Effect of the dynamic pressure on the similarity solution of cylindrical shock waves in a rarefied polyatomic gas
The similarity solution for a strong cylindrical shock wave in a rarefied polyatomic gas is analyzed on the basis of Rational Extended Thermodynamics with six independent fields; the mass density, the velocity, the pressure and the dynamic pressure. A new ODE system for the similarity solution is de...
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| Published in | Ricerche di matematica Vol. 70; no. 1; pp. 195 - 206 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
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01.06.2021
Springer Nature B.V |
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| Abstract | The similarity solution for a strong cylindrical shock wave in a rarefied polyatomic gas is analyzed on the basis of Rational Extended Thermodynamics with six independent fields; the mass density, the velocity, the pressure and the dynamic pressure. A new ODE system for the similarity solution is derived in a systematic way by using the method based on the Lie group theory proposed in the context of the spherical shock wave in a rarefied monoatomic gas in Donato and Ruggeri (J Math Anal Appl 251:395, 2000). The boundary conditions are also specified from the Rankine–Hugoniot conditions for the sub-shock. The derived similarity solution is characterized by only one dimensionless parameter
α
related to the relaxation time for the dynamic pressure. The numerical analysis of the similarity solution is also performed. The solution agrees with the well-known Sedov–von Neumann–Taylor (SNT) solution when
α
is small. When
α
is larger, due to the presence of the dynamic pressure, the deviation from the SNT solution is evident; the strength of a peak near the shock front becomes smaller and the profile becomes broader. |
|---|---|
| AbstractList | The similarity solution for a strong cylindrical shock wave in a rarefied polyatomic gas is analyzed on the basis of Rational Extended Thermodynamics with six independent fields; the mass density, the velocity, the pressure and the dynamic pressure. A new ODE system for the similarity solution is derived in a systematic way by using the method based on the Lie group theory proposed in the context of the spherical shock wave in a rarefied monoatomic gas in Donato and Ruggeri (J Math Anal Appl 251:395, 2000). The boundary conditions are also specified from the Rankine–Hugoniot conditions for the sub-shock. The derived similarity solution is characterized by only one dimensionless parameter α related to the relaxation time for the dynamic pressure. The numerical analysis of the similarity solution is also performed. The solution agrees with the well-known Sedov–von Neumann–Taylor (SNT) solution when α is small. When α is larger, due to the presence of the dynamic pressure, the deviation from the SNT solution is evident; the strength of a peak near the shock front becomes smaller and the profile becomes broader. The similarity solution for a strong cylindrical shock wave in a rarefied polyatomic gas is analyzed on the basis of Rational Extended Thermodynamics with six independent fields; the mass density, the velocity, the pressure and the dynamic pressure. A new ODE system for the similarity solution is derived in a systematic way by using the method based on the Lie group theory proposed in the context of the spherical shock wave in a rarefied monoatomic gas in Donato and Ruggeri (J Math Anal Appl 251:395, 2000). The boundary conditions are also specified from the Rankine–Hugoniot conditions for the sub-shock. The derived similarity solution is characterized by only one dimensionless parameter α related to the relaxation time for the dynamic pressure. The numerical analysis of the similarity solution is also performed. The solution agrees with the well-known Sedov–von Neumann–Taylor (SNT) solution when α is small. When α is larger, due to the presence of the dynamic pressure, the deviation from the SNT solution is evident; the strength of a peak near the shock front becomes smaller and the profile becomes broader. |
| Author | Taniguchi, Shigeru |
| Author_xml | – sequence: 1 givenname: Shigeru surname: Taniguchi fullname: Taniguchi, Shigeru email: taniguchi.shigeru@kct.ac.jp organization: Department of Creative Engineering, National Institute of Technology, Kitakyushu College |
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| Cites_doi | 10.1007/978-1-4612-2210-1 10.1007/s10955-019-02366-5 10.1007/s001610050066 10.1063/1.5125079 10.1016/j.ijnonlinmec.2015.11.003 10.1007/s001610050094 10.1006/jmaa.2000.7073 10.1007/s11587-016-0299-3 10.3934/krm.2018004 10.1007/s00161-011-0213-x 10.1080/00036819508840379 10.1063/1.4967673 10.1007/s10440-014-9939-3 10.1103/PhysRevFluids.3.023401 10.1016/j.ijnonlinmec.2017.10.024 10.1007/978-3-030-29951-4_8 10.1016/j.physleta.2012.08.030 10.1007/978-3-319-13341-6 10.1103/PhysRevE.89.013025 10.1016/j.ijnonlinmec.2015.02.005 10.1063/1.4861368 |
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| Keywords | Rarefied polyatomic gas Cylindrical symmetry 76L05 35L60 76N15 82C35 76M60 Extended thermodynamics Similarity solution Shock wave Dynamic pressure |
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Thermodyn.199810285165285810.1007/s001610050094 – reference: RuggeriTSugiyamaMRational Extended Thermodynamics Beyond the Monatomic Gas2015ChamSpringer10.1007/978-3-319-13341-6 – reference: TaniguchiSArimaTRuggeriTSugiyamaMOvershoot of the non-equilibrium temperature in the shock wave structure of a rarefied polyatomic gas subject to the dynamic pressureInt. J. Non Linear Mech.2016796610.1016/j.ijnonlinmec.2015.11.003 – reference: KosugeSKuoHWAokiKA kinetic model for a polyatomic gas with temperature-dependent specific heats and its application to shock-wave structureJ. Stat. Phys.2019177209401077710.1007/s10955-019-02366-5 – reference: DonatoAOliveriFWhen nonautonomous equations are equivalent to autonomous onesAppl. Anal.199558313138319510.1080/00036819508840379 – reference: RuggeriTNon-linear maximum entropy principle for a polyatomic gas subject to the dynamic pressureBull. Inst. Math. Acad. Sin. 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A doi: 10.1016/j.physleta.2012.08.030 – volume: 11 start-page: 1 year: 2016 ident: 505_CR18 publication-title: Bull. Inst. Math. Acad. Sin. (New Ser.) – volume-title: Rational Extended Thermodynamics Beyond the Monatomic Gas year: 2015 ident: 505_CR5 doi: 10.1007/978-3-319-13341-6 – volume: 89 start-page: 013025 year: 2014 ident: 505_CR14 publication-title: Phys. Rev. E doi: 10.1103/PhysRevE.89.013025 – volume: 72 start-page: 6 year: 2015 ident: 505_CR17 publication-title: Int. J. Non Linear Mech. doi: 10.1016/j.ijnonlinmec.2015.02.005 – volume: 26 start-page: 016103 year: 2014 ident: 505_CR20 publication-title: Phys. Fluids doi: 10.1063/1.4861368 – volume-title: Deviations from Thermal Equilibrium in Shock Waves, Reprinted by Engineering Research Institute year: 1941 ident: 505_CR13 |
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| SubjectTerms | Algebra Analysis Boundary conditions Cylindrical waves Dynamic pressure Geometry Group theory Lie groups Mathematics Mathematics and Statistics Numerical Analysis Polyatomic gases Pressure effects Probability Theory and Stochastic Processes Relaxation time Shock waves Similarity solutions Spherical waves |
| Title | Effect of the dynamic pressure on the similarity solution of cylindrical shock waves in a rarefied polyatomic gas |
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