Direct Simulation Monte Carlo Research Articles

Uncertainty assessment for the extreme hydrodynamic responses of a wind turbine semi-submersible platform using different environmental contour approaches

This paper aims to assess the uncertainty on the extreme responses of a semi-submersible wind turbine using two environmental contour approaches. The approaches are based on the inverse First Order Reliability Method and the direct Monte Carlo Simulation with different sample sizes. The long-term sea states are described by a 3-parameters Weibull distribution for the significant wave height and a conditional log-normal distribution for the zero-up crossing period. Two extreme sea states are extracted from each environmental contour, which are associated with the maximum significant wave height and maximum zero-upcrossing period. A 3-h time domain simulation for each sea state is conducted by adopting a validated numerical model. The root mean square for all the response spectra are estimated and compared to each other. It is observed that despite the small deviation between the significant wave heights resulting from adopting different environmental contour approaches, the deviation between the resulting responses is much more significant. The Gumbel and the generalized extreme value distributions are fitted to the maximum extreme response values for each sea state and unified fitted parameter are obtained.

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.

Direct Simulation Monte Carlo investigation of fluid characteristics and gas transport in porous microchannels

The impetus of the current research is to use the direct simulation Monte Carlo (DSMC) algorithm to investigate fluid behaviour and gas transport in porous microchannels. Here, we demonstrate DSMC’s capability to simulate porous media up to 40% porosity. In this study, the porous geometry is generated by a random distribution of circular obstacles through the microchannel with no interpenetration between the obstacles. The influence of the morphology along with rarefaction and gas type on the apparent permeability is investigated. Moreover, the effects of porosity, solid particle’s diameter and specific surface area are considered. Our results demonstrate that although decreasing porosity intensifies tortuosity in the flow field, the tortuosity reduces at higher Knudsen numbers due to slip flow at solid boundaries. In addition, our study on two different gas species showed that the gas type affects slippage and apparent gas permeability. Finally, comparing different apparent permeability models showed that Beskok and Karniadakis model is valid only up to the early transition regime and at higher Knudsen numbers, the current data matches those models that take Knudsen diffusion into account as well.

Development of MEMS gas actuator for analyzing a gas mixture

In this study, a computational technique is used to investigate the ability of a new MEMS gas actuator (MIKRA) for detection and sensation of the gas mixture. In this actuator, the temperature difference of two arms inside a rectangular domain at rarefied condition induces a Knudsen force which is relative to physical properties of the gas. Both 2d and 3D approaches are applied for the simulation of the flow inside the model. In order to define the flow feature of a low-pressure gas inside the micro gas actuator, a high order equation of Boltzmann should be solved to attain reliable results. Since the domain of this micro gas is non-equilibrium, Direct Simulation Monte Carlo (DSMC) method is applied for the simulation of the model. According to obtained results, a three-dimensional model presents more reliable results and the effect of a gap for three-dimensional model clearly demonstrates the impact of this parameter on the effective Knudsen force

Reliability based design method for buckling of steel columns in fire

Purpose This paper aims to reliability analysis of axially loaded steel columns at elevated temperatures considering the probabilistic features of fire. Design/methodology/approach The response function used in the reliability analysis is based on the non-linear FEM calculations. The stochastic variability of temperature is integrated with the procedure similar to the parameters of loading and material properties. Direct Monte Carlo simulations (MCSs) are implemented for probabilistic analysis. Computational costs are reduced by polynomial approximation of the response function of the column. Findings A design method for practical applications in the common Eurocode format is proposed. The proposed method can be used to estimate the failure probability of a steel column in fire conditions. If standard reliability criteria are applied, the results of the steel column buckling capacity in the fire according to the proposed procedure deviate from the Eurocode results in certain parameter ranges. Originality/value The proposed method for design calculations makes use of the advantages of MCS results, while the need for the tedious amount of calculations for the end user are avoided as the predefined factors are implemented in the procedure of Eurocode format. The proposed method allows better differentiation of the fire probability in the capacity assessment compared to the existing design methods.

New slip boundary condition in high-speed rarefied gas flow simulations

In this paper, we propose a new slip boundary condition in hypersonic gas flow simulations. It is derived by considering the Langmuir isotherm adsorption into the Kaniadarkis et al. model of the kinetic theory of gas. Moreover, the motion of the adsorbed molecules over the surface (i.e. surface diffusion) is considered for the calculation of the mean free path in new slip condition. Three aerodynamic configurations are selected for evaluating new slip condition such as (1) the sharp-leading-edge flat plate, (2) circular cylinder in cross-flow, and (3) the sharp 25°–55° biconic cases. Hypersonic gas flows have the Mach number ranging from 6.1 to 15.6, and the working gases are argon and nitrogen. The simulation results show that new slip condition predicts better slip velocity than the Maxwell slip condition and gives good agreement with the direct simulation Monte-Carlo data for all cases considered in the present work.

Probabilistic analysis of a simple composite blast protection wall system

Terrorism has become a major challenge for the world. Terrorist organizations have raised their activities and their attacks in the last years using explosives. These attacks have left numerous numbers of victims, wreaked massive havoc to basic infrastructure, and increased global concern about the nature of these attacks. Blast wall protection systems can provide a required safety level to reduce injuries/casualties in different attack scenarios. Furthermore, installation and procurement costs could be greatly reduced using readily available materials. This paper investigates the performance of a composite wood-sand-wood blast wall by estimating the probability of exceeding a performance limit state for the wall for a suicide vest threat scenario. Fragility curves were devised using direct Monte Carlo simulations to predict the probability of failure of an equivalent simplified single degree-of-freedom system. The simplified model, calibrated to a 3D finite element analysis of the prototype wall, was used to determine the horizontal displacement at the back center of the wall. The analysis framework was developed to probabilistically evaluate the performance of the proposed blast wall in the presence of uncertainties in structural properties and blast load parameters under increasing intensity of the blast. Uncertainties in the random variables were modeled using appropriate statistical distributions. The analyses results show that under certain conditions the wall can provide the required level of protection for the considered threat scenarios.

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.

Comparison of modern implementations of the direct simulation Monte Carlo method

In this work, collisional schemes of the direct simulation Monte Carlo (DSMC) method are compared. The sensitivity of the schemes to the number of simulated particles is investigated. The original No-Time-Counter (NTC) scheme, proposed by G.A. Bird, its modification NTC-2007 and majorant collision frequency (MCF) scheme, proposed by M. S. Ivanov and S.V. Rogasinsky are considered. For the high-speed Couette flow with parameters corresponding to a near-continuum regime (speed ratio S is equal to 10, Knudsen number Kn is equal to 0.01) the convergence of shear stress component is analysed. Calculations with different total number of the simulated particles (in the range from 500 to 106) were performed. It was shown, that the deviation of NTC-2007 scheme from the reference solution is about four times larger as compared to the MCF scheme. The original NTC scheme exhibits much higher sensitivity to the number of simulated particles.

Direct Monte Carlo simulation of development of the Richtmyer-Meshkov instability on the Ar/He interface

The Richtmyer-Meshkov instability developing on the interface between helium and argon gases hit by a propagating shock wave is simulated numerically. In contrast with conventional approach based on the Navier-Stokes equations, the simulation in the current paper is performed on the molecular level using the Direct Simulation Monte Carlo method. The data averaging over short time periods is employed to decrease statistical scattering. The instability development is successfully reproduced with relatively moderate computer resources used. The time evolution of the transmitted shock wave and contact surface velocities are retrieved from numerical data as well as the instability growth rates.

Adaptive Monte Carlo simulation method for system reliability analysis of slope stability based on limit equilibrium methods

A slope fails if it slides along any slip surface. Proper assessment of slope failure risk in geological and geotechnical engineering needs to account, rationally, for a large, or even unlimited, number of circular and/or non-circular potential slip surfaces, which can be modeled as components of a series system. Nevertheless, the computational efforts for incorporating a large number of potential slip surfaces into slope system reliability analysis might be prohibitively expensive, particularly if non-circular slip surfaces are considered. This paper develops an efficient direct Monte Carlo simulation (MCS) method, called adaptive MCS, for slope system reliability analysis based on limit equilibrium methods (LEM), in which a novel sample manipulation strategy is proposed in lieu of brute-force exploration of failure samples amongst direct MCS samples. Equations are derived for the proposed approach and are illustrated using two slope examples considering circular and non-circular potential slip surfaces, respectively. Results show that the proposed approach provides proper estimates of slope system failure probability considering a large number of circular and/or non-circular potential slip surfaces. It significantly improves the computational efficiency of LEM-based slope system reliability analysis compared with brute-force exploration of failure samples.

Grid criteria for numerical simulation of hypersonic aerothermodynamics in transition regime

Grid is an important factor in numerical simulation of hypersonic aerothermodynamics. This paper introduces three criteria for determining grid size in the transition flow regime when using the computational fluid dynamics (CFD) method or the direct simulation Monte Carlo (DSMC) method. The numerical relationship between these three criteria sizes is deduced according to the one-dimensional fluid theory. Then, the relationship is verified using the CFD method to simulate the flow around a two-dimensional cylinder. At the same time, the dependence of simulation accuracy on grid size in the CFD and DSMC methods is studied and the mechanism is given. The result shows that the simulation accuracy of heat flux especially depends on the normal grid size next to surfaces, where the$Re_{\mathit{cell},w}$criterion and the$\unicode[STIX]{x1D706}_{w}$criterion based on local parameters are applicable and equivalent, while the$Re_{\mathit{cell},\infty }$criterion based on the free-stream parameter is only applicable under the assumption of constant viscosity coefficient and constant temperature wall conditions. On the other hand, the trend of the heat flux changing with grid size obtained by CFD and DSMC is exactly the opposite. Therefore, the grid size must be strictly satisfied with the grid criteria when comparing CFD with DSMC and even the hybrid DSMC with Navier–Stokes method.

DSMC – Simulation of the influence of hydrogen addition on the properties of silicon deposited by HWCVD

The gas phase chemistry in a hot-wire chemical vapor deposition (HWCVD) process, which utilizes an array of heated tungsten wires is analyzed via Direct Simulation Monte Carlo simulation. Process gases are silane (SiH4) and hydrogen (H2). SixHy radical partial pressures are simulated as a function of H2 gas flow for given gas inlet compositions in order to optimize radical partial pressures, leading to higher quality and more ordered Si:H films. The simulation results are compared with a series of deposition runs using an array of 10 heated tungsten wires (600 mm long, 0.53 mm diameter, held at 2100 °C) providing a deposition area of 500 x 600 mm2. H2 gas flows are varied to maximize the crystallinity of Si:H films as measured through Raman spectroscopy. The experimental sets are further compared to the simulation results by means of in-situ mass spectrometry, film thickness measurement, and process pressure measurement.

Mechanisms, Upscaling, and Prediction of Anomalous Dispersion in Heterogeneous Porous Media

AbstractWe study the upscaling and prediction of large‐scale solute dispersion in heterogeneous porous media with focus on preasymptotic or anomalous features such as tailing in breakthrough curves and spatial concentration profiles as well as nonlinear evolution of the spatial variance of the concentration distribution. Spatial heterogeneity in the hydraulic medium properties is represented in a stochastic modeling approach. Direct numerical Monte Carlo simulations of flow and advective particle motion combined with a Markov model for streamwise particle velocities give insight in the mechanisms of preasymptotic and asymptotic solute transport in terms of the statistical signatures of the medium and flow heterogeneity. Based on the representation of equidistantly sampled particle velocities as a Markov process, we derive an upscaled continuous time random walk approach that can be conditioned on the flow velocities and thus hydraulic conductivity in the injection region. In this modeling framework, we identify the Eulerian velocity distribution, advective tortuosity, and the correlation length of particle velocities as the key quantities for large‐scale transport prediction. Thus, the upscaled model predicts the spatial concentration profiles, their first and second centered moments, and the breakthrough curves obtained from direct numerical Monte Carlo simulations in spatially heterogeneous conductivity fields. The presented approach allows to relate the medium and flow properties to large‐scale preasymptotic and asymptotic solute dispersion.

MRT-LBM modelling of the oscillatory gas slide film damping in the transition regime

In this paper, the slide film damping (SFD) of micro-scale oscillatory Couette flow has been researched by an effective multiple relaxation time lattice Boltzmann method (MRT-LBM). The validity and effectiveness of MRT-LBM for solving SFD have been verified through contrasting the velocity distribution between the upper plate and the substrate of MRT-LBM and the direct simulation Monte Carlo (DSMC) model. The impacts of the vibration frequency and gap of plates on the damping are discussed, and the result shows that the nonlinear character of velocity profiles is manifest and SFD increases substantially for a larger vibration frequency in the oscillatory gas flow; SFD reduces obviously with the gap increases. Consequently, the results further confirm the implementation of LBM in analysis of the non-equilibrium micro-scale gas flow.

Time-Dependent Reliability Analysis of Deep Tunnel in the Viscoelastic Burger Rock with Sequential Installation of Liners

The behavior of deep tunnel is usually time dependent due to the sequential construction process as well as the rheological characteristic of the rock mass. Moreover, the uncertainty of different parameters such as the viscoelastic properties can play an essential role on the stability of tunnel and its supports. The reliability analysis based on the probabilistic approach, which has been largely applied in the last 2 decades to treat this kind of problems, presents an efficient tool but its application is usually limited in case of time-independent behavior of tunnel supported by a single liner. This study aims at assessment of time-dependent reliability of deep circular tunnel counting for rheological characteristic of rock mass and sequential construction of liners. Since the reliability analysis, using direct Monte Carlo Simulation and a FEM software could be very time-consuming, we establish firstly a closed form solution for the response of a deep tunnel excavated in the viscoelastic Burger rock accounting for the sequential installation of two liners. The validation of this analytical solution is performed by comparing the results of this solution with some previous existing analytical solutions as well as with numerical results obtained from the finite element simulation in some case studies. Once validated, this analytical solution is used as a fast tool for the time-dependent reliability analysis by direct Monte Carlo Simulation. The influence of different parameters on the probability of failure of a double liners tunnel in respect with its life service, by taking into account of the sequential construction, was discussed in the last part of the paper.

Ab initio calculation of rarefied flows of helium-neon mixture: Classical vs quantum scatterings

In order to faithfully simulate rarefied gas flows of light-weight molecules at cryogenic temperatures down to several kelvins, the Boltzmann equation with the differential cross section calculated from the realistic intermolecular potential should be applied. In the present work, the direct simulation Monte Carlo (DSMC) method with ab initio intermolecular potentials is first implemented into the open-source software dsmcFoam+ for the simulation of general rarefied gas flows. Then, Fourier and Couette flows of the helium-neon mixture are studied for the temperature ranging from 10 K to 2000 K, where the differential cross sections calculated from both classical and quantum mechanics have been used. Our simulation results show that the quantum scattering effects on the heat flux and shear stress are non-negligible when the equilibrium temperature is lower than 500 K. Also, for the Fourier flow, the mole fraction distributions calculated from the quantum scattering are significantly different from those of classical scattering.

Percentage porosity computation of three-dimensional non-convex porous geometries using the direct Monte Carlo simulation

The pursuit of more representative numerical models for open-cell metallic foams requires the computation of volume and percentage porosity of geometries containing randomly distributed interconnected pores, which is one of the main characteristics that determines its mechanical properties. From a mathematical standpoint, the analytical definition of foam geometries forms a three-dimensional non-convex set. It is known that the volume computation of n-dimensional polytopes and sets is a P-hard problem. A common way to approach this problem is using the Monte Carlo techniques; however, efforts are oriented toward the treatment of convex polytopes and polyhedrons. In this article, the Direct Monte Carlo Simulation (DMCS) is used to compute the percentage porosity of three-dimensional non-convex sets. A single-thread Python code was implemented, and tests were run to estimate the percentage porosity of three-dimensional open-cell porous geometries. Measurements of percentage porosity and runtime requirements over cubical and cylindrical geometries containing from 100 to 4000 overlapping spherical pores showed high accuracy and consistency in non-convex three-dimensional sets, while the proposed algorithm achieved a significant reduction in computing time with respect to the currently available method. In the same manner, results from the proposed algorithm were compared with a similar software available, showing a gain in both performance time and accuracy.

Porosity gradients as a means of driving lateral flows at cometary surfaces

The Rosetta spacecraft has provided invaluable and unexpected information about cometary outgassing. The on-board instruments ROSINA, MIRO, and VIRTIS showed non-uniform outgassing of H2O over the surface of the nucleus. Rarefied gas flows display remarkable flow phenomena that may help explain diverse physical observations and models have been used in various engineering applications. Typical examples are flows generated by temperature variations such as thermal creeping flows that may have applications in cometary research. In this paper, we demonstrate how porosity variations in a porous medium combined with rarefaction can also lead to high tangential speed flow at a surface. Outgassing through a porous surface layer has been postulated as one possible mechanism at the cometary surfaces. We use the Direct Simulation Monte Carlo (DSMC) method to investigate such flows. The porous media structure consists of micro computed tomography (micro-CT) image of real Earth rock samples with high resolution. We show that lateral gas density gradients can be produced in a straightforward manner leading to substantial non-radial flow.

A unified stochastic particle Bhatnagar-Gross-Krook method for multiscale gas flows

The stochastic particle method based on Bhatnagar-Gross-Krook (BGK) or ellipsoidal statistical BGK (ESBGK) model approximates the pairwise collisions in the Boltzmann equation using a relaxation process. Therefore, it is more efficient to simulate gas flows at small Knudsen numbers than the counterparts based on the original Boltzmann equation, such as the Direct Simulation Monte Carlo (DSMC) method. However, the traditional stochastic particle BGK method decouples the molecular motions and collisions in analogy to the DSMC method, and hence its transport properties deviate from physical values as the time step size increases. This defect significantly affects its computational accuracy and efficiency for the simulation of multiscale flows, especially when the transport processes in the continuum regime is important. In the present paper, we propose a unified stochastic particle ESBGK (USP-ESBGK) method by combining the molecular convection and collision effects. In the continuum regime, the proposed method can be applied using large temporal-spatial discretization and approaches to the Navier-Stokes solutions with second-order accuracy. Furthermore, it is capable to simulate both the small scale non-equilibrium flows and large scale continuum flows within a unified framework efficiently and accurately. The applications of USP-ESBGK method to a variety of benchmark problems, including Couette flow, thermal Couette flow, Poiseuille flow, Sod tube flow, cavity flow, Taylor-Green vortex, and flow through a slit, demonstrated that it is a promising tool to simulate multiscale gas flows ranging from rarefied to continuum regime.