## 3 Results and Discussions
### Performance of New Omni-Directional Wind-Funnel Design

Table 3: Performance summary of the proposed omni-directional wind funnel in terms of its speed ratio (SR) under different inlet wind speeds. \[[e]=\Big{[}c^{E}\Big{]}^{-1}[d]=\Big{[}s^{E}\Big{]}[d] \tag{6}\] \[\Big{[}\varepsilon^{S}\Big{]}=\Big{[}\varepsilon^{T}\Big{]}-[d]^{t} \Big{[}c^{E}\Big{]}^{-1}[d] \tag{7}\]  
where  
\([c^{E}]\) = compliance matrix at constant electric field;  
\([s^{E}]\) = stiffness matrix at constant electric field;  
\([d]\) = piezoelectric matrix relating strain/electric field;  
\([e]\) = piezoelectric matrix relating stress/electric field;  
\([\varepsilon^{T}]\) = dielectric matrix evaluated at constant stress;  
\([\varepsilon^{S}]\) = dielectric matrix evaluated at constant strain. Computational modal analysis was performed on the coupled bluff splitter body and the electromechanical coupled PVEH plate. It was then by the experimental results obtained from Electronic Speckle Pattern Interferometry (ESPI). As shown in Figure 8, the Finite Element Method (FEM) computational modal analysis results show good agreement with the experimental results obtained, giving a small percentage difference ranging from 0.50% to 1.23% between the computational modal analysis and the experiment, hence, the FE model is considered experimentally validated in terms of the structural aspect. \begin{table}
\begin{tabular}{c c c c} \hline
**Material Properties** & **Steel Bluff Splitter Body** & **Piezoelectric Plate (PZT)** & **Piezoelectric Plate (Brass)** \\ \hline Model Dimensions & \(31.8\times 30\times 2\) mm thick & \(31.8\times 57.3\times 0.191\) mm thick & \(31.8\times 57.3\times 0.128\)mm thick \\ Density & 7850 kg/m\({}^{3}\) & 7800 kg/m\({}^{3}\) & 8830 kg/m\({}^{3}\) \\  & & \(6.6\times 10^{10}\) Pa (x-dir) & \\ Young\({}^{\prime}\)s Modulus & \(20\times 10^{10}\) Pa & \(6.6\times 10^{10}\) Pa (y-dir) & \(1.03\times 10^{11}\) Pa \\  & & \(5.2\times 10^{10}\) Pa (z-dir) & \\  & & \(0.31\) (\(v_{xy}\)) & \\ Poisson\({}^{\prime}\)s Ratio & 0.3 & \(0.242\) (\(v_{yz}\)) & 0.34 \\  & & \(0.242\) (\(v_{xz}\)) & \\  & & \(c_{15}=8.745\) Cm\({}^{-2}\) & \\ Piezoelectric Constants & - & \(c_{31}=-12.77\) Cm\({}^{-2}\) & - \\  & & \(c_{30}=15.41\) Cm\({}^{-2}\) & \\ \hline \end{tabular}
\end{table} 
Table 4: Material properties of PVEH plate model. Figure 7: Dimensions and construction of bluff splitter body and PVEH plate. FSI simulation required the setup in the CFX module and mechanical APDL module for computational fluid and structural dynamic analyses, respectively. The standard Reynolds stress model in ANSYS CFX is based on the \(\varepsilon\)-equation. The CFX-Solver solves the following equations for the transport of the Reynolds stresses [16]. \[ \begin{array}{c}\frac{\partial\left(\mu\overline{u_{i}}u_{j}\right)}{\partial t }+\frac{\partial}{\partial x_{k}}\left(L_{k}p\overline{u_{i}}u_{j}\right)- \frac{\partial}{\partial x_{k}}\left[\left(\mu+\frac{\beta}{3}C_{sp}\frac{ \delta^{2}}{\varepsilon}\right)\frac{\partial\overline{u_{i}}u_{j}}{\partial x _{k}}\right]\\ \qquad\qquad\qquad\qquad\qquad=P_{ij}-\frac{\beta}{3}\delta_{ij}\varphi\pm \Phi_{ij}+P_{ij,b}\end{array}  \tag{8}\]  
where \(\Phi_{ij}\) = pressure-strain correlation, \(P_{ij}\) is the exact production rate of turbulence, \(P_{ij,b}\) is the buoyancy production term, \(\delta_{ij}\) is the Kronecker Delta function, and \(C_{s}\) = 0.22 is the Reynolds stress model constant. One of the most important terms in Reynolds stress models is the pressure-strain correlation, since it acts to drive turbulence towards an isotropic state by redistributing the Reynolds stresses. The Speziale-Sarkar-Gatski (SSG) Reynolds stress model was developed by [PERSON], [PERSON], and [PERSON] and uses a quadratic relation for the pressure-strain correlation. The SSG model is an approach towards the normal Reynolds stress model, which makes it more accurate for homogeneous turbulence and, subsequently, it simulates most flows, especially swirling flows, more accurately. The material properties, as tabulated in Table 3, were used.