Flow evolution and mass transfer in a turbulent rectangular free jet of air with small laminar Schmidt number

Numerical results are presented for flow evolution, mass transfer and evaluation of the turbulent Schmidt number in a turbulent submerged free jet of air with small laminar Schmidt number (Sc = 0.1). A series of Large Eddy Simulation (LES) are carried on in the Reynolds number range from 5000 to 40,000. The numerical results are reported in terms of instantaneous and mean velocities, static pressure, passive scalar fields and turbulent Schmidt number. The numerical results show that the instantaneous cross-stream velocity and the static pressure are null in the Negligible Disturbance Flow (NDF) and the Small Disturbance Flow (SDF) of the instantaneous jet evolution, allowing a new definition of NDF and SDF. Similarly, the numerical mean static pressure is null in the Undisturbed Region of Flow (URF) of the mean evolution, allowing a new definition of URF. The turbulent Schmidt number shows differences at the two smallest Reynolds numbers, Re = 5000 and 10,000, in comparison to the previous numerical results, obtained with a laminar Schmidt number equal to Sc = 1. A theoretical model is proposed for the passive scalar diffusion in the Undisturbed Region of Flow (URF) and the Potential Core Region (PCR), under the hypotheses of self-similarity, according to the Tollmien and Gortler approaches. The solutions of the present theoretical models, at Sc = 0.1, are self-similar in the PCR and in good agreement with the LES numerical results of the passive scalar, while the passive scalar profiles are not self-similar in the URF at the smaller Reynolds numbers, differently from what happens with a laminar Schmidt number in the range 1-100. The theoretical model assumes a turbulent Schmidt number inversely proportional to the mean velocity gradient in the PCR, as suggested by the LES results. The numerical results of the Sc-T in the URF are variable in the range 0-0.85, which is a value commonly suggested in the literature. In the PCR the values of Sc-T are variable between zero and a maximum which is one order of magnitude greater than in the URF.