**4. Parametric Study of the Lattice Core-PCM ITPS**

The use of a PCM is considered here to allow for a reduction of the wall temperature and thus the use of metallic alloys with high specific mechanical properties. The PCM should not be employed with a thermal insulation purpose as, in fact, a high thermal conductivity is needed to improve the thermal energy storage potential and thus reduce the wall temperature. The amount of PCM, i.e., the thickness of the lattice core, is directly related to the thermal response and is thus considered as a geometric parameter. To obtain thermal protection without mass increase, it is inefficient to consider a sandwich structure with a single core in which the PCM is embedded and for which the constraint is the same of a common ITPS, i.e., a maximum bottom face sheet temperature of 100 °C. Exploiting the design flexibility offered by additive manufacturing, a multi-material, hierarchical sandwich structure, as schematically shown in Figure 6, made of two stacked sandwiches can be designed. In the outer sandwich core, the PCM is embedded, whereas the inner one has a thermal insulation functionality.

**Figure 6.** Schematic of a hierarchical lattice core ITPS, in which the PCM is embedded in the outermost core (orange), and a fibrous high temperature insulation is embedded in the innermost core (blue).

The considered material for the lattice structure in which the PCM is embedded is CuCr1Zr, a commonly used alloy for additively manufactured components in the aerospace field. The top face sheet is made of high temperature nickel alloy, i.e., Inconel®718. The center face sheet, lattice core of the insulation layer, and bottom face sheet are, for simplicity of treatment, considered to be made of Inconel 718 as well.

The different parts can be joined via brazing in different steps or via bi-metallic additive manufacturing. Several geometrical parameters influence the thermal performance of the structure, namely unit cell topology, unit cell size, strut radius, and porosity. For cubic unit cells, if the porosity, the unit cell, and the cell size are fixed, the strut radius is obtained as a dependent variable.

The results already present in the literature ([22,23]) allow for the reduction of the number of geometric parameters that must be varied to evaluate the thermal response of the lattice structure-PCM composite. Indeed, the f2ccz cell is consistently the unit cell that exhibits the highest out-of plane thermal conductivity for a given porosity. This is not true for the bcc unit cell, which shows the lowest thermal conductivity. Thus, the chosen unit cell topologies are trivially f2ccz for the PCM core and bcc for the insulation core. Similarly, the porosity of the lattice structure for the insulation core should be as high as possible to reduce both mass and effective thermal conductivity, thus leading to a trivial choice. The same is not true for the PCM core. The effective thermal conductivity should be high enough to improve the thermal energy storage of the PCM, but, as the conductivity increases with diminishing porosity, it should be kept as low as possible to keep mass at a minimum. For this reason, the porosity is varied in a range, as reported in Table 1. Similarly, the PCM core thickness defines the PCM mass available and thus the thermal response. This is therefore also a parameter to be varied in the study. The insulation core thickness is varied as well, as it influences the effective thermal resistance. The geometric parameters and their range are summarised in Table 1.


**Table 1.** Geometrical parameters of the lattice structures with reference to Figure 6.

In addition to the geometrical parameters, the thermo-physical properties of the PCM should be considered. A comparably high thermal diffusivity is beneficial for obtaining a fast expansion of the melting front. However, this is not beneficial to the overall thermal protection purpose. Additionally, a material with comparably high latent heat of fusion should be chosen. The melting point also defines the thermal response of the structure. Finally, density of the material has an obvious influence on the lightweight potential of the component. Therefore, it is clear that the material choice does not have a trivial indication. The parametric study performed in this work includes a plausible domain of geometrical variables and and different materials. In particular, the PCMs listed in Table 2 are considered to cover a wide range of melting point, latent heat of fusion, and thermal diffusivity. The listed properties are considered at room temperature. The listed materials are all compatible with Inconel or materials with higher nobility.


**Table 2.** Thermophysical properties of the studied PCMs with different melting points.

The solution of the problem associated with the composite of metallic lattice core and embedded PCM is not implemented in Hot-STARSHIP. Instead, the commercial solver COMSOL® Multiphysics is used, which is based on the finite element method (FEM). It implements the apparent heat capacity method described in Section 2.2. The homogenisation approaches described in Section 2.3.3 are used for both the PCM and insulation core.
