Velocity and Concentration Distributions of Round and Plane Turbulent Jets

Abstract

The analytical solutions for the velocity distribution of turbulent round and plane jets described in the classical textbook of Schlichting (Boundary Layer Theory 7th edition (1979)) based on boundary-layer approximations are well-known, and have provided the fundamental understanding of the mechanics of turbulent jets. However, the scaling coefficients involved were not well quantified as discussed recently by Mathieu and Scott (An Introduction to Turbulent Flow(2000)). In this paper, it is shown that the coefficients can be better determined by the available experimental measurements in the literature. Furthermore, by assuming that the turbulent diffusivity relates to the eddy viscosity, it is shown that closed-form analytical solutions can also be obtained for the scalar concentration distribution in addition to the velocity distribution. The turbulent Schmidt number is found to be less than 1 for both plane and round jets, and close to the isotropic turbulence value of 0·7 in the round jet case.