Assessment of Multi-Equation Mathematical Models of Turbulence in Estimation of Hydrodynamic Parameters at Submerged Jet

Three-dimensional submerged jet at a sudden expansion includes chaotic hydrodynamics. At a sudden expansion, secondary flows developed adjacent to the potential core of the jet generate turbulence, and the formed eddies cause energy transfer and dissipation and decline of fluid momentum in the zone of established flow. By utilizing an efficient mathematical model of turbulence, hydrodynamic flow parameters can be predicted with a good accuracy in various locations. This paper studies the three-equation mathematical models of turbulence, namely the Walters and Cokljat (k-kl-ω), and the seven-equation Reynolds Stress mathematical model of turbulence. Comparison between the results of computational fluid dynamics using Ansys Fluent software and experimental results shows that Reynolds Stress model of turbulence predicts the results with a higher accuracy. It can be concluded that this higher accuracy is due to the use of individual transport equations for each component of the stress tensor in the normal conditions of inhomogeneous and anisotropic turbulence.
Kinetic energy, very high fluid momentum and pressure fluctuations are among characteristic of a submerged jets at a sudden expansion. How the energy is dissipated by the flow and how the secondary flow structures are generated need an extensive research. In the submerged jets, because secondary flows are developed in the vicinity of jet potential nuclear and eddies are generated in various sizes, the energy is received from the mean flow and will be being dissipated while being transferred. The dissipation process can be observed during the interaction between stress and strain fields of fluid elements (second-order tensor interaction). Formation of eddies with different sizes and decay of them into smaller structures prompt the process of turbulence diffusion. The energy-bearing eddies formed in the vicinity of the jet potential core are displaced by convection terms. After these eddies are displaced, they experience decay and reduction in size (Kolmogorov microscale) and finally disappear. Rotational dynamics around the jet potential core is of a great importance in terms of flow kinetic energy dissipation; it is why the sudden expansion ratio is a number that represents the range of rotation. Therefore, understanding the flow behavior as well as how the resulting energy is generated and dissipated requires the flow parameters to be known. In order to predict the most accurate (closest to reality) values of the hydrodynamic parameters of a submerged jet, it is necessary to utilize an efficient mathematical model. Among the proposed models of turbulence, only the multi-equation Reynolds stress mathematical model has included anisotropy. Based on what have been stated so far, it seems that the existence of discrete transport equations for each component of stress tensor for a fluid and turbulence kinetic energy dissipation as well as comparison with experimental results provide the possibility of acceptable accuracy in predicting the flow hydrodynamic parameters. In this model, the term of turbulence kinetic energy generation from the mean flow, energy dissipation term, and pressure-strain term transferring the turbulence kinetic energy toward different directions of the coordinate axes are among the very important elements of the transport equation.