Jets are a common way to transfer mass among fluids, or from a fluid to a surface. At moderate Reynolds numbers and low turbulent intensities the jet exhibits a Near Field Region (NFR) several diameters long. Numerical results and a theoretical model are presented for the passive scalar diffusion in the NFR of a submerged free jet. Large Eddy Simulations (LES), in the Reynolds number 5000-40,000 and the Schmidt number range 1-100, are performed obtaining the passive scalar fields. Three mathematical models for the passive scalar diffusion are presented; the first one is valid in the NFR, specifically in the Undisturbed Region of Flow (URF), and the other two, obtained under the hypotheses of Tollmien and Görtler momentum spreadings, are valid in the Potential Core Region (PCR). The last two models employ a turbulent Schmidt number inversely proportional to the mean velocity gradient, conclusion obtained by the LES numerical results. The self-similar solutions of the passive scalar show good agreement with the LES results. The wide range of Reynolds and Schmidt numbers investigated gives generality to the results.

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The passive scalar spreading of fluids with laminar Prandtl or Schmidt number, , Pr Sc , equal to 1 in turbulent rectangular submerged free jets is analyzed by means of numerical simulation and theoretical analysis in the Reynolds number range 5000-40,000. The numerical investigation is carried out by means of a three-dimensional (3D) Large Eddy Simulation (LES) approach with the dynamic Smagorinsky model. A new mathematical model allows to obtain a simplified description of the passive scalar spreading in the largest area of the flow field, the Fully Developed Region (FDR). The present three-dimensional (3D) investigation shows that the passive scalar spreading follows a self-similarity law in the Fully Developed Region (FDR), as well as in the mean Undisturbed Region of Flow (URF) and in the Potential Core Region (PCR), similarly to what found in the Near Field Region (NFR) of rectangular submerged free jets, investigated with a two-dimensional (2D) approach. The turbulent Prandtl or Schmidt number is evaluated numerically and is found to be inversely proportional to the mean velocity gradient in the PCR. The present 3D numerical results show that the turbulent Prandtl or Schmidt number is zero in most part of the mean URF, and PCR, while it assumes different values outside. In the FDR the turbulent Prandtl or Schmidt number is constant and approximately equal to 0.7, in agreement with the literature, showing that turbulence affects momentum and passive scalar in a different way.