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Some gas flows which obey Charles’ Law

Published online by Cambridge University Press:  11 April 2006

J. F. Clarke  and
C. A. Cooper
J. F. Clarke
Affiliation:
Department of Aerodynamics, Cranfield Institute of Technology, Bedford MK43 0AL, England
C. A. Cooper
Affiliation:
Department of Aerodynamics, Cranfield Institute of Technology, Bedford MK43 0AL, England
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Abstract

The effects of substantial temperature and hence density changes on a low-speed ‘incompressible’ flow can be modelled by adopting Charles’ Law as one of the equations of state. It is found that planar radial inflows or outflows constitute a group of solutions which are self-similar for arbitrary temperature variations. When the temperature is written as a separable function of radius and polar angle, ordinary differential equations result. Permissible solutions include some with discontinuities in the temperature gradient across a radial line (streamline); this is a rough model of a diffusion flame and it is used to illustrate some features of a variable-density flow in a channel with radial walls in the presence of such a ‘flame’.

Exact analytical solutions are given for the situation in which temperature increases linearly with radius; no boundary layers appear for either outflow or inflow. Approximate analytical solutions are presented for the case of a relatively rapid inflow with temperature independent of the radius; a velocity boundary layer exists at the walls and in the neigh bourhood of the ‘flame’, although the latter is of small velocity amplitude.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 80 , Issue 3 , 2 May 1977 , pp. 423 - 432
Copyright
© 1977 Cambridge University Press

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References

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