Regime Maps for Sloshing in 134.5mm Cylindrical Tanks Reveal Instability at Twice Natural Frequency

Understanding the behaviour of liquids inside moving tanks is critical for ensuring the safety and efficiency of vehicles ranging from aircraft to trains, and researchers are now offering a clearer picture of this complex phenomenon. Francisco Monteiro, Tommaso De Maria, and Samuel Ahizi, working at the von Karman Institute for Fluid Dynamics and Universidad Carlos III de Madrid, lead a team that investigates sloshing, the movement of liquid within a partially filled tank, under vertical acceleration. Their work addresses a particularly dangerous scenario where the tank’s motion excites resonant sloshing, potentially causing structural damage and instability, and they have developed a new method to predict these risks. By combining high-speed video analysis with advanced data processing techniques, the team generates detailed ‘regime maps’ that classify different sloshing patterns across various tank fill levels, offering a valuable tool for optimising vehicle design and operation, alongside contributions from Ramon Abarca, Giuseppe C. A. Caridi and Miguel A. Mendez.

Vertical sloshing within partially filled fuel tanks can significantly compromise vehicle stability and structural integrity, particularly when subjected to harmonic accelerations near twice the natural frequency of the sloshing motion. In these conditions, parametric resonance can occur, driving large-amplitude waves, breaking up the liquid surface, and causing severe mixing within the tank. The research addresses a gap in understanding sloshing under vertical acceleration, increasingly relevant in aviation where fuel tanks experience low-frequency vibrations from turbulence and control inputs. Experiments were conducted using a transparent cylindrical tank, allowing for detailed observation of fluid behaviour. The team’s approach avoids the need for complex interface tracking by utilizing high-speed video recordings and combining prototype-based data labelling with dimensionality reduction via multiscale proper orthogonal decomposition and automatic kernel-based classification.

This innovative method enabled the creation of a dimensionless regime map across three fill ratios, examining liquid fill levels ranging from 0. 40 to 0. 67 relative to the tank diameter. The resulting map distinguishes between stable waves, longitudinal and transverse mode shapes, and regimes where different modes compete with each other. Measurements reveal that the system exhibits distinct sloshing behaviours depending on the fill ratio and excitation conditions.

The team systematically varied the dimensionless vertical acceleration from -0. 94 to 0. 90, the dimensionless displacement amplitude from 0. 02 to 0. 50, and the forcing frequency relative to twice the lowest natural frequency from -1.

20 to 0. 90. Across the tested conditions, the team collected data from 61 to 73 test points for each fill ratio. The developed regime map provides a predictive tool for assessing sloshing-induced loads, supporting structural and operational optimization of fuel systems and offering a significant advancement in mitigating risks associated with parametric resonance, a phenomenon where vibrations amplify due to the interaction between acceleration and fluid dynamics.

Sloshing Regimes Mapped with Data Analysis

This research presents a new data-driven method for identifying distinct regimes of liquid sloshing within partially filled cylindrical tanks, a phenomenon critical to the stability and structural integrity of vehicles. By employing high-speed video analysis and advanced data processing techniques, scientists have successfully mapped out the different sloshing behaviours without relying on complex interface tracking. The team developed a method combining prototype-based data labelling with multiscale proper orthogonal decomposition and automatic kernel-based classification to achieve this. The resulting regime map, generated across three different fill levels, distinguishes between stable sloshing, longitudinal and transverse mode shapes, and conditions where multiple modes compete. Importantly, the experimentally determined natural frequencies of the tank were found to be significantly lower than those predicted by existing theoretical models for flat-ended cylinders, highlighting the importance of considering the tank’s geometry. This map serves as a predictive tool for assessing sloshing-induced loads, offering valuable insights for optimising the structural design and operational parameters of fuel tanks.