(ii) 

 (iii) 



B • TURBULENT FLOW 



Formulas Symbols 



r^i ^ — 4- 4- 1 9X Ui = velocity of surrounding stream 



D Uo = exit velocity of jet at nozzle 



U. - Ui _ 5 X = Ui/Uo 



Uo — Ui X X = axial distance from end of 



2r^ _ /^Y~^ nozzle 



D \xj Xo = distance to end of potential 



(iv) ^ ~ ^1 =-(l + cos ^^ ^ ^^^^ 



Uc — Ui 2 \ 2rmv/ Uo = center line velocity of jet for 



X > Xo 



D = diameter of nozzle 

 r = radial distance from axis 

 U = velocity at r 



Tmv = radius where U = ' — - 



It is noted that formula (i) for the case where X = does not agree 

 with the one given by Hinze and van der Hegge Zijnen, which is 



C/e 6.39 



Reference should be made to Pai's book \111, p. 120] for another form of 

 (ii) and further discussion of the effect of a surrounding stream. 



Turning next to the heated jet in a surrounding stream, we have the 

 problem of the combined effects of a stream velocity and density differ- 

 ences on the velocity and temperature fields. Some experimental infor- 

 mation on the temperature field of the round jet in a supersonic stream 

 was obtained by Rousso and Baughman \1S7\ in connection with an 

 NACA program on jets aimed primarily at answering certain engineer- 

 ing problems. The only known account of work attempting to solve the 

 transfer problem is the paper by Szablewski \1S8\ in which a theoretical 

 development is given, and the experimental work of Pabst \1S9\ is dis- 

 played as a test of the theory. The analysis applies specifically to the 

 round jet and includes large density differences. It does not include the 

 case where the surrounding air is stationary. 



It is left to the reader to consult [i55] for the lengthy analytical 

 development and the complete results. In brief, Szablewski bases his 

 development on turbulent exchange coefficients given by the Prandtl ex- 

 pression (Eq. 29-1). These are introduced into the usual equations ex- 

 pressed in the form of continuity equations for mass, momentum, and 

 heat. The ratio of the exchange coefficient for momentum to that for heat 

 and mass (the turbulent Prandtl number, Fr^ was taken to be 0.5 on 



( 182 ) 



