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Abstract
This work addresses the numerical simulation of incompressible turbulent recirculating channel flows in a backward-facing step. The effects of a small square turbulence promoter on convection heat transfer are evaluated through a parametric study. The governing equations comprise the time-averaged mass, linear momentum, and energy conservation principles in conjunction with the two-equation k–epsilon turbulence model. The study is focused on the assessment of the local and global Nusselt numbers at the channel stepped wall. The main results indicate that a maximum increment around 15% on the average Nusselt number can be achieved by using a small turbulence promoter to disturb the flow. Furthermore, it was found that the peak of the local Nusselt number on the stepped wall is located in the region where the turbulent diffusion is maximum in the near wall region.
NOMENCLATURE
| A | = | area, m2 |
| c | = | specific heat, J kg−1 K−1 |
| = | pressure coefficient, | |
| d | = | edge length of a square promoter, m |
| h | = | channel thickness upstream of the expansion section, m |
| hc | = | heat transfer coefficient, W m−2 K−1 |
| H | = | channel thickness downstream of the expansion section, m |
| k | = | turbulent kinetic energy, |
| kM | = | molecular thermal conductivity, W m−1 K−1 |
| kT | = | turbulent thermal conductivity, W m−1 K−1 |
| l | = | channel length upstream of the expansion section, m |
| L | = | channel length downstream of the expansion section, m |
| Nus | = | local Nusselt number, |
| = | area averaged Nusselt number, | |
| p | = | pressure, Pa |
| = | mean total pressure at the channel entrance, Pa | |
| = | mean total pressure at the channel exit, Pa | |
| = | turbulent Prandtl number, | |
| qM | = | molecular heat flux, |
| qT | = | turbulent heat flux, |
| qw | = | heat flux at the stepped wall, W m−2 |
| = | Reynolds number based on the channel thickness, | |
| = | Reynolds number based on the step height, | |
| s | = | step height, m |
| St | = | Stanton number, |
| T | = | temperature, K |
| T+ | = | dimensionless temperature, |
| T* | = | characteristic temperature, |
| u | = | x velocity component, m s−1 |
| u′ | = | velocity fluctuations, m s−1 |
| = | mean velocity across the entrance channel, | |
| u* | = | friction or shear velocity, |
| u+ | = | dimensionless velocity, |
| u∞ | = | free flow reference velocity, m s−1 |
| v | = | y velocity component, m s−1 |
| v′T′ | = | turbulent correlation, m-K s−1 |
| x | = | coordinate in the x direction, m |
| xR | = | reattachment length, m |
| Xc | = | location of the center of the promoter in the x direction, m |
| y | = | coordinate in the y direction, m |
| y+ | = | dimensionless distance from the wall, |
| Yc | = | location of the center of the promoter in the y direction, m |
Greek Symbols
| δ | = | boundary-layer thickness at the channel entrance, m |
| = | average pressure drop, | |
| ϵ | = | turbulent kinetic energy dissipation rate, J kg−1 s−1 |
| ϵRMS | = | root mean square of the governing equations residuals |
| μ | = | molecular dynamic viscosity, N s m−2 |
| μT | = | turbulent eddy viscosity, |
| ρ | = | density, kg m−3 |
| τw | = | shear stress, Pa |
Subscripts
| e | = | entrance |
| w | = | stepped wall |
Additional information
Notes on contributors
Paulo S. B. Zdanski
Paulo S. B. Zdanski is an associate professor of mechanical engineering at the State University of Santa Catarina. He obtained his D.Sc. degree at the Technologic Institute of Aeronautics (Brazil) in 2003, with research in computational aerodynamics and heat transfer. He is involved in teaching at graduate and postgraduate levels for the Mechanical Engineering program. He has focused his work on devising new numerical strategies for solving heat and fluid flow problems for both Newtonian and non-Newtonian fluids.
Miguel Vaz
Miguel Vaz, Jr., is an associate professor of mechanical engineering at the State University of Santa Catarina. He received his Ph.D. in computational mechanics from Swansea University (UK) in 1998. He is involved in teaching at graduate and postgraduate levels for the Mechanical Engineering and Material Science and Engineering programs. He has worked in computational approaches to multiphysics and coupled problems, especially continuum damage mechanics, ductile failure prediction of fracture-free materials, thermomechanical coupling, and conjugated heat and fluid flow problems.
Gregory T. Gargioni
Gregory T. Gargioni graduated in mechanical engineering at the State University of Santa Catarina in 2013 and is currently a postgraduate student in the same university. He has worked on simulation of heat and fluid flow problems with special interest in heat transfer enhancement techniques.