**3. Simulation Setup**

The AD is compared against the AS models by simulating a three-blade Clipper Liberty 2.5 MW wind turbine located at the EOLOS wind energy research field station in University of Minnesota, USA. The rotor diameter is *D* = 96 m, the hub height is *z*hub = 80 m, and the nacelle has a near cuboidal shape with dimensions of 5.3 m × 4.7 m × 5.5 m. The tower as a cylindrical form with a diameter of 3.0 m at the top and 4.1 m at the bottom, respectively. The readers can find more information about this wind turbine in previous works [22,38,39]. Because of proprietary issues, the details of the blade geometry cannot be released in this paper. Interested readers can contact the EOLOS wind energy consortium (Email: eolos@umn.edu, Address: St. Anthony Falls Laboratory, 2 Third Avenue SE, Minneapolis, MN 55414, USA) at the University of Minnesota for these details.

The capability of the employed AS model has been evaluated for different aspects previously. In [40], the employed method was validated against wind tunnel measurements for the time-averaged flow quantities in the wake, such as the velocity deficit and turbulent intensity. Moreover, validations using the same Clipper wind turbine have shown that the AS model is able to predict accurately the near-wake vortex structures as compared with the field measurement using snow-based super-large-scale particle image velocimetry (SLPIV) [41]. Due to these previous validations, in this work, we consider the AS simulation results as references for evaluating the AD model.

Here we present the computational setup for the simulations carried out in this work. In both AD and AS cases, the size of the computational domain is set as *Lx* × *Ly* × *Lz* = 14*D* × 7*D* × 10*D*, where *x*, *y*, *z* represent the stream-wise, the span-wise, and the vertical directions, respectively. The domain is discretized with a Cartesian grid of *Nx* × *Ny* × *Nz* = 281 × 281 × 143. The grid size is uniform in the *x*, *y* directions with Δ*x* = *D*/20 and Δ*y* = *D*/40. In *z* direction, the mesh is uniform with Δ*z* = *D*/40 in *z* ∈ (0, 2*D*) region to resolve the wind turbine wake and the interaction with the ground, and is gradually stretched to the top of the computational domain.

Figure 1 shows the disk and the surface discretized with unstructured triangular surface mesh. Please note that a nacelle model [11] is employed in both AD and AS cases, otherwise there will be a non-realistic jet flow behind the empty rotor center for the AS method. Furthermore, the vortex shedding from the nacelle plays an important role in the wake evolution because of its interaction with the root vortex and the tip shear layer [21]. Although it would be ideal to take the tower into account to have a complete representation of a realistic wind turbine. However, including the tower (diameter = 3.0 m at the top) gives rise to numerical difficulties since the present study (and most numerical studies on the wind turbine's wake as well) employs a grid which is too coarse to resolve the flow details around the tower, and thus complicates the comparison between the AD and AS models. Furthermore, it was shown in [42] that the effect of tower is limited to the near wake region. For these reasons, the tower was not considered and we focus on the differences caused by the two rotor models.

In the AS simulations, the turbine rotates at a fixed tip speed ratio (TSR = Ω*R*/*U* = 8, where Ω is the rotor rotational speed, *R* is the rotor radius and *U* is instantaneous streamwise velocity averaged over a disk of radius *R* located 1*D* upstream of the turbine). The thrust is recorded at each time step and then averaged to calculate the thrust coefficient *CT* for the AD model. In the AD simulations, the thrust coefficient, which is computed from the corresponding AS simulations, is employed to compute the thrust on disk using Equation (1).

The simulations are conducted with two inflow conditions, i.e., a uniform and a fully developed turbulent inflow. In both cases, the streamwise velocity at the rotor's hub height is *U*hub = 9 m/s. The Reynolds number based on *<sup>D</sup>* and *<sup>U</sup>*hub is equal to *Re* = *DU*hub/*<sup>ν</sup>* = 5.7 × 107. For the turbulent inflow case, the turbulence density is *σu*/*U*hub = 0.08 at the hub height. The flow at inlet boundary is computed from a precursory LES with a larger computational domain of *L* - *<sup>x</sup>* × *L* - *<sup>y</sup>* × *L* - *<sup>z</sup>* = 62*D* × 46*D* × 10*D* to capture large scale eddies in the incoming flow. In this inflow generation approach, the velocity fields on a y-z plane are first saved for each time step in the precursory simulation and then applied at the inlet of the turbine simulation. If the mesh and the size of time step employed in the precursory simulation are different from those in the wind turbine simulations, linear interpolations in both space and time are carried out to obtain the inflow velocity for the turbine simulations. Periodical boundary condition is applied in the horizontal directions. The upper boundary condition is the free slip. The wall

model based on the logarithmic law is applied on the ground (the roughness length is *<sup>z</sup>*<sup>0</sup> = <sup>5</sup> × <sup>10</sup>−<sup>3</sup> <sup>m</sup> for the present cases). For the uniform inflow cases, the boundary condition on the lateral walls is the free slip.

**Figure 1.** The unstructured triangular mesh of wind turbine models. (**a**) AD model. (**b**) AS model.

The simulations use the same fixed time step for both AS and AD cases, which is equal to 1/200 of the rotor rotational period. The time simulated in the turbulent inflow case for time-averaged quantities is equal to 280 rotor revolutions, which is long enough to take into account the influence of the low-frequency large-scale disturbance in the ABL. For the uniform inflow condition, a shorter simulation of 40 rotor revolutions is carried out, for which large-scale eddies are absent in the inflow.

An extra inflow only simulation with an empty computational domain is carried out with the same setups of the turbulent inflow case to help identify the contribution of turbulent large eddies.
