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ABSTRACT
The present numerical work, the first of its kind, aims at establishing the threshold parameters for dynamic similitude (based on the Rayleigh number (Ra)), for free convection in a cylindrical enclosure heated laterally. Ra considered in this study spanned a range between 750 and 8.8 × 108, where the characteristic length, L, used in its definition is represented by the ratio of cylindrical enclosure’s volume to its lateral surface area. The commercial code, ANSYS FLUENT, is used to model a 2-D axisymmetric cylindrical geometry. When comparatively analyzed, the results allowed conclusions associating values of the Ra with flow development from laminar to turbulent.
Nomenclature
| Dω | = | cross-diffusion term |
| g | = | gravity |
| Gr | = | Grashof number |
| k | = | turbulence kinetic energy |
| L | = | characteristic length (volume/lateral area) |
| p | = | pressure |
| Pk | = | generation of turbulence kinetic energy |
| Pω | = | generation of ω |
| Pr | = | Prandtl number |
| R | = | radius of the enclosure |
| Ra | = | Rayleigh number |
| t | = | time |
| T | = | temperature |
| vr | = | radial velocity |
| vz | = | axial velocity |
| Yk | = | dissipation of k |
| Yω | = | dissipation of ω |
| α | = | thermal diffusivity |
| αT | = | turbulent thermal diffusivity |
| β | = | thermal expansion coefficient |
| μ | = | dynamic viscosity |
| μT | = | eddy viscosity |
| ν | = | kinematic viscosity |
| ρ | = | density |
| τ | = | shear stress |
| ω | = | specific dissipation rate |
Nomenclature
| Dω | = | cross-diffusion term |
| g | = | gravity |
| Gr | = | Grashof number |
| k | = | turbulence kinetic energy |
| L | = | characteristic length (volume/lateral area) |
| p | = | pressure |
| Pk | = | generation of turbulence kinetic energy |
| Pω | = | generation of ω |
| Pr | = | Prandtl number |
| R | = | radius of the enclosure |
| Ra | = | Rayleigh number |
| t | = | time |
| T | = | temperature |
| vr | = | radial velocity |
| vz | = | axial velocity |
| Yk | = | dissipation of k |
| Yω | = | dissipation of ω |
| α | = | thermal diffusivity |
| αT | = | turbulent thermal diffusivity |
| β | = | thermal expansion coefficient |
| μ | = | dynamic viscosity |
| μT | = | eddy viscosity |
| ν | = | kinematic viscosity |
| ρ | = | density |
| τ | = | shear stress |
| ω | = | specific dissipation rate |