Numerical Study Of The Effect Of Liquefiable Cargo Sloshing On Motion And Stability Of A Cargo Hold Section

The cargo which may liquefy is a class of bulk granular cargo containing a certain proportion of fine particles and liquid water. During the cargo's transportation by ships, when its water content beyond a certain limit it may liquefy and behave like a fluid acted by external forces, such as vibration and impact of machineries, ship motions and so on. The properties of the liquefiable cargo have become a major risk of occurrence of capsizing for ships transporting it. However, the research related to this topic has not been carried out deeply and widely. In order to explore the capsizing mechanism, a series of work on sloshing of liquefied cargo, coupled roll motion between liquefied cargo and cargo hold section and stability analysis have been carried out based on viscous fluid dynamics theory, three dimensional linear frequency domain potential theory, impulse response function theory and simplified body surface nonlinear theorem.The effect of liquefiable cargo after it liquefied on the roll motion and stability of cargo hold section can be solved through three related problems, which are the sloshing problem of liquefied cargo in a cargo hold with a forced roll motion, problem of solving the motion of cargo hold section in time domain and large amplitude coupled roll motion between the above two. First of all, to investigate the sloshing behavior of liquefied cargo in a cargo hold, its sloshing motion was calculated numerically based on viscous fluid dynamics theory combined with non-Newtonian constitutive equations and then verified. The numerical model comes from a bulk carrier with a DWT of 57,000. The model has a scale of 1:66. The nickel ore slurry with three different water contents was chosen as the liquefied cargo. Its rheological properties are described by non-Newtonian Herschel-Bulkley equation and Bingham equation. Based on the results, the sloshing induced moment changes basically periodically in the cases of three different water contents and different external excitations. According to the deformation of the free surface of the liquefied cargo, the lag effect of the cargo's motion compared to the motion of the cargo hold becomes significant when the water content is low. When the longitudinal baffle was mounted in the cargo hold, the amplitude of sloshing induced moment and the motion of the free surface decreases rapidly when the baffle's ratio changes from 0.4 to 1.0. The damping effect of the baffle is most pronounced in the condition of larger excitation amplitude. The viscosity of the liquefied cargo also changes periodically. But the peak viscosity becomes larger with an increase of the baffle's height. Under the same external excitation amplitude, when the excitation frequency is near 4.8 rad/s the amplitude of the sloshing induced moment is the maximum and the resonance happens. Under the same external excitation frequency, the amplitude of the sloshing induced moment increases basically linearly with the increase of the excitation amplitude. In the end, limited to the volume of the cargo loaded in the cargo hold the increase of the amplitude of the sloshing induced moment tends to be flat and deviates from the linear behavior. To vary the ratio of depth to width by changing the width of the cargo hold and the amplitude of sloshing induced moment decreases gradually with the increase of the ratio. The effect of the ratio on the amplitude of sloshing induced moment becomes weaker when its value increases to a certain limit.Then the numerical model of solving the motion of a floating body in time domain was established based on three dimensional linear frequency domain potential theory and impulse response function theory. A further to consider the large amplitude roll motion of the floating body, the radiation problem, diffraction problem and the static restoring coefficients were calculated in advance. During solving the motion of the floating body the instantaneous values of the hydrodynamic coefficients are acquired based on the data fitting technique. So the simplified body surface nonlinear simulation model in time domain was established. Based on the work described above, the large amplitude coupled roll motion between liquefied cargo and cargo hold section and the stability analysis can be carried out.Finally, the cargo hold section loaded with liquefied cargo was designed and based on the sloshing simulation model of the liquefied cargo, the impulse response function the coupled motion simulation model between the liquefied cargo and the cargo hold section was set up. Through this model, the effect of the sloshing induced moment on the coupled roll motion was checked out. Only consider the effect of the sloshing induced moment, the amplitude of the coupled roll motion is reduced at most of the wave frequencies. The methods used to investigate the stability of ships were analyzed and compared. And then to fully understand the effect of the liquefied cargo on the motion and stability of the cargo hold section, the simplified body surface nonlinear simulation model for the large amplitude coupled roll motion was established. The tilting test of the cargo hold loaded with liquefied cargo was carried out beforehand. Through recording the transverse offset of the cargo's gravity center, the effect of the liquefied cargo movement in the cargo hold on the static restoring coefficients was investigated. The static restoring coefficients are weakened once the motion of the cargo starts. Considering the sloshing induced moment and the weaken effect from the liquefied cargo on the static restoring coefficients in the same time, the obvious asymmetry phenomenon happens in the time history of the coupled roll motion when the wave frequency is in the resonance region. Under the resonance frequency, continue to increase the wave amplitude and the asymmetric phenomenon still appears in the curve of the coupled roll motion and it becomes severe with time going on. Until the restoring moment reaches the minimum and then the capsizing can be happened. Based on the above results, that is the waken effect on the static restoring coefficients from the liquefied cargo's movement in the cargo hold makes the cargo hold section taking a large amplitude roll motion and it cannot return to the former position until the asymmetric phenomenon happens. And the static restoring coefficients are reduced continuously because of the asymmetric movement of the liquefied cargo in the cargo hold, which will aggravate the asymmetric roll motion. In the last, the cargo hold section loses its ability to recover and capsizing happens.