5.2 Material modeling

distribution of different TPS materials that may be operated independently of the thickness distribution. Figure 4 shows an arbitrary distribution of stick primitives

The resulting potential field created by the superposition of sticks modulates

As demonstrative example, a parametric representation of TPS is obtained using a limited set of sticks primitive (nstick = 5), oriented as shown in Figure 5. Skin sticks characterized by a large radius and limited strength are spread over the skin surface in longitudinal direction in order to provide a thickness graded baseline. A constant minimum thickness is superposed in all remaining points of B-grid, ensuring a nonzero value in any point of the grid. Furthermore, additional parametric sticks, specifically positioned and oriented to affect thickness in critical regions as nose, leading edge, and trailing edge, complete the support for TPS and create a rational distribution of insulating material suitable with a reentry mission. Parametric position of sticks and axis of orientation are defined by assigning centroid coordinates xc,zc and angle θth, measured with respect to the system of reference reported in Figure 5.

(not suitable for application purposes) created over the topological map.

Length (l) and strength (th) are expressed with the parametric relations

lf g <sup>q</sup>¼1;…;<sup>5</sup> ¼ ltq ∙ dqmax

adopted for the leading edge (q = 4) and trailing edge (q = 5) sticks.

thf g <sup>q</sup>¼2;…;<sup>5</sup> ¼ th<sup>00</sup>

th<sup>1</sup> ¼ th<sup>0</sup>

8

>>>>>>>>><

>>>>>>>>>:

xc,f g¼ <sup>q</sup>¼1;2;3;4;<sup>5</sup> f g <sup>0</sup>:0;0:0;0:0;1:0;1:<sup>0</sup>

min þ pt<sup>1</sup> ∙ th<sup>0</sup>

a linear variation of point source blob radius. Conversely, a constant radius is

zc,f g <sup>q</sup>¼1;…;<sup>5</sup> ¼ dqmin þ stq ∙ dqmax � dqmin

� �

min

max � th<sup>00</sup>

� �

min

(11)

max � th<sup>0</sup>

min þ ptq ∙ th<sup>00</sup>

Skin (q = 1, 2) and nose sticks (q = 3) have a tapered support obtained imposing

� �

y-coordinate of grid points as shown in Figure 4.

Arbitrary stick distribution created over the topological map.

Hypersonic Vehicles - Past, Present and Future Developments

5.1 Thickness modeling

Figure 4.

22

5. Parametric model of thermal protection system

A similar but completely independent stick-based parameterization has been also defined to model a dynamic distribution map of different insulating materials, denoted here generically as material 1 and material 0 represented with red and blue colors, respectively. We assume that material 1 outperforms material 0. Therefore, material 1 is adopted on the nose, leading edge, and trailing edge, respectively. Differently than sticks used for thickness distribution, this additional set of primitives returns just binary values used to define specific materials. In this case the field function mth (see relation (12)) assumes a constant value equal to one inside the finite support of a stick and zero elsewhere. The parametric equations which describe material assignments are

$$\begin{cases} m\mathbf{x}\_{\boldsymbol{\epsilon}, \{q=1,2,3,4,5\}} = \{0.0, 0.0, 0.0, 1.0, 1.0\} \\\\ m\mathbf{z}\_{\boldsymbol{\epsilon}, \{q=1,\ldots,5\}} = d\_{q\_{\min}} + m t\_{q} \bullet \left(d\_{q\_{\max}} - d\_{q\_{\min}}\right) \\\\ m l\_{\{q=1,\ldots,5\}} = m l t\_{q} \bullet d\_{q\_{\max}} \\\\ m\mathbf{t} l\_{\{q=1,\ldots,5\}} = \mathbf{1} \end{cases} \tag{12}$$



Figure 6.

Figure 7.

25

Topological map created to represent TPS thickness on different RLV configurations.

Parametric Integral Soft Objects-based Procedure for Thermal Protection System Modeling…

DOI: http://dx.doi.org/10.5772/intechopen.85603

Example of thickness and material distribution over RLV configuration (RLV-1): (a, b) thickness modulation

[m]; (c, d) two material map (red/blue color indicates material 1/0, respectively).

Table 1.

Parameters adopted in the modeling of TPS configurations of Figures 7 and 8.

with normalized parameters reported in Table 1.
