How Far Can 13 Moments Go in Modeling Microscale Gas Phenomena?

Gu, Xiao Jun; Barber, Robert W.; Emerson, David R.

doi:10.1080/15567260701337696

Cited by 11 publications

(4 citation statements)

References 12 publications

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“…Accordingly, it can be argued that the heat flow is dominated by the pressure gradient (known as a rarefaction effect [66]) in microchannels with a divergence angle of φ ≤ 2.5. Due to the rarefaction effects, heat flow from cold to hot regions is observed, which is not predictable using the NSF equations because of the neglect of high-order rarefaction terms [67]. Heat flow in the central region of the channel is dominated by the mass flow driven by the pressure gradient.…”

Section: Resultsmentioning

confidence: 99%

Pressure-Driven Nitrogen Flow in Divergent Microchannels with Isothermal Walls

2021

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Gas flow and heat transfer in confined geometries at micro-and nanoscales differ considerably from those at macro-scales, mainly due to nonequilibrium effects such as velocity slip and temperature jump. Nonequilibrium effects increase with a decrease in the characteristic length-scale of the fluid flow or the gas density, leading to the failure of the standard Navier–Stokes–Fourier (NSF) equations in predicting thermal and fluid flow fields. The direct simulation Monte Carlo (DSMC) method is employed in the present work to investigate pressure-driven nitrogen flow in divergent microchannels with various divergence angles and isothermal walls. The thermal fields obtained from numerical simulations are analysed for different inlet-to-outlet pressure ratios (1.5≤Π≤2.5), tangential momentum accommodation coefficients, and Knudsen numbers (0.05≤Kn≤12.5), covering slip to free-molecular rarefaction regimes. The thermal field in the microchannel is predicted, heat-lines are visualised, and the physics of heat transfer in the microchannel is discussed. Due to the rarefaction effects, the direction of heat flow is largely opposite to that of the mass flow. However, the interplay between thermal and pressure gradients, which are affected by geometrical configurations of the microchannel and the applied boundary conditions, determines the net heat flow direction. Additionally, the occurrence of thermal separation and cold-to-hot heat transfer (also known as anti-Fourier heat transfer) in divergent microchannels is explained.

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Section: Resultsmentioning

confidence: 99%

Pressure-Driven Nitrogen Flow in Divergent Microchannels with Isothermal Walls

2021

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“…Accordingly, it can be argued that the heat flow is dominated by the pressure gradient (known as a rarefaction effect [67]) in microchannels with a divergence angle φ ≤ 2.5. Due to the rarefaction effects, heat flow from cold to hot regions is observed, which is not predictable using the NSF equations because of the neglect of high-order rarefaction terms [68]. Heat flow in the central region of the channel is dominated by the mass flow driven by the pressure gradient.…”

Section: Model Validation and Verificationmentioning

confidence: 99%

Pressure-driven Nitrogen Flow in Divergent Microchannels with Isothermal Walls

Ebrahimi,

Shahabi,

Roohi

2021

Preprint

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Gas flow and heat transfer in confined geometries at micro and nano scales differ considerably from those at macro-scales, mainly due to nonequilibrium effects such as velocity slip and temperature jump. The nonequilibrium effects enhance with a decrease in the characteristic length-scale of the fluid flow or the gas density, leading to the failure of the standard Navier-Stokes-Fourier (NSF) equations in predicting thermal and fluid flow fields. The direct simulation Monte-Carlo (DSMC) method is employed in the present work to investigate pressure-driven nitrogen flow in divergent microchannels with various divergence angles and isothermal walls. The thermal fields obtained from numerical simulations are analysed for different inlet-to-outlet pressure ratios (1.5 ≤ Π ≤ 2.5), tangential momentum accommodation coefficients and Knudsen numbers (0.05 ≤ Kn ≤ 12.5), covering slip to free-molecular rarefaction regimes. The thermal field in the microchannel is predicted, heat-lines are visualised, and the physics of heat transfer in the microchannel is discussed. Due to the rarefaction effects, the direction of heat flow is largely opposite to that of the mass flow. However, the interplay between thermal and pressure gradients, which are affected by geometrical configurations of the microchannel and applied boundary conditions, determines the net heat flow direction. Additionally, the occurrence of thermal separation and cold-to-hot heat transfer (also known as anti-Fourier heat transfer) in divergent microchannels is explained.

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“…As the value of Kn increases, more details of moments need to be included in the Grad moment manifold to accurately describe any non-equilibrium phenomenon. Gu and Emerson [17,19] extended the R13 equations into R26 equations, and the VDF is truncated to the incomplete fourth order in Hermite polynomials ( 26 [17]. In addition, the wall boundary conditions for R13 and R26 can also be found in Gu & Emerson [17,20].…”

Section: The Extended R13 and R26 Equationsmentioning

confidence: 99%

Comparative study of the discrete velocity and the moment method for rarefied gas flows

Yang

Emerson

et al. 2019

31st International Symposium on Rarefied Gas Dynamics: Rgd31

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In the study of rarefied gas dynamics, the discrete velocity method (DVM) has been widely employed to solve the gas kinetic equations. However, it is usually computationally expensive in dealing with complex geometry and high Mach number flows. In the present work, both classical third-order time implicit DVM and the moment method are employed in finding steady-state solutions of the force-driven Poiseuille flow and flow past a circle cylinder. Their performance, in terms of accuracy, has been compared and analyzed. Choosing the velocity distribution functions (VDFs) obtained from DVM solutions as the benchmark, we reconstruct the expanded VDFs using regularized 13 moment equations (R13) and regularized 26 moment equations (R26) and then compare the accuracy of the expanded VDFs with different order of Hermite polynomial expansions. From the computed velocity profiles and reconstructed VDFs, we have found that the moment method can extend the macroscopic equations into the early transition regime, and the R26 can relatively accurately represent the characteristics of the VDFs in comparison with the gas kinetic model. Conversely, the Navier-Stokes-Fourier (NSF) equations are not able to produce an accurate description of the expanded distribution functions.

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How Far Can 13 Moments Go in Modeling Microscale Gas Phenomena?

Cited by 11 publications

References 12 publications

Pressure-Driven Nitrogen Flow in Divergent Microchannels with Isothermal Walls

Pressure-Driven Nitrogen Flow in Divergent Microchannels with Isothermal Walls

Pressure-driven Nitrogen Flow in Divergent Microchannels with Isothermal Walls

Comparative study of the discrete velocity and the moment method for rarefied gas flows

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