Supersonic Patches in Steady Irregular Reflection of Weak Shock Waves

Иванов, М. С.; Shoev, Georgy; Khotyanovsky, D. V.; Bondar, Ye. A.; Kudryavtsev, A. N.

doi:10.1007/978-3-642-25685-1_82

Cited by 2 publications

(5 citation statements)

References 8 publications

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“…As the Reynolds number increases, the numerical data presented in the (θ, p/p ∞ ) plane get closer and closer to the inviscid solution being the shock polar intersection in the case discussed here. It is valid both at the von Neumann paradox conditions (Ivanov et al 2012) and in a more typical case considered in the present paper when the three-shock solution exists. At relatively low Reynolds numbers, the shock wave slopes near the triple point are clearly different from those predicted by the three-shock theory, but converge to the inviscid theoretical prediction with increasing Reynolds number.…”

Section: Discussionmentioning

confidence: 74%

“…The computations are performed at various Reynolds numbers Re w using the nested-block grid refinement technique, which was applied earlier in several studies (Defina et al 2008a;Tesdall et al 2008;Ivanov et al 2012) for modelling flows near the triple point. The zeroth level of nesting corresponds to the rectangular domain marked as Block 0 in figure 1.…”

Section: Numerical Proceduresmentioning

confidence: 99%

“…Numerical results: the weak reflection 6.1. Effects of viscosity and passage to the inviscid limit As was noted above, a numerical study of the weak reflection in a steady viscous flow was undertaken earlier by Ivanov et al (2012), and the passage to the inviscid limit was investigated. In that paper, however, only the case where the three-shock solution does not exist (the von Neumann paradox conditions) was considered.…”

Section: Total Enthalpy Behaviour In the Non-rankine-hugoniot Zonementioning

confidence: 99%

“…However, Ivanov et al (2012) demonstrated by solving the Navier-Stokes equations numerically that in the case of the von Neumann paradox, the non-Rankine-Hugoniot zone size decreases and the values of the flow variables downstream from this zone become closer and closer to the inviscid four-wave solution of Guderley (1947Guderley ( , 1962 as the Reynolds number increases. At the same time, the numerical results revealed that viscosity significantly affects the flow even at very high Reynolds numbers (up to Re ≈ 10 9 ).…”

Section: Introductionmentioning

confidence: 99%

“…The first confirmation of this model was obtained only half a century later by solving the Euler equations numerically (Vasilev & Kraiko 1999). Further investigations (Hunter & Brio 2000;Tesdall & Hunter 2002;Hunter & Tesdall 2004;Tesdall, Sanders & Keyfitz 2007, 2008Defina, Susin & Viero 2008a;Defina, Viero & Susin 2008b;Vasilev & Olhovskiy 2009;Tesdall, Sanders & Popivanov 2015;Vasil'ev 2016) showed that, depending on problem parameters, configurations formed due to interaction of weak shock waves can have even more complicated structures and contain additional elements of small size. The experiments by Skews & Ashworth (2005) and Skews, Li & Paton (2009) performed in a large shock tube revealed the existence of a configuration similar to that predicted by Guderley and observed in the inviscid studies mentioned above.…”

Section: Introductionmentioning

confidence: 99%

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Viscous effects in Mach reflection of shock waves and passage to the inviscid limit

et al. 2023

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The influence of viscosity on the Mach reflection of shock waves in a steady flow of a monatomic gas is studied by solving the Navier–Stokes equations numerically. Based on the nested block grid refinement technique, the flow near the shock wave intersection is simulated, and its behaviour with increasing Reynolds number is studied. The computations are performed for the interaction of both strong (free-stream Mach number $M_\infty = 4$ ) and weak ( $M_\infty = 1.7$ ) shock waves. In the strong reflection of shock waves at all Reynolds numbers in the examined range, it is found that there exists a small-size zone behind the shock wave intersection where the flow parameters differ from those predicted by the Rankine–Hugoniot relations and hence deviate from the predictions of the inviscid three-shock theory. The structure of this zone is self-similar: in coordinates normalised to the mean free path of molecules in the free stream. The structure is identical at all Reynolds numbers considered in the study. As the Reynolds number increases, the size of this zone in physical coordinates decreases, but the maximum difference between the viscous and inviscid solutions in this zone remains constant, reaching approximately $10\,\%$ for pressure. In the weak reflection of shock waves, the flow structure behind the shock wave intersection is not self-similar, i.e. the flow fields at different Reynolds numbers do not coincide in the normalised coordinates, but converge, as the Reynolds number increases, to the parameters predicted by the inviscid three-shock theory.

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Section: Discussionmentioning

confidence: 74%

Section: Numerical Proceduresmentioning

confidence: 99%

Section: Total Enthalpy Behaviour In the Non-rankine-hugoniot Zonementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Viscous effects in Mach reflection of shock waves and passage to the inviscid limit

et al. 2023

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Numerical study of viscous effects on centreline shock reflection in axisymmetric flow

Shoev

Ogawa

2019

Physics of Fluids

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Viscous effects on centreline shock reflection in an axisymmetric flow are studied numerically using Navier–Stokes and direct simulation Monte Carlo solvers. Computations at low Reynolds numbers have resulted in a configuration consisting of two shock waves, in contrast to the inviscid theory. On the other hand, computations at high Reynolds numbers have yielded a three-shock configuration in qualitative agreement with the inviscid theory prediction. This behaviour is explained by the presence of the so-called non-Rankine–Hugoniot zone, which accounts for the deviation of the shock structure from the inviscid paradigm. At Reynolds numbers on the verge of the transition from a two-shock to three-shock configuration, extremely high pressure that would be unattainable with the classical Rankine–Hugoniot relation for any shock configuration may occur. An analogy to the Guderley singularity in cylindrical shock implosion has been deduced for the shock behaviour from a mathematical viewpoint.

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Supersonic Patches in Steady Irregular Reflection of Weak Shock Waves

Cited by 2 publications

References 8 publications

Viscous effects in Mach reflection of shock waves and passage to the inviscid limit

Viscous effects in Mach reflection of shock waves and passage to the inviscid limit

Numerical study of viscous effects on centreline shock reflection in axisymmetric flow

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