MAR2010 - Presentation of Wake

Rod Sampson - School of Marine Science and Technology - 6th March 2008

Presentation of ships wake

Resistance & Propulsion (1)MAR 2010

Flow around a propeller is affected by the presence of a hull

Potential and viscous nature of the boundary layer contribute to the development of the wake

Average speed of the water through the propeller plane is usually different (less) than the hull speed

Wake - Overview


FPAP

Wake Gain - Velocity distribution


Wake Gain - Frictional wake component

Viscous flow causes retardation of the flow inside a ships boundary layer

effect increases towards the stern causing a forward velocity component



Boundary layer

Viscous wakePotential wake

Velocity



Mean speed through B.L. is less than the ship speed


Wake Gain - Wave making component


Total Wake

Total wake = Potential wakeViscous wake

Wavemaking wake+ +

Hence Advance speed (Va) is less than the ship speed (V)


Wake definition and wake fraction

Wake is defined as a fraction of ship speed or advance velocity at the propeller plane

Froude wake fraction

Taylor wake fraction

w =V VA

Va

w =V VA

V

Va =V

1 + w

Va = V (1 w)



Wake fraction depends on length and fulness of the ship and increases with hull roughness

A typical moderate speed cargo ship of Cb = 0.70would expect w = 0.30



VA = V (1 w)

?



Wake & Wake Survey

Wake survey involves the detailed measurement of the flow through the propeller disc with the model

towed at a corresponding speed


Area of interest


Text




Wake & Wake Survey

Early measurements used intrusive methods to extract information on flow velocity

Pitot tubes Hot wire anemometry Tuft Strips

Pitot Wake


Pitot Wake

Propeller plane

Pitot comb

Rake can rotate 360 Degrees


Pitot Tube

Stagnation Pressure

Static Pressure

v =

2 (pstagnation pstatic)

2 hole tube - axial

5 hole tube - axial, vertical & horizontal


Pitot rake



Wake & Wake Survey

Modern measurements use non obtrusive methods

Particle image velocimetry PIV Laser doppler anemometry

Both systems are in use in the Department

Rod Sampson - School of Marine Science and Technology - 28th February 2008

LDA Wake

68

(2D)

03 Ju l2002

icepod systemwake0

-100 0 100Z [mm ]

-100

-50

0

50

100

Y[mm]

(2D)

03 Ju l2002

icepod systemwake0


Wake & Wake Survey

Wake measured in one of the above methods behind a model is known as the Nominal wake

VAVS

= (1 wn)


VAVS

VS VAVS

VS(1 w)

w = wake fraction =

1-w = wake =

VA = wake velocity =

Wake Definitions


Wake at any radii

R

r

rh

(1 wn)

(1 wn)x

pi0

x =r

R

mean value

TDC BDC


Wake & Wake Survey

(1 wn)x = 2pi0

(1 wn)rd 2pi0 rd

(1 wn)x = 2pi0

(1 wn)d2pi


Radial Distribution of wake

(1 wn)x

x =r

R

average mean nominal wake

Hubx = 0

x = 1

(1 wn)

Tip (1 wn)xR

r

rh

If


Volumetric flow

The volumetric mean wake flow through the propeller disc is defined as

VS(1 wn) R

rh

2pir dr

Rrh

VS(1 wn) 2pir drmust equal

dr

dr 2pir = ds

VA ds = volume

hub


Wake & Wake Survey

Then solving for

1 wn = Rrh

(1 wn)r r dr Rrh

r dr

x =r

Rr = xR dr = Rdx

substituting:


Wake & Wake Survey

1 wn = 1xh

(1 wn)x x dx 1xh

x dx

1 wn = 1xh

(1 wn)x x dx12 (1 x2h)


Wake & Wake Survey

Nominal Wake is obtained as above based on wake survey carried out in the model basin.

Effective wake which includes the effect of propeller induced velocities is obtained from the model self propulsion tests


Wake & Wake Survey

Mean nominal wake fraction at 15 knots wn = 0.526

From analysis of self propulsion tests the torque identity wake fraction at 15.25 knots wq = 0.483

This wake fraction referred to as the effective wake fraction is smaller than the nominal wake fraction due to the effect of the hull flow (presence of propeller).


Wake & Wake Survey

Predicted ship model wake based on model tests corresponding to:

Ns = 143.1 at 15.25 knots is wq = 0.42

Wake analysis from full scale ship trials wq = 0.38


Wake & Wake Survey

The differences are due to the ship being tested at Froude number similarity and not the Reynolds number

similarity

Propeller Froude Number [Fn]

Application of the Froude number

Open water ~ similarity can be ignored (+depth)

Self propulsion test ~ similarity must be enforced

Cavitation tests ~ similarity can be ignored (no F.S.)



Wake & Wake Survey

The model tests are usually carried out in the towing tank at low speeds whilst the flow around a ship in full

scale is fully turbulent

Propeller Froude Number [Fn]

J should be the same for the model and ship propeller in all tests

VsnsDs

=Vm

nmDm

Using the Advance coefficient relationship


nm =VmVs

=DsDm

ns = 12ns

Advance coefficient [ J ]

nm = 12ns

This relationship allows a rational approach to setting model scale rpm for self propulsion tests

It is however prone to Rn scaling effects


Propeller Reynolds Number [Rn]

Reynolds number cannot be the same for ship & model propeller

If Rn is large enough to ensure fully turbulent flow this assumption is valid

i.e. Rn > 106

Rn =V L



m

sBs

BmRE 105

RE 109

mBm!= sBs


Representation of wake

Ships wake is given in either velocity component or non-dimensionalised with ship speed to give wake

values. It can be represented as follows:

Va [ vs ] at each radii

Vt [ vs ] at each radii

Vr [ vs ] at each radii

(most common)

} (combined Vr)


Wake Comparison

Wake representation - Axial


1 metre/sec tunnel speed

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340 360

Radial Position

Axi

al V

eloci

ty (

m/s

)

0.20r0.51r0.68r0.84r0.92r


Wake representation - Axial

Wake representation - radial


Wake representation - tangential


Wake representation - radial & tangential


Wake representation - contour plot



Wake representation - 2D contour plot

Wake representation - 3D contour plot



End of Presentation

Documents

MAR2010 - Presentation of Wake