Hostname: page-component-586b7cd67f-l7hp2 Total loading time: 0 Render date: 2024-11-28T18:06:02.993Z Has data issue: false hasContentIssue false
  • English
  • Français

The Generalization of a Double Integral Method with Applications to Jets in Unbounded Co-Flows

Published online by Cambridge University Press:  07 June 2016

D. Middleton
D. Middleton*
Affiliation:
Department of Theoretical Mechanics, University of Nottingham
Get access

Summary

The ‘double integral’ method, employed by Squire and Trouncer to calculate the flow of a round turbulent jet in a moving stream, is generalised. Representation of the velocity profile in simple form and use of an arbitrary upper limit of integration in the second application of the momentum integral equation permits the recovery of the well-known similarity solutions for plane and axi-symmetric laminar jets issuing into a quiescent medium. Additionally, an approximation for the decay of centre-line velocity is obtained for the non-similar situation when there is an ambient co-flowing stream. This agrees well with Wygnanski’s perturbation solution for the plane laminar jet. The results of Squire and Trouncer are re-examined in the light of this generalised approach. The work has application to the operation of fluidic sensors.

Type
Research Article
Information
Aeronautical Quarterly , Volume 30 , Issue 1 , February 1979 , pp. 322 - 342
Copyright
Copyright © Royal Aeronautical Society. 1979

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

1 Squire, H.B. and Trouncer, J. Round Jets in a General Stream. Aeronautical Research Council Reports and Memoranda 1974, 1944.Google Scholar
2 Wygnanski, I. The Two-Dimensional Laminar Jet in Parallel Streaming Flow. Journal of Fluid Mechanics, Vol. 27, p 431, 1967.CrossRefGoogle Scholar
3 Schlichting, H. Laminare Strahlausbreitung. Zeitschrift fur Angewandte Mathematik und Mechanik, Vol. 13, p 260, 1933.Google Scholar
4 Bickley, W.G. The Plane Jet. Philosophical Magazine, series 7, Vol. 23, p 727, 1937.Google Scholar
5 Goldstein, S. Modern Developments in Fluid Mechanics. Vols. 1 & 2, Oxford U.P., 1938.Google Scholar
6 Tollmein, W. Berechnung Turbulenter Ausbreitungsvorgänge. Zeitschrift für Angewandte Mathematik und Mechanik, Vol. 6, p 468, 1926.Google Scholar
7 Pozzi, A. and Sabatini, B. Plane Jets in a Moving Medium. American Institute of Aeronautics and Astronautics Journal, Vol. 1, p 1426, 1963.Google Scholar
8 Korobko, V.I. and Fal’kovich, S.V. Non-Self Similar Problems of Jet Flow Theory. Izv. AN SSSR. Mekhanika Zhidkosti i Gaza, Vol. 5, p 80, 1970.Google Scholar
9 Kuethe, A. Investigation of the Turbulent Mixing Regions Formed by Jets. Journal of Applied Mathematics, Vol. 2, p A-87, 1935.Google Scholar
10 Gartshore, I.S. and Newman, B.G. The Turbulent Wall Jet in an Arbitrary Pressure Gradient. Aeronautical Quarterly, Vol. 20, p 25, 1969.CrossRefGoogle Scholar
11 Patel, R.P. Turbulent Jets and Wall Jets in Uniform Streaming Flow. Aeronautical Quarterly, Vol. 22, p 311, 1971.Google Scholar
12 Forstall, W. and Shapiro, A.H. Momentum and Mass Transfer in Coaxial Gas Jets. Journal of Applied Mechanics, Vol. 17, p 399, 1950.Google Scholar
13 Tanney, J.W. Three Fluidic Sensors Using Unbounded Turbulent Jets. Paper R1, Fourth Cranfield Fluidics Conference, Coventry 1970.Google Scholar