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Vortex breakdown of compressible subsonic swirling flows in a finite-length straight circular pipe

Published online by Cambridge University Press:  16 September 2015

Zvi Rusak ,
Jung J. Choi ,
Nicholas Bourquard  and
Shixiao Wang
Zvi Rusak*
Affiliation:
Department of Mechanical, Aerospace and Nuclear Engineering, Rensselaer Polytechnic Institute, Troy, NY 12180, USA
Jung J. Choi
Affiliation:
Department of Mechanical, Aerospace and Nuclear Engineering, Rensselaer Polytechnic Institute, Troy, NY 12180, USA
Nicholas Bourquard
Affiliation:
Department of Mechanical, Aerospace and Nuclear Engineering, Rensselaer Polytechnic Institute, Troy, NY 12180, USA
Shixiao Wang
Affiliation:
Department of Mathematics, University of Auckland, 38 Princes Street, Auckland 1142, New Zealand
*
†Email address for correspondence: [email protected]
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Abstract

A global analysis of steady states of inviscid compressible subsonic swirling flows in a finite-length straight circular pipe is developed. A nonlinear partial differential equation for the solution of the flow stream function is derived in terms of the inlet flow specific total enthalpy, specific entropy and circulation functions. The equation reflects the complicated thermo–physical interactions in the flows. Several types of solutions of the resulting nonlinear ordinary differential equation for the columnar case together with a flow force condition describe the outlet state of the flow in the pipe. These solutions are used to form the bifurcation diagram of steady compressible flows with swirl as the inlet swirl level is increased at a fixed inlet Mach number. The approach is applied to two profiles of inlet flows, solid-body rotation and the Lamb–Oseen vortex, both with a uniform axial velocity and temperature. The computed results provide for each inlet flow profile theoretical predictions of the critical swirl levels for the appearance of vortex breakdown states as a function of the inlet Mach number, suggesting that the results are robust for a variety of inlet swirling flows. The analysis sheds light on the dynamics of compressible flows with swirl and vortex breakdown, and shows the delay in the appearance of breakdown with increase of the inlet axial flow Mach number in the subsonic range of operation. The present theory is limited to axisymmetric dynamics of swirling flows in pipes where the wall boundary layer is thin and attached and does not interact with the flow in the bulk.

JFM classification

Compressible Flows: Compressible Flows Vortex Flows: Vortex breakdown Vortex Flows: Vortex Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 781 , 25 October 2015 , pp. 3 - 27
Copyright
© 2015 Cambridge University Press 

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