Comparison of Kinetic Theory and Hydrodynamics for Poiseuille Flow

Zheng, Yihao; Garcia, Alejandro L.; Alder, B. J.

doi:10.1063/1.1581540

Cited by 42 publications

(87 citation statements)

References 8 publications

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“…Several analytical solutions for the flow field have been presented using the isothermal assumption, for example, the work by Arkilic, Schmidt & Breuer (2001) and Zohar et al (2004). More complicated results have also been obtained numerically using kinetic-based approaches, including the direct simulation Monte Carlo method by Ho & Tai (1998) and Zheng, Garcia & Alder (2000), the information preservation method by Cai et al (2000) and Shen, Fan & Xie (2003), and the gas-kinetic BGK-Burnett method by Xu & Li (2004).…”

Section: Introductionmentioning

confidence: 99%

Gas flows in microchannels and microtubes

Cai

Sun²,

Boyd

2007

J. Fluid Mech.

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This study analyses compressible gas flows through microchannels or microtubes, and develops two complete sets of asymptotic solutions. It is a natural extension of the previous work by Arkilic et al. on compressible flows through microchannels. First, by comparing the magnitudes of different forces in the compressible gas flow, we obtain proper estimations for the Reynolds and Mach numbers at the outlets. Second, based on these estimations, we obtain asymptotic analytical solutions of velocities, pressure and temperature distributions of compressible gas flow inside the microchannels and microtubes with a relaxation of the isothermal assumption, which was previously used in many studies. Numerical simulations of compressible flows through a microchannel and a microtube are performed by solving the compressible Navier-Stokes equations, with velocity slip and temperature jump wall boundary conditions. The numerical simulation results validate the analytical results from this study.

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Section: Introductionmentioning

confidence: 99%

Gas flows in microchannels and microtubes

Cai

Sun²,

Boyd

2007

J. Fluid Mech.

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“…For Poiseuille flow [14,15] and the gas flow within a circular cylinder [16][17][18], viscous effects dominate the system, and the gas does not compress much; therefore, we consider them to test the applicability of NSF.…”

Section: Resultsmentioning

confidence: 99%

Molecular-level study of compressible gaseous continua

Hong

Xiao

et al. 2018

J. Phys. Commun.

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For over 150 years, compressible gaseous continua have usually been formulated in terms of the Navier-Stokes-Fourier (NSF) equations for the macroscopic velocity, pressure and energy as functions of position and time. This study introduces molecular-level investigations of compressible gaseous continua using direct simulation in the Monte Carlo method and molecular dynamics. It is observed that the thermodynamic flux can be generated as long as molecular collisions occur, even without temperature drive and stress tensor work. This is contrary to the general opinion that temperature drive and stress tensor work are the only proximate causes driving thermodynamic flow.

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“…For example, the FP model correctly predicts velocity slip temperature jump at the channel walls, and the local temperature minimum in the centre of the channel. The latter is a phenomenon which cannot be captured by a Navier-Stokes-Fourier system, even if the correct velocity slip and temperature jump are imposed at the wall boundaries (see Zheng, Garcia & Alder 2002;Xu 2003Xu , 2004Taheri, Torrilhon & Struchtrup 2009). In order to study field quantities of flows with higher reference Knudsen numbers, in the following subsection another test case with an imposed temperature difference between left and right walls is considered.…”

Section: Homogeneous Relaxationmentioning

confidence: 99%

Fokker–Planck model for computational studies of monatomic rarefied gas flows

2011

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In this study, we propose a non-linear continuous stochastic velocity process for simulations of monatomic gas flows. The model equation is derived from a FokkerPlanck approximation of the Boltzmann equation. By introducing a cubic non-linear drift term, the model leads to the correct Prandtl number of 2/3 for monatomic gas, which is crucial to study heat transport phenomena. Moreover, a highly accurate scheme to evolve the computational particles in velocity-and physical space is devised. An important property of this integration scheme is that it ensures energy conservation and honours the tortuosity of particle trajectories. Especially in situations with small to moderate Knudsen numbers, this allows to proceed with much larger time steps than with direct simulation Monte Carlo (DSMC), i.e. the mean collision time not necessarily has to be resolved, and thus leads to more efficient simulations. Another computational advantage is that no direct collisions have to be calculated in the proposed algorithm. For validation, different micro-channel flow test cases in the near continuum and transitional regimes were considered. Detailed comparisons with DSMC for Knudsen numbers between 0.07 and 2 reveal that the new solution algorithm based on the Fokker-Planck approximation for the collision operator can accurately predict molecular stresses and heat flux and thus also gas velocity and temperature profiles. Moreover, for the Knudsen Paradox, it is shown that good agreement with DSMC is achieved up to a Knudsen number of about 5.

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Comparison of Kinetic Theory and Hydrodynamics for Poiseuille Flow

Cited by 42 publications

References 8 publications

Gas flows in microchannels and microtubes

Gas flows in microchannels and microtubes

Molecular-level study of compressible gaseous continua

Fokker–Planck model for computational studies of monatomic rarefied gas flows

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