Approximate Analytic Solution of a Self-Similar Piston Moving in an Inhomogeneous Medium

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Dr. B.N.Prasad
Dr. B.N.Prasad

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Self-similar motion for the flow between a piston and strong shock propagating in a non uniform ideal gas at rest has been studied. The solution to the problem is similar to that of hypersonic flows past the power law bodies. The gas ahead of the shock is assumed to be uniform and at rest. This is considered as a particular case of radiative piston problem. The shock is assumed to be very strong and propagating in a medium at rest in which density obeys power laws. This problem with spherical symmetry has got importance in astrophysics. To solve the gas dynamics problem, Chernyii’s expansion techniques have been used in which flow variables are expanded in a series of powers of ε, the density ratio across the strong shock. The approximate analytic solution has been obtained in closed form to the zeroth approximation. The problem discussed belongs to the self-similar motion of the first kind. The resulting analytic solution gives the flow variables distribution for plane, cylindrical, and spherical symmetry for different cases which satisfy the similarity conditions with accurate trend and values.

9 Cites in Articles

References

  1. L Sedov (1945). - Equations for Steady One-Dimensional Compressible Fluid Flow.
  2. M Rogers (1957). Analytic Solutions for the Blast-Wave Problem with an Atmosphere of Varying Density..
  3. G Taylor (1950). The formation of a blast wave by a very intense explosion.
  4. P Bhatnagar,Purshotam Lal (1965). Propagation of a spherical shock in aninhomogeneous selfgravitating or non-gravitating system.
  5. N Kochina,N Melnikova (1958). On the unsteady motion of the gas driven outwards by a piston, neglecting the counter pressure.
  6. M Rogers (1956). The propagation and structure of shock waves of varying strength in a self-gravitating gas sphere.
  7. K Wang (1922). Approximate Solution of a Plane Radiating ``Piston Problem''.
  8. P Sachdev,S Ashraf (1970). Approximate analytical solution of spherical, cylindrical and plane piston problems in an inhomogeneous medium.
  9. N Krashaninikova (1955). On the unsteady motion of a gas displaced by a piston.

Funding

No external funding was declared for this work.

Conflict of Interest

The authors declare no conflict of interest.

Ethical Approval

No ethics committee approval was required for this article type.

Data Availability

Not applicable for this article.

Dr. B.N.Prasad. 2020. \u201cApproximate Analytic Solution of a Self-Similar Piston Moving in an Inhomogeneous Medium\u201d. Global Journal of Science Frontier Research - A: Physics & Space Science GJSFR-A Volume 20 (GJSFR Volume 20 Issue A6): .

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Journal Specifications

Crossref Journal DOI 10.17406/GJSFR

Print ISSN 0975-5896

e-ISSN 2249-4626

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GJSFR-A Classification: FOR Code: 240101
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v1.2

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May 30, 2020

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English

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Self-similar motion for the flow between a piston and strong shock propagating in a non uniform ideal gas at rest has been studied. The solution to the problem is similar to that of hypersonic flows past the power law bodies. The gas ahead of the shock is assumed to be uniform and at rest. This is considered as a particular case of radiative piston problem. The shock is assumed to be very strong and propagating in a medium at rest in which density obeys power laws. This problem with spherical symmetry has got importance in astrophysics. To solve the gas dynamics problem, Chernyii’s expansion techniques have been used in which flow variables are expanded in a series of powers of ε, the density ratio across the strong shock. The approximate analytic solution has been obtained in closed form to the zeroth approximation. The problem discussed belongs to the self-similar motion of the first kind. The resulting analytic solution gives the flow variables distribution for plane, cylindrical, and spherical symmetry for different cases which satisfy the similarity conditions with accurate trend and values.

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Approximate Analytic Solution of a Self-Similar Piston Moving in an Inhomogeneous Medium

Dr. B.N.Prasad
Dr. B.N.Prasad

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