Wake fraction and thrust deduction during ship astern manoeuvres

Transcription

1 Wake fraction and thrust deduction during ship astern manoeuvres J. Artyszuk Maritime University of Szczecin, Poland Abstract A relatively small amount of data concerning the behaviour of propulsion coefficients, i.e. the wake fraction and thrust deduction at high propeller loading, exist so far. Pioneer works in this field are the model tests by Harvald carried out some time ago. The problem relates in particular to the propeller reversing. The common assumption (and the simplest) is a constant value for both parameters in any manoeuvring regime. How sensitive the simulation of a ship stopping and the steady-state astern movement to these coefficients, will be examined. An identification of wake and thrust deduction is attempted based on full-scale astern manoeuvring trials. 1 Introduction The idea behind the wake fraction W and thrust deduction td, referred to as the propulsion (hull-propeller interaction) factors, is to adjust the propeller openwater hydrodynamic characteristics against the hull neighbourhood. For wake fraction two basic approaches are used - a kinematic (nominal wake) and a dynamic one (effective wake). The latter is more important in practical aspects. The wake fraction is responsible for a horizontal shift between the thrust coefficient (or torque coefficient) diagrams of open-water and behind hull conditions - the so called thrust (torque) identity definitions. The thrust deduction takes account for the increase in the hull resistance due to the propeller operation (suction force at the stem), for its determination a detailed knowledge of hull resistance at different speeds is required. The thrust deduction 'produces' a vertical shift in the mentioned thrust coefficient diagrams when thrust identity wake fraction has been already identified. The main objective of wake fraction and thrust deduction estimation (model tests, numerical analyses, full-scale measurements) is to obtain a data necessary

2 for the propulsion design (propeller, main engine). The point of interest for the particular values of the specified propulsion factors is here the region of the ship sea (service) speed and the main engine nominal revolutions. Other areas are not generally covered. The latest development in a ship manoeuvring motion prediction and a computer technology gives some ground for continuation of research performed a long time ago e.g. by Harvald [3], [4] concerning nearly all propeller manoeuvring regimes (combinations of ship speed and propeller revolutions). The wake fraction and thrust deduction, by nature of their above definitions, are commonly expressed as a function of apparent advance ratio (Harvald investigated just fixed pitch propellers - FPPs): In case of the controllable pitch propeller (CPP), probably more helpful appears the slip (pitch) related apparent advance ratio e.g. Artyszuk [l]: This is rather a hypothesis, the Harvald's results are too poor for its validation. The present study undertakes some aspects of W and td identification from fullscale sea trials required for high standards of the ship manoeuvring prediction, deep water conditions are regarded. The ship characteristics are summarised in Tab. l Table 1. Ship main data. TYPE: chemical tanker - PROPELLER: =L type: CPP L = 97.4[m] B = 16.6[m] T = 7.l[m] CB = m = 8950[t] PROPULSION -m: type: diesel P, = 3600[kW] n, = 2.43[11s] D = 4.l[m] P/Dk = AdAo = 0.52 z = 4 WORKING CONDITIONS P/D,,, = P/Dk = 96.5%nn=2.35[1/s] Vxseru = 7.252[m/s] QED~,, = 93.1%Q~~,,,,=208.3 [knm] QED~, = 95%Qn= 223.7[kNm] 2 Assumed model for hull and propeller forces Let's describe the hull resistance force by the following speed square relationship: = OS~LTV~C~, (3) where: The propeller effective thrust is expressed by: FxP = ( ~ - t ~ ) ~ n PID) ~ ~ ~ k ~ ( ~, (5)

3 where: k, - 'four-quadrant' (4-4) CPP thrust coefficient (see e.g. Ruseckij [S]). In case of FPP, k, is a one variable function (but 2-4) where the following combinations are considered: J<O,vx <O and n<o (7) J>O,vx >O and n>o 3 Identification of coefficients at full ahead sea speed Wake fraction obtained by the thrust and torque identity rules are similar to each other, though they significantly differ. To be more strictly, two independent wake fractions shall be used. The thrust-identity wake is a part of the ship manoeuvring motion prediction, while the torque-identity wake governs the propeller shaft behaviour. The latter is very easy to be measured at the full scale. For convenience (the level of inaccuracy accepted), an average value could be applied, or even the thrust-identity wake as equal to the torque-identity definition. The sequence of parameters identification in eqs (3) and (5) is from the wake fraction through the thrust deduction (being fixed relative to the wake fraction) till the hull resistance coefficient - see e.g. Artyszuk [2]. The wake fraction (normal value ca. 0.4) is determined by the following equation (1 0% sea margin propulsion design): The thrust deduction is assumed (for a tanker) to be about half of the wake fraction. For the analysed ship, a constant value 0.2 is employed. Errors due to such a rough estimation are rectified in the next hull resistance coefficient (of course, at least at the service working point): It seems interesting how such scheme of identification is equivalent to model tests (systematic or individual ones), thus firther studies are recommended. Tab. 2 supplies the results. Because the hydrodynamics of the installed CPP is unknown, two CPPs ('A' - p/dk=0.7, 'B' - P/Dk=0.924) and two FPPs published in the open literature are investigated for comparison purposes.

4 propeller I.. source W td Cfih 4 Ship crash stopping Table 2. Parameter identification at service speed. A B C type I CPP4-Q / CPP 4-Q I FPP 1-Q 1 FPP 4-4 ( experiment) Ruseckij [S] (theory) Wagner[9] (l -Q regression) Oosterveld[7] As it is seen from Harvald's investigations, some general facts could be set down with regard to the wake fraction behaviour at crash stopping (though there is a rather essential irregularity between more detailed results for ships pretended to be comparable at first glance). The wake fraction before the reversing starts (maximum speed and revolutions, both positive) is nearly the same soon after (maximum positive speed, maximum negative revolutions). This is just believable to be appropriate also during CPP reversing (pitch change instead of revolutions change). The transient phase (because of a short time) could be omitted. The next rule of thumb is that the wake fraction increases up to high values (Harvald [3]) or low values (Harvald [4]), generally is unsteady, while the ship speed goes down. But at this range of low (apparent) advance ratios, the thrust and torque coefficients constitute practically a horizontal straight line: D (experiment) Nordstrom[5] and thus the thrust or torque predictions are not sensitive at all upon the huge variation in the wake fraction. For the above reasons, a common postulation of keeping the wake constant for crash stopping predictions (mostly due to lack of data) is even justified. More accurate relationships could be drawn by means of on-board propeller torque measurements. From practical poht of view, the ship stopping prediction relies mostly upon proper values of thrust deduction at different loads during manoeuvring (w=const). The change in time of the thrust deduction is according to the following differential equation: t'jt)=l- wdt.(m+m,,)-~~h -(m+cmm22)v,% (11) The change in time of the apparent advance ratio enables to identify the thrust deduction as a unique function of the latter. Due to the following difficulties: 0 during crash stopping, the investigated ship is entirely unstable and unpredictable in yaw direction (three trials give contrasting results), c,,, coefficient in eq. (1 1) demands some further research, 0 no data on propeller control are available with regard to the pitch change law (e.g. in view of the engine overload), 0 no hydrodynamic data of the installed CPP propeller is at hand as mentioned before,

5 due to yaw and drift, a sensitivity analysis should be conducted on the propeller thrust coefficient change with such a motion, the same applies to the wake fraction and thrust deduction, the lack of low-speed resistance curve, the identification of the thrust deduction from full-scale trials is put aside to the future. 5 Steady-state ship speed in ahead and astern motion This section covers aspects of a steady-state speed ensuring the balance of all forces i.e. the speed achievable for the given propeller pitclt'revolutions setting. Is widely recognised (from theory and practice) that during steady-state motion, irrespective of actual speed, the propeller advance ratio (also the apparent one) is fairly constant, keeping the wake fraction and thrust deduction more or less also on the same level. For the motion ahead, the values identified before in the present study shall be utilised. The question is what happens during the astern movement. A few rather consistent conclusions (approximations) from Harvald's model tests could be also drawn with respect to the ship performance in terms of the propulsion coefficients and ship resistance at a steady-state astern speed. Those are: increase of the astern motion resistance by even 50% (see also OCIMF[6]), 0 reduction of the wake fraction by ca. 50%, 0 increase of the thrust deduction by factor of ca. 2, as compared to the ahead values. We are not able to identify exactly all of the above magnitudes (identification ambiguity problems), but it is quite possible to validate whether such observations are sustained in full-scale by available measurements of the investigated ship astern speeds. The steady-state speed could be calculated when the diagram representing krl~2 as the function of J is constructed - see Fig 1. By supplying a particular value of ktl~2, a corresponding value of J is yielded. Substituting now also the known propeller revolutions to eq. (6), the ship speed is reached. Figure 1 : kt/~2 curves for propeller model A-CPP (left) and D-FPP (right).

6 From the balance of the ship motion resistance and the propeller effective tlmst the following expressions apply: -- kt -- LTc;, J' 2D2(1- w)'(l-t,) (ahead motion) k~ - Lqxh (astern motion) J' 2D2(1- w)'(1-t,) For each pitch ratio PID, a separate value of advance ratio is obtained. Fig. 2 shows such results in case of the data collected in Tab. 2 (for astern motion the Harvald's corrections as mentioned before have been imposed upon these data). Figure 2: Propeller advance ratio of steady-state motion. A comparison between the trial data and the predictions is displayed in Fig. 3. For the astern motion, a cumulative contribution of each of the three parameters i.e. astern motion resistance (increase), wake fraction (reduction) and thrust deduction (increase) is additionally demonstrated. The last item in the legend to these charts indicates the situation when all these parameters are modified. The trial data on ship speeds in ahead and astern regimes come from the shipyard's delivery report. This part of the report, however, does not keep a closer look at the circumstances, under which the measurements were conducted: no sea current information (during the earlier contract speed trial, the current of 0. l -0.2[rn/s] was experienced), no information on a possible main engine overload at the maximum astern order, no information on a magnitude (the direction is out of concern in the aspect of accuracy) of the yaw and drift (both always coexist), as normal during astern movement, i.e. whether or not the bow lateral thruster was used to check the yawing. A sensitivity analysis of the latter effect is carried out in the next section. Fig. 4 shows, on the other hand, the propeller torque at different throttles as the ratio of the maximum delivered main engine torque. The propeller model A (CPP data from the experiment, but somewhat different blade geometry, including herein the design pitch ratio) is surprisingly the worst case - too high discrepancy in astern speeds.

7 Figure 3: Speed prediction vs. trial data. Figure 4: Main engine load vs. pitchlrevs setting. The model B (CPP data by the theoretical calculation, but at a more alike pitch ratio) performs much better. In both cases, there is a difference between the actual and predicted speed especially at the low speed range. The reason probably lies in the assumed model of the motion resistance (as linear with speed squared), the research upon the low speed resistance is planned in the future. The models B and D, though ensuring a proper approach at the astern trial data, enable to express only a few affmtive arguments. Notwithstanding, they do not pretend to put a strict evidence that they are much the same (fiom the hydrodynamic point of view) as the mounted propeller, and the change in motion

8 resistance, wake fraction and thrust deduction, as explored by Harvald, is a matter of fact in astern motion. 6 Yawldrift influence upon astern steady-state ship speed The complete differential equation for the surge (longitudinal) speed reads: The astern speed in case of the frequently accompanied yawldrift motion (due to 'propeller lateral thrust') should be always greater. The sway and the yaw speed contribute to the very important centrifugal term in eq. (14) - the underlined component (responsible e.g. for the speed loss in turning manoeuvres). Caused by the stern location of the propeller, both variables v, and uz are of different signs (the same happens during common rudder manoeuvres) and thus the centrifugal term, often assuming large values (huge masses involved), is negative. This is quite identical e.g. to the application of bow lateral thruster when the ship is initially at the rest - the ship, beside the normal yawlsway motion (of the same signs), commences to increase the forward speed up to a very significant value. A new formula, quite identical to eqs. (13) and (14), for a steady state-speed in astern motion in case of the yawldrift reads as follows: k, - LTc& + (m + c,m22)tg(~,. ~ P/L - (15) J 2~~(1-w)~(l-t,) where: Fig. 5 indicates achievable astern speeds when the ship experiences the yawing to starboard (the drift, against a common notion, is also to starboard though initially it assumes port direction): p, = -174["] and G, = -0.3[-]. I I 1 4 +trial +W lout drifffyaw -W ith driftlyaw Figure 5: Astern speed in case of yawldrift (model A).

9 The surge speed v, in eqs. (16) and (17) is positive for the ahead motion and negative for the astern motion. 7 Conclusions It appears that, though the charts developed by Harvald show a significant change of propulsive factors with the apparent advance ratio, the wake fraction has little impact upon the manoeuvring motion prediction near low speed range (low values of advance ratios). Here both the thrust and torque coefficients are of a low sensitivity. By the same reason, a high variation of the wake fraction, as experienced in this region, could be assigned to the measurement errors. This way, more attention should be applied to the thrust deduction, which directly and essentially changes the effective propeller thrust. In the course of the performed research, a very interesting issue has arisen aside, namely the installation of CPP (instead of FPP) enables to assume a bit lower value for the wake fraction. The latter could be well explained if a propeller is looked at as the flow integrator. Symbols - propeller expanded area ratio [-l p - propeller pitch [m] - ship beam [m] P, - main engine power [W] - ship block coefficient [-l p,/d - pitch ratio [-l - hull resistance coefficient [-] p / ~ - design ~ pitch ratio (CPP) [-l - ratio of sway addded mass [-l p, / - service ~ ~ pitch ~ ratio ~ [-] - propeller diameter [m] - max. delivered engine torque mm] - hull resistance - sew. delivered engine torque [Nm] - propeller torque [Nm] - propellereffective thrust [N] - advance ratio [-l - apparent advance ratio [-l - pitch related apparent. ratio [-l - ship draught [m] -time [S] -thrust deduction [-l - service advance ratio [-l -thrust coefficient [-l - propeller torque coefficient [-] - ship length [m] - ship mass [kg] - surge added mass [kg] - sway added mass [kg] - revolutions (actual) [Ils] - revolutions (nominal) [Us] - revolutions (service) [Ils] - surge speed [&S] - service speed [&S] - sway speed [mls] - wake fraction [-l - propeller no. of blades [-l -water density [kg/m31 - ship drift angle [rad] - yaw rate [Us] - relative yaw rate [-l

10 References [l] Artyszuk, J., Propeller Slip Ratio in the Ship Manoeuvring Motion Mathematical Model - Thrust Case, Proc. of the 4th Navigation Symposium, Jun 19-20, Maritime University, Gdynia, [2] Artyszuk, J., The Low-Level Mathematical Model of Ship's Surge Motion, Proc. of the 7th International ScientiJic and Technical Conference on Sea Trafic Engineering, Part I, Maritime University, Szczecin, pp , 1997 (in Polish). [3] Harvald, S.A., Wake and Thrust Deduction at Extreme Propeller Loadings, Publication no. 61, SSPA, Goteborg, [4] Harvald, S.A., Wake and Thrust Deduction at Extreme Propeller Loadings for a Ship Running in Shallow Water, RlNA Trans., 119, pp , [5] Nordstrom, H.F., Screw Propeller Characteristics, Publication no. 9, SSPA, Goteborg, [6] OCIMF, Prediction of Wind and Current Loads on VLCCs, Witherby & Co., London, [7] Oosterveld, M.W.C., Oossanen van, P., Further Computer-Analyzed Data of the Wageningen B-Screw Series, International Shipbuilding Progress (ISP), 22(251-Ju~), pp , [8] Ruseckij, A.A., Controllable Pitch Propeller Hydrodynamics, Sudostroenie, Leningrad, 1968 (in Russian). [9] Wagner, K., On Hydrodynamics of Screw Propellers during Reversing, Schzfiauforschung, 13(3-4), pp , 1974 (in German).