Research ArticleThermal Protection System Design of a Reusable Launch VehicleUsing Integral Soft Objects

Andrea Aprovitola, Luigi Iuspa, and Antonio Viviani

Dipartimento di Ingegneria, Universitá degli Studi della Campania “Luigi Vanvitelli”, Via Roma 29, 81031 Aversa, Italy

Correspondence should be addressed to Antonio Viviani; antonio.viviani@unicampania.it

Received 25 September 2018; Revised 24 December 2018; Accepted 14 February 2019; Published 28 April 2019

Academic Editor: Maj D. Mirmirani

Copyright © 2019 Andrea Aprovitola et al. This is an open access article distributed under the Creative Commons AttributionLicense, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work isproperly cited.

In the present paper, a modelling procedure of the thermal protection system designed for a conceptual Reusable Launch Vehicle ispresented. A special parametric model, featuring a scalar field irradiated by a set of bidimensional soft objects, is developed and usedto assign an almost arbitrary distribution of insulating materials over the vehicle surface. The model fully exploits the autoblendingcapability of soft objects and allows a rational distribution of thermal coating materials using a limited number of parameters.Applications to different conceptual vehicle configurations of an assigned thickness map, and material layout show the flexibilityof the model. The model is finally integrated in the framework of a multidisciplinary analysis to perform a trajectory-based TPSsizing, subjected to fixed thermal constraints.

1. Introduction

In the last decade, a growing number of projects have beenfocused on the development of fully Reusable Launch Vehi-cles (RLV), designed for a crew-rescue mission. Successfuldemonstrative flights of private companies, like SpaceX, Vir-gin Galactic, and Sierra Nevada Corporation, and the activ-ity promoted by the European Space Agency are aimed atimproving operability of RLV [1, 2]. Consequently, a greatdeal of research effort has been put to design RLV as blendedwing-bodies, because of the promising trade-off betweenaerodynamic efficiency, cross-range, and aeroheating perfor-mances during the reentry [3]. The EXPERT (EuropeaneXPErimental Reentry Testbed) program and the IXV(Intermediate eXperimental Vehicle), which performed anatmospheric lifting reentry from orbital speed, are justexamples of such demonstrators developed to predict per-formances of a full-scale vehicle. Besides, the X-37B, anunmanned lifting body developed by Boeing, has been putinto orbit by an Atlas V rocket, performing a successfullifting-guided reentry. Furthermore, the foreseeable oppor-tunity for space tourism represented by experimental flights

of Virgin Galactic’s SpaceShipTwo and SpaceX has alsoemerged [4]. The requirements currently considered forRLV design are (i) to allow a very low-g (nearly 1.5 g) reen-try, with a landing on a conventional runway; (ii) to adopt alight-weight (passive), fully reusable thermal protection sys-tem to withstand several flights without any replacement;and (iii) to provide vehicle autonomy to land at predefinedlocations for rescue issues [2, 3]. In order to fulfill all thoserequirements, the duration of reentry flight increases andconsequently the integrated heat load absorbed by thestructure [2].

The above circumstances may conflict with the adoptionof a fully reusable TPS, eventually restricting the choice ofinsulating materials and penalizing the total mass [5]. How-ever, antithetical requirements between room for the pay-load, weight, and vehicle operability demand a trade-offbetween vehicle shape and TPS sizing. In preliminary designpractice, thousands of design configurations are typicallyevaluated by an optimization algorithm to find the best fit[5–10]. As a consequence, a preliminary appraisal of vehicleperformances is commonly performed using high-efficiency,low-order fidelity methods that give support to a multidisci-

HindawiInternational Journal of Aerospace EngineeringVolume 2019, Article ID 6069528, 14 pageshttps://doi.org/10.1155/2019/6069528

plinary analysis performed with a computational effort whichfit the typical timeline of the conceptual design phase [11].

The aerothermal environment is a basic design criterionfor either TPS sizing or choice of materials [12, 13]. TPS siz-ing is generally performed once the reentry trajectory isassigned, having computed the peak heating flux and thetime integrated heat load [14]. External rocket propulsionsystems allow an RLV a less severe heating due to their differ-ent ascent trajectories.

Therefore, an RLV operates an unpowered crew rescuewith the TPS sized mainly by its aerothermal reentry corri-dor. On the other hand, an RLV that performs an ascentphase with air-breathing propulsion systems is sized consid-ering more severe heating conditions [15]. Several worksdealing with TPS sizing have been published in the literature.Lobbia [8] determined the sizing of a TPS in the frameworkof a multidisciplinary optimization. Material densities andmaximum reuse temperature were computed. TPS masswas estimated assuming the category of materials used forthe space shuttle and thickness distribution assigned on areview of HL-20 materials for each component. Trajectory-based TPS sizing has been proposed by Olynick [13] for awinged vehicle concept. The peak heating temperature wasdetermined considering an X-33 trajectory, discretized in anumber of fixed waypoints. The resulting aerothermal data-base was used as an input for a one-dimensional conductionanalysis, and several one-dimensional stackups of differentmaterials representative of TPS were consequently dimen-sioned. Bradford [15] developed an engineering software toolfor aeroheating analysis and TPS sizing. The tool is applicablein the conceptual design phase, for reusable nonablative ther-mal protection systems. The thermal model was based on aone-dimensional analysis, and TPS was modeled consideringa stackup of ten different material layers. Mazzaracchio [14]proposed a method to identify the optimal combinationbetween the ablative and the reusable part of TPS. This wasdictated by a trade-off between the reentry trajectory andthe TPS sizing. In Wurster and Stone [16], a selection ofdesign trajectories, and wind tunnel data were integratedwith CFD simulations and engineering prediction to performTPS sizing for an HL-20 reentry vehicle. In the present work,following an approach proposed in Ref. [17], a soft object-derived representation for TPS thickness and material assig-nation is introduced. According to the legacy formulation ofthis technique, originally developed in computer graphics(C.G.) for the rendering of complex organic shapes [18],three-dimensional object surfaces are (implicitly) obtainedby defining a set of source points (or even more complexvarieties) irradiating a potential field that is subsequentlyrendered as a chosen isosurface. A major feature offered bythis methodology is that the topology of the regions repre-sented by these objects can be arbitrary and easily controlledjust by altering the mutual spatial position of the primitives.These very desirable properties have made implicit modellingtechniques extremely popular in the field of photorealisticrendering of organic shapes whose topology changes dynam-ically, and many advances and developments have been pro-posed over time to improve their capabilities and/or reducesome unwanted side-effects [19, 20]. In the present paper,

following a quite different paradigm developed in [21], thefull potential field irradiated by a set of bidimensional softobjects is congruently mapped on a discretized paneledRLV shape. The methodology is able to create arbitraryTPS distributions seamlessly increasing the thickness wherecritical heat loads are experienced and dropping out else-where. A similar, slightly modified procedure can also beapplied to create an arbitrary binary map representing mem-bership functions for TPS materials. This binary map can beoperated independently on thickness distribution (or locallysynchronized with different thickness maps). The presentformulation is formalized in the framework of a parametricmodel which exploits simple variations of parameters to per-form the soft object mapping over a discretized surface.Applications of the developed procedure to different vehicleconfigurations show the flexibility of the method. In addition,the procedure can be easily embedded in a multidisciplinarycomputation, to perform a trajectory-based TPS sizing on aRLV subjected to fixed thermal constraint.

2. Methodology

2.1. Soft Object Definition. Soft objects constitute a modellingtechnique introduced in computer graphics to representthree-dimensional objects having complex and organicshapes. Blinn first developed a soft object model to displaythe appearance of electron density clouds in a covalent bondof a molecule [18]. According to the model formulation,curved (closed) surfaces can be modeled defining n ≥ 1potential fields f i, namely, blobs. Several blobs f i can be con-nected smoothly by the self-blending property, by perform-ing an algebraic summation of their potential fields [22]:

F d = 〠n

i=1f i d , 1

The commonly adopted notation

Fi d = f i ∘ di, 2

separates the distance field di

di =x − xi 2ri

, 3

from the field function f i. The strength si = f i di accountsfor the value of f i in a generic point x, at distance di from akey point xi.

The potential field F generated by n blobs can be gener-ally taken into account computing a specific isosurface S(subsequently processed) by a raster conversion algorithm:

S = x ∈ℝ3 ∣ F x = T , 4

where the threshold T in equation (4) selects an isosurface ofF. Blinn originally proposed the “blobby molecule,” anisotropically decaying Gaussian function modulated bystrength, and radius [18]. The blobby molecule is a potential

2 International Journal of Aerospace Engineering

function with infinite support. This aspect affects the com-putational effort in a practical implementation, because ithas to be evaluated in all points of the space. However, inthe literature, several finite support potential functions havebeen proposed for different modelling purposes [22]. Thefield function f i used in the present work has a finite sup-port and assumes normalized values in the range between 0and 1 [22]:

f d =12 + 1

2arctan p − 2pd

arctan p, d < 1,

0, d ≥ 15

The parameter p defines the hardness of blob and con-trols the level of blending between two soft objects.

2.2. Two-Dimensional Integral Soft Object Field. Two-dimen-sional soft objects preserve the self-blending property. How-ever, it is not always easy to create a rational distribution of aset of independent point source objects for application pur-poses. Therefore, blobs are conveniently and easily arrangedin macroaggregates. Figure 1 shows that a potential field iscreated superposing n = 6 discrete blobs having radius rand centers mutually placed on a line segment of length lover an equally spaced two-dimensional grid of step δe = 1/nblob. If δe < 2r two or more blobs superpose, the strengthof the potential field is obtained summing up the strengthsof each blob (yellow colored region). This procedure relieson a similar idea to the one developed in [21] to generateself-stiffened structural panels. Specifically, the full (integral)potential field irradiated by a set of discrete two-dimensionalpoint source blobs generates a seamless potential field. Thisapproach is quite different from isocontour tracking com-monly adopted to represent soft objects.

2.3. Modelling of Two-Dimensional Stick Primitives. A super-position of n point source blobs with key points placed on ageometric segment (straight or curved) is denoted fromnow on as a “stick.” However, as shown in Figure 1(b),equation (1) creates a stick with a support having “bulges.”Increasing the number of sticks, the shape of the supportbecomes more regular. However, the strength is not bounded(see Figure 1(b)). The above drawback is overcome by mod-ifying the definition of the potential field given by equation(1). A bounded potential field, regardless of the number ofthe blobs used on a stick, is obtained with the relation

Fj P =max∀P

F j−1 P ,Gj P , j = 1,⋯, nblobs 6

Equation (6), where F0 P = 0, expresses the globalpotential field Fj P irradiated by a set of j blobs at a genericpoint P of space placed at a distance d from the key points, asthe max between the previous j − 1 potentials accounted forby the assembly layer Fj − 1 P and the current potential Gj

over the plane disk of radius r:

Gj P =f P , d < r,0, otherwise,

7

where nblob is the total number of blobs present on the B-grid.Figures 2(a) and 2(b) show the strength field of a two-dimensional stick primitive obtained using nblob = 6 and 20,respectively, computed with equation (6). By increasing thenumber of blobs on a stick, the strength of F is still boundedto a maximum unit value. Figures 2(c) and 2(d) show thesame behavior for a tapered primitive having a linear varia-tion of the blob radius along the axis of sticks.

3. RLV Shape Modelling and ThermalProtection System Sizing Criteria

In the present work, we assume that the generic shape of anRLV is represented by a grid formed by a quadrangularand/or by a degenerated triangular panel grid. Grid pointsare obtained using a proprietary procedure that authors fullydetailed in [23, 24]. Without going into details of the shapemodel, we remark that the mesh arrangement over the RLVsurface is obtained with no NURBS support surface: athree-dimensional parametric wireframe is created usingcubic rational B-splines and used to reconstruct the compu-tational surface grid. The control parameter allows a widerange of shape variations to handle different design objectives(thermal or dynamical) for a reentry mission. Grid topologyis equivalent to a spherical surface with no singularities (openpoles) and allows a mapping of the points in UV coordinatesover an equivalent cylindrical surface. The above consider-ations ensure a topologically invariant shape. In previouspapers proposed by the authors [23, 24], a multidisciplinaryshape optimization for an RLV comprising a trajectory-based TPS sizing procedure was developed. The TPS wasmodeled using two insulating materials placed at differentlocations along the vehicle surface. A different mapping(thickness distribution and longitudinal location) of the twomaterials with different operational temperature wasadopted. The sizing of insulating materials required the com-putation of aerothermal loads across the reentry trajectoryfrom a LEO orbit up toM∞ = 2, which is considered the limitbelow which thermal heating can be neglected. TPS thicknesswas parametrically sized according to thermal requirementsassumed in the optimization; a simple (but very rough), bilin-ear distribution of the TPS thickness along the longitudinalaxis of the vehicle and a linear distribution across each crosssection were adopted. The maximum allowable temperaturevalues (depending on the adopted material) for the interiorand exterior surfaces of TPS outlined the thermal constraintto be fulfilled by the sizing procedure.

4. Soft Object Design of TPS

4.1. Rationale. The modelling procedure for the TPS isdefined starting from the definition of a set of soft objectswhich are represented on the topological map associatedwith the current morphology of the object, as shown inFigure 3. Consequently, the supports of the sticks are

3International Journal of Aerospace Engineering

�훿e

l

r

(a)

2

1

0.8

0.6

0.4

0.2

1.8

1.6

1.4

1.2

0

(b)

Figure 1: Schematic representation of a stick obtained using point source blobs with centers placed on the linear segment of length l (a);strength field generated by self-blending property (b).

0.8

0.6

0.4

0.2

0

(a)

0.8

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0.2

0

(b)

0.8

0.6

0.4

0.2

0

(c)

0.8

0.6

0.4

0.2

0

(d)

Figure 2: Stick primitives obtained with nblob = 6 and 20: constant radius (a, b); variable radius (c, d). The stick support becomes more regularincreasing nblob; the strength field remains bounded to the unit value.

4 International Journal of Aerospace Engineering

adjusted according to the normalized dimensions relative tothis map. The topological map is emulated introducing atwo-dimensional grid (from now on denoted as B-grid)having the same topology tree as the vehicle open grid(number of points, panels, and connectivity) except forthe unit size. A geometric mapping between the B-gridand the vehicle grid is established, and elements of the B-grid are biunivocally mapped onto corresponding elementsof the vehicle surface (see Figure 3). Several stick primitivesare emulated on the B-grid placing a number of n equallyspaced isotropic blobs, with radius r and length l, in nor-malized units. Stick emulation is performed by overlappingn blobs using the special formulation reported in [21] thatensures a convergent envelope of the finite support and a lim-ited value of the blob strength. An exemplificative spatial dis-tribution of sticks on the B-grid is shown in Figure 3. Positionand orientation of each stick is determined by assigning coor-dinates of centers Ci and precession angles θi, respectively,with respect to a Cartesian frame of reference Oxz orientedas in Figure 3. Therefore, a generic distribution of sticks cre-ated on the vehicle grid is equally mapped on the vehicle sur-face whatever the morphological map considered. In thepresent case, gray colored regions (1) denote points of theB-grid mapped on the windward side of the RLV shape (seeFigure 3), while white regions (2) relate to leeward regionsof the vehicle. Regions of the vehicle surface mainly subjectedto heating peaks during the reentry maneuver are the (i)nose, (ii) leading edge, and (iii) tail. The global potential fieldgenerated by the sticks onto the B-grid is adjusted in a suit-able dimensional scale and subsequently mapped on the

mesh panels of the vehicle surface grid to obtain an easyand powerful control of the thickness distribution. The pro-posed methodology is able to create virtually arbitrary TPSdistributions and can be easily tuned up to locally increasethe thickness where critical heat loads are expected and drop-ping out elsewhere. A similar, slightly modified procedure isalso applied to create an arbitrary binary map distribution ofdifferent TPS materials that may be operated independentlyof the thickness distribution.

5. Parametric Model of a ThermalProtection System

5.1. Thickness Modelling. As a demonstrative example, aparametric representation of a thermal protection system isobtained using a limited set of stick primitives (nstick = 5),oriented as shown in Figure 4. Skin sticks characterized bya large radius and limited strength are spread over the skinsurface in the longitudinal direction in order to provide athickness graded baseline. A constant minimum thicknessis superposed in all remaining points of the B-grid, ensuringa nonzero value in any point of the grid. Furthermore, addi-tional parametric sticks, specifically positioned and orientedto affect thickness in critical regions, such as the nose, lead-ing edge, and trailing edge, complete the support for the TPSand create a rational distribution of insulating material suit-able with a reentry mission. The parametric position ofsticks and the axis of orientation are defined by assigningcentroid coordinates xc and zc and angle θth, measured withrespect to the system of reference reported in Figure 4.

Nos

e

Tail

Lower midline

(a) (b)

Stick

1

2

r

ci

�휃i

1

2

1

2

Lower midline

Leadingedge

x

z

x′z′

Figure 3: Morphological (a) vs. topological (b) map.

5International Journal of Aerospace Engineering

Length (l) and strength (th) are expressed with the paramet-ric relations:

xc, q=1,2,3,4,5 = 0 0, 0 0, 0 0, 1 0, 1 0 ,

zc, q=1,⋯,5 = dqmin+ stq ⋅ dqmax

− dqmin,

l q=1,⋯,5 = ltq ⋅ dqmax,

th1 = thmin′ + pt1 ⋅ thmax′ − thmin′ ,

th q=2,⋯,5 = thmin″ + ptq ⋅ thmax″ − thmin″

8

Skin (q = 1, 2) and nose (q = 3) sticks have a tapered sup-port obtained by imposing a linear variation of the pointsource blob radius. Conversely, a constant radius is adoptedfor the leading edge (q = 4) and trailing edge (q = 5) sticks.

5.2. Material Modelling. A similar but completely indepen-dent stick-based parameterization has been also defined tomodel a dynamic distribution map of different insulatingmaterials, denoted here generically as material “0” and mate-rial “1.” We assume that material “1” outperforms material“0.” Therefore, material “1” is a natural candidate to insulatethe nose, leading edge, and trailing edge. TPS materials areassigned according to a discrete distribution. Differently thansticks used for thickness distribution, this additional set of

Lower midline

(1)

(1)

Zctr3

xctr4

z

xctr5

d4max

d3min

Zctr5

x

�휃

d5min

d5max

d4min

(2)

�휃

�휃

�휃

Figure 4: Arbitrary stick distribution with a longitudinal gradient onto the B-grid adopted for thermal protection system modelling.

6 International Journal of Aerospace Engineering

primitives returns just binary values used to define specificmaterials. In this case, the field function mth (see relationsin (9)) assumes a constant value equal to one inside the finitesupport of a stick and zero elsewhere. Centroid coordinates(mxc,q and mzc,q) and length lq of these additional sticks aregiven by parametric relations in (9) with normalized param-eters reported in Table 1:

mxc, q=1,2,3,4,5 = 0 0, 0 0, 0 0, 1 0, 1 0 ,

mzc, q=1,⋯,5 = dqmin+mtq ⋅ dqmax

− dqmin,

ml q=1,⋯,5 =mltq ⋅ dqmax,

mth q=1,⋯,5 = 1

9

6. Additional Considerations about Integral SoftObjects for TPS Modelling

In order to better clarify the rationale underlying the pro-posed methodology, some additional considerations are pro-vided next. As a general premise, it should be emphasizedthat implicit modelling techniques canonically used in C.G.differ in many respects from those reformulated and usedin the present context. About this, a brief description of theapproaches followed in C.G. is preliminarily given, to high-light both common points and main differences with respectto the illustrated methods. In C.G., implicit modelling iscommonly used for the rendering of complex organic shapes.In these methods, some objects (usually referred to as blobsor primitives) of appropriate dimensionality (2D, 3D), typi-cally represented by their own morphological skeletons, areconceived as “emitters” of suitable finite support field func-tions, expressed as distance laws in an appropriate norm(usually Euclidean). These primitives are allowed to mutuallyinteract with each other by simply overlapping their finitesupports, cumulating in that way the field intensities wheresuperposition takes place. According to an implicit represen-tation, a specific instance (isosurface) of the global field asso-ciated to an assigned isovalue can be finally visualized.Depending on the chosen rendering method (e.g., ray-trac-ing), the isosurface can preserve its implicit formulation orbe evaluated through suitable progressive sampling algo-rithms (i.e., octree) to be translated into discrete polygonalelements, typically triangular meshes. In general, the mathe-matical structure of the isosurfaces will be characterized bysmooth curvatures, highlighting an intrinsic capability togenerate automatic fillets in those spatial regions whereprimitives overlap. Fillets can be controlled locally by intro-ducing a hardness parameter in the field functions, whichmakes the primitives “harder” or “softer” in blending. As pre-viously stated, in the present work, a methodology justroughly inspired by the aforementioned techniques has beenintroduced to arbitrarily control thickness and materialassignment using a limited number of control parameters.The proposed approach uses the same finite support fieldfunctions employed in implicit modelling; therefore, thedesirable capability to generate arbitrary topologies by simplycontrolling the mutual spatial position of primitives is

Table 1: Parameters adopted in the modelling of TPSconfigurations of Figures 5 and 6.

Parameter Value

st1, ad 0

st2, ad 0.01

st3, ad 0.05

st4, ad 1

st5, ad 0.8

lt1, ad 1

lt2, ad 0.1

lt3, ad 1

lt4, ad 1

lt5, ad 1

pt1 , ad 1

pt2 , ad 0.2

pt3 , ad 0.5

pt4 , ad 0.2

pt5 , ad 0.6

d1 min, ad 0.5

d2 min, ad 0.01

d3 min, ad 0.09

d4 min, ad 0.1

d5 min, ad 0.02

thmin′, ad 0.07

thmin″, ad 0.132

mt1, ad 1

mt2, ad 0.01

mt3, ad 0.05

mt4, ad 1

mt5, ad 0.8

mlt1, ad 1

mlt2, ad 0.1

mlt3, ad 1

mlt4, ad 1.2

mlt5, ad 1

mpt1, ad 1

mpt2, ad 1

mpt3, ad 1

mpt4, ad 1

mpt5, ad 1

d1 max, ad 1

d2 max, ad 0.3

d3 max, ad 1

d4 max, ad 0.5

d5 max, ad 0.5

thmax′, ad 0.12

thmax″, ad 0.25

7International Journal of Aerospace Engineering

maintained. However, differently from what is being imple-mented in C.G., where the discrete resolution of the trackedisosurface is often adaptive and conditioned by the expectedrendering quality and the amount of local curvatures, theseprimitives are now just projected onto a two-dimensional flatgrid with a fixed resolution that acts as an extended finitesupport; the global field resulting from primitive interactionis then used integrally, not just represented with single con-tours. Therefore, no implicit formulation is used at all. Thesecircumstances explain the definition of “integral soft objects”(opposed to “implicit modelling”) used in the present contextto describe the “agents” that operate to assemble the maps ofthickness and material. In this new framework, the legacycontrol parameters for field functions adopted in C.G. arestill maintained, although with a different semantic connota-tion. Specifically, the strength parameter has been reinter-preted either as the maximum thickness value of TPSlocally transferred onto the topological map or the maximuminteger value of the set of pointers; instead, the hardnessparameter becomes the thickness gradient with respect tothe distance in the finite support. A major aspect that affectsthe implementation of the method is given by the low spatialresolution of the topological map where TPS thickness andmaterials are transferred. Due to the specific methodologies(panel methods described next) used in the resolution ofthe thermal and fluid dynamic fields on the body at differentspeed regimes, this grid is extremely coarse if compared tothe typical resolutions used in C.G. (only a few hundred qua-drangular elements are used). In addition, the resulting thick-ness and material distributions are sampled only at thecentroids of the panels and assumed constant for each panel.These intrinsic limitations have determined the abovedescribed implementation choices; those rationales arebriefly given here: (i) a stick primitive has been preferredand systematically adopted in this context, because effectiveTPS thickness distributions likely happen along the UV para-metric directions of the topological map. Effectiveness andflexibility of these distributions have been increased by alsoallowing tapered and steerable sticks. (ii) A surrogate repre-sentation of a skeleton-based stick is simply obtained by dis-tributing a finite number of one-point skeleton primitives(circular blobs), mixing each other with the MAX blendingoperator outlined by equation (6). As mentioned earlier, therationale of this choice is that the field function of the assem-bled stick primitive still remains limited, and at the sametime, only a small number of circular blobs (slightly morethan a dozen) are required to obtain a satisfactory envelopeof the finite support without bulges because of the low intrin-sic resolution of the grid combined with the actual rangesassigned to the finite supports of primitives. Moreover, thissimplified approach allows in perspective the definition ofsome other primitives based on different skeletons (homeo-morphic with the line segment, for example, based onsplines) that might potentially ensure more sensitivity inthe TPS definition problem with no major modificationrequired. (iii) Although it is virtually possible to use anysuitable blending function to merge the fields of different pre-assembled primitives (for example, the sum of the local mag-nitudes), the MAX blending function is also still preferred for

this purpose, because the intrinsic capability offered by thisoperator to generate “ziggurat-style” step fields when theinvolved primitives exhibit different strength values has beenconsidered desirable for an effective TPS thicknessdistribution.

7. An Example of TPS Modelling Capabilities

The previously introduced modelling procedure has beenapplied on a conceptual RLV shape created with the modeldescribed in Section 4 and detailed in [23, 24]. The applica-bility of the procedure is shown for the arbitrarily chosen dis-tribution of stick primitives that creates a morphologicallyadaptive TPS on two RLV shapes with different dimensions:RLV-1 with length ltot = 9 8 m, wingspan ws = 5 6 m, andcabin height h = 1 6 m and RLV-2 with length ltot = 15 m,wingspan ws = 9 2 m, and cabin height h = 2 m.

The parameters characterizing the distribution of thick-ness and the materials are reported in Table 1. Figures 5(a)and 5(b) show the application of TPS modelling over the firstconfiguration (RLV-1), on leeward (a) and windward (b) sur-faces. Different colors denote different values of thicknessand are represented in a dimensional scale. It can be observedthat the thickness map can be easily tuned up for best cover-ing of regions where maximum heat loads occurs (i.e., thenose and leading edge). Figure 5 shows the capability to cre-ate arbitrary seamless thickness distributions up to the valueof the baseline thickness which has been arbitrarily set equalto thmin = 0 05 m (denoted in blue color). This correspondsto a region of the leeward surface not covered by the skinstick. Figures 5(c) and 5(d) show the map of two differentinsulating materials created with equation (9). Red colorsindicate material 1, which is placed on regions of the vehiclesubjected to higher heat loads. Comparisons betweenFigures 6(a) and 6(b) and Figures 6(c) and 6(d) also exhibitthe capability of the model to handle independently boththe thickness and material distribution. Finally, Figures 6(a)and 6(b) and Figures 6(c) and 6(d) show the same blob distri-bution adopted either for thickness or for material modellingapplied on a different RLV configuration (RLV-2). The pro-cedure creates, as expected, the same TPS distribution bothfor thickness or materials on two different shapes and iscompletely independent by their morphology.

8. Application of the TPS Sizing Procedure for aConceptual RLV Configuration

The TPS modelling procedure developed in the previous sec-tions has been implemented in the ANSYS® ParametricDesign Language [25], to perform a trajectory-based sizingof a TPS for an RLV designed for a LEO reentry mission. Amultidisciplinary analysis comprising aerodynamics, heatinganalysis, trajectory estimation, and mass estimation is imple-mented to determine the aerothermal loads on the vehicle.The entire flowchart of the procedure has been discussedand detailed in [23, 24]. For the sake of brevity, here, it willbe addressed with reference to the specific application, spec-ifying the assumptions adopted. TPS is designed to withstandheating for an unpowered reentry maneuver performed from

8 International Journal of Aerospace Engineering

an altitude of h t0 = 122 km andM∞ = 23 down toM∞ = 2.The reentry is finalized with a conventional landing per-formed at the prescribed speed. The mission is based on the

following stages during reentry: (1) hypersonic phase, (2)supersonic phase, (3) subsonic phase, and (4) landing. Aswe want to address the applicability of the developed sizing

.050048

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Figure 6: Example of thickness and material distribution over the RLV configuration (RLV-2): (a, b) thickness modulation (m); (c, d) twomaterial maps (blue/red color indicates material “0”/“1,” respectively).

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Figure 5: Example of thickness and material distribution over the RLV configuration (RLV-1): (a, b) thickness modulation (m); (c, d) twomaterial maps (blue/red color indicates material “0”/“1,” respectively).

9International Journal of Aerospace Engineering

methodology for a conceptual design configuration, low-order fidelity methods [3, 5] are used for each subdisciplineto reduce the computational time [11].

8.1. Aerodynamics. Aerodynamic coefficients for the hyper-sonic phase of the reentry are computed with a publicdomain panel flow solver using Newtonian flow theory avail-able in Ref. [26], in the waypoints reported in Table 2.According to Newtonian theory, hypersonic flows are mod-eled as an ensemble of particles impacting the surface of abody approximated to a flat plate at incidence. Therefore,considering a discrete panelization of the body surface, thepressure force δFi acting on the i-th panel having an area δAi and directed along the outward unit normal vector tothe panel n̂i is then computed as δFi = −piδAin̂i. The nondi-mensional force coefficients in a body frame of reference aregiven by

Sref

CX

CY

CZ

≈ −〠N

i=0CpiδAin̂i, 10

computed as the summation of pressure forces over the totalnumber of mesh panels. Newtonian approximation is accept-able in the range of altitudes and Mach numbers up to M∞= 2, as viscous-force contribution in the axial direction onhypersonic bodies decreases with an increasing angle ofattack [3, 8, 27]. Validation of the present computations onaerodynamic coefficients has been previously performed in[24], together verifying the mesh independence of aerody-namic coefficients. Different choices of impact methods areadopted in the computation and are indicated in Table 3.The rationale behind the partitioning of the nose and wing-body region is related to the different flow incidence occur-ring on the wing-body panels requiring the use of appropri-ate compression methods adopted along the windwardregion (see Table 3). A similarity between the flow on thewing-body panels and the flow downstream of an attachedshock can be assumed, and the tangent cone method can beused [8]. Aerodynamic coefficients of the vehicle at anincompressible Mach number are computed by adoptingthe integral formulation of the potential generated at a pointP by a distribution of singularities (sources and doublets)with strength σ and μ, respectively,

ϕP ′ = −14π ∬

SB+SW

1rσ − μ ⋅ ∇

1r

dS, 11

being SB and SW being the body and the wake surface, respec-tively. The freely distributed panel code available in Ref. [28]is adopted for the current computation of this aerodynamicregime. The solver requires a discretization of the geometryby quadrilateral panels with sources and doublets of constantstrength. An approximation of equation (11) on the compu-tational mesh is

〠Np

i=0aiμi + 〠

Np

i=0biσi = 0 12

The unknown values of doublet strength μi are obtainedby solving the linear system of equations obtained by discre-tizing equation (11). To make the solution uniquely defined,tangency condition is applied, i.e., V ⋅ n = 0, and the sourcestrength σi is set equal to σi = ni ⋅V∞ on each control node.Furthermore, a wake surface, still based on quadrilateralpanels, has been added to apply the Kutta condition on eachpanel at the trailing edge. The intensity of the wake panels isset equal to the difference between the doublet strength ofthe upper and lower doublet panels at the trailing edge.Having computed the doublet strengths, the determinationof velocity, pressure, and therefore aerodynamic coefficientsis performed.

8.2. Mass Estimation. The mass of the thermal protection sys-tem mtps has been estimated modelling the TPS with two ofthe materials adopted for the space shuttle thermal insulationsystem whose thermal properties are reported in [29, 30]: theReinforced Carbon-Carbon (RCC) composite and High-Temperature Reusable Surface Insulation (HRSI) tiles, madeof coated LI-900 silica ceramics. RCCmaterial can be selectedfor the thermal insulation of the nose, leading edge, or trail-ing edge, where the peak wall temperature is expected. Amass decoupling model, based on the set of relations reportedin [31], is adopted in the current procedure to compute themass of the vehicle:

mtot =mvehicle +mtps, 13

being

mvehicle =mdry +mecd +mav +mecl +mpar, 14

excluding the contribution of the thermal protection system,wheremdry , mecd, mav, mecl, and mpar are reported in Table 4.The mass of the thermal protection system mtps,

mtps = 〠npanel

i=1ρiSi ⋅ thi, 15

with ρi, Si, and thi being the density of the insulating mate-rial, area of the discrete i-th panel of TPS, and thickness ofthe i-th TPS panel, respectively, computed with the proce-dure developed in Section 5.

8.3. Flight Dynamics. The calculation of the trajectory is per-formed in a nonrotating, inertial, Earth-Centered, Earth-Fixed (ECEF) frame of reference, according to the generalsystem of equation of planetary flight reported in Ref. [32].The vehicle is assumed as a mass point, describing a nonpla-nar reentry trajectory with a constant bank angle μa = 45°,assigned to ensure a cross-range performance. A negativevalue of initial reentry flight-path angle γ = −1 4° is given toavoid the skip phenomenon [32]. The angle of attack changes

10 International Journal of Aerospace Engineering

following an implicitly defined modulation law, reported inTable 2. The initial value of longitude θ, latitude φ, and flightazimuthχ are all set to zero. The vehicle dynamics is describedby a four-degree-of-freedom point mass model. Trajectoryequations have been integrated by using an implicit Newton-Raphson method to reduce the computational time of theoverall procedure, performing a time step sensitivity analysisto ensure convergence of the numerical integration.

8.4. Heating Analysis. The thermal state of the TPS is effi-ciently determined computing its exterior (w2) and interiorwall temperatures (w1) which determines the choice of thematerial. The thermal analysis is only performed on thewindward side as this is the maximum heated region of theTPS; the leeward side of the vehicle is supposed to be thefixed wall temperature region. Heat radiated from the exter-nal TPS wall w2 provides the cooling of the vehicle. Catalyticrecombination, low density effects, and thermal radiationfrom nonconvex surfaces are neglected. The above simplify-ing assumptions are considered reasonable for a conceptualdesign phase and determine a conservative overestimationof the TPS mass. A one-dimensional model of the TPS thick-ness [6] is used to determine TPS interior wall temperaturesTw1 exploiting the exterior TPS surface Tw2 temperature.Radiative equilibrium is assumed on wall w2 [5]:

qw2= εσT4

w2, 16

where ε is the surface emissivity and σ is the Stefan-Boltzmann constant. The convective heating at the wall w2at the stagnation point qw2 stag is approximated using the

following correlation:

qw2 stag = 1 83 ⋅ 10−8 ρ

rnose

0 5V3 1 −

Cpw2Tw2

0 5V2 , 17

where Cpw2 is the specific heat at the wall, ρ the free-streamdensity, and V the vehicle velocity. The windward convectiveheating qw2 win on the vehicle is evaluated using a correla-tion for spheres, cylinders, and flat plates [33]:

qw2 win = CρNVM , 18

where the constant C is specifically characterized for a lami-nar or turbulent boundary layer. TPS wall temperatures aredetermined using kinematic trajectory data, in the range 2≤M∞ ≤ 23 where peak values were expected to occur.Equation (18) is solved using a Newton-Raphson method

to determine the wall temperature Tw2i on each panel ofthe TPS thickness discretized as shown Figure 7. The interiorTPS wall temperature Tw1i is computed at each node of thediscrete i-th panel of the TPS integrating in time a one-dimensional unsteady heat-diffusion model [12, 23]. Boththe initial and boundary conditions assigned as

T yw2,i, 0 = T yw1,i, 0 = 285K, T yw2,i, t = Tw,i,∂T∂y yw1i

= 0,

19

provide a well-posed heat-diffusion problem, numericallysolved with a finite difference method. The thermal state ofTPS is globally defined assuming, for each computational ele-ment i, the following scalar relations:

T Int = 〠npan

iw1=1Tmax,iw1

− Tmax,w1 δi,

TOut = 〠npan

iw2=1Tmax,iw2

− Tmax,w2 δi,20

Table 4: Mass decoupling procedure.

Mass component

Fuse mfuse = 10 59−6SwetCrew mcrew = 12 82 ⋅ 39 66 ⋅N1 002

crew0 6916

Payload bay doors mpldoors = 2 78−6 ⋅ SwetPayload bay(not the doors)

mplbay = 2 35−6 ⋅ Swet + 1 26−6 ⋅ Swet

Dry mass mdry =mfuse +mcrew +mpldoors +mplbay

Electric conversion system mecd = 0 028 ⋅mdry

Avionics mav = 710 ⋅m0 125dry

Table 2: Waypoints adopted for aerodynamic computation.

Waypoint Flow regime Angle of attack Altitude

1 Hypersonic M∞ ≤ 23 44° 40 < z ≤ 122 (km)

2 High supersonic M∞ ≤ 3 6 19° 20 < z ≤ 40 (km)

3 Low supersonic M∞ ≤ 2 14° 10 < z ≤ 20 (km)

4 Subsonic M∞ ≤ 0 3 10° z ≤ 10 (km)

Table 3: Selected impact methods for aerodynamic computations.

Panel regions Windward Leeward

Nose region Modified Newtonian Prandtl-Meyer

Wing-body region Tangent cone (corrected) Prandtl-Meyer

11International Journal of Aerospace Engineering

where the variable δi vanishes for negative values of the dif-ference Tmax,iwi − Tmax,wi

δi =1, Ti,iwj

> Tmax,wj , j = 1, 2,

0, otherwise,21

where it has been supposed that Tmax,w1 = 430 K is the valueof the maximum allowable TPS temperature which adheresto structural elements of the vehicle and Tmax,w2 is the reusetemperature limit depending on the material [30].

Tmax,w2 RCC = 1920K,Tmax,w2 Li‐900 = 1644K

22

8.5. Results. The multidisciplinary analysis previouslydescribed has been applied to perform sizing and materialdistribution of a TPS for an RLV with dimensions chosenequal to length ltot = 8 6 m, wingspan ws = 8 5 m, and cabinheight h = 1 5 m. Thickness distribution of Figures 8(a) and8(b) is obtained by setting nstick = 3.

Position, axis of orientation, and strength of stick primi-tives are manually and iteratively assigned, rationally choos-ing stick parameters, to cover the most heated regions of theTPS surface. A minimum value of the thickness set equal tothmin = 0 05m allows the convergence of the heat conductionproblem (see equation (19)). A maximum value of thicknessis chosen equal to thmax = 0 29 m and takes into account theconservative assumptions made in Section 8.5; therefore, it isexpected to be oversized but in agreement with the approxi-mations used in the conceptual design phase [5]. It is

Adiabatic wallboundary condition

on w1Spacecraft

interior

TPS thickness

Windward ofRV-W

Radiated heatingon i-th panel

qw qrad

Convective heatingon i-th panel

O ≡ yw1Computationalnode

Radiativeequilibrium on w2

. .

Figure 7: One-dimensional discretization of TPS thickness.

.05

.077616

.105232

.132848

.160465

.188081

.215697

.243313

.270929

.298545

(a)

.05

.077616

.105232

.132848

.160465

.188081

.215697

.243313

.270929

.298545

(b)

0

1

(c)

0

1

(d)

Figure 8: Thickness distribution (m) on the conceptual RLV (a, b); two-material distribution on the conceptual vehicle (c, d) (red color: RCC,blue color: Li-900).

12 International Journal of Aerospace Engineering

observed in Figures 9(a) and 9(b) that the seamless distribu-tion of thickness is obtained along the wingspan directions.The nose thickness is increased only on the windward side,because the leeward side is assumed to be at constant temper-ature during the reentry. Figures 8(c) and 8(d) show thebinary material distribution between the RCC and Li-900tiles. The selected configuration fulfills the thermal constraintTw1i ≤ 430 K on each panel i of the discrete interior TPS wallas shown in Figures 9(a) and 9(b), and the computed mass ofthe thermal protection system is mtps = 1996 kg.

9. Conclusions

In the present paper, a special modelling procedure of thethermal protection system designed for a conceptualReusable Launch Vehicle has been developed. A set of mac-roaggregates of point source blobs organized in envelopesof finite supports and with a bounded strength has been suc-cessfully created on the topological map associated with thecomputational grid. Applications of the modelling procedureto different design configurations highlighted the sensitivityand powerful control to radically change the TPS using a lim-ited number of parameters. This feature has been illustratedexecuting a multidisciplinary analysis regarding a conceptualconfiguration where a simple iterative and manual sizing ofthe thermal protection system has been successfully per-formed, without adopting any optimization procedure.

Data Availability

The data supporting the analysis are from previouslyreported studies and datasets, which have been cited in Ref.[20, 21]. Specifically, the multidisciplinary analysis discussedin Section 7 has been performed on an RLV shape formu-lating a multiobjective optimization problem. The problemset-up, including the range of design variables, has beendetailed in [21]. Thermal properties of materials used inthe TPS sizing procedure are available in [27].

Conflicts of Interest

The authors declare that there is no conflict of interestregarding the publication of this paper.

Acknowledgments

This work was supported by Università degli Studi dellaCampania Luigi Vanvitelli.

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197.468223.011248.555274.099299.642325.186350.73376.273401.817427.361

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13International Journal of Aerospace Engineering

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