Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-21T11:42:02.778Z Has data issue: false hasContentIssue false
  • English
  • Français

On the origin of the drag force on dimpled spheres

Published online by Cambridge University Press:  20 September 2019

Nikolaos Beratlis Open the ORCID record for Nikolaos Beratlis [Opens in a new window] ,
Elias Balaras Open the ORCID record for Elias Balaras [Opens in a new window]  and
Kyle Squires Open the ORCID record for Kyle Squires [Opens in a new window]
Nikolaos Beratlis
Affiliation:
School for Engineering of Matter, Transport and Energy, Arizona State University, Tempe, AZ 85281, USA
Elias Balaras*
Affiliation:
Department of Aerospace and Mechanical Engineering, The George Washington University, Washington, DC 20052, USA
Kyle Squires
Affiliation:
School for Engineering of Matter, Transport and Energy, Arizona State University, Tempe, AZ 85281, USA
*
†Email address for correspondence: balaras@gwu.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

It is well established that dimples accelerate the drag crisis on a sphere. The result of the early drag crisis is a reduction of the drag coefficient by more than a factor of two when compared to a smooth sphere at the same Reynolds number. However, when the drag coefficients for smooth and dimpled spheres in the post-critical regime are compared, the latter is higher by a factor of two to three. To understand the origin of this behaviour, we conducted direct numerical simulations of the flow around a dimpled sphere, which is similar to commercially available golf balls, in the post-critical regime. By comparing the results to those for a smooth sphere, it is found that dimples, although effective in accelerating the drag crisis, impose a local drag penalty, which contributes significantly to the overall drag force. This finding challenges the broadly accepted view that dimples only indirectly affect the drag force on a sphere by energizing the near-wall flow and delaying global separation.

JFM classification

Boundary Layers: Boundary layer separation Flow Control: Drag reduction
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 879 , 25 November 2019 , pp. 147 - 167
Check for updates
Copyright
© 2019 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Achenbach, E. 1972 Experiments on the flow past spheres at very high reynolds numbers. J. Fluid Mech. 54 (3), 565–575.Google Scholar
Aoki, K., Ohike, A., Yamaguchi, K. & Nakayama, Y. 2003 Flying characteristics and flow pattern of a sphere with dimples. J. Vis. 6 (1), 67–76.10.1007/BF03180966Google Scholar
Aoki, K., Muto, K., Okanaga, H. & Nakayama, Y. 2009 Aerodynamic characteristic and flow pattern on dimples structure of a sphere. In 10th International Conference on Fluid Control, Measurements, and Visualization, Moscow, Russia.Google Scholar
Aoki, K., Muto, K. & Okanaga, H. 2012 Mechanism of drag reduction by dimple structures on a sphere. J. Fluid Sci. Technol. 7 (1), 1–10.Google Scholar
Balaras, E. 2004 Modeling complex boundaries using an external force field on fixed cartesian grids in large-eddy simulations. Comput. Fluids 33 (3), 375–404.10.1016/S0045-7930(03)00058-6Google Scholar
Balaras, E., Schroeder, S. & Posa, A. 2015 Large-eddy simulations of submarine propellers. J. Ship Res. 59 (4), 227–237.10.5957/jsr.2015.59.4.227Google Scholar
Bearman, P. W. & Harvey, J. K. 1976 Golf ball aerodynamics. Aeronaut. Q. 27 (02), 112–122.Google Scholar
Beratlis, N., Balaras, E. & Squires, K. 2014 Effects of dimples on laminar boundary layers. J. Turbul. 15 (9), 611–627.10.1080/14685248.2014.918270Google Scholar
Beratlis, N., Balaras, E., Squires, K. & Vizard, A. 2016 Simulations of laminar boundary-layer flow encountering large-scale surface indentions. Phys. Fluids 28 (3), 035112.Google Scholar
Choi, J., Jeon, W. & Choi, H. 2006 Mechanism of drag reduction by dimples on a sphere. Phys. Fluids 18, 149–167.10.1063/1.2191848Google Scholar
Choi, H., Jeon, W. & Kim, J. 2008 Control of flow over a bluff body. Annu. Rev. Fluid Mech. 40 (1), 113–139.10.1146/annurev.fluid.39.050905.110149Google Scholar
Hunt, J. C. R., Wray, A. & Moin, P. 1988 Eddies, streams, and convergence zones in turbulent flows. Studying Turbulence Using Numerical Simulation Databases vol. 1, pp. 193–208.Google Scholar
Orlanski, I. 1976 A simple boundary condition for unbounded hyperbolic flows. J. Comput. Phys. 21 (3), 251–269.10.1016/0021-9991(76)90023-1Google Scholar
Pal, A., Sarkar, S., Posa, A. & Balaras, E. 2017 Direct numerical simulation of stratified flow past a sphere at a subcritical reynolds number of 3700 and moderate froude number. J. Fluid Mech. 826, 5–31.Google Scholar
Posa, A., Lippolis, A., Verzicco, R. & Balaras, E. 2011 Large-eddy simulations in mixed-flow pumps using an immersed-boundary method. Comput. Fluids 47 (1), 33–43.10.1016/j.compfluid.2011.02.004Google Scholar
Posa, A., Lippolis, A. & Balaras, E. 2015 Large-eddy simulation of a mixed-flow pump at off-design conditions. Trans. ASME J. Fluids Engng 137 (10), 101302.10.1115/1.4030489Google Scholar
Posa, A. & Balaras, E. 2016 A numerical investigation of the wake of an axisymmetric body with appendages. J. Fluid Mech. 792, 470–498.10.1017/jfm.2016.47Google Scholar
Posa, A. & Balaras, E. 2018 Large-Eddy Simulations of a notional submarine in towed and self-propelled configurations. Comput. Fluids 165, 116–126.Google Scholar
Rahromostaqim, M., Posa, A. & Balaras, E. 2016 Numerical investigation of the performance of pitching airfoils at high amplitudes. AIAA J. 54 (8), 2221–2232.10.2514/1.J054424Google Scholar
Smits, A. J. & Ogg, S. 2004 Aerodynamics of the Golf Ball. pp. 3–27. Springer.Google Scholar
Spalart, P. R. & Watmuff, J. H. 1993 Experimental and numerical study of a turbulent boundary layer with pressure gradients. J. Fluid Mech. 249, 337–371.Google Scholar
Toivanen, J. & Rossi, T. 2001 A parallel fast direct solver for block tridiagonal systems with separable matrices of arbitrary dimension. SIAM J. Sci. Comput. 20, 1778–1796.Google Scholar
Wieselsberger, C. 1922 Weitere feststellungen ber die gesetze des flssigkeits-und luftwiderstandes. Phys. Z. 23, 219–224.Google Scholar
Yang, J. & Balaras, E. 2006 An embedded-boundary formulation for large-eddy simulation of turbulent flows interacting with moving boundaries. J. Comput. Phys. 215 (1), 12–40.Google Scholar