5 The wake field
5.8 Wake field measurement
Measurements of the wake field are required chiefly for the purposes of propeller design and for research where the various aspects of wake field scaling are
Figure 5.17 Types of wake field traversing methods using pitot, total and static head tubes: (a) rotating pitot rake located on shaft and (b) schematic fixed pitot rake
being explored. Until comparatively recently methods of measurement have been intrusive; for example, pitot tubes, hot-wire anemometry, tufts and so on. With these methods the influence on the flow field of locat- ing the measurement apparatus in the flow has always been the subject of much debate. In recent years, how- ever, the use of laser-Doppler techniques has become available for both model and full-scale studies and these require only that beams of laser light are passed into the fluid.
In the case of model scale measurements detailed measurements of the wake field have largely been accomplished by using pitot rakes, which have in some cases been placed on the shaft in place of the model pro- peller, Figure 5.17(a). In these cases the rakes have been rotated to different angular positions to define the wake field characteristics. Alternatively, some experimental facilities have favoured the use of a fixed pitot rake, Figure 5.17(b), in which the ends of the pitot rake are placed in the propeller plane. Such measurements pro- vide quantitative data defining the nominal wake field and are based on the theory of pitot tubes which in turn
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80 Marine propellers and propulsion
Figure 5.18 Pitot-static probe layout
is based on Bernouilli’s equation. For a general point in any fluid flow the following relationship applies:
total head (hT)=static head (hs) +dynamic head (hd)
The pitot-static tube shown in Figure 5.18 essentially comprises two tubes: a total head tube and a static head tube. The openingAmeasures the total head in the direc- tionOxwhilst the portsB, aligned in theOydirection, measure the static head of the fluid. As a consequence from the above relationship, expressed in terms of the corresponding pressures, we have
pd =pT−ps (5.8)
from which v=
2(pT−ps)
ρ (5.9)
Depending on the type of flow problem that requires measurement, the probe is selected based on the infor- mation required and the physical space available. As such total head, static head or pitot-static tubes may be used. Clearly the former two probes only measure one pressure component, whereas the latter measures both values simultaneously. Rakes comprising combinations
Figure 5.19 Typical five-hole total head tube
of total head and static head tubes are sometimes con- structed to enable complete measurement to be made, or alternatively, when space is very limited, total head and static head tubes can be inserted into the flow sequentially.
When directionality of the flow is important, since the foregoing tubes are all unidirectional, special meas- urement tubes can be used. These normally comprise either three- or five-hole total head tubes; an example of the latter is shown in Figure 5.19. From the figure it will be seen that the outer ring of tubes are chamfered and this allows the system to become directional, since opposite pairs of tubes measure different pressures and, from previous calibration, the differential pressures can
The wake field 81
Figure 5.20 Full-scale wake pitot probe: (a) the mounting place of the test equipment; (b) example of one of the six, five-hole pitot tubes (Reproduced with permission from Reference 24)
be related to the angle of incidence of flow relative to the probe axis. References 20 and 21 should be consulted for further detailed discussion of flow measurement by total head and static head tubes, which is a specialist subject in itself.
In the case of full-scale ship wake field measurement the pitot-tube principle has provided much of the data that we have at out disposal at this time. Pitot rakes have either been placed on the shaft in place of the propeller, see for example Canham (Reference 22), to measure full-scale nominal wake or, alternatively, fit- ted to the hull just in front of the propeller to measure the inflow into the propeller (References 23 and 24);
Figure 5.20 shows this type of layout together with the five-hole tube used in this latter case. Clearly in the for- mer case of nominal wake measurement, the ship has to be towed by another vessel, whilst in the latter case it is self-propelled. The pitot rakes, whether they be shaft or hull mounted, are made adjustable in the angular sense so that they can provide as comprehensive a picture as possible of the wake field.
An alternative to the measurement of flow velocity by pitot tube is to use hot-wire or hot-film anemome- try techniques. Such probes rely on the cooling effect of the fluid passing over either the heated wires or hot film to determine the flow velocities. In their most basic form the current passing through the wire is maintained constant and the flow velocity is determined by the volt- age applied across the wire, since the wire resistance is dependent upon the temperature of the wire. A more
Figure 5.21 Hot ‘X’ wire anemometer
complex, but widely used, mode of operation is to employ a feed-back circuit which maintains the wire at constant resistance and as a consequence at constant temperature: the current required to do this is a function of the fluid velocity. Hot-wire anemometers, like pitot tubes, require calibration.
A typical hot-wire anemometer is shown in Figure 5.21, where two wires are arranged in an X configur- ation. If such an ‘X’ wire is located such that the mean velocity is in the plane of the ‘X’ wire it can be used to measure both components of velocity fluctuation in that plane. The more robust hot-film anemometer com- prises a heated element of a thin metallic film placed on a wedge-shaped base which is both a thermal and elec- tric insulator. When used in water, to which it is ideally suited due to its greater robustness, the hot film is cov- ered with a thin layer of insulation to prevent electrical shorting problems.
In many ways the hot-film or -wire anemometer extends the range of fluid measurement scenarios into areas where pitot tubes tend to fail. In particular, since they are small and rapidly responding, they are ideal for measuring fluctuating flows; in particular, the phe- nomena of transition and the structure of turbulent flows. In aerodynamic work hot-wire and film tech- niques have been used widely and very successfully for one-, two- and three-dimensional flow studies. Lomas (Reference 25) and Perry (Reference 26) discuss hot- wire anemometry in considerable detail whilst Scragg and Sandell (Reference 27) present an interesting com- parison between hot-wire and pitot techniques. For full-scale wake field measurements no application of hot-film techniques is known to the author.
Laser-Doppler methods are advanced measurement techniques which can be applied to fluid velocity meas- urement problems at either model or full scale. The laser-Doppler anemometer measures flow velocity by measuring the Doppler shift of light scattered within the moving fluid, and hence it is a non-intrusive meas- urement technique. The light scatter is caused by the passage of tiny particles suspended in the fluid, typically dust or fine sand grains, such that they effectively trace the streamline paths of the fluid flow. In general there are usually sufficient particles within the fluid and in many instances, at full scale, problems of over-seeding can occur.
The operating principle of a laser-Doppler system is essentially described in Figure 5.22. In the case of a
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82 Marine propellers and propulsion
Figure 5.22 Laser-Doppler principle: (a) Doppler shift of a single-incident laser beam; (b) intersecting laser beam arrangement and (c) fringe pattern from two intersecting laser beams
single-laser beam, Figure 5.22(a), the Doppler shift is dependent upon the velocity of the object and the rela- tive angles between the incident and scattered light. Iffi andfsare the frequencies of the incident and scattered beams, then the Doppler shift is given by (fs−fi):
fs−fi=V
λ[ cosθi+cosθs] whereλis the wavelength of the laser.
This expression can be made independent of the position of the receiver, that is the angleθs, by using two laser beams of the same frequency as shown in Figure 5.22(b). This configuration leads to differential Doppler shift seen by the receiver, at some angleφ, as follows:
differential Doppler shift=2V λ sin
θ 2
(5.10) The use, as in this case, of two intersection laser beams of the same frequency leads to the introduction of beam splitting optical arrangements obtaining light from a single laser.
Equation (5.10) can be considered in the context of the physically equivalent model of the interference fringes that are formed when two laser beams intersect.
If the two beams, Figure 5.22(c), are of equal inten- sity and wavelength, the fringe pattern will appear as a series of flat elliptical discs of light separated by regions of darkness. If a particle moves through these fringes it will scatter light each time it passes through a light band at a frequency proportional to its speed. Since the separation of the fringesd is given by the expression λ/(2 sinθ/2) and if the particle moves with a velocity V, it will move from one interference band to another with a frequency
f =2Vsin(θ/2) λ
The scattered light will, therefore, be modulated at this frequency, which is the same as the differential Doppler frequency above. Since the angle θ and the wavelengthλcan be precisely defined, a measurement of the modulation frequency gives a direct measure of the velocity of the particle crossing through the intersection of the laser beams.
In terms of practical measurement capabilities sev- eral modes of operation exist. These, however, chiefly divide themselves into forward- and back-scatter tech- niques. Forward-scatter methods essentially place the laser and photodetector on opposite sides of the meas- urement point, whilst in the back-scatter mode both the laser and photodetector are on the same side. For dis- cussion purposes four methods are of interest in order to illustrate the basic principles of the measurement procedure; these are as follows:
1. Reference beam method.
2. Differential Doppler – forward scatter.
3. Differential Doppler – backward scatter.
4. Multi-colour differential Doppler.
In the case of the reference beam method (Figure 5.23(a), the photodetector is mounted coaxially with the reference laser beam in order to measure the velocity within the fluid normal to the optical axis of the instru- ment. In order to optimize the Doppler signal quality an adjustable neutral density filter is normally used to reduce the intensity of the reference beam.
The wake field 83
Figure 5.23 Laser-Doppler modes of operation: (a) reference beam method; (b) differential Doppler – forward scatter;
(c) differential Doppler – back scatter and (d) multi-colour differential Doppler mode
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84 Marine propellers and propulsion
The differential Doppler, forward-scatter mode of measurement employs two laser beams of equal inten- sity which are focused at a point of interest in the fluid (Figure 5.23(b)). The scattered light can then be picked up by the photodetector, which is inclined at a suitable angleαto the optical axis of the instrument: the angleα is not critical, since the detected Doppler frequency is independent of the direction of detection. This method is often employed when the intensity of the scattered light is low. Furthermore, the method has obvious advantages over the preceding one since the photodetector does not have to be located on the reference beam.
The backward-scatter differential Doppler mode (Figure 5.23(c)) permits the laser optics and the meas- urement optics to lie on the same side of the flow measurement point – an essential feature if full-scale ship wake measurements are contemplated. The disad- vantage of this type of system is that the intensity of the back-scattered light is usually much lower than that of the forward-scattered light. This normally requires either a higher concentration of scattering particles or a higher laser power to be used to overcome this problem.
The three foregoing systems only measure velocities in one component direction. To extend this into two or more velocity components a multi-colour system must be used. Figure 5.23(d) outlines a two-colour back- scatter differential Doppler mode. In such a system the transmitting optics splits a dual-colour laser beam into converging single-colour beams with a combined dual- colour central beam; that is, three beams in total. The beams are then focused at the point where the mea- surement is required and the scattered light is returned through the receiving optics, mounted coaxially with the transmitting optics, and then diverted to photodetec- tors – one for each colour light. The two views shown in Figure 5.23(d) are in reality a single unit contain- ing both sets of optics. The ability of such systems to detect two velocity components can be visualized
Figure 5.24 Two-colour fringe model (Courtesy: DANTEC Electronics Ltd)
from Figure 5.24, in which the two pairs of fringe pat- terns are made to intersect in orthogonal planes and give a resultant fringe pattern of the type shown in the measurement volume. In this way the particles pass- ing through this measurement volume will scatter light from both orthogonal fringe patterns.
For shipboard measurements a laser system of con- siderable power is required, and this requires both a carefully designed mounting system to avoid vibra- tion problems and the provision of adequate cooling arrangements. At model scale less powerful systems are required and these can be of the forward-scatter type since the limitation of approaching the measure- ment from one side of the flow does not normally apply.
Reference 28 provides a very good introduction to the subject of later-Doppler anemometry.
References and further reading
1. Huse, E. Effect of Afterbody Forms and After- body Fins on the Wake Distribution of Single Screw Ships. NSFI Report No. R31-74, 1974.
2. Carlton, J.S., Bantham, I. Full scale experience relating to the propeller and its environment.Pro- pellers 78 Symposium, Trans. SNAME, 1978.
3. Prohaski, C.W., Lammeren, W.P.A. van.
Mitstrommessung on Schiffsmodellen, Heft 16, S.257, Schiffban 1937.
4. Lammeren, W.P.A. van. ‘Analysis der voort- stuwingscomponenten in verband met het schal- effect bij scheepsmodelproven’, blz.58, 1938.
5. Harvald, Sv.Aa. Potential and frictional wake of ships.Trans. RINA, 1972.
6. Harvald, Sv.Aa.Wake of Merchant Ships. Danish Technical Press, 1950.
7. Schoenherr, K.E. Propulsion and propellers.Prin- ciples of Naval Architecture,2, p. 149, 1939.
8. Taylor, D.W.Speed and Power of Ships, 1933.
9. Harvald, Sv.Aa.Estimation of Power of Ships, ISP, 1977.
10. Holtrop, J. A statistical re-analysis of resistance and propulsion data. ISP,31, November 1988.
11. Lammeren, W.P.A. van, Troost, L., Koning, J.G.
Weerstand en Voortsluwing van Schepen, 1942.
12. Huang, T.T., Groves, N.C. Effective wake: theory and experiment.13th ONR Symposium, 1980.
13. Sasajima, H., Tanaka, I., Suzuki, T. Wake distribu- tion of full ships.J. Soc. Nav. Arch., Japan, 120, 1966.
14. Hoekstra, M. Prediction of full scale wake char- acteristics based on model wake survey.Int. Ship- building, Prog. No. 250, June 1975.
15. Truesdell, C. Two measures of vorticity.Rational Mech. Anal.2, 1953.
16. Mockros, F.L. The Significance of Vorticity, Vortex Motion and Dissipation in Turbulent Fluid Flows.
The wake field 85 Dissertation, University of California, Berkeley,
CA, 1962.
17. Oswatitsch, K. Über Wirbelkennzahlen und Wirbel- musse.Z. Angew. Math. Phys.,20, 1969.
18. Gunsteren, L.A. van, Pronk, C. Propeller design concepts.Int. Shipbuilding Prog.,20(227), 1973.
19. Odabasi, A.Y., Fitzsimmons, P.A. Alternative methods for wake quality assessment. Int. Ship- building Prog.,25(282), February 1978.
20. Pankhurst, R.C., Holder, D.W.Wind Tunnel Tech- nique. Pitman, London, 1952.
21. Piercy, N.A.Aerodynamics. English Universities Press, London, 1937.
22. Canham, H.J.S. Resistance, propulsion and wake tests with HMS Penelope, Trans. RINA, Spring Meeting, 1974.
23. Naminatsu, M., Muraoka, K. Wake distribution measurements an actual tanker and its large scale model,Proc. 14th ITTC.
24. Fagerjord, O.Experience from Stern Wake Meas- urements during Sea Trial, Norwegian Maritime Research, No. 2, 1978.
25. Lomas, C.G.Fundamentals of Hot-wire Anemom- etry. Cambridge University Press, Cambridge, 1986.
26. Perry, A.E.Hot Wire Anemometry. Clarendon Press, Oxford, 1982.
27. Scragg, C.A., Sandell, D.A. A statistical evalu- ation of wake survey techniques.Int. Symp. on Ship Viscous Resistance, SSPA, Göteborg, 1978.
28. Durst, F., Melling, A., Whitelaw, J.H.Principles and Practice of Laser-Doppler Anemometry. Aca- demic Press, UK, 1976.
29. Kerwin, J.E., Keenan, D.P., Black, S.D., Diggs, J.G.
A Coupled Viscous/Potential Flow Design Method for Wake Adapted Multi-Stage Ducted Propulsors.
Trans. SNAME,102, 1994.
30. Kerwin, J.E., Taylor, T.E., Black, S.D., McHugh, G.P. A Coupled Lifting Surface Analysis Tech- nique for Marine Propulsors in Steady Flow.Proc.
Propeller/Shafting Symp., Virginia, 1997.
31. Warren, C.L., Taylor, T.E., Kerwin, J.E. Coupled Viscous/Potential Flow Method for the Prediction of Propulsor-Induced Manoeuvring Forces. Proc.
Propeller/Shafting Symp, Virginia. Beach, 2000.
32. Hsin, C.Y., Chou, S.K., Chen, W.C. A New Pro- peller Design Method for the POD Propulsion System.Proc. 24th Symp. on Naval Hydrodynam., Fukuoka, Japan, 2002.
33. Choi, J.K., Kinnas, S.A. Prediction of Non- Axisymmetric Effective Wake by a Three- Dimensional Euler Solver. J. Ship Res., 45 (1), 2001.
34. Choi, J.K., Kinnas, S.A. Prediction of Unsteady Effective Wake by a Euler Solver/Vortex-Lattice Coupled method.J. Ship Res.,47(2), 2003.
35. Lee, H., Kinnas, S.A., Gu, H., Naterajan, S.
Numerical Modelling of Rudder Sheet Cavita- tion Including Propeller/Rudder Interaction and the Effects of a Tunnel.CAV 2003, Osaka, Japan, 2003.