## 2 Numerical Simulations and Wind Tunnel Tests
### Turbulence Model
#### 2.2.3 DES Method  
DES is a hybrid method that combines the RANS and LES methods to simulate turbulent flow within a flow field. RANS is utilized in the near-wall region, while LES is employed in regions of flow separation and wake. Compared to LES, DES reduces the requirement for grid resolution and enhances computational efficiency. In contrast to RANS, DES improves simulation accuracy within the separation region. Various turbulence models are employed by different DES methods and are briefly described below.  
[PERSON] et al. [36] proposed the Detached Eddy Simulation Spalart-Allmaras (DES-SA) model, which is based on the Spalart-Allmaras equation. This model employs a hybrid length scale \(L_{DES}\), instead of the wall distance \(d\). The hybrid length scale is defined as the minimum value between the local grid spacing and the near-wall distance. The expression for the hybrid length scale is as follows:  
\[L_{DES}=\text{min}(L_{RANS},C_{DES}\Delta) \tag{5}\]where \(C_{DES}\) represents the scale factor, generally taken as \(C_{DES}\) = 0.65; \(\Delta\) is the sublattice scale, taken as \(\Delta\) = max {\(\Delta x\), \(\Delta y\), \(\Delta z\)}; and \(\Delta x\), \(\Delta y\), \(\Delta z\) are the grid scales in the \(x\), \(y\), \(z\) directions, respectively.  
The Detached Eddy Simulation Realizable \(k\)-\(\epsilon\) (DES-RK) model employs the transport equations for \(k\) and \(\epsilon\) from the REA model to compute the eddy viscosity in the RANS region and solve for the subgrid-scale viscosity in the LES region. In the DES-RK model, the dissipation term in the transport equation for turbulent kinetic energy, \(k\), is modified to \(k^{3/2}/L_{DES}\), where \(L_{DES}\) represents the hybrid length scale. The expression for the hybrid length scale is as follows:  
\[L_{DES}=\min(L_{REA},C_{DES}\Delta) \tag{6}\]  
where the value of the sublattice scale \(\Delta\) is the same as that of Equation (5), and the value of the scale factor \(C_{DES}\) is 0.61.  
The Detached Eddy Simulation Shear Stress Transport (DES-SST) model was proposed by [PERSON] (1993) and is based on the SST model. The DES-SST model incorporates the hybrid length scale \(L_{DES}\). In the SST model, the length scale is defined as \(l_{SST}=\sqrt{k}/\beta^{*}\omega\), while in the DES-SST model, the hybrid length scale is defined as follows:  
\[L_{DES}=\min(L_{SST},C_{DES}\Delta) \tag{7}\]  
where the subgrid scale \(\Delta\) and the scale factor \(C_{DES}\) are the same as in Equation (6).  
[PERSON] et al. (1993) proposed the Delayed Detached Eddy Simulation SST \(k\)-\(\omega\) (DDES-SST) model with a hybrid length scaled by  
\[L_{DES}=\min\biggl{(}L_{SST},\frac{C_{DES}\Delta}{1-F_{SST}}\biggr{)} \tag{8}\]  
[PERSON] et al. (1993) developed an Improved Delayed Detached Eddy Simulation SST (IDDES-SST) model, which improves the sublattice scale \(\Delta\), the expression of which is shown below.  
\[\Delta=\min\{\max[C_{w}d_{w},\ C_{w}h_{w},\ l_{w}],\ h_{\max}\} \tag{9}\]  
where \(C_{w}\)= 0.15, \(h_{\max}\)= max{\(\Delta x\), \(\Delta y\), \(\Delta z\)} and has the same meaning as the sublattice scale in Equation (5); \(l_{w}\) is the total length of the grid for wall normal; and \(d_{w}\) is the distance between the midpoint of the flow field and the nearest wall.  
This section provided a brief overview of the differences between various turbulence models. Both the DES and LES methods are capable of simulating unsteady wind fields, while the RANS method is limited to simulating steady wind fields. A comparison of these three methods reveals that the RANS method has the lowest computational cost but correspondingly fewer degrees of freedom in its analysis. In contrast, the LES and DES methods require longer computational times but offer higher simulation accuracy.