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Journal ArticleDOI: 10.1063/5.0039071

Homogeneous relaxation and shock wave problems: Assessment of the simplified and generalized Bernoulli trial collision schemes

04 Mar 2021-Physics of Fluids (AIP Publishing LLC AIP Publishing)-Vol. 33, Iss: 3, pp 032004
Abstract: The impetus of this paper is to assess the newly suggested direct simulation Monte Carlo (DSMC) collision schemes, that is, the “Simplified Bernoulli Trails (SBT)” and “Generalized Bernoulli Trials (GBT)” schemes in the prediction of the higher-order moments of the velocity distribution function for both confined and non-confined gas flows. Two fundamental rarefied gas dynamics problems are considered: spatially homogeneous relaxation process of a gas flow from a non-Maxwellian condition given by Bobylev–Krook–Wu exact (analytical) solution of the Boltzmann equation and the stationary shock wave problem. To perform the relaxation test, SBT and GBT schemes were implemented in the DSMC0F program. For the shock wave test, changes were made in the DSMC1 code to include the SBT and GBT schemes. A detailed comparison of the SBT and GBT collision schemes in treating the higher-order moments of the velocity distribution function and comparison with theory and the solution of the standard No-Time-Counter (NTC) method and its new variant, nearest neighbor scheme, using the DS1 code, is reported. Some higher moments beyond the usual moments were computed. The results of the fourth moment of the velocity distribution function in the homogeneous relaxation problem show that while both collision schemes produce identical results at an ample time, the initial relaxation process indicates the difference between the schemes. Even though the NTC schemes required a large number of particles per cell to produce the same results as the theory, the SBT scheme successfully simulates the solution using a low number of particles per cell.

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Topics: Relaxation (approximation) (54%), Bernoulli's principle (53%), Bernoulli trial (52%) ... read more

5 results found

Journal ArticleDOI: 10.1016/J.IJTHERMALSCI.2021.107280
Feng Han1, Xiaowei Wang1, Fan Zhao1, Shiwei Zhang1  +1 moreInstitutions (1)
Abstract: Gas separation can be achieved via thermally induced flows inside a microchannel. To obtain the optimum parameters for the best gas-separation efficiency, the direct simulation Monte Carlo (DSMC) method is used to numerically simulate a ratchet-like patterned microchannel with triangular hot plates. The analysis is based on the molar fraction of binary gas mixtures (He–Xe) in a steady state. The influence of temperature, Knudsen number, surface accommodation coefficient, and geometric parameters of the microchannel on its gas separation efficiency are studied using the controlled variable method. Results show that the separated heavier gas species (Xe) is mainly accumulated in wide or narrow microchannel at the last stage of the microchannel. The gas-accumulating position can be controlled by changing the microchannel width, microchannel length, and ratchet angle. The lighter gas moves from the cold to the hot side and concentrates in the hot region, while the heavier gas concentrates in the cold region. The gas separation efficiency improves as the temperature difference increases and the surface accommodation coefficient of the inclined surface decreases. The surface accommodation coefficient directly affects the transition between the thermal edge flow and radiometric flow near the upper tip of the triangle in the microchannel. The gas separation efficiency with a radiometric flow at the upper tip of the triangle is better than that with a thermal edge flow. In addition, the study gives the optimum parameter values for the best gas separation efficiency. These results can be applied to the realization and design of gas separators in various industry fields.

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Topics: Microchannel (66%), Gas separation (58%), Knudsen number (51%) ... read more

1 Citations

Open accessJournal ArticleDOI: 10.1063/5.0051455
Ehsan Roohi1, Yonghao Zhang2Institutions (2)
13 Apr 2021-Physics of Fluids

1 Citations

Open accessJournal ArticleDOI: 10.1063/5.0054289
Ziqu Cao1, Craig White1, Konstantinos Kontis1Institutions (1)
16 Jun 2021-Physics of Fluids
Abstract: When compressed gas is ejected from a nozzle into a low-pressure environment, the shock wave diffracts around the nozzle lip and a vortex loop will form. The phenomenon has been widely investigated in the continuum flow regime, but how the shock diffraction and vortex behave under rarefied flow conditions has not received as much attention. It is necessary to understand this transient flow in rarefied environments to improve thrust vector control and avoid potential contamination and erosion of spacecraft surfaces. This work provides numerical results of the vortex loop formation caused by shock wave diffraction around a 90° corner using the direct simulation Monte Carlo method and the compressible Navier–Stokes equations with the appropriate Maxwell velocity slip and the von Smoluchowski temperature jump boundary conditions. The Mach number and rarefaction effects on the formation and evolution of the vortex loop are discussed. A study of the transient structures of vortex loops has been performed using the rorticity concept. A relationship of mutual transformation between the rorticity and shear vectors has been discovered, demonstrating that the application of this concept is useful to understand vortex flow phenomena.

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Topics: Vortex (65%), Mach number (56%), Shock wave (56%) ... read more

1 Citations

Journal ArticleDOI: 10.1063/5.0050571
25 May 2021-Physics of Fluids
Abstract: Well-known polars in classical shock wave theory, that is, flow deflection angle-shock angle (θ-β), hodograph (u*,v*), and pressure deflection (θ-P*) diagrams, are investigated for the rarefied gas flows using a recently proposed shock wave detection technique by Akhlaghi and coworkers. The agreement between the obtained polars with the analytical relations in classical shock wave theory has been shown in the continuum limit for the cases of supersonic flow over the wedge and cylinder geometries. Investigations are performed using the RGS2D direct simulation Monte Carlo solver for supersonic gas flows over a circular cylinder at continuum limit and Kn = 10−4, 10−3, 0.01, 0.03, 0.07, and 0.10. Two species of nitrogen and argon at various Mach numbers of 1.5, 3.0, and 10.0 are considered. The shock polars are investigated along bow shock waves in front of the cylinder. The results indicate that rarefaction significantly affects the shock polars. As Knudsen number increases, shock angle, maximum flow deflection angle, and aft shock pressure increase. However, velocity components after the shock wave decrease as the flow becomes more rarefied. These effects are stronger for θ-β polar under the weak shock condition. Meanwhile, they are stronger for θ-P* and hodograph polars in strong shock situations.

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Topics: Bow shock (aerodynamics) (68%), Shock wave (65%), Shock (fluid dynamics) (63%) ... read more

Open accessPosted Content
Xianli Su1, Chuandong LinInstitutions (1)
Abstract: How to accurately probe chemical reactive flows with essential thermodynamic nonequilibrium effects is an open issue. Via the Chapman-Enskog analysis, the local nonequilibrium particle velocity distribution function is derived from the gas kinetic theory. It is demonstrated theoretically and numerically that the distribution function depends on the physical quantities and derivatives, and is independent of the chemical reactions directly. Based on the simulation results of the discrete Boltzmann model, the departure between equilibrium and nonequilibrium distribution functions is obtained and analyzed around the detonation wave. Besides, it has been verified for the first time that the kinetic moments calculated by summations of the discrete distribution functions are close to those calculated by integrals of their original forms.

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Topics: Distribution function (63%), Kinetic theory of gases (57%), Boltzmann constant (54%) ... read more

34 results found

Book ChapterDOI: 10.1007/3-540-32386-4_9
Henning Struchtrup1Institutions (1)
01 Jan 2005-

436 Citations

Journal ArticleDOI: 10.1103/PHYSREVLETT.36.1107
Max Krook1, Tai Tsun Wu1Institutions (1)
Abstract: Using two models, we study the relaxation to a Maxwell distribution in the context of classical kinetic theory For the first model, an exact solution of the nonlinear Boltzmann equation is derived For the second model, an asymptotic solution exhibits the remarkable feature of a transient tail population sometimes much larger than the equilibrium Maxwell distribution This phenomenon may be of importance for calculating rates of fast chemical reactions and for controlled thermonuclear fusion

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Topics: Maxwell–Boltzmann distribution (62%), Boltzmann equation (56%), Kinetic theory of gases (55%) ... read more

193 Citations

Journal ArticleDOI: 10.1063/1.3067865
29 Jan 2009-Physics of Fluids
Abstract: The accuracy of a recently proposed direct simulation Monte Carlo (DSMC) algorithm, termed “sophisticated DSMC,” is investigated by comparing simulation results to analytical solutions of the Boltzmann equation for one-dimensional Fourier–Couette flow. An argon-like hard-sphere gas at 273.15 K and 266.644 Pa is confined between two parallel, fully accommodating walls 1 mm apart that have unequal temperatures and unequal tangential velocities. The simulations are performed using a one-dimensional implementation. In harmony with previous work, the accuracy metrics studied are the ratios of the DSMC-calculated transport properties and Sonine polynomial coefficients to their corresponding infinite-approximation Chapman–Enskog theoretical values. The sophisticated DSMC algorithm is shown to reproduce the theoretical results to high precision. The efficiency of the sophisticated DSMC algorithm relative to the original algorithm is demonstrated for a two-dimensional “real-world” application.

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82 Citations

Open accessJournal ArticleDOI: 10.1016/J.JCP.2009.03.021
Abstract: The convergence rate of a new direct simulation Monte Carlo (DSMC) method, termed ''sophisticated DSMC'', is investigated for one-dimensional Fourier flow. An argon-like hard-sphere gas at 273.15K and 266.644Pa is confined between two parallel, fully accommodating walls 1mm apart that have unequal temperatures. The simulations are performed using a one-dimensional implementation of the sophisticated DSMC algorithm. In harmony with previous work, the primary convergence metric studied is the ratio of the DSMC-calculated thermal conductivity to its corresponding infinite-approximation Chapman-Enskog theoretical value. As discretization errors are reduced, the sophisticated DSMC algorithm is shown to approach the theoretical values to high precision. The convergence behavior of sophisticated DSMC is compared to that of original DSMC. The convergence of the new algorithm in a three-dimensional implementation is also characterized. Implementations using transient adaptive sub-cells and virtual sub-cells are compared. The new algorithm is shown to significantly reduce the computational resources required for a DSMC simulation to achieve a particular level of accuracy, thus improving the efficiency of the method by a factor of 2.

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Topics: Rate of convergence (52%)

81 Citations

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