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ABSTRACT
This numerical study investigates turbulent flow characteristics and heat transfer augmentation in a rectangular channel with elliptical cylinders and protrusions. The height of protrusions is changed to quantify interactions with surrounding elliptical cylinders. Flow structures, temperature distributions, and heat transfer characteristics are obtained with a standard k − ε turbulence closure model. Cases are run at Reynolds numbers of 15,000 and 20,000. Combinations of protrusion and elliptical cylinder geometries give higher heat transfer rates than a case without protrusions. Additionally, Nusselt numbers increase with increases in height of protrusions and an optimum height-to-footprint diameter ratio is found.
Nomenclature
| a, b | = | the long and short radius of elliptical cylinders |
| D | = | the footprint diameter of protrusions |
| Dh | = | the hydraulic diameter of the channel |
| e | = | the interval between the cylinder and protrusion |
| f | = | the Fanning friction factor |
| f0 | = | the Fanning friction factor of the smooth channel |
| Gk | = | the generation of turbulence kinetic energy due to the mean velocity gradients |
| Gb | = | the generation of turbulence kinetic energy due to buoyancy |
| h | = | the height of protrusions |
| k | = | the turbulence kinetic energy |
| L | = | the total length of the channel |
| L′ | = | the feature length of the cylinder, i.e., the diameter of the cylinder |
| Nu | = | the Nusselt number |
| Nu0 | = | the Nusselt number of the smooth channel |
| Nu(i) | = | the local Nusselt number |
| p | = | pressure |
| Pr | = | the Prandtl numbers |
| qi | = | the local heat flux |
| Re | = | Reynolds number |
| S | = | the distance between cylinders in the streamwise direction |
| Sk | = | a user-defined source term |
| Sε | = | a user-defined source term |
| T | = | temperature |
| Tf | = | the mean temperature |
| Ti | = | the local temperature |
| uin | = | the averaged inlet velocity to the channel |
| uz | = | the dimensionless velocity along the z direction |
| YM | = | the contribution of fluctuating dilatation in compressible turbulence |
| Δy | = | the mesh size close the wall of bluff body |
| ΔP | = | the inlet-to-outlet pressure drop |
| ε | = | the rate of dissipation |
| λ | = | the thermal conductivity of the fluid |
| μ | = | the dynamic viscosity of the fluid |
| μt | = | the turbulent viscosity |
| ρ | = | flow density |
| σε | = | the turbulent Prandtl number for ε |
| σk | = | the turbulent Prandtl number for k |
| = | the local wall shear stress |
Nomenclature
| a, b | = | the long and short radius of elliptical cylinders |
| D | = | the footprint diameter of protrusions |
| Dh | = | the hydraulic diameter of the channel |
| e | = | the interval between the cylinder and protrusion |
| f | = | the Fanning friction factor |
| f0 | = | the Fanning friction factor of the smooth channel |
| Gk | = | the generation of turbulence kinetic energy due to the mean velocity gradients |
| Gb | = | the generation of turbulence kinetic energy due to buoyancy |
| h | = | the height of protrusions |
| k | = | the turbulence kinetic energy |
| L | = | the total length of the channel |
| L′ | = | the feature length of the cylinder, i.e., the diameter of the cylinder |
| Nu | = | the Nusselt number |
| Nu0 | = | the Nusselt number of the smooth channel |
| Nu(i) | = | the local Nusselt number |
| p | = | pressure |
| Pr | = | the Prandtl numbers |
| qi | = | the local heat flux |
| Re | = | Reynolds number |
| S | = | the distance between cylinders in the streamwise direction |
| Sk | = | a user-defined source term |
| Sε | = | a user-defined source term |
| T | = | temperature |
| Tf | = | the mean temperature |
| Ti | = | the local temperature |
| uin | = | the averaged inlet velocity to the channel |
| uz | = | the dimensionless velocity along the z direction |
| YM | = | the contribution of fluctuating dilatation in compressible turbulence |
| Δy | = | the mesh size close the wall of bluff body |
| ΔP | = | the inlet-to-outlet pressure drop |
| ε | = | the rate of dissipation |
| λ | = | the thermal conductivity of the fluid |
| μ | = | the dynamic viscosity of the fluid |
| μt | = | the turbulent viscosity |
| ρ | = | flow density |
| σε | = | the turbulent Prandtl number for ε |
| σk | = | the turbulent Prandtl number for k |
| = | the local wall shear stress |
Acknowledgments
A part of this work was performed using computing resources at the University of Minnesota Supercomputing Institute.