A propeller on a vessel subject to high waves may experience large vertical motions relative to the free surface because of wave elevation and vessel wave- frequency motion. This can result in large and abrupt thrust losses. The losses may be contributed to three effects: loss of effective propeller disc area, ven- tilation, and a lift hysteresis effect. In this work, ventilation will be used as a common term for all these losses. In the literature, sometimes the term aeration is also used.
2.3 Loss effects 33
Loss of effective disc area
If the propeller emerges from the water, a thrust loss due to loss of effective propeller disc area is experienced (Gutsche, 1967; Fleischer, 1973). The corre- sponding thrust loss factor βT Acan be found from a simple geometrical consid- eration, by assuming that the resulting thrust is proportional to the submerged propeller disc area:
βT A= real µ 1 −arccos(h/R)π +h/R π p 1 − (h/R)2 ¶ . (2.73)
Here, h/R is the relative submergence, with h the propeller shaft submergence and R the propeller radius. An alternative representation, where also the pro- peller hub diameter is accounted for, is given in Koushan (2004). This loss model is assumed to be valid for any propeller loading. A simplified, piecewise linear representation is given by:
βT A≈ 0.5 + 0.5(min(max(h/R, −1), 1)). (2.74)
An alternative representation is given in Minsaas et al. (1983) based on the results from Faltinsen et al. (1980):
βT A= ⎧ ⎨ ⎩ 0, h/R < −0.48, 1 − 0.675(1 − 0.769h/R)1.258, −0.48 ≤ h/R ≤ 1.3, 1, h > 1.3. (2.75)
(2.75) includes contributions from the so-called Wagner effect. This is conve- nient if the dynamic effects of ventilation can be neglected, and only the average thrust values are needed. In the following, the alternative representation (2.75) will not be used, since the Wagner effect is included as a part of the lift hysteresis effect. The three representations are compared in Figure 2.10.
Ventilation
Ventilation may occur when a propeller is operating in the proximity of the free surface. If the propeller loading is sufficiently high, the low pressure on the propeller blades may create a funnel through which air is drawn from the free surface. This phenomenon is connected with co-orientation of the energy in the surrounding water. The propeller sets up a rotating flow which causes the free surface to deform, and a vortex starts to develop. Unless the rotating flow is disturbed, this is a self-amplifying process, and the vortex develops into a funnel. Air cavities then spread on the propeller blades, reducing their lift and drag. A fully ventilated propeller may lose as much as 70-80% of its thrust and torque. Several thorough studies of ventilated and partially submerged propellers have been performed, see e.g. Shiba (1953), Gutsche (1967), Kruppa (1972), Brandt (1973), Fleischer (1973), Scherer (1977), Hashimoto et al. (1984), Guoqiang et al. (1989), and Olofsson (1996). Additional results and further
−2 −1.5 −1 −0.5 0 0.5 1 1.5 2 0 0.2 0.4 0.6 0.8 1 h/R β TA Exact Linear Alternative
Figure 2.10: Comparison of three different representations for the thrust loss due to loss of effective disc area: exact (2.73), linear (2.74), and alternative (2.75).
studies with respect to vessel operational performance can be found in Faltinsen et al. (1980), Minsaas et al. (1983, 1986, 1987), Karlsen et al. (1986), and Lehn (1992). Ventilation is in the above references typically divided in three regimes: non-ventilated, partially ventilated, and fully ventilated.
Non-ventilated regime: The propeller is deeply submerged, or fully sub- merged and with low propeller loading. No ventilation occurs.
Partially ventilated regime: The propeller is partly, but not stationary ven- tilated. That is, the level of ventilation and the location of the air cavities on the propeller are time-varying. For high Ja, this regime is persistent. For low
Ja, it is an unstable regime that mainly exists as a transition between the two
other regimes.
Fully ventilated regime: A single ventilated cavity covers each of the propeller blades, meaning that the pressure on the suction side of the propeller blades is almost atmospheric. This is a relatively stable condition.
The three regimes are sketched as a function of Jaand h/R in Figure 2.11,
based on a similar figure in Olofsson (1996). The partially ventilated, unstable regime for low Ja is marked as unstable. The regimes that are relevant for DP
are indicated on the Ja-axis.
The thrust loss factor due to ventilation is termed βT V 0, and is in general
expected to be a function of shaft speed, advance velocity, and submergence.
Lift hysteresis
For ventilation to terminate, the supply of air to the cavities on the propeller blades must be stopped. The three most apparent causes for the funnel from
2.3 Loss effects 35 J h/R a Non-ventilated regime Partially ventilated regime Fully-ventilated regime Unstable regime
1
Fully submerged Partially submerged DP regimeFigure 2.11: Ventilation flow regimes, with the regimes relevant for DP indicated on the Jaaxis. Adopted from Olofsson (1996).
the surface to collapse are increased submergence of the propeller, disturbances in the water, and decreased loading of the propeller. For a propeller in dy- namic operating conditions, a combination of the two first causes will lead to termination of the ventilation incident relatively soon after the propeller is fully submerged. When the air supply to the cavities is stopped, two events must take place before the full thrust is restored:
1. The cavities on the propeller blades must vanish in order to restore the suction-side pressure.
2. The produced lift of the propeller blades must build up.
It appears that the first of these two effects has not been explicitly discussed in the literature. However, a lot can be learned by studying the behavior of the air cavities on the propeller blades, as done in Koushan (2006). It seems apparent that the result is a time delay before the lift starts building up.
When the ventilated cavities disappear, there will be a sudden increase in lift on the propeller blades. Wagner (1925) studied a similar problem for a two- dimensional foil, and found that the sudden increase was 50% of the steady-state lift, see also Newman (1977) or Durand (1963). The Wagner function gives the ratio between the instantaneous lift and the steady-state lift, and shows that the foil must travel about 20 chord lengths to recover its full lift. A similar behavior is seen for a propeller that is moving in and out of ventilated condition, as first
suggested by Faltinsen et al. (1980). According to Koushan (2004), a typical propeller with pitch ratio P/D = 1 must travel about 4 revolutions at full submergence to regain its full thrust.
For a propeller moving in and out of ventilated condition due to e.g. vessel motion and waves, the combination of these two effects means that the thrust build-up when the propeller stops ventilating is slower than the thrust loss when the propeller starts ventilating. This gives a hysteresis in the thrust production, with a corresponding thrust loss factor termed βT H.
Total thrust and torque loss
With βT Adue to loss of disc area from (2.73), βT V 0due to ventilation, and βT H due to the lift hysteresis effect, the total thrust loss factor βT V is calculated from:
βT V = βT AβT V 0βT H. (2.76)
The corresponding torque loss factor βQV should always be larger than βT V, since otherwise increasing loss would give increasing propeller efficiency. Based on previous results, Faltinsen et al. (1980) and Minsaas et al. (1983) suggested using the relationship:
βQV = (βT V)m, 0 < m < 1. (2.77)
Typical values for m are 0.8 − 0.85 for an open propeller (Gutsche, 1967), 0.65 for a ducted propeller, and 0.575 for a tunnel thruster (Karlsen et al., 1986). In the following, the lumped parameters βT V and βQV will for simplicity be called ventilation loss factors.
The nature of the ventilation loss effects for low-speed applications will be investigated further in the next section, where experimental results with a ven- tilated propeller are presented, and an associated ventilation simulation model developed.