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ABSTRACT
This study presents the thermal behavior of two young turbulent spots merging into a longitudinal direction on an isothermal flat plate for the local Reynolds number between 6.1 × 104 and 1.3 × 105 in a low freestream turbulence water tunnel having a turbulent intensity of 1.16%. The two turbulent spots are generated by water injection through a 1-mm-diameter hole in the perpendicular direction of the mainstream flow with a dimensionless separating time (Δτ) of 42.08, 84.16, and 126.24. Thermochromic liquid crystals are utilized mutually with an image processing technique to extract the spot characteristics qualitatively and quantitatively. The results demonstrate that the following turbulent spot directly causes an increase in the local Nusselt number and heat rate within the footprint of the merging spots. The relatively highest increase in this study occurs when Δτ = 84.16. The average Nusselt number and effectiveness characterize differently in the intersection zone, non-intersection zone of the leading spot, and non-intersection zone of the following spot. The results confirm that turbulent spots under the boundary layer transition augment the heat transfer rate to the level of full turbulence by not only their spot maturity but also the merging mechanism. Finally, the heat transfer mechanism is discussed and the predictive formulas for the Nusselt number and heat flux of the longitudinal merging of turbulent spots for Δτ from 0 to 126.24 are provided.
Nomenclature
| As | = | Heat transfer area within spot footprint (m2) |
| B | = | Blue signal value |
| cp | = | Specific heat capacity (J/kgK) |
| Ein | = | Energy inflow (W) |
| Eg | = | Energy source (W) |
| Est | = | Energy storage (W) |
| G | = | Green signal value |
| H | = | Hue signal value |
| hx | = | Heat transfer coefficient (W/m2 °C) |
| k | = | Thermal conductivity of water (W/m·°C) |
| I | = | Intensity signal value |
| Nuavg | = | Average Nusselt number |
| Nux | = | Local Nusselt number |
| Pr | = | Prandtl number |
| Q | = | Rate of heat transfer (W) |
| q | = | Heat flux (W/m2) |
| qns | = | Heat flux through turbulent spot area on unperturbed surface (W/m2) |
| qs | = | Heat flux through turbulent spot (W/m2) |
| R | = | Red signal value |
| Ra | = | Average roughness (m) |
| Rq | = | rms roughness (m) |
| Rt | = | Maximum peak to valley roughness (m) |
| Rz | = | Average peak to valley roughness (m) |
| Rex | = | Local Reynolds number |
| S | = | Saturation signal value |
| t | = | Time (s) |
| Ts | = | Surface temperature (°C) |
| Tα | = | Freestream temperature (°C) |
| U | = | Velocity (m/s) |
| Uα | = | Freestream velocity (m/s) |
| V | = | Volume (m3) |
| X | = | Dimensionless streamwise distance |
| x | = | Streamwise distance (m) |
| x0 | = | Streamwise location of spot generator (m) |
| Y | = | Dimensionless spanwise distance |
| y | = | Spanwise distance (m) |
| Z | = | Color constant |
Greek symbols
| α | = | Half-spreading angle (°) |
| δ | = | Laminar boundary layer thickness (m) |
| δ* | = | Boundary layer displacement thickness at spot generator (m) |
| Δτ | = | Dimensionless interval between two injections |
| ξ | = | Unheated starting length (m) |
| ε | = | Turbulent spot effectiveness |
| εavg | = | Average turbulent spot effectiveness |
| ρ | = | Density (kg/m3) |
| τ | = | Dimensionless time |
Acknowledgments
The authors would like to acknowledge financial support from the Thailand Research Fund (TRF)-MRG5980056 and gratefully thank Assoc. Prof. Dr. Chawalit Kittichaikarn for the valuable advice.