B • TURBULENT FLOW 



files. However, the density difference was not large after the distance of 

 7 or 8 nozzle diameters required for the flow to become fully developed. 

 For example, at 15 diameters pi/pc = 1.3 when pi/po = 2. For a density 

 ratio of this order there is no essential departure from similarity in any 

 of the profiles, so that the spread is found to be proportional to x and 

 the decrease of velocity and temperature along the axis is found to be 

 inversely proportional to x. 



Cleeves and Boelter [128] made measurements of velocity and tem- 

 perature in a round jet with an initial temperature difference of 650°C. 

 The jet issued vertically from a pipe 1-g- inches in diameter at velocities 

 ranging from 13 to 56 ft/sec. They did not detect any difference in the 

 radial velocity distribution between the isothermal jet and the hot jet. 

 In short, they found no effect of the decreased density on the rate of 

 spreading of the jet. This disagrees with the results of Corrsin and Uberoi. 

 They did, however, find the velocity on the axis decreased more for the 

 hot jet than for the isothermal jet. The decrease was greater than that 

 found by Corrsin and Uberoi, as would be expected from the higher tem- 

 perature, but their isothermal results for the velocity on the axis do not 

 agree with those of Corrsin and Uberoi. The Corrsin and Uberoi results 

 should perhaps be given the greater weight in view of the accurate con- 

 trol over experimental conditions. 



Since high relative velocities, and the compressibility and heating 

 effects associated with them, are generally found close to a nozzle, the 

 magnitude of these effects is of most interest in connection with the 

 mixing-zone problem. Abramovich [129] investigated the effects by apply- 

 ing the vorticity transfer version of mixing length theory to the plane 

 mixing zone between a stream of uniform velocity and a medium at rest, 

 restricting the treatment to air speeds up to Mach number unity and 

 temperature differences up to 120°C. He found that cooling the stream 

 increased the width of the mixing zone, with the boundary on the stream 

 side showing practically all of the effect. The effect of increasing the ve- 

 locity was to decrease the width of the mixing zone, again with only the 

 boundary on the stream side being affected. However, the predicted 

 effects were such that practically identical velocity distributions were 

 indicated if on the one hand a low speed stream is cooled to AT = — 60°C 

 and on the other hand a stream of Mach number unity has a stagnation 

 temperature equal to that of the stationary medium (static temperature, 

 AT" = — 60°C). Thus a jet cooled either by extraction of heat or by adi- 

 abatic expansion will have a more rapidly diverging mixing region than 

 a jet having the same static temperature as the surrounding medium. 

 This would not be consistent with the findings of Corrsin and Uberoi. 



Gooderum, Wood, and Brevoort [ISO] measured the density distribu- 

 tion with an interferometer in the mixing zone of a jet issuing from a 

 3 by 3-inch nozzle at a Mach number of 1.6. The stagnation temperature 



( 178 > 



