Fully Attached (FA) Flow:

Flow is wetted on pressure and

suction sides (some base

ventilation can occur)

Fully Ventilated (FV) Flow:

Suction-side flow is separated,

and a large, stable cavity of

atmospheric gas is entrained

Partially Ventilated (PV) Flow:

An atmospheric cavity is

entrained, but does not reach

the immersed tip.

Calm free

surface

Foil tip

Aerated Tip Vortex

Re-entrant Jet 0 5 10 15 20 25 30

0

0.5

1

1.5

2

2.5

3

, deg

Fn

h =

U

(gh

)-1/2

Ventilation Boundaries, ARh=1.5

ℎ

𝑐

Numerical Setup

• Finite element analysis (FEM/FEA)

• Natural modes found using Abaqus Standard with Lanczos Solver

• Foil meshed with first-order SC8R shell elements

– Aluminum and PVC hydrofoils simulated

• Water domain meshed with AC3D8R acoustic fluid elements (water)

– Inviscid, incompressible, and infinite Froude number

assumptions

• Cavity meshed with AC3D8R acoustic fluid elements (air)

– Cavity represented with simplified geometry

Experimental Setup

• Experiments conducted on aluminum strut only

• Foil mounted on steel “test-frame”

– Vibration excited by hammer-strikes on foil

– FFT of 10-second window used to identify frequencies

– Foil’s tip submerged to depth ℎ in water-filled drum

• Several hammer-strike trials conducted in towing tank (FA and FV regimes)

– Accelerometer mounted to foil tip

Mode Shapes

PolyTec OFV-353 Single-

Point LDV Vibrometer

Atmospheric Ventilation

• Entrainment of incondensable gas (e.g. air) or a vapor/air mixture into low-pressure flow

Properly-designed superventilating geometries entrain a gaseous cavity to reduce drag

– Enhancement of stability and efficiency at high speeds

• Problematic at off-design conditions

– Up to 70% reduction in lift; 50% reduction in lift/drag ratio

– Sudden and drastic changes in loading can cause control, stability, and structural issues

• Ventilation changes the vibratory response of partially/fully submerged structures

– Added mass and damping change with ventilation and depend upon operating conditions

– Particularly important with progress toward lightweight/flexible marine structures

Relevance:

• Safety and controllability of any vessel relying upon ventilation-prone systems

• High speed and heavily loaded lifting surfaces are particularly vulnerable

– Surface piercing propellers/hydrofoils

– Supercavitating propellers/foils operating at shallow immersion

– Dynamic positioning thrusters or propulsors at low advance ratio

Objectives:

• Use experimental and numerical methods to parametrically study the effect of ventilation on

hydrodynamic and structural response of a canonical surface piercing strut.

Stage #1: Hydrodynamic Effects of Ventilation (Experimental)

• Conducted at UofM Marine Hydrodynamics Laboratory

– Parameter space defined by 𝐴𝑅ℎ, 𝐹𝑛ℎ, 𝛼

The Effects of Ventilation on the Hydrodynamic and Structural Response of

Surface-Piercing Struts Casey Harwood, Andrew Stankovich, Francisco Miguel, Prof. Julie Young, Prof. Steven Ceccio

Department of Naval Architecture & Marine Engineering, University of Michigan

Surface-piercing J-foil on

Americas Cup catamaran Source: Oracle Team USA

Numerical model of surface-

piercing propeller Source: Young and Savander, 2011

Chord Length 𝑐 11 in

Foil Span 𝑆 36 in

Max Foil Thickness 𝑇 1.1 in

Tip Immersion Depths ℎ 5.5, 11, 16.5 in

Immersed Aspect Ratio 𝐴𝑅ℎ = ℎ/𝑐 0.5, 1.0, 1.5

Velocities 𝑈 2-20 ft/s (0.6-6 m/s)

Submergence-based Froude No. 𝐹𝑛ℎ = 𝑈/ 𝑔ℎ 0.5 - 4.5

Chord-based Reynolds No. 𝑅𝑒𝑐 = 𝑈𝑐/𝜈 1.7 × 105 − 1.7 × 106

Chord-based Weber Number 𝑊𝑒 = 𝜌𝑈2𝑐/𝜎 1.42 × 103 − 1.42 × 105

Stage #2: Structural Effects of Ventilation (Numerical and Experimental

6-DOF Load Cell

at Foil Root 3-Axis Accelerometer

on Test Frame

ℎ

Solid and fluid

domains used in

numerical model

Conclusions

Hydrodynamic Response

• FA, FV, and PV flow regimes have been identified in parametric space

• Overlapping stability regions indicate bi-stability in flow regimes

• Hydrodynamic loads form hysteresis loop when passing through bi-stable regions

Structural Response

• Low-order modes agree well between numerical and experimental results

– Coupling with test frame modifies higher-order modes

• Natural frequencies decrease with increasing depth-of-immersion

• Natural frequencies in FV flow are bounded by frequencies in FA regime and

frequencies in “dry” testing

• Directional-dependence of added mass tensor affects modes differently with

changing depth-of-immersion and flow regime

– Some re-ordering of modes occurs

– Frequency coalescence may occur

Future Work

• Experiments using PVC hydrofoil to parametrically study the dynamic fluid and

structural response of flexible ventilated hydrofoils.

Experiment Simulation

Chord Length 𝑐 11 in 11 in

Foil Span 𝑆 39 in 39 in

Max Foil Thickness 𝑇 1.1 in 1.1 in

Tip Immersion

Depths ℎ 0, 5.5, 11, 16.5 in 0 - 36 in

Immersed Aspect

Ratio 𝐴𝑅ℎ = ℎ/𝑐 0, 0.5, 1.0, 1.5 0 - 3.3

Velocities 𝑈 0 ft/s (0 m/s) 0 ft/s (0 m/s)

Submergence-based

Froude No. 𝐹𝑛ℎ = 𝑈/ 𝑔ℎ 0 ∞

Material - 6061 Aluminum Aluminum, PVC

ℎ

0 5 10 15 20 25 300

0.5

1

1.5

2

2.5

3

, deg

Fn

h =

U

(gh

)-1/2

Ventilation Boundaries, ARh=1.5

FA

PV

FV

Inception (Separation)

Stabilization

Washout

Reattachment

0 5 10 15 20 25 300

0.5

1

1.5

2

2.5

3

, deg

Fn

h =

U

(gh

)-1/2

Ventilation Boundaries, ARh=1.5

0 5 10 15 20 25 300

0.5

1

1.5

2

2.5

3

, deg

Fn

h =

U

(gh

)-1/2

Ventilation Boundaries, ARh=1.5

0 5 10 15 20 25 300

0.5

1

1.5

2

2.5

3

, deg

Fn

h =

U

(gh

)-1/2

Ventilation Boundaries, ARh=1.5

Effect of Flow Regime on

Hydrodynamic Response

• Lift decreases significantly

with inception of ventilation

• Hydrodynamic forces &

moments form hysteresis

loop with changing 𝛼 and

𝐹𝑛ℎ

Overlapping stability

regions indicate bi-

stable flow

Regime Stability Regions (𝑨𝑹𝒉 = 𝟏. 𝟓)

Solid Elements

Acoustic Fluid

Elements

Effect of Immersion Depth in Fully-Attached Regime • Frequencies decrease monotonically with immersion depth

• Modes are affected differently as a result of directional

dependence in added mass

• Differences in 2nd bending mode probably due to coupling

with test-structure’s natural modes in experiments

0 0.5 1 1.50

50

100

150

200

Immersion Aspect Ratio, ARh

Freq

uen

cy, H

z

Dashed = ExperimentalSolid = Numerical

X-Bend 1

X-Bend 2

Z-Twist 1

Experimental/Numerical Comparison of Modal

Frequencies (Aluminum Hydrofoil)

Experimental results from

immersion in water-filled drum

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170

0

0.2

0.4

0.6

0.8

1

Frequency, Hz

Fre

qu

en

cy

Co

nte

nt

X-1 Mode (FEA)

X-2 (FEA)

Z-1 (FEA)

Fnh=2.5; FA (Exp)

Fnh=2.5; FV (Exp)

Effect of Regime on Modal Frequencies (𝜶 = 𝟏𝟒∘; 𝑨𝑹𝒉 = 𝟏. 𝟎)

Colored regions

indicate bounds

between FA and

FV frequencies

predicted with

FEA.

Effect of Flow Regime on Structural Response • Frequencies in the FV regime are bounded by the frequencies

in the FA regime and dry conditions.

• Modal frequencies in the FV regime are moderately higher

than in the FA regime

• Difficult to resolve 2nd bending mode in experiments

− Coupling with structure of the towing carriage

• Added mass and ventilation affect modes differently

− Potential for frequency coalescence / merging of modes

Acknowledgements:

• Support comes from:

–Naval Engineering Education Center (Award no. N65540-10-C-003), with support

from Dr. Thomas Fu of the Naval Surface Warfare Center, Carderock Division

– The National Research Foundation of Korea (NRF) grant funded by the Korean

government (MEST) (GCRC-SOP Grant no. 2012-0004783)

• This material is based upon work supported by the National Science Foundation Graduate

Student Research Fellowship under Grant No. DGE 1256260.

1 1 .5 2 2 .5 30

0 .5

F nh

= U∞

(g h )−1 /2

CL

3D

1 1 .5 2 2 .5 30

0 .1

0 .2

F nh

= U∞

(g h )−1 /2

Cm

In stan tan eo us

S teady S ta te F A

S teady S ta te F V

S teady S ta te P V

Lift/Moment Coefficients Plotted Against 𝑭𝒏𝒉

(𝜶 = 𝟏𝟎∘; 𝑨𝑹𝒉 = 𝟏. 𝟓) Lift Coefficient Plotted Against 𝜶

(𝑭𝒏𝒉 = 𝟐; 𝑨𝑹𝒉 = 𝟏. 𝟓)

Effect of Regime and 𝑨𝑹𝒉 on Modal Frequencies (Numerical)

(Aluminum Hydrofoil) (PVC Hydrofoil)

3rd Exp Mode 2nd Exp. Mode 1st Experimental Mode

Discrepancy likely due

to imperfect boundary-

conditions at root

Discrepancy in 2nd mode likely due to

imperfect boundary-conditions at root