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An experimental and numerical study of the viscous stability of a round laminar vertical jet with and without thermal buoyancy for symmetric and asymmetric disturbances

Published online by Cambridge University Press:  29 March 2006

J. C. Mollendorf  and
B. Gebhart
J. C. Mollendorf
Affiliation:
Engineering Research Center, Western Electric Co., Inc., Princeton, New Jersey
B. Gebhart
Affiliation:
Upson Hall, Cornell University, Ithaca, New York
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Abstract

The fully viscous hydrodynamic stability equations for a round laminar vertical jet have been numerically solved using the proper boundary-layer base-flow velocity profile and for both symmetric and asymmetric disturbances. The symmetric mode is found to be unconditionally stable. The first asymmetric mode is found to be unstable and characteristics are compared with previous calculations. The computed critical Reynolds number for this mode is 9·4, which agrees with the calculations of Burridge (1968). Disturbance amplitude-ratio contours are also calculated and related to the convection of disturbances in the flow.

The effect of thermal buoyancy on jet stability is assessed by solving the fully viscous equations, coupled through buoyancy, and using a buoyancy-perturbed jet flow. A Prandtl number σ of 6·7 is used, and positive thermal buoyancy is found to have a destabilizing effect. Stability characteristics for the limiting case of buoyancy, a purely thermal point-source plume, are determined for a Prandtl number of 2.

Finally, an experiment was performed using water jets in water (σ ≈ 4·52–5·89) and a new method of jet production is described. The effect of varying amounts of thermal buoyancy on the laminar length of a jet undergoing naturally occurring transition was determined experimentally. These experiments confirm the calculated destabilizing effect of buoyancy. An empirical correlation is presented for the laminar length of a jet. Also, the effect of both symmetric and asymmetric artificially induced disturbances was determined experimentally. The disturbance amplitude ratio at which transition to turbulence takes place is found to be much less than for buoyant flows adjacent to a wall. The effects of frequency and amplitude of the artificial disturbances were experimentally determined and the trends are found to be consistent with the results of small disturbance theory.

The principal new result is that positive thermal buoyancy destabilizes jet flow, and consequently calls into question earlier experimental studies wherein jet flows were observed by density differences. Another new result is the calculation. of amplitude-ratio contours for a non-buoyant jet and the quantitative description of jet stability in terms of these contours along paths of constant physical frequency. A comparison of the non-buoyant theory with experimental jets containing varying amounts of thermal buoyancy indicates that transition did not occur at a well-defined value of the amplitude ratio. Perhaps experiments with truly non-buoyant jets and/or more detailed buoyant calculations could explain this remaining question.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 61 , Issue 2 , 6 November 1973 , pp. 367 - 399
Copyright
© 1973 Cambridge University Press

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