B • TURBULENT FLOW 



It appears that no basic investigations have been carried out which 

 would give us information on the turbulent structure and the boundary- 

 configuration when the surrounding medium is moving. Corrsin and 

 Kistler [117] call attention to the limiting case where a turbulent and a 

 nonturbulent stream are in contact with no mean relative velocity, and 

 infer that the diffusing mechanism will be much the same as when a rela- 

 tive velocity exists. If this is so, it follows that mixing again depends on 

 the velocity and scale of the mixing motions as determined by a relation 

 of the type of Eq. 29-1. We know that travel of the surrounding stream 

 along with the jet lessens the divergence and decay of jet velocity. In a 

 very real sense the jet fluid rides along with the outer stream and reaches 

 a distance x from the nozzle in a shorter time. Fluid has had less time to 

 diffuse and as a consequence has traveled a shorter distance laterally. 

 Correspondingly, it has had less time to mix, and it would be expected 

 that a greater distance is now required for the similarity regime to pre- 

 vail. In the absence of any firm knowledge of the turbulent structure, 

 the usual concepts are applied by investigators in this field, namely that 

 either mixing length or turbulent exchange coefficient are constant over 

 a cross section. 



Using mixing length theory for momentum transfer, Kuethe [109] in- 

 vestigated the plane mixing region between streams moving in the same 

 direction with different relative velocities and also treated the mixing 

 zone of the round jet from the nozzle to the end of the potential core 

 for the case where the outside medium is at rest. Gortler [127] later de- 

 veloped the relations for the plane mixing region between two streams 

 on the basis of a turbulent exchange coefficient given in the form of Eq. 

 29-1. Szablewski [136] then extended this method to the core-containing 

 region of the round jet for the case where the surrounding stream has 

 different velocities. Squire and Trouncer [136], using mixing length theory, 

 applied to momentum transfer developed relations for the characteristics 

 of the round jet for various velocities of the surrounding stream, including 

 both the initial core-containing region and the fully developed region. In 

 addition they calculated the inflow velocity in the region surrounding the 

 jet. All of the methods apply to incompressible, isothermal flow. 



All of the methods agree, at least qualitatively, in showing a marked 

 effect of velocity of the outer stream on the rate of jet spreading and 

 decay of velocity differences. The effect depends on the ratio Ui/Uo, 

 where Ui is the outer stream velocity and Uo is the jet exit velocity. As 

 the ratio increases, the divergence decreases, the core region extends 

 farther from the nozzle, and the velocity increments decrease more slowly 

 with X. When Ui/Uo = 0, the core region extends only to about 5 orifice 

 diameters from the nozzle. When Ui/Uo = 0.5, the distance is increased 

 to 11 diameters according to Szablewski and to 8.1 diameters according 

 to Squire and Trouncer. Each of these two methods requires that a single 



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