TITLE:
Compressible and Choked Flows in Rotating Passages
AUTHORS:
Nolan J. Dyck, Anthony G. Straatman
KEYWORDS:
Compressible Flows, Rotational Flows
JOURNAL NAME:
Open Journal of Fluid Dynamics,
Vol.9 No.1,
February
15,
2019
ABSTRACT: The present study revisits the rotating duct problem examined by Polihronov
and Straatman (J. Polihronov and A. G. Straatman, Phys. Rev. Lett. v. 109, p.
054504 (2012)). Starting from the general compressible Euler equations in a
non-stationary reference frame closed form expressions for velocity, temperature,
density and pressure along the duct are determined. The present results
are more general than those obtained by Polihronov and Straatman, as the
change of in-frame kinetic energy has been retained. The improvement of
the present results over Polihronov and Straatman’s is demonstrated by
comparison with the results of a computational fluid dynamics study. The
new results have been further generalized to the case of a rotating duct with
varying cross-sectional area, and again for a general curved passage in
three-dimensional space. The work required or derived from the rotating
duct has also been computed. The choked flow condition within the passage
of varying cross-sectional area has been identified, along with the constraints
which must be placed on the Mach, Rossby, and tip Mach numbers to avoid
choked flow. Finally, a straightforward technique to identify any locations
where an ideal rotating flow in a constrained passage will become sonic has
been presented.