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ABSTRACT
A computation of turbulent natural convection in enclosures with the elliptic-blending based differential and algebraic flux models is presented. The primary emphasis of the study is placed on an investigation of accuracy of the treatment of turbulent heat fluxes with the elliptic-blending second-moment closure for the turbulent natural convection flows. The turbulent heat fluxes are treated by the elliptic-blending based algebraic and differential flux models. The proposed models are applied to the prediction of turbulent natural convections in a 1:5 rectangular cavity and in a square cavity with conducting top and bottom walls. It is shown that both the elliptic-blending based models predict well the mean velocity and temperature, thereby the wall shear stress and Nusselt number. It is also shown that the elliptic-blending based algebraic flux model produces solutions which are as accurate as those by the differential flux model.
Nomenclature
| gi | = | gravity acceleration |
| Gk | = | generation term of turbulent kinetic energy due to gravity |
| H | = | height of cavity |
| k | = | turbulent kinetic energy |
| L | = | length scale or width of cavity |
| Lθ | = | thermal length scale |
| n | = | normal vector defined by Eq. (13) |
| p | = | pressure |
| Pk | = | generation term of turbulent kinetic energy |
| Pr | = | Prandtl number |
| Ra | = | Rayleigh number |
| t | = | time |
| T | = | time scale defined by Eq. (15) |
| = | turbulent heat flux | |
| Ui | = | Cartesian velocity components |
| = | Reynolds stress | |
| xi | = | Cartesian coordinates |
| y | = | normal distance from the wall |
| α | = | blending function |
| αθ | = | thermal blending function |
| β | = | thermal expansion coefficient |
| ε | = | dissipation rate of turbulent kinetic energy |
| μ | = | dynamic viscosity |
| ν | = | kinematic viscosity |
| ρ | = | density |
| Θ | = | temperature |
| = | temperature variance | |
| Subscript | = | |
| ref | = | pertaining to reference |
| w | = | pertaining to wall |
Nomenclature
| gi | = | gravity acceleration |
| Gk | = | generation term of turbulent kinetic energy due to gravity |
| H | = | height of cavity |
| k | = | turbulent kinetic energy |
| L | = | length scale or width of cavity |
| Lθ | = | thermal length scale |
| n | = | normal vector defined by Eq. (13) |
| p | = | pressure |
| Pk | = | generation term of turbulent kinetic energy |
| Pr | = | Prandtl number |
| Ra | = | Rayleigh number |
| t | = | time |
| T | = | time scale defined by Eq. (15) |
| = | turbulent heat flux | |
| Ui | = | Cartesian velocity components |
| = | Reynolds stress | |
| xi | = | Cartesian coordinates |
| y | = | normal distance from the wall |
| α | = | blending function |
| αθ | = | thermal blending function |
| β | = | thermal expansion coefficient |
| ε | = | dissipation rate of turbulent kinetic energy |
| μ | = | dynamic viscosity |
| ν | = | kinematic viscosity |
| ρ | = | density |
| Θ | = | temperature |
| = | temperature variance | |
| Subscript | = | |
| ref | = | pertaining to reference |
| w | = | pertaining to wall |