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The laminar and turbulent mixing of jets of compressible fluid. Part II The mixing of two semi-infinite streams

Published online by Cambridge University Press:  28 March 2006

L. J. Crane
L. J. Crane
Affiliation:
Department of Mathematics, The Royal College of Science and Technology, Glasgow
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Abstract

This paper presents the application of the methods developed in a previous paper (Part I, Crane & Pack 1957) to the mixing of two parallel streams for both laminar and turbulent flows. The effects of both high velocity and large temperature difference are treated together. The method used consists in developing the stream function in a double series of powers of two parameters, the first being the Mach number and the second depending on the temperature difference of the streams. Analytical expressions are found for the terms up to the second order in the series for the stream function when the streams do not differ too greatly in velocity and temperature. However, when one of the streams is at rest the analytical method is no longer sufficiently accurate, and for this case numerical solutions are given.

For laminar mixing the most important effect is that of ’change of scale’, as was found in Part I for a laminar jet at large distances from the orifice. For turbulent half-jets the effect of ’change of scale’ and the effect of the perturbation terms due to the Mach number of the flows are approximately equal and opposite, leaving the form of the velocity profile sensibly unchanged from that in incompressible flow. This last result is confirmed by comparison with some experiments of Laurence (1955) on a two-dimensional jet at M = 0·7. Lastly, the effect of temperature differences is shown to be relatively unimportant even when these are fairly considerable.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 3 , Issue 1 , October 1957 , pp. 81 - 92
Copyright
© 1957 Cambridge University Press

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References

Crane, L. J. & Pack, D. C. 1957 J. Fluid Mech. 2, 449.
Görtler, H. 1942 Z. angew. Math. Mech. 22, 244.
Johannesen, N. H. 1957 Aero. Res. Counc., Lond., Unpub. Rep. no. 18967.
Laurence, J. C. 1955 Nat. Adv. Comm. Aero., Wash., Tech. Note no. 3561.
Lessen, M. 1949 Nat. Adv. Comm. Aero., Wash., Tech. Note no. 1929.
Lock, R. C. 1951 Quart. J. Mech. Appl. Math. 4, 42.
Pai, S. I. 1954 Fluid Dynamics of Jets. Princeton: Van Nostrand.