Numerical Predictions of Heat Transfer and Flow Structure in a Square Cross-Section Channel with Various Non-Spherical Indentation Dimples

Abstract

The present study employs arrays of different shapes of surface dimples to determine the most optimal configurations for augmenting surface heat transfer rates, as pressure drop penalties are minimized. Six different dimple shapes are investigated (spherical indentation (case A), super-ellipse (case D), two ellipse-spherical arrangements with the long axis oriented both parallel and normal to the bulk flow direction (cases B1 and B2, respectively), and two egg-spherical arrangements with the half ellipse with longer axis pointed both away and towards the bulk flow direction (cases C1 and C2, respectively). The dimples in these arrays are aligned with each other, as they are located on one surface of a square cross-section channel in six different streamwise rows. All turbulent fluid flow and surface heat transfer results are obtained using computation fluid dynamics with a k−ϵ RNG turbulence model, and constant heat flux thermal boundary conditions applied to all channel surfaces. Flow development is provided, both before and after the middle channel section, which contains each dimple array. Numerically predicted results are qualified using grid-independent predictions of experimental data for one baseline dimple array arrangement. The channel inlet Reynolds number ranges from 8,000 to 24,000. The dimple shapes with the best overall performance (depending upon the Reynolds number and performance criteria considered) are the spherical indentation arrangement (case A), and the ellipse-spherical arrangement with the long axis oriented normal to the bulk flow direction (case B2). Overall, the most optimal heat transfer augmentations seem to occur when the largest indented cross-section area is oriented perpendicular to the streamwise direction, since larger areas are then available for shear layer re-attachment over downstream portions of the associated dimples. Also important for such augmentations are dimple surface geometry transitions and surface curvature diameters, as illustrated by thermal performance which decreases as surface shapes have more numerous or more significant discontinuities, or when local surface curvature diameters are too small. Overall, the present results also show that such configuration sensitivities appear to increase with Reynolds number.