Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-18T22:18:38.359Z Has data issue: false hasContentIssue false
  • English
  • Français

Unsteady, viscous, circular flow

I. The line impulse of angular momentum

Published online by Cambridge University Press:  28 March 2006

Merwin Sibulkin
Merwin Sibulkin
Affiliation:
Convair Scientific Research Laboratory, San Diego
Get access Rights & Permissions [Opens in a new window]

Abstract

In this paper a study of the energy-transfer processes associated with the motion of a viscous, heat-conducting fluid is begun. The class of motions considered are unsteady, two-dimensional, vortical flows. After developing simplified equations of motion and energy appropriate to this type of flow in the low Mach-number limit, general solutions of the momentum equations are presented.

The concept of a line impulse of angular momentum is introduced as an example of this class of motions for which a solution of the energy field is obtainable in closed form. The solution for the line impulse can be viewed as a combination of velocity, pressure, and temperature waves concurrently radiating from the origin of the impulse and decaying with time. Particular examples of the development of the energy field of the impulse in both liquids and gases are presented for selected values of Prandtl number. The energy-transfer processes are discussed in some detail, and the resulting differences in the energy fields for liquid gases are emphasized.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 11 , Issue 2 , September 1961 , pp. 291 - 308
Copyright
© 1961 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

Carslaw, H. S. & Jaeger, J. C. 1959 Conduction of Heat in Solids, 2nd edn. Oxford University Press.
Erdelyi, A., Magnus, W., Oberhettinger, F. & Tricomi, F. G. 1954 Tables of Integral Transforms, Vol. 1. New York: McGraw-Hill.
Howarth, L. (ed.) 1953 Modern Developments in Fluid Dynamics, High Speed Flow, Vol. 1. Oxford University Press.
Jahnke, E. & Emde, F. 1945 Tables of Functions. New York: Dover.
Keenan, J. H. 1941 Thermodynamics. New York: John Wiley.
Mcleod, A. R. 1922 The unsteady motion produced in a uniformly rotating cylinder of water by a sudden change in the angular velocity of the boundary. Phil. Mag., 44, 1–14.CrossRefGoogle Scholar
Pai, S-I. 1956 Viscous Flow Theory. I. Laminar Flow. Princeton: Van Nostrand.
Sibulkin, M. 1960 Unsteady, viscous, circular flow. Part I. The line impulse of angular momentum. Convair Sci. Res. Lab., San Diego, Res. Note no. 39.Google Scholar
Taylor, G. I. 1918 On the dissipation of eddies. Adv. Comm. Aero., Lond., Rep. and Mem. no. 598. (Available in Batchelor, G. K. (ed.) 1960, The Scientific Papers of G. I. Taylor, Vol. II, p. 96. Cambridge University Press.)Google Scholar