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ABSTRACT
Rough surfaces are widely used to enhance convective heat transfer by the promotion of higher turbulence levels. The present article reports simulations of the flow and heat transfer in a 2-D rib-roughened passage using a number of advanced Reynolds-averaged Navier-Stokes (RANS) turbulence models including eddy-viscosity models (EVM) and a Reynolds stress model (RSM). Large eddy simulation (LES) is also conducted and results are compared against experimental measurements. In addition, the effects of rib thermal boundary condition on heat transfer are also investigated. In the present work, the blockage ratio of the transversely mounted rectangular ribs is 10% and the rib pitch-to-height ratio of 9 is selected. The Reynolds number, based on the channel bulk velocity and hydraulic diameter, is 30,000. The RANS-based turbulence models investigated here are the k-ω-SST, the v2-f, the ϕ-f, and the elliptic blending RSM. All computations are undertaken using the commercial and industrial CFD codes STAR-CD and Code_Saturne, respectively. Of all the models, the LES predictions were found to be in the best agreement with the experimental data, while the k-ω-SST and EB-RSM returned the least accurate results.
Nomenclature
| A | = | cross-sectional area of the channel |
| b | = | rib width |
| cf | = | local friction coefficient |
| Cp | = | pressure coefficient [(p – pref)/(0.5ρUb2)] |
| Cμ | = | coefficient in the turbulent viscosity of k-ϵ turbulence models |
| De | = | hydraulic diameter (4A/P) |
| H | = | channel height |
| k | = | height of the rib or turbulent kinetic energy |
| L | = | length scale or computational domain length |
| Nu | = | Nusselt number |
| p | = | pressure |
| P | = | pitch or wetted perimeter |
| = | wall heat flux | |
| Re | = | Reynolds number, (Ub De/ν) |
| T | = | mean temperature |
| Ts | = | turbulent timescale |
| Ui, ui | = | mean and fluctuating velocity components in Cartesian coordinates |
| Uτ | = | friction velocity [(|τw|/ρ)1/2] |
| x | = | streamwise coordinate |
| y | = | coordinate or distance to the wall |
| y+ | = | dimensionless distance from the wall (yUτ/ν) |
| ε | = | dissipation rate of the turbulent kinetic energy |
| θ | = | fluctuating temperature |
| λ | = | thermal conductivity |
| μ | = | dynamic viscosity |
| μt | = | turbulent viscosity |
| ν | = | kinematic viscosity (μ/ρ) |
| ρ | = | density |
| σk1 | = | coefficient in the SST model |
| σt | = | turbulent Prandtl number |
| τw | = | wall shear stress |
| ω | = | dissipation rate per unit of kinetic energy (ϵ /Cμ k) |
| Subscripts | = | |
| b | = | bulk |
| ref | = | reference |
| t | = | turbulent |
| w | = | wall |
| Additional symbols are defined in the text. | = |
Nomenclature
| A | = | cross-sectional area of the channel |
| b | = | rib width |
| cf | = | local friction coefficient |
| Cp | = | pressure coefficient [(p – pref)/(0.5ρUb2)] |
| Cμ | = | coefficient in the turbulent viscosity of k-ϵ turbulence models |
| De | = | hydraulic diameter (4A/P) |
| H | = | channel height |
| k | = | height of the rib or turbulent kinetic energy |
| L | = | length scale or computational domain length |
| Nu | = | Nusselt number |
| p | = | pressure |
| P | = | pitch or wetted perimeter |
| = | wall heat flux | |
| Re | = | Reynolds number, (Ub De/ν) |
| T | = | mean temperature |
| Ts | = | turbulent timescale |
| Ui, ui | = | mean and fluctuating velocity components in Cartesian coordinates |
| Uτ | = | friction velocity [(|τw|/ρ)1/2] |
| x | = | streamwise coordinate |
| y | = | coordinate or distance to the wall |
| y+ | = | dimensionless distance from the wall (yUτ/ν) |
| ε | = | dissipation rate of the turbulent kinetic energy |
| θ | = | fluctuating temperature |
| λ | = | thermal conductivity |
| μ | = | dynamic viscosity |
| μt | = | turbulent viscosity |
| ν | = | kinematic viscosity (μ/ρ) |
| ρ | = | density |
| σk1 | = | coefficient in the SST model |
| σt | = | turbulent Prandtl number |
| τw | = | wall shear stress |
| ω | = | dissipation rate per unit of kinetic energy (ϵ /Cμ k) |
| Subscripts | = | |
| b | = | bulk |
| ref | = | reference |
| t | = | turbulent |
| w | = | wall |
| Additional symbols are defined in the text. | = |
Acknowledgements
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, Professor D. Laurence, and Dr. I. Afgan. The authors are also grateful to EDF for the use of its BlueGene P supercomputer for the LES simulations.