«DESIGN OF AN INTEGRAL THERMAL PROTECTION SYSTEM FOR FUTURE SPACE VEHICLES By SATISH KUMAR BAPANAPALLI A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL ...»
The geometric design variables of the ITPS need to be altered in such a way so as to obtain a minimum weight structure that can satisfy the various requirements of a TPS and a loadbearing member. This is a formidable task given the often-conflicting requirements of a TPS and a load-bearing structure and explains why such a structure has not been developed over the years.
It is very much a possibility that the outcome of this effort could be to establish that such a structure is not feasible or, even when feasible, it may be a prohibitively heavy design.
Nevertheless, it is a good concept worth investing some research efforts, especially since such a design could not be found anywhere in literature.
The ITPS is not being designed with any particular vehicle in mind and is not a “one-sizefits-all” design. For different vehicles, the ITPS designs and geometries have to be suitably modified as per the thermal and structural requirements. It may not be able to withstand high heating rates and large integrated heat loads because it is a passive TPS concept. It may need to be combined with other TPS concepts such as ablative TPS when used on space capsules, for instance. It can replace the structure below the ablators of Apollo TPS, shown in Figure 2-2.
Some of the obvious design challenges associated with the ITPS development are discussed below with the aid of the dimensions of the proposed corrugated-core ITPS design.
This will demonstrate the typical difficulties associated with an ITPS design.
Thickness of the Webs. Decreasing the thickness of the webs helps to reduce the mass of the ITPS. The thermal protection requirements dictate that the conductivity of the core be as low as possible. This would result in less heat being conducted away from the top face sheet and would raise the temperature of the top surface close to the radiation equilibrium temperature resulting in majority of the incident heat being re-radiated out. Since the conductivity of the insulation material is a material selection issue, the only way to decrease the conductivity of the core is to decrease the thickness of the webs. But this would weaken the structural link between top and bottom face sheets. Large transverse aerodynamic pressure loads on the top face sheet could cause the webs to buckle. In this case, the mass and thermal protection requirements agree with one another but contradict the structural requirements Height of the Panel. The height of the panel is the mid-plane to mid-plane distance between the two face sheets. The thermal protection requirements dictate that the height be as large as possible to increase the heat conduction path. However, this would not only increase the weight of the TPS considerably, but also make the webs longer and more susceptible to buckling due to transverse loads. In this case, the mass and structural requirements agree with one another while contradicting the thermal protection requirements.
Spacing between two Webs. Increasing the lateral spacing between the webs helps keep the areal density of the ITPS low (Areal density is the mass per unit area of the ITPS). However, this would lead to a design in which there would be long unsupported sections of face sheets between the webs that may be susceptible to buckling due to in-plane mechanical or thermal compressive loads. Increasing the spacing also means that the heat incident on a larger area would be conducted by a lesser number of webs. Thus, in this case, the mass and thermal protection requirements agree with one another while contradicting the structural requirements.
Thickness of Top Face Sheet. Decreasing the thickness of the top face sheet helps reduce the ITPS mass. But thinner top face sheet is very much susceptible to buckling due to in-plane thermal compressive loads. Additionally, a thin face sheet may deflect excessively under transverse pressure loads and this may cause a transition from laminar to turbulent boundary conditions , which in turn may cause severe local aerodynamic heating. Thus, in this case, the mass and structural requirements in conflict with each other while the thermal protection requirements do not have a significant influence.
Angle of Corrugations. This is the angle that the webs make with the face sheets. Keeping this angle close to 90° would lead to the lightest ITPS design. However, it would also shorten the heat conduction path and make the webs susceptible to buckling due to transverse pressure loads.
In this case, the thermal protection and structural requirements agree with one another while contradicting the mass requirements.
Thickness of the Bottom Face Sheet. Decreasing the thickness of the bottom face sheet helps keep the mass of the ITPS low. However, the bottom face sheet of the ITPS is the most effective thermal mass and, therefore, its thickness may be required to be high in order to increase the heat sink capacity of the ITPS. A thick bottom face sheet would also be capable of withstanding higher in-plane loads. Again, the thermal protection and structural requirements agree with one another while contradicting the mass requirements.
The discussion above effectively demonstrates the challenges associated with the ITPS design. The aim of the current research is to identify more of these issues and to develop methodologies towards designing an ITPS.
This section elaborates on the reasons behind the choice of the constraints for the optimization problem (see the subsection The Optimization Problem in Section 1.4).
ITPS panels form the outer skin of the vehicle, which encompasses the crew compartment (in space capsules) or liquid fuel tanks (in X-33 like design). The temperature of the bottom surface determines the amount of heat flowing into the vehicle interiors. Thus, peak bottom surface temperature is an important constraint.
While peak temperature of any part of the ITPS panel should be within allowable limits, only the peak bottom surface temperature considered critical. This is because initial heat transfer analyses had indicated that the peak temperature of the top surface is always close to the radiation equilibrium temperature, as will be demonstrated in the Chapter 3. It is predominantly determined by the emissivity of the top surface, which typically has a value of 0.8 to 0.85 [12,13]. Increasing the emissivity is a manufacturing and material selection issue and not a design issue. The amount of heat entering into the vehicle can be decreased considerably by decreasing the heat conduction path. This will increase the top surface temperature slightly and thus more heat is radiated out. However, this increase in temperature is small, typically of the order of 40 K. Thus, the top surface temperature is not a quantity that can be significantly influenced by changing the ITPS design. It is determined by the radiation equilibrium temperature which is determined by the incident heat flux on the vehicle and the emissivity of the top surface. The temperature of the rest of the structure is then dictated only by the limit imposed on the bottom face sheet.
When the whole ITPS panel buckles as a plate, it is referred to as global buckling. When the buckling is limited to a part of the panel, such as one of the webs or a section of the face sheets, it is referred to as local buckling. Global buckling may not be a factor influencing the ITPS design because the ITPS panel is expected to be a thick panel. However, local buckling can be a major design driver because the ITPS structure is made of thin plates, which are susceptible to buckling due to compressive stresses.
The third constraint deals with the maximum stresses allowed by the materials. It should be noted that some parts of the structure are at very high temperatures and temperature dependence of material properties, like yield stress and Young’s modulus, should be taken into account.
Constraint 4 imposes the limits on the deflection of the top surface because excessive deflection of the top surface could lead to extremely high local aerodynamic heating . Due to heat input, the temperature of the whole panel increases. Some of the heat is transferred to the stringers, for example, and the whole vehicle grows in size. This overall deflection is not of a major concern, as it does not change the aerodynamic profile of the vehicle significantly.
However, local deflections, such as face sheet dimpling, can lead to severe local aerodynamic heating. Therefore, when the limit on top surface deflection is imposed, the overall increase in size of the vehicle should be deducted from it.
2.6 Background on Corrugated-Core and Truss-Core Sandwich Structures The ITPS panel geometry considered for this research work is similar to corrugated-core and truss-core sandwich structures. Therefore, it is relevant to present the literature survey related to these structures in order to distinguish the current research effort as well as to put the work in perspective.
There are 3 major research groups that have focused their research efforts on truss-core and corrugated-core sandwich panels: Wicks and Hutchinson [24,25], Lu, et al [26,27], and Evans, et al [28–35]. Wicks and Hutchinson derived simple analytical formulas to approximate the forces and moments between the trusses and the face plates. These formulas were used for imposing the constraints in the optimization problem to obtain a panel with minimum weight for a given applied load. Panels were designed for bending and transverse shear loads and the constraints imposed were related to face sheet and core yielding and buckling.
Lu, et al [26,27], used two different approaches to optimize truss-core sandwich panels for bending, transverse shear and compression loading. In the first approach , they directly combine finite element analysis with optimization techniques. Details about the finite element analysis were not provided in the paper. In the second approach , homogenization techniques and unit cell analysis were used to obtain analytical formulas for the stresses in the trusses and the face sheets. Some comparison of the analytical formulas and 3-d finite element analysis was also presented. In both cases the panels were optimized to minimize mass and increase the natural frequency while constraints were imposed by considering face sheet and core yielding and buckling.
Evans, et al [28–35], developed analytical formulas for forces in various members of both truss-core and corrugated-core panels using unit cell analysis. The core geometries analyzed were truss-cores with tetragonal, pyramidal, and kagome configurations [29,31,32] and prismatic cores with corrugated and diamond (or textile) configurations [28,30,32,33]. The analytical formulas were compared with simple finite element unit cell models for verifying their accuracy [29,31,34]. Comparison of forces and stresses for a full sandwich panel was not carried out. The optimizations were carried out to obtain minimum weight structures while satisfying the buckling and yielding criteria.
In all the above mentioned analyses, bending, transverse shear and crushing loads were considered for analysis. Further, the height of these sandwich panels was between 10 to 20 mm.
This kind of approximate analysis is not very suitable for ITPS applications because the ITPS panels have much larger height, typically above 80 mm, and a far fewer number of unit cells per panel, typically 4 to 10. Even though the geometry of the ITPS panels is similar to sandwich panels, the large height-to-length ratio and the small number of unit cells in the ITPS panels make the panel behavior different. One of the biggest disadvantages of the analytical methods is that they cannot accurately predict the stresses and deflections at the panel edges where the boundary conditions are imposed. In many cases, the maximum stresses or buckling occurs at the panel edges and could be the deciding factor in the optimization. One of the most severe loads influencing the design of ITPS panels is the large temperature gradient between the top and the bottom face sheet. The research works on truss-core and corrugated-core sandwich structures that has been summarized in this section do not consider such a load in their optimization procedures.
Optimization to design an ITPS panel is a multidisciplinary optimization process as it combines the two fields of heat transfer and structural analysis. The geometric design variables (Section 1.4) influence both the heat transfer and structural response of the structure. Therefore, there is need to study the various optimization techniques used for MDO problems. The background on multi-disciplinary optimization (MDO) relevant to this research work can be obtained from two important review efforts—one by Sobieszczanski-Sobieski and Haftka  and the other by Guruswamy and Obayashi . Brief summary of the two papers is presented here along with relevant examples.
Reference  summarizes the various methods used by researchers to tackle MDO problems and focuses particularly on aerospace design optimization. It was surmised that in most cases it is impractical to couple design space search (DSS) to a multidisciplinary analysis as this could lead to a very frequent calls to analysis execution. In the ITPS design, an attempt was unsuccessfully made to directly couple the MATLAB optimizer (fmincon) to the ABAQUS FE analysis package. After several calls to the analysis software the optimizer was unable to find a feasible search direction. While the inability to find a feasible search direction was blamed on the lack of robustness on the part of fmincon, it is also true that even with a robust optimization algorithm the search would require a very large number of FE analysis calls. Further, it cannot be guaranteed that the optimized design is actually a global optimum and not a local optimum.