Interaction of shock and discontinuity waves at the stellar surfaces

A self-similar model of gas dynamics and heat transfer behind the shock wave was developed with allowance for the effects of slippage and dissipation. The model takes into account the impact of the following factors: shock wave intensity ( U∞/ Us), physical properties (Prandtl number Pr), thermodynamic gas properties (van der Waals numbers Wa a, Wa b), slippage effects (Knundsen number Kn), and dissipation (Brinkman number Br), as well as the relation of the temperatures of the flow and the wall ( T0/ Tw). The numerical solution was performed with the help of MATLAB software, as well as an in-house code written using the programming language C++ to verify the accuracy of calculations. The study demonstrated that for the case at hand, the Reynolds analogy holds under the influence of all mentioned factors provided that Pr = 1, except for the conditions when the effects of mechanical energy dissipation become significant. The paper presents the results of calculations of the velocity and temperature profiles, friction, and heat transfer coefficients (Nusselt numbers).

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Self-similar analysis of gas dynamics for van der Waals gas in slipping flow after normal shock wave

Авраменко

Shevchuk

Kovetskaya

et al. 2023

Physics of Fluids

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Lie group transformation method for shock wave in rotating non-ideal gas with or without magnetic field, and interaction of characteristic shock with weak discontinuity

Nath,

Kadam

2023

Physics of Fluids

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An analytical solution for power-law shock paths and a numerical solution for exponential-law shock paths to the system of equations that describes a cylindrical shock wave in a rotating non-ideal gas with or without an axial magnetic field is determined by utilizing the Lie group invariance method. In an undisturbed medium, the axial magnetic field and azimuthal fluid velocity are meant to be variable; however, the density is taken to be constant. The liberty to choose the value of arbitrary constants that are in the equation for an infinitesimal generator gives rise to three different cases, i.e., the power law, a particular case of the power law, and the exponential-law shock paths. In the power-law case, a particular solution in an analytical form is obtained, while for an exponential-law case, a numerical solution is obtained. By considering this analytical solution, the development of the characteristic shock and its interaction with a weak discontinuity are also discussed. The effects of the rotational and non-idealness parameters on the characteristic shock and on the acceleration wave's amplitude are discussed. The expressions for the jump in shock acceleration and the amplitude of the transmitted and reflected wave are obtained.

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How do various forces affect pressure waves in bubbly flows?

Arai,

Kanagawa

2024

Physics of Fluids

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This study investigated the weakly nonlinear propagation of pressure waves in compressible, flowing water with spherical microbubbles, considering various forces. Previous theoretical studies on nonlinear pressure waves in bubbly flows did not consider the forces acting on the bubbles, although the validity of ignoring these forces has not been demonstrated. We focused on every possible force such as drag, gravity, buoyancy, and Bjerknes (acoustic radiation) forces acting on bubbles and studied their effects on pressure waves in a one-dimensional setting. Using a singular perturbation method, the Korteweg–de Vries–Burgers equation describing wave propagation was derived. The following results were obtained: (i) Bjerknes force on the bubbles enhanced the nonlinearity, dissipation, and dispersion of the waves; (ii) Drag, gravity, and buoyancy forces acting on the bubbles increased wave dissipation; (iii) Thermal conduction had the most substantial dissipation effect, followed by acoustic radiation, drag, buoyancy, and gravity. We confirmed that the dissipation due to forces on gas bubbles was quantitatively minor.

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Interaction of shock and discontinuity waves at the stellar surfaces

Cited by 5 publications

References 17 publications

Self-similar analysis of gas dynamics for van der Waals gas in slipping flow after normal shock wave

Self-similar analysis of gas dynamics for van der Waals gas in slipping flow after normal shock wave

Lie group transformation method for shock wave in rotating non-ideal gas with or without magnetic field, and interaction of characteristic shock with weak discontinuity

How do various forces affect pressure waves in bubbly flows?

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