Plastron induced drag reduction and separation delay on a
hydrophobic sphere at finite Reynolds numbers
B. R. K. Gruncell∗, N. D. Sandham∗ , and G. McHale†
This study explores the potential for achieving a drag reduction with a superhydrophobic sphere coated in a plastron (air layer). The system is modelled as a
solid sphere encapsulated in an air layer of uniform thickness, subject to an external
flow field (see Fig 1). A previous analytical study of this problem for Stokes flow1
demonstrated that a drag reduction can approach 20%.
This work validates the analytic theory and extends the analysis to Reynolds
numbers (Re) up to 100, including the effects of inertia and flow separation. The
flow is simulated in a 2D axisymmetric formulation using a commercial CFD package.
The plastron is modelled using a coupled wall boundary condition such that the airwater interface is fixed, whilst ensuring the matching of tangential velocity and shear
stress across the interface. The results showed that the CFD package is capable of
accurately simulating flow past a solid sphere up to Re = 100, capturing the attached
vortex that appears above a Reynolds number of 24 and matching the drag coefficient
to better than 1% across 5 orders of magnitude.
The simulations verified the analytic results of plastron induced drag reduction
at a Reynolds number of 0.001, but slowly depart from the analytic solution as the
Reynolds number is increased. Inertial effects act to increase the effect of the plastron and result in a larger drag reduction. Furthermore, the attached vortex that is
apparent for a solid sphere, is completely suppressed over the Reynolds number range
explored in this study (see Fig 2). This delay in separation is evident even for thin
plastrons (0.005D) and results in a total drag reduction of up to 50%.
The authors would like to gratefully acknowledge the funding provided for this
project by EPSRC, with grant EP/G058318/1.
∗ AFM
Group, University of Southampton, UK
of Computing, Engineering & Information Sciences, Northumbria University, UK
1 McHale, Flynn & Newton, Soft Matter 7, 10100 (2011).
† School
Figure 1: Schematic of plastron
Figure 2: Pathlines around a solid sphere (top) and
bearing solid sphere
plastron bearing sphere (bottom) at Re = 100