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Abstract
We present fluid flow and heat transfer of a slot jet impingement heat transfer at a small value of the nozzle-to-plate spacing at which a secondary peak in the Nusselt number is observed. Large eddy simulation has been performed with a finite-volume-based computational fluid dynamics code and using a dynamic Smagorinsky model. The optimum domain size and grid for large eddy simulation (LES) have been produced based on LES computations on a coarse mesh and Reynolds-averaged Navier–Stokes-based computations. Two inflow conditions, namely, using the vortex method and no perturbations, were compared. The present LES results, using the vortex method, capture the secondary peak in the Nusselt number better as compared to the case with no perturbations. Results show that mean velocity profile in the stagnation region deviates from the standard law of the wall. Further, large-scale vortical structures were observed near the location of the secondary Nusselt number peak. Increases in both the streamwise and wall normal turbulence fluctuations are observed near the secondary peak in the Nusselt number. The secondary peak in Nusselt number is found to be associated with the combined effect of flow acceleration and an increase in the turbulence kinetic energy.
Nomenclature
| B | = | slot jet width |
| cp | = | specific heat of the working fluid, J/K |
| Cs | = | Smagorinsky constant |
| G | = | low pass filter |
| H | = | distance from the nozzle exit to the impingement plate, m |
| k | = | turbulence kinetic energy, m2/s2 |
| LESIQν | = | index of quality criterion for LES |
| Nu | = | local Nusselt number at the wall |
| p | = | static pressure, Pa |
| PrSGS | = | subgrid scale Prandtl number |
| qSGSj | = | subgrid-scale heat flux, m-K/s |
| S | = | magnitude of strain rate tensor |
| Sij | = | strain rate tensor |
| t | = | time coordinate |
| T | = | temperature, K |
| Trms | = | root mean square temperature, K |
| U | = | mean streamwise velocity, m/s |
| ui | = | velocity vector, m/s |
| uτ | = | friction velocity, m/s |
| u′ | = | fluctuating velocity in the streamwise direction, m/s |
| U+ | = | mean streamwise velocity in wall co-ordinates, U+ = U/uτ |
| V | = | mean wall-normal velocity, m/s |
| v′ | = | fluctuating velocity in the wall normal direction, m/s |
| V0 | = | nozzle exit velocity, m/s |
| x | = | distance in the streamwise direction, m |
| x′ | = | dummy space coordinate at each grid cell to perform filtering, m |
| y | = | distance in the wall normal direction, m |
| z | = | distance in the spanwise or homogenous direction, m |
| y+ | = | normal distance from the wall in wall coordinates, y+ = yuτ/ν |
| ▵x+ | = | size of the grid in x-direction in wall coordinates |
| ▵z+ | = | size of the grid in z-direction in wall coordinates |
Greek Symbols
| ▵ | = | filter width or grid size |
| ϵ | = | dissipation rate, m2/s3 |
| η | = | Kolmogorov length scale, m |
| ν | = | kinematic viscosity, m2/s |
| νSGS | = | subgrid scale eddy viscosity, m2/s |
| ρ | = | density, kg/m3 |
| τSGSij | = | subgrid scale stress tensor, Pa |
| Γ | = | thermal diffusivity, m2/s |
| ΓSGS | = | subgrid scale thermal diffusivity, m2/s |
| ϕ | = | any flow variable, e.g., pressure, velocity, etc. |
| λ | = | thermal conductivity, W/m-K |
| δij | = | Kronecker delta |
Subscript
| i,j | = | index of coordinate direction |
| rms | = | root mean square value of a variable |
Superscripts
| + | = | nondimensional quantity in wall coordinates |
| ∧ | = | resolved quantity |
| ∼ | = | subgrid quantity |
Additional information
Notes on contributors
Rabijit Dutta
Rabijit Dutta is a Ph.D. student in the Department of Applied Mechanics at the Indian Institute Technology Delhi. He received his master's degree from the Indian Institute of Technology Delhi in 2009. His topic of research is modeling of wall-bounded turbulent flows and heat transfer.
Anupam Dewan
Anupam Dewan is a professor in the Department of Applied Mechanics, Indian Institute of Technology (IIT), Delhi. He obtained his bachelor's degree in mechanical engineering from Kurukshetra University, India, and master's and Ph.D. degrees in mechanical engineering from the Indian Institute of Science Bangalore. He was a professor of mechanical engineering at the Indian Institute of Technology, Guwahati, before joining IIT Delhi in May 2009. He was earlier a DAAD Visiting Scientist (for 3 months) and guest professor (for 3 months) at the Institute for Hydromechanics, University of Karlsruhe, Germany, and an Alexander von Humboldt Research Fellow at the Institute of Fluid Mechanics, University of Erlangen-Nuremberg, Germany, for 14 months. His areas of specialization include computational fluid dynamics and heat transfer; mathematical modeling of engineering turbulent flows; turbulent convective heat transfer; and renewable energy. Prof. Dewan has co-authored 95 refereed journal and conference publications. He has authored a book, Tackling Turbulent Flows in Engineering, published in 2011 by Springer.
Balaji Srinivasan
Balaji Srinivasan did his B.Tech. in aerospace engineering from the Indian Institute of Technology Madras and his M.S. in aeronautics from Purdue University. He finished his doctorate in aerospace engineering from Stanford University in 2005. He has been a faculty member in the Department of Applied Mechanics, IIT Delhi, since 2008. His research interests include computational and theoretical fluid dynamics, numerical analysis, and turbulence.