Drag-reduction for Marine Vehicles: Learning from the Dolphin? by: - PowerPoint PPT Presentation

Drag-reduction for Marine Vehicles: Learning from the Dolphin? by: A(Tony).D. Lucey Dedicated to, and acknowledging the work of, Professor P.W. Carpenter (R.I.P April 2008) . Joint Technical Session of the Mechanical Panel of Engineers Australia, WA, The Institution of Mechanical Engineers, and American Society of Mechanical Engineers. 26th November, 2008, Perth, WA

Contents 1. Gray’s paradox (1936) 2. Laminar and turbulent boundary layers 3. Kramer’s pioneering experiments (1957, 1960) 4. Theoretical predictions of transition delay 5. Theory verified - the Gaster Experiments (1987) 6. Hydro-elastic instabilities of compliant coatings 7. Design of artificial dolphin skins Technical conclusions 8. Gray’s paradox re-assessd… 9. What have we learned from the dolphin? 2

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4 1. GRAY’S (1936) PARADOX

The Paradox Following contemporary naval engineering practice, Gray (1936) modelled the dolphin body as a flat plate – skin friction only and no dynamic effects – to estimate drag assuming transition occurred at = 2 x 10 6 Re x POWER = DRAG x SWIMMING SPEED He found that to swim at 10 m/s the specific muscle power output required was 7 x mammalian norm ( of 40 W/kg) Gray proposed that “if the flow is free from turbulence… power agrees closely…” - i.e. dolphins maintain laminar flow over their entire length 5

2. Laminar and turbulent boundary layers Boundary layers over a flat plate (Van Dyke 1990) Turbulent profile – high friction Laminar profile – low friction 6

Boundary-layer transition from laminar to turbulent – 2D, low disturbance environment – ‘natural transition’ Amplifying Tollmien-Schlichting wave 7

8 Tollmien-Schlichting waves in natural transition Schubauer & Skramstadt (1947)

Hypothesis for dolphin’s maintenance of laminar (boundary- layer) flow… hence skin-friction reduction Dolphin’s skin is able to ‘damp out’ Tollmien-Schlichting waves and thereby postpone transition Structure of dolphin’s epidermis (a) Longitudinal cross-section; (b) horizontal section through AA ’ ; (c) Lateral cross-section. Key: a, cutaneous ridges (or microscales); b , dermal papillae; c, dermal ridge; d, upper epidermal layer; e, fatty tissue. Carpenter, Davies & Lucey (2000) 9

3. Kramer’s pioneering experiments (1957, 1960) Sea-based towing tests of slender body with a compliant coating 10

Kramer’s design of ‘artificial dolphin skin’ c.f. dolphin’s epidermis Up to 60 % drag reduction at 18 m/s. Kramer believed that damping fluid eliminated Tollmien-Schlichting waves… not true! But… laminar-flow properties were confirmed theoretically Carpenter & Garrad (1985, 1986), Lucey & Carpenter (1995) 11

Experimental attempts to emulate Kramer’s results The 1960’s saw a flurry of ill-fated experiments that, overall, seemed to demonstrate that compliant coatings increased drag. e.g. Puryear (1962) – ridge-formation on coated test specimen By 1970, Bushnell (NASA) effectively concluded that compliant-coating was ill-founded as a technology. However, what had been lacking was a proper theoretical foundation for the design of experiments 12

4. Theoretical predictions of transition delay Compliant-wall models Flexible-plate plus spring foundation – simple one-dimensional (surface – based) model Single and two-layer (visco-) elastic slab(s) – two-dimensional (volume– based) model (From Carpenter 1991) Fluid-structure interaction: Solve flow equations and wall equations concurrently linked by interfacial conditions 13

Schematic stability diagram for 2D Tollmien-Schlichting waves in a boundary layer over rigid and compliant walls Wave damped amplifying (inside loop) frequency ω Results for: 1 Rigid Compliant More Compliant Reynolds number flow Compliant wall Range of T-S wave amplification 14

Summary: effect of compliant coatings on Tollmien-Schlichting waves Using classical hydrodynamic stability approach (Orr-Sommerfeld equation) – suppression of T-S waves theoretically possible – Benjamin (1960), Landahl (1962), Carpenter & Garrad (1985), Lucey & Carpenter (1995) – hence transition delay Attenuation occurs because wall compliance disrupts the energy- production mechanism of the growth of Tollmien-Schlichting waves A sufficiently compliant wall can eliminate Tollmien-Schlichting waves entirely! Structural damping in the wall undermines the beneficial effects of wall compliance – hence, is destabilising. 15

5. Theory verified - the Gaster Experiments (1987) Very careful (3 year program) experiments in a towing tank at National Physical Laboratories, UK Measured the growth in amplitude of excited Tollmien-Schlichting waves at the leading edge of a compliant panel [Gaster’s (1987) paper entitled “ Is the dolphin a red herring?”] 16

Experiment Theory Equivalent scale Rigid-wall results Compliant-wall results Theoretical prediction of wall-based instability (Lucey & Carpenter 1995) Experiment: Experiment: more 17 compliant compliant

Principal outcomes of the Gaster experiments 1. Wall compliance does attenuate Tollmien-Schlichting waves as predicted by theory – hence transition delay is possible. 2. The softer the wall, the greater the effect… 3. But… if wall is too soft, a different instability – Travelling-Wave Flutter (TWF) – sets in and this triggers premature transition Neutral stability loops – waves of given frequency TWF Critical TWF Critical are unstable within each Reynolds Reynolds number number with loop wall damping (Lucey & Carpenter 1995) 18 Reynolds number or distance from leading edge

6. Hydro-elastic instabilities of compliant coatings: Initial condition 6.1 Travelling-wave flutter (TWF) Numerical simulations of boundary- layer flow over plate-spring type compliant wall using (grid-free) discrete-vortex method and boundary-element method for flow solution (Pitman & Lucey 2004) Key point: downstream propagating wave amplifies, upstream attenuates 19 Increasing time

6.2 Divergence instability View from above compliant panel Flow Nonlinear divergence waves appear as quasi-two-dimensional ridges – with very slow downstream travel – Gad-el-Hak, Blackwelder & Riley (1985) 20

Flow Initial condition: yery low amplitude deformation applied at panel mid-point Prediction of divergence from linear instability to saturated nonlinear waves Numerical simulations of potential flow over plate- spring type compliant wall using boundary-element method for flow solution (Lucey et al. 1997, Pitman 2007) 21 Increasing time

Three dimensional simulation of divergence linear instability – plate-spring wall. (Lucey 1998) At time T At time 2T Flow At time 3T At time 4T Note: emergence of quasi two-dimensional unstable waves from a 22 three-dimensional form of initial excitation

Comparison of TWF and divergence instabilities Flow Increasing time TWF – amplifies only as wave travels downstream of Divergence – downstream source of excitation – travelling wave but amplifies convective instability both upstream and downstream of source of excitation – (Carpenter, Lucey & Davies 2001) absolute instability 23

Summary of main instabilities in flow over compliant walls Effect of structural Effect of wall Wave Instability Instability damping in Prediction methods compliance character type wall on onset Convective Orr-Sommerfeld Eqn. Tollmien- Modest Negative Schlichting Stabilising Destabilising downstream Tailored spectral energy wave waves travelling methods (Class A) Rayleigh Eqn. Fast Convective Asymptotic methods downstream Travelling- Positive Destabilising Stabilising Tailored spectral travelling wave flutter energy wave methods (Class B) Numerical simluation Laplace Eqn. Static at Absolute onset – Special numerical Divergence Destabilising No effect slow K-H type methods; boundary- downstream (Class C) element, discrete- after onset vortex Plus others – e.g. coalescence of T-S waves and TWF – and nonlinear effects. 24

7. Design of artificial dolphin skins Overall strategy: Make wall sufficiently flexible to maximise suppression of Tollmien-Schlichting waves…. But not succumb to hydroelastic instabilities Optimise! 5 key parameters: Lower-layer Elastic modulus Lower-layer thickness Lower-layer damping coefficient Upper-layer flexural rigidity Upper-layer damping coefficient 25

Results of optimisation… Transition length can be extended by a factor of 5.7 (Carpenter & Morris (1990), Dixon, Lucey & Carpenter (1994) and others since) All such optimisations suggest for compliant coatings optimized for transition delay: Surface-wave speed = 0.7 x Flow speed 26

Illustrative cases of skin- friction drag reduction Based on slender body theory 1. Length 6 m, speed 36 m/s – 1% drag reduction 2. Length 2 m, speed 1.54 m/s – 76% drag reduction (From: Klinge, Lucey & Carpenter 2000) 27

Illustrative cases of skin- friction drag reduction… …continued Based on slender body theory 1. Length 2.6 m, speed 23.1 m/s – 5% (14%)* drag reduction 2. Length 7 m, speed 2.6 m/s – 17% (25%)* drag reduction *Note: Some account included here for beneficial effect of compliance on the turbulent boundary layer (From: Klinge, Lucey & Carpenter 2000) 28