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Drag Reduction for Flow Across Superhydrophobic and Leidenfrost Surfaces Glen McHale University of Northumbria at Newcastle Michael I. Newton Nottingham Trent University Neil Sandham, Brian Gruncell, Angela Busse University of Southampton
Materials Research Society, Boston, USA 5th December 2013
Public Understanding website: http://www.naturesraincoats.com/
Overview
27 December 2013
1. Perfectly Hydrophobic Sphere
– Experimental Motivation
– Analytical Model for Creeping Flow
2. Computational Fluid Dynamics
– Higher Re
– Solid Surface Fractions
3. Channels and Pipes
– Boundary Conditions for Couette, Channel and Pipe Flows
– Analytical Results for Pipes
27 December 2013
Perfectly Hydrophobic Sphere
Perfectly Hydrophobic Sphere
3
Experimental Motivation
27 December 2013
McHale, G. et al., Appl. Phys. Lett. 94 (2009) art. 064104.
Solid sphere Plastron bearing
sphere
Same sphere
Dr Carl
Evans
Superhydrophobic Sphere with Plastron Sphere with Leidenfrost Effect
Vakarelski et al., Phys. Rev. Lett. (2011) 106
27 December 2013
Creeping Flow – Boundary Conditions
Stokes Drag (Low Re) Hadamard-Rybczynski Encapsulated Droplet
Hadamard-Rybczynski drag is 25% less than Stokes drag
Fundamental boundary condition is not “no-slip”, but is continuity of shear stress
Well-known drag reduction effects for gas bubbles with non-rigid interfaces in water
Fluid, 2
Solid
Fluid, 2
Fluid
, 1
Fluid, 2
Fluid, 1
Fluid
McHale, G., et al., Soft Matter 6 (2010) 714.
Compound Droplet – Air Lubricated Flow
27 December 2013
Sphere
Sphere Sphere
Sphere
Perfectly Hydrophobic Model
Drag Reduction Factor
Air Encapsulated (Plastron) Results
xSH= Drag of sphere with plastron/drag of sphere
gl = ratio of dynamic viscosities extent of air lubrication
e = ratio of b/a extent of obstruction cross-section
Solid, water and air can be replaced
by a combination of any three fluids
McHale, G., Flynn, M.R. & Newton, M.I., Soft Matter (2011) 7 art. 10100.
Drag correction as function of normalized plastron
thickness (various gas-to-liquid viscosity ratios).
Drag Correction Factor
27 December 2013
Drag Reduction and Slip Length
Slip Length
Normalized slip length, ls/b, as a function of
normalized plastron thickness, h/b.
Slip length at low h/b is an order of magnitude larger than plastron thickness
ls(-1+ lg/4)h
CD24xSH/Re
McHale, G., Flynn, M.R. & Newton, M.I., Soft Matter (2011) 7 art. 10100.
27 December 2013
CFD: High Re and Solid Surface Fractions
CFD: High Re and Solid Surface Fractions
8
Drag Reduction with Re and h/b
27 December 2013
CFD (FluentTM) Calculations at Higher Re
Gruncell, B.R.K., et al., Phys. Fluid. (2013) 25 art. 043601.
Backflow and Separation
Stokes flow
drag reduction
Axial vel. at top of sphere
(Re=0.001, h/b=0.1)
Onset of separation
at Re=24
Recirculation within Plastron
Apparent slip 0.4U
CFD Calculations seem reliable
27 December 2013
Suppression of Vortices and Separation
Plastron or Leidenfrost layers can narrow wake and reduce drag
Gruncell, B.R.K., et al., Phys. Fluid. (2013) 25 art. 043601.
Sphere
Modification of separation points and
suppression of vortices.
Separation Suppression (Re=100, h/b=0.1)
Vortex
Plastron
Suppression of attached vortices occurs
for 30<Re<100 (limit of calculation)
Suppression of Vortices
Flow Patterns at Re =100
27 December 2013
Superhydrophobicity – Solid Surface Fraction
Gruncell, B.R.K., et al., Phys. Fluid. (2013) 25 art. 043601.
Solid Surface Fraction (Fs) Effects (h/b=0.1) Axisymmetric
baffles
Without baffles
With baffles
Fs=0.1, Re=100
Drag
increase
Drag
decrease
27 December 2013
Channels and Pipes
Channels and Pipes
12
27 December 2013
Model Systems – Analytical Framework
Busse, A., et al., J. Fluid Mech. (2013) 727 488 (Also see: A.P. Tsai, 736)
Four Flow Cases
1. Couette flow
2. Symmetric pressure-driven channel flow
3. One sided pressure-driven channel flow
4. Pipe flow
Boundary Conditions
1. Simplify to perfectly hydrophobic gas layer boundary
2. Continuity of shear stress across gas-liquid interface
3. Continuity of velocity at gas-liquid interface
4. Zero net mass flow rate in gas layer ( recirculation) rather than
usual assumption of equal pressure gradient
Drag Reduction*
*Apparent slip lengths can also be calculated.
27 December 2013
Results for Pipes
Busse, A., et al., J. Fluid Mech. (2013) 727 488 (Also see: A.P. Tsai, 736)
Flow Profiles
Recirculation within Plastron
Optimum gas
thickness
Optimum thickness of air layer (Plastron) is a competition between increased
lubrication by air and increased obstruction of core cross-sectional area for flow
27 December 2013
1. Developed an analytical model of perfect encapsulating air (or vapour) layers
2. At low Re, air lubrication versus increased cross-section optimum thickness
3. At high Re, vortex suppression even higher drag reduction
4. CFD suggests solid surface fraction rapidly suppresses drag reduction mechanism
5. Drag reduction most effective for higher Re and low solid surface fractions
6. General alternative boundary condition recirculating air (or vapour) layer
7. Applied new boundary condition to channel and pipe flows
8. At low Re, air lubrication versus obstruction of core optimum thickness
The End
Group website and reprints: http://www.naturesraincoats.com/
Summary
Acknowledgements UK EPSRC, UK Sport, Dstl
Dr. Morris Flynn (Alberta)
Mr. Ian Campbell, Dr. Martyn Prince (Southampton)
Dr. Carl Evans, Dr. Neil Shirtcliffe (Nottingham Trent)
Dr Scott Drawer (UK Sport), Dr Stuart Brewer (Dstl),
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