## 3 Results
The worst case is reached with 45\({}^{\circ}\) fibers' inclination (Figure 8h) because the velocity achieves its maximum value only in the central zones of the periodic foam. In Figure 9, the negative effect of the stagnation zones can be appreciated. In fact, as shown in Figure 9a, the air temperature behind the fibers is higher if compared with air temperature shown in Figure 9b. Despite that, the latter presents a _j/j_0 ratio which is over the unity (1.064). This means that E1-2, 45\({}^{\circ}\) performs better than the reference circular struts even at the highest investigated velocity. Nevertheless, when considering a possible application of heat exchangers adopting periodic open cell metal foams, it is needed to deeply investigate even the hydraulic performance of periodic foams. From Figure 7b,d,f, it can be noticed that the elliptical foams, up to 30\({}^{\circ}\) fiber inclination, present lower (or, at most, equal) friction factors if compared with the reference structures. Moreover, the friction factor ratios tend to decrease as the velocity increases. Only the 45\({}^{\circ}\) oriented struts show _ff\({}_{0}\)_ always greater than 1 for all the 5 investigated inlet velocities. When comparing the velocity contours at fixed inlet velocity (for example, 4 m s\({}^{-1}\), Figure 8b,d,f,h, it is clear that, as the angle attack increases, a greater frontal fiber surface is seen by the airflow. Therefore, the greater frontal surface acts as an additional obstacle to the main flow. If the inclination of 45\({}^{\circ}\) (Figure 8h) is likened to 0\({}^{\circ}\) (Figure 8b), it is evident how the stagnant zones are remarkably more extended in the first case as compared to the second one, justifying the increase in pressure drops (in terms of friction factors). From the hydraulic performance point of view, the elliptical E2-2 Kelvin cell-based metal foam (Figure 7f) can be considered the worst case: in fact, 30\({}^{\circ}\) presents a _ff\({}_{0}\)_ curve which flattens along the unity, meaning that no hydraulic performance improvement can be obtained with respect to the circular struts' reference foam. Moreover, even worse, 45\({}^{\circ}\) (Figure 7f) shows a noticeable increase in _ff\({}_{0}\)_ curve which, at 4 m s\({}^{-1}\), is almost two times higher than the value for reference case (_ff\({}_{0}\)_ = 1.904). For the same orientation and inlet velocity values, E1-2 has only some of 7% greater friction factor value as compared to C0 (_ff\({}_{0}\)_ = 1.071). The relevant different hydraulic behavior can be attributed to their intrinsic geometrical properties. From Table 1, it can be noticed that both foams present the same \(\beta\) (0.556) but different \(\alpha\) (1.359 for E1-2, 1.800 for E2-2). A greater \(\alpha\) results in a higher frontal surface seen by the air, causing additional flow disturbances and flow restrictions (Figure 10) as well as an increase in abrupt pressure drops (Figure 11), consequently. Besides, more inhomogeneous pressure gradients can be observed for E2-2 if compared with E1-2, thus affecting the hydraulic behavior negatively. Figure 10: Velocity contours for (**a**) E1-2 and (**b**) E2-2, 45\({}^{\circ}\) 4 m s\({}^{-1}\). Figure 9: Temperature contours for E1-2, 45\({}^{\circ}\), at 2 m s\({}^{-1}\) (**a**) and 4 m s\({}^{-1}\) (**b**). As shown in Figure 11b, E2-2 can have local pressure gradients which can be some of 65% higher than E2-1. In fact, a maximum local pressure difference of 246.7 Pa was calculated for E2-2, being 150.6 Pa for E1-2.