# Wind Forces and Flow Patterns of Three Tandem Prisms with a Small Height-Width Ratio
## 2 Outline of Wind Tunnel Tests and Numerical Simulations  
### Pressure Measurements by Wind Tunnel Tests  
Wind pressure measurements of three rectangular prisms with a small height-width ratio were carried out in a close circuit boundary layer wind tunnel located at Beijing Jiaotong University, China. The test section of the wind tunnel was 3.0 m wide and 2.0 m high. The spire-roughness technique was employed to simulate the atmospheric boundary layer over an open country terrain with a length scale of 1/200. As shown in Figure 1a, the measured longitudinal turbulence intensity profile (\(I_{U}\)) and mean wind velocity profile (\(U\)/\(I_{H}\)) with a power-law exponent \(\alpha\)= 0.12 followed the atmospheric boundary layer of the open terrain in the standard \"Load Code for the Design of Building Structures (GB50009)\" [15]. \(U_{H}\) and \(I_{U,\,H}\) are the mean wind speed and turbulence intensity at prism height \(H\), where \(U_{H}\) is 7.6m/s and \(I_{U,\,H}\) is 0.11. The non-dimensional power spectrum densities of longitudinal velocity at \(H\) is presented in Figure 1b. The corresponding turbulence integral scale in longitudinal wind direction is \(L_{u}\) = 0.35 m, which satisfies the similarity law for the length scale. The Reynolds number using the prism width \(W\) and the mean velocity 7.6 m/s is 1.0 \(\times\) 10\({}^{5}\). The experimental prism arrangement and the wind direction of incident flow are displayed in Figure 2a, where three rectangular prisms are arranged along the long edge of the prism. The three prisms were the same size, which was 0.3 m long (\(L\)), 0.2 m wide, (\(W\)) and 0.08 m high (\(H\)), and the frontal \(H\)/W of the prism was equal to 0.4. The geometric scale ratio was 1/200. In order to investigate interference effects of the prism spacing on wind loads of three tandem prisms, sixteen spacing ratios of the clear spacing (\(S\)) to the width (\(W\)) of prisms \(S\)/\(W\) = 0.2, 0.4, 0.5, 0.6, 0.7, 0.8, 1, 1.2, 1.4, 1.6, 2, 2.4, 2.8, 3.2, 4, and 4.8 were considered. The definition of this tandem arrangement is the same as that in Sakamoto and Haniu [2]. The test on an isolated prism was also carried out. As shown in Figure 2b, 125 pressure taps were arranged on the roof and the four walls of each prism. Fluctuating pressures on all three rectangular prisms were measured at the sampling frequency of 312 Hz. The mean wind speed at the top of the prism was 7.6 m/s, and the velocity scale ratio was 1/4. The sampling duration was about 90 s (about 75 min in reality). All measured fluctuating pressures were corrected with the frequency transfer function of the tube system [16]. The maximum blockage ratio was 0.2%, and no model blockage correction was conducted. Fluctuating pressure coefficients \(C_{pi}(t)\) of three rectangular prisms are defined as:  
\[C_{pi}(t)=(P_{i}(t)-P_{static})/0.5\rho U_{H}^{2} \tag{1}\]  
where \(P_{i}(t)\) is the measured pressure of tap \(i\) at time \(t\); \(\rho\) is the air density; and \(U_{H}\) and \(P_{static}\) are the free-stream velocity and the static pressure at the reference height, respectively,  
Figure 1: Information of incident flow: (**a**) Simulated atmosphere boundary layer; (**b**) Longitudinal power spectrum density. Figure 2: Prism configuration and pressure tap arrangement: (**a**) Prisms arrangement and wind direction; (**b**) Prism pressure taps. where the model does not affect the flow. The reference height is taken as the height of the prism \(H\). Investigated wind force coefficients include drag coefficients \(C_{D}(t)\) (along-wind), lateral lift coefficients \(C_{LL}(t)\) (cross-wind) in the horizontal direction, and roof uplift coefficients \(C_{RL}(t)\) in the vertical direction, and they are defined as:  
\[C_{D}(t)=F_{D}(t)/0.5\rho U_{H}^{2}A_{D} \tag{2}\]  
\[C_{LL}(t)=F_{LL}(t)/0.5\rho U_{H}^{2}A_{LL} \tag{3}\]  
\[C_{RL}(t)=F_{RL}(t)/0.5\rho U_{H}^{2}A_{RL} \tag{4}\]  
where \(F_{D}\), \(F_{LL}\), and \(F_{RL}\) are the drag, the lateral lift and the roof uplift, respectively, as shown in Figure 2a.