A Generalized Approach to Energy Accommodation in Gas-Surface Interactions for Satellite Aerodynamics in Very-Low-Earth-Orbit

Core Concepts

This technical note presents a novel, generalized expression for calculating the temperature ratio between reflected and impinging gas particles in gas-surface interactions, improving the accuracy of satellite aerodynamics modeling in the Very-Low-Earth-Orbit regime.

Abstract

Bibliographic Information:

Tuttas, F., Traub, C., Pfeiffer, M., & Fichter, W. (2024). Generalized Treatment of Energy Accommodation in Gas-Surface Interactions for Satellite Aerodynamics Applications (arXiv:2411.11597v1). arXiv.

Research Objective:

This technical note aims to address the limitations of existing approaches for handling energy accommodation in gas-surface interaction (GSI) models used for satellite aerodynamics in the Very-Low-Earth-Orbit (VLEO) regime. The authors aim to derive a generalized expression for the temperature ratio of reflected to impinging particles that remains valid for any molecular speed ratio, including hypothermal flows.

Methodology:

The authors begin by discussing the theoretical background of GSI models, energy accommodation, and the temperature of reflected particles. They then derive a general expression for the average energy of impinging particles, considering factors like molecular speed ratio and the angle of incidence. This expression is then used to derive a generalized formula for the temperature ratio, which is the key contribution of this note. Finally, the authors derive a simplified hyperthermal approximation from the general expression and compare it to an existing approximation to demonstrate its improved accuracy.

Key Findings:

• Existing approximations for the temperature ratio in GSI models are primarily valid for hyperthermal flows and lose accuracy at lower molecular speed ratios.
• The authors derive a novel, generalized expression for the temperature ratio that remains valid for any molecular speed ratio, including hypothermal flows.
• A simplified hyperthermal approximation derived from the general expression demonstrates higher accuracy and faster convergence compared to existing approximations.

Main Conclusions:

The generalized expression for the temperature ratio enhances the understanding and modeling of gas-surface interactions in VLEO, potentially leading to more accurate simulations and improved applications in satellite aerodynamics. Utilizing this expression in GSI models extends their applicability to a wider range of scenarios, including suborbital flights with hypothermal flows.

Significance:

This research contributes to the field of satellite aerodynamics by providing a more accurate and generalized approach to modeling energy accommodation in gas-surface interactions. This has implications for various applications, including the computation of thermospheric density data from satellite dynamics and the development of more efficient satellite attitude and orbit control systems.

Limitations and Future Research:

While the note provides a significant theoretical contribution, further research is needed to quantify the practical impact of the generalized expression and the new approximation on the overall accuracy of GSI models and their applications. Future work could involve incorporating the derived expressions into existing GSI models and comparing their performance against real-world satellite data.

Stats

The energy accommodation coefficient (αE) is typically assumed to be in the range of about 0.9 to 1.0 for VLEO applications.
The atmosphere in the VLEO regime is dominated by atomic oxygen.

Quotes

"In the context of satellite aerodynamics in the Very-Low-Earth-Orbit (VLEO) regime, accurate modeling of gas-surface interactions (GSI) is crucial for determining aerodynamic forces and torques."
"This note aims to contribute to the research field by providing a more generalized treatment of energy accommodation which is valid for any molecular speed ratio and retains the general validity of the GSI model even in hypothermal flows."

Key Insights Distilled From

Generalized Treatment of Energy Accommodation in Gas-Surface Interactions for Satellite Aerodynamics Applications

by Friedrich Tu... at arxiv.org 11-19-2024

https://arxiv.org/pdf/2411.11597.pdf

Deeper Inquiries

How might this generalized approach to energy accommodation in GSI models be adapted for use in other areas of fluid dynamics research or engineering applications beyond satellite aerodynamics?

This generalized approach to energy accommodation in gas-surface interaction (GSI) models, particularly the derivation of a general expression for the temperature ratio applicable to any molecular speed ratio, holds substantial potential for various applications beyond satellite aerodynamics. Here are a few examples:

Microfluidics and Vacuum Systems: In microfluidic devices or vacuum systems, where the mean free path of gas molecules becomes comparable to the characteristic length scales of the system, the continuum assumption of traditional fluid dynamics breaks down. GSI models become crucial in understanding and predicting flow behavior in these scenarios. The generalized approach, being valid for a wide range of molecular speed ratios, can accurately model energy exchange at the fluid-solid interface, leading to more precise predictions of heat transfer, pressure distribution, and flow rates in these systems.

High-Altitude Flight and Hypersonic Flows: While the paper focuses on VLEO, the generalized approach can be extended to higher altitude applications where the atmosphere is even more rarefied. Similarly, in hypersonic flows, where gas temperatures can be extremely high, the assumption of hyperthermal flow might not always hold. The general expression for the temperature ratio, being valid for any molecular speed ratio, can provide more accurate predictions of aerodynamic heating and drag forces acting on high-speed vehicles.

Thin Film Deposition and Etching: In semiconductor manufacturing processes like thin film deposition and etching, accurate control of gas-surface interactions is critical. The generalized approach can be incorporated into models to predict the sticking coefficient, energy transfer, and scattering behavior of gas molecules impinging on the substrate surface. This can lead to improved process control, higher film quality, and reduced defects.

Catalytic Converters and Surface Chemistry: The efficiency of catalytic converters and other chemical processes involving gas-surface reactions depends heavily on the energy exchange between the gas molecules and the catalyst surface. The generalized approach can be used to model the energy accommodation coefficient and predict the rate of energy transfer, leading to a better understanding of reaction kinetics and optimization of catalyst design.
The key takeaway is that the generalized approach provides a more fundamental and versatile framework for modeling energy accommodation in GSI, making it adaptable to a wide range of applications where gas-surface interactions play a significant role.

Could the assumption of diffuse reflection in GSI models, while simplifying calculations, be a significant limiting factor in accurately representing real-world gas-surface interactions, especially at highly rarefied atmospheric conditions?

Yes, the assumption of purely diffuse reflection in GSI models, while simplifying calculations, can indeed be a limiting factor in accurately representing real-world gas-surface interactions, especially at highly rarefied atmospheric conditions. Here's why:

Specular Reflection and Intermediate Scattering: In reality, gas-surface interactions are far more complex than purely diffuse reflection. Depending on the surface properties, incident angle, and energy of the impinging gas molecules, a portion of the molecules may undergo specular reflection, where the angle of incidence equals the angle of reflection. Additionally, there exists a range of intermediate scattering behaviors between perfectly diffuse and specular reflection.

Surface Roughness and Contamination: Real surfaces are not perfectly smooth. Surface roughness and the presence of contaminants can significantly influence the scattering behavior of gas molecules. These imperfections can lead to a combination of diffuse, specular, and intermediate scattering, which cannot be accurately captured by models assuming only diffuse reflection.

Rarefied Gas Effects: At highly rarefied conditions, the mean free path of gas molecules becomes large compared to the surface features. In such cases, the assumption of a Maxwellian velocity distribution for reflected molecules, inherent in diffuse reflection models, might not hold true. The reflected molecules may retain some memory of their incident velocity distribution, leading to deviations from the predictions of purely diffuse reflection models.

Influence on Momentum and Energy Exchange: The type of reflection directly impacts the momentum and energy exchange between the gas and the surface. Diffuse reflection assumes complete accommodation of tangential momentum, while specular reflection assumes no accommodation. The actual momentum and energy accommodation coefficients can vary significantly depending on the scattering behavior, influencing the accuracy of aerodynamic force and heat transfer predictions.
To improve the accuracy of GSI models, particularly at highly rarefied conditions, it is crucial to consider more realistic scattering kernels that account for both diffuse and specular reflection components. Models incorporating accommodation coefficients for both tangential and normal momentum components, as well as energy accommodation, can provide a more comprehensive representation of real-world gas-surface interactions.

Considering the increasing density of objects in low Earth orbit, how might the understanding of gas-surface interactions contribute to mitigating the risks associated with space debris and ensuring the long-term sustainability of space exploration?

The increasing density of objects in low Earth orbit (LEO) poses a significant threat to the long-term sustainability of space exploration. Understanding gas-surface interactions (GSI) can play a crucial role in mitigating the risks associated with space debris in several ways:

Accurate Prediction of Orbital Decay: Atmospheric drag, primarily governed by GSI, is a dominant force affecting the orbital lifetime of objects in LEO. Precise modeling of GSI, incorporating realistic accommodation coefficients and scattering kernels, can lead to more accurate predictions of orbital decay rates for space debris. This information is vital for assessing collision risks, planning debris mitigation maneuvers, and estimating the long-term evolution of the debris environment.

Design of Debris Mitigation Technologies: A deeper understanding of GSI can aid in developing effective debris mitigation technologies. For instance, drag augmentation devices, such as deployable sails or tethers, can be designed to enhance atmospheric drag and accelerate the deorbiting of defunct satellites or debris. Accurate GSI models can optimize the design of these devices for maximum drag enhancement.

Development of "Design for Demise" Guidelines: By incorporating GSI considerations into spacecraft design, engineers can minimize the creation of new debris. "Design for demise" guidelines can promote the use of materials and configurations that promote complete atmospheric burn-up upon re-entry, reducing the likelihood of debris surviving to reach the ground.

Assessment of Long-Term Debris Evolution: GSI models are essential for long-term simulations of the space debris environment. By accurately accounting for atmospheric drag and its influence on debris orbits, these models can predict the evolution of the debris population over time, assess the effectiveness of different mitigation strategies, and inform policy decisions regarding space sustainability.

Improved Space Situational Awareness: Accurate GSI models, coupled with observations of space debris, can enhance space situational awareness. By improving our ability to track and predict the trajectories of debris objects, we can enhance collision avoidance maneuvers for operational spacecraft and improve the safety of future missions.
In conclusion, a thorough understanding of gas-surface interactions is not just an academic exercise but a critical element in addressing the growing challenge of space debris. By improving our ability to predict and manipulate atmospheric drag, we can develop effective mitigation strategies, design more responsible spacecraft, and ensure the long-term sustainability of space exploration for future generations.