Investigations of Turbulent Mixing Regions

Abstract

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. The mixing length is assumed proportional to the breadth of the mixing region with a proportionality constant which is the only empirical constant in the theory. In Part II 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 streams of different velocities separated initially by a plane surface. Distributions of the tangential and normal velocities in the mixing region are given. Part III deals with the turbulent mixing region surrounding axially symmetric jet issuing into fluid at rest. The problem is solved, as far as the core of potential flow extends, by the application of a new method of approximation directly to the partial differential equation of motion. 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 Part IV the empirical constant occurring in the assumption for the mixing length is evaluated. Velocity profiles in the mixing region of an axially symmetric jet were measured by means of a pitot tube and good agreement is found between theory and experiment. Finally, some measurements or the velocity fluctuations, made by means of the hot-wire anemometer, are given.