The Rosetta spacecraft is en route to comet 67P/Churyumov-Gerasimenko for a rendezvous, landing, and extensive orbital phase beginning in 2014. Model studies of the coma will be required not only for planning of the mission and interpretation of spacecraft data, but also for an expectedly large amount of complementary remote observational data that will be obtained in the meantime. A full-scale simulation of the coma under conditions occurring during the mission can be done only on the basis of a kinetic model. In this work we present a newly developed direct simulation Monte Carlo model of a multispecies coma, where components of the coma are coupled through momentum exchange and photochemical processes, and its application to the case of comet Churyumov-Gerasimenko. It is shown that kinetic effects determine the state of the coma, which limits applicability of a hydrodynamics approach. The study of the coma was performed in the region starting from the surface of the nucleus and extending up to 106 km, which allows incorporation of a realistic model of the gas production from the nucleus from a thermophysical model of a porous ice/dust mixture accounting for the thermal reradiation, the subsurface sublimation and recondensation, and the subsurface mass and energy transport. The results obtained present states of the coma for a series of stages throughout the Rosetta mission and can serve for the planning of the mission as well as for the interpretation of ground-based observations during the 2009 and 2016 apparitions.

https://iopscience.iop.org/article/10.1086/590376/pdf

A Global Kinetic Model for Cometary Comae: The Evolution of the Coma of the Rosetta Target Comet Churyumov-Gerasimenko throughout the Mission

This study investigates the effects of continuum breakdown on the surface aerothermodynamic properties (pressure, shear, heat transfer rate) of a sphere in Mach 10, 25, and 45 flows of nitrogen gas in regimes varying from continuum to rarefied gas. A rotational energy relaxation model is employed in the computational fluid dynamics code and is tested to confirm its accuracy. As the global Knudsen number is increased, from continuum flow to a rarefied gas, the amount of continuum breakdown seen in the flow and on the surface is increased. This increase in continuum breakdown affects the surface properties, such that an increase in the differences between computational fluid dynamics and direct simulation Monte Carlo method is observed. As the Mach number is increased, the amount of continuum breakdown observed in the flow is increased, but the gradient length local Knudsen number stays approximately constant. Even though the amount of continuum breakdown has increased, the difference between computational fluid dynamics and direct simulation Monte Carlo method remains relatively constant. The last part of this study compares the results of the sphere with that of the analogous cylinder case. At the same global Knudsen number, the differences in the surface properties between computational fluid dynamics and direct simulation Monte Carlo method increase when the simulation is run axisymmetrically.

/pdf/effects-of-continuum-breakdown-on-the-surface-properties-of-16dwf3utt4.pdf

Effects of Continuum Breakdown on the Surface Properties of a Hypersonic Sphere

Switching criteria for hybrid hydrodynamic/molecular gas flow solvers are developed, and are demonstrated to be more appropriate than conventional criteria for identifying thermodynamic non-equilibrium. For switching from a molecular/kinetic solver to a hydrodynamic (continuum-fluid) solver, the criterion is based on the difference between the hydrodynamic near-equilibrium fluxes (i.e. the Navier–Stokes stress and Fourier heat flux) and the actual values of stress and heat flux as computed from the molecular solver. For switching from hydrodynamics to molecular/kinetic, a similar criterion is used but the values of stress and heat flux are approximated through higher order constitutive relations; in this case, we use the R13 equations. The efficacy of our proposed switching criteria is tested within an illustrative hybrid kinetic/Navier–Stokes solver. For the test cases investigated, the results from the hybrid procedure compare very well with the full kinetic solution, and are obtained at a fraction of the computational cost.

/pdf/switching-criteria-for-hybrid-rarefied-gas-flow-solvers-2dyv6z8r6z.pdf

Switching criteria for hybrid rarefied gas flow solvers

conditions has become critical. Because the governing equations of fluid dynamics typically used to model subsonic and supersonic flow contain only lim- ited mathematical terms representing non-equilibrium flow (e.g., velocity and temperature gradients), attempts to extend their validity have provided much insight. Many of the interesting and open problems remaining in the field of fluid mechanics are concerned with the study of nonequilibrium phenomena. Nonequilibrium phenomena in fluids typically result from the propensity of the constituent molecules to undergo changes in their internal energy state during collisions. These events occur at some finite rate and not every encounter results in significant changes. If molecular collisions alter the macroscopic properties of the fluid over time, they may be regarded as nonequilibrium phenomena. Nonequilibrium eects complicate the analysis of fluid flow. The conventional equations of continuum fluid mechanics do not address these eects.

Development of Continuum Onset Criteria with Direct Simulation Monte-Carlo Using Boltzmann's H-Theorem: Review and Vision

Three intermolecular collision models have been used in Monte Carlo direct-simulation computations. Their merits have been assessed by comparing the predictions given for two contrasting flows with experimental results. In one flow viscous effects were predominant; in the other the rapid compression ahead of a blunt body was the feature concentrated upon. In both examples the flows were rarefied and hypersonic and the gas was diatomic and rotationally excited. Refs.

https://espace.library.uq.edu.au/view/UQ:8762/jfm1983DDHM.pdf

An evaluation of some collision models used for Monte Carlo calculations of diatomic rarefied hypersonic flows

An application of the direct simulation Monte Carlo method, which is claimed to give a solution of the full Boltzmann equation. The breakdown of translational equilibrium in steady cylindrical and spherical expansions was studied for both hard sphere and Maxwell molecules. The study of spherical expansions was extended to the combined translational and rotational breakdown in a gas of rough sphere molecules. The breakdown of translational equilibrium in a complete one-dimensional rarefaction wave in a hard sphere gas was also studied. The application of the method generally followed standard procedures, except for the unsteady flow, in which a Lagrangian system of cells moving with the fluid was used in place of the usual Eulerian cells fixed in physical space. The onset of nonequilibrium was marked by the divergence of the separate kinetic temperatures based on the molecular velocity components parallel and normal to the flow direction. The region of simulation of the steady expansion generally covered only a restricted range of Mach number in the vicinity of the point of breakdown. However, several runs were made over a wide range of Mach number and the temperatures were plotted against radius r in order to obtain an over-all picture of the process. The results gave qualitative support to one of the major predictions of the BGK theory— that the freezing of the parallel temperature Tx occurs gradually over a wide range of Mach number and is much less rapid for Maxwell molecules than for hard sphere molecules. In the case of the normal temperature Tn, there is a qualitative difference between the results for the two molecular models. The Monte Carlo calculation for the Maxwell molecules gave a Tn curve that remains above the r~ / 3 continuum curve and could well be consistent with the r" prediction of the BGK theory. However, for the simulation with hard sphere molecules, the Tn curve falls below the continuum curve. A rarefaction parameter P was defined by the ratio of the logarithmic time derivative of density p, following the motion of the fluid, to the collision frequency v in the gas. That is, The departure of the temperature ratio Tx/Tn from unity gives the best indication of translational breakdown, and it was plotted against P for all the steady expansion runs. These involved two geometries, three molecular models and Mach numbers ranging from 2 to 20. In all cases, the breakdown of equilibrium occurred at a value of P of approximately 0.04. If the hard sphere formula for collision frequencyin terms of viscosity coefficient is substituted into Eq. (1), this leads to the following empirical breakdown criterion for steady expansions

G.A. Bird

Papers

SYNOPTIC: Breakdown of Translational and Rotational Equilibrium in Gaseous Expansions