scholarly journals Evaporation Boundary Conditions for the Linear R13 Equations Based on the Onsager Theory

Entropy ◽  
2018 ◽  
Vol 20 (9) ◽  
pp. 680 ◽  
Author(s):  
Alexander Beckmann ◽  
Anirudh Rana ◽  
Manuel Torrilhon ◽  
Henning Struchtrup
Keyword(s):  
Kinetic Theory ◽  
Boundary Conditions ◽  
Rarefied Gas ◽  
Continuum Hypothesis ◽  
Direct Simulation Monte Carlo ◽  
Transport Equations ◽  
Particle Methods ◽  
Navier Stokes ◽  
Knudsen Numbers ◽  
Constant Coefficients

Due to the failure of the continuum hypothesis for higher Knudsen numbers, rarefied gases and microflows of gases are particularly difficult to model. Macroscopic transport equations compete with particle methods, such as the Direct Simulation Monte Carlo method (DSMC), to find accurate solutions in the rarefied gas regime. Due to growing interest in micro flow applications, such as micro fuel cells, it is important to model and understand evaporation in this flow regime. Here, evaporation boundary conditions for the R13 equations, which are macroscopic transport equations with applicability in the rarefied gas regime, are derived. The new equations utilize Onsager relations, linear relations between thermodynamic fluxes and forces, with constant coefficients, that need to be determined. For this, the boundary conditions are fitted to DSMC data and compared to other R13 boundary conditions from kinetic theory and Navier–Stokes–Fourier (NSF) solutions for two one-dimensional steady-state problems. Overall, the suggested fittings of the new phenomenological boundary conditions show better agreement with DSMC than the alternative kinetic theory evaporation boundary conditions for R13. Furthermore, the new evaporation boundary conditions for R13 are implemented in a code for the numerical solution of complex, two-dimensional geometries and compared to NSF solutions. Different flow patterns between R13 and NSF for higher Knudsen numbers are observed.

scholarly journals Evaporation Boundary Conditions for the Linear R13 Equations Based on the Onsager Theory

2018 ◽  
Author(s):  
Alexander Felix Beckmann ◽  
Anirudh Singh Rana ◽  
Manuel Torrilhon ◽  
Henning Struchtrup
Keyword(s):  
Kinetic Theory ◽  
Boundary Conditions ◽  
Rarefied Gas ◽  
Continuum Hypothesis ◽  
Transport Equations ◽  
Particle Methods ◽  
Navier Stokes ◽  
Knudsen Numbers ◽  
Constant Coefficients ◽  
Onsager Theory

Due to failure of the continuum hypothesis for higher Knudsen numbers, rarefied gases and microflows of gases are particularly difficult to model. Macroscopic transport equations compete with particle methods, such as DSMC to find accurate solutions in the rarefied gas regime. Due to growing interest in micro flow applications, such as micro fuel cells, it is important to model and understand evaporation in this flow regime. Here, evaporation boundary conditions for the R13 equations, which are macroscopic transport equations with applicability in the rarefied gas regime, are derived. The new equations utilize Onsager relations, linear relations between thermodynamic fluxes and forces, with constant coefficients, that need to be determined. For this, the boundary conditions are fitted to DSMC data and compared to other R13 boundary conditions from kinetic theory and Navier-Stokes-Fourier (NSF) solutions for two one-dimensional steady-state problems. Overall, the suggested fittings of the new phenomenological boundary conditions show better agreement to DSMC than the alternative kinetic theory evaporation boundary conditions for R13. Furthermore, the new evaporation boundary conditions for R13 are implemented in a code for the numerical solution of complex, two-dimensional geometries and compared to NSF solutions. Different flow patterns between R13 and NSF for higher Knudsen numbers are observed.

Numerical Methods for the Kinetic Theory of Fluids

2018 ◽  
Author(s):  
Sauro Succi
Keyword(s):  
Molecular Dynamics ◽  
Monte Carlo ◽  
Numerical Methods ◽  
Kinetic Theory ◽  
Computational Efficiency ◽  
Lattice Boltzmann ◽  
Direct Simulation Monte Carlo ◽  
Particle Methods ◽  
Direct Simulation ◽  
Simulation Monte Carlo

This chapter provides a bird’s eye view of the main numerical particle methods used in the kinetic theory of fluids, the main purpose being of locating Lattice Boltzmann in the broader context of computational kinetic theory. The leading numerical methods for dense and rarified fluids are Molecular Dynamics (MD) and Direct Simulation Monte Carlo (DSMC), respectively. These methods date of the mid 50s and 60s, respectively, and, ever since, they have undergone a series of impressive developments and refinements which have turned them in major tools of investigation, discovery and design. However, they are both very demanding on computational grounds, which motivates a ceaseless demand for new and improved variants aimed at enhancing their computational efficiency without losing physical fidelity and vice versa, enhance their physical fidelity without compromising computational viability.

scholarly journals The sound of a pulsating sphere in a rarefied gas: continuum breakdown at short length and time scales

2019 ◽  
Vol 871 ◽  
pp. 668-693 ◽  
Author(s):  
Y. Ben-Ami ◽  
A. Manela
Keyword(s):  
Time Scales ◽  
Rarefied Gas ◽  
Molecular Layer ◽  
Direct Simulation Monte Carlo ◽  
Acoustic Power ◽  
Navier Stokes ◽  
System Response ◽  
Low Frequencies ◽  
Continuum Breakdown ◽  
Short Time

The pressure field of a pulsating sphere is a canonical problem in classical acoustics, used to illustrate the acoustic efficiency of a monopole source at continuum conditions. We consider the counterpart vibroacoustic and thermoacoustic problems in a rarefied gas, to investigate the effect of continuum breakdown on monopole radiation. Focusing on small-amplitude normal-to-boundary mechanical and heat-flux excitations, the perturbation field is analysed in the entire range of gas rarefaction and input frequencies. Numerical calculations are carried out via the direct simulation Monte Carlo method, and are used to validate analytical predictions in the free-molecular and near-continuum regimes. In the latter, the regularized thirteen moments model (R13) is applied, to capture the system response at states where the Navier–Stokes–Fourier (NSF) description breaks down. Comparing with the continuum inviscid solution, the results quantitate the dampening effect of gas rarefaction on source point-wise strength and acoustic power. At near-continuum conditions, the acoustic field is composed of exponentially decaying ‘compression’, ‘thermal’ and ‘Knudsen-layer’ modes, reflecting thermoviscous and higher-order rarefaction effects. With reducing rarefaction, the contributions of the latter two modes vanish, and the former degenerates into the ideal-flow inverse-to-distance decaying wave. Stronger attenuation is obtained with increasing rarefaction, where boundary sphericity results in a ‘geometric reduction’ of the molecular layer affected by the source. Notably, while the R13 model at low frequencies appears valid up to moderate gas rarefaction rates, both the NSF and R13 descriptions break down at common low Knudsen numbers at higher frequencies. Further study should therefore be carried out to extend the applicability of moment models to unsteady flows with short time scales.

A Hybrid Fokker-Planck-DSMC Solution Algorithm for the Whole Range of Knudsen Numbers

2013 ◽  
Author(s):  
M. Hossein Gorji ◽  
Stephan Küchlin ◽  
Patrick Jenny
Keyword(s):  
Gas Flow ◽  
Rarefied Gas ◽  
Time Integration ◽  
Computational Cost ◽  
Direct Simulation Monte Carlo ◽  
Large Cell ◽  
Solution Algorithm ◽  
Rarefied Gas Flows ◽  
Knudsen Numbers ◽  
Fokker Planck

In this work, we present a hybrid algorithm based on the Fokker-Planck (FP) kinetic model and direct simulation Monte Carlo (DSMC) for studies of rarefied gas flows. A particle based FP solution algorithm for rarefied gas flow simulations has recently been devised by the authors. The motivation behind the FP approximation is purely computational, i.e. due to the fact that the resulting random processes are continuous in time the computational cost of the corresponding time integration becomes independent of the Knudsen number. However, the method faces limitations for flows with very high Knudsen numbers (larger than approximately 5). In the method presented here, the FP approach is coupled with DSMC in order to gain from the efficiency of the FP model and from the accuracy of DSMC at small and large cell based Knudsen numbers, respectively.

Flow and thermal field investigation of rarefied gas in a trapezoidal micro/nano-cavity using DSMC

2021 ◽  
pp. 2150162
Author(s):  
Mostafa Zakeri ◽  
Ehsan Roohi
Keyword(s):  
Knudsen Number ◽  
Thermal Field ◽  
Rarefied Gas ◽  
Direct Simulation Monte Carlo ◽  
Field Investigation ◽  
Gas Flows ◽  
Fourier Law ◽  
Rarefied Gas Flows ◽  
Knudsen Numbers ◽  
Simulation Monte Carlo

The impetus of the this study is to investigate flow and thermal field in rarefied gas flows inside a trapezoidal micro/nano-cavity using the direct simulation Monte Carlo (DSMC) technique. The investigation covers the hydrodynamic properties and thermal behavior of the flow. The selected Knudsen numbers for this study are arranged in the slip and transition regimes. The results show the center of the vortex location moves by variation in the Knudsen numbers. Also, as the Knudsen number increases, the non-dimensional shear stress increases, but the distribution deviates from a symmetrical profile. The cold to hot transfer, which is in contrast with the conventional Fourier law, is observed. We show that the heat transfer is affected by the second derivative of the velocity. By increasing the Knudsen number, the transferred heat through the walls decreases, but the contraction/expansion effects on the temperature in the corner of the cavity become higher.

scholarly journals Slip Velocity Distribution in a Parallel Plate Channel on Asymmetric Thermal Boundary Condition

2016 ◽  
Vol 35 ◽  
pp. 113-126
Author(s):  
Md Tajul Islam
Keyword(s):  
Boundary Conditions ◽  
Velocity Distribution ◽  
Parallel Plate ◽  
Control Volume ◽  
Navier Stokes ◽  
Working Fluid ◽  
Slip Boundary Conditions ◽  
Cross Sectional ◽  
Slip Boundary ◽  
Knudsen Numbers

Steady, laminar and fully developed flows in parallel plate microchannel with asymmetric thermal wall conditions are solved by control volume technique. In order to examine the influence of Reynolds number and Knudsen number on the velocity distributions, a series of simulations are performed for different Reynolds and Knudsen numbers. Nitrogen gas is used as working fluid and we assume the fluid as continuum but employ the slip boundary conditions on the walls. The Navier-Stokes and energy equations are solved simultaneously. The results are found in good agreement with those predicted by analytical solutions in 2D continuous flow model employing first order slip boundary conditions. It is concluded that the rarefaction flattens the velocity distribution. If the product of Reynolds numbers and Knudsen numbers is fixed, the cross sectional average velocity is fixed for incompressible flow.GANIT J. Bangladesh Math. Soc.Vol. 35 (2015) 113-126

scholarly journals On the modelling of isothermal gas flows at the microscale

2008 ◽  
Vol 604 ◽  
pp. 235-261 ◽  
Author(s):  
DUNCAN A. LOCKERBY ◽  
JASON M. REESE
Keyword(s):  
Boundary Conditions ◽  
Constitutive Relations ◽  
Navier Stokes ◽  
Test Case ◽  
Gas Flows ◽  
Hydrodynamic Models ◽  
Slip Boundary ◽  
Knudsen Numbers ◽  
Isothermal Gas ◽  
Non Equilibrium

This paper makes two new propositions regarding the modelling of rarefied (non-equilibrium) isothermal gas flows at the microscale. The first is a new test case for benchmarking high-order, or extended, hydrodynamic models for these flows. This standing time-varying shear-wave problem does not require boundary conditions to be specified at a solid surface, so is useful for assessing whether fluid models can capture rarefaction effects in the bulk flow. We assess a number of different proposed extended hydrodynamic models, and we find the R13 equations perform the best in this case.Our second proposition is a simple technique for introducing non-equilibrium effects caused by the presence of solid surfaces into the computational fluid dynamics framework. By combining a new model for slip boundary conditions with a near-wall scaling of the Navier--Stokes constitutive relations, we obtain a model that is much more accurate at higher Knudsen numbers than the conventional second-order slip model. We show that this provides good results for combined Couette/Poiseuille flow, and that the model can predict the stress/strain-rate inversion that is evident from molecular simulations. The model's generality to non-planar geometries is demonstrated by examining low-speed flow around a micro-sphere. It shows a marked improvement over conventional predictions of the drag on the sphere, although there are some questions regarding its stability at the highest Knudsen numbers.

The planar Couette flow with slip and jump boundary conditions in a microchannel

2016 ◽  
Vol 22 (4) ◽  
Author(s):  
Mohamed Hssikou ◽  
Jamal Baliti ◽  
Mohammed Alaoui
Keyword(s):  
Heat Flux ◽  
Boundary Conditions ◽  
Direct Simulation Monte Carlo ◽  
Ideal Gas ◽  
Navier Stokes ◽  
Heat Conducting ◽  
Direct Simulation ◽  
Dilute Gas ◽  
Viscous Heat ◽  
Simulation Monte Carlo

AbstractThe steady state of a dilute gas enclosed within a rectangular cavity, whose upper and lower sides are in relative motion, is considered in the slip and early transition regimes. The DSMC (Direct simulation Monte Carlo) method is used to solve the Boltzmann equation for analysing a Newtonian viscous heat conducting ideal gas with the slip and jump boundary conditions (SJBC) in the vicinity of horizontal walls. The numerical results are compared with the Navier–Stokes solutions, with and without SJBC, through the velocity, temperature, and normal heat flux profiles. The parallel heat flux and shear stress are also evaluated as a function of rarefaction degree; estimated by the Knudsen number

Analysis for Rarefied Gas Flow in a Rotating Cylinder

2009 ◽  
Author(s):  
H. Futagami ◽  
H. Ninokata
Keyword(s):  
Gas Flow ◽  
Rarefied Gas ◽  
Isotope Separation ◽  
Direct Simulation Monte Carlo ◽  
Rotating Cylinder ◽  
Navier Stokes ◽  
Operating Pressure ◽  
Direct Simulation ◽  
Navier Stokes Equation ◽  
Simulation Monte Carlo

Behaviors inside rotating cylinders where the range of operating pressure is very wide, i.e. from subatmospheric to almost vacuum are subject of this study. The flow near the rotating axis is very rarefied. If a flow becomes rarefied, the flow cannot be treated as that of a continuum media. Therefore the flow cannot be analyzed by the method based on solving Navier-Stokes equation. One of the promising methods is considered to be DSMC (Direct Simulation Monte Carlo) method based on Boltzmann equation ([1]). In this paper, fundamental validation analyses related to isotope separation in a rotating cylinder calculations of endplate type centrifuge were performed for the parametric study, with DSMC. The results were compared with the experimental results by Groth et al ([2]). The validity of the calculations and its limit were also discussed.

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