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Generalized Knudsen Number for Unsteady Fluid Flow.

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Unsteady gas flow scaling is explored. A new dimensionless parameter, the unsteady flow Knudsen number, unifies experimental data by accounting for finite size and high strain rate effects, rooted in Galilean invariance.

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Area of Science:

  • Fluid dynamics
  • Statistical mechanics
  • Non-equilibrium thermodynamics

Background:

  • The Navier-Stokes equations, a cornerstone of fluid dynamics, are based on continuum and local equilibrium assumptions.
  • These assumptions break down in rarefied gases or under high strain rates, necessitating alternative descriptions.
  • Unsteady flows generated by oscillating bodies present unique challenges to existing fluid dynamic models.

Purpose of the Study:

  • To investigate the scaling behavior of unsteady gas flows generated by an oscillating body.
  • To identify the physical mechanisms responsible for the failure of Navier-Stokes equations in rarefied gases.
  • To develop a unified scaling parameter for unsteady rarefied gas flows.

Main Methods:

  • Experimental manipulation of an oscillating body in a gas.
  • Independent variation of the body's linear dimension and oscillation frequency.
  • Analysis of flow behavior as gas rarefaction is systematically increased.

Main Results:

  • Two distinct physical mechanisms for Navier-Stokes failure were identified: breakdown of the continuum hypothesis (finite size effects) and violation of local equilibrium (high strain rate).
  • All experimental data were successfully collapsed using a single dimensionless scaling parameter.
  • This parameter, a proposed Knudsen number for unsteady flow, incorporates both linear dimension and frequency.

Conclusions:

  • A unified scaling parameter, the unsteady flow Knudsen number, effectively describes the transition from Navier-Stokes to kinetic flow regimes.
  • This parameter is fundamentally linked to Galilean invariance, providing a theoretical basis for the observed scaling.
  • The study offers a new perspective on rarefied gas dynamics and the limits of continuum fluid mechanics.