4.1. Comparison of Scour Depth between Free Twin Propeller and Quay Wall
Cui et al. [
30] found that a twin-propeller without a quay wall scours into three structures: small scour pits, large scour pits, and scour deposits. The maximum scour depth was in the middle of the large scour pit. Differences between the internal and external rotating propellers at the transverse position of the maximum scour depth were observed. The maximum scour depth could be predicted using Equations (7)–(9).
The results showed that the twin-propeller jet could not diffuse freely along the axial direction. The scour structure was influenced by the distance between the quay wall and propeller.
Figure 6 shows the comparison between the axial scour depths of the scour structure under the influence of the quay wall. When the outflow plane of the internal rotating twin propellers was 3
Dp away from the vertical baffle, the maximum scour depth measured at the outflow plane was 0–20 mm above the sand bed. The free scour without the baffle was 0–10 mm below the sand bed, which was attributed to the high-speed backflow and vortex formed by the twin-propeller jet impinging on the baffle. This was caused by the deposition of sand particles owing to the reverse movement of the entrained sand particles. When there was no baffle, the position of x = 0
Dp was observed for the structure of the small scour pit. The scour depth should be below the sand bed. From x = 0
Dp to x = 3
Dp, the scour depth increased almost along the fixed slope and reached the maximum scour depth at x = 3
Dp. The maximum scour depth was located on the central axis of the two propellers, and its value was 70 mm. At a short distance (10 mm) from the downstream of 3
Dp to the vertical baffle, the scour depth decreased, which could be attributed to the strong bond between the sand particles and baffle plate, and the jet diffusion on the baffle could not push the sand. When the effect of baffles is neglected, previous studies have shown that the maximum scour depth is approximately 41.5 mm. Hence, the barrier effect of the quay wall increased the scour depth by 68%. The maximum scour depth of the external twin-propeller increased by 56% compared with that without the quay wall effect (
Figure 6b). Therefore, when the twin propellers were very close to the quay wall, the scour damage was more severe. When the distance between the twin propellers and baffle was 5
Dp (
Figure 5d and
Figure 6c), the scour depth of the twin propellers exceeded that without the quay wall, and the maximum scour depth increased by up to 24%.
Figure 6e,f shows the maximum scour depth of the internal and external rotating twin propellers at 7
Dp. From the propeller outflow plane to the position of the maximum scour depth (x = 3
Dp), the scour structure with or without baffles was almost unchanged, and the maximum scour depth of the main scour pit was also almost equal. From x = 3
Dp to x = 7
Dp, the maximum scour depth gradually increased with an increment of 20–35% under the condition of quay wall obstruction, and there was no significant sediment peak near x = 5
Dp. Thus, the scour depth continued to increase. The scour depth lies in the local scour zone near the quay wall. The maximum scour depth, in this case, was analogous to the main scour pit.
In
Figure 6, the test data presented in Cui et al. [
30] are used for comparison because similar tests were performed using twin propellers, but the difference was that the blocking effect of the vertical quay wall was considered in this paper. However, a few research results on double-helix vertical quay wall scours are available in the literature. The author applied the scour test data of the Hamill single propeller to improve the test results (
Figure 7). The maximum scour axis of each group of tests in this study was dimensionless with the unlimited scouring axis of a single propeller. The abscissa represented the dimensionless axial distance (x/
Dp). When the distance from the quay wall was 3
Dp, the maximum scour depth of the inner and outer rotating twin-propeller slurries were located on the central axis near the quay wall, and the maximum scour depth axis of the Hamill single screw was also located near 3
Dp. The ratio of the maximum scour depth
was approximately 2–2.3. With an increase in the distance between the twin-screw slurry and vertical quay wall, the maximum scour depth was still located at the axial distance of 3
Dp at the position of x/
Dp = 5
Dp. Although local large scour pits were excavated near the quay wall, these pits had significantly shallower depths than the scour depth at the 3
Dp position, and
was 1.4–1.6. At the distance from x/
Dp = 7
Dp, a gentle scour pit was formed between x/
Dp = 3
Dp and x/
Dp = 5
Dp, and
was approximately 1.5–1.7. According to Hamill, the maximum scour depth near the quay wall can be calculated using Equation (10).
The maximum scour depth (
) of the twin propellers and the distance between the propeller and sand bed did not satisfy Equation (11) proposed by Hamill. In this study, the axial distance divided by the propeller diameter is dimensionless, i.e., the axial distance was expressed as x/
Dp.
For the quay wall at an infinite distance, it can be considered that the quay wall could not influence the scour of the twin propellers. The empirical coefficient of the twin-propeller scour was derived by Cui et al. [
31], in which the quay wall was assumed to be infinitely far away from the twin-propeller. The ratio of the maximum scour depth of the twin-propeller to the unlimited scour depth of the single propeller (
) should be 1.2 for ICRTP and 1.1 for ECRTP. In this study, the total length of the flume was 1.2 m, and the free diffusion distance downstream of the propeller x/
Dp > 15, which could be considered as an unlimited scouring condition. Based on the test data and the above assumptions, the relationship between the maximum scour depth of the twin propellers near the quay wall, and the axial distance was established (
Figure 8). The maximum scour depth of the twin propellers near the quay wall could be predicted simply. The internal propeller was predicted using Equation (12), and the external propeller was predicted using Equation (13).
The practical application of the prediction formula proposed in this study is compared with the empirical formula proposed by predecessors. According to the prediction formula (Equation (10)) proposed by Hamill, the maximum scour depth near the quay wall is related to the distance between propeller and quay wall. The proposed formula proposed by Ryan et al. [
32] takes the Froude number into account, as Equation (14). Yuksel et al. [
33] added the gap of the propeller (
G) to these factors, as shown in Equation (15). Take 5
Dp spacing as a comparative case, the comparison between the calculated results and the experimental results are shown in
Figure 9. Hamill et al. [
19], Ryan et al. [
32], and Yuksel et al. [
33] studied the scour depth of a single propeller near the quay wall. This study is aimed at the scour of twin propellers. The maximum scour depth is much higher than that of a single propeller. The maximum variation is 49%, which occurs in the case of ICRTP with a 3
Dp spacing.
4.2. Scour Patterns with Existence of Quay Wall
Cui et al. [
31] extensively investigated the scour structure of internal and external rotating twin propellers without considering a quay wall. In general, the scour structure can be defined based on six characteristic parameters: maximum scour depth, maximum scour depth location, maximum scour width, length of main scour pit, maximum deposition height, and maximum deposition position. Based on 1–6 groups of test data, the relationships of the six characteristic parameters between the external and internal rotating twin propellers at 3
Dp, 5
Dp, and 7
Dp away from the quay wall were analyzed (
Table 4,
Table 5 and
Table 6).
Among the characteristics were the maximum scour depth (εtmax, q is the maximum scour depth influenced by the quay wall; εtmax, e is the ECRTP without considering the quay wall effect; εtmax, i is the ICRTP without considering the quay wall effect), the position of the maximum scour depth ( is the location of the maximum scour depth influenced by the quay wall; Xtm, e is the ECRTP without considering the quay wall effect; Xtm, i is the ICRTP without considering the quay wall effect), the maximum scour width (Wm, q is the maximum scour width affected by the quay wall; Wtm, e is the ECRTP without considering the quay wall effect; Wtm, i is the ICRTP without considering the effect of the quay wall), the length of the main scour pit ( is the length of the main scour pit influenced by the quay wall; is the ECRTP without considering the quay wall influence; is the ICRTP without considering the quay wall effect), the height of deposition ( is the maximum deposition height considering the quay wall; is the ECRTP without considering the quay wall effect; is the ICRTP without considering the quay wall effect), and the position of the maximum deposition height ( is the maximum deposition position influenced by the quay wall; is ECRTP without considering the quay wall; is the ICRTP without considering the effect of the quay wall).
The maximum scour depth of twin-propeller proposed in this study can play a guiding role in practical engineering. It mainly includes two methods; one is to control the distance between propeller and quay wall structure. According to the original structure design of the port, the maximum scour depth of the structure is predicted. The safe distance between the ship propeller and the port structure can be deduced. The other method is it is necessary to consider the maximum scour damage that may occur when the ship berths. So that increases the foundation depth of quay wall, or lays a protective layer near the port. The reinforcement depth of quay wall can refer to Equations (12) and (13) proposed in this study. It is worth noting that there is a limitation of this study. When a ship is entering or leaving a port, it is a dynamic process with a low velocity so that the distance between the propellers and the quay wall is constantly changing. This study is not suitable for ships entering and leaving the port at low speed. Because the scour hole is moving when the ship is sailing, it is applicable to the case of ships berthing at the port.