Stern Twin-Propeller Effects on Harbor Infrastructures. Experimental Analysis

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Article Stern Twin-Propeller Effects on Harbor Infrastructures. Experimental Analysis

Anna Mujal-Colilles 1,* , Marcel· la Castells 2, Toni Llull 1, Xavi Gironella 1 and Xavier Martínez de Osés 2

1 Marine Engineering Laboratory, Department of Civil and Environmental Engineering, Universitat Politècnica de Catalunya, C/ Jordi Girona 1, 08034 Barcelona, Spain; [email protected] (T.L.); [email protected] (X.G.) 2 Department of Nautical Science and Engineering, Universitat Politècnica de Catalunya, Pla de Palau, 18, 08003 Barcelona, Spain; [email protected] (M.l.C.), [email protected] (X.M.d.O.) * Correspondence: [email protected]; Tel.: +34-93-401-7017

Received: 12 October 2018; Accepted: 30 October 2018; Published: 2 November 2018

Abstract: The growth of marine trafﬁc in harbors, and the subsequent increase in vessel and propulsion system sizes, produces three linked problems at the harbor basin area: (i) higher erosion rates damaging docking structures; (ii) sedimentation areas reducing the total depth; (iii) resuspension of contaminated materials deposited at the seabed. The published literature demonstrates that there are no formulations for twin stern propellers to compute the maximum scouring depth. Another important limitation is the fact that the formulations proposed only use one type of maneuvering during the experimental campaign, assuming that vessels are constantly being undocked. Trying to reproduce the real arrival and departure maneuvers, 24 different tests were conducted at an experimental laboratory in a medium-scale water tank using a twin propeller model to estimate the consequences and the maximum scouring depth produced by stern propellers during the backward/docking and forward/undocking scenarios. Results conﬁrm that the combination of backward and forward scenario differs substantially from the experiments performed so far in the literature using only an accumulative forward scenario, yielding deeper scouring holes at the harbor basin area. The results presented in this paper can be used as guidelines to estimate the effects of regular vessels at their particular docking location.

Keywords: harbor management; erosion; sediment transport; propeller erosion

1. Introduction The significant growth experienced by regular shipping lines and the marine transportation industry over the last 20 years is producing severe problems for old marinas designed to host smaller vessels with lower docking frequencies. New, bigger and more powerful propulsion systems and deeper draft vessels are needed nowadays to satisfy the demands on marine traffic. However, this increase in propulsion system and vessel sizes is affecting the docking infrastructures and the operability of the entire harbor. The main problem is the change in bed morphology of the harbor: entrance channels suffer high rates of erosion and the changes on harbor basins seafloor combine both erosion and sedimentation. A recent field study of a particular harbor basin [1], showed that the erosion in these areas of the port can reach a depth up to the same order of magnitude as the stern propeller’s diameter. The effects of the erosion are different depending on the location of the scouring hole. If the erosion is located close to the toe of the docking wall it can seriously affect the stability of the berth infrastructure. On the other hand, if the erosion is located at more central areas of the harbor basin, a problem arises with the deposition of the eroded sediment along the harbor basin,

Water 2018, 10, 1571; doi:10.3390/w10111571 www.mdpi.com/journal/water Water 2018, 10, 1571 2 of 14 reducing its operability for larger draft vessels and the area has to be dredged often enough for safe navigation (with sufficient keel clearance). Moreover, an environmental problem can also arise from the scouring effects of stern twin propellers of the vessels, and the increase in marine traffic in ports is also increasing the accumulation of heavy contaminants in some areas of the harbor. One of the engineering solutions to improve the water quality of the harbor is to trap the contaminated sediment below a layer of coarser gravel [2]. However, as reported by [3,4], the action of stern propellers over the seafloor can negate the solution and free the contaminated sediment creating an important issue that correlates sediment resuspension of contaminants due to the stern propellers’ effects and water quality requirements of the cruise shipping industry. Therefore, the growth of marine traffic in harbors and its subsequent increase in vessel and propulsion system sizes produces three linked problems at the seabed of the harbor basins: (i) higher erosion rates damaging docking structures; (ii) sedimentation areas reducing the total depth of the harbor basin and its operability; and (iii) resuspension of contaminated materials deposited at the seabed. The formulation published and used so far to investigate the erosion rates of ship’s propellers is based on empirical equations with a dependent variable named efflux velocity, V0. Efflux velocity is defined as the average velocity of the flux nearby a single propeller in a plane parallel to the propeller blades. The first empirical equation for V0 was developed by [5,6], and detailed the expression for V0 based on the application of the momentum and mass conservation equations to an ideal actuator disk. Later, other authors proposed more complicated empirical equations based on the momentum equation, and including the particular characteristics of propellers, such as: the number of blades, the expanded area ratio, the propeller pitch and the hub diameter [5,7–11]. However, the former equations were developed considering a single propeller. The guidelines published in [12] proposed two mathematical methods to extrapolate the efflux velocity of a single propeller to twin propellers, but [13] demonstrated that the empirical formulas to compute efflux velocity clearly overestimated the experimental results of a twin propeller model. The maximum erosion can be computed either (i) using the efflux velocity to obtain the bed velocity [7,8,14] and then computing the Shields parameter; or (ii) using empirical formulas developed in physical experiments with a single propeller model [15–22]. For the first case, ref. [13] found that bed velocity for twin propellers was estimated properly if the formulation proposed by [8] was used, but [13] did not compute the maximum erosion. In the second case, [1] compared the previous formulations to a real case and concluded that all of them clearly overestimated by far the real scouring actions, and only [17,21], using the confined propeller jet equation, yielded results close to reality, but doubled the real maximum scouring depth. Therefore, no formulations for twin propellers are present in the literature to compute both the efflux velocity and the maximum scouring depth. Another important limitation is the fact that the formulations proposed only use one type of maneuvering during the experimental campaign, assuming that vessels are constantly being undocked at the same point, but never docked. This paper deals with the results obtained at an experimental laboratory using a twin propeller model to estimate the maximum scouring depth produced by stern propellers. As a novel incorporation, and in order to compare results with the real scouring effects at harbor basin, the research includes two different maneuvering conditions: undocking maneuvering (forward scenario) only to compare twin results with single propeller erosion published in the literature; and, alternatively, docking and undocking maneuvering (back and forth scenario) in the same harbor basin. The experimental setup is described in the second section, while the results are presented in the third section and discussed in the fourth section. The fifth section summarizes the conclusions of the research.

2. Experimental Setup Experiments were conducted in the Marine Engineering Laboratory at the UPC-Barcelona Tech University in a medium-scale water tank named LaBassa [13]. Figure1 presents a sketch of the tank, Water 2018, 10, x FOR PEER REVIEW 3 of 14

propeller and the sediment bed, 𝑋 is the distance between the propeller plane and the front wall, and 𝑎 is the distance between the center of the two propellers. Initially, the experiment was designed to scale a real Ro-Ro vessel with a daily docking Waterfrequency2018, 10 at, 1571 a particular harbor basin. The scaling factor was set to 1/25 using the Froude number3 of to 14 scale dynamic effects, but including the Reynolds self-similarity criteria found in [23,24] to assure a turbulent flow beyond the propellers and neglect the viscous effects. Twin 4-blade inward rotating wherepropellersDp iswith the a diameterpitch ratio of of the 0.9 propellers,and an expandedch is the area clearance ratio of distance0.75 were between used. The the diameter center ofof the propellerpropellers and was the 0.25 sediment m and the bed, distanceXw is thebetween distance prop betweenellers was the 0.6 propeller m. The planetotal duration and the frontof a single wall, andtest wasap is 30 the min, distance scanning between the bed the se centerdiment of theevolution two propellers. at 5 min intervals.

Figure 1.1. SchematicSchematicview view of of LaBassa LaBassa tank. tank. (a )(a Lateral) Lateral view view with with a zoom a zoom on at on the at helices the helices zone; zone; (b) Front (b) view.Front Hwview. is Hw the wateris the heightwater height and Hs and isthe Hs sedimentis the sediment height. height.

Initially,A total of the 24 experiment different wastests designed were obtained to scale by a real combining Ro-Ro vessel the withfollowing a daily variables: docking frequencyclearance atdistance, a particular front wall harbor distance, basin. speed The scaling rotation, factor 𝑛, and was the set maneuver to 1/25 usingscenario the (forward; Froude number back and to forth), scale dynamicas detailed effects, in Table but including 1. Forward the Reynoldsmaneuvering self-similarity tests follow criteria the found sequence: in [23 ,24(i)] initialization to assure a turbulent of the flowsediment beyond bed the to a propellers horizontal and plane; neglect (ii) 5 themin viscous run at a effects. determined Twin 4-bladerotationinward speed; (iii) rotating scanning propellers of the withsediment a pitch bed; ratio (iv) of repeat 0.9 and steps an expanded (ii)–(iii) for area a total ratio run of 0.75 of 30 were min. used. Back The and diameter forth maneuvering of the propellers tests wasfollow 0.25 the m sequence and thedistance from the between second propellersstep: (ii) 5 wasmin 0.6run m. in Thebackward total duration mode; (iii) of a scanning single test ofwas the 30sediment min, scanning bed; (iv) the 5 bedmin sedimentrun in forward evolution mode; at 5 (v) min sc intervals.anning of the sediment bed; (vi) repetition of secondA totalto fifth of 24steps different for a teststotal wererun of obtained 30 min. by combining the following variables: clearance distance, front wall distance, speed rotation, n, and the maneuver scenario (forward; back and forth), as detailed in TableTable1. Forward1. Tests description. maneuvering Each teststest contains follow 3 the different sequence: values (i) of initialization n (300, 350, 400) of and the an sediment analysis bedof to a horizontalthe sediment plane; bed (ii) evolution 5 minrun every at 5 a min. determined Total duration rotation of a speed;single test: (iii) 30 scanning min. of the sediment bed; (iv) repeat steps (ii)–(iii) for a total run of 30 min. Back and forth maneuvering tests follow the sequence 𝒄 w from the second step:𝒉 (m) (ii) 5 min X run (m) in backward Maneuver mode; (iii) Test scanning n (rpm) of the Time sediment (min) bed; (iv) 5 min Forward T1-fwd run in forward mode; (v) scanning7𝐷 of the sediment bed; (vi) repetition of second to fifth steps for a Back & Forth T1-b&f total run of 30 min.𝑐, =𝐷 Sediment used in the experiments wasForward a D = 250 µT2-fwdm uniform fine sand. Sediment was not scaled 10𝐷 50 300 Back & Forth T2-b&f from the prototype due to the limitations of finer sand in model reproductions.350 0-5-…-30 Two @ULTRALAB UWS 1M Echo Sounders measured the surfaceForward of the sedimentT3-fwd bed layer after each 5 min-run. The Echo 7𝐷 400 Sounders were hanging from a mechanizedBack & arm Forth covering T3-b&f an area of 3.5 m × 2.8 m with blanking 𝑐, ≅1.6𝐷 distances at the edges of the tank (0.25 mForward front wall andT4-fwd 0.9 m at each lateral wall), as shown in 10𝐷 Figure2. Echo Sounders were separated byBack 7.5 & cm Forth in the y T4-b&fdirection, and measured at a 40 Hz sampling frequency. Therefore, the 3D render was build up using 40 longitudinal profiles parallel to the long edge of the LaBassa tank. Water 2018, 10, 1571 4 of 14

Table 1. Tests description. Each test contains 3 different values of n (300, 350, 400) and an analysis of the sediment bed evolution every 5 min. Total duration of a single test: 30 min.

ch (m) Xw (m) Maneuver Test n (rpm) Time (min) Water 2018, 10, x FOR PEER REVIEW 4 of 14 Forward T1-fwd 7Dp Back & Forth T1-b&f Sedimentch,min = D pused in the experiments was a 𝐷 = 250 μm uniform fine sand. Sediment was not Forward T2-fwd scaled from the prototype10D p due to the limitations of finer sand in model reproductions. Two @ULTRALAB UWS 1M Echo SoundersBack measured & Forth the surface T2-b&f of the sediment bed layer after each 5 300 350 400 0-5- . . . -30 min-run. The Echo Sounders were hangingForward from a mechanized T3-fwd arm covering an area of 3.5 m × 2.8 m 7D with blanking distances at thep edges of the tank (0.25 m front wall and 0.9 m at each lateral wall), as ∼ Back & Forth T3-b&f shownch,max in Figure= 1.6D p2. Echo Sounders were separated by 7.5 cm in the y direction, and measured at a 40 Forward T4-fwd Hz sampling frequency. 10Therefore,Dp the 3D render was build up using 40 longitudinal profiles parallel to the long edge of the LaBassa tank.Back & Forth T4-b&f

Figure 2. Scaled plain view of LaBassa. Cross zone covers the zone measured with the Echo Sounds. 3. Results 3. Results At each test, a scan of the measuring area yielded results like the example shown in Figure3. At each test, a scan of the measuring area yielded results like the example shown in Figure 3. Upper plots (Figure3a,b) represent the situation where the propellers are closer to the sediment bed Upper plots (Figure 3a,b) represent the situation where the propellers are closer to the sediment bed (ch,min) and to the front quay wall (Xw = 7Dp). On the contrary, Figure3c,d, shows the opposite (𝑐,) and to the front quay wall (𝑋 =7𝐷). On the contrary, Figure 3c,d, shows the opposite conditions, with the propellers further from sediment bed (ch,max) and from the front quay wall conditions, with the propellers further from sediment bed (𝑐,) and from the front quay wall (𝑋 = (Xw = 10Dp). 10𝐷 ). The scans provide visual information of the eroded and deposited areas and their morphological The scans provide visual information of the eroded and deposited areas and their morphological shape. Each subplot of Figure3 indicates the existence of two eroding zones: (i) the scouring hole shape. Each subplot of Figure 3 indicates the existence of two eroding zones: (i) the scouring hole created below the propellers at the harbor basin area, HB; and (ii) the effects of the jet flow at the created below the propellers at the harbor basin area, HB; and (ii) the effects of the jet flow at the vicinity of the front wall (this is at the toe of the docking wall, DW). The former is originated by the vicinity of the front wall (this is at the toe of the docking wall, DW). The former is originated by the direct impact of the jet flow at the sediment bed, whereas the latter is produced by the returning flow direct impact of the jet flow at the sediment bed, whereas the latter is produced by the returning flow with a clear vertical component towards the sediment bed due to the existence of the docking wall. with a clear vertical component towards the sediment bed due to the existence of the docking wall. The differences between the two scouring areas were reported in [17], although they are not mentioned The differences between the two scouring areas were reported in [17], although they are not explicitly. In their communication, when the propellers are closer to the front wall (Xw < 4Dp), mentioned explicitly. In their communication, when the propellers are closer to the front wall (𝑋 < the scouring effects at the harbor basin are limited. However, when the distance increases (Xw > 6Dp), 4𝐷 ), the scouring effects at the harbor basin are limited. However, when the distance increases (𝑋 > both effects of the propeller jet are detected. These two eroded zones are not always disconnected from 6𝐷 ), both effects of the propeller jet are detected. These two eroded zones are not always each other and can sometimes merge, forming a unique eroded area depending on maneuver scenario, disconnected from each other and can sometimes merge, forming a unique eroded area depending time evolution, and n, ch, and Xw variables, as will be further detailed in Section 3.1. on maneuver scenario, time evolution, and n, 𝑐 , and 𝑋 variables, as will be further detailed in Section 3.1.

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FigureFigure 3.3. Sediment Sediment bed bed scanning scanning results results after after 30 30 min min of of propeller propeller run.run. run. Black Black lines lines represent represent zz z == = 0.0. Red Red lineslines indicate indicateindicate the thethe position positionposition of of the the propeller propeller propeller planes. planes. planes. ( (aa ()a) T1-fwd, )T1-fwd, T1-fwd, n n n= = 400 =400 400 rpm, rpm, rpm, ( (bb) () bT1-b&f, T1-b&f,) T1-b&f, n n = =n 400 400= 400 rpm; rpm; rpm; ( (cc)) (T4-fwd,T4-fwd,c) T4-fwd, n n = =n 300 300=300 rpm; rpm; rpm; ( (dd)) (T4-b&f, dT4-b&f,) T4-b&f, n n = = n300 300= 300rpm. rpm. rpm.

AccordingAccording to to the the resultsresults obtainedobtained obtained fromfrom from thethe the experiments,experiments, experiments, maximummaximum maximum erodederoded eroded depth, depth, depth,ε ε maxεmaxmax, ,is is located locatedlocated atat thethe symmetrysymmetrysymmetry planeplane betweenbetweenbetween thethethe propellers,propellers,propellers, regardlessreregardlessgardless ofofof thethethe engine engineengine order ororderder (ahead/forward (ahead/forward(ahead/forward or or astern/backwardastern/backward direction).direction). WhenWhen When aa a twintwin twin propellepropelle propellerrr modelmodel rotates rotates inward inward in inin the the aheadahead directiondirection (forward(forward scenario), scenario),scenario), the thethe left-hand left-handleft-hand propeller propellerpropeller rotates rotatesrotates to to starboardto starboardstarboard and andand the thethe right rightright hand handhand to port, toto port,port, and and theand flux thethe atfluxflux the atat symmetry thethe symmetrysymmetry plane planeplane between betweenbetween propellers propellerspropellers is towards isis towardstowards the bed thethe [ 13 bedbed], increasing [13],[13], increasingincreasing the action thethe action ofaction a single ofof aa propellersinglesingle propellerpropeller due to theduedue sum toto thethe of eachsumsum propellerofof eacheach propellerpropeller flow. On flow.flow. the contrary, OnOn thethe contrary, ifcontrary, the twin ifif propeller thethe twintwin model propellerpropeller is rotating modelmodel outwardsisis rotatingrotating in outwardsoutwards the astern inin direction thethe asternastern (backward directiondirection (backw(backw scenario),ardard thescenario),scenario), right hand thethe rightright propeller hahandnd rotates propellerpropeller to starboard rotatesrotates toto andstarboardstarboard the left and and hand the the to left left port; hand hand thus, to to port; theport; flux thus, thus, at the the flux symmetryflux at at the the symmetry planesymmetry is moving plane plane upwards,isis moving moving andupwards, upwards, the maximum and and the the scouringmaximummaximum action scouring scouring should action action be concentratedshould should be be concentrated concentrated below each below below propeller. each each However, propeller. propeller. Figure However, However,4 plots Figure Figure an example 4 4 plots plots ofanan theexampleexample reality of of whenthe the reality reality the astern when when telegraphthe the astern astern ordertelegraph telegraph (backward) orde orderr (backward) (backward) is used for is is the used used first for for time. the the first first The time. time. result The The extends result result toextendsextends the rest toto ofthethe backward restrest ofof backwardbackward runs, where runs,runs, the wherewhere maximum thethe maximummaximum scouring depthscouringscouring is still depthdepth found isis stillstill at the foundfound centerline. atat thethe Therefore,centerline.centerline. Therefore, whenTherefore, the flowwhen when of the the twin flow flow propellers of of twin twin propellers propellers reaches the reaches reaches sediment the the sediment sediment bed, the bed, separatedbed, the the separated separated flows of flows flows each propellerofof each each propeller propeller have already have have already beenalready mixed been been with mixed mixed maximum with with maximum maximum velocities velocities velocities at the symmetry at at the the symmetry symmetry plane. plane. plane.

Figure 4. Transversal profile of T4-b&f, n = 400 rpm, t = 5min. (a) 3D scan of the sediment bed. Red FigureFigure 4.4. TransversalTransversal profileprofile ofof T4-b&f,T4-b&f, nn == 400400 rpm,rpm, tt == 5min.5min. ((aa)) 3D3D scanscan ofof thethe sedimentsediment bed.bed. RedRed line: transversal profile located at x = 2.5 m; (b) Transversal profile. Dashed line: symmetry plane line:line: transversaltransversal profileprofile locatedlocated atat xx == 2.52.5 m;m; ((bb)) TransversalTransversal profile.profile. DashedDashed line:line: symmetrysymmetry planeplane between propellers. Gray ellipses: distorted sketch of the propellers using real location with respect to betweenbetween propellers.propellers. GrayGray ellipses:ellipses: didistortedstorted sketchsketch ofof thethe propellerspropellers usingusing realreal locationlocation withwith respectrespect the y axis. toto the the y y axis. axis.

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3.1. Forward Tests 3.1. Forward Tests In the case of forward tests, the time evolution of the longitudinal profile located at the centerline In the case of forward tests, the time evolution of the longitudinal longitudinal profile profile located at the centerline between the propellers, plotted in Figure 5, helps to understand the merging of the eroded area at the between the propellers, propellers, plotted plotted in in Figure Figure 5,5 ,helps helps to to understand understand the the merging merging of ofthe the eroded eroded area area at the at harbor basin and the eroded area close to the toe of the wall, outlined previously. For low-speed theharbor harbor basin basin and and the theeroded eroded area area close close to tothe the to toee of of the the wall, wall, outlined outlined previously. previously. For low-speed revolutions (e.g., 300 rpm, Figure 5a), the scouring profile retains a clear distinction between the two revolutions (e.g., (e.g., 300 300 rpm, rpm, Figure Figure 5a),5a), the the scouring scouring profile profile retains retains a clear a clear distinction distinction between between the thetwo scouring areas. When the revolution speed increases, Figure 5b,c, the separation between the zones twoscouring scouring areas. areas. When When the revolution the revolution speed speed increase increases,s, Figure Figure 5b,c, 5theb,c, separation the separation between between the zones the is not maintained over time and disappears after 15–20 min of the experiment. After this stage, the zonesis not ismaintained not maintained over time over and time disappears and disappears after after15–20 15–20 min of min the of experiment. the experiment. After After this thisstage, stage, the erosion at the vicinity of the docking wall dominates the profile. theerosion erosion at the at thevicinity vicinity of the of thedocking docking wall wall dominates dominates the theprofile. profile.

Figure 5. Longitudinal profilesprofiles of T3-fwd located at centerlinecenterline between propellers. Red line indicates thethe position of of the the propellers. propellers. Gray Gray dashed dashed line line separates separates the the dockin dockingg wall wall scouring scouring area area (left (left of the of thedashed dashed line) line) and andharbor harbor basin basin scouring scouring area area (right (right of the of thedashed dashed line). line). (a) 300 (a) 300rpm; rpm; (b) (350b) 350rpm; rpm; (c) (400c) 400 rpm. rpm. Figure5 also identifies the location of a third scouring hole created slightly upstream of the Figure 5 also identifies the location of a third scouring hole created slightly upstream of the propellers due to the suction effects of the propellers. This zone is thought to be a negative pressure propellers due to the suction effects of the propellers. This zone is thought to be a negative pressure area that is strong enough to resuspend the sediment particles deposited immediately downstream of area that is strong enough to resuspend the sediment particles deposited immediately downstream the propellers. of the propellers. HB Results of maximum eroded depth due to the im impactspacts of of the jet at the harbor basin basin area, area, 𝜀εmax,, Results of maximum eroded depth due to the impacts of the jet at the harbor basin area, 𝜀, considering the forward tests are plotted in Figure6. Lines are colored according to the different considering the forward tests are plotted in Figure 6. Lines are colored according to the different scenarios. InIn generalgeneral terms, terms, when when the the propellers propellers are are closer closer to the to sedimentthe sediment bed ( cbedh = (c𝑐hmin =𝑐, black, lines),black scenarios. In general terms, when the propellers are closer to the sediment bed (𝑐 =𝑐, black scouring depth is almost twice as high as the results obtained with the propellers are located further lines), scouring depth is almost twice as high as the results obtained with the propellers are located fromfurther the from bed the (ch =bedchmax (𝑐,=𝑐 gray lines)., gray On lines). the other On the hand, other the hand, distance the todistance the front to wallthe front does wall not seemdoes further from the bed (𝑐 =𝑐, gray lines). On the other hand, the distance to the front wall does tonot play seem an to important play an role,important since therole, differences since the betweendifferencesXw between= 7Dp (continuous 𝑋 =7𝐷 (continuous lines) and X lines)w = 10 andDp not seem to play an important role, since the differences between 𝑋 =7𝐷 (continuous lines) and (dashed𝑋 = 10𝐷 lines) (dashed are not lines) significant. are not significant. 𝑋 = 10𝐷 (dashed lines) are not significant.

Figure 6. Maximum scouring depth of forward scenarios du duee to the impact of the propeller jet at the harbor basin area. Black lines c 𝑐==𝑐c ,,, graygray lines linesc 𝑐==𝑐c ,,, continuous continuous lines linesX 𝑋= = 77D𝐷, dasheddashed harbor basin area. Black lines 𝑐h =𝑐h,,min , gray lines 𝑐h =𝑐h,,max , continuous lines 𝑋w = 7𝐷p, dashed lines X𝑋w = 10 10𝐷Dp. .((aa) )300 300 rpm; rpm; (b (b) )350 350 rpm; rpm; (c (c) )400 400 rpm. rpm. lines 𝑋 = 10𝐷. (a) 300 rpm; (b) 350 rpm; (c) 400 rpm.

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The significant decrease in 𝜀 of T3-fwd-400 rpm, Figure 6c, is caused by the merging of the Watertwo scouring2018, 10, 1571 areas already discussed at the beginning of this section. In fact, the results of maximum7 of 14 scouring depth at the harbor basin, 𝜀, are obtained from the centerlines plotted in Figure 5c, where the centerline behavior changes substantially after a 15 min run (yellow line). This also occurs for T1- HB fwd-400The rpm, significant Figure decrease 6c, after 20 in εmin,max ofbut T3-fwd-400 at smaller magnitudes. rpm, Figure6 c, is caused by the merging of the two scouringThe differences areas already between discussed the revolution at the beginning speeds in of Fi thisgure section. 6 are significant In fact, the at results the early of maximum stages of HB scouringthe tests, depthbut become at the less harbor important basin, ε maxafter, are a 30 obtained min run, from although the centerlines maximum plotted scouring in Figure depth5 isc, always where thehigher centerline for larger behavior values of changes n. A steady substantially state is cons afteridered a 15 minto be run reached (yellow after line). 30 min, This according also occurs to the for T1-fwd-400results presented rpm, Figurein Figure6c, after6, the 20 results min, butobtained at smaller using magnitudes. the formula proposed by [17] and the steady- state Thetime differences established between by [25]. the revolution speeds in Figure6 are significant at the early stages of the tests,In the but vicinity become of lessthe docking important wall, after Figure a 30 min7, th run,e evolution although of maximumthe maximu scouringm scouring depth depth is always at the higher for larger values of n. A steady state is considered to be reached after 30 min, according to docking wall, 𝜀, has a completely different behavior from the evolution of the maximum scouring the results presented in Figure 6, the results obtained using the formula proposed by [ 17] and the depth at the harbor basin, 𝜀. The blanking area close to the wall in the present experiment (see steady-stateFigure 2) can time reduce established the absolute by [ 25values]. of maximum eroded depth at the vertical wall by up to 5 cm. However,In the the vicinity results of presented the docking herein wall, are Figure used 7qual, theitatively evolution to differentiate of the maximum the two scouring scouring depth areas DW atand the obtain docking the wall,ordersεmax of ,magnitude has a completely of the differentdifferences behavior between from the theevolution evolution of the of thescouring maximum hole HB scouringproduced depth by the at direct the harbor impact basin, of theεmax propeller. The blanking jet to the area sediment close to thebed wall at the in theharbor present basin experiment area, and (seethe effects Figure 2of) canthe reducereturning the flux absolute at the values toe of of th maximume docking erodedwall. The depth differentiation at the vertical between wall by the up two to 5eroded cm. However, areas clearly the resultsindicates presented that the hereinbehavior are of used the qualitativelyerosion is different, to differentiate depending the on two the scouring area of areasstudy. and Moreover, obtain the in ordersthe forward of magnitude scenarios, of the the differences final erosion between at the the vertical evolution wall of can the scouringreach higher hole producedvalues (in bythe the case direct of T4-fwd-400 impact of the rpm, propeller three jettime tos the larger) sediment than bedthe atmaximu the harborm erosion basin area,depth and at the effectsharbor ofbasin the returningarea. flux at the toe of the docking wall. The differentiation between the two eroded areasClose clearly to the indicates wall, the that increase the behavior of the erosion of the erosionis clearly is affected different, by dependingthe speed revolution; on the area maximum of study. Moreover,eroded depth in the can forward be two scenarios,or three times the finalbigger erosion when at n theincreases vertical from wall 300 can rpm, reach Figure higher 7a, values to 400 (in rpm, the caseFigure of 7c, T4-fwd-400 although rpm, the erosion three times has appare larger)ntly than not the reached maximum the erosionasymptotic depth state. at the harbor basin area.

Figure 7. Maximum scouring depth of forward scenarios du duee to the impact of the returning ﬂuxflux at the dockingdocking wall.wall. BlackBlack lineslines c𝑐h ==𝑐ch,, min, graygray lineslines c𝑐h ==𝑐ch,,max,, continuouscontinuous lineslinesX 𝑋w == 77D𝐷p, dasheddashed lines X𝑋w = 10 10𝐷Dp. .((aa) )300 300 rpm; rpm; ( (bb)) 350 350 rpm; rpm; ( (cc)) 400 400 rpm. rpm. Negative Negative values values indicate deposition, whereas positive values are erosion.erosion.

CloseThe maximum to the wall, erosion the increase at the oftoe the of erosion the vertical is clearly wall affected depends by on the the speed clearance revolution; distance maximum (black eroded depth can be two or three times bigger when nincreases from 300 rpm, Figure7a, to 400 rpm, and gray lines in Figure 7), with higher values of 𝜀 when the propellers are further from the Figure7c, although the erosion has apparently not reached the asymptotic state. sediment bed, this is 𝑐 =𝑐,. Likewise, the distance between the propeller plane and the vertical wall Thealso maximuminfluences erosionthe final at re thesults toe of of the verticalmaximum wall scouring depends depth on the at clearance the toe of distance the docking (black wall. and gray lines in Figure7), with higher values of εDW when the propellers are further from the sediment In Figure 7, when the propellers are closer maxto the vertical wall (𝑋 =7𝐷 continuous lines), the = bed,maximum this is erodedch ch ,depthmax. Likewise, is always the higher, distance regard betweenless of the the propeller values of planethe other and variables. the vertical wall also inﬂuences the ﬁnal results of the maximum scouring depth at the toe of the docking wall. In Figure7, when3.2. Back the and propellers Forth Tests are closer to the vertical wall (Xw = 7Dp continuous lines), the maximum eroded depth is always higher, regardless of the values of the other variables. The introduction of the back-and-forth scenarios attempts to reproduce the scouring process 3.2.similar Back to and prototype Forth Tests effects in real harbor basins, since it combines docking and undocking

The introduction of the back-and-forth scenarios attempts to reproduce the scouring process similar to prototype effects in real harbor basins, since it combines docking and undocking maneuvers. Water 2018, 10, 1571 8 of 14 Water 2018, 10, x FOR PEER REVIEW 8 of 14 maneuvers.Tests shown Tests in Figure shown8 start in Figure with a 8 horizontal start with sedimenta horizontal bed, sediment representing bed, arepresenting new or a recently a new ﬁxed or a recentlyharbor basin.fixed harbor Then a basin. vessel Then docks a vessel at a particular docks at quaya particular using thequay astern using engine the astern telegraph engine order telegraph at the orderend of at the the maneuver, end of the in themaneuver, backwards in direction,the backwa Figurerds 8direction,a. Then, theFigure undocking 8a. Then, maneuver the undocking can start, maneuverwith the twin can propellersstart, with workingthe twin ahead,propellers in the working forward ahead, direction, in the Figure forward8b. direction, Figure 8b.

FigureFigure 8. 8. 3D3D scans scans of of the the sediment sediment bed bed for for the the T2-b&f T2-b&f scenario, scenario, nn == 350 350 rpm. rpm. (a (a) )t t== 5 5min—backward; min—backward; ((bb)) tt == 10 10 min—forward; min—forward; ( (cc)) tt == 15 15 min—backward; min—backward; (d (d) )t t== 20 20 min—forward. min—forward.

InIn Figure Figure 8,8, a sequence of the back-and-forth scenario shows the evolution of the sediment bed andand the the formation formation of of three three scouring scouring holes: holes: a a first first one one located located slightly slightly upstream upstream of of the the propellers propellers (right (right sideside of of the the red red line) line) and and formed formed mainly mainly during during the the backward backward runs runs (Figure (Figure 8a,c);8a,c); a second one located downstreamdownstream of of the the propellers, propellers, originated originated during during the the forward forward runs runs (Figure (Figure 8b,d)8b,d) and similar to the mainmain hole hole present present in in the the forward forward scenarios; scenarios; and, and, finally, finally, a a third third one one in in the the vicinity vicinity of of the the front front wall, wall, formedformed by by the the impact impact of of the the propeller propeller flux flux at at the the wall wall during during the the forward forward runs runs (Figure (Figure 8b,d).8b,d). The first first twotwo are are originated originated by thethe impactimpact ofof thethe jet jet flow flow at at the the sediment sediment bed, bed, whereas whereas the the latter latter is causedis caused by by the thereturning returning flux flux of the of the original original propeller propeller jet. Whenjet. When the vesselthe vessel finishes finishes the dockingthe docking maneuver maneuver with with both bothpropellers propellers working working backward/astern, backward/astern, Figure Figure8a, the 8a, sediment the sediment erosion erosion is located is located underneath, underneath, slightly slightlyupstream upstream of their of vertical their vertical position. position. Afterwards, Afterwards, when the when undocking the undocking maneuver maneuver starts, with starts, the with twin thepropellers twin propellers rotating rotating forward/ahead, forward/ahead, the action the towardsaction towards the sediment the sediment bed starts bed downstreamstarts downstream of the ofpropellers, the propellers, as seen as in seen Figure in 8Figureb, and the8b, scouringand the sc holeouring created hole during created the during previous the maneuver previous maneuver reduces its reducesdepth slightly its depth (see slightly Figure (see9). During Figure the9). During next step, the simulating next step, asimulating second docking a second maneuver docking consecutive maneuver consecutivewith the two with maneuvers the two previously maneuvers described, previously Figure de8scribed,c, the scouring Figure hole8c, the created scouring downstream hole created of the downstreampropeller decreases of the propeller in depth atdecreases the same in time depth as the at mainthe same scouring time holeas the of main the first scouring docking hole maneuver of the firstincreases docking its maneuver size. Finally, increases Figure its8d size. shows Finally, the scan Figure following 8d shows two the backward scan following maneuvers two backward and two maneuversforward maneuvers, and two forward reproduced maneuvers, intercalatedly reproduced and iteratively.intercalatedly In this and plot, iteratively. the last In five this minutes plot, the of lastthe five forward minutes run haveof the increased forward therun downstreamhave increased hole, the decreased downstream the upstreamhole, decreased hole, and the influencedupstream hole,the area and closeinfluenced to the the wall area enough close toto createthe wall the enough third scouring to create hole the third in the scouring vicinity ofhole the in vertical the vicinity front ofwall. the However,vertical front this wall. influence However, on the this vertical influence front wallon the shows vertical up earlierfront wall if the shows centerline up earlier longitudinal if the centerlineprofiles are longitudinal plotted, see profiles Figure9 are. The plotted, light purple see Figure line in9. FigureThe light9 is purple the first line erosion in Figure profile 9 producedis the first erosionafter a 5profile min run produced in astern after engine a 5 ordermin run mode, in astern and the engine scouring order action mode, is concentratedand the scouring upstream action theis concentratedvertical location upstream of the propellers,the vertical whereaslocation theof th accretione propellers, is located whereas both the upstream accretion and is located downstream. both upstreamHowever, and after downstream. a 5 min run in However, the forward after direction a 5 min (dark run in purple the forward lines in Figuredirection9), the(dark scouring purple action lines inslightly Figure increases 9), the scouring the depth action of the slightly main scouringincreases holethe depth and,at of the the same main time, scouring reduces hole the and, accretion at the same time, reduces the accretion downstream of the propellers, starting a new scouring hole at this particular point, and also starts acting near the vertical wall.

Water 2018, 10, 1571 9 of 14 downstreamWater 2018, 10, x ofFOR the PEER propellers, REVIEW starting a new scouring hole at this particular point, and also starts9 of 14 actingWater 2018 near, 10, the x FOR vertical PEER REVIEW wall. 9 of 14

Figure 9. Time evolution of the centerline longitudinal profile between propellers for the T2 b&f Figurescenario. 9.9. RedTime line evolution indicates of the the position centerline of the longitudinal propellers. profile proﬁle(a) 300 rpm;between (b) 350propellers rpm; (c )for 400 the rpm. T2 b&f scenario. Red line indicates the position of the propellers. (a) 300 rpm; ((b)) 350350 rpm;rpm; ((cc)) 400400 rpm.rpm. The results of maximum scouring depth in the scenarios combining docking and undocking The results of maximum scouring depth in the scenarios combining docking and undocking maneuversThe results (back-and-forth) of maximum at scouringthe harbor depth basin in area, the 𝜀scenarios, are plottedcombining in Figure docking 10. Inand this undocking case, the HB maneuvers (back-and-forth) at the harbor basin area,εmax, are plotted in Figure 10. In this case, mainmaneuvers differences (back-and-forth) arise when theat the rotation harbor speed basin incr area,eases 𝜀 independently, are plotted in of Figure the clearance 10. In this distance case, (anthe the main differences arise when the rotation speed increases independently of the clearance distance unexpectedmain differences behavior arise of when the erosionthe rotation in the speed harbor incr basin,eases independentlybased on forward of the engine clearance order distance scenario (an in (an unexpected behavior of the erosion in the harbor basin, based on forward engine order scenario Figureunexpected 6, where behavior the effects of the of erosion the clearance in the distanceharbor basin, are evident). based on Similarly, forward no engine differences order scenarioamong the in in Figure6, where the effects of the clearance distance are evident). Similarly, no differences among scenariosFigure 6, wherewith different the effects distances of the clearance between distance the prop areellers evident). and the Similarly, vertical no wall differences (Xw) are among found the in the scenarios with different distances between the propellers and the vertical wall (Xw) are found in Figurescenarios 10, withshowing different that thisdistances is not betweena key parameter the prop inellers the depthand the of verticalthe scouring wall (Xw)hole atare the found harbor in Figurebasin. 1010,, showingshowing that that this this is is not not a keya key parameter parameter in thein the depth depth of the of scouringthe scouring hole athole the at harbor the harbor basin. basin.

Figure 10. Maximum scouring depth of back-and-forth scenarios due to the impact of the propeller jet at the harbor basin area. Black lines c = c , gray lines c = c . Continuous lines Xw = 7Dp, jetFigure at the 10. harbor Maximum basin scouringarea. Black depth lines of 𝑐 hback-and-forth=𝑐hmin, gray linesscenarios 𝑐h =𝑐 duehmax to. Continuousthe impact of lines the 𝑋propeller = 7𝐷, dashed lines X𝑋w = 10 10𝐷Dp. .((aa) )300 300 rpm; rpm; (b (b) )350 350 rpm; rpm; (c (c) )400 400 rpm. rpm. jet at the harbor basin area. Black lines 𝑐 =𝑐, gray lines 𝑐 =𝑐. Continuous lines 𝑋 = 7𝐷, Figuredashed lines10 confirms 𝑋 = 10𝐷 that. (a) 300 the rpm; combination (b) 350 rpm; of (c backward) 400 rpm. and forward flux direction, trying to Figure 10 confirms that the combination of backward and forward flux direction, trying to reproduce arrival and departure maneuvers at the real harbor basin, differs substantially from the reproduce arrival and departure maneuvers at the real harbor basin, differs substantially from the experimentsFigure 10 performed confirms so that far inthe literature, combination and previously of backward in this and article forward (Figure flux6), direction, using only trying forward to experiments performed so far in literature, and previously in this article (Figure 6), using only enginereproduce telegraph arrival orders. and departure maneuvers at the real harbor basin, differs substantially from the forward engine telegraph orders. experimentsThe behavior performed of ahead so far and in asternliterature, direction and previously combining in back this and article forth (Figure maneuvering 6), using yields only The behavior of ahead and astern direction combining back and forth maneuvering yields interestingforward engine results telegraph in terms orders. of evolution and maximum scouring depth magnitudes. In Figure 10, interesting results in terms of evolution and maximum scouring depth magnitudes. In Figure 10, whenThe the behavior speed revolution of ahead increases, and astern the direction effects on combining the sediment back bed and are forth more maneuvering significant, yielding yields when the speed revolution increases, the effects on the sediment bed are more significant, yielding deeperinteresting scouring results holes in terms at the harborof evolution basin areaand thatmaximum are more scouring significant depth than magnitudes. in the experiments In Figure using 10, deeper scouring holes at the harbor basin area that are more significant than in the experiments using onlywhen the the forward speed revolution maneuver, increases, Figure6. Apparently,the effects on the the asymptotic sediment bed stage are is notmore reached significant, in any yielding of the only the forward maneuver, Figure 6. Apparently, the asymptotic stage is not reached in any of the back-and-forthdeeper scouring experiments. holes at the harbor basin area that are more significant than in the experiments using back-and-forthonly the forward experiments. maneuver, Figure 6. Apparently, the asymptotic stage is not reachedDW in any of the When looking at the effects of the returning flux at the toe of the vertical wall, εmax, Figure 11 plots When looking at the effects of the returning flux at the toe of the vertical wall, 𝜀, Figure 11 theback-and-forth maximum eroded experiments. depth at the intersection between the sediment bed and the docking wall. In this plotsWhen the maximum looking ateroded the effects depth of at thethe returninintersectiong flux between at the thetoe sedimentof the vertical bed and wall, the 𝜀 docking, Figure wall. 11 Inplots this the case, maximum contrary eroded to what depth succeeded at the intersectionin the forward between scenarios, the sediment the maximum bed and eroded the docking depth at wall. the toeIn this of the case, wall contrary is smaller to what when succeeded compared in to the the forward maximum scenarios, eroded the depth maximum at the harbor eroded basin depth area, at the as seentoe of in the Figure wall is10, smaller except when in the compared cases of final to the erosion maximum in T3 eroded and T4 depth for n at = the400, harbor where basin 𝜀 area,≈𝜀 as. seen in Figure 10, except in the cases of final erosion in T3 and T4 for n = 400, where 𝜀 ≈𝜀.

Water 2018, 10, 1571 10 of 14 case, contrary to what succeeded in the forward scenarios, the maximum eroded depth at the toe of Waterthe wall 2018,is 10, smaller x FOR PEER when REVIEW compared to the maximum eroded depth at the harbor basin area, as seen10 of 14 in DW HB Figure 10, except in the cases of ﬁnal erosion in T3 and T4 for n = 400, where εmax ≈ εmax. However, in However,the same way in the as same in the way forward as in scenario, the forward the erosionscenario in, the the erosion vicinity in of the verticalvicinity wallof the is vertical still growing wall isafter still 30 growing min, meaning after 30 that min, the meaning steady statethat the for steady scouring state depth for scouring is expected depth to be is higher.expected Higher to be rotationhigher. Higherspeed valuesrotation yield speed deeper values eroded yield depth, deeper and eroded the impact depth, of and the the returning impact ﬂux of the on maximumreturning flux eroded on maximumdepth is greater eroded when depth the is greater propellers when are the located propellers further are from located the further sediment from bed. the Atsediment the same bed. time, At thelower same distances time, lower between distances the propeller between plane the propeller and the vertical plane and wall, the continuous vertical wall, lines continuous in Figure 11 lines, cause in Figuredeeper 11, scouring cause deeper holes at scouring the toe. holes at the toe.

Figure 11. Figure 11. MaximumMaximum scouring scouring depth depth of of back-and-forth back-and-forth scenarios scenarios due due to to the the impact impact of of the the returning returning flux at the docking wall. Black lines ch = ch,min, gray lines ch = ch,max, Continuous lines Xw = 7Dp, flux at the docking wall. Black lines 𝑐 =𝑐,, gray lines 𝑐 =𝑐,, Continuous lines 𝑋 = 7𝐷, dashed lines Xw = 10Dp.(a) 300 rpm; (b) 350 rpm; (c) 400 rpm. dashed lines 𝑋 = 10𝐷. (a) 300 rpm; (b) 350 rpm; (c) 400 rpm. Figure 11 confirms the information outlined in Figure9 regarding the influence of the forward Figure 11 confirms the information outlined in Figure 9 regarding the influence of the forward runs on the erosion at the toe of the vertical wall. Thus, εDW in Figure 11 starts increasing only when runs on the erosion at the toe of the vertical wall. Thus, 𝜀max in Figure 11 starts increasing only when the propellers are working ahead/forward for the first time, at t = 10 min, showing that it already the propellers are working ahead/forward for the first time, at t = 10 min, showing that it already influences this area of the sediment bed. Moreover, astern/backward runs (t = 5(2n + 1), n = 0, 1, 2) influences this area of the sediment bed. Moreover, astern/backward runs (𝑡=5(2𝑛 + 1 ,𝑛=0,1,2) do not have any influence on the erosion at the toe of the vertical wall, since εDW does not deviate do not have any influence on the erosion at the toe of the vertical wall, since 𝜀max does not deviate from the value of the previous run. from the value of the previous run. 4. Discussion 4. Discussion The jet flow originated by stern propellers causes severe damage to the toes of the docking structuresThe jet during flow originated approximation by stern and departurepropellers maneuvers. causes severe However, damage the to evolution the toes ofof the the maneuver docking structuresalong the during harbor approximation basin also affects and itsdeparture sediment maneuvers. bed throughout However, the the entire evolution maneuver, of the producingmaneuver alongscouring the holes harbor and basin the motion also affects of eroded its sediment sediment. bed This throughout latter effect hasthe noentire influence maneuver, on the producing stability of scouringharbor structures, holes and but the the motion deposition of eroded of the sediment. scoured materialThis latter at effect other areashas no of influence the harbor on basin the stability reduces ofthe harbor operability structures, of the basinbut the itself. depo Atsition the same of the time, scoured as described material in at the other Introduction areas of section,the harbor the effectsbasin reducesof the stern the propellersoperability during of the harborbasin itself. maneuvers At the cansame affect time, particular as descri bed protectionsin the Introduction designed section, to trap thecontaminated effects of the sediment stern propellers below them. during harbor maneuvers can affect particular bed protections designedThe studyto trap of contaminated the maximum sediment eroded below depth them. produced by the stern propeller jet flow in different scenariosThe study has led of the to the maximum definition eroded of the depth jet itself. produced In particular, by the stern the focus propeller of this jet study flow in has different tried to scenariosreproduce has the led consequences to the definition of this jetof flowthe jet with itself. the In influence particular, of a the vertical focus wall of simulatingthis study has the berthingtried to reproduceinfrastructures the consequences during docking of andthis undockingjet flow with maneuvers. the influence It is important of a vertical to outline wall simulating that the width the berthingand length infrastructures of the LaBassa during tank docking were large and enough undocking to avoid maneuvers. the influence It is important of the lateral to outline walls that and the the widthopposite and vertical length wall,of the as LaBassa concluded tank by were [13]. large Moreover, enough the to experimental avoid the influence facility only of the allowed lateral a walls fixed andconfiguration the opposite with vertical respect wall, to as the concluded vertical wallby [13]. and Moreover, the sediment the experimental bed. However, facility given only the allowed former alimitations fixed configuration of the experimental with respect facility, to the the vertical results presentedwall and throughoutthe sediment the bed. document However, can begiven used the as formerguidelines limitations to estimate of the the experimental effects of regular facility, vessels the results at their presented particular throughout docking location. the document can be used as guidelines to estimate the effects of regular vessels at their particular docking location. According to the sediment bed 3D scans obtained using 24 different configurations of the location and speed revolution of the propellers during both docking and undocking maneuvers close to a vertical wall, the vessel produces two different erosion areas: (i) nearby the propellers, that is, at the harbor basin area; and (ii) at the toe of the vertical wall. Each scouring hole is caused by the jet

Water 2018, 10, 1571 11 of 14

According to the sediment bed 3D scans obtained using 24 different configurations of the location and speed revolution of the propellers during both docking and undocking maneuvers close to a vertical wall, the vessel produces two different erosion areas: (i) nearby the propellers, that is, at the harbor basin area; and (ii) at the toe of the vertical wall. Each scouring hole is caused by the jet flow of the propellers and its interaction with the horizontal (seafloor) and vertical (berthing wall) limits of the basin. The scouring hole at the harbor basin is originated by the impact of the jet flow with the bed sediment, regardless of the engine telegraph order under which the propellers are running (ahead/forward or astern/backward). Ref. [26] defines the expansion angle as the angle between the impact point of the exterior jet flow and the sediment bed. If the clearance distance is of the order of 20 cm, the expansion angle can be from 13◦ to 20◦, which, in the present experiments, should be a distance of between 70 and 112 cm. However, according to the results obtained, the impact distance from the propeller plane to the maximum erosion depth in the harbor basin is around 70 cm in T1-fwd and below 70 cm in T2-fwd. When the propellers are rotating astern, the distance is reduced substantially to down to 30 cm. In the case of ch,max, according to [26], the expansion angle should reduce to 10◦ and, therefore, the jet may impact 230 cm downstream of the propeller plane. In the present experiments, the jet impacted the sediment bed at a distance of around 100 cm. These differences from the results presented by [26] are mainly due to the influence of the vertical wall, particularly when the clearance distance is larger. The results of maximum scouring depth at the harbor basin depend on the successive engine telegraph orders in which the propellers are rotating. When the experiments are performed using only the forward direction, the maximum erosion depth depends mainly on the speed rotation and the clearance distance, with a slight influence on the distance between the stern propeller plane and the vertical wall. Moreover, at large values of speed rotation, the scouring hole at the harbor basin merges with the scouring hole at the toe of the vertical wall when the propellers are in the closer position with respect to this vertical wall. If the scenario combining back-and-forth tests is used, the maximum eroded depth only changes with the rotation speed, see Figure 10, with no influence on the clearance distance and the distance to the vertical wall. This combination of engine telegraph order yields interesting results in terms of the formation of the scouring holes. The experiments were performed starting with astern/backward engine telegraph orders, and the first scouring hole at the harbor basin was formed upstream the propellers, at a shorter distance from them. The depth of this hole, Figure 10, is almost twice as large as the depth of the first five minute run in the ahead/forward engine telegraph order, as shown in Figure6. Actually, the depth of the scouring hole obtained at the end of the experiments is significantly larger when the two telegraph orders (ahead/astern) are combined. When [1] computed the maximum eroded depth using the formulas presented in the literature, they concluded that only two equations, [17,21], yielded feasible results, although they were twice the real value. The formulas were presented after experimental work using either a single propeller in forward continuous mode or a simple jet impacting a sediment bed, respectively. The final results of maximum scouring depth when back-and-forth combinations are used are not twice the final scouring depth using only ahead/forward engine telegraph order, if we compare Figures6 and 10, although they are still higher. Therefore, the previous equations should still be used, bearing in mind that they clearly overestimate the maximum eroded depth. The scouring hole at the toe of the vertical wall is caused by the returning flux of the propellers. The vertical component of the flux at the wall erodes the area at the intersection between the vertical wall and the sediment bed. In some particular cases of the only forward scenarios, Figure7, for low speed revolution, the initial stages of the sediment bed evolution cloase to the toe of the wall present a small sedimentation. This is an apparent sedimentation produced by the lack of data at areas close to the vertical wall due to the blank measuring area, 25 cm, as seen in Figure2. Thus, small erosion at the toe of the wall shall be expected. Water 2018, 10, 1571 12 of 14

The results indicate that the influence of the revolution speed is the most important in the erosion phenomenon close to the toe of the wall, rather than other variables, regardless of the direction of propeller rotation in which the experiments were performed. In general terms, maximum values of εmax are obtained for minimum values of Xw, as expected, since the jet is more energetic when it impacts the wall, and thus the returning flux has a higher velocity. Surprisingly, this is not the case for minimum values of the clearance distance ch; according to Figures7 and 11, the scouring holes at the toe of the vertical wall are deeper when the propellers are further from the sediment bed (gray lines). This can be explained by the variation in the impact angle; the impact angle decreases for larger values of ch, and the distance at which the jet impacts the sediment bed increases, being closer to the vertical wall. Therefore, the loss of momentum due to the impact of the sediment bed is produced at areas closer to the vertical wall, and the flux velocities reaching the wall are higher. The results obtained from the equation proposed by [17] for the maximum scouring depth in the presence of a vertical wall estimate a maximum erosion for ch,min of between 15 and 25 cm, which is congruent with the results obtained for maximum scouring depth in the harbor basin (see Figure6), but underestimates the erosion at the toe of the vertical wall (see Figure7). Moreover, maximum scouring depth in the vicinity of the docking wall did not reach the steady state during the presented experiments, meaning that the maximum erosion depth should be expected to be larger than the present results. In the case of ch,max, the equation proposed by [17] yields results for maximum erosion depth of 25 to 35 cm, higher than εmax for ch,min, which are only valid for the results obtained at the docking wall, although they overestimate the minimum values (see Figure7). In the scenario combining back-and-forth tests, the erosion at the toe of the wall starts only when the ahead/forward engine telegraph order is run, which is at 10 min. The astern/backward engine telegraph order, and therefore the docking maneuver, does not have any impact on the erosion close to the vertical wall, Figure 11. However, the erosion in this area is not exactly equal to the accretion of the harbor basin scoured hole in Figure 10. In fact, the erosion produced by the ahead/forward engine telegraph orders is larger than the sedimentation occurred at the scouring hole of the harbor basin, indicating that other accretion areas are produced when the propellers rotate inwards.

5. Conclusions The analysis of experimental work performed to estimate the scouring effects produced by stern propellers during docking and undocking maneuvers has pointed out the need to include the effects of twin propeller configurations and propeller rotation direction. The present contribution introduced the use of twin propeller experimental results and the description of the consequences and erosion evolution of the sediment bed when incorporating back-and-forth scenarios. During docking and undocking maneuvers, the effects of stern propellers can be divided into two different actions: (i) the impact of the propeller flow on the sediment bed, producing important scouring holes at the harbor basin area; and (ii) the impact of the propeller flow on the docking wall, and its subsequent returning flux, eroding the toe of the vertical wall. The use of a continuous ahead/forward scenario in the experiments presented in the literature underestimates the maximum erosion depth at the harbor basin, and overestimates the effects at the toe of the wall. This is due to the importance that the forward scenario has with regard to erosion rates, since the backward scenario creates deeper scouring holes than the forward rotating direction using the same revolution speed. However, the present experiments did not reach the asymptotic state, and the erosion at the toe of the vertical wall in the back-and-forth scenarios should continue increasing, reaching the maximum values of the continuous forward scenarios. The variables used in the present experiments also play an important role when comparing the continuous-forward scenarios and the back-and-forth scenarios. Apparently, neither the clearance distance nor the distance to the vertical wall seem to influence the maximum eroded depth at the harbor basin for back-and-forth scenarios, although they are important in the erosion at the toe of the docking wall. As expected, when the propellers are closer to the vertical wall, the effects on the Water 2018, 10, 1571 13 of 14 maximum eroded depth are more significant. On the contrary, further distances to the sediment bed produce deeper scouring holes at the toe. This indicates that and increase in draft particulars may not increase the final erosion depth, but further research is needed along these lines. The results presented in this contribution highlight the need to further investigate the consequences of stern propellers on seafloors. The increase in the problems produced by docking vessels in several harbors requires the existence of a tool available to harbor authorities to predict scouring processes and prevent them. More experimental and field data is needed in order to better predict both the potential erosion and sedimentation at the harbor basin.

Author Contributions: A.M.-C. and X.G. conceived and designed the experiments; A.M.-C. and T.L. performed the experiments and analyzed the data; M.l.C., X.G. and X.M.d.O. contributed on the analysis tools; A.M.-C. and M.l.C. wrote the paper. Funding: This work has been supported by MINECO (Ministerio de Economía y Competitividad) and FEDER (Unión Europea—Fondo Europeo de Desarrollo Regional “Una Manera de hacer Europa”) from the Spanish Government through project TRA2015-70473-R. Acknowledgments: We greatly acknowledge the technical staff of the UPC CIEMLAB for their support throughout the experiments: Joaquim Sospedra, Jordi Cateura and Òscar Galego. Conﬂicts of Interest: The authors declare no conﬂict of interest.

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