Add super-Gaussian velocity model for vertical-axis wind turbines

[vallbog]

Super-Gaussian velocity model

This PR adds a super-Gaussian velocity model for vertical-axis wind turbines (VAWTs). The model is based on (Ouro & Lazennec, 2021) and allows the wake to have different characteristics in the cross-stream $y$ and vertical direction $z$. This would be the first velocity model for VAWTs in FLORIS since all existing models are for traditional horizontal-axis wind turbines (HAWTs).

This is a part of a series of PRs (please see #701 for an overview). The focus of this PR is to correctly generate the velocity field behind a single VAWT using the new velocity model. Further infrastructure for VAWTs, e.g. for calculating turbine powers, are added in #701.

In addition to the super-Gaussian model, new solvers vawt_solver and full_flow_vawt_solver are added. No turbulence model is included in these since I don't know if existing turbulence models can be applied to VAWTs. A new example 30_vertical_axis_turbine.py shows a characteristic wake of a VAWT.

Validation of the velocity model

Here we check if this FLORIS-implementation of the super-Gaussian model is correct. A validation script (link in the next section) recreates figures from (Ouro & Lazennec, 2021) showing velocity deficit profiles for 6 different cases (detailed in table 2 of the article mentioned). External Large Eddy Simulation (LES) data from (Shamsoddin & Porté-Agel, 2020) and (Abkar, 2019) is used as a reference.

One of the figures created by the validation script is shown below as an example. It shows velocity deficit profiles at five locations downstream of a single VAWT. For simplicity, one may think of the inflow as homogeneous. Coordinates $x/D$, $y/D$, and $z/D$ are in the streamwise, cross-stream, and vertical direction respectively, and normalized by the turbine diameter $D$. The dashed lines show the extent of the turbine which has a height-to-diameter ratio of about 2 in this case. The red lines are generated by FLORIS and the black circles are external LES data. See #699 for details about how the velocity profiles figure is created in general.

The super-Gaussian model is in good agreeement with the LES data in the case shown above. However, compared to figure 9 in (Ouro & Lazennec, 2021), the FLORIS-implementation gives a slighly lower value of the maximum velocity deficits at $x/D$ = 3.0 and 6.0. This difference (in maximum normalized velocity deficit) is about 0.05 and it's among the largest differences observed between the FLORIS super-Gaussian implementation and the article super-Gaussian results in all 6 cases.

The reason for the difference above is unknown at the moment. I've double-checked the derivation of the model in the article, the implementation in FLORIS, and the model input parameters. Nevertheless, I believe that the results from the FLORIS-implementation are close enough.

Validation script

The validation script validation/validate_super_gaussian_vawt.py can be found in the branch validation/VAWT-super-Gaussian. It is only available to the FLORIS maintainers because I cannot share the LES data. However, all 6 figures created by the script can be found below:
velocity_deficit_profiles.zip

Impacted areas of the software

Compared to #699, the main changes are in:
floris/simulation/wake_velocity/super_gaussian_vawt.py
floris/simulation/solver.py

[misi9170]

Closing, see discussion in #701 regarding supporting VAWT modeling