Natural sloshing frequencies of liquid cargo in road tankers

Abstract

Knowing the free sloshing frequencies of liquid cargo is important as manoeuvres performed by the vehicle should not represent even near-to-resonance situations. However, the precise laboratory determination of sloshing frequencies can be difficult. Measurements on scale models are described in this paper for two conventional and one original tank geometric design. A method for predicting natural sloshing frequencies is also desirable in order to make rapid analyses of potential tank designs before undertaking any laboratory work. In this paper, the suitability of approximating the natural frequencies by the known result for a rectangular tank is considered, by means of comparison to the scale-model tests. The approximation is fair since it always falls within 10% of the corresponding measured result. Moreover, the error is observed to be systematic, leading to some interesting physical interpretation: consistent underestimation of the first natural frequency is explained as an early reflection of waves due to rapid change of depth with respect to the wavelength; consistent overestimation of higher natural frequencies is explained by means of the slight variation in wave speed across the tank, due to the depth variation. The hydrodynamic analysis also provides some physical insight into the role of the different characteristic dimensions in the tank (fetch and depth curves vs. fill ratio) in controlling the rate of change of natural frequency as the fill ratio increases.