Direct Simulation Monte Carlo Simulations Research Articles

Highly dilute gas flows over an ellipse

This paper presents recent investigation results on free molecular flows over a diffusely or specularly reflective ellipse, by using the gaskinetic theory. A virtual density distribution along the diffusely reflective surface is introduced to aid the investigations. Many local surface properties are obtained, including the surface slip velocity and coefficients for pressure, friction, and heat flux. Global coefficients for aerodynamic forces and moments and mass center–force center distances are also obtained by integrating the local surface distributions. In the end, analytical expressions for the flowfields around a diffusely or specularly reflective ellipse are also obtained. Special non-dimensional parameters, such as temperature and speed ratios, are explicitly embedded in these expressions. Particle simulations with the direct simulation Monte Carlo (DSMC) method are performed to validate the above results. Those expressions need computers for evaluations; however, the cost is very minor when compared with DSMC simulations. The approaches are heuristic to investigate other external collisionless flows, and the load coefficients can be considered as baseline references at the high Knudsen number limit. By using these collisionless flow results, it is feasible to further study less rarefied gas flows over an ellipse, for example, with an asymptotic method. Swift parameter studies based on these solutions can be performed to study their effect.

Analysis of gas flow over a cylinder at all Knudsen numbers based on non-newtonian constitutive models

This paper is focused on the gas properties over a cylinder from continuum to rarefied regimes based on the non-Newtonian constitutive model. This new constitutive model is first derived from Eu’s nonequilibrium ensemble method, which is intended for accurate description of nonequilibrium flows. Some assumptions and simplifications are made during the establishing progress of the new constitutive model by both Eu and Myong. To verify its accuracy, temperature contours and skin frictions around the cylinder are simulated by this new model. The inflow Mach number is equal to 10 and the Knudsen number ranges from 0.002 to 0.05. All simulation results are compared with Navier–Stokes (NS) and the direct simulation Monte Carlo (DSMC) methods in detail. The comparisons of friction around the surface show that the non-Newtonian constitutive models are better than the linear constitutive relations of NS equations for the prediction of nonequilibrium flow and much more close to DSMC simulation results.

Contribution of viscosity to the circulation deposition in the Richtmyer–Meshkov instability

This study focuses on the process of the circulation deposition in the Richtmyer–Meshkov instability (RMI). The growth rate of circulation and its sources are theoretically and numerically studied to reveal the physical mechanism of the viscosity in the circulation deposition process. We derive a predicting model of the circulation rate for RMI. More importantly, all the contributing sources are separately predicted. Particularly, the viscous source, which previously lacked theoretical or numerical investigations, is efficiently predicted. The RMI problems in a large range of initial conditions are simulated with the direct simulation Monte Carlo (DSMC) method to verify our predicting model and further reveal the circulation deposition mechanism. The DSMC simulations provide reliable quantification of the circulation deposition (especially viscous contribution) for RMI due to its molecular nature. Our model predicts the circulation rate, baroclinic and viscous sources accurately for all the cases in comparison with the simulations. A new physical insight into the mechanism of viscosity in RMI is provided. Unlike the previous understandings that nearly all circulation deposition in RMI comes from the baroclinic source, this study reveals the hidden positive contribution of the viscous source, especially for high Mach number conditions (up to 11 % of total circulation rate). For RMI, the large viscosity gradient inside the shock waves plays a crucial role in the circulation deposition even under high Reynolds number conditions. Our study also provides exciting opportunities to further understand the viscous contribution to the vorticity dynamics in the reshocked RMI and shock wave–turbulence interactions.

Three-dimensional DSMC simulation of thermal Knudsen force in micro gas actuator for mass analysis of gas mixture

High precision detection and measurement of the components of a gas mixture are highly significant in chemical industries. In the textile industry, CO2 is widely used to dye the textile material without water called Supercritical Fluid Dyeing Technology. In this study, a computational technique is applied to investigate the ability of an innovative MEMS gas actuator (MIKRA) for the sensation of the specific component in the gas mixture. This work also investigated various mixtures of gases and various relative concentrations of CO2 to N2. In this actuator, the temperature dissimilarity of two arms at rarefied conditions produces a Knudsen force. Due to the micro size of this sensor, this actuator is highly significant for the inaccessible detection domain. This work tries to reveal the main mechanism for this sensor to increase the precision of the detection. The flow patterns of a mixture gas within this micro gas sensor are examined by Direct Simulation Monte Carlo (DSMC) method since the domain of this micro gas is non-equilibrium. According to the obtained results, a three-dimensional model presents more reliable results and the effect of a gap for the three-dimensional model demonstrates the impact of this parameter on the effective Knudsen force.

Coarse-grain cross sections for rovibrational excitation and dissociation of the [formula omitted] system

We present a method to generate analytical coarse-grain cross sections for internal energy excitation and dissociation of nitrogen and apply it to the NASA Ames N2-Nab initio database. State-resolved cross sections from this database are reduced using the Uniform RoVibrational-Collisional bin model. With a 10-bin system as example we compare two sets of coarse-grain cross sections: one obtained by analytical inversion and another by direct binning. With analytical inversion we manage to compress the entire set of state-resolved data into a small set of parameters, sufficient to reconstruct the main features of the full database. This has the potential of massively reducing the computational cost in large-scale direct simulation Monte Carlo (DSMC) calculations, both concerning memory requirements and execution time. Combining this coarse-grain model with the N2-Nab initio database will enable much higher-fidelity DSMC simulation of nonequilibrium dissociation in shock-heated flows than is currently possible with conventional models.

Interaction of rigid body motion and rarefied gas dynamics based on the BGK model

In this paper we present simulations of moving rigid bodies immersed in a rarefied gas. The rarefied gas is simulated by solving the Bhatnager-Gross-Krook (BGK) model for the Boltzmann equation. The Newton-Euler equations are solved to simulate the rigid body motion. The force and the torque on the rigid body is computed from the surrounded gas. An explicit Euler scheme is used for the time integration of the Newton-Euler equations. The BGK model is solved by the semi-Lagrangian method suggested by Russo &amp; Filbet ^{[<span class="xref"><a href="#b22" ref-type="bibr">22</a></span>]}. Due to the motion of the rigid body, the computational domain for the rarefied gas (and the interface between the rigid body and the gas domain) changes with respect to time. To allow a simpler handling of the interface motion we have used a meshfree method for the interpolation procedure in the semi-Lagrangian scheme. We have considered a one way, as well as a two-way coupling of rigid body and gas flow. We use diffuse reflection boundary conditions on the rigid body and also on the boundary of the computational domain. In one space dimension the numerical results are compared with analytical as well as with Direct Simulation Monte Carlo (DSMC) solutions of the Boltzmann equation. In the two-dimensional case results are compared with DSMC simulations for the Boltzmann equation and with results obtained by other researchers. Several test problems and applications illustrate the versatility of the approach.

Systematic direct simulation Monte Carlo approach to characterize the effects of surface roughness on accommodation coefficients

The effects of surface roughness on accommodation coefficients are studied using the direct simulation Monte-Carlo (DSMC) approach. DSMC simulations are carried out by varying the roughness parameters. An empirical relationship between surface roughness and accommodation coefficients is established.

DSMC simulation of hydrogen dissociation on wire surface in resting gas

In the present work, the specific features of the simulation of hydrogen dissociation on the surface of a heated wire in a resting gas by the direct simulation Monte Carlo (DSMC) method were studied. The influence of the boundary conditions on the processes occurring near the wire, in particular, on the rate of atomic hydrogen production, was studied. The obtained data were compared with the experimental data.

Evaluation of particle-based continuum methods for a coupling with the direct simulation Monte Carlo method based on a nozzle expansion

This paper investigates three different particle-based continuum methods, the ellipsoidal statistical Bhatnagar-Gross-Krook (ESBGK) and Fokker-Planck (ESFP) methods and the Low Diffusion (LD) method, for a coupling with the direct simulation Monte Carlo (DSMC) method. After a short description of the methods and their implementation, including the coupling concept for the LD-DSMC, simulation results of a nozzle expansion are compared with available experimental measurements and a DSMC simulation. Excellent agreement between ESBGK, ESFP, and DSMC can be observed in the throat of the nozzle, while the LD method fails to predict the correct velocity, temperature, and density profile. Further downstream, only the DSMC and the coupled ESBGK/ESFP-DSMC simulations are able to reproduce the measured rotational temperature profiles. A performance comparison shows the possible computational savings of a coupled ESBGK/ESFP-DSMC simulation, where a speedup of four orders of magnitude can be observed compared to a regular DSMC simulation.

Hypersonic flow over Stardust Re-entry Capsule using ab-initio based chemical reaction model

Hypersonic air flow around the Stardust Re-entry Vehicle for diverse ambient conditions is investigated using the Direct Simulation Monte Carlo (DSMC) method. In the present work, the flow field and surface properties on the re-entry vehicle are compared for simulations employing two different chemical reaction models: the traditional phenomenological Total Collision Energy (TCE) model and a new chemical reaction model based on ab-initio principles. The reactive cross-section used in the new chemical reaction model are calculated using Quasi-Classical Trajectory method and employs highly accurate Potential Energy Surfaces. Conditions prevailing at 68 km, 80 km and 100 km are simulated and for two re-entry speeds. It is found that the DSMC simulations with the new ab-initio based chemical reaction model predicts higher heat flux and heat load on the re-entry vehicle surface compared to the simulations employing the TCE model. The difference in the heat flux predicted by the two models is most evident at 80 km. This is a significant inference for engineers designing the Thermal Protection Systems. It is observed that there are significant differences in the estimation of mole fraction of NO by the two models. The limitations of the present model and future scope are discussed in detail.

Direct simulation Monte Carlo applications to liquid-vapor flows

The paper aims at presenting Direct Simulation Monte Carlo (DSMC) extensions and applications to dense fluids. A succinct review of past and current research topics is presented, followed by a more detailed description of DSMC simulations for the numerical solution of the Enskog-Vlasov equation, applied to the study of liquid-vapor flows. Results about simulations of evaporation of a simple liquid in contact with a dense vapor are presented as an example.

Direct simulation Monte Carlo study of metal evaporation with collimator in e-beam physical vapor deposition

The flow properties and substrate deposition rate profile, which are the important parameters in electron beam physical vapor deposition, are investigated computationally in this article. Collimators are used to achieve the desired vapor beam and deposition rate profile in some applications. This increases the difficulty measuring boundary conditions and the size of the liquid metal pool inside the collimators. It is accordingly hard to obtain accurate results from numerical calculations. In this article, two-dimensional direct simulation Monte Carlo (DSMC) codes are executed to quantify the influence of uncertainties of boundary conditions and pool sizes. Then, three-dimensional DSMC simulations are established to simulate cerium and neodymium evaporation with the collimator. Experimental and computational results of substrate deposition rate profile are in excellent agreement at various evaporation rates and substrate heights. The results show that the DSMC method can assist in metal evaporation with a collimator.

Kinetic modeling of unsteady hypersonic flows over a tick geometry

Hypersonic separated flows over the so-called “tick” geometry have been studied using the time-accurate direct simulation Monte Carlo (DSMC) method and global linear theory. The free stream condition for two experimental cases studied in the free-piston shock tunnel (named T-ADFA) was modeled. These two cases span a Knudsen number from transitional to continuum, a Mach number of about 10, a free stream enthalpy from 10 to 3 MJ/kg, a Reynolds number varying by a factor of four, and a leading edge geometry varied from sharp to one with a bevel of 0.2 mm. For the first time, the time dependence of flow macroparameters on the leading edge nose radius and the Reynolds number are studied using global linear theory. High-fidelity DSMC simulations showed that the temporal behavior of the separation region, which has significant effects on the surface parameters, depends closely on the leading edge bluntness and wall temperature. The formation of a secondary vortex was seen in about 2 ms for the sharp leading edge, whereas in the rounded leading edge geometry, it formed at earlier 0.7 ms. At a steady state, the size and structure of the separation zone, vortex structures, and surface parameters predicted by DSMC were found to be in good agreement with computational fluid dynamics for the higher density case. Finally, linear stability theory showed that for some leading edge shapes and flow densities, the time to reach the steady state was longer than the facility measurement time.

Direct simulation Monte Carlo simulation of thermal fluctuations in gases

Work done by the authors on the Direct Simulation Monte Carlo (DSMC) simulation of thermal fluctuation in gases is summarized here. The calculation of the gas transport properties via the Green-Kubo formulas is discussed. Results from classical trajectory DSMC simulations of molecular oxygen show how the approach can be used to validate a particular interaction model (a Potential Energy Surface in this case). Direct experimental validation of the dynamics of spontaneous density fluctuations is also possible due to its connection to the spectrum measured in Rayleigh-Brillouin light scattering experiments (RBS). A number of examples of the DSMC simulation of RBS spectra for atomic gases and their mixtures, and for a molecular gas (oxygen) are discussed. Finally, an extension of the method is discussed that allows discussion of small density-dependent nonideality effects in the RBS spectra of SF6.

Characterizing deviation from equilibrium in direct simulation Monte Carlo simulations

A fundamental and yet computationally feasible parameter based on the characteristic function of the velocity distribution function (VDF) is proposed for determining the deviation from near-equilibrium conditions in rarefied flow simulations using the direct simulation Monte Carlo (DSMC) method. The proposed parameter utilizes the one-to-one correspondence between the VDF and its characteristic function (or Fourier transform), thereby correlating the deviation of the VDF (from a Chapman-Enskog VDF) with the deviation of the characteristic function (also from that of a Chapman-Enskog VDF). The results are first presented for an unsteady Bobylev solution for approach to equilibrium in 0-D, free-molecular Fourier-Couette flow problem and the Mott-Smith solution for the shock wave all of which have analytical solutions for the VDF, thereby confirming that the proposed parameter indeed captures the deviation from near-equilibrium conditions accurately. The utility of the proposed parameter is then demonstrated using two benchmark problems—Couette flow (over a range of Knudsen numbers) and structure of a normal shock (for upstream Mach numbers of 1.5, 3, and 5)—solved using the DSMC method. While the current work only presents results for benchmark one-dimensional DSMC simulations, the approach can be extended easily to rarefied flows in higher dimensions. Therefore, the proposed parameter has the potential to be used for understanding the nature of VDF and its deviation from near-equilibrium conditions at all locations in a flow field without the need for explicitly sampling the VDF.

Multi-scale thermal response modeling of an AVCOAT-like thermal protection material

A multi-scale modeling approach based on the stochastic Direct Simulation Monte Carlo (DSMC) and walker methods is developed to understand the complex flows and thermophysical phenomena through a syntactic foam TPS, similar to AVCOAT. Using novel, unstructured adaptive mesh refinement/Octree grids and newly developed subsonic boundary conditions, the counter-flow transport of boundary layer and pyrolysis gases through the porous microstructure is modeled for the first time. Permeability of the microstructure models having porosities of 0.71 and 0.86 is computed in the DSMC simulations and compared to a fibrous TPS material. The rigorous development of a stochastic based thermal response model that can couple convective, conductive, and radiative heat transfer through a porous material having non-uniform thermophysical properties and high temperature gradients is presented and compared with a one-dimensional finite-volume approach. The material thermal response is found to be dominated by conduction, yet, the interactions between boundary layer and pyrolysis species on the actual 3-D geometry, which cannot be considered in traditional material response solvers, may in fact cause them to underpredict the TPS material temperature.

Radiometric flow in periodically patterned channels: fluid physics and improved configurations

With the aid of direct simulation Monte Carlo (DSMC), we conduct a detailed investigation pertaining to the fluid and thermal characteristics of rarefied gas flow with regard to various arrangements for radiometric pumps featuring vane and ratchet structures. For the same, we consider three categories of radiometric pumps consisting of channels with their bottom or top surfaces periodically patterned with different structures. The structures in the design of the first category are assumed to be on the bottom wall and consist of either a simple vane, a right-angled triangular fin or an isosceles triangular fin. The arrangements on the second category of radiometric pumps consist of an alternating diffuse–specular right-angled fin and an alternating diffuse–specular isosceles fin on the bottom wall. The third category contains either a channel with double isosceles triangular fins on its lowermost surface or a zigzag channel with double isosceles triangular fins on both walls. In the first and the third categories, the surfaces of the channel and its structures are considered as diffuse reflectors. The temperature is kept steady on the horizontal walls of the channel; thus, radiometric flow is created by subjecting the adjacent sides of the vane/ratchet to constant but unequal temperatures. On the other hand, for the second category, radiometric flow is introduced by specifying different top/bottom channel wall temperatures. The DSMC simulations are performed at a Knudsen number based on the vane/ratchet height of approximately one. The dominant mechanism in the radiometric force production is clarified for the examined configurations. Our results demonstrate that, at the investigated Knudsen number, the zigzag channel experiences maximum induced velocity with a parabolic velocity profile, whereas its net radiometric force vanishes. In the case of all other configurations, the flow pattern resembles a Couette flow in the open section of the channel situated above the vane/ratchet. To further enhance the simulations, the predictions of the finite volume discretization of the Boltzmann Bhatnagar–Gross–Krook (BGK)–Shakhov equation for the mass flux dependence on temperature difference and Knudsen number are also reported for typical test cases.

Gas rarefaction in high power impulse magnetron sputtering: comparison of a particle simulation and volume-averaged models

We calculate the rarefaction of Ar background gas in front of a magnetron caused by sputtered target material atoms (so called ‘sputtering wind effect’) during pulsed sputtering. For a detailed analysis, we use a three-dimensional particle simulation using the direct simulation Monte Carlo (DSMC) method. We compare the results with those of two volume-averaged (V-A) models describing the same problem but with significantly lower computational demands. The comparison is made for three values of flux of sputtered atoms (expressed as ‘sputtering current’ in the units of amperes) and for three target materials (Zr, Al and C) sputtered from a circular target of diameter placed in a chamber with realistic geometry. Ar rarefaction is more pronounced for target atoms with higher mass, but the difference between the three target materials is surprisingly small. The region where Ar is significantly rarefied extends much further from the target than a typical extent of the high-density plasma confined by the magnetic field. The V-A models provide good approximation of the time evolution of the target material density in front of the target compared to the DSMC simulation. However, the presented V-A models underestimate (in all but one case) the magnitude of Ar rarefaction during the pulse-on time and also predict faster return to equilibrium during the pulse-off time comared to the DSMC simulation.

Parametric study of water vapor and water ice particle plumes based on DSMC calculations: Application to the Enceladus geysers

The field parameters – number density, velocity components and temperature – for the Enceladus geysers, and possibly similar jets from other bodies, such as Europa, Ceres or comets, are expensive to obtain using physically correct simulation methods, such as the Direct Simulation Monte Carlo (DSMC) approach. It would be very useful to be able to correctly reproduce all the different states that the flow is undergoing while expanding into vacuum, from a high density and collisional state near the surface to free-molecular and collisionless at high altitude without resorting to expensive DSMC simulations in every case. In this work, we consider a two-phase water vapor/grain mixture exiting a circular vent, assuming a uniform radius of the water ice grains, and study how the field parameters can be fitted at an altitude of 10 km, where the flow is collisionless. To do so, we define simple functional forms for each of these fitted parameters, and we study how their coefficients vary as a function of the vent exit parameters, i.e. the vent radius, the water mixture mass flow, the water vapor/water ice mass ratio, the water ice grain radius, the water vapor and water ice exit speed, the vent exit angle and flow temperature. We define polynomial approximations to model these variations. We show that all the vent parameters have nearly-independent influences on the radial profiles at 10 km, except for the water vapor and water ice exit speed, for which we considered cross-correlations. We finally show that the geyser field parameters can be reconstructed using our parametric study for variations of the vent parameters within the range considered here, and in a time frame of a few milliseconds. The results of the parametrizations presented in this study can now be used to propagate the geyser field parameters using computationally inexpensive free molecular/ballistic codes up to higher altitudes. The DSMC results that have been run for this paper are available at an online repository.

Nonequilibrium flow through porous thermal protection materials, Part II: Oxidation and pyrolysis

Micro scale simulations are performed of flow through porous (pyrolyzing) thermal protection system (TPS) materials using the direct simulation Monte Carlo (DSMC) method. DSMC results for permeability are validated with computational fluid dynamics (CFD) calculations and theory, for simple porous geometries under continuum flow conditions. An artificial fiber-microstructure generation code FiberGen is used to create triangulated surface geometry representative of FiberForm® (FiberForm) material. DSMC results for permeability of FiberForm are validated for a range of pressures (transitional flow conditions) and agree with experimental measurements. Numerical uncertainty is determined to be within 2% if sufficiently large portions of the microstructure are included in the computation. However, small variations in fiber size and angle bias can combine to give +30% uncertainty when comparing with experimental permeability data. X-ray microtomography scans of FiberForm are used to create microstructure geometry for incorporation within DSMC simulations of coupled oxygen diffusion and gas-surface chemistry in the presence of a blowing pyrolysis gas. In-depth penetration of atomic oxygen is limited to 0.2–0.4 mm for the range of Knudsen number and pyrolysis gas conditions studied.