Existing Techniques for the Design of Ducted Propulsor Blading

Some of the companies and institutions involved in the design of ducted propulsors are, perhaps understandably, rather secretive about the detailed techniques they employ in the design of ducted propulsor blading. However, based on published literature, and the rather limited knowledge of the author, the following alternative methods of blade design seem to be most widely employed:-

2.3.1 "Trial-and-Error"

It is usually possible to obtain an approximate blade design based either on some

existing design or simplified theory. Using either experimental tests or a

computational analysis method, this blade geometry can be systematically modified on a "trial-and-error" basis until the desired performance is achieved. This type of approach, which relies heavily on the experience of the designer, is time-consuming, and, if experimental techniques are employed, expensive. As such this approach is only normally used to "fine tune" a blade design during the later stages of the design process, immediately prior to construction.

2.3.2 Standard Series Data

Another approach to propulsor blading design is the use of standard propeller series data, such as the Ka ducted propeller series presented in [9]. However, considering the sensitivity of blade performance to the environment in which a particular propulsor operates, one might reasonably conclude that blade design from standard propeller series is unlikely to give optimum propulsive efficiency at the propulsor design point. Given the cost associated with the installation of a propulsor duct, one might conclude that a more sophisticated approach to design is warranted, at least for large-ship applications of ducted propulsors where the potential for fuel savings is huge. Additionally, for certain cases such as twin blade row propulsors, standard series data is not available, and therefore cannot be used.

2.3.3 Actuator Disc/Lifting Line Theory

Blading may be designed using the computational results of either actuator disc or lifting line based analysis methods (such those given in [16], [26], [32] and [33]), which compute the propulsor flow field based on a specified blade circulation or blade loading distribution rather than from input blade shapes. Alternatively, the output

from one of the load optimisation methods presented in [39], [40] and [41] may be used. In either instance the blade may be considered as series of "blade elements" [44], whereby at each radius the blade is assumed to act as a two-dimensional hydrofoil. There are then two possible approaches:-

1) From the analysis method the relative flow angles at the blade leading and

trailing edges can be obtained, with the blade chord being selected from the pressure loading predictions. The camber line of each blade element can then be designed as a curve that aligns with the relative flow at the leading and trailing edges. These blade elements can then be combined to generate a surface which can be faired if required. A blade thickness distribution, based on structural considerations, can then be superimposed to obtain the final blade geometry.

The major disadvantage of this method is that away from the blade leading and trailing edges the choice of camber line path is completely arbitrary; considerable skill and experience must be involved in obtaining a satisfactory blade pressure distribution.

Although not mentioned explicitly in any of the literature reviewed, this approach, whilst rather crude, is highly plausible, and has probably been used in the past.

2) Utilising the output from the analysis method, each blade element can be

designed by aligning its camber line with the predicted relative velocity field at the blade trailing edge, as outlined by Falcao de Campos [33]. Blade chord can then be chosen based on the estimated blade loading distribution, the final design being obtained by applying a suitable blade thickness distribution, such as those given for open propellers by O'Brien [44].

The resulting designs are, however, in many ways inferior to those obtained from 1) above, as the adoption of flat camber lines ensures a non-zero blade incidence at the design point. For highly loaded blades

such a flow regime may result in a harsh pressure gradient around the

blade leading edge, and such undesirable flow phenomena as cavitation or flow separation.

As a result, the elemental camber lines are often modified using lifting surface correction factors in order to achieve zero (ideal) incidence at the leading edge. Further correction factors, either theoretical or empirical, can be applied to account for errors associated with neglecting blade chord, blade thickness, blade number and skew. For ducted propellers Falcao de Campos [33] suggests the use of lifting surface correction factors given by Morgan et al [34] for open propellers.

If the effects of shear flow are not included in the analysis method, as is often the case, they are usually accounted for by superimposing some representative velocity profile onto the velocities predicted at the blading (see Dr. Falcao de Campos's contribution in [42]).

It is this type of approach that seems to be most widely used in ducted propulsor design. Although relatively simple to use, this technique relies on a rather confusing array of assumptions regarding slipstream contraction, wake geometry and blade shapes, the net effect of which is that blade shapes become increasingly inaccurate for higher blade loadings. Furthermore, once the radial distribution of circulation has been specified, the designer is left with very little control over blade shape.

Both the above blade element methods rely on the blade-induced swirl being either specified or computed by the analysis method.

2.3.4 Inverse Design

The final means of ducted propulsor blade design is the inverse design approach, as outlined in Section 2.2.3. Of the existing blade inverse design methods, that of Dyne [3] represents a computational implementation of the blade element/analysis method design procedure discussed in Section 2.3.3, with the addition of an iterative procedure to determine duct shape; as such it would be expected to suffer from similar limitations. Meanwhile the inverse design method given by Furuja and Chiang [38] seems to have a number of limitations, as summarised in Section 2.1.3, and, to date, appears not to have been widely adopted.

2.4 The Potential for the Application of Turbomachine Methods to the