![Sample our Engineering & Technology journals, sign in here to start your access, latest two full volumes FREE to you for 14 days]({"type":"image" , "src" : "/sda/5933/TOC-Subject-Sample-2021-Engineering-Tech.jpg"})
ABSTRACT
In this study, streamwise-periodic fully developed turbulent flow and heat transfer in a duct is investigated numerically. The governing equations are solved by using the finite-control-volume method together with nonuniform staggered grids. The velocity and pressure terms of the momentum equations are solved by the SIMPLE algorithm. A cyclic tri-diagonal matrix algorithm (TDMA) is applied in order to increase the convergence rate of the numerical solution. Four versions of the low-Reynolds-number k-ε model are used in the analysis: Launder-Sharma (1974), Lam-Bremhorst (1981), Chien (1982), and Abe-Kondoh-Nagano (1994). The results obtained using the models tested are analyzed comparatively against some experimental results given in the literature. It is discussed that all the models tested failed in the separated region just behind the ribs, where the turbulent stresses are underpredicted. The local Nusselt numbers are overpredicted by all the models considered. However, the Abe-Kondoh-Nagano low-Re k-ε model presents more realistic heat transfer predictions.
Nomenclature
| cp | = | specific heat |
| Cµ, C1, C2 | = | turbulence model constants |
| D | = | dumping function in the k equation |
| Dh | = | hydraulic diameter |
| E, f1, f2 | = | dumping functions in the ε equation |
| fµ | = | dumping function in the Prandtl-Kolmogorov relationship, Eq. (14) |
| Gk | = | generation of kinetic energy |
| h | = | rib height |
| H | = | channel height |
| k | = | turbulent kinetic energy |
| kf | = | thermal conductivity of air |
| L | = | length of one periodic module |
| = | mass flow rate | |
| Nu, Nu(x) | = | local Nusselt Number |
| P | = | pressure |
| = | periodic part of pressure | |
| Pr | = | molecular Prandtl number |
| Prt | = | turbulent Prandtl/Schmidt number in Eq. (5) |
| = | heat flux | |
| = | total heat input | |
| Re | = | Reynold number based on channel height, H |
| Rt, Ry, Rε | = | local turbulence Reynolds numbers |
| T | = | temperature |
| = | periodic part of temperature | |
| Tb | = | local bulk temperature |
| Tw | = | local wall temperature |
| = | turbulent stress tensor | |
| = | turbulent heat flux | |
| uε | = | Kolmogorov velocity scale [= (με/ρ)1/4] |
| uτ | = | friction velocity ( |
| U | = | axial mean (time-averaged) velocity |
| Ui | = | mean velocity components in the xj direction (U, V) |
| Um | = | mean velocity in the channel |
| V | = | transverse mean velocity |
| x, y | = | axial and transverse coordinates |
| xi | = | Cartesian coordinates in tensor notation (x, y) |
| xR | = | reattachment length |
| y+ | = | dimensionless normal distance from the nearest wall |
| α | = | overrelaxation factor in Eq. (17) |
| β | = | mean channel pressure gradient across a periodic module |
| γ | = | nonperiodic temperature gradient across a periodic module |
| δij | = | Kronecker delta function |
| ε | = | dissipation rate of turbulent kinetic energy |
| λ | = | friction factor |
| μ | = | molecular dynamic viscosity |
| μt | = | turbulent dynamic viscosity |
| ν | = | molecular kinematic viscosity |
| νt | = | turbulent kinematic viscosity |
| ρ | = | air density |
| σε, σk | = | turbulent Prandtl numbers for the k and ε equations |
| τw | = | surface shear stress |
Nomenclature
| cp | = | specific heat |
| Cµ, C1, C2 | = | turbulence model constants |
| D | = | dumping function in the k equation |
| Dh | = | hydraulic diameter |
| E, f1, f2 | = | dumping functions in the ε equation |
| fµ | = | dumping function in the Prandtl-Kolmogorov relationship, Eq. (14) |
| Gk | = | generation of kinetic energy |
| h | = | rib height |
| H | = | channel height |
| k | = | turbulent kinetic energy |
| kf | = | thermal conductivity of air |
| L | = | length of one periodic module |
| = | mass flow rate | |
| Nu, Nu(x) | = | local Nusselt Number |
| P | = | pressure |
| = | periodic part of pressure | |
| Pr | = | molecular Prandtl number |
| Prt | = | turbulent Prandtl/Schmidt number in Eq. (5) |
| = | heat flux | |
| = | total heat input | |
| Re | = | Reynold number based on channel height, H |
| Rt, Ry, Rε | = | local turbulence Reynolds numbers |
| T | = | temperature |
| = | periodic part of temperature | |
| Tb | = | local bulk temperature |
| Tw | = | local wall temperature |
| = | turbulent stress tensor | |
| = | turbulent heat flux | |
| uε | = | Kolmogorov velocity scale [= (με/ρ)1/4] |
| uτ | = | friction velocity ( |
| U | = | axial mean (time-averaged) velocity |
| Ui | = | mean velocity components in the xj direction (U, V) |
| Um | = | mean velocity in the channel |
| V | = | transverse mean velocity |
| x, y | = | axial and transverse coordinates |
| xi | = | Cartesian coordinates in tensor notation (x, y) |
| xR | = | reattachment length |
| y+ | = | dimensionless normal distance from the nearest wall |
| α | = | overrelaxation factor in Eq. (17) |
| β | = | mean channel pressure gradient across a periodic module |
| γ | = | nonperiodic temperature gradient across a periodic module |
| δij | = | Kronecker delta function |
| ε | = | dissipation rate of turbulent kinetic energy |
| λ | = | friction factor |
| μ | = | molecular dynamic viscosity |
| μt | = | turbulent dynamic viscosity |
| ν | = | molecular kinematic viscosity |
| νt | = | turbulent kinematic viscosity |
| ρ | = | air density |
| σε, σk | = | turbulent Prandtl numbers for the k and ε equations |
| τw | = | surface shear stress |