1. Introduction

Currently a number of projects related to the development of reusable launch vehicles (RLV) both single-stage-to-orbit (SSTO) and two-stage-to-orbit (TSTO) are ongoing. This trend relates to objectives of future space missions that demand to improve vehicle operability, reducing at the same time flight costs of putting payload into orbit. Several preliminary studies/experiments related to this design scenario have been carried on. The European Space Agency developed two demonstrators, the EXPERT (European eXPErimental Re-entry Test-bed) program and the Intermediate eXperimental Vehicle (IXV), which performed an atmospheric lifting reentry from orbital speed [1]. Besides, an unmanned lifting body developed by Boeing X-37B has been put in orbit by an Atlas-5 rocket and performed a successful lifting-guided reentry. Furthermore, a growing demand for space tourism has emerged also in recent years [2]; therefore, a great deal of research effort has been put to design RLV as blended wing bodies also allowing a conventional and more comfortable landing on runways. The main requirements currently considered for RLV design are (i) to perform very low-g (nearly 1.5 g) reentry; (ii) to adopt a lightweight (passive), fully reusable thermal protection system (TPS) to withstand several flights without any replacement; and (iii) to provide vehicle autonomy to land at a predefined location for crew rescue

[3, 4]. In order to fulfill all those requirements, the duration of reentry flight increases and consequently the integrated heat load absorbed by the structure [3]. the thickness where critical heat loads are experienced and dropping out elsewhere. A similar, slightly modified procedure is also applied to create an arbitrary binary map of different TPS materials that may be operated independently (or synchronized) with the thickness distribution. The present formulation is formalized in the framework of a parametric model which exploits simple variations of parameters to perform the soft object mapping over discretized surface. Applications of the developed procedure to different arbitrary vehicle shape show the flexibility of the

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

Soft objects constitute a modeling technique which typically represents a domain using a scalar field, namely, a field function F, defined over a three-dimensional

<sup>j</sup>Fð Þ¼ <sup>x</sup> <sup>T</sup> � � (1)

Fið Þ¼ d fi ∘ di (3)

(2)

(4)

(5)

<sup>S</sup> <sup>¼</sup> <sup>x</sup><sup>∈</sup> <sup>R</sup><sup>3</sup>

that is, an isosurface S of the field function F specified by the threshold T represents an object instance using a raster conversion algorithm. Soft object modeling overcomes the drawback given by the parametric surfaces; that is, they automatically allow a self-blending between different primitives. Therefore, complex shapes can be modeled defining n ≥ 1 potential field fi, with origin in points xi, and the blending among them is formally accounted by the algebraic summation of

F dð Þ¼ ∑ fi

composes the distance metric di (which determines the shape of the objects associated to the key point xi), with the field function fi, being x the point of space

> di <sup>¼</sup> <sup>j</sup><sup>x</sup> � <sup>x</sup><sup>i</sup> j jj <sup>k</sup> ri

A more powerful representation used in soft object modeling is based on mor-

phological skeleton that synthesizes the morphological properties of a given domain. A skeleton Sk can be defined as a basic geometric entity (such as points, segments, and plain closed domains) around which more complex shapes can be created once the distance function is provided. The simplest soft object was introduced by Blinn that originally proposed the "blobby molecule," an isotropically

f dð Þ¼<sup>i</sup> exp � di

where d is the Euclidean distance (k = 2 in Eq. (4)). Blobby molecule is a soft object defined around a point skeleton, and its field function has an infinite support.

2 2 !

decaying Gaussian function modulated in strength and radius [16]:

ð Þ di n

i¼1

method.

2. Soft objects definition

their potential fields fi [18]:

A commonly adopted notation

in which the function is evaluated:

17

space. An implicit surface S defined as

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

The above consideration incidentally demands a trade-off among several nonlinear conflicting design objectives, also satisfying a number of constraint functions. As an example, the design of the TPS of an RLV performing a suborbital lifting reentry requires a mandatory compromise between the maximum allowed peak heating and the integrated heat load. This requirement may conflict with the adoption of a fully reusable TPS, either limiting the choice of material category or penalizing the total mass. In preliminary design practice, thousands of design configurations are typically evaluated by an optimization algorithm to find the best fit [5–11]. Therefore, a preliminary appraisal of vehicle performances is commonly performed using high-efficiency, low-order fidelity methods that give a support to a multidisciplinary analysis performed with a computational effort which fit the typical timeline of the conceptual design phase [11]. In current studies, TPS sizing is performed using several simplified assumptions, carrying out a one-dimensional heat conduction analysis with panel thickness modeled using stackups of different materials [12].

The aerothermal environment is a basic design criterion for either TPS sizing or choice of materials [13, 14]. Several works dealing with TPS sizing have been published in literature. Lobbia [8] determined the sizing of a TPS in the framework of a multidisciplinary optimization. Material densities and maximum reuse temperature were computed. TPS mass was estimated assuming the category of materials used for the space shuttle and thickness distribution assigned on a review of HL-20 materials for each component. Trajectory-based TPS sizing has been proposed by Olynick [13] for a winged vehicle concept. The heating peak was determined considering an X-33 trajectory, discretized in a number of fixed waypoints. The resulting aerothermal database was used as an input for a one-dimensional conduction analysis, and several one-dimensional stackups of different materials representative of TPS were consequently sized. Bradford et al. [14] developed an engineering software tool for aero-heating analysis and TPS sizing. The tool is applicable in the conceptual design phase for reusable, non-ablative TPS. The thermal model was based on a one-dimensional analysis, and TPS was modeled considering a stackup of ten different material layers. Mazzaracchio [15] proposed a method to perform the sizing of a TPS depending on the locations of ablative and reusable zone on a TPS considering the coupling between trajectory and heat shield. Multidisciplinary analysis, integrating a procedural NURBS-based shape representation, is adopted for a preliminary design [3]. NURBS parameterization allows a simple control over the aerodynamic shape using a limited number of sensitive design parameters acting as geometrical modifiers.

However, derivation of a unique parameterization to describe the overall changes of geometry resulting from a shape optimization is not always possible, and several surfaces are used to parameterize different parts of the geometry. Implicit surfaces are a powerful and alternative tool for creating shapes due to their smooth blending properties enabling creation of arbitrary shape. In the present work, a soft object-derived representation for TPS thickness and material attribution is introduced. According to the legacy formulation of this technique, originally developed in computer graphics for the rendering of complex organic shapes [16], threedimensional object surfaces are (implicitly) obtained by defining a set of source points (or even more complex varieties) irradiating a potential field that is subsequently tracked according to an assigned isosurface. Following a quite different paradigm developed in [17], the full potential field irradiated by a set of bydimensional soft objects is congruently mapped on a discretized RLV shape. The methodology is able to create arbitrary TPS distributions seamlessly increasing

Parametric Integral Soft Objects-based Procedure for Thermal Protection System Modeling… DOI: http://dx.doi.org/10.5772/intechopen.85603

the thickness where critical heat loads are experienced and dropping out elsewhere. A similar, slightly modified procedure is also applied to create an arbitrary binary map of different TPS materials that may be operated independently (or synchronized) with the thickness distribution. The present formulation is formalized in the framework of a parametric model which exploits simple variations of parameters to perform the soft object mapping over discretized surface. Applications of the developed procedure to different arbitrary vehicle shape show the flexibility of the method.
