Systematic studies for recording squat and trim together with ship-induced pressure and wave systems when passing through channels in confined shallow water

Author: K. Uliczka

Boundary conditions

The studies into the dynamic behaviour of very large Post-Panamax container ships when passing through waterways of confined width and depth were conducted in BAW-DH’s shallow water basin (length approx. 100 m, width approx. 35 m, max. water depth 0.7 m) at 1:40 scale in accordance with Froude’s model laws.
The dimensions and investigated parameters for the model ships used were as follows:

Designation	Length	Beam	Draught	UKCR*	cB-value**	SR+	Weight trim	KG++
-	m	m	m	m	-	-	-	m
JUMBO	320	40	14,5	1-2	0,740	6,29	Hard	11,8
MEGA-JUMBO	360	55	15,5	1-1,5-2	0,677	6,10	Hard	10,2

*UKCR: under-keel-clearance, **cB: block coefficient , +SR: slenderness ratio, ++KG: centre of gravity above keel The Froude numbers amounted to 0,27 < Fr_h < 0,68. The Reynolds numbers were determined to be 3,1 · 10⁶ < Re < 6,2 · 10⁷ (factor 10 > Re_KRIT,erf). Fulfilling the geometric and dynamic similarity conditions ensured that the studies would deliver valid forecasts. The waterway cross-sections and (partial-)cross-sectional ratios are presented in Figure 1 taking the MEGA-JUMBO as an example:

• Trapezoidal profile, central course, cross-sectional ratios n = 25, 20, 15, 10.
• Trapezoidal profile, off-centre course, partial cross-sectional ratios nT = 10/5, 20/10, 25/10.
• Combined profile, off-centre course, partial-cross-sectional ratios nT = 25/10, 20/10, 10/5.

File:Fahwasserquerschn MegaJumbo b1.jpg

Figure 1: Waterway cross-sections studied including (partial) cross-sectional ratios for the MEGA-JUMBO, amongst others (60k)

Comments:
Cross-sectional ratio n = A / A_S
where: A wetted area of waterway
A_S submerged midship cross-section
Partial-cross-sectional ratio n_T = A_T / 0,5 A_S
where: A_T area of wetted partial-cross-section (from course to bank)

As well as measuring ship dynamics (squat, trim), the speed-dependent changes in the water level in a transverse profile were also assessed and analysed. Selected results are presented and evaluated below.

Selected results – squat and trim

The following relationships have been identified, taking the MEGA-JUMBO measurement results as an example:

• Smaller cross-sectional ratios between the submerged midship cross-section and the wetted cross-section mean higher speed-dependent squat values (Figure 2).
• Various waterway ratios relating to shape and width, from infinite to narrow waterway widths and down to fairways in shallow open water lead to a marked increase in squat (Figure 3).

File:Querschn Squat MegaJumbo b2.jpg

Figure 2: Impact of cross-sectional ratios on speed-dependent squat behaviour when passing approach channels (MEGA-JUMBO) (60k)

File:Squat Revier MegaJumbo b3.jpg

Figure 3: Impact of waterway cross-sections on speed-dependent squat behaviour when passing approach channels (MEGA-JUMBO) (160k)

The results of the extensive studies demonstrate that both fairway depth and waterway width (i.e. the cross-section of the waterway construction) must be factored into the preliminary calculation of maximum speed- and vessel-dependent squat, particularly in longer approach channels to major seaports such as the tidal Elbe, the tidal Weser or the Schelde flowing into the port of Antwerp, in order for the WSV to guarantee ease and safe shipping to seaports.

Selected results – ship-generated load

The changes in water level measured at the same time as ship dynamics (drawdown z_A, primary wave H_P and secondary wave H_S) as well as their cross-section-dependent distribution within the waterway are shown in Figures 4 and 5, taking the drawdown z_A as an example::

• A central course generates a symmetrical distribution and decrease in speed-dependent drawdown in the waterway cross-section (Figure 4, central course, left-hand side).
• At low UKC values, the partial-cross-sectional ratio determines the decrease in drawdown towards the bank (Figure 4, off-centre course, right-hand side).
• Comparing the two charts in Figure 4 highlights the decrease in drawdown in the waterway cross-section that depends on the passing clearance between ship and bank: on the right-hand bank, the drawdown load is virtually the same as the partial-cross-sectional ratios are similar. On the left-hand bank, however, the larger passing clearance of the moving ship means a much lower load at the foot of the embankment.