# Resistance & Propulsion (1) MAR Presentation of ships wake

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1 Resistance & Propulsion (1) MAR 2010 Presentation of ships wake

2 Wake - Overview 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

3 Wake Gain - Velocity distribution AP FP

4 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

5 Wake Gain - Velocity distribution Boundary layer Velocity Viscous wake Potential wake

6 Wake Gain - Velocity distribution Mean speed through B.L. is less than the ship speed

7 Wake Gain - Wave making component

8 Total Wake Total wake = Potential wake Viscous + wake + Wavemaking wake Hence Advance speed (Va) is less than the ship speed (V)

9 Wake definition and wake fraction Wake is defined as a fraction of ship speed or advance velocity at the propeller plane Froude wake fraction w = V V A V a V a = V 1 + w Taylor wake fraction w = V V A V V a = V (1 w)

10 Wake definition and wake fraction Wake fraction depends on length and fulness of the ship and increases with hull roughness A typical moderate speed cargo ship of Cb = 0.70 would expect w = 0.30

11 Wake definition and wake fraction V A = V (1 w)?

12 Wake & Wake Survey Wake survey involves the detailed measurement of the flow through the propeller disc with the model towed at a corresponding speed

13 Wake definition and wake fraction Area of interest

14 Wake definition and wake fraction Text

15 Wake & Wake Survey Early measurements used intrusive methods to extract information on flow velocity Pitot tubes Hot wire anemometry Tuft Strips

16 Pitot Wake

17 Pitot Wake Propeller plane Rake can rotate 360 Degrees Pitot comb

18 Pitot Tube Static Pressure 2 hole tube - axial 5 hole tube - axial, vertical & horizontal Stagnation Pressure v = 2 (p stagnation p static ) ρ

19

20 Pitot rake

21 Wake & Wake Survey Modern measurements use non obtrusive methods Particle image velocimetry PIV Laser doppler anemometry Both systems are in use in the Department

22 LDA Wake Ju l2002 ice p od s ystem wake 0 (2D) 68 Rod Sampson - School of Marine Science and Technology - 28th February 2008

23 Wake & Wake Survey Wake measured in one of the above methods behind a model is known as the Nominal wake V A V S = (1 w n )

24 Wake Definitions w = wake fraction = V S V A V S 1-w = wake = V A = wake velocity = V A V S V S (1 w)

25 Wake at any radii (1 w n ) θ R r x = r R r h mean value (1 w n ) x 0 TDC π BDC θ

26 Wake & Wake Survey (1 w n ) x = 2π 0 (1 w n ) r dθ 2π 0 rdθ (1 w n ) x = 2π 0 (1 w n ) θ dθ 2π

27 Radial Distribution of wake x = 1 R Tip (1 w n ) x r r h (1 w n ) average mean nominal wake If x = r R Hub x = 0 (1 w n ) x

28 Volumetric flow The volumetric mean wake flow through the propeller disc is defined as V S (1 w n ) must equal R r h R r h 2πr dr V S (1 w n ) 2πr dr dr d r 2πr = ds hub V A d s = volume

29 Wake & Wake Survey Then solving for 1 w n = R r h (1 w n ) r r dr R r h r dr substituting: x = r R r = xr dr = Rdx

30 Wake & Wake Survey 1 x h (1 w n ) x x dx 1 w n = 1 x h x dx 1 x h (1 w n ) x x dx 1 w n = 1 2 (1 x2 h )

31 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

32 Wake & Wake Survey Mean nominal wake fraction at 15 knots wn = From analysis of self propulsion tests the torque identity wake fraction at knots wq = 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).

33 Wake & Wake Survey Predicted ship model wake based on model tests corresponding to: Ns = at knots is wq = 0.42 Wake analysis from full scale ship trials wq = 0.38

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

35 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.)

36 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

37 Propeller Froude Number [Fn] J should be the same for the model and ship propeller in all tests Using the Advance coefficient relationship V s n s D s = V m n m D m

38 Advance coefficient [ J ] n m = V m V s = D s D m n s = λ 1 2 λns n m = λ 1 2 ns This relationship allows a rational approach to setting model scale rpm for self propulsion tests It is however prone to Rn scaling effects

39 Propeller Reynolds Number [Rn] R n = V L If Rn is large enough to ensure fully turbulent flow this assumption is valid ν Reynolds number cannot be the same for ship & model propeller i.e. R n > 10 6

40 R E 10 9 δ s B s δ m B m δ s B s R E 10 5 δ m B m

41 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: V a [ vs ] at each radii θ [ vs ] at each radii V t θ [ vs ] at each radii V r θ } (combined (most common) Vr)

42 Wake Comparison

43 Wake representation - Axial

44 Wake representation - Axial metre/sec tunnel speed Axial Velocity (m/s) r 0.51r 0.68r 0.84r 0.92r Radial Position

45 Wake representation - radial

46 Wake representation - tangential

47 Wake representation - radial & tangential

48 Wake representation - contour plot

49 Wake representation - 2D contour plot

50 Wake representation - 3D contour plot

51 End of Presentation

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