609 research outputs found

    Importance Sampling Variance Reduction for the Fokker-Planck Rarefied Gas Particle Method

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    Models and methods that are able to accurately and efficiently predict the flows of low-speed rarefied gases are in high demand, due to the increasing ability to manufacture devices at micro and nano scales. One such model and method is a Fokker-Planck approximation to the Boltzmann equation, which can be solved numerically by a stochastic particle method. The stochastic nature of this method leads to noisy estimates of the thermodynamic quantities one wishes to sample when the signal is small in comparison to the thermal velocity of the gas. Recently, Gorji et al have proposed a method which is able to greatly reduce the variance of the estimators, by creating a correlated stochastic process which acts as a control variate for the noisy estimates. However, there are potential difficulties involved when the geometry of the problem is complex, as the method requires the density to be solved for independently. Importance sampling is a variance reduction technique that has already been shown to successfully reduce the noise in direct simulation Monte Carlo calculations. In this paper we propose an importance sampling method for the Fokker-Planck stochastic particle scheme. The method requires minimal change to the original algorithm, and dramatically reduces the variance of the estimates. We test the importance sampling scheme on a homogeneous relaxation, planar Couette flow and a lid-driven-cavity flow, and find that our method is able to greatly reduce the noise of estimated quantities. Significantly, we find that as the characteristic speed of the flow decreases, the variance of the noisy estimators becomes independent of the characteristic speed

    Particle kinetic simulation of high altitude hypervelocity flight

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    In this grant period, the focus has been on the effects of thermo-chemical nonequilibrium in low-density gases, and on interactions between such gases and solid surfaces. Such conditions apply to hypersonic flows of re-entry vehicles, and to the expansion plumes of small rockets. Due to the nonequilibrium nature of these flows, a particle approach has been adopted. The method continues to undergo refinement and application to typical flows of interest. A number of studies have been performed for flows in thermo-chemical nonequilibrium. The effects of vibrational nonequilibrium on the rate of dissociation were studied for diatomic nitrogen. It was found that a new model reproduced the nonequilibrium behavior observed experimentally

    Aerothermodynamic Analysis of a Reentry Brazilian Satellite

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    This work deals with a computational investigation on the small ballistic reentry Brazilian vehicle SARA (acronyms for SAt\'elite de Reentrada Atmosf\'erica). Hypersonic flows over the vehicle SARA at zero-degree angle of attack in a chemical equilibrium and thermal non-equilibrium are modeled by the Direct Simulation Monte Carlo (DSMC) method, which has become the main technique for studying complex multidimensional rarefied flows, and that properly accounts for the non-equilibrium aspects of the flows. The emphasis of this paper is to examine the behavior of the primary properties during the high altitude portion of SARA reentry. In this way, velocity, density, pressure and temperature field are investigated for altitudes of 100, 95, 90, 85 and 80 km. In addition, comparisons based on geometry are made between axisymmetric and planar two-dimensional configurations. Some significant differences between these configurations were noted on the flowfield structure in the reentry trajectory. The analysis showed that the flow disturbances have different influence on velocity, density, pressure and temperature along the stagnation streamline ahead of the capsule nose. It was found that the stagnation region is a thermally stressed zone. It was also found that the stagnation region is a zone of strong compression, high wall pressure. Wall pressure distributions are compared with those of available experimental data and good agreement is found along the spherical nose for the altitude range investigated.Comment: The paper will be published in Vol. 42 of the Brazilian Journal of Physic

    DSMC investigation of rarefied gas flow through diverging micro- and nanochannels

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    Direct simulation Monte Carlo (DSMC) method with simplified Bernoulli-trials (SBT) collision scheme has been used to study the rarefied pressure-driven nitrogen flow through diverging microchannels. The fluid behaviours flowing between two plates with different divergence angles ranging between 0^{\circ} to 17^{\circ} are described at different pressure ratios (1.5{\le}{\prod}{\le}2.5) and Knudsen numbers (0.03{\le}Kn{\le}12.7). The primary flow field properties, including pressure, velocity, and temperature, are presented for divergent microchannels and are compared with those of a microchannel with a uniform cross-section. The variations of the flow field properties in divergent microchannels, which are influenced by the area change, the channel pressure ratio and the rarefication are discussed. The results show no flow separation in divergent microchannels for all the range of simulation parameters studied in the present work. It has been found that a divergent channel can carry higher amounts of mass in comparison with an equivalent straight channel geometry. A correlation between the mass flow rate through microchannels, the divergence angle, the pressure ratio, and the Knudsen number has been suggested. The present numerical findings prove the occurrence of Knudsen minimum phenomenon in micro- and Nano- channels with non-uniform cross-sections.Comment: Accepted manuscript; 25 Pages and 11 Figures; "Microfluidics and Nanofluidics

    A Multiscale Particle Approach for Continuum/Rarefied Flow Simulation

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    Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/77289/1/AIAA-2008-1184-250.pd

    Employing per-component time step in DSMC simulations of disparate mass and cross-section gas mixtures

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    A new approach to simulation of stationary flows by Direct Simulation Monte Carlo method is proposed. The idea is to specify an individual time step for each component of a gas mixture. The approach consists of modifications mainly to collision phase and recommendation on choosing time step ratios. It allows softening the demands on the computational resources for cases of disparate collision diameters of molecules and/or disparate molecular masses. These are the cases important in vacuum deposition technologies. Few tests of the new approach are made. Finally, the usage of new approach is demonstrated on a problem of silver nanocluster diffusion in carrier gas argon in conditions of silver deposition experiments.Comment: The goal of submission is to find native English speaker willing to help me polish the paper. This is paper draft sent to Communications in Computational Physics. It is recommended to publication. The need of polishing was one of editors decision. See Additional data for MS Word source fil
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