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Investigation of the effects of superhydrophobic surface treatment on the dynamics of the flow in the near wake of a sphere using spatial dynamic mode decomposition

Shaun Davey, Callum Atkinson, Julio Soria

Abstract

Viscous drag arises from the fluid at a surface having zero relative velocity, a phenomenon known as the no-slip condition. Superhydrophobic surfaces, when submerged in water, trap a layer of air in their surface texture, partially replacing the liquid-solid interface with a liquid-gas interface. This air layer, called the plastron, results in partial slip at the surface, thereby reducing the viscous drag. In turbulent flows, large fluctuations in pressure and velocity can deplete or completely remove the plastron from the surface. This makes evaluating the effects of superhydrophobic surface treatments on flow dynamics particularly challenging. This study examines the impact of a sustained plastron on the dynamics in the shear layer of a sphere, achieved by supplying air at low pressure through pores in the sphere's surface. Instantaneous planar velocities in the wakes of spheres, both with and without superhydrophobic surface treatment, are measured within a plane passing through the spheres' centre. Dynamic mode decomposition (DMD) is applied to the velocity fluctuations in the shear layer to evaluate how superhydrophobic surface treatment affects the instabilities there. It is shown that the addition of the pores has a relatively small effect on the instabilities in the shear layer, while they are significantly changed by the addition of superhydrophobic surface treatment when the plastron is sustained.

Investigation of the effects of superhydrophobic surface treatment on the dynamics of the flow in the near wake of a sphere using spatial dynamic mode decomposition

Abstract

Viscous drag arises from the fluid at a surface having zero relative velocity, a phenomenon known as the no-slip condition. Superhydrophobic surfaces, when submerged in water, trap a layer of air in their surface texture, partially replacing the liquid-solid interface with a liquid-gas interface. This air layer, called the plastron, results in partial slip at the surface, thereby reducing the viscous drag. In turbulent flows, large fluctuations in pressure and velocity can deplete or completely remove the plastron from the surface. This makes evaluating the effects of superhydrophobic surface treatments on flow dynamics particularly challenging. This study examines the impact of a sustained plastron on the dynamics in the shear layer of a sphere, achieved by supplying air at low pressure through pores in the sphere's surface. Instantaneous planar velocities in the wakes of spheres, both with and without superhydrophobic surface treatment, are measured within a plane passing through the spheres' centre. Dynamic mode decomposition (DMD) is applied to the velocity fluctuations in the shear layer to evaluate how superhydrophobic surface treatment affects the instabilities there. It is shown that the addition of the pores has a relatively small effect on the instabilities in the shear layer, while they are significantly changed by the addition of superhydrophobic surface treatment when the plastron is sustained.

Paper Structure

This paper contains 14 sections, 24 equations, 10 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Superhydrophobic Surfaces
  3. Flow Structures in the Wake of A Sphere
  4. The Current Work
  5. Methodology
  6. Experimental Facility
  7. Vertical Water Tunnel
  8. Sphere Design
  9. Experimental Method
  10. Dynamic Mode Decomposition
  11. Application of Dynamic Mode Decomposition to the Flow Over Spheres
  12. Results
  13. Discussion
  14. Concluding Remarks

Figures (10)

  • Figure 1: (a) Vertical water tunnel facility and (b) experimental field of view (reproduced from davey2025experimental).
  • Figure 2: Aerofoil crossbeam and sting used for mounting the sphere (reproduced from davey2025experimental).
  • Figure 3: Cut-away view of 3D-printed sphere models for the (a) smooth reference sphere and (c) porous spheres with and without superhydrophobic surface treatment (reproduced from davey2025experimental).
  • Figure 4: Image of the plastron formed on the superhydrophobic sphere, taken with a non-PIV camera (reproduced from davey2025experimental).
  • Figure 5: Proportion of DMD modes with an energy share of 5% or more for each cumulative TKE for the (a) REF, (b) PRS and (c) SHS spheres. Black dotted lines indicate the chosen TKE for each sphere.
  • ...and 5 more figures