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ABSTRACT
The evolution of turbulent rectangular submerged free jets is described in the literature by the presence of two regions of flow: the potential core region (PCR) and the fully developed region (FDR). However, experiments carried out in the last decade showed that a third region of flow is present, the undisturbed region of flow (URF), so-called in the average visualization, or the negligible disturbances flow (NDF) plus the small disturbances flow (SDF), so-called in the instant visualization. The URF is located between the slot exit and the beginning of the PCR. The main characteristics of URF, and NDF, are that velocity and turbulence profiles remain almost equal to those measured on the slot exit, and the height of the jet remains equal to the slot one. In the SDF the jet height undergoes small variations, i.e., contractions or expansions, but without formation of the vortex. To date, no numerical evidence of the presence of URF has been given by the literature. The present study, which concerns a two-dimensional jet, presents Large Eddy Simulations (LES), carried out at four Reynolds numbers, which are able to predict and characterize URF. The present numerical results are compared to previous theoretical approaches and confirm the presence of URF, between the slot exit and the PCR. Moreover, URF has a self-similar behavior and a new law for the evolution of the momentum is proposed.
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 |
| Δ | = | 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 |
| Δ | = | 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 |