Modeling Thermal Behavior of Advanced Materials for Space Applications using a Finite

Element Code

Alicia J. BroederdorfDr. Thomas S. Gates

Research and Technology DirectorateDurability, Damage Tolerance, and Reliability Branch

NASA Langley Research CenterAugust 9, 2006

ABSTRACTTwo advanced material systems were modeled using a multiphysics finite element code, COMSOL, to simulate their thermal behavior in space applications. The first involved designing a new carbon nanotube (CNT) composite material for use as a replacement for the Liquid Cooling and Ventilation Garment the astronauts currently wear. The selective placement of highly thermally conductive CNT within the polymeric material was desired to accommodate the varied heat flux over the surface of the human body. The model demonstrated the ability to tailor the material for specific geometric and thermal responses through variation of the thermal conductivity of the material. The second material related to the new spacecraft being designed by NASA for human exploration, the Crew Exploration Vehicle (CEV). There are several designs for the CEV Crew Module (CM) structure and materials. A section of one of those designs includes a multifunctional material system which was modeled to represent the thermal response during re-entry of the CM through Earth’s atmosphere. The model proved that the thermal protection system (TPS) will adequately protect the underlying layers from degradation by the extreme heat.

INTRODUCTIONModeling represents an important part of the design process. It allows multiple ideas to be tested without fabricating and experimenting with the individual designs, saving not only money but time and resources. In addition, ideas can become more refined through modeling, allowing for the fabrication of a more sophisticated design. There are many finite element codes available for modeling. COMSOL is a multiphysics finite element code that couples basic equations from various concentrations such as heat transfer, electromagnetics, structural mechanics, acoustics, and fluid dynamics to create a representative model. COMSOL allows users to define the relevant properties and boundary conditions in each respective area and then solves the coupled model allowing for post processing of data from each concentration.

Two separate problems were modeled using COMSOL to determine the thermal behavior of advanced materials for space applications. The first includes modeling a carbon nanotube (CNT) composite material to replace the current liquid cooling and ventilation garment (LCVG) that the astronauts currently use. The second problem involves modeling a section of the structure and materials of a design concept for the Crew Module (CM), part of the new Crew Exploration Vehicle (CEV) that is currently being designed as the replacement spacecraft for the shuttle.

MODELING PROCESSThere exists a distinct process for creating a model in a finite element code. First, the geometry is created to represent the given problem. The geometry can be 1-D, 2-D, 3-D, or axial symmetric involving 2-D or 3-D. The dimension of the geometry is dependent on the problem. If there are only boundary conditions and loads in two dimensions, then the 2-D geometry would be used instead of the 3-D geometry regardless of the fact that the object is three dimensional. The simplest geometry of the problem that still accurately represents the model is used in order to allow for a finer mesh, or more degrees of freedom, resulting in a more detailed analysis. Features can be added to the geometry for use in processing the data. Surfaces, lines, and points

that do not affect the actual geometry of the problem are often added in areas of high interest within the model for a detailed view of the analysis.

After the geometry has been created, the material properties and boundary conditions must be defined. There are multiple options for doing this. The first method is to create an interpolated function from given data. Another possibility is to create an expression based on the variables in the problem. For example, a temperature boundary can be defined in terms of the spatial variables x, y, and z. Constants can be defined in COMSOL and used in expressions as well. Furthermore, direct scalar numbers can also be entered for quantities. The type of problem (heat transfer, electromagnetics, structural mechanics, ect.) determines what material properties will be needed, as well as what type of boundary conditions need to be specified.

Upon defining these quantities, a mesh is created by discritizing the problem using elements. For 2-D analysis, either quadrilateral or triangular elements are used. Tetrahedral, hexahedral, or prism elements are used in 3-D analysis. The mesh is refined either over the whole geometry or specific areas depending on what the problem entails. A more refined mesh captures a more accurate idea of what is actually occurring. The mesh is often refined around irregularities in the geometry or in an area where material properties change. The size of the elements and the growth rate, or the rate at which the elements get larger over the geometry, can also be defined.

After the mesh has been created, it is time to solve the problem. The three main analyses in COMSOL include a static, transient, and parametric case. Solver parameters can be tailored according to tolerance in the convergence during solving, initial guesses, and the variable to be varied in a parametric analysis. Once the model has been solved, the data must be processed. There are several options built into COMSOL for this step including surface, boundary, edge, slice, and line plots. Streamlines, arrows, and countour lines can be added to a plot to clarify the data. In addition, animations can be created in the transient or parametric analysis to permit examination of what occurred in the material throughout the analysis. Specific time steps may be examined for each of these plot types as well.

To model complex problems, the problem is often simplified and the complexity is slowly increased. This allows for a greater understanding of what is being modeled and provides points to check basic concepts to verify that the model is correct. This process was used for the two separate problems involving the CNT composite material and the section of the structure for the CM concept.

CARBON NANOTUBE COMPOSITE MATERIALA new CNT composite material is being developed to create a garment to replace the current LCVG. Selective placement of functionalized CNTs that are highly thermally conductive within the polymeric material is desired to accommodate the varied heat flux over the human body. The current LCVG, seen in Figure 1, contains 48 tubes which create pinch points and are awkward for the astronauts. This necessitates a comfort garment which adds mass for the astronaut to carry around, which can be a problem on the Moon or Mars where there is gravity present. Considerable mass is also added to the suit from the 300 feet of tubing. The supporting fabric, needed for the tubing system, floats above the actual tubing and does not contribute to the heat

removal. A goal in designing a new suit with the CNT composite material is to reduce the weight of the cooling garment by 50%.

Several aspects of the functionalized CNTs were varied in a molecular level model to create different thermal conductivities of the material. The thermal conductivity was found as a function of CNT volume fraction, CNT length, interfacial thermal resistance, grafting density, and grafted chain length. A COMSOL model was required to demonstrate how the molecular level changes translated into an overall system response. Thus, the data from the molecular level model was used as input for the COMSOL model.

Considering the complexity of the model regarding the material properties, a basic model was first created with known isotropic Aluminum material properties. This allowed the boundary conditions to be varied finding the most representative set for the given problem. To begin, all sides of the material were thermally insulated except for one. This trial resulted in the material having a constant temperature equal to what was applied, as expected. Next, a temperature was applied on one side of the material and another temperature was applied on the opposite side while keeping the remaining sides thermally insulated. In the static analysis, this resulted in a uniform temperature gradient throughout the material which was also expected. Next, various temperatures were defined on the boundaries as an expression of the spatial variables x, y, and z to simulate the varied temperatures over the human body. A temperature expression based on spatial variables, 300 + 3*(x*100) - 1.5*(y*100), was applied along the bottom to create a temperature gradient throughout the material. All three temperature gradients for the different cases can be seen in Figure 2.

Figure 2Left: Material with constant temperature applied along bottom face. Middle: Two constant temperatures applied along top and bottom faces of material. Right: Temperature expression based on spatial variables applied along bottom face of material.

Figure 1: Current LCVG

Figure 4: Temperature gradients of materials with various shaped cutouts. Shapes include a circle, equilateral triangle, D, and an arbitrary shape.

Once the boundary conditions were determined, a study on how varying the thermal conductivities was performed. The purpose of this investigation was explore what the factors between the thermal conductivities needed to be to get the desired thermal response. Three transient cases were performed varying only the thermal conductivity of the material each time. The material was initially 200 K with a constant temperature of 303 K applied at the bottom edge over the ten minute analysis. A graph comparing the temperature through the materials at 1.5 minutes into the analysis is shown in Figure 3. It can be observed that a small increase in the thermal conductivity (a factor of 5) does not change the material response significantly when compared to a thermal conductivity that is a factor of 10 greater.

A geometric study was also conducted to determine the affect of different geometric holes on the temperature gradient through the material. Symmetric shapes such as circles and equilateral

triangles, as well as nonsymmetric shapes such as a ‘D’ and an arbitrary nonsymmetric shape were all modeled to find the resulting temperature gradient. The material had similar constraints to the thermal conductivity study model, with the material at an initial temperature of 200 K and an applied temperature of 303 K at

the bottom face through a ten minute transient analysis. The temperature gradient for each of the materials with the cut out shapes at 7.5 minutes is shown in Figure 4.

After the initial studies had been performed and it was determined the model was developed correctly, a model was created to represent that actual CNT composite material. To simulate the selective placement of the CNTs in the material, a layered model was created with each subdomain having a separate thermal conductivity based on the molecular level modeling.

Figure 3: Plot comparing thermal conductivities and their affect on the temperature through the material.

Temperature in Y Direction through Material [1.5 min, 303k Applied, 200k Initially]

185

235

285

0 0.002 0.004 0.006 0.008 0.01 0.012 0.014

Distance in Y Direction [m]T

empe

ratu

re [K

]

k = 2k = 10k = 100

Figure 6: Temperature through CNT composite material in +Z direction.

A rectangular material was formed with a temperature of 303 K defined on the bottom surface to simulate body temperature and 116 K defined on the top surface to represent the lowest temperature in low Earth orbit as well as on the Moon, while the remaining four sides were thermally insulated. The bottom layer had the highest thermal conductivity of 44.0805 W/mK with decreasing conductivity up through the layers of 35.3180, 26.5487, and 8.9897 W/mK. The density was defined as 940 kg/m3 and the heat capacity as 3140.1 J/kg °C. A surface through the middle of the material and a line transersing the thickness of the material in the +Z direction were added to the initial geometry for postprocessing purposes. The temperature gradient of the surface and the temperature of the line through the material can be found in figure 5 and 6 respectively.

CM STRUCTURE AND MATERIALSThe shuttle currently in use by NASA to conduct missions in space is scheduled to be retired in 2010. The need for a new, more efficient spacecraft demands additional research to adequately create a vehicle. There are several designs being developed, one of which includes a multifunctional material system consisting of several layers of various materials. These composite materials are designed to provide structural integrity, micrometeoroid-orbital debris damage resistance, and thermal protection. To offer a realistic look at how the spacecraft will perform, a section of the structure and materials of the CM design was modeled to simulate re-entry through Earth’s atmosphere where the CM will encounter temperatures of up to 3000 °F.

Due to the fact that the temperature gradient through the thickness was only desired, a 2-D geometry was created. The thickness and material of each layer is shown in Table 1 below. The protective coating on the outside of the spacecraft will be exposed to Earth’s atmosphere, while the adhesive sealant is in contact with the pressure vessel. The material properties for many layers were defined as functions based on temperature and thus resulted in nonlinear temperature gradients through the layers.

The boundary conditions were defined to simulate re-entry. A temperature of 3000 °F was applied on the protective coating outer layer while all of the layers were defined as 76.3 °F

Temperature through Material

115

165

215

265

0 0.005 0.01 0.015 0.02Distance in Z Direction [m]

Tem

pera

ture

[K]

Figure 5: Temperature of gradient through middle of the CNT composite material.

initially. The three remaining sides were thermally insulated. The 3000 °F simulated the most extreme temperature the CM would encounter during re-entry, while the 76.3 °F represented the touch temperature of what the pressure vessel is required to maintain to provide a safe environment for the astronauts. A transient analysis was performed to determine how the temperature was distributed throughout the layers during the re-entry. The analysis was executed for 30 minutes, as that is approximately the time for landing the current shuttle and would serve as a worst case scenario of the CM being exposed to the most extreme temperature.

Material ThicknessProtective Coating 0.01"

TPS VariableRTV 0.06"

Adhesive Sealant 0.06"Ceramic Cloth 0.005"Graphite Fiber 0.0044"

Foam 4.0"Kevlar 0.04"

Graphite Fiber 0.0044"Adhesive Sealant 0.06"

To optimize the design, the thermal protection system (TPS) thickness was varied to find the minimum thickness and thus reduce the size and weight of the structure. Four models were created with a different TPS thickness each of 0.25, 0.5, 1.0, and 1.5 in. The boundary conditions previously outlined were applied to each model. The resulting temperature gradient through the layers for each model at the end of the 30 minute analysis can be seen in Figure 7.

The TPS was also modeled using modified thermal conductivity functions. This provided a range of values for the TPS performance to account for a difference in the actual thermal

Figure 7: Temperature gradient through layers showing the effect of various TPS thicknesses.

Table 1: The materials and thicknesses of each layer.

conductivities and the values used for the materials in the model. Each model had the thermal conductivity, k, of the TPS modified to 1.25k and 0.5k. The thermal conductivity function for the TPS layer was simply multiplied by 0.5 and 1.25. The resulting temperature gradients throughout each thickness based on the two modified and original thermal conductivities can be found in Figure 8.

Temperature Through Layers [30 min Total, 0.25in TPS]

0

500

1000

1500

2000

2500

3000

4.1 4.2 4.3 4.4 4.5

Distance Through Layers in Y Direction [in]

Tem

pera

ture

[°F]

k

0.5k

1.25k

Foam

Graphite Fiber

Ceramic Cloth

AdhesiveSealantRTV

TPS

ProtectiveCoating

Temperature Through Layers [30 min Total, 0.50in TPS]

0

500

1000

1500

2000

2500

3000

4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8

Distance Through Layers in Y Direction [in]

Tem

pera

ture

[°F]

k

0.5k

1.25k

Foam

Graphite Fiber

Ceramic Cloth

AdhesiveSealantRTV

TPS

ProtectiveCoating

Temperature Through Layers [30 min Total, 1.0in TPS]

0

500

1000

1500

2000

2500

3000

4.1 4.3 4.5 4.7 4.9 5.1 5.3

Distance Through Layers in Y Direction [in]

Tem

pera

ture

[°F]

k

0.5k

1.25k

Foam

Graphite Fiber

Ceramic Cloth

AdhesiveSealantRTV

TPS

ProtectiveCoating

Temperature Through Layers [30 min Total, 1.5in TPS]

0

500

1000

1500

2000

2500

3000

4.1 4.3 4.5 4.7 4.9 5.1 5.3 5.5 5.7

Distance Through Layers in Y Direction [in]

Tem

pera

ture

[°F]

k

0.5k

1.25k

Foam

Graphite Fiber

Ceramic Cloth

AdhesiveSealantRTV

TPS

ProtectiveCoating

CONCLUSIONModels were successfully created for the selective placement of CNTs in the CNT composite material and simulating a multifunctional material experiencing re-entry through Earth’s atmosphere for the CM design concept. The CNT composite model proved that the material can be designed for specific geometries and thermal responses. The two preliminary studies proved this capability of the model while the four layered model combined these concepts into one model representing the actual material by using data from the molecular modeling as input for the material properties. This model allows for a more comprehensive analysis to be completed on the material by adding mechanical loads and varied temperatures to simulate the material on an astronaut.

Figure 8: Four plots showing the temperature through the layers for the modified thermal conductivities and thicknesses of the TPS.

The model of the CM structure was very helpful in the design process. It demonstrated that the TPS will be able to provide adequate protection against the extreme heat to prevent degradation of the underlying materials. It provided a range of performance data for thermal conductivities to offer a more realistic look at how the TPS will handle the extreme heat. The performance for the TPS at different thermal conductivities and thicknesses allows the design to be optimized to reduce the weight and size of the overall structure. The model provides more freedom of the design of the structure by providing the capability of altering the other layers’ material properties, such as thermal conductivity and their thickness to determine the effect on the overall structure.