Propeller off design conditions

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Analysis of twin screw ships' asymmetric propeller behaviour bymeans of free running model tests

A. Coraddu a, G. Dubbioso b, S. Mauro b, M. Viviani a,n

a University of Genoa, DITEN, Naval Architecture Unit, Via Montallegro 1, 16145 Genova, Italyb CNR-INSEAN, Via di Vallerano 139, 00128 Rome, Italy

a r t i c l e i n f o

Article history:Received 24 July 2012Accepted 6 April 2013

Keywords:ManoeuvrabilityTwin screw shipsPropulsionWarshipsShip control systems

a b s t r a c t

Twin screw ships may experience considerably asymmetric propeller functioning during manoeuvres.This phenomenon may result in large power fluctuations during tight manoeuvres, with increases ofshaft torque up to and over 100% of the steady values in straight course and considerable unbalances;this, in its turn, may be potentially dangerous, especially in case of particularly complex propulsion plantconfigurations, such as those with coupled shaftlines. A joint research project supported by the ItalianNavy has been set up in order to deeply investigate the phenomenon, by means of large scale modeltesting and related numerical simulations. In the present work, the extensive experimental campaignresults on a free running model of a twin-screw ship are presented, allowing to obtain a deeper insight ofthe problem. In particular, tests have been carried out simulating different simplified control schemes,starting from the most common constant rate of revolution tests and including different controlstrategies (constant torque and power). Usual standard manoeuvres (turning circle, zigzag and spiral)have been carried out, providing results for asymmetric shaft functioning and ship manoeuvrabilitybehaviour. Results from the present analysis allow to obtain the complete model for the time domainsimulation of asymmetric shaft functioning.

& 2013 Elsevier Ltd. All rights reserved.

1. Introduction

The problem of ship manoeuvrability has acquired increasingimportance over the last decades, with particular attention to thecapability to predict ship manoeuvring characteristics. This neces-sity was considerably boosted by the introduction of the man-oeuvrability Standards by the International Maritime Organisation(IMO, 2002). Many studies have been developed for years on thetopic of manoeuvrability, however not many of them are centredon twin screw ships, providing a considerable lack of informationand difficulties for the designer to cope with this problem.In some studies, an alternative form of the Mathematical ModelingGroup (MMG) model is presented, including the various modifica-tions needed to deal with the asymmetric behaviour of the shipshaftlines during manoeuvres (Kang et al., 2008; Khanfir et al.,2011); in other studies, the importance of hull appendagesconfiguration is investigated, and possible ways to improve man-oeuvrability predictions are presented (Di Mascio et al., 2011;Dubbioso and Viviani, 2012). The present work is focused on aspecific aspect of twin screw ship manoeuvrability, and in parti-cular on the asymmetric propeller behaviour during manoeuvres.

This asymmetric functioning may be considered as a side effect ofmanoeuvrability which affects the propulsion system behaviour;moreover, it may also affect ship manoeuvrability itself, becominga topic of interest from many points of view.

In general, it is well known that marine propulsion plants canexperience large power fluctuations during tight manoeuvres,with considerable increases of shaft torque up to and over 100%of the steady values in straight course. Moreover, in the case oftwin-screw ships, the two shaft lines dynamics can presentconsiderable asymmetric behaviour, with significant unbalancesof power and torque.

This phenomenon has already been analysed (Viviani et al.,2007), by considering a series of turning circle manoeuvres atdifferent speeds and rudder angles performed during sea trials fordifferent twin screw ships; in addition to this results at modelscale for only one ship were considered. This analysis allowed tounderline a common trend for asymmetric shaft power increasedespite significant differences between the various ships consid-ered, in terms of dimensions, ship type and propulsion system, andit also allowed to gain a first insight into possible scale effects. InSection 2, a brief overview of the main outcome of this preliminarywork is reported. A simplified approach to the problem by meansof the adoption of an asymmetric variation of wake fraction duringmanoeuvres was proposed, and this was introduced into a simu-lator with promising results (Viviani et al., 2008).

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Ocean Engineering

0029-8018/$ - see front matter & 2013 Elsevier Ltd. All rights reserved.http://dx.doi.org/10.1016/j.oceaneng.2013.04.013

n Corresponding author. Tel.: +39 103532547; fax: +39 103532127.E-mail address: [email protected] (M. Viviani).

Ocean Engineering 68 (2013) 47–64


The phenomenon of asymmetric loading of shaftlines, if notcorrectly considered, may be potentially dangerous. As an exam-ple, in case of particular propulsion plant configurations in whichtwo shaft lines are driven by a unique prime motor, the connectingreduction gear can be subject to significant unbalances. This kindof propulsion plant is in fact not very common, however it ispresent in some recent applications, such as fast naval ships.

With this in mind, a joint research project supported by theItalian Navy (PROSSIMA—PROpulSion StrategIes in MAnoeuvrabil-ity) has been conducted in the past years. In this project, anextensive campaign of free running model tests and simulationshas been carried out and developed in cooperation by CNR-INSEAN, University of Genoa (DINAEL) and CETENA,, with thescope of providing data for the development of a simulatorincluding the ship propulsion system and manoeuvrability. Thissimulator may become a useful tool for ship propulsion systemsand automation design (Altosole et al., 2008, 2010), being com-plementary to free running model tests and allowing the intro-duction of elements which can hardly be represented in modelscale (such as Controllable Pitch Propellers, effective propulsionsystem functioning and automation effect, etc.).

The main focus of this paper will be on the experimentalcampaign and related results, comparing the effect of the different

control strategies adopted (constant RPM, constant torque andconstant power). Furthermore, some results obtained with thedeveloped simulator in model scale will be also presented.

2. Summary of previous work

In the present section, a brief overview of the main outcome ofprevious works is reported. As already mentioned, a series of fullscale turning circle manoeuvres, evaluating the asymmetric shaftpower increase at different speed and rudder angle were consid-ered in a preliminary analysis (Viviani et al., 2007),. The used datacovered different twin screw naval ships of different types, rangingfrom rather slow Auxiliary ships and Replenishment and Logisticsupport ships to fast Frigates and Corvettes, with rather significantvariations in terms of hull shape and propulsion system. All shipspresented a twin screw propulsion configuration with completelyseparated propulsion plants, however, prime movers were various,including Diesel Engines, Electrical Motors and Gas Turbines,or combinations of them; both CPP and FPP configurations werepresent in the analysis.

In Figs. 1 and 2 stabilized power increases (recorded during thesteady part of the turn) obtained for all ships are summarized for

Fig. 1. Internal shaft—stabilized power increase (Viviani et al., 2007).

Fig. 2. External shaft—stabilized power increase (Viviani et al., 2007).

A. Coraddu et al. / Ocean Engineering 68 (2013) 47–6448


internal and external shafts (with respect to the turn) respectivelyas a function of rudder angle; results at different speeds areincluded in the graph, since the effect of ship speed proved to berather limited, as long as automation is not acting to limit load onthe shaftlines. In addition to experimental points, best-fit curves(linear in correspondence to external shaft, quadratic in corre-spondence to internal shaft) are reported, together with a bandindicating a range of plus and minus 10%.

Even if the presented data obviously present a certain scatter, arather clear tendency with a stabilized power increase rangingfrom about 85% to about 105% for external shaft and from 30% to50% for internal shaft, was found.

In addition to this analysis, turning circle tests results wereprocessed by means of the “asymmetric wake fraction variation”concept in order to obtain corrective coefficients to simulateshaftline asymmetry. The procedure recalls somehow the classicalself propulsion test analysis, even if with some necessary assump-tions and differences.

For each manoeuvre, the stabilized part of the turn is consid-ered, evaluating from kinematics the effective velocity in corre-spondence to both shaftlines. As a consequence, it is possible todetermine the relative rotative efficiency ηr (assumed as equal tothe one obtained during self propulsion tests) and, in its turn, KQ

value for both shafts:

KQ ¼ Qηr

ρn2D5 ð1Þ

where Q and n are the mean torque and shaft revolutions duringstabilised turn, respectively.

Using this value, it is possible to evaluate the equivalent openwater propeller advance coefficient J (using torque identity) andconsequently the ð1−wÞ value during turn. It has to be noticed thatthe presented results were obtained by assuming constant pro-peller characteristic curves (i.e. neglecting the effect of obliqueflow on propeller).

ð1−wÞ ¼ JnDu

ð2Þ

Comparing this result with the correspondent value in straightmotion, a coefficient Δw representing wake fraction variation wascomputed:

ð1−wÞStab ¼ ð1−wÞStraight−Δw ð3Þ

This approach is schematised in Fig. 3; in particular, two effectsare superimposed during manoeuvres, i.e. a first symmetricalvariation of advance coefficient due to speed reduction duringturn, and an asymmetric variation of advance coefficient, whichresults in asymmetric loading of shaftlines.

Wake fraction variation Δw values in general presented asimilar trend, with negative values in correspondence to internal

shaft, reducing overload due to speed loss in turn, and positivevalues in correspondence to external shaft, increasing shaft over-load. Selected values obtained for ships which are more similar topresent one are reported in Fig. 4 for maximum rudder angle(7351) turning circle manoeuvres. As it can be seen, a rather largescatter is present in this case. It has to be noted that, even if allships considered in previous analyses show the same trend, somecases exist in which a reversed trend appeared; as an example, inAtsavapranee et al. (2010) results of a similar work on rotating armon the DDG51 hull were reported, showing an opposite trend, withexternal propeller that are less loaded than the internal one. Thiscan be probably due to a combination of different effects, such aspropeller rotation, local wake structure and rudder induced effect(rudder blockage). Regarding propeller rotation, it has to be notedthat this is certainly not the sole factor to be considered, sincevalues reported belong to ships with both possible configurations.It should be noticed, moreover, that the physical meaning of thiswake fraction variation is contradictory to what could be expected,leading to an apparent speed reduction in correspondence to theexternal shaft, which is expected to work in a less disturbed flowduring turn, and an acceleration in correspondence to the internalshaft, which is expected to be more “covered” by the hull wakeduring turn. From this point of view, many different effects are inreality present, among which the most important probably are:

� propeller is working in an oblique flow,� tangential velocity may be present at propeller plane, due to

vortex shedding from the hull, and� in general, perturbed wake affects propeller behaviour.

First point is particularly important for external propeller, forwhich no flow straightening effect is expected, thus resulting inthe maximum oblique flow; other effects may be more importantfor internal propeller, which in general experiences a rather non-uniform and complex wake. From this point of view, therefore, thewake fraction variation has to be considered as an artificial way toinclude all these effects in one correction, rather than as a real

0

0.2

0.4

1.2

1.4

K Q

0.25 0.50 0.75 1.00 1.25 1.50

J

J1 JstraightJ2(int)J2(ext)

KQ1

KQstraight

KQ2(int)

KQ2(ext)

1) Spe d reductione

wext wint

2) As mmetricy al w

Fig. 3. Asymmetric variation of advance coefficient J during manoeuvres.

Fig. 4. Asymmetric variation of wake fraction during manoeuvres.

Table 1Main model characteristics.

L/B 7.5B/T 3.25CB 0.5

A. Coraddu et al. / Ocean Engineering 68 (2013) 47–64 49


acceleration or deceleration of the longitudinal speed. As it will beseen in Section 6, this approach turned out to be very effectivefrom the point of view of the simulation of the asymmetric shaftfunctioning, thus it was deemed acceptable. Moreover, it shouldbe noticed that the inclusion of some effects, such as modifiedpropeller characteristic curves due to oblique flow, do not sig-nificantly modify the results, thus the present approach wasmaintained. In Section 7, results from a different analysis, carriedout by means of RANSE approach, are briefly summarized, stres-sing the importance of the direct analysis of flow field at stern for acomplete understanding of the phenomenon.

Another important issue is represented by scale effects; inViviani et al. (2007) a comparison of results from free runningmodel tests and sea trials for a ship whose type and configurationare the same of the ship used for this study, was reported, allowingto have a first insight into this problem.

Results showed that, for the particular tested configuration,power increases tend to be underestimated during free runningmodel tests, with values that are lower by about 10–15% incorrespondence to maximum rudder angle for both external andinternal shafts. It is obvious that validity of this result is limited tothe specific ship, and cannot be generalised. Results from thepresent work, if coupled with full scale results, could provide inthe future a further insight into this problem, thus presenting apossible added value of the research.

3. Ship characteristics

The ship selected for this analysis is a fast twin screw/twinrudder ship, similar to those analysed in previous studies (Vivianiet al., 2007). The main characteristics of the ship are reported inTable 1 where L is the ship's length, B is the ship's beam, T is thedraft, CB is the block coefficient. As a matter of fact and due toconfidentiality reasons, it is not possible to provide complete dataregarding the ship

A large model of the ship (about 7.2 m long), as depicted inFig. 5 was manufactured in order to carry out free running modeltests. In Section 4, the experimental facility and setup are brieflysummarized.

4. Experimental facility and setup

In this section, the experimental facility and instrumentationadopted by CNR-INSEAN are briefly described (Section 4.1), thenthe complete list of performed tests is provided (Section 4.2).

4.1. CNR-INSEAN outdoor manoeuvring basin and model setup

The experimental activities are carried out in Nemi's naturalvolcanic lake located 40 km away from the main CNR-INSEANbuildings. It is an ideal location where long-term dead-calm water

conditions are frequent in a non-anthropic natural and environ-mentally protected area. The water surface is large enough toallow the execution on any kind of manoeuvring test regardlessthe model size and speed. For the sake of clarity, Figs. 6 and 7 witha Google maps satellite view (Decimal GPS coordinate lat.12.700377702713013 long. 41.720448924843765) and the officialITTC facility data sheet are included, respectively.

On-board of the unmanned model, each propeller shaft isdriven by a dedicated electric brushless motor; in order tosimulate a possible cross-connect configuration, both shafts maybe connected by a chain and a suitable reduction gear. The overallenergy demand of the system is provided by a diesel electricgenerator. Each shaft line is equipped with a dynamometer for themeasurements of propeller loads, namely torque and thrust; inparticular, thrust measurement is a new element with respect toexperiments both at full and model scale presented in Viviani et al.(2007). In Fig. 8 the model setup is schematized.

In addition to tests carried out with the standard approachkeeping constant propeller RPM during manoeuvres, a series oftests with different propulsion settings, i.e. constant propellertorque and constant propeller power,have been considered. Con-stant torque and power configurations are obtained by modifyingthe value of the limit voltage VLIM during the manoeuvres. Thecontrol system continuously monitors the torque (or power)during manoeuvre, and varies the VLIM value in a feedback controlloop in order to keep them constant. Details of the controller aredescribed in Mauro and Dubbioso (2012). In particular, the controlsystem acts to limit the feeding voltage to the brushless motor inorder to fix the power/torque release. In present tests, both powerand torque are kept constant to the value recorded during theapproach phase.

The self-propelled unmanned free-running model usually isfully equipped with all the technical devices (DGPS, IMUs, torqueand thrusts metres on the propeller axis, dynamo-tachometers,

Fig. 5. Ship model at INSEAN (left) and during manoeuvrability tests (right).

Fig. 6. Satellite view.



real-time data transmission devices, etc.) necessary to carry outthe experimental activities.

All tests are carried out in a calm environment, in order to avoidexternal disturbances. This allows to achieve a satisfactory repeti-tiveness, as confirmed by repeatability analyses which were carriedout for this specific case (as reported in (Mauro et al. 2012)

4.2. Performed tests

As already mentioned, tests were carried out in correspon-dence to three different simplified control strategies, i.e. constantRPM, constant torque and constant power. It is worth mentioningthat for the first two configurations shaftlines were completelyseparated, while during the constant power tests, shaftlines werecoupled by means of the above mentioned chain, thus forcing

shaft revolutions to remain equal during the whole test; in thiscase, total power was kept constant, while the two shafts stillbehave differently due to their asymmetric functioning.

In all configurations, the constant value (RPM, torque or power)imposed during the manoeuvre is set to the one recorded duringthe approach phase in steady rectilinear motion. Being the modelequipped with fixed pitch propellers, constant torque and powertests are obtained by means of shaft revolutions reduction.

In correspondence to all the control strategies, the followingset of manoeuvres has been carried out at two different speeds(FN equal to about 0.25 and 0.375):

� Turning circle (7151,7251,7351).� Zig-zag 101/101 and 201/201.� Dieudonnée spiral test.

Fig. 7. ITTC Official data sheet.



Constant RPM tests results may be directly compared with thoseobtained in the previous studies (Viviani et al., 2007; Dubbioso et al.,2010). Moreover, these tests were also analysed in order to obtainsuitable coefficients for shaft asymmetric functioning simulation, asreported in Section 5.1. Constant torque and power tests allowed todirectly compare results in correspondence to different controlstrategies (Section 5.2), moreover they provided useful data forfurther validation of simulation model (Section 6).

5. Experimental campaign results

5.1. Constant RPM tests

In Figs. 9 and 10, typical results of constant RPM tests are reportedfor 351 turning circle and 201/201 zigzag tests at lower Froudenumber. In both cases, thrust and torque variation (equal to powervariation being RPM constant) with respect to initial value are plotted.

The asymmetric behaviour of shaftlines is clearly evidenced,with a considerable overload of the external shaft, superimposedto the effect of advance speed reduction during manoeuvre.

Results in correspondence to other manoeuvres with lowerrudder angle are in line with the ones reported, with obviouslyless significant unbalances of shaft functioning during manoeuvre,and are omitted for the sake of shortness.

In Figs. 11 and 12, the main macroscopic parameters of theturning circle manoeuvre (non-dimensional values of advance andtactical diameter and thrust and torque increases during man-oeuvre) are reported for the two ship speeds considered. Inparticular, Fig. 12 clearly evidences the asymmetric behaviour,which is similar in the two speeds.

As a first analysis, the results of turning circle manoeuvreswere compared with those presented in previous works. Fig. 13shows stabilised power increases obtained in correspondence todifferent rudder angles and velocities. The black crosses, whitedots and black dots represent present results in model scale,previous results in model scale and previous results in full scalerespectively.

It is evident that the results that have been obtained presentthe same behaviour (at least qualitatively) of previous ones.Nevertheless, shaftline overload is lower in the analysed t casefor both internal (nearly constant value, with an increase ofabout 5%) and external shaft (about 50% increment). As it couldbe expected, these results are more in line with previous ones inmodel scale, even if also in this case power increases are lower.

As a second step, corrective coefficients in order to simulateasymmetric shaft functioning were evaluated. The chosen appro-ach is exactly the same as the one already presented in Section 2,however in the present case, an additional analysis is performedconsidering the availability of thrust data.

In particular, once J value during manoeuvre is identified,thrust coefficient KT is also evaluated, from which nominal thrustTNOM in open water conditions is obtained. Comparing it withmeasured thrust in free running model tests, TMEAS , a furtherthrust correction factor, Γ, is obtained.

TNOM ¼ KTρn2D4 ð4Þ

Γu ¼ TTNOM

ð5Þ

In Fig. 14 the asymmetric wake fraction variation valuesobtained at different speeds and rudder angles are presented. It

Fig. 8. Model setup.



Fig. 9. 351 Turning circle – FN 0.25 – trajectory, ship speed, Q/Q0, T/T0.

Fig. 10. 201/201 Zigzag – FN 0.25 – heading angle, ship speed, Q/Q0, T/T0.



0 10 20 30 400

2

4

6

8

δ [°]

X90

/ L

X90

/ L 0.250 FN

X90

/ L 0.375 FN

0 10 20 30 400

2

4

6

8

10

δ [°]

Y18

0 / L

Y180

/ L 0.250 FN

Y180

/ L 0.375 FN

Fig. 11. Advance and tactical diameter during turning circle manoeuvre at different rudder angles and constant RPM—Froude numbers¼0.25 and 0.375.

Froude number= 0.250

Froude number= 0.375

Fig. 12. Main propulsion parameters during turning circle manoeuvre at different rudder angles—Froude numbers¼0.25 and 0.375.

Fig. 13. Stabilised power increase during turn.



can be observed how the wake fraction variation Δw values arerather large, especially for the internal shaft (with maximumabsolute values in correspondence to tighter turns up to about0.3, reducing shaft overload due to speed loss in turn), whileslightly positive values can be observed for the external shaft,increasing shaft overload.

Results obtained for the thrust correction factor Γ are presentedin Fig. 15; as it can be seen, values are rather limited, being lowerthan 5%, underlining that the asymmetric load taken into accountwith Δw represents the majority of the effects.

It has to be remarked that a parallel analysis was carried outwith similar steps, but considering at first thrust instead of torque,similarly to analysis of self propulsion tests. In particular, steps areas follows:

� considering mean measured thrust, KT value during turn isevaluated,

� advance coefficient is evaluated from propeller open water tests,� asymmetric ð1−wÞ is computed by means of (2), and thus Δw� comparing torque value during turn with expected nominal

value, a torque correction factor is evaluated.

Results from this analysis are omitted since, as it could beexpected, they did not provide any added value, with similarresults in terms of asymmetric wake fraction variation and torquecorrection factor near to unit value. The unique advantage, if any,of this procedure is merely formal, being more similar to theconventional self propulsion test analysis. However, the procedurestarting from torque value is considered preferable since it may beapplied, as done in Viviani et al. (2007), to full scale tests, forwhich thrust value is usually not available due to the difficultiesconnected to its measurement.

5.2. Constant torque and power tests

Figs. 16 and 17 present the main results obtained consideringthe constant torque and power controls for the most criticalturning circle manoeuvre, including both kinematic and propellerfunctioning parameters. Results are also compared to valuesobtained with constant RPM configuration.

The influence of control strategy is rather limited in terms ofusual macroscopic parameters, as visible in Fig. 16; similar resultswere obtained for other parameters and other manoeuvres, andare omitted for the sake of shortness. The main difference betweendifferent control strategies is represented by speed variationduring manoeuvre, magnified in the case of turning circle at largerrudder angles. Due to the different propeller revolutions in turn,the speed reduction is larger in correspondence to constant torquetests and lower in correspondence to constant RPM tests. Thisspeed reduction is also propagated to other velocities; turningcircle trajectory is almost invariant in all cases, with the shipmoving more slowly at constant torque. This effect is clearlyevidenced by the non-dimensional yaw rate (not reported forthe sake of shortness), which remains constant, confirming theparallel reduction of all velocities involved in the manoeuvre.

Effect of different control strategies in terms of shaft revolu-tions, torque, power and thrust during the turning circle man-oeuvre is represented, clearly evidencing the considerabledifferences of various approaches; in particular, external shaftmeasured data are reported, since they show the most signi-ficant variations due to higher overload. Only in the case ofconstant power control (external plus internal shaft) total poweris reported, consistently with the control strategy. As it could beexpected, the maximum shaft revolutions reduction is obtained inthe case of constant torque control; and also thrust variations areconsiderably reduced. Results of the particular control strategy

Fig. 14. Wake fraction variation during turn.

Fig. 15. Thrust correction factor variation during turn.



with constant power control, are evidenced in Fig. 17. The value oftotal power is effectively kept constant during manoeuvre; never-theless the two shafts still present unbalances (not reported in thefigure) since the two fixed pitch propellers present the same

revolutions reduction. In full scale this unbalance might be compen-sated by adjusting separately propeller pitches (in case of CPPs).

For the sake of completeness, Figs. 18 and 19 highlight thecomplete results of thrust, torque and power variations during

Fig. 16. 351 Turning circle – different control strategies – FN 0.25—kinematic parameters.

Fig. 17. 351 Turning circle – different control strategies – FN 0.25—N/N0, P/P0, Q/Q0, T/T0 (external shaft).



turn for the different control strategies in correspondence to thetwo speeds considered, showing again the same features alreadydiscussed.

In particular, considering the constant power case, only onecurve is obviously represented for the RPM variation duringmanoeuvre, and the correspondent figures of torque, thrust and

CONSTANT RPM CONTROL

CONSTANT POWER CONTROL

Fig. 18. Asymmetric propeller functioning during turning circle manoeuvre at different rudder angles in correspondence to different control strategies—Froudenumber¼0.25.



power show the residual unbalances which are experienced withthis configuration, in which total power only is constant. More-over, it is again noticeable that the behaviour at the two ratherdifferent velocities is considerably similar.

6. Simulations

Coefficients obtained in previous analysis have been introducedinto a propulsion and manoeuvrability simulator developed inSIMULINKs environment at DITEN in past years in order to test itscapability to capture the shaft asymmetric behaviour; an overviewof the main blocks present in the simulator is given in Fig. 20,while a complete description of the various parts is omitted for thesake of brevity, and may be found in Dubbioso et al. (2010). In thisparticular case, the propulsion part was limited, considering onlythe electrical motor and a simplified representation of its control.Unbalancing coefficients evaluated in the previous section areintroduced in the simulator at each time step as a function of thedrift angle, as proposed in Viviani et al. (2008).

This section presents the results of some simulations andcompares them with experimental results. Figs. 21 and 22 show,as an example, results related to turning circle and zigzagmanoeuvres at higher speed and constant RPM control, showinga good agreement.

From this point of view, it has to be noted that, regarding themanoeuvrability part, hydrodynamic coefficients initially evalu-ated by means of regressions developed at DITEN (Dubbioso andViviani, 2012) were suitably tuned in order to reduce errors inkinematic characteristics. This approach was considered accepta-ble, since the main focus of this activity was on the asymmetricshaft behaviour and its effect on propulsion, thus it was decided toeliminate other possible sources of discrepancies.

As it can be seen, asymmetric shaft behaviour is correctlyrepresented, even if in the case of turning circle a slight over-estimation (about 10%) of internal shaft torque is present; dis-crepancies are very small in case of zigzag manoeuvre.

Similar results were also obtained for other manoeuvres andcontrol strategies, and are omitted in present paper. For the sake ofcompleteness, however, propeller RPM, torque and power varia-tions during turn are presented in Figs. 23 and 24 for the tworemaining control strategies, showing again a very goodagreement.

7. Alternative analysis of asymmetric shaft functioning

In the results presented the main focus has been centred on theeffects that the propulsion device of a twin screw vessel experi-ences during a maneuver. As it has been discussed, the hydro-dynamic phenomena causing the propeller's overloading andunbalancing are mainly related to the hull wake features incorrespondence to the internal and external propeller. Moreover,hull wake during a typical steady tight turn is extremely compli-cated because it is primarily affected by separation phenomenaand the presence of large vortical structures detached from thehull. In order to gain more insight into the characteristics of thehull under dynamic motion and its effect on the propulsion device,an alternative approach has been recently proposed (Mauro et al.2012); in this section, the key aspects and principal results aresummarized.

In particular, numerical simulations have been carried out bymeans of the CNR-INSEAN in-house CFD solver χnavis in order toestimate the flow field around the hull, especially in correspon-dence to the stern region and the propellers. In this preliminaryinvestigation, a simplified hull geometry has been considered,

CONSTANT TORQUE CONTROL

Fig. 18. Continued.



CONSTANT RPM CONTROL

CONSTANT POWER CONTROL

Fig. 19. Asymmetric propeller functioning during turning circle manoeuvre at different rudder angles in correspondence to different control strategies—Froudenumber¼0.375.



namely the bare hull fitted with bilge keels and centerline skegwithout propeller shafts and brackets (see Fig. 25).

The choice for this simplified configuration is supported by thenumerical results of a manoeuvreing ship presented in Broglia et al.(2011) and Durante et al. (2010), where it was emphasized that thestrong vortical structures developed during the maneuver wereprimarily originated in correspondence to the bilge keels and theskeg. The simulations have been carried out for the lower speedconsidering two conditions: ship in rectilinear motion (approachphase) and ship in the steady turn at the highest rudder angle. In thesecond case, kinematics conditions (yaw rate, absolute speed anddrift, neglecting roll angle) have been imposed to be equal to thoseexperienced during the experiments. In both cases the propellernominal wake has been evaluated. In particular, the absolute velocityand yaw rate have been set from measurements (absolute velocitycorrespondent to FN¼0.194 and nondimensional turning radius R′¼2.2); the drift angle, not directly measured during the experiments,was set equal to 101, which is a typical value for frigate type vessel.Once the nominal wake has been evaluated, propeller loads (thrustand torque) corresponding to the computed nominal wake (on boththe internal and external side) have been evaluated off-line from theuRaNSE solver. Propellers are modelled by means of a suitable BladeElement and Momentum Theory (BEMT) model extended to treatoblique flow. In this model, the propeller blades are described bymeans of the hydrodynamic characteristics of 2D sections encounter-ing a variable flow in terms of angle of attack and velocity magnitudeduring one complete revolution.

In Fig. 26 the model wake during the steady turn in correspon-dence to the propeller disks is represented in terms of axialvelocity (u), nondimensionalised with respect to ship longitudinalspeed. It is worth emphasizing that in the steady turn condition,the velocity field over the two propellers is asymmetric, leading tothe asymmetric propeller behaviour. Moreover, it can be evi-denced that the flow in the leeward side is more complicated

with respect to the windward one, because it is mainly influencedby the hull wake and the presence of a large vortical region in thelower half of the disk.

Regarding the external propeller, the main effect is clearlygiven by the lateral speed as it could be expected since theshaftline is directly exposed to free stream, without significantinterference by the hull.

The propeller loads (considering constant RPM functioning)and in particular their percentage increase with respect to thevalues experienced in the approach phase, that were evaluated bythe BEMT model with the (computed) hull wake are reported inTable 2 and compared to the experimental results recorded duringthe free running test. It is evident that the BEMT model is able tocapture the overall shafts behaviour. In particular, the externalpropeller is more loaded with respect to the internal one, even if aslightly lower asymmetry is predicted (with lower thrust at theexternal shaft and higher thrust at the internal shaft). Regardingtorque, internal shaft presents similar a tendency. Moreover,numerical values seem to over predict experimental ones, even ifpercentage variations are in line with experiments. From this pointof view, it has to be stressed that torque is more influenced bysectional drag coefficients, and therefore a finer tuning withrespect to open water curves might improve this result. Consider-ing the complexity of the phenomenon and the approximationintroduced by neglecting interactions among the propeller and thehull and the simplified propeller model, results can be consideredvery promising. This analysis shows the very complex phenomenawhich are present in reality, whose effect in terms of global shaftoverload is captured with the adoption of the simplified modelpresented in the paper. Many efforts are still needed in order tofully understand these phenomena. In particular, the analysis ofthe effects of the presence of propeller shaft and brackets is stillongoing as well the direct inclusion of a simplified model in theCFD solver.

CONSTANT TORQUE CONTROL

Fig. 19. Continued.



8. Conclusions

This paper presents the, results of an extensive experimentalcampaign on a free running model of a twin-screw ship, carriedout in the framework of the project PROSSIMA.

Tests included standard turning circle, zigzag and spiral man-oeuvres at two different speeds, and were carried out withdifferent control strategies, namely constant propeller revolutions,torque and power.

The analysis of tests provided information about ship man-oeuvrability in general and asymmetric shaft behaviour duringmanoeuvres, allowing to obtain a complete simulator for thepropulsion system and manoeuvrability (in model scale), bymeans of a simplified, but effective, approach.

The comparison of simulated results and experimentaldata were satisfactory, even in presence of control strategiesdifferent from the one used to obtain unbalancing co-efficients, thus showing the robustness of the presented

Fig. 20. Overview of manoeuvrability and propulsion simulator.

Fig. 21. Simulations vs. experiments – 351 turning circle – FN 0.375 – constant RPM – trajectory, ship speed, Q=Q0, T=T0.



approach. It is believed, therefore, that the simulator maybe modified in order to represent various aspects of thefull scale ship (such as CPP, real automation and propul-sion plant characteristics, etc.), allowing the designer to obtaina better insight in the functioning of various components and

to develop the correct control schemes in order to optimizethem.

Nevertheless, many aspects still need to be investigated, suchas possible scale effects (already pointed out in Viviani et al.(2007), but still to be confirmed) and currently available

Fig. 22. Simulations vs. experiments – 201/201 zigzag – FN 0.375 – constant RPM – heading angle, ship speed, Q/Q0, T/T0.

Fig. 23. Simulations vs. experiments – 351 turning circle – FN 0.375 – constant torque – N/N0, Q/Q0, P/P0, T/T0.



regression formula for hydrodynamic coefficients calculations;moreover, a deeper analysis in the complex phenomena invol-ving stern flow is needed, in order to gain a better insight intothem. For what regards scale effects, once full scale data will beavailable, they will be further compared with present data inmodel scale, allowing to increase understanding of this phe-nomenon. Regarding the formulas for hydrodynamic coefficientscalculations, they still need improvement, since values ofcoefficients had to be tuned in this work in order to obtain asufficiently correct simulation of manoeuvrability characteris-tics. From this point of view, it will be necessary to furtherinvestigate complex effects such as hull/appendages and hull/propeller/rudder interactions (e.g. flow straightening coeffi-cients) during manoeuvres. It is believed that, in order to obtainthis goal, sets of dedicated experimental campaigns (both atPMM and with free running tests) would be beneficial; inparallel to these tests, numerical calculations (e.g. RANS calcu-lations) may allow to reduce model testing efforts if correctlycalibrated. Numerical approaches, as shown in the preliminarycalculations presented in Section 7, may allow to provide afurther (and more physical) insight into the problem of shaftasymmetric behaviour during turn. As a consequence, this mayhelp to overcome the presented simplified approach which, asmentioned, is very effective in terms of global propulsion

system simulations during turn (at least considering meanvalues), but does not allow to capture the real flow effects atstern. As an example, the non-stationary functioning of both thepropellers in turn due to the lateral flow on the external shaftand to the complex wake system on the internal shaft may notbe considered with the mentioned approach, even if it may be

Fig. 24. Simulations vs. experiments – 351 turning circle – FN 0.375 – constant power – N/N0, Q/Q0, P/P0, T/T0.

Fig. 25. Simplified geometry considered.

Fig. 26. Propeller inflow during steady turn: u (up), v (down).



significant in terms of propeller cavitation (in full scale) and itsside effects (pressure pulses, radiated noise).

Acknowledgements

This work has been carried out in the framework of projectPROpulSion StrategIes in Manoeuvrability (PROSSIMA), fundedwithin the PNRM by the Italian Navy.

References

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Table 2Propellers overload—comparison of numerical and experimental results.

Internal External

T/T0 Q/Q0 T/T0 Q/Q0

BEMT 23.9 11.5 60.6 43.3EXP 9.0 4.6 80.1 54.2


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