Rory van Doorn et al. 1

Bow Thruster Currents at Open Quay Constructions on Piles

Rory van Doorn Dockwise, Breda, Netherlands Teus Blokland Rotterdam, Engineering Department, Netherlands Tiedo Vellinga Port of Rotterdam and Delft University of Technology, Netherlands Henk Verheij Deltares and Delft University of Technology, Netherlands Henk Jan Verhagen Delft University of Technology, Delft, Netherlands

Summary The hydraulic loads on the slope at open quay constructions on piles is investigated. The propeller (bow thruster) jet induces hydraulic loads on the slope, which could result in scour holes and damage to the quay construction. Performed scale model tests provide details about the hydraulic loads in this specific situation with an inclining slope and piles. Measurements are compared to calculations with the equation for an unconfined propeller jet, to include in the design of open quay constructions on piles.

Introduction In many ports berths consist of a slope covered with a deck on piles. Usually the slope is protected with some armourstone. Because of an increase in the use of powerful bow thrusters, the load on the slope protection increases, which may require heavier armour. However, replacing the armour below a deck is complicated and consequently very costly.

Bow thrusters at open quay constructions on piles have not been investigated yet, and available engineering guidelines are based on free propeller jets without piles on a slope (SCHOKKING [2002], RÖMISCH [2006]). In this research scale model tests were performed to provide details about the hydraulic loads in such situations and as result, recommendations are provided for engineering purposes. This research focuses on the hydraulic loads due to bow thrusters.

Figure 1. Schematic view of open quay construction

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Hydraulic load Concluding from the literature review, commonly the ‘Dutch’ and ‘German’ engineering guidelines are used to predict hydraulic loads from propeller jets. PIANC [1997] contains engineering guidelines for propeller jets and soon a new guideline on this subject is being published, PIANC [2013].

‘Dutch’ method BLAAUW AND VAN DE KAA [1978] and VERHEIJ [1983] derived the following equations, for the determination of the flow field behind a propeller.

1 3

0 2

0

1.15w

PU

D

(1)

2

0, 0 0

U 2.8 exp 15.4 for 2.8x r

D rn U x D

x x

(2)

Equation (2) is valid for situations in which the jet propagation is not restricted by any confinement like a bottom, a slope or a water surface. If there is a confining surface, the actual velocities near this surface can deviate from the equation for a unconfined jet. In the situation of a propeller jet perpendicular to a slope, equation (2) results in the following x-coordinate of the location of the maximum current velocity on the slope:

max 2

2 15.41 1

cotUx K L with K

K (3)

For this equation x=0 at the outflow opening of the propeller or thruster and x=L at the slope. In the present study measured flow velocities on a slope (with or without piles) will be compared with the flow velocities resulting from the equations (1) and (2) for a unconfined jet. The measured locations of the maximum current will be compared with the result of equation (3).

Protection Hydraulic loads by propeller jets and the resulting bed protection are commonly approached using an Izbash type equation, taking into account mean flow velocities combined with a factor to count for turbulence intensities. Equation (4) is commonly applied in case of propeller jets to determine required stone diameters according VERHEIJ [1985].

2

,max

50 ,2

b

Iz cr h

UD m

g

(4)

In (4) maximum mean flow velocities are included and the critical stability coefficient accounts for a

certain turbulence intensity. In the ‘Dutch method’ Iz,cr = 2.6 to 3.0 for propeller jets (CIRIA, CUR AND

CETMEF [2007]). The required D50 for the present model tests are calculated using Iz,cr = 3.0.

Influence of turbulence As the turbulence intensity plays an important role in propeller jets, measuring of the turbulence intensities was included in the set-up for the scale model tests.

By using the turbulence intensity as an input in the Izbash equation, the adopted β = 3.0 is no longer

necessary. This β coefficient is used as a safety factor to include the unknown turbulence intensity.

From the scale model tests the turbulence intensity is known as well. With this as an input, follows:

22

50'

2Iz

hg D m u p u

(5)

Commonly (SCHIERECK [2004], ROUBOS [2006]) a factor p = 3 is applied. Consequently a 0.13 % probability of exceeding follows by the Normal distribution. For situations with ‘normal’ turbulence it is

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supposed that the relative turbulence intensity r is about 0.1, while = 0.7. This results in Iz,0,p = 0.41. This value is used to calculate the required D50 using u & u’.

22

2

,0,

2

,0,

2

,0,

'

with

1

0.7 1 3 0.1 0.41 0.41

Iz p

Iz p

Iz p

u p u u

p r

Laboratory tests Starting point for the tests was a 7,000 TEU container vessel, with a 2.75 metre bow thruster diameter. This vessel and an open quay construction on piles (diameter 0.75 m, centre to centre distance 5 m) were scaled using a length factor 25. In the Delft University’s Laboratory of Fluid Mechanics, a basin of 10 by 2 metres was used to test different scenarios. Ten scenarios were tested using scale model tests (see Table 1). Each scenario was different by changing one of the following parameters: slope angle, rough or smooth slope, bow thruster distance to the slope, with or without piles and in case of piles a displacement parallel to the slope. Most of the tests were carried out with a slope 1:1.5 due to space limitations.

Furthermore, mean velocities and fluctuations were measured in each scenario using an Acoustic Doppler Velocimeter (ADV) in order to determine the hydraulic loads on the (non erodible) bed. Thruster outflow velocity measurements were done, whereas the main part consisted of velocity measurements near the bed. Using an ADV with a sample frequency of 25 Hz, turbulent velocity fluctuations were measured, which are part of the hydraulic bed loads.

Findings

Difference between measurements and calculations Table 1 contains for all scenarios the factor difference between the results from the measurements and the results according to the Dutch formulas for an unconfined propeller jet and for stone stability (the engineering guidelines according to the ‘Dutch method’). For example, a factor 1.15 means that a certain parameter is 1.15 times larger in the measurements, compared to the results of the equations.

Table 1: Measurements compared to calculations

Factor difference measurement/calculation

Scenario Slope Water depth

L/D0 Cover Pile alignment

Mean velocity

D50 using u

D50 using u & u’

S1 1:2.5 0.42 m 6.2 smooth no piles 1.11 1.23 1.17

S2 1:1.5 0.42 m 6.2 smooth no piles 1.07 1.14 2.02

S3 1:1.5 0.63 m 6.2 smooth no piles 1.19 1.43 1.39

S4 1:1.5 0.63 m 6.2 rough no piles 1.26 1.58 1.47

S5 1:1.5 0.63 m 4.0 rough no piles 1.16 1.36 1.07

S6 1:1.5 0.63 m 6.2 smooth axis at piles 1.41 1.98 1.83

S7 1:1.5 0.63 m 6.2 smooth axis mid between piles

1.36 1.86 0.89

S8 1:1.5 0.63 m 6.2 rough axis mid between piles

1.63 2.69 1.94

S9 1:1.5 0.63 m 6.2 rough axis quart between piles

1.72 2.95 1.72

S10 1:1.5 0.63 m 6.2 rough axis at piles 1.58 2.49 2.02

Note: In the model tests D0 = 0.11 m.

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Remarks: it cannot be excluded that maximum bed loads in S1 and S2 are not measured due to un-usable measurements close to the propeller and a limited number of measurements for these scenarios. And in scenarios with a rough slope the X-coordinate of axis intersection with slope is 0,096 m different to scenarios with a smooth slope. For all scenarios the height of the propeller jet axis above the horizontal bottom was the same, namely 0.244 m

Effects due to variations in parameters The effect of each variation in parameter is provided in Table 2. Here the factor difference between two scenarios is calculated for the mean velocities and two methods regarding the stone diameter. The factor difference for ‘D50 using u’ is equal to the squared ‘mean velocity’ factor, because the mean velocity is used as an input for this D50.

Table 2: Effects due to parameter variations

Varied Parameter Value Scenario Mean velocity

D50 using u

D50 using u & u’

Slope angle 1:1.5 / 1:2.5 S2 / S1 0.97 0.93 1.73

Water depth 0.63 / 0.42 S3 / S2 1.12 1.25 0.68

Slope angle & water depth S3 / S1 1.08 1.16 1.18

x/D0 4.0 / 6.2 S5 / S4 0.93 0.86 0.73

Roughness, without piles rough / smooth S4 / S3 1.05 1.11 1.06

Roughness, piles frontal rough / smooth S10 / S6 1.12 1.25 1.11

Roughness, piles mid rough / smooth S8 / S7 1.20 1.44 2.19

Piles, smooth

piles front / without piles

S6 / S3 1.18 1.39 1.32

piles mid / without piles

S7 / S3 1.14 1.30 0.64

Piles, rough

piles front / without piles

S10 / S4 1.25 1.57 1.38

piles mid / without piles

S8 / S4 1.30 1.69 1.32

piles quart / without piles

S9 / S4 1.36 1.86 1.17

The most relevant parameters are discussed below.

Variation in slope angle The factor difference S2/S1 for the mean velocity is 0,97, which is almost equal to 1. This makes it reasonable that the model tests with further parameter variations using a relatively steep slope of 1:1.5 are also valid for less steep slopes. It however should be remembered that scenarios S1 and S2 have only a limited number of valid measurements points, which makes the measured factor difference not very accurate.

Changed water depth According to equation (3) and (5), S3 requires a stone diameter equal to S2. The water level is raised from 0.42 to 0.63 metre and measurements show an increase in the maximum load. This can partly be a spurious effect because of limited measuring points. A physical reason for this could be the increased branch off by the jet towards the slope. This phenomenon is described in WL [1988]. Consequently the jet ‘hits’ the inclining slope at a smaller distance from the outflow opening, which explains the increased slope load.

In addition, because of less measurement results in S2, variation in slope angle and water depth are compared together. This shows in table 2 a difference factor of 1.08 for mean flow velocities, which is a relatively small difference, showing the relevance of the performed scale model tests.

Distance to slope With the outflow opening at a smaller distance to the slope, measurements show results fitting better to the calculations. This holds for mean flow velocities as well as turbulence intensities.

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In addition to the change in water depth, the shorter distance of the outflow opening to the slope could result in less branching off by the jet, because of less distance to encounter branching off.

If branching off by the jet is underestimated using equation (3), this would explain the factor 0.93 for the mean flow velocity. Due to the fact that the jet is branching off less, the distance between propeller and the location where the jet hits the slope is larger, where a larger distance results in a larger decrease in mean flow velocities.

Roughness For scale model tests with a rough bed, all results show a larger factor difference compared to tests with smooth slopes. Without piles the factor difference is 1.05 for mean flow velocities, whereas with piles frontal placed, this increases to 1.12. Largest difference (1.20) is observed for situations with the jet axis pointed mid between two rows of piles.

These results clearly show that a rough-bed has a significant influence on results from the scale model tests. No variations in stone diameters (variations in roughness) have been tested.

Piles In case of a situation with piles compared to a situation without piles, all difference factors are larger than one, which means that these measurements provide larger hydraulic loads compared to situations without piles. One value is clearly different; 0.64 for S7 compared to S3. Turbulence intensities in S7 show less peaks compared to all other scenarios, causing this low value. An explanation for this deviating result is not found.

Equation (3) for a unconfined jet results in relatively large underestimation factor for situations with piles, especially for a rough surface.

Pile location Within the scenarios for situations with piles the vessel and thereby the bow thruster is shifted in the longitudinal direction, parallel to the slope. Hereby the outflow opening was tested frontal to a row of piles, as well as mid between two rows of piles. The determining situation for maximum bed load follows from the measurements. Maximum bed load, including turbulence intensity, occurs when the bow thruster axis is in line with a row of piles.

Mean velocities for rough bed scenarios, however, are smaller with piles in front, compared to piles at mid- and quart-position. In contradiction, smooth bed scenarios show larger mean velocities with piles in front, compared to piles at mid-position. Further research is recommended to explain this contradiction.

Hydraulic load without piles VAN DOORN [2012] focuses on the hydraulic load for a situation with piles. From the scale model tests follows that the current design method however, underestimates the mean flow velocities for an inclining slope (without piles). Hereby some further details for an inclining slope without piles are determined, which is the basis for an inclining slope with piles.

The location of maximum flow velocities is different compared to equation (4), which is not unexpected because equation (4) is derived from equation (3) which describes the flow distribution for a unconfined propeller jet.

The maximum bed load follows when diffusion of the bow thruster jet is assumed under an angle of 1:2.4 to 1:18.6. This location is for all ten scale model scenarios located at the inclining slope. With the bow thruster at a larger distance from the inclining slope, also the toe of the bed protection could be the location of maximum bed loads.

Maximum mean flow velocities are underestimated in all scenarios, using equation (3). In all situations without piles, mean flow velocities are underestimated with a factor 1.07 to 1.26. Translated into the hydraulic bed load, with the velocity to the power two, this is a factor 1.14 to 1.58. Analysis of measurements taking into account the turbulence intensities, results in a hydraulic bed load that is

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underestimated by a factor 1.07 to 2.02 for situations without piles, which reduces to 1.07 to 1.47 for rough situations.

Hydraulic load with piles An important aspect is the mean flow velocity near the slope. In combination with the turbulence intensities this is determining, in the current design methods, for bed protections. Compared to situations without piles, piles result in larger mean flow velocities and larger hydraulic slope loads. Mean flow velocities for situations with piles are underestimated by a factor 1.36 to 1.72, using equation (3). Translated into the hydraulic bed load, this is a factor 1.86 to 2.95 for the required D50.

Including turbulence intensities from the measurements and p = 3, this results in a factor 0.89 to 2.02. Taking only rough scenarios into account provides a factor 1.72 to 2.02, from Table 1.

As a rough approximation for the mean flow velocities around piles the following can be used:

1 2

PG DU U

G

(9)

Piles in the scale model have a diameter of 0.03 m and a centre-to-centre distance of 0.20 m. For a situation with piles, the available ‘flow area’ thereby reduces to 85 % of the original area. If this approach would be valid, the flow velocity for the situation with piles would be 118 % of the original flow velocity without piles. This approach seems to be a good approximation, with Table 2 containing difference factors of 1.14 to 1.36 in case of comparing situations with piles to situations without piles.

Potentially oscillating vectors The results are discussed with time-averaged vectors. In reality, the flow direction at one single location is not constant. In the design method for a rock protection, the influence the flow direction with respect to slope direction of the slope angle and angle of internal friction for stones are included.

According to CIRIA ET AL. [2007], the influence of the slope angle is calculated by:

2 2 2 2

tan

cos sin cos tan sin sin

s

h

u s u

m

(11)

This angle of the velocity component can be calculated from the measurements. Because of a certain turbulence intensity one would expect an oscillating angle of the flow direction. This can be visualized by plotting the samples of one measurement time series in a rose.

Figure 3. Oscillating flow direction for scenario 10 at (x,y) = (1250,2195)

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Figure 3 shows an example plot based on 3340 samples (for one single measurement location), acquired at a frequency of 25 Hz by the ADV. The angle of the momentary velocity vector varies between about -10 and +40 degrees. The average angle is 15 degrees, which is the angle for the average velocity vector. It is not investigated how the magnitude of the velocity vector varies with the direction of the vector. Probably the maximum current velocity does not occur at the most deviating directions of -10 and +40 degrees. A certain variation of the velocity vector should be taken into account when calculating the stability coefficient mh in equation (5), for example a variation between 0 and +30 degrees. The average angle of 15 degrees would result in a slope coefficient of 0.688 instead of 0.670 for flow straight up the slope. However, for an angle of 30 degrees this would result in a slope coefficient of 0.747. Due to the linear relation with the stone diameter, the required stone diameter for an angle of 30 degrees is 11% larger than for 0 degrees.

The flow direction can be considered as an average angle with a certain standard deviation, which fits well to a Normal distribution. Because of the available time for research in Van Doorn [2012], no extensive analysis of oscillating vectors had been executed. It is recommended to do further research in this subject, because of significant consequences for bed protection. A remark should be made, that in the performed scale model tests no measurements were undertaken at locations very close to piles (< 0.5 times the pile diameter). Very close to the piles the flow direction can deviate more.

Discussion The ‘Dutch’ equations for a unconfined propeller jet are compared to the measurements.

Propeller-jet characteristics First, the outflow velocity is slightly overestimated using the current design method. Calculation of momentum flux shows a 1.52 m/s outflow velocity in scale model tests, whereas 1.60 m/s was calculated with equation (1) based on an estimated thrust coefficient. This difference could be due to measuring errors or an overestimation of the propeller thrust coefficient. It seems that the thrust coefficient was overestimated, because the applied propeller rotational speed was 1021 rpm while the propeller was designed to operate at 3000 rpm.

Measured relative turbulence intensities near the bed are up to 0.55 at locations of maximum mean flow velocity. BLAAUW AND VAN DE KAA [1978] provided relative turbulence intensities up to 0.3 in the jet axis and up to 0.6 at larger radial distances. It should be mentioned that current engineering guidelines mainly use 0.3 (SCHIERECK [2004]) as value for the relative turbulence intensity, while measurements show relative turbulence intensities up to 0.55 at critical locations.

Propeller jet diffusion According to VERHEIJ [1985], Oebius and Schuster did report in 1975 on diffusion of the jet under an angle of 18.8 and 20.8 degrees, which is 1:2.94 and 1:2.63 for respectively undisturbed extension of the jet or a restriction by water level and bed. According to VAN DOORN [2012] angles up to 1:2.4 follow from the model tests with piles, which introduce extra flow obstruction.

Design methods for open quay constructions on piles need to be updated with this larger diffusion angle, which effects the location of maximum load. Sideways diffusion is considered less important and therefore not discussed. However, analysis of a sideways diffusion could be performed using the available data from VAN DOORN [2012].

Velocity distribution The measured velocity distribution at the inclining slope deviates from equation (3) for an unconfined jet. However, besides the value and the location of maximum bed load, the velocity distribution according to BLAAUW AND VAN DE KAA [1978] is in good agreement with the measurements. Sideways diffusion by the propeller jet shows a good match with equation (3), also for situations with piles.

Hydraulic bed load As analysed, the hydraulic load for a situation with piles was found up to 2.02 times larger compared to a situation without piles. However, this is only valid for this specific combination of scale model dimensions. Possibly smaller or larger hydraulic loads may occur with different pile diameters or centre-to-centre distances. Remark: no measurements of hydraulic loads were performed close to the

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piles, within 0.5 pile-diameter distance from piles. Larger maximum hydraulic loads may occur in this region.

Concluding, hydraulic loads at inclining slopes with and without piles are underestimated using equation (3) for an unconfined jet. In addition, hydraulic loads as presented in VAN DOORN [2012] should be further investigated using a non-fixed bed protection. Recently research is done by HOAN

[2008], which clearly describes potential damage to a bed protection and presents a method to determine bed transport.

Besides hydraulic loads at rock protection using armour stone, further research is recommended with other types of bed protection such as concrete mattresses. In order to provide sufficient bed protection, accurate and correct flow velocities should be applied meaning according to this research higher flow velocities than up to now. Future research with erodible bed protection is needed to investigate damage levels and required bed protection.

Conclusions From the investigations the following can be concluded:

In all situations the measured maximum time averaged current velocity on the slope is under-estimated by equation (3) for an unconfined propeller jet. The underestimation factor is about: 1.1 to 1.2 for a smooth slope without piles, 1.25 for a rough slope without piles, 1.4 for a smooth slope with piles, 1.6 to 1.7 for a rough slope with piles.

It is reasonable that the difference factors measured on a relatively steep slope of 1:1.5 are also valid for a less steep slope, while the two test with different steepness show comparable difference factors. However more research on the influence of the slope steepness is recommended.

Using the Dutch equations for an unconfined propeller jet, the location of maximum bed load is calculated higher on an inclining slope compared to the measurements. Depending on the slope angle, roughness and piles, the location of the maximum load from a bow thruster is at an angle between 1:18.6 and 1:2.4 from the propeller jet axis; the location of the maximum bed load furthermore seems to depend strongly on obstacles such as piles on a slope. Piles in front of the propeller jet result in a larger angle;

The direction of the time averaged velocity vector on the slope can deviate 15 degrees from the direction of the propeller jet (which is perpendicular against the slope), while the momentary velocity shows larger deviations due to turbulent fluctuations. This deviation of the velocity vector from the jet direction has negative effects for armour stone stability and should be taken into account when calculating the slope coefficient in the equation of Izbash.

Measured hydraulic bed loads, including turbulence intensities with p = 3, for a rough bed without piles are underestimated by a factor 1.07 to 1.47, and with piles by a factor 1.72 to 2.02, using current engineering method. This means that the hydraulic load is a factor up to 1.38 times larger in a situation with piles compared to situations without piles.

References BLAAUW, H.B. AND VAN DE KAA, E.J. [1978] Erosion of bottom and sloping banks caused by the

screwrace of maneuvering ships, publication 202, WL | Delft Hydraulics, Delft, The Netherlands CIRIA, CUR AND CETMEF [2007] The rock manual. C683 the use of rock in hydraulic engineering.

CIRIA, London. HOAN, N.T. [2008] Stone stability under non-uniform flow, Delft University of Technology, Delft, The

Netherlands PIANC [1997] Guidelines for the design of armoured slopes under open piled quay walls. PIANC,

Brussels, Belgium. PIANC [2013] Guidelines for berthing structures related to thrusters. PIANC, Brussels, Belgium RÖMISCH, K. [2006] Erosion potential of bow thrusters on canal banks (in German). Binnenschifffahrt –

ZfB 11. SCHIERECK, G.J. [2004] Introduction to bed, bank and shore protection, engineering the interface soil

and water. Delft University Press, Delft, The Netherlands SCHOKKING, L.A. [2002] Bowthruster-induced damage, Delft University, MSc Thesis, Delft, The

Netherlands

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VAN DOORN [2012] Bow thruster currents at open quay constructions on piles, Delft University of Technology, MSc Thesis, Delft, The Netherlands

VERHEIJ, H.J. [1983] The stability of bottom and banks subjected to the velocities in the propeller jet behind ships. Proceedings 8th Int. Harbour Congress, Antwerp, Belgium, pp. 1-11.

VERHEIJ, H.J. [1985] Erosion of bank protections along inland waterways – propellers jets and stability of bed material (in Dutch). WL | Delft Hydraulics, report M1115-VII & Xa, Delft, The Netherlands.

WL [1988] Erosion of bank protections along inland waterways – Technical recommendations for bank protections (in Dutch). WL | Delft Hydraulics, report M1115-VIII, Delft, The Netherlands

List of symbols D pile diameter [m]

0D diameter of the jet just behind the propeller, located at the point of

maximal contraction

02 0.71 pD D D at thrusters without tunnel

00.85 pD D propeller-jet combinations in a tunnel

01.00 pD D at ducted thrusters

[m]

50D diameter of stone that exceeds the 50% value of sieve curve [m]

pD propeller diameter [m]

G spacing between piles [m] g acceleration due to gravity [m/s

2]

TK propeller thrust coefficient [-]

L distance between the thruster outflow opening and the slope, measured horizontally along the jet axis.

[m]

hm

slope coefficient to account for stone stability on an inclining slope [-]

n coefficient for the number of propellers:

2 for two propellers

[-]

pn rotational speed of the propeller [s-1

]

P engine power [W]

p exceeding factor for Normal distribution ( P = 3 is equal to 99.865 %) [-]

r radial distance to the propeller axis [m]

0U flow directly behind a propeller, located at the point of maximal

contraction of the jet [m/s]

1U disturbed mean flow velocity [m/s]

2U undisturbed mean flow velocity [m/s]

,x axisU flow velocity along jet axis [m/s]

,x rU flow velocity distribution [m/s]

x distance in the axial direction [m]

u angle of the velocity vector with respect to the upward slope direction (0 = upwards the slope)

[⁰]

slope angle [⁰]

P pile groups coefficient, 1.0 for alignment used in this research [-]

,Is cr critical stability coefficient (commonly 2.5 – 3.0) [-]

relative density of rock [-]

s angle of repose (for armour stone 40⁰ - 42⁰) [⁰]

w density of water [kg/m3]