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Results for “direct simulation Monte Carlo methods”

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NASA NTRS1988

Direct simulation of three-dimensional hypersonic flow about intersecting blunt wedges

The general three-dimensional direct simulation Monte Carlo method is used to study the hypersonic flow around two blunt wedges that intersect at a 90 deg angle. Results are obtained for the transitional flow regimes found at 85 and 100 km altitude with a reentry velocity of 7.5 km/s. The disturbance field in front of the double-wedge body is found to be larger than that produced by a single wedge. Surface pressures and flow densities are higher near the wedge intersection, whereas surface heating and shear streses are greater at locations removed from the corner. Results also show that three-dimensional flow structure occurs only near the wedge corner, and that the flow monotonically approaches the limiting two-dimensional wedge flow case in the spanwise direction.

Celenligil, M. Cevdet↗

DOE OSTI2023

Adjoint DSMC for nonlinear spatially-homogeneous Boltzmann equation with a general collision model

We derive an adjoint method for the Direct Simulation Monte Carlo (DSMC) method for the spatially homogeneous Boltzmann equation with a general collision law. This generalizes our previous results in Caflisch et al., which was restricted to the case of Maxwell molecules, for which the collision rate is constant. The main difficulty in generalizing the previous results is that a rejection sampling step is required in the DSMC algorithm in order to handle the variable collision rate. We find a new term corresponding to the so-called score function in the adjoint equation and a new adjoint Jacobian matrix capturing the dependence of the collision parameter on the velocities. The new formula works for a much more general class of collision models.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2024

First operation and validation of simulations for the divertor cryo-vacuum pump in Wendelstein 7-X

Ten cryo-vacuum pumps (CVPs) were installed in the subdivertor region of each island divertor in the stellarator Wendelstein 7-X (W7-X) and operated for the first time during the recently completed plasma campaign OP2.1. A pumping speed of 70 ± 1 $\frac{m^3}{s}$ was measured during dedicated tests with known hydrogen gas injection. Based on a conductance model, the estimated pumping speed ranges from 86-93 $\frac{m^3}{s}$ for different sticking coefficients between 0.6 and 0.8. After completion of the initial tests the CVPs were operated successfully throughout the campaign, with regeneration performed once a week. Neutral gas pressures in the subdivertor in the range of 10 −4 mbar are well within the molecular flow regime and limit the particle exhaust capabilities of the CVPs. Simulations of the neutral gas pressure in the three-dimensional complex geometry of the subdivertor were performed using the DIVGAS code based on the direct simulation Monte Carlo method and a model implemented in the steady-state thermal package in ANSYS, which are in agreement with the measured values during plasma operation.

Cryo-vacuum pumping↗

DOE OSTI2021

Adjoint DSMC for nonlinear Boltzmann equation constrained optimization

Applications for kinetic equations such as optimal design and inverse problems often involve finding unknown parameters through gradient-based optimization algorithms. Based on the adjoint-state method, we derive two different frameworks for approximating the gradient of an objective functional constrained by the nonlinear Boltzmann equation. While the forward problem can be solved by the DSMC method, it is difficult to efficiently solve the high-dimensional continuous adjoint equation obtained by the “optimize-then-discretize” approach. This challenge motivates us to propose an adjoint DSMC method following the “discretize-then-optimize” approach for Boltzmann-constrained optimization. We also analyze the properties of the two frameworks and their connections. Here, several numerical examples are presented to demonstrate their accuracy and efficiency.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Modeling DC electrical breakdown using a truncated emission spectrum for trapped radiation

Spontaneously emitted radiation from excited atoms can be of principle importance in certain modes of electrical breakdown, especially positive streamers and some regimes of Townsend breakdown. The electrostatic particle-in-cell code Aleph utilizes the direct simulation Monte Carlo method to compute radiation transport. When there is strong radiation trapping, this approach is limited in that it must resolve the timescale associated with self-absorption. This renders many cases computationally intractable as sub-femtosecond time steps can be required to compute solutions for phenomena that occur over nanoseconds or microseconds. For two specific cases which exhibit strong radiation trapping, we find that spontaneous emissions having a frequency near the line center are inactive in the breakdown process and can be neglected. This enables larger time steps and a computational speedup of up to two orders of magnitude is observed. Some considerations for determining the validity of making such an approximation for Townsend breakdown problems and positive ionization wave problems are presented.

Roberds, N. A.↗

DOE OSTI2023

Thermal-fluctuation effects on small-scale statistics in turbulent gas flow

Kolmogorov's theory of turbulence assumes that the small-scale turbulent structures in the energy cascade are universal and are determined by the energy dissipation rate and the kinematic viscosity alone. However, thermal fluctuations, absent from the continuum description, terminate the energy cascade near the Kolmogorov length scale. Here, we propose a simple superposition model to account for the effects of thermal fluctuations on small-scale turbulence statistics. Furthermore, for compressible Taylor–Green vortex flow, we demonstrate that the superposition model in conjunction with data from direct numerical simulation of the Navier–Stokes equations yields spectra and structure functions that agree with the corresponding quantities computed from the direct simulation Monte Carlo method of molecular gas dynamics, verifying the importance of thermal fluctuations in the dissipation range.

42 ENGINEERING↗

DOE OSTI2025

Rarefied xenon flow in orificed hollow cathodes

A parametric study is conducted to quantify the effect of the keeper electrode geometry on the xenon neutral flow quantities within orificed hollow cathodes, prior to ignition. The keeper impinges directly on the flow out of the cathode orifice and its geometry influences the product between the pressure in the orifice–keeper region and the cathode-to-keeper distance. A representative cathode is simulated using the Direct Simulation Monte Carlo method. The numerical model is first validated with computational results from the literature. A parametric study is then conducted. Parameters include the cathode pressure–diameter in the range of 1–5 Torr cm and the following geometric ratios (and ranges): cathode orifice-to-inner radii (0.1–0.7), keeper orifice-to-cathode orifice radii (1–5), and keeper distance-to-cathode-orifice diameter (0.5–10). It is found that, if both keeper and cathode have identical orifice radii, the flow remains subsonic in the orifice-to-keeper region. In most cases, however, the flow becomes underexpanded and supersonic, and the static pressure within the orifice-to-keeper region is, on average, 4% that of the upstream pressure value. The orifice–keeper region pressure increases with either a decrease in the keeper orifice diameter or an increase in the distance between cathode and keeper, in agreement with literature data. Both trends are explained through conservation laws. A statistical study of numerical results reveals that the ratio of ignition-to-nominal mass flow rates has a most probable value of 50, which suggests that heaterless cathode ignition at a minimum DC voltage may be achieved by increasing the input mass flow rate by a factor of 50.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

Hydrodynamic fluctuations near a Hopf bifurcation: Stochastic onset of vortex shedding behind a circular cylinder

Here, we investigate hydrodynamic fluctuations in the flow past a circular cylinder near the critical Reynolds number Re c for the onset of vortex shedding. Starting from the fluctuating Navier-Stokes equations, we perform a perturbation expansion around Re c to derive analytical expressions for the statistics of the fluctuating lift force. Molecular-level simulations using the direct simulation Monte Carlo method support the theoretical predictions of the lift power spectrum and amplitude distribution. Notably, we have been able to collect sufficient statistics at distances Re ⁡/ Re c – 1 = O ⁡(10 –3 ) from the instability that confirm the appearance of non-Gaussian fluctuations, and we observe that they are associated with intermittent vortex shedding. These results emphasize how unavoidable thermal-noise-induced fluctuations become dramatically amplified in the vicinity of oscillatory flow instabilities and that their onset is fundamentally stochastic.

42 ENGINEERING↗

DOE OSTI2021

Effect of slip on vortex shedding from a circular cylinder in a gas flow

Most studies of vortex shedding from a circular cylinder in a gas flow have explicitly or implicitly assumed that the no-slip condition applies on the cylinder surface. To investigate the effect of slip, vortex shedding is simulated using molecular gas dynamics (the direct simulation Monte Carlo method) and computational fluid dynamics (the incompressible Navier-Stokes equations with a slip boundary condition). A Reynolds number of 100, a Mach number of 0.3, and a corresponding Knudsen number of 0.0048 are examined. For these conditions, compressibility effects are small, and periodic laminar vortex shedding is obtained. Slip on the cylinder is varied using combinations of diffuse and specular molecular reflections with accommodation coefficients from zero (maximum slip) to unity (minimum slip). Although unrealistic, bounce-back molecular reflections are also examined because they approximate the no-slip boundary condition (zero slip). The results from both methods are in reasonable agreement. The shedding frequency increases slightly as the accommodation coefficient is decreased, and shedding ceases at low accommodation coefficients (large slip). The streamwise and transverse forces decrease as the accommodation coefficient is decreased. Based on the good agreement between the two methods, computational fluid dynamics is used to determine the critical accommodation coefficient below which vortex shedding ceases for Reynolds numbers of 60–100 at a Mach number of 0.3. Finally, conditions to observe the effect of slip on vortex shedding appear to be experimentally realizable, although challenging.

42 ENGINEERING↗

DOE OSTI2025

Software For Advanced Large-scale Analysis Of Magnetic Confinement For Numerical Design, Engineering & Research (salamander)

As magnetic confinement fusion energy gains traction internationally to enable abundant energy production, designing components for fusion systems is a pressing challenge. During the planned lifetime of a fusion device, components evolve in extreme environments and must withstand large, repeated thermal loads and bombardment by 14 MeV neutrons, plasma ions, and neutral particles (deuterium, tritium, and helium), corrosive conditions, etc. All these physical processes take place simultaneously, interact in intricate ways, and impose important constraints that can affect performance. Experimental data is rare and costly to obtain, making design particularly challenging. Predictive computational frameworks must be an integral part of an accelerated and cost-effective design process by modeling fusion system performance in simulated environments. To better understand component degradation and operational impacts on their performance, the Software for Advanced Large-scale Analysis of MAgnetic confinement for Numerical Design, Engineering & Research (SALAMANDER) is designed as an open-source, fully integrated, multiphysics, multiscale, NQA-1 compliant framework facilitating 3D, high-fidelity fusion system modeling. To that end, SALAMANDER is a MOOSE-based framework, and therefore leverages MOOSE upstream libraries such as PETSc and libMesh to deliver sophisticated finite element, finite volume, and nonlinear solver technology for fusion energy simulations. SALAMANDER couples MOOSE physics module capabilities—such as thermal hydraulics, heat conduction, Navier-Stokes, and thermomechanics—with tritium transport via TMAP8, neutronics via Cardinal, and nascent particle-in-cell capabilities. Direct simulation Monte Carlo methods will be used to address neutral transport near the walls. By coupling all these physics in an integrated application, SALAMANDER will enable high-fidelity modeling of irradiation levels and plasma exposure conditions of plasma facing components and their impact on heat and tritium distributions, as well as the resulting mechanical constraints experienced by the plasma facing components and performance of blanket systems. Furthermore, SALAMANDER will be particularly suited for engineering studies thanks to the stochastic tool module readily available in MOOSE, allowing for extended uncertainty quantification and risk analysis studies. It is also able to use computer-aided design (CAD) meshes to model complex geometries, which is indispensable for fusion systems. SALAMANDER therefore supports design, safety, engineering, and research projects for magnetic confinement fusion systems

Simon, Pierre-Clement [Idaho National Laboratory (↗

NASA NTRS1973

Experimental study of shock-wave reflection from a thermally accommodating wall.

Shock-tube experiments have been conducted to study the nonequilibrium gas-surface interaction which occurs when a thick shock wave in argon reflects from a coplanar, heat-conducting wall. Fast-response instrumentation was used to monitor variations in temperature and normal stress on the surface of the shock-tube end wall during and immediately following reflection of the incident shock wave. The laboratory observations are compared with computer predictions obtained by Deiwert using the direct-simulation Monte Carlo method, and excellent agreement is obtained when a suitable average thermal accommodation coefficient is chosen for the wall surface.

Hanson, R. K.↗

NASA NTRS1974

Reflection of a thick planar shock wave from a coplanar surface

The reflection of a thick shock wave from an adsorbing surface has been studied for argon and neon test gases using the direct simulation Monte Carlo method and laboratory shock-tube experiments. In the simulation, collisions between gas atoms were calculated with a point-center repulsive intermolecular potential, and collisions between gas atoms and the surface were described by a simple two-parameter model which includes the effects of adsorption and thermal accommodation. Experimental data included normal stress and temperature time histories on the surface of a shock-tube and wall. These data and published data of density variations near the end wall were compared with simulation results to assess the influence of adsorption and accommodation on the flowfield and the surface and also to infer optimum values for the surface-interaction model parameters. Good quantitative agreement between simulation and laboratory data was found with this simple surface-interaction model.

Deiwert, G. S.↗

NASA NTRS1975

Analysis of a semiclassical model for rotational transition probabilities

A semiclassical model proposed by Pearson and Hansen (1974) for computing collision-induced transition probabilities in diatomic molecules is tested by the direct-simulation Monte Carlo method. Specifically, this model is described by point centers of repulsion for collision dynamics, and the resulting classical trajectories are used in conjunction with the Schroedinger equation for a rigid-rotator harmonic oscillator to compute the rotational energy transition probabilities necessary to evaluate the rotation-translation exchange phenomena. It is assumed that a single, average energy spacing exists between the initial state and possible final states for a given collision.

Deiwert, G. S.↗

NASA NTRS1976

Monte Carlo calculations of diatomic molecule gas flows including rotational mode excitation

The direct simulation Monte Carlo method was used to solve the Boltzmann equation for flows of an internally excited nonequilibrium gas, namely, of rotationally excited homonuclear diatomic nitrogen. The semi-classical transition probability model of Itikawa was investigated for its ability to simulate flow fields far from equilibrium. The behavior of diatomic nitrogen was examined for several different nonequilibrium initial states that are subjected to uniform mean flow without boundary interactions. A sample of 1000 model molecules was observed as the gas relaxed to a steady state starting from three specified initial states. The initial states considered are: (1) complete equilibrium, (2) nonequilibrium, equipartition (all rotational energy states are assigned the mean energy level obtained at equilibrium with a Boltzmann distribution at the translational temperature), and (3) nonequipartition (the mean rotational energy is different from the equilibrium mean value with respect to the translational energy states). In all cases investigated the present model satisfactorily simulated the principal features of the relaxation effects in nonequilibrium flow of diatomic molecules.

Yoshikawa, K. K.↗

NASA NTRS1978

One-dimensional outgassing problem

A predominantly numerical study, using the direct-simulation Monte Carlo method, of the flow from outgassing surfaces with plane, cylindrical, or spherical geometry is presented. The numerical results for the plane flow case are compared with existing theoretical and experimental results and also with a new formulation of the jump conditions across the Knudsen layer between the surface and the continuum outflow. This outflow is sonic for the free expansion case but subsonic in the presence of back-pressure effects. The self-scattered return flux is 19% of the outgassed flux in the sonic outflow case and increases at lower Mach numbers. Thermal accomodation and reflection of this return flux produces an outgassing cooling effect. The cylindrical and spherical geometries introduce an additional Knudsen number defined by the ratio of the mean free path in the effusing gas to the radius. The plane flow results apply when this Knudsen number is less than 0.001 and, when it is of order unity or above, the return flux is inversely proportional to it.

Tran Cong, T.↗

NASA NTRS1978

Monte Carlo solution of Boltzmann equation for a simple model of highly nonequilibrium diatomic gases - Translational rotational energy relaxation

Theoretical results pertaining to internally excited translational-rotational energy relaxation in a spatially uniform diatomic gas far removed from solid boundaries are obtained by solving the Boltzmann equation by means of the Monte Carlo direct simulation method. The analysis is based on calculations involving three different types of initial conditions: equilibrium, nonequilibrium-equipartition (i.e., equipartition is satisfied, but the distributions are perturbed), and nonequilibrium-nonequipartition (i.e., both equipartition and the distributions are perturbed). Results of monatomic-gas simulations are also included to facilitate comparisons with the coupled translational-rotational relaxation simulations, and some simulations for a normal shock-wave structure are briefly examined. The results show that: (1) single-step transitions are the significant mechanisms of intermodal energy transfer; (2) translational-rotational transitions are coupled most efficiently for low-lying states of rotationally excited molecules and least efficiently for highly rotationally excited molecules; and (3) relaxation occurs via a successive set of distributions that are not Maxwell-Boltzmann (nonlocal Maxwellian).

Yoshikawa, K. K.↗

NASA NTRS1979

Solution of Boltzmann equation for highly nonequilibrium diatomic gases rotational translational energy relaxation

The direct simulation Monte Carlo method is applied to solve the Boltzmann equation for collisions between internally excited diatomic gases in highly nonequilibrium states. The semiclassical transition probability is incorporated in the simulation for energy exchange between rotational and translational energy. The results provide details on the fundamental mechanisms of gas kinetics where analytical methods are impractical. The validity of the local Maxwellian assumption and relaxation time, rotational-translational energy transition, and a velocity analysis of the inelastic collision are discussed in detail.

Yoshikawa, K. K.↗

NASA NTRS1981

Spacecraft outgas ambient flow interaction

An investigation has been made of the extent to which outgassed or emitted molecules return to a spacecraft as a result of intermolecular collisions with ambient freestream molecules. The governing parameters are discussed and heuristic arguments are used to predict the combination of parameters that is most likely to describe the return flux ratio. This is then tested by an extensive set of numerical calculations using the direct simulation Monte Carlo method. Computations have been made for the flow past spheres and past circular cylinders with their axes normal in the stream. The numerical results lead to empirical expressions that can be used for engineering estimates in spacecraft contamination studies.

Bird, G. A.↗