Shock-wave structure formation by nanosecond discharge in helium

Znamenskaya, I. A.; Иванов, И. Э.; Kryukov, I. A.; Mursenkova, I. V.; Timokhin, M. Yu.

doi:10.1134/s1063785014060273

Cited by 9 publications

(4 citation statements)

References 7 publications

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“…Previously, only the linear variant of the R13 system (10) [6,17] and the nonlinear variant (7)-(9) were used for supersonic flows in general, and for the problem of the shock wave structure in particular, whereas the fourth-order terms with respect to the Knudsen numbers were neglected [7,8]. Numerical results for the R13 system and DSMC computations were obtained in a wide range of Mach numbers (1.0<M<8.0).…”

Section: Results and Dicussionmentioning

confidence: 99%

The analysis of different variants of R13 equations applied to the shock-wave structure

Timokhin

Struchtrup

Kokhanchik

et al. 2016

AIP Conference Proceedings

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Section: Results and Dicussionmentioning

confidence: 99%

The analysis of different variants of R13 equations applied to the shock-wave structure

Timokhin

Struchtrup

Kokhanchik

et al. 2016

AIP Conference Proceedings

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“…2015, 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).…”

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%

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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“…The difference between them lies in the relations for higher order moments [8,9]. It has been shown that all variants are well applicable for numerical modelling of the moderately rarefied slow gas flows and allow the modelling of main nonequilibrium effects in low-velocity micro-flow problems [10,11,12,13,14,15,16,17] and some moderately rarefacted supersonic flows [5,18,19,15,20,21,22]. The difficulty is that the solid wall boundary conditions for R13 equations were obtained from one of the variants [10] which is not applicable to near hypersonic flows [9].…”

Section: Introductionmentioning

confidence: 99%

R13 moment equations applied to supersonic flow with solid wall interaction

Timokhin¹,

Struchtrup²,

Kokhanchik³

et al. 2019

31st International Symposium on Rarefied Gas Dynamics: Rgd31

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R13 moment set of equations is the regularization of original Grad 13-moment system. Several variants of R13 equations were presented after the first publication. The difference between them lies in the relations for higher order moments. It has been shown that all variants are well applicable for numerical modelling of the moderately rarefied slow gas flows and allow the modelling of main nonequilibrium effects in micro-flow problems. The difficulty is that the solid wall boundary conditions for R13 equations were obtained from one of the variants which is not applicable to near hypersonic flows. This study is devoted to the demonstration of the numerical results of R13 linear and nonlinear variants for supersonic flow over the flat plate. The R13 numerical solutions are compared with DSMC results computed by the SMILE++ software system.

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Shock-wave structure formation by nanosecond discharge in helium

Cited by 9 publications

References 7 publications

The analysis of different variants of R13 equations applied to the shock-wave structure

The analysis of different variants of R13 equations applied to the shock-wave structure

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

R13 moment equations applied to supersonic flow with solid wall interaction

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