R13 moment equations applied to supersonic flow with solid wall interaction

Timokhin, M. Yu.; Struchtrup, Henning; Kokhanchik, A. A.; Bondar, Ye. A.

doi:10.1063/1.5119614

Cited by 4 publications

(4 citation statements)

References 31 publications

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“…2014; Timokhin, Ivanov & Kryukov 2018; Timokhin et al. 2019). The tensor form of the regularized 13-moment system (R13) can be written as where pressure is determined by the ideal gas law and is the relaxation time obtained with the viscosity coefficient .…”

Section: Gas Flow Models and Numerical Methodsmentioning

confidence: 99%

“…There are many examples of successful applications of this system of equations for slow moderately rarefied flows (Torrilhon & Struchtrup 2008;Torrilhon 2016;Claydon et al 2017;Baliti, Hssikou & Alaoui 2019;Westerkamp & Torrilhon 2019). It has been shown that the R13 equations predict the internal structure of shock waves quite accurately (Torrilhon & Struchtrup 2004;Timokhin et al 2015Timokhin et al , 2017 and can be successfully applied to modelling of supersonic flows (Torrilhon 2006;Znamenskaya et al 2014;Timokhin, Ivanov & Kryukov 2018;Timokhin et al 2019). The tensor form of the regularized 13-moment system (R13) can be written as…”

Section: The Regularized 13-moment Equationsmentioning

confidence: 99%

See 1 more Smart Citation

Regular reflection of shock waves in steady flows: viscous and non-equilibrium effects

Bondar,

Shoev,

Timokhin

2024

J. Fluid Mech.

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Numerical analysis of a steady monatomic gas flow about the point of the regular reflection of a strong oblique shock wave from the symmetry plane is conducted with the Navier–Stokes–Fourier (NSF) equations, the regularized Grad 13-moment (R13) equations and the direct simulation Monte Carlo (DSMC) method. In contrast to the inviscid solution to this problem completely defined by the Rankine–Hugoniot (RH) relations, all three models predict a complicated flow structure with strong thermal non-equilibrium and a long wake with flow parameters not predicted by the RH relations. The temperature $T_y$ related to thermal motion of molecules in the direction normal to the symmetry plane has a maximum inside the reflection zone while in a planar shock wave the maximum is observed for the $T_x$ temperature. The R13 equations predict these features much better than the NSF equations and are in good agreement with the benchmark DSMC results. An analysis of the flow with the conservation equations was conducted in order to evaluate the effects of various processes on a fluid element moving along the symmetry plane. In contrast to the shock wave where effects of viscosity and heat conduction are one-dimensional with zeroth net contribution to the fluid-element energy across the shock, the flow across the zone of the shock reflection is dominated by two-dimensional effects with positive net contribution of viscosity and negative contribution of heat conduction to the fluid-element energy. These effects are believed to be the main source of the wake with parameters deviating from the RH values.

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Section: Gas Flow Models and Numerical Methodsmentioning

confidence: 99%

Section: The Regularized 13-moment Equationsmentioning

confidence: 99%

Regular reflection of shock waves in steady flows: viscous and non-equilibrium effects

Bondar,

Shoev,

Timokhin

2024

J. Fluid Mech.

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“…The difference between different gas models can also be observed by these analytical results. Besides, we will also compare our results with the results of R13 equations for Maxwell molecules with a modified viscosity coefficient, which have been used in some literature to approximate the dynamics for non-Maxwell gases [35,38,27,31,33].…”

Section: Introductionmentioning

confidence: 91%

“…In the resulting 13 equations, convert the coefficients to the variables σ ij and q j according to (33).…”

Section: Semi-linearization Of R13 Equatoins and Derivation Of Bounda...mentioning

confidence: 99%

Flows Between Parallel Plates: Analytical Solutions of Regularized 13-Moment Equations for Inverse-Power-Law Models

Hu,

Yang,

Cai

2020

Preprint

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We study the structure of stationary channel flows predicted by the regularized 13-moment equations. Compared with the previous work [28], we focus on gases whose molecules satisfy the general inverse power law. The analytical solutions are obtained for the semi-linear equations, and the structures of Couette, Fourier, and Poiseuille flows are solved by coupling the general solutions with newly derived boundary conditions. The results show excellent agreement with the reference solution in the slip-flow regime. Our results also show that the R13 equations derived from inverse power law models can have better accuracy than the R13 equations of Maxwell molecules with altered viscosity.

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Flows between parallel plates: Analytical solutions of regularized 13-moment equations for inverse-power-law models

Yang

Cai

2020

Physics of Fluids

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We study the structure of stationary channel flows predicted by the regularized 13-moment equations. Compared with the work of Taheri et al. [“Couette and Poiseuille microflows: Analytical solutions for regularized 13-moment equations,” Phys. Fluids 21, 017102 (2009)], we focus on gases whose molecules satisfy the general inverse power law. The analytical solutions are obtained for the semi-linear equations, and the structures of Couette, Fourier, and Poiseuille flows are solved by coupling the general solutions with newly derived boundary conditions. The results show excellent agreement with the reference solution in the slip-flow regime. Our results also show that the R13 equations derived from inverse-power-law models can have better accuracy than the R13 equations of Maxwell molecules with altered viscosity.

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R13 moment equations applied to supersonic flow with solid wall interaction

Cited by 4 publications

References 31 publications

Regular reflection of shock waves in steady flows: viscous and non-equilibrium effects

Regular reflection of shock waves in steady flows: viscous and non-equilibrium effects

Flows Between Parallel Plates: Analytical Solutions of Regularized 13-Moment Equations for Inverse-Power-Law Models

Flows between parallel plates: Analytical solutions of regularized 13-moment equations for inverse-power-law models

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