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Compression Effects on Thermal Conductivity of Fibrous Flexible External Insulation

This study develops a representative volume element (RVE) framework that directly links the mechanical compression of random fibrous networks to thermal analysis, successfully predicting the nonlinear increase in effective thermal conductivity for silica-based and alumina flexible external insulation under varying compressive pressures.

Original authors: Xiongjie Che, Seng Min Han, Ruihai Xin, Nam Seo Goo

Published 2026-10-01

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Xiongjie Che, Seng Min Han, Ruihai Xin, Nam Seo Goo

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

When a spacecraft returns to Earth, it does not simply fall; it plunges through the atmosphere at speeds that generate temperatures capable of melting steel. To survive this fiery descent, engineers rely on thermal protection systems, often in the form of flexible blankets that wrap around the vehicle's hull. These blankets are not solid blocks of material but are composed of countless tiny, randomly arranged fibers, creating a sponge-like structure filled mostly with air. The air trapped between the fibers acts as a barrier, slowing the flow of heat from the outside world to the delicate machinery inside. However, these blankets are not static; during flight, they are squeezed and compressed by aerodynamic forces. When a fibrous blanket is squashed, the fibers are pushed closer together, and the air pockets shrink. This physical change alters how heat moves through the material, potentially making the insulation less effective exactly when it is needed most. Understanding this relationship between pressure and heat flow is critical for designing spacecraft that can safely return from space.

A team of researchers at Konkuk University in South Korea set out to understand exactly how this compression changes the thermal performance of a specific type of flexible insulation made from silica fibers. While scientists have long known that compressing insulation increases its ability to conduct heat, the precise mechanism was difficult to pin down. Previous studies often treated the mechanical squeezing of the fibers and the subsequent flow of heat as two separate events, or they relied on simplified guesses about how the fibers rearranged themselves. The researchers wanted to see the actual process: to watch the fibers move, touch, and form new connections as they were squeezed, and then immediately measure how those specific changes affected the heat passing through.

To achieve this, the team built a digital model of the insulation that acted as a microscopic window into the material. They started by examining real samples of the silica felt using powerful imaging tools to measure the size and direction of the individual fibers. They found the fibers were roughly seven and a half micrometers wide and oriented in random directions, creating a chaotic but uniform web. Using this data, they constructed a virtual cube, a tiny representative volume, filled with thousands of these fibers and the air surrounding them. This digital cube was not just a static picture; it was a dynamic model that could be physically compressed. The researchers applied a virtual force to squeeze the cube, simulating the pressure the insulation would feel in a real spacecraft. As the cube shrank, the digital fibers moved, bent, and pressed against one another, creating new points of contact that did not exist before.

Once the virtual cube was compressed to a specific thickness, the researchers paused the mechanical simulation and switched to a thermal analysis. They filled the gaps between the now-squeezed fibers with a virtual air domain and applied a temperature difference across the top and bottom of the cube. They then watched how heat traveled through this new, denser arrangement. The results revealed a clear story: as the material was compressed, the fibers packed tighter, and the number of places where fibers touched each other increased significantly. These contact points became high-speed highways for heat. The researchers observed that heat flowed much more rapidly through these specific contact zones than through the rest of the fiber or the surrounding air. Because the fibers were now touching more often, the solid material provided a more direct path for heat to bypass the insulating air, causing the overall insulation to become less effective.

The team tested their model against real-world experiments using samples of the silica insulation. They measured how much heat passed through the material when it was subjected to different levels of pressure, ranging from a light touch to a heavy squeeze. The predictions from their digital model matched the physical experiments with remarkable precision, differing by less than two percent. This close agreement confirmed that their approach of directly linking the mechanical deformation of the fibers to the thermal analysis was accurate. The model successfully captured the non-linear way in which the insulation's performance degrades as pressure increases, proving that the formation of new fiber-to-fiber contacts is the primary driver of this change.

To ensure their method was not just a lucky fit for this specific type of silica fiber, the researchers applied the same digital framework to a different material: an alumina-based insulation used in other aerospace applications. This material had different fiber sizes, densities, and physical properties. Despite these differences, the model reproduced the experimental trends for this second material as well, showing that the increase in heat flow under pressure followed a similar pattern. The researchers noted that at extremely high pressures, where fibers might break or become permanently damaged, the model's predictions began to drift from reality, indicating a limit to where this specific simulation approach works. However, for the range of pressures typical in many aerospace applications, the method proved robust.

This work provides a practical and reliable way to predict how flexible thermal blankets will behave under the stress of flight. By directly simulating the movement of individual fibers and the air around them, engineers can now design insulation systems with greater confidence, knowing exactly how much performance will be lost when the material is compressed. The study moves beyond simple estimates to offer a clear, visual understanding of the microscopic changes that dictate the macroscopic safety of a spacecraft. It demonstrates that the key to better insulation lies not just in the material itself, but in understanding how that material rearranges its internal structure when the world pushes back against it.

Technical Summary: Compression Effects on Thermal Conductivity of Fibrous Flexible External Insulation

Problem Statement
Flexible thermal insulation, such as silica-based Flexible External Insulation (FEI), is critical for reusable launch vehicles due to its ability to conform to complex surfaces while providing thermal protection. However, the effective thermal conductivity of fibrous insulation is highly sensitive to mechanical compression. Compression alters the internal fiber network by increasing fiber density and inducing fiber-to-fiber contacts, thereby creating new conductive paths. While experimental studies have established that conductivity increases with compression, they provide only macroscopic responses and cannot explicitly resolve how individual fiber rearrangements and contact formations drive these changes. Existing numerical models often treat thermal and mechanical analyses separately: thermal models typically prescribe fiber geometry or contact conditions without deriving them from actual mechanical deformation, while mechanical models rarely transfer the resulting deformed geometry to subsequent heat transfer calculations. This study addresses the need for a unified framework that directly links the mechanical compression of a random fiber network to its thermal response.

Methodology
The authors developed a Representative Volume Element (RVE) framework that integrates mechanical deformation with steady-state heat transfer analysis. The methodology proceeds through the following stages:

Microstructure Characterization and RVE Generation:
- Microstructure data (fiber diameter, orientation) were obtained via Scanning Electron Microscopy (SEM) and Micro-Computed Tomography (Micro-CT) of silica-based FEI.
- A stochastic cubic RVE (initially $100 \, \mu m$ side length) was generated using a Random Sequential Adsorption (RSA) algorithm. Fibers were placed with isotropic orientation and non-overlapping constraints, including periodic boundary conditions to ensure continuity across faces.
- The fiber diameter was set to an average of $7.5 \, \mu m$ , and the fiber volume fraction was controlled to match experimental porosity.
Mechanical Compression Simulation:
- Mechanical compression was simulated using Abaqus/Explicit. Only the fiber network was modeled as linear elastic solids ( $E = 70 \, GPa$ ); the air phase was excluded from the mechanical analysis.
- Compression was applied via rigid plates moving at a constant velocity until target thicknesses were reached. These target thicknesses were derived from experimental load-thickness data to ensure the simulation matched specific experimental compression states (loads of 152.0, 250.1, and 348.1 N).
- Contact between fibers and between fibers and plates was defined with a friction coefficient of 0.3.
Geometry Reconstruction and Thermal Analysis:
- The deformed fiber geometries from the mechanical simulation were reconstructed into solid bodies using Blender and FreeCAD to correct surface distortions.
- An air domain was generated around the compressed fibers using Boolean operations in Abaqus/CAE. Fiber-to-fiber contacts formed during compression were represented as continuous solid regions, eliminating the need for artificial thermal contact resistance parameters between fibers.
- Steady-state heat transfer analysis (Abaqus/Standard) was performed on the fiber-air model. Boundary conditions included a $2^\circ C$ temperature difference across the compression direction and adiabatic lateral surfaces.
- Effective thermal conductivity ( $k_{eff}$ ) was calculated from the averaged heat flux and the compressed RVE thickness.
Validation and Extension:
- The model was validated against experimental data for silica-based FEI at a mean temperature of $280^\circ C$ .
- The framework was subsequently applied to Saffil alumina insulation, utilizing different fiber diameters ( $3 \, \mu m$ ), material properties, and compression states to test generalizability.

Key Results

RVE Size Sensitivity: Increasing the RVE side length from $100 \, \mu m$ to $200 \, \mu m$ resulted in a negligible change (0.40%) in predicted effective thermal conductivity, confirming that the $100 \, \mu m$ RVE is sufficient for capturing the effective properties.
Compression Mechanism: The simulations revealed that compression reduces the air volume and increases fiber packing density. Crucially, the model captured the formation of new fiber-to-fiber contacts. Heat flux analysis showed localized regions of high flux near these contact points, indicating that compression creates additional solid conduction paths.
Validation with Silica FEI: The RVE model successfully reproduced the nonlinear increase in effective thermal conductivity observed in experiments. The maximum deviation between numerical predictions and experimental results was 1.98% across the tested compression states.
Application to Saffil Alumina: When applied to Saffil alumina felt (with distinct fiber size, density, and material properties), the framework reproduced the experimental trend of increasing conductivity with pressure at low to moderate compression levels. Three independently generated random RVEs showed consistent behavior. However, deviations increased at high compressive pressures ( $>0.84 \, MPa$ ), where the model did not account for fiber breakage or saturation of contact formation observed in the physical material.

Significance and Claims
The paper claims that the proposed RVE framework provides a practical and direct approach for predicting compression-dependent heat transfer in random fibrous insulation. By mechanically deforming the fiber network and reconstructing the thermal model from the resulting geometry, the method avoids the need to prescribe arbitrary contact conditions or density changes in the thermal model.

The authors assert that this approach:

Directly links mechanical deformation to thermal response, capturing the physical mechanism of contact-induced conductivity increases.
Is applicable beyond the primary validation material (silica-based FEI) to other random fibrous insulations with different geometric and material properties, as demonstrated with Saffil alumina.
Offers a general numerical route for evaluating how compression-induced microstructural changes affect thermal performance, though the authors modestly note that the model's accuracy diminishes under severe compression where fiber damage and complex contact saturation occur.

The study concludes that while simplifications exist (e.g., constant fiber diameter, neglect of radiation and natural convection), the framework effectively captures the dominant conductive mechanisms driven by compression in high-porosity fibrous insulation.

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