## 1 Introduction
Besides, it must be considered that, due to their intrinsic stochastic nature, they cannot be reproduced with always the same geometrical characteristics. It is evident that this can limit their heat transfer enhancement capacity, and, consequently, their adoption in practical applications. Therefore, periodic metal foams (i.e., known as periodic cellular structures) have recently received great attention by researchers. The potentiality of periodic foams is, undoubtedly, their tunability [10], which can lead to a high level of final product customization [11]. Nowadays, different technologies can support the ordered foam development and diffusion [12]. One of them is the additive manufacturing (AM) technology. The latter has been continuously developing and it is considered suitable to generate complex periodic structures [13] with, in some cases, affordable costs [14]. Pioneering work on ordered foams can be attributed to [PERSON] [15]. The author revealed that the best approximation of an open cell foam can be obtained by the replication of a single cell shaped as a tetrakaidecahedron with slightly curved faces. [PERSON] [15] considered the so-built tetrakaidecahedron to be the cell shape which caused the surface area per unit volume to be minimized. Starting from [PERSON]'s [15] work, [PERSON] [16] developed a new structure consisting of 8 isovolumetric polyhedra. Six of them have 14-faced cells (12 pentagonal faces and 2 hexagonal ones) whilst the others are two pentagonal dodecahedra. Compared with a same-volume porous structure made of [PERSON] cells, the Weaire and Phelan [16] one leads to a surface area which is some of 0.3% smaller. Even though other models can be retrieved in literature [17; 18; 19; 20; 21], [PERSON] [15] and Weaire and Phelan [16] ones are considered the best representation of real open cell foams [22]. From a numerical point of view, one approach to investigate thermal-hydraulic behavior of stochastic foams is to firstly reproduce them via tomography-based techniques [23; 24] and, successively, importing the obtained foams in a CFD software. It is known that numerical analyses can usually be cheaper than experimental ones. Nevertheless, the generation of the geometry by means of computational techniques is the cheapest way to describe transport phenomena [22]. Therefore, generating periodic cell foams seems suitable to address this purpose. [PERSON] et al. [25] made a comparison between numerically estimated heat transfer coefficients and pressure drops in a structure obtained by means of tomography-based procedure with the same variables calculated in Lord Kelvin's structure. [PERSON] et al. [22] adopted the Lord Kelvin and Weaire-Phelan models to find a simple geometric approximation of an open cell to describe convective heat transfer and pressure drop. The authors compared the two models. Different porosities (0.85, 0.9, 0.95) were tested. In terms of friction factor, Lord Kelvin structures led to 10% always lower values than Weaire-Phelan ones. Therefore, it was stated that the simplest Lord Kelvin cells did not affect the solution accuracy significantly. As it was affirmed for stochastic open cell foams, geometrical parameters influence the thermo fluid dynamic performance even of the structured porous media. Additionally, in periodic foams, the strut shapes were found to have a not-negligible impact on the thermal-hydraulic behavior. [PERSON] et al. [26] investigated metal foams with concave or convex triangular struts at constant porosity. The authors revealed that the concave one showed better convective heat transfer performance with contemporary lower pressure drop than the convex one. [PERSON] et al. [27] studied pressure drop and heat transfer performance of Kelvin cell-based foams with circular and elliptical struts. In particular, the authors transformed the circular struts into elliptical ones by adopting two different criteria: the first was to maintain the same section strut perimeter while the second was to maintain constant the section area.