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ABSTRACT
In this study, numerical simulations are conducted to investigate the effects of dimple positions on the endwall heat transfer and friction factor in a pin fin wedge duct. The dimple diameter is the same as the pin fin diameter, while the ratio between dimple depth and dimple diameter is 0.2. Three different dimple positions are investigated (i.e., directly upstream of the pin fins, in a staggered manner relative to the pin fins, or in line with the pin fins. The Reynolds number ranges from 10,000 to 50,000. Results for endwall Nusselt number, friction factor, and flow structure are included. For convenience of comparison, the pin fin wedge duct without dimples is studied as baseline. It is found that dimples can effectively enhance endwall heat transfer. Among the tested parameters, the dimple position in line with the pin fins provides the best heat transfer enhancement, with low friction factor penalty. However, the various dimple positions have distinct effects on the friction factor depending on the flow structure near the dimple zone. For the first position, the friction factor is markedly increased due to flow impingement, recirculation, and mixing, while for the second and third positions, the friction factor is changed slightly due to different flow behaviors.
Nomenclature
| d | = | pin fin diameter |
| D | = | equivalent hydraulic diameter of inlet |
| dm | = | dimple diameter |
| f | = | friction factor |
| f0 | = | friction factor in smooth channel |
| h | = | heat transfer coefficient |
| H1 | = | inlet height |
| H2 | = | outlet height |
| Kp | = | pressure drop |
| L | = | duct length |
| Li | = | inlet extent length |
| Lo | = | outlet extent length |
| Nu | = | Nusselt number |
| Nu0 | = | Nusselt number in smooth channel |
| Nud | = | pin fin row Nusselt number |
| Pr | = | Prandtl number |
| pi | = | inlet total pressure |
| po | = | outlet total pressure |
| q | = | heat flux |
| Re | = | Reynolds number |
| Sx | = | streamwise distance between the pin fins |
| Sy | = | spanwise distance between the pin fins |
| Tw | = | endwall temperature |
| Tair | = | inlet air temperature |
| U0 | = | mean velocity of inlet |
| Ub | = | mean velocity at outlet |
| W | = | width of duct |
| δ | = | depth of dimple |
| λ | = | thermal conductivity of air |
| μ | = | dynamic viscosity |
| ρ | = | density of air |
Nomenclature
| d | = | pin fin diameter |
| D | = | equivalent hydraulic diameter of inlet |
| dm | = | dimple diameter |
| f | = | friction factor |
| f0 | = | friction factor in smooth channel |
| h | = | heat transfer coefficient |
| H1 | = | inlet height |
| H2 | = | outlet height |
| Kp | = | pressure drop |
| L | = | duct length |
| Li | = | inlet extent length |
| Lo | = | outlet extent length |
| Nu | = | Nusselt number |
| Nu0 | = | Nusselt number in smooth channel |
| Nud | = | pin fin row Nusselt number |
| Pr | = | Prandtl number |
| pi | = | inlet total pressure |
| po | = | outlet total pressure |
| q | = | heat flux |
| Re | = | Reynolds number |
| Sx | = | streamwise distance between the pin fins |
| Sy | = | spanwise distance between the pin fins |
| Tw | = | endwall temperature |
| Tair | = | inlet air temperature |
| U0 | = | mean velocity of inlet |
| Ub | = | mean velocity at outlet |
| W | = | width of duct |
| δ | = | depth of dimple |
| λ | = | thermal conductivity of air |
| μ | = | dynamic viscosity |
| ρ | = | density of air |