*5.4. Thermal Response of the Lattice Core-PCM ITPS*

In Figure 12, the wall temperature variations during the re-entry trajectory for different PCMs are shown. The geometric parameters are fixed to allow comparability between the results (*tcPCM* = 10 mm, = 0.9, *tcins* = 40 mm). The other parameters are fixed a priori, as reported in Table 1.

It can be noticed that a low temperature peak at the top face sheet corresponds to the eutectic mixture Li2CO3(22%)-Na2CO3(16%)-K2CO3, which, however, exhibits a much higher melting point. This indicates that the thermal behaviour is ascribed to only sensible heat storage. This indicates that the material is not suitable for lightweight latent heat thermal energy storage, as its thermal behaviour is only related to the high thermal mass.

Erythritol, which is the lightest material and also exhibits the lowest melting point, is not suitable for the application. Although a low melting point is advantageous, the low latent heat of fusion compared to other materials makes it an inappropriate choice. The KCl-MgCl2 mixture exhibits a comparably high latent heat, which is shown via the flattening of the temperature curve around its melting point. However, the melting point is higher than that of the LiCl-LiOH mixture, which also shows the highest latent heat of fusion. Thus, the material choice for further consideration in the geometric parametric study falls on the LiCl-LiOH mixture.

**Figure 12.** Temperature evolution on top and bottom face sheets for different PCMs.

In the following Figures 13–15, the parametric study for different geometrical parameters is described. Figure 13 shows the wall temperature (top face sheet) evolution for different PCM core thicknesses and porosities of the lattice structure. It can be noticed that the thickness has the highest influence on the thermal behaviour. Diminishing returns in terms of wall temperature reduction are observed with increasing thickness. On the other hand, for a small core thickness, the effect of varying porosity, and thus varying effective thermal conductivity, is marginal. However, for increasing core thicknesses, the effective thermal conductivity becomes more relevant. Indeed, the difference between wall temperature peaks at different porosities increases for the same core thickness.

One can notice that the peak of the temperature curve corresponding to a wall thickness of 20 mm and porosity = 0.95 is higher than the one corresponding to a core thickness 10 mm and porosity = 0.9. Even in this case, diminishing returns are observed. Higher peak temperature reductions are observed, e.g., between = 0.95 and = 0.9 than between = 0.85 and = 0.8.

If one considers mass as a limiting constraint, no trivial optimum exists. To minimise mass, porosity should be as high as possible, as the lattice core material is heavier than the PCM material. The core thickness has a cubic relationship with the bending stiffness of the structure. Therefore. it can not be a priori minimised.

One should notice that all configurations considered are effective in reducing the wall temperature with respect to the case of sensible thermal energy storage of, e.g., a corrugated core ITPS. Indeed even for a core thickness of only 5 mm, the wall temperature reaches a peak of maximum 797 K (524 °C) , which is well below the maximum operative temperature of both Inconel 718 and CuCr1Zr alloys. Therefore, a valid range of core thickness between 5 mm and 10 mm can be considered for application. All in all, a sweet spot can be identified at a core thickness of 10 mm and a porosity of = 0.9. In such a configuration, the wall temperature does not drastically overshoot the melting point of the PCM.

**Figure 13.** Temperature evolution for different PCM core thicknesses (*tcPCM* ) and porosities () of the lattice structure.

Figure 14 shows the temperature curves for the top face sheet and the bottom face sheet for different insulation core thicknesses. The PCM core geometrical features are fixed at the identified optimum. The porosity of the insulation core is fixed at = 0.95 to obtain a low effective thermal conductivity. Increasing the thickness leads to higher thermal resistance, which can be observed with the progressively flattening temperature curves of the bottom face sheet. The temperature of the top face sheet is marginally influenced by the insulation core, as the temperature curves for such a point of the component are dominated by the latent heat thermal energy storage. Considering the bottom face sheet temperature constraints previously described, the case of an insulation core thickness of 10 mm should be discarded. On the other hand, an insulation core thickness of 50 mm does not bring appreciable differences with respect to the thinner 40 mm case. Therefore, it should also be discarded. Table 4 summarizes the final material choice and the identified valid geometrical parameters range. Finally, Figure 15 shows the temperature curves of different positions along the out-of-plane direction for the case of a hierarchical sandwich with a PCM core thickness of 10 mm, = 0.9, and a thickness of the insulation layer of 40 mm.

**Figure 14.** Top and bottom face sheet temperature evolution for different thicknesses of the insulation layer (*tcins* ).


**Figure 15.** Temperature profile of the hierarchical sandwich structure (*tcPCM* 10 mm, = 0.9, *tcins* 40 mm) with schematic description of the evaluation points considered.

One can observe that the overall areal weight of the obtained composite is higher than both solutions previously considered. This is mainly due to the high density of the structural materials in face sheets and lattice cores. However, a proper treatment of the overall mass cannot ignore the contribution of the structural design to the mass budget. This is described in what follows.

#### *5.5. Preliminary Structural Design*

It was shown that an ablative material can offer the best thermal protection capability at the minimum mass from a thermal design point of view. This conclusion is not trivial when considering the structural performance. In particular, regarding a heavily loaded structural element, such as the ADD discussed in this work, the structural mass can represent the highest contribution to the overall mass budget. Considering a sandwich ITPS could therefore be advantageous for overall mass reduction. Having both the thermal and the structural mass integrated within one component, no add-on mass such as in the case of the ablative TPS is present. Additionally, from the operative point of view of an RLV, a reusable passive TPS is considered advantageous compared to ablative materials. However, ITPSs not only face mechanical loads due to the dynamic pressure, but additional thermo-mechanical ones. Therefore, a mechanical analysis of the considered solutions is necessary to assess the overall lightweight potential of the considered solutions. The thermal loads applied are the ones corresponding to the time step at which the highest thermal gradient is present. The mechanical load is the same for all three structures, namely the maximum dynamic pressure distribution (see Figure 7).

In the following, the two thermally optimised ITPS concepts from above are analysed using FEM simulations under mechanical and thermal loads. For the ablative TPS concept, a CFRP sandwich structure is designed iteratively to function as a load-bearing structure attached to the inside of the ablative layer of the ADD. This allows for a comparison of structural performance as well as total mass of the concepts. The following configurations were chosen from the previous sections:


The three configurations are tested under the same mechanical boundary conditions described in Section 5.1 (see Figure 7).
