5 The wake field
5.5 Effective wake field
Classical propeller theories assume the flow field to be irrotational and unbounded; however, because the propeller normally operates behind the body which is being propelled these assumptions are rarely satisfied.
When the propeller is operating behind a ship the flow field in which the propeller is operating at the stern of the ship is not simply the sum of the flow field in the absence of the propeller together with the propeller- induced velocities calculated on the basis of the nominal wake. In practice a very complicated interaction takes place which gives rise to noticeable effects on propeller performance. Figure 5.9 shows the composition of the velocities that make up the total velocity at any point in the propeller disc. From the propeller design view- point it is the effective velocity field that is important since this is the velocity field that should be input into propeller design and analysis procedures. The effective velocity field can be seen from the figure to be defined in one of two ways:
effective velocity=nominal velocity +interaction velocity or
effective velocity=total velocity
−propeller induced velocity
⎫⎪
⎪⎪
⎪⎬
⎪⎪
⎪⎪
⎭ (5.7)
If the latter of the two relationships is used, an iterative procedure can be employed to determine the effective wake field if the total velocity field is known from meas- urements just ahead of the propeller. The procedure used for this estimation is shown in Figure 5.10 and has been shown to converge. However, this procedure has the dis- advantage of including within it all the shortcomings of the particular propeller theory used for the calculation of the induced velocities. As a consequence this may lead to an incorrect assessment of the interaction effects aris- ing, for example, from the differences in the theoretical treatment of the trailing vortex system of the propeller.
An alternative procedure is to use the former of the two formulations of effective velocity defined in equation (5.7). This approach makes use of the nominal wake field measured in the towing tank, this being a con- siderably easier measurement than that of measuring the total velocity, since for the nominal velocity measure- ment the propeller is absent. Several approaches to this problem have been proposed, including those known as the V-shaped segment and force-field approaches.
The V-shaped segment method finds its origins in the work of Huang and Groves (Reference 12), which was based on investigations of propeller–wake interaction for axisymmetric bodies. This approach is perhaps the simplest of all effective wake estimation procedures since it uses only the nominal wake field and princi- pal propeller dimensions as input without undertaking detailed hydrodynamic computations. In the general case of a ship wake field, which contrasts with the
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72 Marine propellers and propulsion
Figure 5.6 Van Lammeren’s curves for determining the radial wake distribution (Reproduced with permission from Reference 6)
axisymmetric basis upon which the method was first derived by being essentially non-uniform, the velocity field is divided into a number of V-shaped segments over which the general non-uniformity is replaced with an equivalent uniform flow. The basis of a V-shaped segment procedure is actuator disc theory, and the computations normally commence with an estimate of the average thrust loading coefficient based on a mean effective wake fraction; typically such an estimate comes from standard series open water data. From this estimate an iterative algorithm commences in which an induced velocity distribution is calculated, which then allows the associated effective velocities and their radial locations to be computed. Procedures of this type do not take into account any changes of flow structure caused by the operating propeller since they are based on the approximate interaction between a propeller and a thick stern boundary layer.
An alternative, and somewhat more complex, effect- ive wake estimation procedure is the force-field method.
Such approaches usually rely for input on the nomi- nal wake field and the propeller thrust together with an estimate of the thrust deduction factor. These methods calculate the total velocity field by solving the Euler and continuity equations describing the flow in the vicinity of the propeller. The propeller action is modelled by an actuator disc having only an axial force component and a radial thrust distribution which is assumed constant circumferentially at each radial station. The induced velocities, which are identified within the Euler equa- tions, can then, upon convergence, be subtracted from the total velocity estimates at each point of interest to give the effective wake distribution.
Clearly methods of effective wake field estimation such as the V-shaped segment, force-field and the (T–I) approaches are an essential part of the propeller design
The wake field 73
Figure 5.7 The radial variation of the wake coefficient of single-screw ships (D/L=0.04) (Reproduced with permission from Reference 6)
and analysis procedure. However, all of these methods lack the wider justification from being subjected to correlation, in open literature, between model and full- scale measurements. Indeed the number of vessels upon which appropriate wake field measurements have been undertaken is minimal for a variety of reasons; typically cost, availability and difficulty of measurement. The lat- ter reason has at least been partially removed with the advent of laser-Doppler techniques which allow effect- ive wake field measurement; nevertheless, this is still a complex procedure.
The analytical treatment of effective wake prediction has gained pace during recent years. A coupled vis- cous and potential flow procedure was developed by Kerwinet al. (References 29 and 30) for the design of an integrated propulsor driving an axisymmetric body.
In this method the flow around the body was computed
with the aid of a RANS code with the propulsor being represented by body forces whose magnitudes were esti- mated using a lifting surface method. As such, in this iterative procedure the RANS solver estimated the total velocity field from which the propeller-induced veloci- ties were subtracted to derive the effective propulsor inflow. Warren et al. (Reference 31) used a simi- lar philosophy in order to predict propulsor-induced manoeuvring forces in which a RANS code was used for flow calculations over a hull, the appendages and a duct. The time averaged flow field was then input into a three-dimensional lifting surface code which estimated the time varying forces and pressures which were then re-input into the RANS solver in an iterative fashion until convergence was achieved. Hsinet al. in Reference 32 developed Kerwin’s ideas to a podded propulsor system in order to predict hull–propeller interaction.
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74 Marine propellers and propulsion
Figure 5.8 (a) The radial variation of the wake coefficient for models having twin screws (D/L=0.03) and (b) the radial variation of the wake coefficient for twin-screw ships (D/L=0.03) (Reproduced with permission from
Reference 6)
Figure 5.9 Composition of the wake field
Figure 5.10 (T–I) approach to effective wake field estimation
Choi and Kinnas (References 33 and 34) developed an unsteady effective wake prediction methodology by coupling an unsteady lifting surface cavitating pro- peller procedure with a three-dimensional Euler code.
In this arrangement the propeller effect is represented by unsteady body forces in the Euler solver such that the unsteady effective wake both spatially and tempo- rally can be estimated. Using this method it was found that the predicted total velocity distribution in front of the propeller was in good agreement with measured data. Leeet al.in Reference 35 studied rudder sheet cavitation with some success when comparing theoreti- cal predictions with experimental observation. In this procedure a vortex lattice method was coupled to a three-dimensional Euler solver and boundary element method; the latter being used to calculate the cavitating flow around the rudder.
Considerable progress is being made in the estima- tion of effective wake using advanced computational analyses and this trend looks set to continue for the foreseeable future.