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ABSTRACT
Laminarization is an important topic in heat transfer and turbulence modeling. Recent studies have demonstrated that several well-known turbulence models failed to provide accurate prediction when applied to mixed convection flows with significant re-laminarization effects. One of those models, a well-validated cubic nonlinear eddy-viscosity model, was observed to miss this feature entirely. This paper studies the reasons behind this failure by providing a detailed comparison with the baseline Launder–Sharma model. The difference is attributed to the method of near-wall damping. A range of tests have been conducted and two noteworthy findings are reported for the case of flow re-laminarization.
Nomenclature
| Bo | = | = buoyancy parameter, 8 × 104Gr/(Re 3.425 Pr0.8) |
| cf | = | = local friction coefficient |
| Cμ | = | = constant in eddy-viscosity models |
| D | = | = pipe diameter |
| Eϵ | = | = near-wall source term |
| fμ | = | = damping function |
| gi | = | = acceleration due to gravity |
| Gr | = | = Grashof number, |
| k | = | = turbulent kinetic energy, |
| Nu | = | = Nusselt number, |
| p | = | = pressure |
| Pk | = | = rate of shear-production of k, |
| Pr | = | = Prandtl number, cpμ/λ |
| = | = wall heat flux | |
| R | = | = pipe radius |
| Re | = | = Reynolds number, UbD/v |
| Ret | = | = turbulent Reynolds number, |
| S | = | = strain parameter |
| T | = | = temperature |
| T+ | = | = non-dimensional temperature, (Tw–T)/Tτ |
| Tτ | = | = friction temperature, |
| U+ | = | = non-dimensional velocity, U/Uτ |
| Uτ | = | = friction velocity, |
| Ui, ui | = | = mean, fluctuating velocity components in Cartesian tensors |
| = | = Reynolds stress tensor | |
| = | = turbulent heat flux | |
| x, y | = | = streamwise and wall-normal coordinates |
| y+ | = | = dimensionless distance from the wall, yUτ/v |
| Greek Symbols | = | |
| B | = | = coefficient of volumetric expansion |
| δij | = | = Kronecker delta |
| E | = | = rate of dissipation of k |
| Λ | = | = thermal conductivity |
| μ | = | = dynamic viscosity |
| ν | = | = kinematic viscosity, μ/ρ |
| νt | = | = turbulent viscosity |
| ρ | = | = density |
| σt | = | = turbulent Prandtl number |
| τw | = | = wall shear stress |
| Subscripts | = | |
| 0 | = | = forced convection |
| b | = | = bulk |
| t | = | = turbulent |
| w | = | = wall |
Nomenclature
| Bo | = | = buoyancy parameter, 8 × 104Gr/(Re 3.425 Pr0.8) |
| cf | = | = local friction coefficient |
| Cμ | = | = constant in eddy-viscosity models |
| D | = | = pipe diameter |
| Eϵ | = | = near-wall source term |
| fμ | = | = damping function |
| gi | = | = acceleration due to gravity |
| Gr | = | = Grashof number, |
| k | = | = turbulent kinetic energy, |
| Nu | = | = Nusselt number, |
| p | = | = pressure |
| Pk | = | = rate of shear-production of k, |
| Pr | = | = Prandtl number, cpμ/λ |
| = | = wall heat flux | |
| R | = | = pipe radius |
| Re | = | = Reynolds number, UbD/v |
| Ret | = | = turbulent Reynolds number, |
| S | = | = strain parameter |
| T | = | = temperature |
| T+ | = | = non-dimensional temperature, (Tw–T)/Tτ |
| Tτ | = | = friction temperature, |
| U+ | = | = non-dimensional velocity, U/Uτ |
| Uτ | = | = friction velocity, |
| Ui, ui | = | = mean, fluctuating velocity components in Cartesian tensors |
| = | = Reynolds stress tensor | |
| = | = turbulent heat flux | |
| x, y | = | = streamwise and wall-normal coordinates |
| y+ | = | = dimensionless distance from the wall, yUτ/v |
| Greek Symbols | = | |
| B | = | = coefficient of volumetric expansion |
| δij | = | = Kronecker delta |
| E | = | = rate of dissipation of k |
| Λ | = | = thermal conductivity |
| μ | = | = dynamic viscosity |
| ν | = | = kinematic viscosity, μ/ρ |
| νt | = | = turbulent viscosity |
| ρ | = | = density |
| σt | = | = turbulent Prandtl number |
| τw | = | = wall shear stress |
| Subscripts | = | |
| 0 | = | = forced convection |
| b | = | = bulk |
| t | = | = turbulent |
| w | = | = wall |
Acknowledgments
The authors are pleased to acknowledge the contribution of their colleagues in the School of Mechanical, Aerospace and Civil Engineering (MACE) at the University of Manchester, especially Dr. M.A. Cotton and Professor D. Laurence.