Andrew C. Walker

Comparing Physical Drag Coefficients Computed Using Different Gas-Surface Interaction Models

Drag coefficient is a major source of uncertainty in calculating the aerodynamic forces on satellites in low Earth orbit. Closed-form solutions are available for simple geometries under the assumption of free molecular flow; however,mostsatelliteshavecomplexgeometries,andamoresophisticatedmethodofcalculatingthedragcoefficient is needed. This work builds toward modeling physical drag coefficients using the direct simulation Monte Carlo method capable of accurately modeling flow shadowing and concave geometries. The direct simulation threedimensional visual program and the direct simulation Monte Carlo analysis code are used to compare the effects of two separate gas–surface interaction models: diffuse reflection with incomplete accommodation and quasi-specular Cercignani–Lampis–Lordmodels.Resultsshowthatthetwogas–surfaceinteractionmodelscomparewellataltitudes below ∼500 km during solar maximum conditions and below ∼400 km during solar minimum conditions. The differenceindragcoefficientofasphereat ∼800 kmcalculated usingthetwogas–surfaceinteractionmodels is ∼6% during solar maximum and increases to ∼10% during solar minimum. The difference in drag coefficient of the GRACE satellite computed using the two gas–surface interaction models at ∼500 km differs by ∼15% during solar minimum conditions and by ∼2–3% during solar maximum conditions.

Drag Coefficient Model Using the Cercignani–Lampis–Lord Gas–Surface Interaction Model

Drag coefficient calculations using the Cercignani–Lampis–Lord quasi-specular gas–surface interaction model have been used to derive modified closed-form solutions for several simple geometries. The key component of the modified closed-form solutions is a relation between the normal energy and normal momentum accommodation coefficients, which is valid within ∼0.5% over the global parameter space. The modified closed-form solutions are made self-consistent by relating the effective energy accommodation to the partial pressure of atomic oxygen through a Langmuir isotherm. The modified closed-form solutions are compared to fitted drag coefficients and drag coefficients computed using two other gas–surface interaction models: diffuse reflection with incomplete accommodation and Maxwell’s model. Comparison during solar maximum conditions shows that both the diffuse reflection with incomplete accommodation and Cercignani–Lampis–Lord models agree with fitted drag coefficients within ∼2% below ∼500  km altitude. ...

New density estimates derived using accelerometers on board the CHAMP and GRACE satellites

Atmospheric mass density estimates derived from accelerometers onboard satellites such as CHAllenging Minisatellite Payload (CHAMP) and Gravity Recovery and Climate Experiment (GRACE) are crucial in gaining insight into open science questions about the dynamic coupling between space weather events and the upper atmosphere. Recent advances in physics-based satellite drag coefficient modeling allow derivation of new density data sets. This paper uses physics-based satellite drag coefficient models for CHAMP and GRACE to derive new estimates for the neutral atmospheric density. Results show an average difference of 14–18% for CHAMP and 10–24% for GRACE between the new and existing data sets depending on the space weather conditions (i.e., solar and geomagnetic activity levels). The newly derived densities are also compared with existing models, and results are presented. These densities are expected to be useful to the wider scientific community for validating the development of physics-based models and helping to answer open scientific questions regarding our understanding of upper atmosphere dynamics such as the sensitivity of temporal and global density variations to solar and geomagnetic forcing.

Simulation Of Plasma Interaction With Io's Atmosphere

One dimensional Direct Simulation Monte Carlo (DSMC) simulations are used to examine the interaction of the jovian plasma torus with Io’s sublimation atmosphere. The hot plasma sweeps past Io at ∼57 km/s due to the external Jovian magnetic and corotational electric fields and the resultant energetic collisions both heat and dissociate the neutral gas creating an inflated, mixed atmosphere of SO2 and its daughter products. The vertical structure and composition of the atmosphere is important for understanding Io’s mass loading of the plasma torus, electron excited aurora, and Io’s global gas dynamics. Our 1D simulations above a fixed location on the surface of Io allows the O+ and S+ ions to drift down into the domain where they then undergo elastic and charge exchange collisions with the neutral gas. Each electron’s position is determined by the motion of a corresponding ion; however, the electrons retain their own velocity components which are then used during elastic, ionization, and excitation collisio...

Sensitivity Analysis towards Probabilistic Re-Entry Modeling of Spacecraft and Space Debris

We present work towards the development of a new tool, FOSTRAD (Free Open Source Tool for Re-entry of Asteroids and Debris) that will use a combination of the spacecraftand object-oriented approaches and will incorporate uncertainty quantification. The current work presents progress towards incorporating uncertainty quantification by performing aeroand aerothermo-dynamic sensitivity analyses for a sphere, cube, and a cylinder with respect to the uncertain atmospheric and object parameters. The sensitivity analysis is performed using high fidelity tools such as the Direct Simulation Monte Carlo (DSMC) and the Computational Fluid Dynamics (CFD) methods. In FOSTRAD, aerodynamic computations in the continuum and free molecular regimes are performed using Modified Newtonian Theory and the free molecular analytical models of Schaaf and Chambre, respectively. For the rarefied transition regime, recently developed sigmoid bridging function is used for better tracking of the data. Analytical aerothermodynamic relations for strong shocks exist only for blunt objects that have a finite radius of curvature at the nose (like a sphere), but not for sharp-edged objects such as the cube and cylinder. We use the results from the sensitivity analyses to develop mathematical relations for the variation of aerothermodynamic properties for cube and cylinder. We also develop mathematical relations for the heat flux distribution on the surface of these objects.

DSMC Simulations of the Plasma Bombardment on Io's Sublimated and Sputtered Atmosphere.

The DSMC method is used to model the interaction of the jovian plasma torus with Io’s SO2 sublimation and sputtered atmosphere just prior to eclipse. The SO2 frost sublimes on the warm dayside and photo and neutral chemistry, the dominant source of the daughter species (SO, O2, O, and S) are included. To model the plasma interaction with the sublimation atmosphere, a two-timestep method is utilized in which the neutrals are assumed to be stationary while electrons and ions are moved and collided over a much smaller timestep. The dominant ion-neutral interactions (non-reactive and resonant charge exchange) are included. Sputtering of SO2 molecules from the frost-covered surface is dependent on the incident ion energy and the surface frost temperature. Io’s surface is assumed to be uniformly covered by SO2 surface frosts with the temperature computed based on radiative equilibrium with insolation. We investigate the effect that the plasma interaction with Io’s atmosphere has on atmospheric composition and structure, circumplanetary winds, and the escape rate of material from Io to the plasma torus. The dense sublimation atmosphere reduces sputtering from SO2 surface frosts over much of the dayside; however, sputtering was found to be a significant contributor to the nightside atmosphere. The plasma pressure on the sublimation atmosphere has a substantial effect on the day-to-night winds. Not only does the plasma pressure induce an overall retrograde wind in Io’s atmosphere just prior to entry into eclipse, but the atmospheric scale height is reduced by the plasma pressure on the trailing hemisphere. Molecular oxygen is a minor species on the dayside but is found to be the dominant nightside species because it is non-condensable and the loss rates due to atmospheric escape or dissociation are slow.

Loki - A lava lake in rarefied circumplanetary cross flow

The interaction between Io’s largest hot spot, Loki, and Io’s circumplanetary winds is simulated using the direct simulation Monte Carlo (DSMC) method. Our three‐dimensional simulation models the rarefied pressure‐driven boundary layer flow over a “hot” disk in the presence of a weak gravitational field. The pressure gradient which forces winds away from the subsolar point toward the nightside is caused by the variation in insolation over the surface. The rarefaction varies strongly with time of day due to the exponential dependence of the vapor pressure on the surrounding surface frost temperature (KnHS≈1×10−4 to 0.5 where KnHS = λ/R, λ is the mean free path, and R is Loki’s effective radius). The spread of heat from the hot spot, the equilibration of pressure over the hot spot, and separation of the boundary layer are examined. The spread of heat away from the hot spot is approximately controlled by δ = tRADU/R (tRAD is the radiation time scale and U is the mean wind speed). For cross flow speed conside...

Different Implementations of Diffuse Reflection with Incomplete Accommodation for Drag Coefficient Modeling

Diffuse reflection with incomplete accommodation is the favored gas–surface interaction model for calculating the drag coefficient of satellites in low Earth orbit, where drag is the largest source of uncertainty in the orbital trajectory of satellites. Closed-form solutions have incorporated the variation of the energy accommodation coefficient through equating the total energy of the incident and reflected flows; however, this leads to an incorrect reflected velocity distribution for incomplete accommodation. The problem is highlighted by investigating the velocity distribution functions for a gas reflected from a flat plate at zero accommodation. A physically accurate implementation for diffuse reflection with incomplete accommodation based on the Cercignani–Lampis–Lord gas–surface interaction model is compared with the closed-form solutions that equate the incident and reflected energy of the flow. The Cercignani–Lampis–Lord gas–surface interaction model shows the conservation of energy on a molecule-...

Io’s Atmospheric Freeze‐out Dynamics in the Presence of a Non‐condensable Species

One dimensional direct simulation Monte Carlo (DSMC) simulations are used to examine the effect of a trace non‐condensable species on the freeze‐out dynamics of Io’s sulfur dioxide sublimation atmosphere during eclipse and egress. Due to finite ballistic times, essentially no collapse occurs during the first 10 minutes of eclipse at altitudes above ∼100 km, and hence immediately after ingress auroral emission morphology above 100 km should resemble that of the immediate pre‐eclipse state. In the absence of a non‐condensable species the sublimation SO2 atmosphere will freeze‐out (collapse) during eclipse as the surface temperature drops. However, rapid collapse is prevented by the presence of even a small amount of a perfect non‐condensable species due to the formation of a static diffusion layer several mean free paths thick near the surface. The higher the non‐condensable mole fraction, the longer the collapse time. The effect of a weakly condensable gas species (non‐zero sticking/reaction coefficient) w...

Modeling Io’s Sublimation‐Driven Atmosphere: Gas Dynamics and Radiation Emission

Io’s sublimation‐driven atmosphere is modeled using the direct simulation Monte Carlo method. These rarefied gas dynamics simulations improve upon earlier models by using a three‐dimensional domain encompassing the entire planet computed in parallel. The effects of plasma impact heating, planetary rotation, and inhomogeneous surface frost are investigated. Circumplanetary flow is predicted to develop from the warm subsolar region toward the colder night‐side. The non‐equilibrium thermal structure of the atmosphere, including vibrational and rotational temperatures, is also presented. Io’s rotation leads to an asymmetric surface temperature distribution which is found to strengthen circumplanetary flow near the dusk terminator. Plasma heating is found to significantly inflate the atmosphere on both day‐ and night‐sides. The plasma energy flux also causes high temperatures at high altitudes but permits relatively cooler temperatures at low altitudes near the dense subsolar point due to plasma energy depleti...