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

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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?

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• 1. GRAY’S (1936) PARADOX

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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 Rex = 2 x 106 POWER = DRAG x SWIMMING SPEED He found that to swim at 10 m/s the specific muscle power

• utput 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

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• 2. Laminar and turbulent boundary layers

Boundary layers over a flat plate (Van Dyke 1990) Laminar profile – low friction Turbulent profile – high friction

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Boundary-layer transition from laminar to turbulent – 2D, low disturbance environment – ‘natural transition’

Amplifying Tollmien-Schlichting wave

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Tollmien-Schlichting waves in natural transition

Schubauer & Skramstadt (1947)

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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

(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)

Structure of dolphin’s epidermis

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• 3. Kramer’s pioneering experiments (1957, 1960)

Sea-based towing tests of slender body with a compliant coating

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Kramer’s design of ‘artificial dolphin skin’

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) c.f. dolphin’s epidermis

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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

• n 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

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• 4. Theoretical predictions of transition delay

Compliant-wall models Fluid-structure interaction: Solve flow equations and wall equations concurrently linked by interfacial conditions

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)

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Wave frequency Reynolds number damped amplifying (inside loop) Compliant wall Results for: Rigid Compliant More Compliant

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ω

Range of T-S wave amplification flow

Schematic stability diagram for 2D Tollmien-Schlichting waves in a boundary layer over rigid and compliant walls

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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.

Summary: effect of compliant coatings on Tollmien-Schlichting waves

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• 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

• f excited Tollmien-Schlichting

waves at the leading edge of a compliant panel [Gaster’s (1987) paper entitled “ Is the dolphin a red herring?”]

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Rigid-wall results Compliant-wall results

Experiment Theory Experiment: compliant Experiment: more compliant

Equivalent scale

Theoretical prediction of wall-based instability (Lucey & Carpenter 1995)

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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 are unstable within each loop (Lucey & Carpenter 1995)

TWF Critical Reynolds number TWF Critical Reynolds number with wall damping Reynolds number or distance from leading edge

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• 6. Hydro-elastic instabilities of compliant coatings:

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)

Increasing time Initial condition

Key point: downstream propagating wave amplifies, upstream attenuates

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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)

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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)

Initial condition: yery low amplitude deformation applied at panel mid-point Increasing time

Flow

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Three dimensional simulation of divergence linear instability – plate-spring wall. (Lucey 1998)

Flow

At time T At time 2T At time 3T At time 4T

Note: emergence of quasi two-dimensional unstable waves from a three-dimensional form of initial excitation

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Comparison of TWF and divergence instabilities

Increasing time

TWF – amplifies only as wave travels downstream of source of excitation – convective instability Divergence – downstream travelling wave but amplifies both upstream and downstream

• f source of excitation –

absolute instability Flow

(Carpenter, Lucey & Davies 2001)

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Summary of main instabilities in flow over compliant walls

Instability Effect of wall compliance Effect of structural damping in wall on

• nset

Wave character Instability type Prediction methods Tollmien- Schlichting waves Stabilising Destabilising Modest downstream travelling Convective Negative energy wave (Class A) Orr-Sommerfeld Eqn. Tailored spectral methods Travelling- wave flutter Destabilising Stabilising Fast downstream travelling Convective Positive energy wave (Class B) Rayleigh Eqn. Asymptotic methods Tailored spectral methods Numerical simluation Divergence Destabilising No effect Static at

• nset –

slow downstream after onset Absolute K-H type (Class C) Laplace Eqn. Special numerical methods; boundary- element, discrete- vortex

Plus others – e.g. coalescence of T-S waves and TWF – and nonlinear effects.

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• 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

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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

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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)

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Illustrative cases of skin- friction drag reduction… …continued

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 Based on slender body theory

(From: Klinge, Lucey & Carpenter 2000)

*Note: Some account included here for beneficial effect of compliance on the turbulent boundary layer

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Turbulent skin-friction reduction using compliant coatings

Choi et al. (1997) conducted experiments that demonstrated up to a 6% decrease in drag for turbulent boundary-layer over a compliant coating. However, elastic modulus of coating was much higher (although thickness similar) than that required for maintaining laminar flow

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The way forward: multiple compliant panels

Evolution of Tollmien-Schlichting waves

• ver a rigid-complaint-rigid surface

Carpenter, Lucey & Davies (2001) based

• n Davies & Carpenter (1997)

Attenuation of Tollmien- Schlichting waves possible for very short compliant panels… that are much less susceptible to hydro- elastic instability Design Strategy: use streamwise arrays of compliant panels with properties optimised to local Reynolds number

Indefinite postponement of transition possible?

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Conclusions… so far

• Demonstrated, both experimentally and theoretically, that

compliant coatings are capable of extending laminar flow… hence skin-friction drag reduction.

• Design of effective compliant coatings requires a sound

knowledge of the diversity of waves that can exist within the flow-structure system.

• There is the prospect of indefinitely postponing transition by

using arrays of compliant panels each of which is optimised for local flow conditions.

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• 8. Gray’s paradox reassessed

Major assumptions in Gray’s modelling Effects of dolphin’s swimming motions neglected (assumed a rigid body) Laminar-to-turbulent transition of boundary layer occurs at Re= 2 x 10^6 (flat plate value) Swimming speed = 10 m/s Mammalian muscle power = 40 W/kg How good are these assumptions?

“…specific muscle power output required was 7 x mammalian norm…”

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Is drag increased by the unsteady flow associated with propulsion? Lighthill (1971) suggested a 4- to 5-fold rise in drag due to boundary-layer thinning in the unsteady flow… but this neglects effect of re-laminarization due to flow acceleration. Anderson et al. (2001) observed the predicted BL thinning on fish but found that the drag was only 1.5 times the rigid-body value. Barrett et al. (1999) actually observed a 50 % drag reduction on their swimming robot tuna. Hence… probably OK to assume there is no drag rise for an actively swimming dolphin.

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Streamwise pressure distribution exists along dolphin body due to its shape – favourable pressure gradient reduces T-S wave growth. consistent with observations by Romanenko (2002) on dolphins. Hence:

From Aleev (1977)

Ret = 0.5 x ReL

What is the appropriate transitional Reynolds number? i.e. about 10,000,000 for a 2 m long dolphin swimming at 10 m/s

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What is the swimming speed of a dolphin?

Most reliable aircraft-based observations of a school of common dolphins. Grushanskaya & Korotkin (1973) measured ultimate speed of c. 11 m/s.

But typical sustained speed in the range 3.5 to 5 m/s

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Power output of muscles?

Muscle performance depends on type of fibre

• Slow oxidative fibres

Mainly aerobic metabolism Slow sustained activity Relatively slow contraction rates

• Fast glycolic fibres

Mainly anaerobic metabolism Short-burst activity High power output Very high intrinsic contraction speeds Power output is 2 to 17 times that of slow fibres Dolphin muscle has both types of fibre Sustained aerobic output = 40 W/kg (Parry 1949) Short-duration anaerobic output = 110 W/kg (Weis-Fogh & Alexander 1977)

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So… new estimates of swimming speed in m/s

Case CD Sustained Power output (40W/kg) Maximum 110 W/kg Ret = 2 ×106 (Gray) 0.0025 5.6 7.9 Ret = 13.75×106 0.0015 6.6 9.3 Laminar 0.00025 12.08 16.9 Gliding dolphin 0.0023* (0.0015)

• *based on body area only.

Thus there is no paradox!

Hence… no need to invoke special laminar flow properties of skin!

(from Babenko & Carpenter 2003)

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So… does the dolphin have a need for laminar-flow control?

Most scientists have followed Gray and focused on maximum sustained swimming speed. Laminar flow needed to reach 10 m/s but not to reach commonly

• bserved speeds. In any case the ‘porpoising’ swimming mode is used

at high speeds…. Laminar-flow control more likely required for conserving energy during: Slower long-duration swimming ‘Gliding’ during deep diving

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Energy efficient deep diving

From Williams et al. (2000) Red: gliding; Black: powered swimming

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Evidence that the dolphin does have a laminar-flow control capability

In vivo measurement of dolphin-skin properties Madigosky et al. (1986) Optimised double-layer ‘artificial dolphin skins’ have a free-wave speed of 6.5 m/s for a design flow speed of 9 m/s. Results imply that dolphin skin optimized for ca. 9 m/s Locations of surface wave-speed measurements Grey circles: 6-7 m/s; Open circles: no measurement.

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Skin folding – hydro-elastic instability (divergence) at high swimming speeds

From Essapian (1955)

Optimised double-layer ‘artificial dolphin skins’ experience divergence instability with a wavelength 40 mm at 9 m/s. Wavelength of divergence on dolphin measured at 35-40 mm This suggests that dolphin skin is an optimized compliant coating (that fails beyond its design flow speed)

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Cutaneous ridges - aligned normal to the streamwise direction

from Ridgway & Carder (1993)

Oblique Tollmien-Schlichting waves grow fastest over compliant walls. Numerical simulation of Ali & Carpenter (2002) show that their growth rate is reduced by c. 25 % when cutaneous ridges are present. Implies that dolphin skin has evolved for laminar-flow control

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Note that dolphins also have dermal ridges Lateral spacing is ca. 10-15 mm. Therefore not adapted through evolution into riblets for turbulent flow.

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And… Other direct evidence of laminar flow over dolphin body Hot-film & pressure-sensor measurements Kozlov et al. (1974), Pyatetskii et al. (1982) Romanenko (1986)

Overall conclusion is that fluctuation level in boundary layer over dolphin is much lower than comparable rigid body.

Can conclude that while Gray’s paradox has probably been resolved, there is much evidence that dolphin skin does possess the capability for laminar-flow control

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• 9. What have we learned from the dolphin?
• How to design a technology capable of significant transition delay and

thus reduced skin-friction drag… with the prospect of indefinite postponement of laminar-to-turbulent transition

• Vastly increased scientific knowledge of the physics of fluid-structure

interaction… with applications in, for example: Biomechanics – blood flow, respiration… Structural acoustics (in the presence of mean flow) Industry – sails, parachutes, convertible car roofs… Fluid-energy harvesting devices (where flow-induced instability can be exploited)

• New theoretical and computational techniques that have a multiplicity of

applications.

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Acknowledgments to: Prof Peter Carpenter, Dr Mark Pitman, A/Prof Chris Davies, Dr Gerard Cafolla and the many others with whom I have had the pleasure to work on compliant coatings