# Wind Forces and Flow Patterns of Three Tandem Prisms with a Small Height-Width Ratio
## 2 Outline of Wind Tunnel Tests and Numerical Simulations
### Large Eddy Simulations Setup  
The CFD numerical simulation is adopted to analyze the wake characteristics among three prisms with the Ansys Fluent software package. Considering that the RANS models are not suitable to capture the unsteady wake among prisms, the 3D Large Eddy Simulations (LES) turbulence model is employed in this present study. The LES uses the filter function to separate the large and small eddies, and the large eddies directly calculate by the Navier-Stokes (N-S) equations, while the small eddies are calculated using a sub-grid scale (SGS) model. For the SGS model, the dynamic Smagorinsky-Lilly (DSL) is adopted. The pressure-velocity coupling uses the PISO algorithm. The second-order implicit scheme is selected for the temporal discretization, and the bounded central differencing is applied in momentum equations. The computational domain and boundary conditions are shown in Figure 3. The prism size is the same as the wind tunnel tests, and the blockage ratio is 1.5%, which is much smaller than the CFD best practice guidelines [17]. The fluctuating algorithm vortex method (VM) is used for fluctuating wind velocity inlet, which has been confirmed to predict the wind flow around the prism [18]. In this present study, the number of vortices is 200 [19]. At the inlet of the LES (\(X\)/\(H=-10\)), the wind flow with a turbulence intensity profile and a mean wind velocity profile are imposed. The incident flow gradually stabilizes after a distance development of \(10H\), and then the simulated atmospheric boundary layer approaching the upstream prism (\(X\)/\(H=0\)) is similar to that in the wind tunnel test, as shown in Figure 1a. The mean wind velocity and the turbulence intensity at the prism roof height are 7.6 m/s and 0.11, respectively. The simulated longitudinal turbulence spectrum at the prism roof height is presented in Figure 1b, and the corresponding turbulence integral scale in longitudinal wind direction is \(L_{u}=0.28\) m. The Reynolds number using the prism width and the mean velocity 7.6 m/s is about 1.0 \(\times\) 10\({}^{5}\) in LES, which is consistent with wind tunnel tests. To check the grid sensitivity, results based on three types of grids (coarse, basic, and fine) in the case of \(S\)/\(W=0.7\) are compared. The numbers of computational meshes for coarse grids, basic grids, and fine grids are 6.6 \(\times\) 10\({}^{6}\), 1.0 \(\times\) 10\({}^{7}\), and 1.4 \(\times\) 10\({}^{7}\), respectively. The average value of the non-dimensional wall distance \(y^{+}\) for the three types of grids  
Figure 3: The schematic of computational domain and boundary conditions. is close to 1, and the average values of non-dimensional wall distances \(x^{+}\) and \(z^{+}\) for the three types of grids are both close to 4. The computational mesh details of basic grids around three prisms are shown in Figure 4, and the coarse grids and fine grids are not shown for brevity. The non-dimensional time steps \(\Delta t^{*}=\Delta tU_{H}/H\) in terms of coarse grids, basic grids, and fine grids are 0.04, 0.02, and 0.01, respectively. For all simulations, the maximum courant numbers are less than 1.5. To ensure the stable turbulent condition in the computation domain, the data are recorded after 2 s from the beginning of the simulation, and the sampling frequency is 312 Hz, which is the same as wind tunnel tests. Because the LES transient calculation consumes much time and computational cost, all simulations are sampled for 12 s (about 10 min in reality), except for the special case of \(S/W=0.7\), which is sampled for 30 s (about 25 min in reality). Figure 5 shows the relative difference \(\varepsilon\) (\(\varepsilon=|C_{EXP}-C_{Numerical}|/C_{EXP}\)) for mean and RMS forces coefficients of three prisms (\(S/W=0.7\)) between the results of the wind tunnel tests and the results of the numerical simulations using three types of grids.