Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-19T06:04:17.380Z Has data issue: false hasContentIssue false
  • English
  • Français

Conically similar viscous flows. Part 3. Characterization of axial causes in swirling flow and the one-parameter flow generated by a uniform half-line source of kinematic swirl angular momentum

Published online by Cambridge University Press:  20 April 2006

R. Paull  and
A. F. Pillow
R. Paull
Affiliation:
Department of Mathematics, University of Queensland
A. F. Pillow
Affiliation:
Department of Mathematics, University of Queensland
Get access Rights & Permissions [Opens in a new window]

Abstract

In Part 1 of this series conservation principles for ring circulation and kinematic swirl angular momentum were developed for general axisymmetric incompressible viscous flow. These principles were then used to classify the four independent axial causes of swirl-free conically similar viscous flow. Part 2 provided a detailed analysis of the one-parameter swirl-free flows that are generated by each one of the axial singularities acting alone. The present paper extends, to swirling flow, the description of the axial singularities that drive axisymmetric viscous flow. In the special case of conically similar viscous flow, two independent half-line sources of swirl angular momentum suffice to complete the set of axial singularities that can generate such swirling flows. The individual strengths of the six independent axial causes provide a complete characterization of all conically similar viscous flows that can be generated in this way. This Part 3 completes the task of analysing in detail the independent one-parameter flows generated by axial causes by studying the flow caused by uniform production of kinematic swirl angular momentum on a half-axis. This flow demonstrates how swirl may induce an axial half-plane flow. For large swirl circulation strengths, swirl angular momentum diffuses and convects so as to fill slightly more than half the space with an almost constant density of swirl angular momentum. A well-developed internal boundary layer, in the form of an outward radial jet, then separates this region from one in which the flow is almost irrotational. The jet entrains two impinging convection fields. The angular location of the jet is determined by relating the axial component of moment of whirl produced at the origin to the strength of the swirling circulation singularity on the axis.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 155 , June 1985 , pp. 359 - 379
Copyright
© 1985 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Gol'dshtik, M. A. 1960 A paradoxical solution of the Navier–Stokes equations. Prikl. Math. Mekh. 24, 610–621.Google Scholar
Hoffmann, J. A. 1974 Similarity solutions for the interaction of a potential vortex with free stream sink flow and a stationary surface. Trans. ASME I: J. Fluids Engng 96, 49–54.Google Scholar
Kidd, G. J. & Farris, G. J. 1968 Potential vortex flow adjacent to a stationary surface. Trans. ASME E: J. Appl. Mech. 35, 209–215.Google Scholar
Paull, R. & Pillow, A. F. 1985 Conically similar viscous flows. Part 2. One-parameter swirl-free flows. J. Fluid Mech. 155, 343–358.Google Scholar
Pillow, A. F. & Paull, R. 1985 Conically similar viscous flows. Part 1. Basic conservation principles and characterization of axial causes in swirl-free flow. J. Fluid Mech. 155, 327–341.Google Scholar
Schwiderski, E. W. 1969 On the axisymmetric vortex flow over a flat surface. Trans. ASME E: J. Fluid Mech. 36, 614–619.Google Scholar
Serrin, J. 1972 The swirling vortex. Phil. Trans. R. Soc. Lond. A 271, 325–360.Google Scholar
Whang, Y. C. 1968 Laminar diffusion flame in the core of the vortex. Phys. Fluids 11, 31–37.Google Scholar
Wygnanski, I. 1970 Swirling axisymmetrical laminar jet. Phys. Fluids 13, 2455–2460.Google Scholar
Yih, C.-S., Wu, F., Garg, A. K. & Leibovich, S. 1982 Conical vortices: a class of exact solutions of the Navier–Stokes equations. Phys. Fluids 25, 2147–2158.Google Scholar