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ABSTRACT
In this study, numerical simulations of turbulent steam forced convection in a three-dimensional angled ribbed channel with constant heat flux are investigated. The elliptical, coupled, steady-state, and three-dimensional governing partial differential equations for turbulent forced convection are solved numerically using the finite volume approach. The standard k−ϵ turbulence model is applied to solve the turbulent governing equations. Numerical results are first validated using reference’s data reported in the literature and the maximum discrepancy between them is 3%. The effects of Reynolds number, angled rib height ratio, angled rib pitch ratio, and rib angle on the friction factor ratio and averaged Nusselt number are investigated. Numerical results show that the increase in heat transfer is accompanied by an increase in the friction factor ratio of the steam, the minimum friction factor ratio occurs at θ = 30○ and the maximum friction factor ratio is found at θ = 60○. In addition, after the validation of the numerical results, the numerical optimization of this problem is also presented by using the response surface methodology coupled with computational fluid dynamic method.
Nomenclature
| = | turbulent model coefficients | |
| Cp | = | specific heat of constant pressure, J/kg · K |
| D | = | hydraulic diameter, mm |
| E | = | thermal performance factor |
| e | = | rib height, mm |
| f | = | friction factor |
| I | = | turbulent intensity |
| k | = | turbulent kinetic energy, m2/s2 |
| k | = | conduction heat transfer coefficient, W/m · K |
| L1 | = | inlet length, mm |
| L2 | = | length of the heating zone, mm |
| L3 | = | outlet length, mm |
| = | average Nusselt number | |
| n | = | normal vector |
| p | = | rib pitch, mm |
| P | = | pressure, Pa |
| Pr | = | Prandtl number |
| q″ | = | heat flux, W/m2 |
| Re | = | Reynolds number |
| T | = | temperature, K |
| u, v, w | = | velocity component, m/s |
| x, y, z | = | Cartesian x-, y-, z-coordinate |
| Greeks symbols | = | |
| θ | = | rib angle |
| ϵ | = | turbulent kinetic energy dissipation, m2/s3 |
| ρ | = | density of the fluid, kg/m3 |
| µt | = | turbulent viscosity, kg/m · s |
| σϵ, σk | = | k-ε turbulence model constant for ϵ and k |
| Subscripts | = | |
| 0 | = | smooth channel |
| f | = | fluid |
| in | = | inlet |
| s | = | solid |
| w | = | wall |
Nomenclature
| = | turbulent model coefficients | |
| Cp | = | specific heat of constant pressure, J/kg · K |
| D | = | hydraulic diameter, mm |
| E | = | thermal performance factor |
| e | = | rib height, mm |
| f | = | friction factor |
| I | = | turbulent intensity |
| k | = | turbulent kinetic energy, m2/s2 |
| k | = | conduction heat transfer coefficient, W/m · K |
| L1 | = | inlet length, mm |
| L2 | = | length of the heating zone, mm |
| L3 | = | outlet length, mm |
| = | average Nusselt number | |
| n | = | normal vector |
| p | = | rib pitch, mm |
| P | = | pressure, Pa |
| Pr | = | Prandtl number |
| q″ | = | heat flux, W/m2 |
| Re | = | Reynolds number |
| T | = | temperature, K |
| u, v, w | = | velocity component, m/s |
| x, y, z | = | Cartesian x-, y-, z-coordinate |
| Greeks symbols | = | |
| θ | = | rib angle |
| ϵ | = | turbulent kinetic energy dissipation, m2/s3 |
| ρ | = | density of the fluid, kg/m3 |
| µt | = | turbulent viscosity, kg/m · s |
| σϵ, σk | = | k-ε turbulence model constant for ϵ and k |
| Subscripts | = | |
| 0 | = | smooth channel |
| f | = | fluid |
| in | = | inlet |
| s | = | solid |
| w | = | wall |
Acknowledgments
We really appreciate the Ministry Science and Technology of Taiwan for supporting this project under contract no. NSC102-2221-E-006-173-MY3.