Advertisement

Journal of Marine Science and Technology

, Volume 14, Issue 1, pp 51–68 | Cite as

Prediction of the forces acting on container carriers in muddy navigation areas using a fluidization parameter

  • Guillaume Delefortrie
  • Marc Vantorre
Original Article

Abstract

To assess the safety of navigation in muddy areas, a comprehensive captive manoeuvring model test program was executed. Based on the results of this experimental program, a four-quadrant manoeuvring model was built with a separate set of coefficients for each combination of under-keel clearance and mud layer characteristics. The disadvantage of this model is that only conditions corresponding with the experimental ones can be simulated. A more consolidated mathematical model was needed. This was achieved with the introduction of a fluidization parameter that determines the corresponding hydrodynamically equivalent depth above a solid bottom. As a result, the under-keel clearance dependency of a given mathematical manoeuvring model can be reformulated in such way that the effect of any realistic muddy condition is included. In this article, the modelling of the hull forces, the propeller thrust and torque, and the forces acting on the rudder will be discussed.

Keywords

Nautical bottom Mud Manoeuvring Container Fluidization Captive model testing 

List of symbols

ai

Regression coefficient (–)

AEP

Expanded area ratio of propeller (–)

AR

Rudder area (m2)

B

Ship beam (m)

CB

Block coefficient (–)

CD

Drag coefficient (–)

CL

Lift coefficient (–)

CT(Q)

Thrust (torque) coefficient (–)

DP

Propeller diameter (m)

F

Force component (–)

FX

Longitudinal rudder force (N)

FY

Lateral rudder force (N)

f

Function (–)

g

Function (–)

g

Gravity constant (m/s2)

G*

Function (–)

h

Depth/thickness (m)

h*

Hydrodynamically equivalent depth (m)

Izz

Moment of inertia about z-axis (kg m2)

J

Advance (–)

J

Apparent advance (–)

KT(Q)

Thrust (torque) coefficient (–)

k

Sway velocity or yaw rate (m/s or rad/s)

L, LPP

Ship length (m)

m

Ship mass (kg)

N

Yawing moment (Nm)

n

Propeller rate (1/s)

Ni

Hydrodynamic derivative \( \left({{i}} = \dot{\text{v}}, \; \dot{\text{r}}, \; \ldots \right) \)

N′(β)

Non-dimensional yawing moment due to drift: \( N^{\prime}\left( \beta \right) = \frac{N\left( \beta \right)}{{\frac{1}{2}\rho L^{2} T\left( {u^{2} + v^{2} } \right)}}\left( {\text{--}} \right) \)

N′(γ)

Non-dimensional yawing moment due to yaw: \( N^{\prime}\left( \gamma \right) = \frac{N\left( \gamma \right)}{{\frac{1}{2}\rho L^{2} T\left( {u^{2} + \left( {\tfrac{1}{2}rL} \right)^{ 2} } \right)}}\left({\text{--}}\right) \)

N′(χ)

Non-dimensional yawing moment due to yaw–drift correlation: \( N^{\prime}\left( \chi \right) = \frac{N\left( \chi \right)}{{\frac{1}{2}\rho L^{2} T\left( {v^{2} + \left( {\tfrac{1}{2}rL} \right)^{2} } \right)}}\left({\text{--}}\right) \)

P

Ship’s length or draught (m)

P

Propeller pitch (m)

QP

Propeller torque (Nm)

r

Yaw rate (rad/s)

\( \dot{r} \)

Yaw acceleration (rad/s2)

sgn

Sign function (–)

T

Ship draught (m)

TP

Propeller thrust (N)

TEU

Twenty feet equivalent unit (–)

u

Longitudinal velocity (m/s)

uP

Longitudinal velocity at propeller (m/s)

\( \dot{{u}} \)

Longitudinal acceleration (m/s2)

UKC

Under keel clearance

v

Lateral velocity (m/s)

VR

Velocity near rudder (m/s)

\( \dot{\text{v}} \)

Lateral acceleration (m/s2)

w

Wake factor (–)

X

Longitudinal force (N)

Xi

Hydrodynamic derivative \( \left({{{i}} = \dot{{u}},\; \ldots} \right) \)

X′(β)

Non-dimensional longitudinal force due to drift: \( X^{\prime}\left( \beta \right) = \frac{X\left( \beta \right)}{{\frac{1}{2}\rho LT\left( {u^{2} + v^{2} } \right)}}\left( {\text{--}} \right) \)

X′(γ)

Non-dimensional longitudinal force due to yaw: \( X^{\prime}\left( \gamma \right) = \frac{X\left( \gamma \right)}{{\frac{1}{2}\rho LT\left( {u^{2} + \left( {\tfrac{1}{2}rL} \right)^{2} } \right)}}\left( {\text{--}} \right) \)

X′(χ)

Non-dimensional longitudinal force due to yaw–drift correlation: \( X^{\prime}\left( \chi \right) = \frac{X\left( \chi \right)}{{\frac{1}{2}\rho LT\left( {v^{2} + \left( {\tfrac{1}{2}rL} \right)^{2} } \right)}}\left( {\text{--}} \right) \)

xG

Longitudinal position of centre of gravity (m)

Y

Sway force (N)

Yi

Hydrodynamic derivative \( \left({{\text{i}} = \dot{\text{v}},\;\dot{\text{r}},\ldots} \right) \)

Y′(β)

Non-dimensional lateral force due to drift: \( Y^{\prime}\left( \beta \right) = \frac{Y\left( \beta \right)}{{\frac{1}{2}\rho LT\left( {u^{2} + v^{2} } \right)}}\left( {\text{--}} \right) \)

Y′(γ)

Non-dimensional lateral force due to yaw: \( Y^{\prime}\left( \gamma \right) = \frac{Y\left( \gamma \right)}{{\frac{1}{2}\rho LT\left( {u^{2} + \left( {\tfrac{1}{2}rL} \right)^{2} } \right)}}\left( {\text{--}} \right) \)

Y′(χ)

Non-dimensional lateral force due to yaw–drift correlation: \( Y^{\prime}\left( \chi \right) = \frac{Y\left( \chi \right)}{{\frac{1}{2}\rho LT\left( {v^{2} + \left( {\tfrac{1}{2}rL} \right)^{2} } \right)}}\left( {\text{--}} \right) \)

α

Angle of attack of flow (°)

β

Drift angle, Eq. 14 (°)

γ

Yaw rate angle, Eq. 15 (°)

δ

Rudder angle (°)

ε

Hydrodynamic angle, Eq. 42 (°)

ε*

Apparent hydrodynamic angle, Eq. 50 (°)

μ

Dynamic viscosity (Pa s)

μ

Non-dimensional dynamic viscosity: μ′ = μ/(1 Pa s) (–)

\(\Uppi\)T

Keel penetration parameter, Eq. 17 (–)

\(\Uppi\)

Alternative keel penetration parameter, Eq. 20 (–)

ξi

Regression coefficient or function (–)

ρ

Density (kg/m3)

ρ*

Non-dimensional density, Eq. 47 (–)

Φ

Fluidization parameter (–)

Φij

Regression coefficient (–)

χ

Drift–yaw correlation angle, Eq. 16 (°)

Subscripts

1

Water layer

2

Mud layer

H

Hull

P

Propeller

Q

Torque

R

Rudder

T

Thrust

Notes

Acknowledgments

The generalised mathematical model is based on experimental results obtained at and in close co-operation with Flanders Hydraulics Research (Antwerp, Belgium) and has been developed in the framework of the research project Validation of the Nautical Bottom Concept by order of the Flemish Government (ref 16 EB/0501), Belgium.

References

  1. 1.
    PIANC (1997) Approach channels––a guide for design. Final report of the joint working group PIANC and IAPH, in cooperation with IMPA and IALA. Supplement to bulletin no. 95, PIANC, BrusselsGoogle Scholar
  2. 2.
    De Vlieger H (1991) Economic methods of channel maintenance: optimization of maintenance dredging. Terra et Aqua 45:32–51Google Scholar
  3. 3.
    Kerckaert P, Malherbe B, Bastin A (1985) Navigation in muddy areas––the Zeebrugge experience. Bulletin 48, PIANC, Brussels, pp 127–135Google Scholar
  4. 4.
    Malherbe B (1990) Towards a definition of the nautical bed in mud deposits: the concept of rheologic transition RT. In: International workshop on cohesive sediments: towards a definition of “mud”. KBIN, BrusselsGoogle Scholar
  5. 5.
    Brossard C, Delouis A, Galichon P et al (1990) Navigability in channels subject to siltation. In: Proceedings of the 22nd international coastal engineering conference. American Society of Civil Engineers, Reston, pp 3088–3101Google Scholar
  6. 6.
    Sellmeijer R, Van Oortmerssen G (1983) The effect of mud on tanker manoeuvres. In: Spring meetings, paper no. 7, The Royal Institution of Naval Architects, LondonGoogle Scholar
  7. 7.
    Vantorre M, Coen I (1988) On sinkage and trim of vessels navigating above a mud layer. In: Harbour congress, The Royal Society of Flemish Engineers, AntwerpGoogle Scholar
  8. 8.
    Doctors LJ, Zilman G, Miloh T (1996) The influence of a bottom mud layer on the steady-state hydrodynamics of marine vehicles. In: 21st symposium on naval hydrodynamics. National Academies Press, Washington, pp 727–742Google Scholar
  9. 9.
    Miloh T (1995) Ship motion in non-homogeneous media. Ship Technol Res 42(3):140–156MathSciNetGoogle Scholar
  10. 10.
    Miloh T, Tulin MP, Zilman G (1992) Dead water effects of a ship moving in stratified seas. Trans Am Soc Mech Eng J Offshore Mech Arctic Eng 115:105–110Google Scholar
  11. 11.
    Wu GX (1993) The representation of a body advancing in a stratified fluid by singularity distribution. Int Shipbuild Prog 40(422):127–135Google Scholar
  12. 12.
    Zilman G, Miloh T (1995) Hydrodynamics of a body moving over a mud layer––part 1: wave resistance. J Ship Res 39(3):194–201Google Scholar
  13. 13.
    Zilman G, Kagan L, Miloh T (1996) Hydrodynamics of a body moving over a mud layer––part 2: added mass and damping coefficients. J Ship Res 40(1):39–45Google Scholar
  14. 14.
    Zilman G, Miloh T (1996) Hydrodynamics of a body moving over a mud layer. In: Proceedings of the 20th symposium on naval hydrodynamics. National Academy Press, Washington, 18 ppGoogle Scholar
  15. 15.
    Stern F, Bulgarelli U, Gustafsson L et al (1999) Uncertainty analysis in EFD: uncertainty assessment methodology. ITTC quality manual, 4.9-03-01-01Google Scholar
  16. 16.
    Delefortrie G, Vantorre M, Eloot K (2005) Modelling navigation in muddy areas through captive model tests. J Marine Sci Technol 10(4):188–202CrossRefGoogle Scholar
  17. 17.
    Ogawa A, Kasai H (1978) On the mathematical model of manoeuvring motion of ships. Int Shipbuild Prog 25(292):306–319Google Scholar
  18. 18.
    Oltmann P, Sharma SD (1984) Simulation of combined engine and rudder maneuvers using an improved model of hull-propeller-rudder interactions. 15th symposium on naval hydrodynamics. National Academies Press, Washington, pp 83–108Google Scholar
  19. 19.
    Delefortrie G, Vantorre M, Verzhbitskaya E, Seynaeve K (2007) Evaluation of safety of navigation in muddy areas through real-time manoeuvring simulation. J Waterw Port Coast Ocean Eng 133:125–135CrossRefGoogle Scholar
  20. 20.
    Gronarz A (1993) A mathematical model for manoeuvring simulation on shallow water. In: Proceedings of the international conference on marine simulation and ship manoeuvrability (MARSIM), Saint John’sGoogle Scholar
  21. 21.
    Kijima K, Nakiri Y, Tsutsui Y, Matunaga M (1990) Prediction method of ship manoeuvrability in deep and shallow waters. In: Proceedings of MARSIM and ICSM 90, Tokyo, pp 311–318Google Scholar
  22. 22.
    Li M, Wu X (1990) Simulation calculation and comprehensive assessment on ship maneuverabilities in wind, wave, current and shallow water. In: Proceedings of MARSIM and ICSM ‘90, Tokyo, pp 403–411, 459–465Google Scholar
  23. 23.
    Delefortrie G, Vantorre M (2007) Modeling the maneuvering behavior of container carriers in shallow water. J Ship Res 51(4):287–296Google Scholar

Copyright information

© JASNAOE 2009

Authors and Affiliations

  1. 1.Flanders Hydraulics ResearchAntwerpBelgium
  2. 2.Maritime Technology DivisionGhent UniversityGhentBelgium

Personalised recommendations