blade sections by reducing the radial pitch distribution and camber in that region. However, a numerical design method has then to be used in order to secure a compatible relation between camber and pitch as stressed by Johnsson, (1983) who we quote (nearly exactly) in the fol-lowing:
"What can happen, if such a procedure is not used, is illustrated in
Figure 12.9. Here the original propeller (picked out of a systematic series)
was rejected by the shipowner mainly because unacceptable vibration and
noise were experienced on the ship trials. To improve the situation in
these respects, the pitch distribution and blade form were changed, but
the flat face of the blade sections was maintained, i.e. the radial camber
distribution was not changed, see Figure 12.9. The results of the full-scale
tests with the new propeller (P1868), which were confirmed at model tests
in the SSPA cavitation tunnel, showed that a certain reduction of the
vibration excitation was obtained at the blade frequency. The tendency to
cavitation erosion (present already on the original propeller, according to
the model tests), was however seriously aggravated, the result being that
the new propeller was regarded as unacceptable in this respect. An
ana-lysis of the design showed that the camber of the outer sections, (having
been determined from the hydrodynamically irrevelant condition that the
face of the blade sections should be flat), was too large compared to the
camber of the inner sections. As a result of this, the extension of
cavitation became large in the middle part of the blade, which in turn
gave a cavity having a convex trailing edge. This is known to promote
cavitation damage. This effect was present already at the original
propel-254 Propeller Design via Computer and Practical Considerations
256 Propeller Design via Computer and Practical Considerations
Pragmatic Considerations
257
ler but was amplified when reducing the pitch of the outer sections, without making the corresponding reduction of the camber.
A more successful design for the same case is shown in Figure 12.10. For this propeller design calculations were made, using lifting-surface theory, the result being that the pitch and camber fit each other. It is evident from Figure 12.10 that this propeller has much less cavitation damage than the empirically designed propeller, the vibration excitation level and efficiency being the same.II
Effects of Blade Form
An effective measure to reduce vibratory pressures and shaft forces is to employ extreme skew. (A prediction that a relative reduction in vibratory thrust of 100 per cent could be achieved by 100 per cent skew (blade tips of each blade at same angular location as the root of the following blade) was made by Ritger
&
Breslin (1958) via an approximate theory employ-ing unsteady-section theory combined with the steady-state procedure of Burrill (1944)). It is obvious that when the blades are sufficiently skewed the sections pass through the wake "spike" or valley in a staggered fashion thus reducing the forces remarkably as compared with a blade whose locus of mid~hords is radially straight. When combining skew and tip-region unloading Johnsson's experience indicates the necessity of em-ploying a "rigorous calculation" (procedure) as a drastic change in blade form affects the relation between radial distribution of circulation, pitch and camber. His point is made in Figure 12.11 where three widely diffe-rent blade forms are shown which all have the same radial distribution of circulation. The pitch and camber distributions obtained by two different design methods are also shown. The approximate method is based on lift-ing-line calculations with camber~orrection factors from the literature being used for determining the final values of pitch and camber at each section. Using this process, the same radial distributions of pitch and cam-ber are obtained for all three designs.The other design method, based on a rigorous lifting-surface representa-tion, determines different radial distributions of camber, and particularly pitch, for the three blade forms. It is evident from Johnsson's calculations that the lifting-line method with so-called lifting-surface corrections yields much too large pitches at the outer sections of the skewed blades. In this way the beneficial influence of skew on vibration excitation ".... is reduced and sometimes eliminated".
This experience should not be surprising as the influences of the chord-wise geometry and especially the radially induced velocity are not ac-counted for in lifting-line theory with approximate corrections.
We may encapsulate findings from recent extensive experimental studies at SSP A Maritime Consulting, Sweden of the influence of radial load reduction and skew in the following:
Efficiency (Refer to Figure 12.13)
i. The radial pitch distribution is the most important parameter in regard to efficiency of propellers with conventional blade form and equal blade area.
ii. Loss of efficiency with tip unloading is smaller in "behind" condi-tion than in open water.
iii. Efficiency loss from tip unloading is reasonably predicted by cal-culation.
iv. A propeller having extreme skew has efficiency equal to the cor-responding propeller with conventional blade form (Le., having the same radial circulation distribution).
Pressure Fluctuations (Refer to Figure 12.14)
i. Radial pitch variation is the most important parameter for reduc-tion of vibratory pressures at blade frequencies for conventional blade forms; design principles and blade area being of less import-ance.
ii. At twice and higher-order blade frequencies, unloading of the tips is not effective in reducing these amplitudes.
iii. Designs with extreme skew show significant reductions in vibra-tory pressure amplitudes over the entire frequency range.
Cavitation Damage
i. An increasing extent of cavitation damage attends reduction of pitch without a corresponding reduction of camber in the tip region. (Refer to Figure 12.9)
ii. In the designs tested the extent (area) of cavitation damage is only slightly reduced with increasing tip unloading and skew.
It is necessary to note, as has Johnsson, (1983), that structural analysis via finite elements of extremely skewed blades showed that high stresses can be expected in some parts of the blades, particularly in the reversing and backing modes.
258 Propeller Design via Computer and Practical Considerations Pragmatic Considerations
259
260 Propeller Design via Computer and Practical Considerations Pragmatic Considerations 261
Hull- Wake Characteristics