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Vacuum formation behind the expansion wave in a piston motion problem.
Satoshi Taguchi1, Shigeru Takata
1Department of Mechanical Engineering and Intelligent Systems, University of Electro-Communications, Chofu, Tokyo 182-8585, Japan.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 26, 2012
Summary
High-speed piston motion in one-dimensional gas dynamics exhibits two behaviors. Below critical speed, gas approaches equilibrium; above it, a non-equilibrium vacuum forms.
Area of Science:
- Physics
- Fluid Dynamics
- Kinetic Theory
Background:
- Understanding gas behavior under extreme conditions is crucial for fluid dynamics.
- Kinetic theory provides a microscopic approach to macroscopic gas properties.
Purpose of the Study:
- To numerically investigate the long-time behavior of one-dimensional gas motion driven by a high-speed piston.
- To identify critical piston speeds that alter gas dynamics.
Main Methods:
- Numerical simulation based on the kinetic theory of gases.
- Analysis of gas properties such as density, pressure, and temperature components.
Main Results:
- At sub-critical piston speeds, gas approaches a local equilibrium, resembling isentropic solutions.
- At super-critical speeds, a highly non-equilibrium region with low pressure forms behind the expansion tail.
- Significant differences arise between parallel and perpendicular temperature components, with density vanishing to form a vacuum.
Conclusions:
- Piston speed critically determines the gas's long-time behavior, transitioning from equilibrium to non-equilibrium states.
- High-speed piston motion can induce vacuum formation and significant temperature anisotropies, deviating from classical gas dynamics.
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