Gas-surface Interaction Model Research Articles

Numerical framework for the development of atmosphere-breathing electric propulsion for Earth and Mars atmosphere

Atmosphere-breathing electric propulsion systems provide a competitive advantage for the lower orbit altitudes since the propellant is collected directly from the atmosphere. The effectiveness of this technology depends on crucial aspects such as the collection and compression performance characterization, as well as the drag estimation and compensation. In the first part of this study, the lower Mars and Earth atmospheric characterization is derived based on current models and mission data. This characterization is a reliable dataset for the boundary conditions for the simulations carried out in the second part of this study. The proposed computational framework based on the Direct Simulation Monte Carlo method aims to investigate the collection and compression performances and to estimate the drag. The numerical comparison with a literature case validates the numerical setup presented in this study. The effect of different gas-surface interaction models is investigated by comparing the results yielded by the Maxwellian model (fully specular and partially diffuse reflection) and the Cercignani-Lampis-Lord model. Since the intermolecular collisions can become more relevant at the inlet of the ionization stage, both the variable hard and variable soft sphere models are briefly examined, as well as the inclusion of gas-phase reactions. Finally, the simulation results of the two cases for the low Mars orbit (150 and 140 km) are compared to the Earth case (180 km).

The effects of energy accommodation of reflected gas molecules on flow structures during expired spacecraft reentry

To study the influence of energy accommodation of scattering gas molecules on flow fields during large expired spacecraft reentry, a more elaborated gas-surface interaction model, compared with full Maxwellian diffuse model, is employed in implicit algorithms based on Boltzmann model equation. The characteristic distributions around cylinder at different fluid regimes are accordingly obtained by implicit algorithms, Navier-Stokes solver and DSMC ((Direct Simulation Monte Carlo) method. And the consistency of these results is verified. It is confirmed that present algorithms are capable of solving external flow problems covering various fluid regimes. Then the simulation results see that under current conditions set in the paper, pressure and temperature are proportional to wall activation (ω=Tw/T∞, Tw is surface temperature, T∞ denotes as free stream temperature), but their amplitudes alter with ω at different fluid regimes. As for the effects of energy accommodation coefficients (αe), both pressure and temperature profiles vary in a linear way with αe. However, the variation ranges of these parameters are diverse with regard to different fluid regimes. These observations are favor to the construction of efficient forecasting software, which could predict the flight path of large defunct spacecraft. In this forecasting software, the external ballistics computations and aerothermodynamic simulations are synchronously carried out.

Rarefied gas–surface interaction under multi-incidence parameter coupling conditions: A molecular dynamics simulation

An effective gas–surface interaction model is crucial for accurately predicting the aerodynamic thermal properties of hypersonic vehicles. However, the applicability of classical interface models has been severely challenged under hypersonic conditions since the boundary properties predicted by different gas-surface interaction models vary greatly, which seriously threatens the flight safety. Therefore, in order to accurately describe gas–surface interaction under hypersonic conditions, we analyzed the reflection behavior of the gas on a silicon-based surface through molecular dynamics simulations and presented a modified Maxwell model. Furthermore, the dependence of model parameters on incident energy, angle, and gas type was also obtained. By analyzing gas–surface interaction time and potential well depth, the endogenous mechanism of the accommodation coefficient variation under multi-incidence parameter coupling conditions is revealed. These results not only elucidate the microscopic mechanism of gas–surface interaction but also provide an important basis for establishing accurate boundary conditions for larger-scale simulations.

Molecular Dynamics Study of Gas–Surface Interactions on -Cristobalite Surface

In the present work, nonreactive gas–surface interactions between nitrogen molecules and a -cristobalite surface are analyzed using the molecular dynamics framework. A sampling method is employed to perform trajectory calculations, and the tangential momentum accommodation coefficient is computed. The credibility of the reactive force field potential to model cristobalite is investigated, and the effect of the surface and gas temperatures on the tangential momentum accommodation coefficient is studied in detail. The obtained value of the tangential momentum accommodation coefficient (from molecular dynamics analysis) is used as an input parameter in the Maxwell gas–surface interaction model using the direct simulation Monte Carlo method to investigate the surface heat flux on the nose region of a model reentry vehicle. The computed heat-flux results obtained using a molecular-dynamics-derived accommodation coefficient are found to be in excellent agreement with the experimental data.

Stochastic modeling of physical drag coefficient – Its impact on orbit prediction and space traffic management

Ambitious satellite constellation projects by commercial entities and the ease of access to space in recent times have led to a dramatic proliferation of low-Earth space traffic. It jeopardizes space safety and long-term sustainability, necessitating better space domain awareness (SDA). Correct modeling of uncertainties in force models and orbital states, among other things, is an essential part of SDA. For objects in the low-Earth orbit (LEO) region, the uncertainty in the orbital dynamics mainly emanate from limited knowledge of the atmospheric drag-related parameters and variables. In this paper, which extends the work by Paul et al. (2021), we develop a feed-forward deep neural network model for the prediction of the satellite drag coefficient for the full range of satellite attitude (i.e., satellite pitch ∈ (-90°,+90°) and satellite yaw ∈ (0°,+360°)). The model simultaneously predicts the mean and the standard deviation and is well-calibrated. We use numerically simulated physical drag coefficient data for training our neural network. The numerical simulations are carried out using the test particle Monte Carlo method using the diffuse reflection with incomplete accommodation gas-surface interaction model. Modeling is carried out for the well-known CHAllenging Minisatellite Payload (CHAMP) satellite. Finally, we use the Monte Carlo approach to propagate CHAMP over a three-day period under various modeling scenarios to investigate the distribution of radial, along-track, and cross-track orbital errors caused by drag coefficient uncertainty. The key takeaways of this paper are - (a) a constant drag coefficient cannot be used for reliable SDA purposes, and (b) stochastic machine learning models allow for the computation of drag coefficients in a timely manner while providing reliable uncertainty estimates.

Performance characterization and kinetic analysis of atmosphere-breathing electric propulsion intake device

An atmosphere-breathing electric propulsion (ABEP) system is designed to capture and compress the rarefied atmosphere through an intake device in very-low-Earth-orbit (VLEO). This study numerically characterizes the intake performance according to the design parameters, including the geometry of the tapered chamber, gas-surface interaction (GSI) models, surface temperature, aspect ratio, and sizing. The design of grid ducts is examined for different gaps, lengths, and yaw angles. The influence of intermolecular collisions is also investigated. The diffuse GSI model is chosen as a realistic model at VLEO due to the adsorption of atomic oxygen. The direct simulation Monte Carlo method is employed to calculate the capture efficiency, compression ratio, particle flow rate, and number density as the four indicators of intake performance. The flow conditions are obtained using the NRLMSISE-00 model, with a target altitude range of 180–220 km. In addition, a comprehensive design is proposed and the related propellant characteristics are investigated using kinetic analysis. Multi-modality is found in the particle velocity distribution, which implies non-equilibrium of the ABEP propellant.

MODELING of Rarefied Gas Flows Inside a Micro-Nozzle Based on the DSMC Method Coupled with a Modified Gas–Surface Interaction Model

In this study, we first considered the influence of micro-nozzle wall roughness structure on molecular collision and reflection behavior and established a modified CLL model. The DSMC method was used to simulate and analyze the flow of the micro-nozzle in the cold gas micro-propulsion system, and the deviation of simulation results before and after the improvement of CLL model were compared. Then, the rarefied flow characteristics under a small needle valve opening (less than 1%) were focused on the research, and the particle position, molecular number density, and spatial distribution of internal energy in the micro-nozzle were calculated. The spatial distributions of the flow mechanism in the micro-nozzle under different needle valve openings were compared and analyzed. It was found that when the needle valve opening is lower than 1%, the slip flow and transition flow regions move significantly upstream of the nozzle, the free molecular flow distribution region expands significantly, and the relationship between thrust force and needle valve opening is obviously different from that of medium and large needle valve openings. The effect of nitrogen temperature on the rarefied flow and thrust force is also discussed in this research. The numerical results showed that as gas temperature increases, the molecular internal energy, momentum, and molecular number density near the nozzle exit are enhanced. The thrust at small needle valve openings was significantly affected by the temperature of the working mass. The results of this study will provide key data for the design and development of cold gas micro-thrusters.

Numerical Simulation of Plasma Plume With Gas–Surface Interaction and Chemical Reaction Coupling Effect Based on DSMC-PIC Parallel Algorithm

The spatio-temporal evolution of plasma plumes is accompanied by a series of complex chemical reactions and gas–surface interactions that crucially affect the working characteristics and performance of plasma devices. The direct simulation Monte Carlo (DSMC) and particle-in-cell (PIC) hybrid parallel algorithm is often used to numerically simulate such phenomena. This article discusses the gas–surface interaction models of neutral molecules as elucidated by the parallel DSMC-PIC program. These models include the Maxwell model, the Cercignani–Lampis–Lord model, the complete diffuse reflection (CDR) gas–surface reflection model, and coupling with H combined reactions at the wall. Meanwhile, we consider the ion gas–surface interaction models, which include the CDR model and coupling of the four wall chemical reactions of ions. In addition, the dissociation reactions of H2 and recombination reactions of H are considered in the flow field. For various combinations of models, the simulations reveal the structural characteristics, number density, and coupling effects of gas–surface reflections, gas–surface chemical reactions, chemical reactions in the flow field and electric field, and spatio-temporal evolution of H2, H, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$X$ </tex-math></inline-formula> , <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\text{H}_{2}^{+}$ </tex-math></inline-formula> , and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\text{H}^{+}$ </tex-math></inline-formula> , which are shown by the structural characteristics of the number-density contours for different model combinations and analyzed in detail. The gas–surface interaction critically influences the number-density distribution near the wall and in the main flow. It also strongly affects the number-density distribution of light neutral molecules but not heavy neutral molecules and ions and produces the wall stacking effect. Apart from the stacking area, it has an indirect influence on the number-density distribution. The chemical reactions of ions on the wall affect the number-density distribution of all particles in the flow field and decisively affect the ions near the wall. Acceleration by the electric field intensifies the ion diffusion. The effect of coupling of gas–surface interaction and acceleration by the electric field is obvious. Via the number density and temperature, the chemical reactions in the flow field strongly affect the distribution of neutral molecules at the inlet; further, from the inlet, this effect weakens. Neutral particles and ions interact mainly through collisions.

A modified Cercignani–Lampis model with independent momentum and thermal accommodation coefficients for gas molecules scattering on surfaces

To accurately predict the aerodynamic forces and heating of hypersonic vehicles, an elaborate gas–surface interaction (GSI) model is essential to describe the rarefied gas effect at the interface. By far, the Cercignani–Lampis (CL) model is the most sophisticated GSI model, but it has not been systematically examined under hypersonic conditions where the gas flow possesses large velocity and temperature differences relative to the boundary surface. In this work, the accuracy of the CL model is first assessed by comparing with molecular dynamics simulation results under a variety of conditions of temperature and velocity differences, surface temperature, and surface roughness. It is found that the tangential scattering kernel of CL model is perfect only when the surface is smooth and the gas kinetic energy is close to the surface kinetic energy. To accurately capture the momentum and temperature of the reflected gas molecules, a modified CL model with independent momentum and thermal accommodation coefficients is developed. A hybrid diffusive and modified CL model is further proposed to account for the adsorption phenomenon. With these modifications, the new GSI model can accurately describe the scattering of gas molecules in a wider range of hypersonic rarefied gas flows.

Advanced analytical model for orbital aerodynamic prediction in LEO

The growing interest in low earth orbit (LEO) applications demands for accurate modeling of orbital aerodynamics. But classical analytical models of aerodynamic coefficients in free molecule flow, such as the Sentman’s model, Schamberg’s model and Schaaf-Chambre model, were built upon over simplistic gas-surface interaction models, which degrade the fidelity of aerodynamic prediction. This work presents a new analytical model of orbital aerodynamic coefficients based on the state-of-the-art Cercignani–Lampis–Lord (CLL) gas-surface interaction model, where lobular quasi-specular scattering pattern and separate accommodation degree for different velocity components can be well captured. A key component of the new model is a rigorous function approximation solution of the reflected normal momentum flux based on the CLL model which is derived for the first time and is validated within 1% for any hypothermal flow and surface accommodation conditions. Closed-form analytical solutions of aerodynamic coefficients for simple convex geometries are obtained and exhibit high accuracy (within 0.1%) in typical LEO scenarios. The new analytical model surpasses the classical models in some important aspects, such as overcoming the diffuse scattering hypothesis constraint, considering the variation of normal momentum exchange with the surface incidence angle and being applicable in any hypothermal flow situation. In virtue of the advanced CLL model and feasibility of coupling with the panel method technique, the new analytical model is promising to provide more accurate predictions on the orbital aerodynamic coefficients for LEO applications.

Evaluation of Sublimation Kinetics for Phenolic Impregnated Carbon Ablator

Recession analyses of stagnation tests conducted in NASA Ames Research Center arcjet facilities with surface heat fluxes high enough for carbon char to sublimate are performed and compared with data. The axisymmetric recession computations are based on both the finite-rate gas–surface interaction model and the standard chemical equilibrium surface ablation model. The finite-rate gas–surface interaction model is studied using three different sets of sublimation coefficients, which are obtained through direct measurements. The standard chemical equilibrium ablation model is established through the tables. The ablating material used in these arcjet tests is phenolic impregnated carbon ablator. The prediction of axisymmetric surface recession is achieved by implicitly coupling a material thermal response code and a flow code. The material thermal response code used in this study is the Two-Dimensional Implicit Thermal-Response and Ablation program, which predicts charring material thermal response and shape change. The flow code solves the reacting Navier–Stokes equations using the data parallel line relaxation method. The recession predictions for three selected arcjet conditions with various base radii are presented. The effect of sticking coefficient for carbon sublimation on recession prediction is investigated, and the prediction discrepancy between finite-rate and chemical equilibrium models is examined and discussed in detail.

Satellite drag coefficient modeling for thermosphere science and mission operations

Satellite drag modeling remains the largest source of uncertainty affecting space operations in low Earth orbit. The uncertainty stems from inaccurate models for mass density and drag coefficient. Drag coefficient modeling also impacts scientific knowledge on the physics and dynamics of the upper atmosphere through the estimation of high-fidelity mass density from measurements of acceleration on-board satellites. Efforts over the last decade have pushed drag coefficient modeling in the right direction, however, have resulted in multiple methods and tools. We provide a comprehensive review of the drag coefficient modeling methods and tools. Current scale differences between thermospheric data sets mostly originate from errors in the aerodynamic modeling, specifically in the modeling of the satellite outer surface geometry and the gas-surface interactions. Enhancing these models’ accuracy is intrinsically connected to the satellite drag fidelity for science and operations. A team of invested scientists recently met under the community-driven International Space Weather Action Teams (ISWAT) initiative to discuss and consolidate the efforts towards a drag coefficient modeling baseline for consistency in science and operations. In this paper, we compare the available methods for drag coefficient modeling, their impact on the derived density estimates, and make recommendations for adoption of baseline methods for science and operations. Results show that the differences in derived densities estimates can reach tens of percent at altitudes above 4̃50 km during solar minimum conditions resulting mainly from differences in the modeling of gas-surface interactions. As a result, we conclude and recommend that robust uncertainty quantification be an integral part of any modeling efforts that employ the high-fidelity accelerometer derived density estimates. We also conclude and recommend that gas-surface interaction models that account for impact of altitude and solar variations be employed moving forward. Finally, we recommend future science missions to improve our understanding of gas-surface interactions and eventually the upper thermosphere variability.

CO2 number density measurement in a shock tube with preheated carbon surface

The interaction between a heated carbon-based material and high-temperature air may produce ablation gas species such as CO2, affecting heat transfer onto the surface of a thermal protection system. The prediction of ablation gas production is critical for heat flux prediction and the design of a thermal protection system. In this study, we present a system that measures the number density of CO2 formed by the gas–surface interaction between a hot carbon surface and high-temperature gas. The heated carbon wall is exposed to high-temperature air by using a shock tube and surface heating model. The surface temperature of the carbon wall is measured using two-color ratio pyrometry. The number density of CO2 is predicted by performing numerical calculations for the shock tube flow with gas–surface interaction modeling. The number density of CO2 molecules is measured using infrared emission spectroscopy. The measured CO2 number density is 9.60 × 1023 m−3 at an area-weighted average surface temperature of 1212 K. The measured number density matches the predicted value within an error of 6%. The proposed system is applicable for CO2 number density measurement under various gas–surface interaction conditions, and it can be used for the investigation of ablative gas production and numerical research on gas–surface interactions.

Gas-surface interaction in rarefied gas flows through long capillaries via the linearized Boltzmann equation with various boundary conditions

Reliable gas–surface interaction modeling is of major importance in consistent simulation of rarefied gas flows with applications in vacuum technology and micro-electromechanical systems. The effectiveness of the most prominent kinetic boundary conditions, namely the ones by Maxwell, Cercignani-Lampis and Epstein, is elaborated by numerically solving the classical plane Poiseuille and thermal creep flows via the linearized Boltzmann equation, subject to these boundary conditions. The flow rates are provided in a wide range of the gas rarefaction for many values of the accommodation coefficients of each scattering kernel, identifying in parallel, the sensitivity of the flow rates in small variations of the free parameters. A comparison with available experimental data is performed to deduce that the Cercignani-Lampis and Epstein scattering kernels, compared to the Maxwell one, are more suitable to characterize coupled momentum and energy accommodation modes. With these boundary conditions, the accommodation coefficients may be extracted by fitting computations with measurements, in the Poiseuille flow in a wide range of gas rarefaction, but in the thermal creep flow, experimental data under rarefied conditions, as high as possible, are recommended. The present work may be useful in determining the measurement conditions and uncertainties, allowing accurate extraction of the accommodation coefficients.

State-specific boundary conditions for nonequilibrium gas flows in slip regime.

Boundary conditions for fluid-dynamic variables of strongly nonequilibrium multicomponent gas mixture flows in slip regime are derived systematically by two different approaches. The flow is described in the framework of the state-to-state model for coupled detailed vibrational and chemical kinetics. The specular-diffusive model is applied for particles interaction with the solid wall, and the surface is assumed to be partially catalytic with possible state-specific chemical reactions and vibrational energy transitions described by a simple model based on the analogy with recombination coefficients. The first theoretical approach uses the technique proposed by Grad whereas the second one is based on the kinetic boundary condition. It is shown that for the Maxwell scattering kernel the two approaches are equivalent; at the same time, the approach based on the kinetic boundary condition provides more rigorous mathematical description of the problem and can be easily generalized for other scattering kernels and gas-surface interaction models accounting for surface inner geometry. The resulting boundary conditions are expressed in terms of state-specific transport coefficients: thermal conductivity, multicomponent diffusion of vibrational states, thermal diffusion, shear and bulk viscosity, and relaxation pressure. The dependence of the boundary conditions on the normal mean stress is obtained for the first time. Under thermal equilibrium conditions, the derived expressions reduce to known relations obtained earlier in the one-temperature approach.

ADBSat: Methodology of a novel panel method tool for aerodynamic analysis of satellites

ADBSat is a novel software that determines the aerodynamic properties of any body in free-molecular flow. Its main advantage is the fast approximation of the aerodynamics of spacecraft in the lower end of the low-Earth orbit altitude range. It is a novel implementation of a panel method, where the body is represented as a set of fundamental elements and the sum of their individual aerodynamic properties makes up the properties of the whole. ADBSat's approach treats the shape as a set of flat triangular plates. These are read from a CAD geometry file in the Wavefront format, which can be created with most common CAD programs. A choice of gas-surface interaction models is available to represent the physics of free-molecular flow under different conditions. Its modular design means that other models can be easily and quickly implemented. It also benefits from a new shading algorithm for fast determination of elemental flow exposure. An example case is presented to show the capability and functionality of the program. Program summaryProgram Title: ADBSatCPC Library link to program files:https://doi.org/10.17632/622n2yjg4w.1Licensing provisions: GPLv3Programming language: MATLABDeveloper's repository link:https://github.com/nhcrisp/ADBSatNature of problem: Quickly and accurately determining the aerodynamics of satellites in free-molecular flow.Solution method: A new implementation of the panel method has been devised. The satellite shape is passed to the program as a CAD model, comprised of a set of flat triangular plates. ADBSat then calculates the aerodynamic characteristics of each element using an appropriate mathematical model, and sums the contributions for the overall properties of the body. A novel shading algorithm identifies and removes the panels which do not contribute to the calculations due to being protected from the flow by other body features. ADBSat also has the capability to account for different materials within the shape.Additional comments including restrictions and unusual features: MATLAB's Aero-space Toolbox is required for the determination of environmental parameters, unless otherwise provided by the user. As the program takes as an input a completed model of the spacecraft, the user is responsible for all mesh quality checks. The methods employed therein are only valid for strict free-molecular flow, which the user must ensure. The accuracy of the method decreases for surfaces with high concavity or multiple particle impingement.

Competing effects of surface catalysis and ablation in hypersonic reentry aerothermodynamic environment

Under hypersonic flow conditions, the complicated gas-graphene interactions including surface catalysis and surface ablation would occur concurrently and intervene together with the thermodynamic response induced by spacecraft reentry. In this work, the competing effects of surface heterogeneous catalytic recombination and ablation characteristics at elevated temperatures are investigated using the Reactive Molecular Dynamics (RMD) simulation method. A Gas-Surface Interaction (GSI) model is established to simulate the collisions of hyper-enthalpy atomic oxygen on graphene films in the temperature range of 500–2500 K. A critical temperature Tc around 900 K is identified to distinguish the graphene responses into two parts: at T < Tc, the heterogeneous surface catalysis dominates, while the surface ablation plays a leading role at T > Tc. Contradicting to the traditional Arrhenius expression that the recombination coefficient increases with the increase of surface temperature, the value is found to be relatively uniform at T < Tc but declines sharply as the surface temperature increases further due to the competing ablation effect. The occurrence of surface ablation decreases the amounts of active sites on the graphene surface for oxygen adsorption, leading to reduced recombination coefficient from both Langmuir-Hinshelwood (L-H) and Eley-Rideal (E-R) mechanisms. It suggests that the traditional Computational Fluid Dynamics (CFD) simulation method, which relies on the Arrhenius-type catalysis model, would result in large discrepancies in predicting aerodynamic heat for carbon-based materials during reentry into strong aerodynamic thermal environment.

Design and Optimization of vacuum Intake for Atmosphere-Breathing electric propulsion (ABEP) system

Atmosphere-breathing electric propulsion system is a concept for space mission for ultra-low Earth orbit, which can collect the rarefied atmospheric particles as propellant to compensate the aerodynamic drag. In the best case, it can extend the lifetime of spacecraft without carrying any propellant. As the key component of Atmosphere-breathing electric propulsion system, intake device can capture the ambient particles and drive propellant to electric thruster. Considering the requirement of propellant mass flow and ionization efficiency, the performance of intake needs to be improved, including capture efficiency and compression ratio. The previous studies about intake device are summarized and analyzed firstly in this paper, and a new intake device is proposed that consists of tapered chamber, grid ducts and tube. Then, the inlet boundary conditions are set based on the NRLMSISE-00 atm model, such as particle species, natural temperature, number density and so on. Lastly, the intake performance is analyzed under different gas-surface interaction models through Direct Simulation Monte Carlo method. Simulation results show that the combination of parabola chamber, honeycomb grid ducts and a certain length of tube is benefit to intake device under the mixture reflection model of specular and diffuse. The capture efficiency is 65.79% with a high compression ratio of 210.2.

A parameter-free physical model for gas–surface interaction

Phenomenological gas–surface interaction models and various slip models are nowadays used as the boundary condition in the study of rarefied gas flows and microflows at the microscopic and macroscopic levels, respectively. However, most existing models depend on certain accommodation coefficients which are difficult to be determined prior to application. A physical-based gas–surface interaction model developed recently shows great flexibility and promising performance in capturing the complex gas–surface interaction process at the boundary. Particularly, the new model only employs three input parameters with clear physical meanings. In this work, a “bottom-up” approach for determining the input parameters of the model from the microscopic properties of the gas–surface system is explored. Because of the limitation of the estimation model for the local collision accommodation coefficient, this approach is restricted to light gas-heavy solid surface systems. Consequently, the physical-based gas–surface interaction model no longer involves unknown parameters like the accommodation coefficients in the traditional boundary conditions for rarefied gas flows. Benchmarked by molecular dynamics simulations of the non-isothermal gas–surface interaction process, the parameter-free gas–surface interaction model can accurately predict the reflected velocity distribution as well as the accommodation coefficients on the surface with different corrugation, binding strength, and relative stiffness. Its capability of capturing the influences of surface temperature and gas molecular mass on the gas–surface energy exchange is also demonstrated.

Inverting gas-surface interaction parameters from Fourier drag-coefficient estimates for a given atmospheric model

Satellite drag-coefficient is a highly dynamic parameter that captures the physics of the interactions between the atmosphere and the satellite surface. Physical models, known as Gas-Surface Interaction Models (GSIMs), can be used to compute the time variations in the drag-coefficient in orbit. But many input parameters to such models are not known accurately, that consequently introduce uncertainties in the drag-coefficient. This work outlines a framework to invert GSIM parameters from estimates of the drag-coefficient that are obtained during orbit determination, under the assumption of a known atmospheric density. The Fourier drag-coefficient models, developed previously by the authors, are used to model the drag-coefficient in the filtering methodology. These models allow estimation of higher-order frequencies in the drag-coefficient that are functions of the orbital and satellite attitudinal variations. In this work, it is demonstrated that information about the GSIM parameters can be obtained from estimated Fourier drag-coefficients. To that end, an extensive observability analysis of the Fourier drag-coefficient models is carried to determine the coefficients that can be estimated from tracking data.