4.3(b), it could be shown that the wake of this disc is in the far field an adequate substitution of the wake of the turbine. This outcome is similar to the results found by Aubrunet al. (2013), Lignaroloet al. (2015), and Lignaroloet al. (2016). For example, the centerline velocity downstream both WGTs has recovered depending on the inflow turbulence to 55%-65% of the inflow velocity at X/D=3 in Aubrun et al. (2013), matching the recovery atX/D=4.69 obtained in this study. The differences may be explained by the lower TSR of
5.8 in Aubrunet al.(2013) and the adapted thrust of the disc. In Lignarolo et al.(2016), the centerline velocity is atX/D=2.2 approximately 10% of the inflow downstream the turbine, and approximately 30% downstream the disc, which is in agreement with the results obtained in the here presented study. Also, the analysis of the mean velocity downstream the turbine shows a similar centerline evolution to Keaneet al.(2016). Here, the wake recovery for a comparable inflow velocity of 7 m/s starts aroundX/D≈2, and atX/D≈4.5, the wake has recovered to approximately 65% of the inflow velocity.
Looking at the evolution from the near field to the far field, an influence of higher ambient turbulence levels on the wake recovery is not visible in case of the disc. However, as the break down of the tip vortex structure downstream the turbine is influenced by the ambient turbulence, differences can be identified in the wake of the turbine. The differences in the flow behavior close to the WGTs are caused by the fundamentally different turbulence mixing mechanisms.
In the next step, the evolution of the turbulence intensity is evaluated.