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Abstract
Numerical computations are performed to analyze the influence of aiding thermal buoyancy on the phenomenon of suppression of flow separation in power-law fluids around a circular object. The idea has been borrowed from some recent similar works in Newtonian fluids. Owing to the contradictory behavior of shear-thinning and shear-thickening fluids in regard to the separation mechanism, we intend to understand the role of superimposed thermal buoyancy on the suppression phenomena in non-Newtonian power-law fluids, for which a range of power-law indices (0.4 to 1.8) is considered. The Reynolds numbers are kept intentionally low, within 10 to 40, such that the isothermal flow remains steady and separated without imposition of thermal buoyancy. The buoyancy causes a delay in the separation, thereby affecting the suppression phenomena. We determine the critical heating parameter (Richardson number) for the complete suppression of the flow separation and from there we construct a bifurcation diagram to show the typical flow regime evolved due to the complex interplay between the aiding thermal buoyancy and fluid rheology. The Richardson number in the simulation lies in the range 0 to 0.35, keeping the Prandtl number fixed at 50. The heat transfer rates from the object are also obtained and important inferences are drawn in regard to the inhibition/augmentation of heat transfer due to fluid rheology.
NOMENCLATURE
| B | = | blockage ratio, d/H |
| CD | = | total drag coefficient, |
| CDP | = | pressure drag coefficient, |
| CDV | = | viscous drag coefficient, |
| cp | = | constant pressure specific heat (J/kg-K) |
| d | = | diameter of the cylinder (m) |
| FD | = | total drag force (N) |
| FDP | = | pressure drag force (N) |
| FDV | = | viscous drag force (N) |
| g | = | acceleration due to gravity (m/s2) |
| Gr | = | Grashof number, |
| h | = | local heat transfer coefficient (W/m2-K) |
| Ld | = | downstream length (m) |
| Lu | = | upstream length (m) |
| Lr | = | dimensionless recirculation length, |
| H | = | width of computational domain (m) |
| I2 | = | second invariant of the rate of strain tensor, |
| k | = | thermal conductivity of fluid (W/m-K) |
| m | = | consistency index |
| Nu | = | local Nusselt number, hd/k |
| n | = | power-law index |
| p | = | dimensionless pressure, |
| Pe | = | Peclet number, Re Pr |
| Pr | = | Prandtl number, |
| Re | = | Reynolds number, |
| Ri | = | Richardson number, Gr/Re2 |
| T | = | temperature [K] |
| U | = | dimensionless velocity, |
| u, v | = | dimensionless velocity components, |
| x, y | = | dimensionless rectangular coordinates, |
Greek Symbols
| β | = | volumetric expansion coefficient (1/K) |
| ϵ | = | rate of deformation tensor, |
| φ | = | circumferential angle (o) |
| η | = | generalized viscosity function, |
| θ | = | dimensionless temperature, |
| ρ | = | density of fluid (kg/m3) |
| τ | = | stress tensor, 2ηϵij |
| ξ | = | normal direction |
Subscripts
| avg | = | average |
| cr | = | critical |
| i, j | = | tensoral notation |
| R | = | resultant |
| w | = | cylinder surface |
| ∞ | = | free-stream |
Superscript
| - | = | dimensional quantity |
Additional information
Notes on contributors
Satish Kumar Gupta
Satish Kumar Gupta is an undergraduate student in mechanical engineering from the National Institute of Technology, Durgapur, India. He has published 10 research articles in various peer-reviewed journals and conferences. His areas of interests are CFD, magnetohydrodynamics, nanofluid and non-Newtonian fluid flow, heat transfer, underground coal gasification, and slurry transport.
Sudipta Ray
Sudipta Ray is a Ph.D. scholar in the Department of Aerospace Engineering at the Indian Institute of Technology Kharagpur, India. Earlier he was associated with CSIR–CMERI, Durgapur, India, as a senior project fellow. He received his bachelor of technology degree from Kalyani Government Engineering College and his master's degree in mechanical engineering from Jadavpur University, India. He has published five research articles in various peer-reviewed journals. His areas of interests are CFD, hydrodynamics of underwater vehicles, magnetohydrodynamics, and non-Newtonian fluids.
Dipankar Chatterjee
Dipankar Chatterjee is a senior scientist in the CSIR–Central Mechanical Engineering Research Institute, India. Earlier he was associated with LPMI, Arts et Métiers Paris Tech, France, as a postdoctoral researcher. He received his Ph.D. from the Department of Aerospace Engineering, Indian Institute of Technology Kharagpur, India. He has published 90 international journal and conference papers. His main interests are computational modeling of fluid flow and heat transfer over bluff obstacles, turbulence, phase change and reactive flow process modeling, lattice Boltzmann modeling, and electromagnetohydrodynamic interactions in macro- and microflows.