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ABSTRACT
The evolution of turbulent rectangular submerged free jets has been investigated numerically with a two-dimensional (2D) approach by the present authors and, by using the large eddy simulations (LES) at several Reynolds numbers. The average numerical results confirmed the presence of the undisturbed region of flow (URF) located between the slot exit and the beginning of the potential core region (PCR) previously observed experimentally at the University of Rome “Tor Vergata” by Gori and coworkers. The 2D study of the present authors carried out under the conditions previously investigated in the literature, showed that the URF has a self-similar behavior, and proposed a new law for the evolution of the momentum. The present paper extends the LES to three-dimensional (3D) rectangular submerged free jets, in the range from Re = 5,000 to Re = 40,000, showing that the self-similar behavior of URF is also present in the 3D numerical simulations, as well as in the PCR and in the fully developed region (FDR).
Nomenclature
| Latin | = | |
| a | = | generic field or similarity coefficient |
| c | = | Tollmien coefficient |
| D | = | diameter |
| e | = | Görtler coefficient |
| f | = | similarity function |
| g | = | spatial filter function |
| h | = | dimensionless half-height of the slot |
| H | = | dimensional height of the slot |
| k | = | kinetic energy |
| p | = | instantaneous static pressure |
| P | = | mean static pressure |
| Re | = | Reynolds number |
| S | = | shear rate |
| t | = | time |
| u | = | instantaneous axial velocity |
| U | = | mean axial velocity |
| v | = | instantaneous cross-stream velocity |
| V | = | mean cross-stream velocity |
| v | = | instantaneous cross-stream velocity |
| x | = | streamwise coordinate |
| y | = | cross-stream coordinate |
| Greek | = | |
| δ | = | identity tensor |
| ▵ | = | filter width |
| ζ | = | Tollmien similarity variable |
| η | = | similarity variable |
| ν | = | kinematic viscosity |
| ξ | = | Görtler similarity variable |
| τ | = | sub-grid stress tensor |
| ψ | = | stream-function |
| Ψ | = | stream-function of Tollmien and Görtler |
| Ω | = | domain dimension |
| Subscripts | = | |
| 0 | = | initial |
| h | = | hydraulic |
| in | = | inlet |
| sgs | = | sub-grid scale |
| T | = | turbulent |
Nomenclature
| Latin | = | |
| a | = | generic field or similarity coefficient |
| c | = | Tollmien coefficient |
| D | = | diameter |
| e | = | Görtler coefficient |
| f | = | similarity function |
| g | = | spatial filter function |
| h | = | dimensionless half-height of the slot |
| H | = | dimensional height of the slot |
| k | = | kinetic energy |
| p | = | instantaneous static pressure |
| P | = | mean static pressure |
| Re | = | Reynolds number |
| S | = | shear rate |
| t | = | time |
| u | = | instantaneous axial velocity |
| U | = | mean axial velocity |
| v | = | instantaneous cross-stream velocity |
| V | = | mean cross-stream velocity |
| v | = | instantaneous cross-stream velocity |
| x | = | streamwise coordinate |
| y | = | cross-stream coordinate |
| Greek | = | |
| δ | = | identity tensor |
| ▵ | = | filter width |
| ζ | = | Tollmien similarity variable |
| η | = | similarity variable |
| ν | = | kinematic viscosity |
| ξ | = | Görtler similarity variable |
| τ | = | sub-grid stress tensor |
| ψ | = | stream-function |
| Ψ | = | stream-function of Tollmien and Görtler |
| Ω | = | domain dimension |
| Subscripts | = | |
| 0 | = | initial |
| h | = | hydraulic |
| in | = | inlet |
| sgs | = | sub-grid scale |
| T | = | turbulent |