The turbulent mixing of two jets of fluid of the same density is investigated theoretically by means of Prandtl’s theory of turbulence and the results compared with experiment.
A solution obtained by Tollmien for the mixing region of a plane jet, in which he considers the fluid bounding the jet at rest, is extended to the general case of the mixing of two parallel streams of different velocities. Distributions of the tangential and normal velocities in the mixing region are given. The solution is worked out for two different conditions imposed on the normal velocity at the boundary of the mixing region.
Next, the turbulent mixing region surrounding an axially symmetrical jet issuing into fluid at rest is considered. The problem is solved, as far as the core of potential flow extends, by the application of a new method of approximation. The velocity field, as determined by a second approximation to the velocity profiles, is given. An extension of the method of solution, applicable to problems in which the velocity profiles differ widely, is mentioned.
In the theory applied in this paper, the mixing length is assumed proportional to the breadth of the mixing region. The proportionality factor which is the only empirical quantity in the theory was experimentally evaluated. Velocity profiles in the mixing region of an axially symmetrical jet were measured by means of a pitot tube and good agreement is found between theory and experiment.
Measurements of velocity fluctuations in the core of potential flow near the jet mouth and in the mixing region at a distance of 9.3 diameters were made by means of the hot-wire anemometer.