Drag Reduction for Flow Across Superhydrophobic and Leidenfrost Surfaces
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1 Drag Reduction for Flow Across Superhydrophobic and Leidenfrost Surfaces Glen McHale Michael I. Newton Neil Sandham, Brian Gruncell, Angela Busse University of Northumbria at Newcastle Nottingham Trent University University of Southampton Materials Research Society, Boston, USA 5 th December 2013 Public Understanding website:
2 Overview 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
3 Perfectly Hydrophobic Sphere Perfectly Hydrophobic Sphere 3
4 Experimental Motivation Superhydrophobic Sphere with Plastron Solid sphere Same sphere Plastron bearing sphere Sphere with Leidenfrost Effect Dr Carl Evans McHale, G. et al., Appl. Phys. Lett. 94 (2009) art Vakarelski et al., Phys. Rev. Lett. (2011) 106
5 Creeping Flow Boundary Conditions 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 Stokes Drag (Low Re) Hadamard-Rybczynski Encapsulated Droplet Fluid, 2 Fluid, 2 Fluid, 2 Solid Fluid, 1 Fluid, 1 Fluid Hadamard-Rybczynski drag is 25% less than Stokes drag McHale, G., et al., Soft Matter 6 (2010) 714.
6 Compound Droplet Air Lubricated Flow Perfectly Hydrophobic Model Air Encapsulated (Plastron) Results Sphere Sphere Solid, water and air can be replaced by a combination of any three fluids Drag Reduction Factor Sphere Sphere x SH = 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 McHale, G., Flynn, M.R. & Newton, M.I., Soft Matter (2011) 7 art
7 Drag Reduction and Slip Length Drag Correction Factor Slip Length l s (-1+ lg /4)h C D 24x SH /Re Drag correction as function of normalized plastron thickness (various gas-to-liquid viscosity ratios). Normalized slip length, l s /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 McHale, G., Flynn, M.R. & Newton, M.I., Soft Matter (2011) 7 art
8 CFD: High Re and Solid Surface Fractions CFD: High Re and Solid Surface Fractions 8
9 CFD (Fluent TM ) Calculations at Higher Re Drag Reduction with Re and h/b Backflow and Separation Axial vel. at top of sphere (Re=0.001, h/b=0.1) Apparent slip 0.4U Recirculation within Plastron Stokes flow drag reduction Onset of separation at Re=24 CFD Calculations seem reliable Gruncell, B.R.K., et al., Phys. Fluid. (2013) 25 art
10 Suppression of Vortices and Separation Suppression of Vortices Separation Suppression (Re=100, h/b=0.1) Vortex Sphere Plastron Suppression of attached vortices occurs for 30<Re<100 (limit of calculation) Modification of separation points and suppression of vortices. Plastron or Leidenfrost layers can narrow wake and reduce drag Gruncell, B.R.K., et al., Phys. Fluid. (2013) 25 art
11 Superhydrophobicity Solid Surface Fraction Flow Patterns at Re =100 Axisymmetric baffles Solid Surface Fraction (F s ) Effects (h/b=0.1) Drag increase Drag decrease Without baffles With baffles F s =0.1, Re=100 Gruncell, B.R.K., et al., Phys. Fluid. (2013) 25 art
12 Channels and Pipes Channels and Pipes 12
13 Model Systems Analytical Framework 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 Four Flow Cases 1. Couette flow 2. Symmetric pressure-driven channel flow 3. One sided pressure-driven channel flow 4. Pipe flow Busse, A., et al., J. Fluid Mech. (2013) (Also see: A.P. Tsai, 736)
14 Results for Pipes Flow Profiles Drag Reduction* Recirculation within Plastron Optimum gas thickness *Apparent slip lengths can also be calculated. Optimum thickness of air layer (Plastron) is a competition between increased lubrication by air and increased obstruction of core cross-sectional area for flow Busse, A., et al., J. Fluid Mech. (2013) (Also see: A.P. Tsai, 736)
15 Summary 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 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), The End Group website and reprints:
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