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A simplified model, based upon physical principles, is proposed the simulate the effect of sloshing on the pressure developed in the tanker chambers. The model has been validated in good extent, with experimental data from full scale testing. The characteristic that mostly affects the pressure developed with the chambers of the tanker is the length of the chamber. While a reduction in this property could decrease the pressure developed within a given chamber, the analysis should take into account an overall approach, as a shortening of the individual chambers would influence the number of chambers necessary to carry a certain amount of product. Consequently, the resulting model could be used to study different effects of the sloshing cargo on the carrying vehicles, including the length and position of the chambers along the tanker body.
Figure 10 illustrates the theoretical results from the simplified model considered, together with the experimental data. These results and measurements are presented one next to the other, in order to facilitate the validity analysis of the proposed simulation methodology.
These results illustrate that the trends are comparable for both sets of data, that is, a similar range is obtained for all of the variables reported. A lower pressure is generated in chamber 5, which is attributed to the shorter length of this chamber. However, such increase in pressure does not correspond exactly to the difference of lengths, as the ratio of lengths would cause a differential pressure of 2.3/1.23 = 1.86, while the ratio of average pressures is on the order of 2. That is, there is an incremental, which is associated to the maximum height attained by the fluid in the chamber. The major difference between both sets of data, the experimental and theoretical, is that the theoretical do not include much of the noise and random oscillations reported in the experimental data. Such noise, however, is of very low amplitude, in comparison with the maximum values attained. The practical applications of these results could be in the area of chamber design, so that the effects of the length of the chambers be taken into account. That is, such greater lengths for the fluid in the chamber would involve larger pressures and consequently, greater stresses. However, the analysis should include an overall perspective, that is, the shortening of the chambers would imply an increase in the number of chambers, for a certain total payload, and the superposition effect of pressures, should be considered. On the other hand, the analysis could be extended to characterize the effects of the distribution of the lengths of the different chambers along the axis of the tanker, as the different resulting forces could have different effects on the pitch response of the road tanker.
A dynamic simulation model for a tanker ship along the Rhine River has been proposed, based on a simplified computational scheme, involving a two-degree-of-freedom roll plane multibody system, subjected to lateral accelerations estimated on the basis of measured data. The resulting equations of motion are solved through the transition matrix approach. The results suggest that many contributing factors were involved in the capsizing of the ship, including the relatively high speed of the river water and the meandering path of the infrastructure, further affected by dynamic effects derived from the behavior of the payload and from the steering maneuvers performed.