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A Fokker–Planck based kinetic model for diatomic rarefied gas flows
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10.1063/1.4811399
/content/aip/journal/pof2/25/6/10.1063/1.4811399
http://aip.metastore.ingenta.com/content/aip/journal/pof2/25/6/10.1063/1.4811399
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

(a) Temporal evolution of normalized rotational energy in comparison with the LT solution (67) . For the FP simulation two different time steps of Δ = τ and Δ = τ/3 were used. (b) Distribution of the molecular rotational energy at equilibrium. The FP result is depicted by the solid line, where the Boltzmann distribution at temperature is depicted by symbols.

Image of FIG. 2.
FIG. 2.

(a) Temporal evolution of normalized vibrational energy in comparison with the LT solution (67) . For the FP simulation two different time steps of Δ = τ and Δ = τ/3 were used. (b) Distribution of the molecular vibrational energy at equilibrium. The FP result is depicted by the solid line, where the Boltzmann distribution at temperature is depicted by symbols.

Image of FIG. 3.
FIG. 3.

Planar Couette flow of nitrogen. The profile of the mean velocity of nitrogen is depicted along the -coordinate (perpendicular to the flow direction). The solid lines represent FP results, circles DSMC results, and the dashed line the Navier–Stokes solution (i.e., the linear velocity profile).

Image of FIG. 4.
FIG. 4.

Computational cost comparison between FP simulations and DSMC. The ratio between computational time required for DSMC and the FP model, i.e., , is shown as a function of the Knudsen number.

Image of FIG. 5.
FIG. 5.

(a) Shock thickness comparison between FP results and experiments by Alsmeyer. The FP results are shown by symbols and experiments are shown by solid line. At the reciprocal shock thickness for cases with = 30 K and 3000 K are shown by squares. (b) Normalized density profiles of = 4 in nitrogen at different upstream temperatures using FP.

Image of FIG. 6.
FIG. 6.

(a) Shock profile for in nitrogen. FP results are shown by lines and experiments of Robben and Talbot by symbols. (b) PDF of rotational energy for a shock in nitrogen. FP results are shown by symbols and experiments of Robben and Talbot by dashed lines. The solid lines show the equilibrium distributions at upstream and downstream conditions. In between, two different locations were considered, i.e., /* ∈ {0, 4.1}.

Image of FIG. 7.
FIG. 7.

(a) Shock profile for in nitrogen. FP results are shown by lines and experiments of Robben and Talbot by symbols. (b) PDF of rotational energy for a shock in nitrogen. FP results are shown by symbols and experiments of Robben and Talbot by dashed lines. The solid lines show the equilibrium distributions at upstream and downstream conditions. In between, four different locations were considered, i.e., /* ∈ {−12.9, −3.5, 0, 2.3}.

Image of FIG. 8.
FIG. 8.

(a) Shock profile for in nitrogen. FP results are shown by lines and experiments of Robben and Talbot by symbols. (b) PDF of rotational energy for shock in nitrogen. FP results are shown by symbols and experiments of Robben and Talbot by dashed lines. The solid lines show the equilibrium distributions at upstream and downstream conditions. In between, four different locations were considered, i.e., /* ∈ { − 6.3, −4.23, −1.06, 3.17}.

Image of FIG. 9.
FIG. 9.

Hypersonic nitrogen flow over a wedge using the FP model. Translational temperature at top, rotational temperature at middle, and vibrational temperature at bottom.

Image of FIG. 10.
FIG. 10.

Temperature contours for hypersonic nitrogen flow over a wedge using different approaches. (a) Vibrational temperature contours from the FP model. (b) Translational temperature contours from the FP model. (c) Vibrational temperature contours from DSMC using level to level transition model. (d) Translational temperature contours from DSMC using level to level transition model. Figs. 10(c) and 10(d) are reprinted with permission from I. D. Boyd, Phys. Fluids , 1785–1791 (1991). Copyright 2008, American Institute of Physics.

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/content/aip/journal/pof2/25/6/10.1063/1.4811399
2013-06-28
2014-04-18
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: A Fokker–Planck based kinetic model for diatomic rarefied gas flows
http://aip.metastore.ingenta.com/content/aip/journal/pof2/25/6/10.1063/1.4811399
10.1063/1.4811399
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