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where {v} represents the design variables, TB is the peak bottom face sheet temperature, TBis the maximum allowable bottom face sheet temperature, {B} is an array containing the allowable buckling eigenvalues, λL is the minimum allowable buckling eigenvalue, {σ} is a vector containing the maximum stresses in the panel, σallowable is the maximum allowable stress in the panel, uT is the maximum deflection of the top face sheet in the thickness direction, and uT-allowable is the maximum allowable deflection of the top face sheet.

1.4.2 Geometry and Design Variables The geometry of the ITPS structure with corrugated-core design is shown in Figure 1-1.

This geometry can be completely described using the following 6 geometric variables:

1. Thickness of top face sheet, tT,

2. Thickness of webs, tW,

3. Thickness of bottom face sheet, tB,

4. Angle of corrugations, θ,

5. Height of the sandwich panel (center-to-center distance between top and bottom face sheets), h,

6. Length of a unit-cell of the panel, 2p.

1.4.3 Analysis: Finite Element Methods Heat transfer, buckling and stress analyses have to be carried out on the ITPS structure in order to formulate the temperature and other structural constraints. In this research, all the analyses were carried out by finite element (FE) methods using ABAQUS® finite element package.

Heat transfer finite element analyses were carried out to determine the maximum bottom face sheet temperatures and temperature distributions in the ITPS, buckling FE analyses were carried out to determine the smallest buckling eigenvalues, and stress analyses were carried out to determine the maximum stresses in the ITPS and the maximum deflection of the top surface.

Details of these analyses, and load and boundary conditions used are presented in Chapter 3.

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Figure 1-1. A unit cell of the corrugated-core ITPS design. The six variables describing the geometry are illustrated. Directions y and z of the global coordinate system of the ITPS panel are also shown (x-axis comes out perpendicular to the plane of the paper).

1.4.4 Loads and Boundary Conditions The ITPS can be considered an extension of or improvement over the ARMOR TPS design [12–14]. Therefore, in the design process the aerodynamic heat load and the mechanical loads from a VentureStar RLV design were used [12,13]. The design performance and weights are also compared with those of the ARMOR TPS, in order to gain a perspective on the ITPS design with respect to the current designs. The material selection for the designs was also similar to that of the ARMOR TPS. Details have been presented in Chapter 5.

1.4.5 Formulation of Constraints The relation between the geometric design variables and the constraints was established in the form of response surface approximations. Hundreds of FE analyses were conducted at design points in a suitably chosen design space. The design points were obtained with the help of an optimized Latin-Hypercube Sampling technique. Results from FE analyses were used to fit quadratic polynomials called response surface approximations. For each constraint, one or more response surface approximation was obtained in the form of a complete quadratic polynomial in terms of the design variables. The response surface approximations can approximately predict the value of a constraint, given an arbitrary combination of design variables. The process for obtaining these approximations has been described in Chapter 4.

Generation of response surface approximations requires a large number of function evaluations, or in this case a large number of FE analyses. It is not possible to carry out these FE analyses manually. Therefore, a MATLAB® code called ITPS Optimizer was developed for this process, which has the capability to automatically carry out hundreds of FE analyses in conjunction with ABAQUS® FE package.

1.4.6 Optimized Designs The response surface approximations were generated from the data obtained from the ITPS Optimizer using least squares approximation method. These response surface approximations were then used for the optimization process, which was carried out using the Matlab® optimizer subroutine fmincon( ).

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This chapter presents background relevant to this research work. First a discussion on the general types of TPS used on space vehicles is presented followed by a summary of the history of TPS and NASA. Then a discussion on the need for an ITPS and the various challenges related to ITPS design is presented. As the ITPS panel geometry is similar to corrugated-core or trusscore sandwich structures, a brief summary of the research work related to these sandwich structures is presented. Finally, literature on multidisciplinary optimization (MDO) and response surface approximations technique is presented.

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Type of TPS and specific designs can depend on the magnitude and duration of aerodynamic heating. Even on the same vehicle several different TPS may be used, as the heating varies over the vehicle surface. TPS approaches can be broadly classified into 3 categories: active, semi-passive, and passive [11: p.24].

2.1.1 Active TPS Active TPS have an external system that supplies coolant to continually remove heat or to block the heat from reaching the structure. There are three commonly discussed active TPS concepts [11: p.28]: transpiration, film and convective cooling. In transpiration and film cooling a fluid is ejected from the vehicle surface, which flows along the surface and evaporates by absorbing the aerodynamically-generated heat, thus, preventing the heat from reaching the surface of the vehicle. Convective cooling is a more practical TPS concept and has been studied for use in the airframe structure of National Aerospace Plane [11: p.28]. In this concept, a coolant is circulated through passages in the airframe to remove heat that has been absorbed from aerodynamic heating. In all these cases, an external pumping system is required to bring the fluid from a coolant reservoir to the surface. The weight of the coolant is added to the launch weight along with the weight of the pumping system. Further, the design of these active coolant components is very complicated and may lead to high maintenance costs.

2.1.2 Semi-passive TPS Semi-passive TPS use a working fluid to remove heat from the TPS but require no external system to circulate the fluid. Two of the most frequently discussed semi-passive TPS concepts are heat pipes and ablators. Heat pipes are suitable for regions where there is extremely high, localized heating close to a cooler region. Heat pipes embedded in carbon-carbon TPS have been studied for the wing leading edge of the National Aerospace Plane [17]. In this concept, heat is absorbed by the working fluid in the hotter area. This heat vaporizes the fluid and the vapor flows into the cooler regions where it condenses by giving up heat to the cooler structure. The coolant is then brought back to the hotter regions by the capillary action of a wick.

Ablators are very practical and attractive concepts for thermal protection and were extensively used on space capsules like Apollo and Soyuz. Ablators undergo chemical changes by absorbing the aerodynamic heat and generate gases, thus, blocking the majority of the heat from reaching the vehicle surface. Apollo used a phenolic epoxy resin ablator for thermal protection [5,6]. While ablation has been successfully used for small areas for thermal protection, it is not a viable concept for large vehicle surfaces like the Space Shuttle Orbiter.

2.1.3 Passive TPS Passive TPS radiate the heat from top surface and/or absorb heat into the structure during high heating periods and dissipate it after the heating subsides. Passive TPS have no working fluids to remove or dissipate heat. Passive systems have the simplest designs and are suitable for low heat loads. For high heat loads the weight of the passive TPS becomes prohibitively high.

Three different types of passive TPS are discussed here: heat sink, hot structure and insulated structure.

Heat Sink. In this concept, a major portion of the incident heat load on the TPS is absorbed into the TPS structure. The amount of heat that can be absorbed is determined by the specific heat capacity and maximum service temperature of the TPS material, and initial temperature of the TPS structure. For higher heat load, higher amount of TPS material has to be added. But the structure weight could become large for high heat loads. The biggest advantage of heat sink concept is that it leads to a simple and reliable design. Heat sink approach has been implemented on early ICBMs and the afterbodies of the Mercury and Gemini reentry vehicles [4,11: p.25].

Hot Structure. The temperature of a hot structure is allowed to increase close to the radiation equilibrium temperature, so that a major portion of the heat is radiated out of the TPS.

Radiation equilibrium temperature is the temperature of the surface at which the heat flux radiated out is equal to the incident heat flux. The radiation equilibrium temperature is determined by the emissivity of the top surface of the TPS. The radiation equilibrium temperature for heat fluxes on the Space Shuttle Orbiter could be as high as 3000 F [10]. Thus, materials used for a hot structure TPS need to have extremely high service temperatures.

Insulated Structure. This structure has features of both hot structure and heat sink. The outer surface of the TPS is insulated from the underlying structure using insulation materials.

Since the insulation material conducts only a fraction of the total incident heat, the temperature of the top surface increases close to radiation equilibrium temperature and radiates away most of the heat. The structure also acts as a heat sink and stores the heat that has been absorbed.

Insulation TPS are usually not designed to withstand significant mechanical loads. They are made of thin gauge material and low-density insulation materials.

Most of the active and semi-passive TPS concepts have the capacity to accommodate large heat fluxes for long periods of time. However, these TPS require overcoming a number of technological challenges and still may have a complicated design and high operating costs in the form of maintenance and additional launch costs for coolant and pumping systems. The prohibitive technological challenges and operating costs limit the use of these TPS to small areas where there is severe aerodynamic heating. For most part of the vehicle surfaces, passive TPS concepts are used. The ITPS is based on the passive TPS concept.

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Since its conception in 1958, NASA has been heavily involved in research related to manned-space flight. Of the numerous technical challenges for manned flights, TPS is one of the most critical. The history of TPS in NASA’s manned space flights can be described using details from three vehicles: a) Apollo, b) Space Shuttle Orbiter, c) X33/VentureStar.

The Apollo program ran from 1963 to 1972.. It had two predecessors capable of human space flight: Mercury (1959–1963) and Gemini (1963–1966), from which the technologies were derived to develop TPS forApollo [4,5] (See Figure 2-1). It was designed to land men on the Moon and bring them back safely to the Earth. The spacecraft was launched into space and propelled towards the Moon using a three-stage rocket, Saturn V. After completing the lunar mission, the only component that came back to the Earth was the Apollo Command Module, which carried the astronauts. The Command Module was designed for a ballistic reentry to Earth, in other words, it just fell to the Earth from the space, and the reentry speeds were as high as 35,000 km/hr [5]. This resulted in severe aerodynamic heating on the front face and relatively lower heating on the afterbody. The high heating rates necessitated the use of ablative TPS on these capsules. From among a large number of ablators developed for this program [6], a lowdensity ablation material, AVCOAT 5026-39/HC-GP was used [6]. The Apollo heat shield structure is shown in Figure 2-2. In order to increase the ablator tensile strength, it was injected into a fiberglass reinforced-nylon-phenolic honeycomb structure, which was bonded to a brazed stainless steel honeycomb structure. The functions of the stainless steel honeycomb substructure were to hold the ablator in place and to transfer the aerodynamic loads to the aluminum honeycomb panel at the bottom, which was the primary load bearing structure. The differential thermal expansions between the stainless steel and aluminum honeycombs were accommodated by using a slip-stringer strain-isolation system [5]. The ablator was designed to maintain the temperature at the ablator-stainless steel honeycomb interface below 600 F. The space capsules were for one time use only. None of the parts were reused for the next missions.

The Space Shuttle Orbiter was a drastically different manned space flight concept than the space capsules. Development of the orbiter began in the late 1960s and the first successful manned launch was in 1981. The Orbiter’s shape is similar to commercial airplanes. It is a vertical-take-off-horizontal-landing vehicle. During reentry, the Space Shuttle navigates through the atmosphere similar to airplanes, except that it flies at hypersonic speeds of over Mach 20 during early stages of reentry. The Space Shuttle reentry phase is much longer than that of the space capsules because the Shuttle has a much longer reentry trajectory unlike the ballistic reentry of the capsules. The Space Shuttle Orbiter is much larger and has a complicated aerodynamic profile when compared to space capsules. As a result, the aerodynamic heating rates and the integrated heat loads vary considerably over the surface. The large surface area ruled out the use of non-reusable ablative heat shields. Therefore, most of the Space Shuttle surface is covered with passive reusable ceramic TPS materials, which have excellent insulation and high temperature resistance properties.

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Figure 2-1. Pictures of the space capsules. A) Mercury. B) Gemini. C) Apollo. and D) Thickness of ablative material at different locations on the Apollo capsule.

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Figure 2-2. Apollo heat shield structure. (Obtained from Reference [5]).

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