# Experimental Assessment of RANS Models for Wind Load Estimation over Solar-Panel Arrays
## 3 Numerical Model  
RANS simulations have been carried out in a three-dimensional computational domain reproducing the wind-tunnel test section. Due to symmetry, the domain spans the half-width of the tunnel (0.2 m), while the height is equal to 0.26 m in order to reproduce the flat-plate/ceiling distance of the wind-tunnel experiment. The length of the domain is set to 1.1 m, long enough ensure that the boundary conditions do not affect the results on the region of interest. The leading edge of the first panel in the array having a distance of 0.1 m from the upstream boundary of the domain located at the leading edge of the flat plate. In order to reduce the mesh size, symmetry has been applied along the longitudinal-vertical plane of the computational domain. Figure 3 shows the contour of the computational domain used for the simulations. Non-slip boundary conditions have been applied on the walls, ceiling and floor of the domain, as well as on the panel surfaces. Pressure outlet condition has been applied at the downstream boundary, with a temperature of 300 K and a static pressure of 101,325 Pa, while inlet velocity condition matching the one obtained from the experiments has been applied at the upstream boundary. The inlet velocity profile is set to match the PIV measurements. The simulation is initialized using the initialization algorithm available in ANSYS-Fluent. The assessment has been carried out on four different RANS closure models. The first closure model is the \(k\)-\(\epsilon\) model [32]. It uses two transport equations, one for the turbulent kinetic energy \(k\), and one for the turbulent dissipation rate \(\epsilon\). This model assumes that the flow is fully turbulent, and thus the effects of molecular viscosity can be neglected. The second closure model assessed is the SST \(k\)-\(\omega\) model [23]. It puts together the robust and accurate formulation of the \(k\)-\(\omega\) model in the near-wall regions with the free-stream independence of \(k\)-\(\epsilon\) model far from the wall [33]. The model works in such a way that \(k\)-\(\omega\) model [34] is activated in the near-wall region. The third closure model assessed, the transition SST model [35], was originally proposed as a variation of the SST \(k\)-\(\omega\) model. It is a four-equation model based on the coupling of the SST \(k\)-\(\omega\) model with two additional transport equation, one for the intermittency and one for the transition onset criteria, in terms of momentum-thickness Reynolds number. All three aforementioned closure models rely on the Boussinesq hypothesis to model the Reynolds stresses (\(\rho_{\infty}\overline{u_{i}^{\prime}u_{j}^{\prime}}\)), where the Reynolds decomposition of the velocity field (\(u=U+u^{\prime}\)) is used to refer to the mean (\(U\)) and fluctuating quantities (\(u^{\prime}\)) and the subscripts i and j indicate the velocity component  
Figure 3: Computational domain. according to the [PERSON] notation. This hypothesis assumes the eddy viscosity \(\mu_{t}\) as an isotropic scalar quantity in the Reynolds stresses equation, defined as:  
\[-\rho_{\infty}\overline{u_{i}^{\prime}u_{j}^{\prime}}=\mu_{t}\left(\frac{\partial u _{i}}{\partial x_{j}}+\frac{\partial u_{j}}{\partial x_{i}}\right)-\frac{2}{3} \left(\rho_{\infty}k+\mu_{t}\frac{\partial u_{k}}{\partial x_{k}}\right). \tag{1}\]  
This assumption works well for flows dominated by only one of the Reynolds stresses. However, when these model are used to simulate complex flows with high degree of anisotropy, like separated wake after solar panels, the results are not satisfactory [36]. The fourth and last closure model assessed in this study is the Reynolds Stress Model (RSM), developed by [PERSON] et al. [37] on the basis on the works of [PERSON] [38] and [PERSON] [39]. It is characterised by solving all the components of the turbulent transport, instead of relying on the Boussinesq hypothesis.