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On the Decay of Laminar Jets in Ambient Streams

Published online by Cambridge University Press:  07 June 2016

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

Earlier analysis, Middleton, of the laminar discharge of a ‘strong’ incompressible jet, due to a line or point source of momentum, into an unbounded co-flowing stream of the same density, is extended to the case of plane and round ‘weak’ jets the velocity in which only slightly exceeds the ambient velocity. In addition to recovering Goldstein’s solutions for ‘wake-like’ flows, use of the momentum integral equation provides approximate relationships for the decay of the centre velocities from the strong to the weak situations. Comparison is made with Wygnanski’s perturbation approach, suitably extended, and it is concluded that for the plane jet case, for which the agreement is better, the curve for the centre-plane velocity is correct to within about 12% throughout its range. The present approach is applicable to any flow for which a similarity solution exists as a first order solution, and is especially suitable when two such solutions exist for large and small values of an appropriate parameter. Its use also throws light on the form to be adopted for a perturbation expansion.

Type
Research Article
Information
Aeronautical Quarterly , Volume 32 , Issue 2 , May 1981 , pp. 83 - 96
Copyright
Copyright © Royal Aeronautical Society. 1981

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References

1 Middleton, D. The generalization of a double integral method with applications to jets in unbounded co-flows. Aeronautical Quarterly, Vol. 30, p 322, 1979.CrossRefGoogle Scholar
2 Goldstein, S. On the two-dimensional steady flow of a viscous fluid behind a solid body. Proceedings of the Royal Society, Series A, Vol. 124, p 545, 1933.Google Scholar
3 Wygnanski, I. The two-dimensional laminar jet in parallel streaming flow. Journal of Fluid Mechanics, Vol. 27, p 431, 1967.CrossRefGoogle Scholar
4 Bickley, W.G. The plane jet. Philosophical Magazine, Series 7, Vol. 23, p 727, 1937.Google Scholar
5 Schlichting, H. Laminare Strahlausbreitung. Zeitschrift für Angewandte Mathematik und Mechanik, Vol. 13, p 260, 1933.CrossRefGoogle Scholar