Reynolds analogy for the Rayleigh problem at various flow modes

A. A. Abramov and A. V. Butkovskii
Phys. Rev. E 94, 013110 – Published 18 July 2016

Abstract

The Reynolds analogy and the extended Reynolds analogy for the Rayleigh problem are considered. For a viscous incompressible fluid we derive the Reynolds analogy as a function of the Prandtl number and the Eckert number. We show that for any positive Eckert number, the Reynolds analogy as a function of the Prandtl number has a maximum. For a monatomic gas in the transitional flow regime, using the direct simulation Monte Carlo method, we investigate the extended Reynolds analogy, i.e., the relation between the shear stress and the energy flux transferred to the boundary surface, at different velocities and temperatures. We find that the extended Reynolds analogy for a rarefied monatomic gas flow with the temperature of the undisturbed gas equal to the surface temperature depends weakly on time and is close to 0.5. We show that at any fixed dimensionless time the extended Reynolds analogy depends on the plate velocity and temperature and undisturbed gas temperature mainly via the Eckert number. For Eckert numbers of the order of unity or less we generalize an extended Reynolds analogy. The generalized Reynolds analogy depends mainly only on dimensionless time for all considered Eckert numbers of the order of unity or less.

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  • Received 14 October 2015
  • Revised 26 May 2016

DOI:https://doi.org/10.1103/PhysRevE.94.013110

©2016 American Physical Society

Physics Subject Headings (PhySH)

Fluid Dynamics

Authors & Affiliations

A. A. Abramov* and A. V. Butkovskii

  • Central Aerohydrodynamic Institute (TsAGI) 1, Zhukovsky street, 140180 Zhukovsky, Russia

  • *alabr54@mail.ru
  • albutkov@mail.ru

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Issue

Vol. 94, Iss. 1 — July 2016

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