Passive scalar diffusion in three-dimensional turbulent rectangular free jets with numerical evaluation of turbulent Prandtl/Schmidt number

Abstract

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.

Influence of grid resolution on the spectral characteristics of noise radiated from turbulent jets: Sound pressure fields and their decomposition

“…Standard models with constant coe cient are usually too dissipative in the initial free shear layer of the jet, thus delaying its transition. Dynamic models can overcome this issue [50][51][52][53], potentially at the price of stability, which is not always desirable when simulating complex flows. This is one reason why implicit LES (or ILES) has been widely adopted in the literature [21,54,55], since the absence of excessive SGS viscosity allows accurate capture of the jet behaviour, especially near the nozzle.…”

Large eddy simulation and self-similarity analysis of the momentum spreading in the near field region of turbulent submerged round jets

“…Self-similar laws for the momentum spreading in turbulent jets have been proposed in the past, as Tollmien (1926), Kuethe (1935), Zel'dovich (1937, Görtler (1942), Batchelor (1954, Angelino et al (2016), Boghi et al (2016), also if several papers have concluded of its impossible formulation, and can be exemplified by Tennekes and Lumley (1963). Self-similar solutions for the passive scalar diffusion in turbulent jets have been proposed, as well, in Boghi et al (2017) and Di Venuta et al (2018a).…”

Numerical simulation and self-similarity of the mean mass transfer in turbulent round jets

“…Self-similarity in passive scalar spreading was studied with DNS in [17]. The mean passive scalar was found self-similar in the FDR, with the Large Eddy Simulation (LES) approach, for round [18] and planar jets [19].…”