## 3 Results
By employing the Darcy-Forcheimer equation (Equation (10)), which approximates the pressure gradient's curve with a second-order function of the parameter \(\chi\) defined as the product of the foam porosity and the inlet velocity, the permeability \(K\) (Equation (11)) and the Forcheimer coefficient \(\varphi\) (Equation (12)) for all the simulated geometries can be calculated, and the results are reported in Figure 5:0  
Figure 5:1 Figure 5:2 (11) Figure 5:3  
For the sake of brevity, only the values of pressure gradients for E1-2 and E2-2 were reported in Figure 5:4  
Figure 5:5 Pressure contours for (**a**) E1-2 and (**b**) E2-2, 45\({}^{\circ}\) 4 m s\({}^{-1}\). Figure 5:6 K (**a**) and \(\varphi\) (**b**) trends as function of the fiber orientation. It can be appreciated that for all the fiber orientations, the pressure drops have a parabolic trend, which is in line with Equation (10). As the angle of attack increases, for a given inlet velocity, the pressure gradient increases. In fact, as shown in Figure 12, 45\({}^{\circ}\) fiber inclination foams present greater values of K and \(\varphi\) if compared against the same geometry at lower angles of attack. It can be concluded that, from a hydraulic point of view, an increase of the angle of attack results in a pressure drop increase. Nevertheless, aiming at establishing the best thermal performance among the different investigated configurations, it is interesting to analyze the interstitial HTC (Equation (7)) as a function of the pumping power per area density (PPD) (W m\({}^{-2}\)). This parameter is defined as the ratio between the product of pressure drops \(\Delta P\) (Pa) and volumetric flow rate \(\dot{V}\) (m\({}^{3}\) s\({}^{-1}\)), and heat transfer area \(A\) (m\({}^{2}\)) as given by:  
Figure 5:7  
From Figure 14, the results show that E1-1 and E1-2 (which are very similar, see Table 1) present a better thermal performance if compared with other configurations. Assuming a constant value for the PPD, E1-1 and E1-2 give a value for HTC which is always higher, for all the investigated fiber orientations. Nevertheless, considering a possible implementation of periodic cell metal foams in real applications, it is fundamental to analyze the global performance of the foams. In particular, it must be taken into account the contemporary needs of high thermal transfer characteristics and low pressure drops. Usually, a trade-off between these two conflicting needs must be found. Figure 5:8 Pressure drop trends as function of inlet velocity for (a) E1-2 and (b) E2-2. Therefore, among the possible Performance Evaluation Criteria (PEC) [28], the following one, as reported in Equation (14), was used as a function of Reynolds number (Equation (15)), to compare the different configurations:  
Figure 5:9  
Figure 6:0  
Figure 6:1  
Focusing on Figure 15, the PEC as function of Re can be appreciated. It is evident that the elliptical struts overcome the circular ones for almost all the investigated configurations. Only E2-2 30\({}^{\circ}\) and 45\({}^{\circ}\) present PEC values lower than C0. For all the Kelvin cell- based metal foams, the global performance becomes worse as the fiber inclination increases for all the Re numbers. As already explained, higher angles of attack led to a better thermal performance at the expanse of pressure drop. Therefore, if interested in evaluating the global enhancement of the thermal-hydraulic behavior of the elliptical struts' foams with respect to circular ones, E1-2 with 0\({}^{\circ}\) angle of attack can be proposed as the best compromise, reaching a PEC value which is 22% higher than that for reference case, at Re = 200. Figure 6:2 HTC as function of PPD curves’ trend for all the investigated KMFs’ configurations.