Experimental study of propeller and ducted propeller’s wake inducted scour

This study investigates the scour profile, scour hole depth, deposition mound height, and the positions produced by the propeller and the ducted propeller that vary over time. The terrains produced by the Ka4-70 propeller and the Ka4-70 propeller + No. 19A duct are obtained using a linear laser three-dimensional terrain scanning system. Compared with the Acoustic Doppler velocimetry (ADV) and other approaches, the system presented here could efficiently and precisely capture the terrain. The principle and system layout are elaborated in this work. Notably, the system can perform underwater scanning. Moreover, compared with the ADV, our system is more efficient and has a smaller data interval. The scour profile, max scour depth and height, and their positions over time are analyzed. The development of the ducted propeller scour is faster than that of the propeller. The ducted propeller scour has a longer, narrower, and shallower influence range compared to the propeller scour. The scour hole range is bigger than that of the scour deposition mound. The general trends of the propeller and ducted propeller development are similar. In each development, the terrain is also morphologically similar at different phases. In addition, the relationship between the max deposition mound position and the max scour hole depth is analyzed, and a scour classic formula is used to fit the scour data on a time scale.


Introduction
With the development of large-scale and high-power ships, increasing attention has been paid to the impact of propeller jets on the marine industry.The most common implications of a propeller jet are local scour and bed sediment resuspension.Albertson et al. (1948) obtained the distribution law of the propeller jet velocity by making a submerged jet and presenting the equation for the initial velocity of the propeller jet under certain conditions using the Gaussian normal probability density function.Blaauw et al. (1978) measured the propeller wake velocity using a flowmeter and corrected Albertson's empirical formula.Chiew and Lim (1996) performed experiments to analyze the bed scour by the jet.They used the wall jet to simulate the propeller jet and explore the effect of jets on the scour holes at different positions.They found that the depth becomes smaller as the distance from the jet hole grows further because the jet's energy dissipates in the surrounding fluid, leading the jet to fail in scouring the bed.Hong et al. (2013) divided the scour process of a propeller into four phases as follows: initial, developmental, stable, and progressive.He also divided the scour terrain into three parts, namely, a small local scour underneath the propeller, a main scour hole downstream of the propeller, and a deposition mound placed at the border of the scour, and pointed out that the maximum depth is related to time, density Froude number, propeller radius, and distance from the bed.Hong et al. (2013) used the acoustic Doppler velocimetry (ADV) profiler to capture the velocity field downstream of the propeller and analyzed the mean and the turbulent flow field.
Considering with and without the lateral limit, Hamill et al. (1999) found that the propeller scour hole terrain is symmetrical along the axis and that the upright wall effect caused the propeller scour terrain depth to be deeper than that in other conditions.By contrast, by using a three-dimensional (3D) terrain laser scanner, Penna et al. (2019) found that the terrain was not symmetrical along the axis because the propeller jet may be rotating in a way that makes the scour hole of one side deeper than that of the other side and makes the deposition mound of the other side higher than that of one side.Wei and Chiew (2017) also found this phenomenon in their propeller scour experiments and divided the distance of the propeller from the slope into three zones, namely, far, medium, and near.Ferraro et al. (2021) experimented with the scour terrain variation over time in the presence of a uniform inflow environment using (ADV) and 3D terrain laser scanners to obtain the terrain data produced by the propeller.They found that when the inflow direction was the same as that of the propeller jet, the propeller scour hole became longer and more symmetrical along the axis.When the propeller was far away from the bed, the length:width ratio increased in the stable phase.They also used the propeller scour terrain to perform particle image velocimetry experiments and numerical simulations.Evidently, a measurement system that can rapidly and accurately obtain the terrain data produced by the propeller and the ducted propeller must be developed.Ferraro et al. (2022) explored the flow intensity effects on the propeller jet scour and performed a spectral analysis to estimate the scour hole evolution.They compared the results obtained with the numerical model results and, for the first time, numerically investigated the plane boundary effects on the characteristics of a propeller jet with and without an incoming flow.
Most of the current experiments used the ADV.However, it is a single-point measurement; hence, the experiment efficiency is low.The linear laser 3D terrain scanning system has been widely used in these experiments to measure the terrain data.Will and Pennington (1971) first proposed the usage of coded light for 3D measurements to solve the matching problem in machine vision.Saitama University (Ryo and Kawasaki 2003) achieved the rapid measurement of general objects using a 3D measurement system comprising a laser and a camera, which are the basic compositions of the system proposed in the present work.Giambruno et al. (2011) conducted the linear laser scanning of underwater objects using a binocular stereo-vision system and analyzed the quality of the 3D scanning system in an underwater environment with different turbidity levels.Meanwhile, Sagawa et al. (2014) employed a single-camera projector system using a grid color-coded projection based on the de Bruijn sequence to realize the 3D measurement of high-speed moving objects through single image acquisition.
The present study uses an underwater linear laser 3D terrain scanning system to obtain the terrain data produced by a propeller and a ducted propeller.This system is waterproof; thus, the measurement time interval can be set to a small value, which enables us to measure the scour depth and position varying over time.This paper mainly discusses the experimental setup, linear laser 3D terrain scanning system, and analyses of the scour profile, max scour depth, max deposition mound height, and positions varying over time.
The remainder of this paper is structured as follows: Section 1 shows some experiments on the propeller scour and the linear laser 3D terrain scanning system; Section 2 presents the instruments used in the experiment performed in this work and the system principle and explains the performance of the proposed system in comparison to that of ADV; Section 3 elaborates on the experiment and analysis results; and Section 4 provides the conclusions and prospected work.

Details and information on the propeller and the duct
The propeller used in this experiment was a right-handed Ka4-70 propeller, which has a diameter of 10 cm and a blade number of 4 and is powered by a drive controlled at 500 rpm.The hub-to-propeller ratio was 0.167.The propeller area ratio was 0.7. Figure 1

Experimental pool and experimental setup
The experimental pool was 4 m long, 1 m high, and 2 m wide (Fig. 2).
The model sand utilized in the experiments was quartz sand with a median grain size of d 50 = 0.728 mm.The Fig. 1 Propeller extension profile specific gravity was 2.65 kg/m 3 .The submerged capacity was 1.65.The uniformity coefficient was 1.61.Figure 3 illustrates the particle size distribution.The test position was filled with sand, covering a 0.3 m depth.

Terrain measurement system
The linear laser 3D terrain scanning system was used to measure the terrain data produced by the propeller and the ducted propeller.The system accuracy was up to 1 mm, meeting the experimental requirements.The principle and the system layout are as explained below.

Principle of the linear laser 3D terrain scanning system
The principle of the linear laser 3D terrain scanning system was based on laser triangulation.Upon hitting the terrain for measurement, the linear laser could be misaligned due to different heights.The camera reflects this phenomenon by showing the laser line at different pixel positions.Analyzing the pixel positions enables the system to calculate the terrain coordinates and import them into Tecplot.Tecplot builds the scour terrain produced by the propeller and the ducted propeller and provides information on the max depth of the scour hole, the max height of the deposition mound, their positions, and so on.
Figure 4 shows how the camera and the laser are arranged in the linear laser 3D terrain scanning system.The camera is perpendicular to the horizontal plane.The laser hits the terrain for measurement at an angle, and the angle can be measured.The system can obtain the coordinates in world coordinates by analyzing the laser position in the camera.

Component of the linear laser 3D terrain scanning system
The linear laser 3D terrain scanning system comprises three slides, a camera, and a laser (Fig. 5).
The two slides are parallel to the axis, while the other is perpendicular to it.One of the slides parallel to the axis is an active slide for the belt module.The other slide parallel to it is an aluminum alloy slide that serves as a support and does not generate power.The slide perpendicular to the axis is a screw slide that ensures the camera obtains  all the terrain data produced by the propeller and the ducted propeller.
The camera used was FLIR GS3-U3-23S6C-C, with a frame rate that could be selected between 0 and 163 fps to help choose the X interval and a resolution of 1920*1080.
The X interval is defined as the ratio of the slide speed to the camera frame rate.A small X interval depends on a high slide speed and a small camera's frame rate.In this experiment, 1 mm was selected as the X interval.The ratio of the camera's frame rate to the slide speed was 1.The slide speed was 50 mm/s, and the camera's frame rate was 50 fps, ensuring the measure of system stability.

Calibration
The relationship between the pixel and world coordinates is obtained as follows: where k is the scaled factor, m is the pixel coordinate, A is intrinsic, and R and T are extrinsic.The calibrations aim to obtain k, A, R, and T.
The calibrations included Zhang's calibration (Zhang 2000) and the laser plane calibration.
Zhang's calibration eliminates the camera distortion and determines the relationship between the pixel and world coordinates.In other words, this calibration's results could convert the information from the camera into a coordinate in the world coordinate.The system obtained the intrinsic and the extrinsic through this calibration and converted them into three linear equations for the coordinate conversion.In this process, the scaled factor used four linear equations, which was why the laser plane was calibrated.The laser plane calibration produced the laser plane equation, which could be the fourth linear equation.The calibration process is explained below.
First, Zhang's calibration was employed to obtain the intrinsic and the extrinsic.MATLAB and a checkboard calibration board were used to complete the calibration.Photos of the checkboard calibration board were then taken at different heights and imported into MATLAB's camera calibrator.The intrinsic and the extrinsic were shown in the camera parameters.Next, the scale factor was acquired through laser plane calibration.The laser obtained the laser plane equation at different heights.Z was already known; therefore, only three were unknown: X, Y, and scale factor.These were calculated with the intrinsic and the extrinsic.The laser plane equation was fitted using MATLAB's curve fitting with the laser positions at different heights.This equation reflected the role of the scale factor in the coordinate conversion.
Considering some errors, a curve was fitted to calibrate the results of the linear laser 3D terrain scanning system.Accordingly, 1 cm boards were used to obtain the data for curve fitting.Figure 6 displays the curve.
(1) km = A(RT )M The system code included laser stripe extraction and pixel coordinate conversion.Laser stipe extraction determines the laser pixel coordinate in the pictures.A combination of extreme value and threshold methods was used to ensure extraction accuracy and rapidity.The principle behind this was based on the Gaussian energy distribution.The pixel coordinate conversion was achieved with the results of the two abovementioned calibrations.The final result was refined using the revised curve.The coordinates were then calculated.The laser plane calibration and the terrain coordinate calculation required laser stripe extraction and pixel coordinate conversion.The difference between laser plane calibration and terrain coordinate calculation was as follows: three unknowns existed in the laser plane calibration, while four unknowns existed in the terrain coordinate calculation.Therefore, the laser plane calibration code does not require Z, while the terrain coordinate calculation requires the laser plane calibration result.

Experiment layout
Figure 7 presents the experimental layout.The sand was 2.6 m long, 0.3 m high, and 2 m wide.The distance from the propeller to the sand was 0.1 m, while that from the propeller to the wall was 0.94 m.According to Lv et al. ( 2017), the error caused by the wall is less than 5% when the propeller diameter is less than one-third of the water holes.

Test procedure
First, the sand was leveled.Next, the propeller or the ducted propeller was positioned.The camera and the laser were then placed in a flat-bottom glass container and positioned in the slide system.The propeller or the ducted propeller was driven to rotate, produce, and scan scour terrain.Different time intervals were selected according to different periods.Between 0 and 6 min and 10 and 30 min, 3 and 4 min were selected as the time intervals, respectively.Between 1 and 1 h and 30 min, 10 min was chosen as the time interval.Between 1 h and 30 min and 2 h, 15 min was taken as the time interval.Between 2 and 3 h, 20 min was selected as the time interval.Between 3 and 5 h, 30 min was chosen as the time interval.Between 5 and 9 h, 40 min was taken as the time interval.Lastly, between 9 and 18 h, 1 h was selected as the time interval.The selections were based on the terrain change rate.The terrain would quickly change first and then stabilize.The linear laser 3D scanning system was used to capture the terrain information produced by the propeller and the ducted propeller.The information was then imported into the MATLAB code for terrain data acquisition and terrain exportation.

Comparison of the scour profiles obtained from the laser scanner and ADV
ADV is commonly used to obtain terrain data.Therefore, comparing its results with those of the system can improve the system accuracy.Figure 8 shows the ducted propeller scour profile for 60 min.Figure 9 illustrates the propeller scour profile for the same duration.
The trends and the data were similar; thus, the system data can be trusted.The system required only 10 min to obtain the terrain, while ADV needed a few hours.Moreover, the system data interval was less than that of ADV.

Experiment results and discussion
Figure 10 displays the scour profile produced by the ducted propeller at 500 rpm. Figure 11 presents the scour profile produced by the propeller at 500 rpm.In Figs. 10 and 11, X stands for the distance from the propeller to the terrain points, while Z denotes the relative height of the terrain to the origin.X reflects the influence range of the propeller jet.Hence, in Figs. 10 and 11, the influence of the ducted propeller jet is longer than that of the propeller jet.This phenomenon is reflected in the deposition mound and max influence positions.The propeller jet influence is  deeper than that of the ducted propeller jet.This phenomenon is reflected in the deposition mound height and scour hole depth.The propeller scour development rate is faster than that of the ducted propeller scour.These phenomena could reflect the beam action of the duct.The propeller jet is more concentrated because of the duct; thus, the influence of the duct propeller jet is farther but shallower than that of the propeller jet.The scour hole length is also bigger than the deposition mound length.Fredsøe et al. (1992) suggested that the scour beneath a single pipeline can be approximated as follows: where S(t) is the time-dependent scour depth; t is time; S ef is the equilibrium scour depth; and T f is the characteristic timescale of the scour process.This formula is the classic formula used in scour experiments; hence, it was used here to fit the curves: T * is a nondimensional time scale; g denotes gravitational acceleration; d 50 is the median grain size; and D is the propeller diameter.Table 1 presents the results.H(t) is the max deposition mound height.S(t) is the max scour hole depth.X d is the max deposition mound height position.X S is the max scour hole depth position.
Figure 12 shows the deposition mound height.The deposition mound height produced by the propeller was higher than that produced by the ducted propeller.The terrain produced by the propeller reached a stable state earlier.Their trends were the same.The propeller terrain remained unchanged after 12 h, while the ducted propeller terrain remained unchanged after 15 h.In other words, the latter needed more time to develop. (2) Figure 13 displays the scour hole and max scour hole depths.The scour hole depth produced by the propeller was deeper than that produced by the ducted propeller.This phenomenon was similar to that observed in the height.In short, these phenomena were interrelated.
The development speed of the propeller was faster than that of the ducted propeller.The max deposition height and max scour hole depth of the propeller were in a stable  state earlier than the ducted propeller.A comparison of the scour hole depth and the deposition mound height revealed that the height value was higher than the scour hole depth value.The max deposition height and max scour hole depth trends were basically the same.The positions of the max deposition mound height and depth also depicted dynamic stabilizations instead of particular positions.These results reflected that the propeller jet scour is the sand transport.Figures 14 and 15 depict that in the initial phase, the propeller's max deposition mound height position was bigger than the maximum deposition mound height position of the ducted propeller.This was due to the initial development speed of the propeller being bigger than that of the ducted propeller.However, the propeller development reached a stable state earlier than the ducted propeller; thus, the propeller's max deposition mound height position was smaller than that of the ducted propeller in the end.Throughout the phase, the propeller's max scour hole depth position was bigger than that of the ducted propeller.The distance from the max scour hole depth position to the max deposition mound height position of the ducted propeller was also longer than that of the propeller.The distance trend first increased, and then decreased, and eventually stabilized.
Figure 16 shows a line in the terrain of the ducted propeller scour hole within 30 min, exhibiting a phenomenon that was different from the propeller scour terrain shown in Fig. 17.In short, the scour hole range was bigger than that of the scour deposition mound.The terrain was not symmetrical along the axis.The scour hole depth of one side was deeper than the other side, and the deposition mound height of the other side was higher than that of one side.These results were consistent with the conclusions of Penna et al. (2019).The trends of these two conditions were similar, and their development processes were morphologically the same at different phases.

Conclusions and prospects
This study investigated the terrain data produced by the propeller and the ducted propeller varying over time by using a linear laser 3D terrain scanning system.Notably, the system can perform underwater scanning.Compared  with ADV, which is commonly used in obtaining terrain data, the proposed system is more efficient and has a smaller data interval.The system data are similar to those of ADV; therefore, the system results are credible.The following preliminary conclusions were obtained in this work: (1) The influence range of the ducted propeller jet was longer, narrower, and shallower than that of the propeller.
(2) The terrain produced by the propeller developed faster than that produced by the ducted propeller but reached a stable state earlier than the latter.
(3) The propeller and ducted propeller development trends were similar.In each development, the terrains were also morphologically similar at different phases.The distance trends from the max scour hole depth position to the max deposition mound height position initially showed an increase, then a decrease, and finally a stable state.The final max deposition mound height position of the propeller was smaller than that of the ducted propeller.The final max scour hole depth position of the former was bigger than that of the latter.However, in the initial phase, the max deposition mound height position of the propeller was bigger than that of the ducted propeller.The scour hole range was also bigger than that of the scour deposition mound.
In the future, more experiments will be performed to fit the formulas for the propeller scour.Cameras will also be connected to eliminate the errors caused by the sliding movement.These will yield more precise results.Lastly, the 1080 min deposition mound data must be more precise.
depicts the propeller extension profile.The duct number is No. 19A.The leaf tip gap is 0.1 cm according to Zhang et al. (2015).

Fig. 2
Fig. 2 Experimental pool used in the experiment

Fig. 4
Fig. 4 Camera and laser layout

Fig. 8
Fig. 8 Ducted propeller scour profile obtained by ADV and the proposed system

Fig. 9
Fig. 9 Propeller scour profile obtained by ADV and the proposed system

Fig. 16
Fig. 16 Terrain of the ducted propeller scour varying over time

Table 1
Test conditions and results of the current experiments