Direct Simulation Monte Carlo Calculations Research Articles

Surface recombination in the direct simulation Monte Carlo method

This work is aimed at the development of surface chemistry models for the Direct Simulation Monte Carlo (DSMC) method applicable to non-equilibrium high-temperature flows about reentry vehicles. Probabilities of adsorption and Eley-Rideal recombination dependent on individual properties of each particular molecule and frequencies of desorption and Langmuir-Hinshelwood recombination are determined from macroscopic reaction rate data. Various macroscopic finite-rate surface reaction sets are used for the construction of the DSMC surface recombination models for the reaction cured glass and α-alumina surfaces. The models are implemented in the SMILE++ software system for DSMC computations, and detailed verification of the code is performed. The proposed approach is used to study the effects of surface recombination on the aerothermodynamics of a blunt body at high-altitude reentry conditions.

Nonlinear thermal effects in unsteady shear flows of a rarefied gas

We study the response of a rarefied gas in a slab to the motion of its boundaries in the tangential direction. Different from previous investigations, we consider boundaries displacements at nonsmall Mach ($\mathrm{Ma}$) numbers, coupling the dynamic and thermodynamic gas states, and deviating the system from its low-velocity isothermal condition. The problem is studied in the entire range of gas rarefaction rates, combining limited case ballistic- and continuum-flow analyses with direct simulation Monte Carlo computations. A nonlinear solution is derived in the ballistic regime for arbitrary velocity profiles and amplitudes. At near-continuum conditions, a slip-flow time-periodic solution is obtained for the case of oscillatory boundary motion, by expanding the flow field in an asymptotic Mach power series. The effect of replacing between isothermal and adiabatic surfaces is examined. The results indicate that, at all Knudsen ($\mathrm{Kn}$) numbers, the thermodynamic fields and normal velocity component are dominated by double-frequency (and descending higher-order even-frequency harmonic) time dependence, different from the fundamental-frequency time dependence dominating the tangential gas velocity. At continuum-limit conditions, this stems from the quadratic viscous dissipation term (negligible at low-Mach conditions), coupling the square of the tangential velocity gradient as a forcing term. System nonlinearity also results in an unsteady normal force acting on the boundaries, overcoming the tangential force with increasing $\mathrm{Ma}$. A marked difference from the latter is that the normal force either decreases with $\mathrm{Kn}$ or, at sufficiently small actuation frequencies, varies nonmonotonically with $\mathrm{Kn}$, reaching a maximum at some intermediate rarefaction conditions.

Continuum Simulations of Hypersonic Flows in Chemical and Thermal Nonequilibrium

The ability of the Navier–Stokes equations to capture the effects of strong chemical and thermal nonequilibrium on gas composition in a manner similar to the direct simulation Monte Carlo (DSMC) method is tested with the introduction of a nonequilibrium chemistry model. Although this chemistry model has the ability to reasonably reproduce measured Arrhenius rates in conditions of thermal equilibrium, it results in reaction rates that vary significantly for the most commonly used Arrhenius rates in conditions of thermal nonequilibrium. The nonequilibrium chemistry model is implemented in the three-temperature Navier–Stokes computational fluid dynamics (CFD) solver, Data-Parallel Line Relaxation (DPLR), and tested on high-altitude, hypersonic flow conditions. The results of the simulations show that the model predicts a greater amount of NO compared with previous Navier–Stokes using nonequilibrium quasi-classical trajectory derived rates and remains consistent with DSMC computations over altitudes ranging from 53.5 to 87.5 km. The most commonly used chemistry model for Navier–Stokes solvers was found unable to match this performance, indicating the importance of including nonequilibrium effects when modeling chemically reacting hypersonic flowfields.

Assessment of the LD-DSMC hybrid method for hypersonic rarefied flow

Hypersonic aerothermodynamics for a probe entering a planetary atmosphere is an important issue in space exploration. The probe experiences various Knudsen number regimes, ranging from rarefied to continuum, due to density variation in the planet’s atmosphere. To simulate such multiscale flows, a novel hybrid particle scheme is employed in the present work. The hybrid particle scheme employs the direct simulation Monte Carlo (DSMC) method in rarefied flow regions and the low diffusion (LD) particle method in continuum flow regions. Numerical procedures in the low diffusion particle method are implemented within an existing DSMC algorithm. The hybrid scheme is assessed using two hypersonic, blunt body flow problems: Mach 10 nitrogen flow over a sphere, and Mach 40 carbon dioxide flow over the Mars Path Finder each with a global Knudsen number of 0.002. Standard DSMC and CFD results are compared with the LD-DSMC hybrid simulation results. The hybrid scheme results show good overall agreement with results from standard DSMC computation, while CFD is inaccurate especially in the wake where a highly rarefied region exists. The LD-DSMC hybrid solution is able to increase computational efficiency upto 50% in run time in comparison to DSMC. And sensitivity to numerical parameters of the LD-DSMC method is also studied.

Effects of neutral distribution and external magnetic field on plasma momentum in electrodeless plasma thrusters

The effects of neutral distribution and an external magnetic field on plasma distribution and thruster performance are numerically investigated using a particle-in-cell simulation with Monte Carlo collisions (PIC-MCC) and the direct simulation Monte Carlo (DSMC) method. The modeled thruster consists of a quartz tube 1 cm in diameter and 3 cm in length, where a double-turn rf loop antenna is wound at the center of the tube and a solenoid is placed between the loop antenna and the downstream tube exit. A xenon propellant is introduced from both the upstream and downstream sides of the thruster, and the flow rates are varied while maintaining the total gas flow rate of 30 μg/s. The PIC-MCC calculations have been conducted using the neutral distribution obtained from the DSMC calculations, which were applied with different strengths of the magnetic field. The numerical results show that both the downstream gas injection and the external magnetic field with a maximum strength near the thruster exit lead to a shift of the plasma density peak from the upstream to the downstream side. Consequently, a larger total thrust is obtained when increasing the downstream gas injection and the magnetic field strength, which qualitatively agrees with a previous experiment using a helicon plasma source.

Nonequilibrium diffusive gas dynamics: Poiseuille microflow

We test the recently developed hierarchy of diffusive moment closures for gas dynamics together with the near-wall viscosity scaling on the Poiseuille flow of argon and nitrogen in a one micrometer wide channel, and compare it against the corresponding Direct Simulation Monte Carlo computations. We find that the diffusive regularized Grad equations with viscosity scaling provide the most accurate approximation to the benchmark DSMC results. At the same time, the conventional Navier–Stokes equations without the near-wall viscosity scaling are found to be the least accurate among the tested closures.

Gas Near a Wall: Shortened Mean Free Path, Reduced Viscosity, and the Manifestation of the Knudsen Layer in the Navier–Stokes Solution of a Shear Flow

For the gas near a solid planar wall, we propose a scaling formula for the mean free path of a molecule as a function of the distance from the wall, under the assumption of a uniform distribution of the incident directions of the molecular free flight. We subsequently impose the same scaling onto the viscosity of the gas near the wall, and compute the Navier-Stokes solution of the velocity of a shear flow parallel to the wall. This solution exhibits the Knudsen velocity boundary layer in agreement with the corresponding Direct Simulation Monte Carlo computations for argon and nitrogen. We also find that the proposed mean free path and viscosity scaling sets the second derivative of the velocity to infinity at the wall boundary of the flow domain, which suggests that the gas flow is formally turbulent within the Knudsen boundary layer near the wall.

Quantifying the Direct Influence of Diffusive Mass Transfer in Rarefied Gas Mixing Simulations

This work utilizes the direct simulation Monte Carlo (DSMC) calculations and examines the influence of rarefication on the mixing length and effective diffusion coefficient in a two-species mixing problem. There have been efforts in past rarefied mixing flow studies to bridge between the mixing evolution rate and Knudsen number. A careful review of those efforts shows that the past derived relations did not determine the weights of Reynolds (or Peclet) number in the rarefaction influences. Although they indicated that an increase in Knudsen would decrease the mixing length, such reductions were primarily due to the Reynolds (or Peclet) reduction. Therefore, those studies could not explicitly appraise the contribution of rarefaction in the total mass diffusion magnitude. This work focuses specifically on the role of rarefaction in the total diffusive mass transfer magnitude in rarefied gas mixing problems. It excludes the contributions of momentum and heat to the mass diffusion via imposing suitable velocity, pressure, and temperature fields in the mixer domain. The results show that there will be some decreases in the diffusive mass fluxes and some increases in the mixing length as Knudsen increases. Using the Fick’s law, the effective diffusion coefficient is then calculated in the mixer zone. The results show that this coefficient may vary considerably throughout the mixer zone due to the local rarefaction level variation. The results of all investigated cases indicate that the trends of their effective diffusion coefficient variations approach to a limiting value as the rarefaction level decreases.

Analytic Free-Molecular Aerodynamics for Rapid Propagation of Resident Space Objects

Aerodynamic forces and moments are significant perturbations on low-Earth-orbiting objects, second in magnitude to the nonspherical gravity field. Traditionally, the aerodynamic perturbations are calculated using a direct simulation Monte Carlo method. Under certain assumptions, these forces and moments can be described analytically via free-molecular flow theory. Using symbolic manipulation techniques, exact expressions for the free-molecular aerodynamics of analytic shapes can be derived. In this investigation, analytic expressions for the aerodynamic force and moment coefficients of primitive and composite parametric surfaces are derived, then validated against industry-standard direct simulation Monte Carlo techniques. A framework for the rapid and accurate calculation of free-molecular aerodynamics of composite geometries based on superposition is described. This framework is applied to axisymmetric composite geometries. Results within 6% of direct simulation Monte Carlo calculations are obtained in 0.05% of the time. The analytic aerodynamics models enable rapid trajectory and uncertainty propagation for low-Earth-orbiting objects. A case study on aerodynamic perturbations of a low-Earth-orbit nanosatellite is included to demonstrate application of these analytic models. The case study shows that these derived analytical free-molecular aerodynamics produce results that are applicable to inclusion in rapid trajectory propagation tools for orbit prediction and conceptual mission design.

Aerothermodynamic correlations for high-speed flow

Heat flux and drag correlations are developed for high-speed flow over spherical geometries that are accurate for any Knudsen number ranging from continuum to free-molecular conditions. A stagnation point heat flux correlation is derived as a correction to the continuum (Fourier model) heat flux and also reproduces the correct heat flux in the free-molecular limit by use of a bridging function. In this manner, the correlation can be combined with existing continuum correlations based on computational fluid dynamics simulations, yet it can now be used accurately in the transitional and free-molecular regimes. The functional form of the stagnation point heat flux correlation is physics based, and was derived via the Burnett and super-Burnett equations in a recent article, Singh & Schwartzentruber (J. Fluid Mech., vol. 792, 2016, pp. 981–996). In addition, correlation parameters from the literature are used to construct simple expressions for the local heat flux around the sphere as well as the integrated drag coefficient. A large number of direct simulation Monte Carlo calculations are performed over a wide range of conditions. The computed heat flux and drag data are used to validate the correlations and also to fit the correlation parameters. Compared to existing continuum-based correlations, the new correlations will enable engineering analysis of flight conditions at higher altitudes and/or smaller geometry radii, useful for a variety of applications including blunt body planetary entry, sharp leading edges, low orbiting satellites, meteorites and space debris.

Using a direct simulation Monte Carlo approach to model collisions in a buffer gas cell.

A direct simulation Monte Carlo (DSMC) method is applied to model collisions between He buffer gas atoms and ammonia molecules within a buffer gas cell. State-to-state cross sections, calculated as a function of the collision energy, enable the inelastic collisions between He and NH3 to be considered explicitly. The inclusion of rotational-state-changing collisions affects the translational temperature of the beam, indicating that elastic and inelastic processes should not be considered in isolation. The properties of the cold molecular beam exiting the cell are examined as a function of the cell parameters and operating conditions; the rotational and translational energy distributions are in accord with experimental measurements. The DSMC calculations show that thermalisation occurs well within the typical 10-20 mm length of many buffer gas cells, suggesting that shorter cells could be employed in many instances-yielding a higher flux of cold molecules.

DSMC analysis of bipropellant thruster plume impingement on a geostationary spacecraft

To quantify the potential contamination induced by exhaust plume from the MBB 10 N bipropellant thruster firing, we performed plume impingement analyses on the sensitive surfaces. The heat and mass fluxes of chemical species on the spacecraft surfaces and on the specific area of sensor units (optical port and radiator) were evaluated. A fully unstructured three-dimensional Direct simulation Monte Carlo (DSMC) code was developed and validated with measurements. A geostationary satellite with an optical port and radiator was selected and the actual configuration of the satellite was simplified by considering a bipropellant thruster, which is a major plume source to the sensitive surfaces, two communication antennas, and satellite panels. The DSMC computations show that the mass distribution or plume gas composition is unevenly distributed due to the mass separation effect, which occurs from the rapid expansion into vacuum especially around the nozzle lip at the backflow region. H2O is known as the most critical contaminant species; however, its plume impingement effect on the sensitive surfaces is negligible compared to the evaporation rate calculated by Langmuir’s evaporation equation. Not only have the results contributed to the geostationary satellite development, but also these findings are expected to be significant in designing spacecraft configurations and useful in the trade-off studies.

Particle Ellipsoidal Statistical Bhatnagar–Gross–Krook Approach for Simulation of Hypersonic Shocks

To reduce the computational costs related to direct simulation Monte Carlo computations for low Knudsen number flows, a new particle method, based on the ellipsoidal statistical Bhatnagar–Gross–Krook model of the Boltzmann equation, is investigated. In this method, a fraction of the computational particles in a cell is selected for velocity reassignment from the local Maxwellian distribution based the local collision frequency and an even smaller fraction is selected for internal mode energy reassignment based on the rotational and vibrational relaxation rates. A scaling algorithm is used to decrease the required number of particles per cell and to guarantee that the energy and momentum are conserved in each time step. The accuracy and efficiency of the ellipsoidal statistical Bhatnagar–Gross–Krook method are tested in three different test cases and the results are compared with the direct simulation Monte Carlo solution and experiment as well. The ellipsoidal statistical Bhatnagar–Gross–Krook approach is found to provide good agreement with direct simulation Monte Carlo solutions, however, a factor of 2 speed up compared with direct simulation Monte Carlo is only achieved when the collision frequency is sufficiently high.

Restricted Collision List method for faster Direct Simulation Monte-Carlo (DSMC) collisions

The ‘Restricted Collision List’ (RCL) method for speeding up the calculation of DSMC Variable Soft Sphere collisions, with Borgnakke–Larsen (BL) energy exchange, is presented. The method cuts down considerably on the number of random collision parameters which must be calculated (deflection and azimuthal angles, and the BL energy exchange factors). A relatively short list of these parameters is generated and the parameters required in any cell are selected from this list. The list is regenerated at intervals approximately equal to the smallest mean collision time in the flow, and the chance of any particle re-using the same collision parameters in two successive collisions is negligible. The results using this method are indistinguishable from those obtained with standard DSMC. The CPU time saving depends on how much of a DSMC calculation is devoted to collisions and how much is devoted to other tasks, such as moving particles and calculating particle interactions with flow boundaries. For 1-dimensional calculations of flow in a tube, the new method saves 20% of the CPU time per collision for VSS scattering with no energy exchange. With RCL applied to rotational energy exchange, the CPU saving can be greater; for small values of the rotational collision number, for which most collisions involve some rotational energy exchange, the CPU may be reduced by 50% or more.

Transport and Distribution of Hydroxyl Radicals and Oxygen Atoms from H2O Photodissociation in the Inner Coma of Comet 67P/Churyumov–Gerasimenko

With a combination of the Direct Simulation Monte Carlo (DSMC) calculation and test particle computation, the ballistic transport process of the hydroxyl radicals and oxygen atoms produced by photodissociation of water molecules in the coma of comet 67P/Churyumov–Gerasimenko is modelled. We discuss the key elements and essential features of such simulations which results can be compared with the remote-sensing and in situ measurements of cometary gas coma from the Rosetta mission at different orbital phases of this comet.

Resolution of the vibrational energy distribution function using a direct simulation Monte Carlo-master equation approach

The direct simulation Monte Carlo (DSMC) method is the primary numerical technique for analysis of rarefied gas flows. While recent progress in computational chemistry is beginning to provide vibrationally resolved transition and reaction cross sections that can be employed in DSMC calculations, the particle nature of the standard DSMC method makes it difficult to use this information in a statistically significant way. The current study introduces a new technique that makes it possible to resolve all of the vibrational energy levels by using a master equation approach along with temperature-dependent transition rates. The new method is compared to the standard DSMC technique for several heat bath and shock wave conditions and demonstrates the ability to resolve the full vibrational manifold at the expected overall rates of relaxation. The ability of the new master equation approach to the DSMC method for resolving, in particular, the high-energy states addresses a well-known, longstanding deficiency of the standard DSMC method.

Rovibrational Energy Transitions and Coupled Chemical Reaction Modeling of H+H2and He+H2in DSMC

A method of describing the rovibrational energy transitions and coupled chemical reactions in the direct simulation Monte Carlo (DSMC) calculations is constructed for H( 2 S)+H₂(X 1 Σg) and He( 1 S)+H₂(X 1 Σg). First, the state-specific total cross sections for each rovibrational states are proposed to describe the state-resolved elastic collisions. The state-resolved method is constructed to describe the rotational-vibrational-translational (RVT) energy transitions and coupled chemical reactions by these state-specific total cross sections and the rovibrational state-to-state transition cross sections of bound-bound and bound-free transitions. The RVT energy transitions and coupled chemical reactions are calculated by the state-resolved method in various heat bath conditions without relying on a macroscopic properties and phenomenological models of the DSMC. In nonequilibrium heat bath calculations, the state-resolved method are validated with those of the master equation calculations and the existing shock-tube experimental data. In bound-free transitions, the parameters of the existing chemical reaction models of the DSMC are proposed through the calibrations in the thermochemical nonequilibrium conditions. When the bound-free transition component of the state-resolved method is replaced by the existing chemical reaction models, the same agreement can be obtained except total collision energy model.

Relaxation rates in the Maxwellian collision model and its variable hard sphere surrogate

The variable hard sphere and related models have proven to be accurate and computationally convenient replacements for the inverse power law model of classical kinetic theory in direct simulation Monte Carlo calculations. We attempt to provide theoretical support for this remarkable success by comparing the relaxation rates in the linearized Boltzmann equation for the Maxwellian collision model with those of its variable hard sphere surrogate. The comparison demonstrates that the linearized collision operator with variable hard sphere interactions can accurately approximate the linearized collision operator with Maxwellian inverse power law interactions under well-defined and broadly applicable conditions. Extensions of the analysis to the general inverse power law model and to more realistic intermolecular potentials are briefly discussed.

Unified Gas Kinetic Scheme and Direct Simulation Monte Carlo Computations of High-Speed Lid-Driven Microcavity Flows

AbstractAccurate simulations of high-speed rarefied flows present many physical and computational challenges. Toward this end, the present work extends the Unified Gas Kinetic Scheme (UGKS) to a wider range of Mach and Knudsen numbers by implementing WENO (Weighted Essentially Non-Oscillatory) interpolation. Then the UGKS is employed to simulate the canonical problem of lid-driven cavity flow at high speeds. Direct Simulation Monte Carlo (DSMC) computations are also performed when appropriate for comparison. The effect of aspect ratio, Knudsen number and Mach number on cavity flow physics is examined leading to important insight.

Coma dust scattering concepts applied to the Rosetta mission

This paper describes basic concepts, as well as providing a framework, for the interpretation of the light scattered by the dust in a cometary coma as observed by instruments on a spacecraft such as Rosetta. It is shown that the expected optical depths are small enough that single scattering can be applied. Each of the quantities that contribute to the scattered intensity is discussed in detail. Using optical constants of the likely coma dust constituents, olivine, pyroxene and carbon, the scattering properties of the dust are calculated. For the resulting observable scattering intensities several particle size distributions are considered, a simple power law, power laws with a small particle cut off and a log-normal distributions with various parameters. Within the context of a simple outflow model, the standard definition of Afρ for a circular observing aperture is expanded to an equivalent Afρ for an annulus and specific line-of-sight observation. The resulting equivalence between the observed intensity and Afρ is used to predict observable intensities for 67P/Churyumov–Gerasimenko at the spacecraft encounter near 3.3AU and near perihelion at 1.3AU. This is done by normalizing particle production rates of various size distributions to agree with observed ground based Afρ values. Various geometries for the column densities in a cometary coma are considered. The calculations for a simple outflow model are compared with more elaborate Direct Simulation Monte Carlo Calculation (DSMC) models to define the limits of applicability of the simpler analytical approach. Thus our analytical approach can be applied to the majority of the Rosetta coma observations, particularly beyond several nuclear radii where the dust is no longer in a collisional environment, without recourse to computer intensive DSMC calculations for specific cases. In addition to a spherically symmetric 1-dimensional approach we investigate column densities for the 2-dimensional DSMC model on the day and night side of the comet. Our calculations are also applied to estimates of the dust particle densities and flux which are useful for the in-situ experiments on Rosetta.