**5. Results and Discussion**

## *5.1. Boundary Conditions*

The ADD is extended via a group of mechanisms with two anchoring points on the structure. One at the root, the other at half of the ADD's longitudinal length, as schematically shown in Figure 7. Rigid body elements are used to connect the fixation points to the structure. All translational and two rotational degrees of freedom (DOFs) are restricted. Only the rotational DOF about the y-axis is not.

**Figure 7.** Mechanical boundary conditions (in black) and mechanical load (in red) acting on the ADD: (**a**) in a longitudinal view of the ADD, (**b**) in a circumferential cut (A–A) view.

The input convective heat flux is obtained from the reference mission analysed in the Recovery and Return to Base project of the Horizon 2020 programme. In this work, the focus lies on the ADDs of the first stage analysed within the project.

During ascent, the four identical quarter shells (Figure 1) form a cylindrical shell and function together as primary structure of the launcher's interstage. During atmospheric reentry, the ADDs are extended to act as aerodynamic decelerators and therefore experience high mechanical and thermal loads.

Based on the re-entry mission analysis, computational fluid dynamic (CFD) simulations were performed to obtain the heat flux distribution on the rocket body at the point of maximum heat flux of the trajectory, which corresponds to an altitude of 35 km and

MACH = 8 speed. To obtain the heat flux variation as a function of time, the trajectory data is analysed with the Sutton–Graves formula [38]. The heat flux distribution on the ADDs as a function of time and longitudinal position along the component is obtained via interpolation and is reported in Figure 8a. The time *t* = 0 corresponds to the moment of the point of the descent trajectory at which the input convective heat flux at stagnation point first reaches 1 kW/m2. In a similar way, the pressure distribution is obtained and is reported in Figure 8b.

(**a**)

(**b**)

**Figure 8.** (**a**) Heat flux distribution along the ADD longitudinal coordinate as a function of time; (**b**) dynamic pressure distribution along the ADD longitudinal coordinate as a function of time.

The overall simulation time for the transient thermal analysis is 250 s. Although the convective heating approaches zero after approximately 100 s from the considered initial condition, additional simulation time is considered to take into account heat diffusion within the structure. Although, after the hypersonic and supersonic phases of the flight, convective cooling takes place on the body, the conservative assumption is made that only radiative cooling takes place. To simplify the representation of the thermal analysis, only a section of the ADD is considered in the following. The time curve corresponding to the local maximum of 400 kW/m2 at the longitudinal position of 2.2 m on the ADD is considered. The pressure distribution is applied on the whole component.

The thermal boundary conditions of the problem are schematically shown in Figure 9. It should be noted that the simulation of the ablative TPS differs from the ITPS cases because of the presence of blowing of the ablation products. The input convective heat flux is corrected via a blowing-corrected heat transfer coefficient, which is calculated as in [39]. The value for the term *ρeueCH* still needs to be assumed and is conservatively defined to be 0.3 as in [33]. The output radiative heat flux is obtained assuming heat transfer with the environment at room temperature. The emissivity of the TFS of the ITPS is assumed to be 0.8. The emissivity of the ablative material depends on the char grade and is obtained from empirical data implemented in the material model.

**Figure 9.** Applied thermal boundary conditions for (**left**) an ablative material and (**right**) for an homogenised ITPS with different cores.

#### *5.2. Thermal Response of the Ablative TPS*

The analysed material is PICA [40]. It exhibits a low recession rate, however, it also has a relatively high thermal conductivity. The root finding algorithm described in Section 3 is used to obtain the minimal thickness of the material. Figure 10a shows the temperature evolution at different points within the material as a function of re-entry time. Figure 10b shows the recession as a function of re-entry time. In Figure 10a, z is considered the thickness coordinate, which is fixed in space, i.e., the origin lies on the outer edge of the virgin ablative material. For this reason, several temperature curves end abruptly, indicating that the material at the corresponding coordinate ablated away at the given time point. The recession s is obtained by the subtraction of the initial thickness of the virgin material and the position of the moving ablating surface, as shown in Figure 9. The minimum thickness obtained is 47 mm, and a recession of 14.3 mm takes place. The additional material that does not ablate until the end of re-entry is necessary to respect the imposed constraint at the back-face temperature. Due to the relatively high thermal conductivity of PICA, much more material is needed for a proper insulation. The areal weight is 10.75 kg/m2.

**Figure 10.** (**a**) Temperature evolution during re-entry. Wall indicates the receding outer surface, whereas the other temperature curves are at fixed z coordinate; (**b**) material recession of the ablative PICA TPS during re-entry.
