Transient particle dynamics and statistical force and stress metrics for design validation.
Tank sloshing — the violent motion of liquids inside partially filled containers — is one of the most underestimated challenges in industrial operations. When liquids oscillate during transport or operation, they generate dynamic loads that can destabilize entire systems, from tanker trucks to LNG carriers. Such transient forces can cause:
Across industries — from aerospace to energy storage — uncontrolled sloshing affects both safety and performance. To address these issues, engineers increasingly rely on numerical simulation. Experimental testing remains valuable but is costly and limited in scale. Methods such as Smoothed Particle Hydrodynamics (SPH) allow accurate prediction of free-surface motion under realistic operating conditions. Even without full structural coupling, SPH can deliver wall-resolved stress data, providing a practical foundation for assessing transient loads and improving tank design.
Methods
Understanding and mitigating tank sloshing requires combining analytical, experimental, and numerical approaches. Each method offers a distinct way to capture the complex fluid motion and its interaction with the tank structure, forming a comprehensive framework for safe and efficient design.
In this work, the SPH solver is used as a standalone tool — without structural coupling — but still capable of computing wall-resolved stress metrics directly from the particle field. These stress values offer quantitative insight into the time-dependent forces induced by sloshing, enabling preliminary assessment of tank stability and helping define requirements for mitigation systems such as baffles or damping discs.
Solutions
To illustrate the use of numerical methods in assessing sloshing severity, a demonstration case is presented using Smoothed Particle Hydrodynamics (SPH) in Ansys FreeFlow.
Geometry. The model consists of a horizontal cylindrical tank with ellipsoidal end-caps. The complete set of dimensions is shown in the figure below. The motion was defined in the positive Z-axis.
Motion Frame. Rather than attempting to reproduce every possible operational condition, this demonstration focuses on a single representative —and intentionally severe— braking scenario. A deceleration of 0.7 g corresponds to full emergency braking for heavy road tankers, as specified in FMVSS 121 (Air Brake Systems) and referenced in SAE J2909 and multiple sloshing studies in the Journal of Fluids and Structures and Applied Ocean Research. Under such braking, the liquid exhibits the largest free‐surface excursions and generates the highest transient loads on the tank shell, which is why 0.7 g is widely used as a benchmark for assessing worst‐case sloshing severity and for evaluating the need for mitigation devices such as baffles or damping discs.
For this demonstration, the tank undergoes a single linear translation consisting of three sequential motion stages, consistent with braking envelopes described in FMVSS 121, SAE J2909 and ADR 6.8:
Outputs. The available modules in FreeFlow allow the calculation of internal fluid motion, as well as the forces and stresses acting on solid surfaces. Two simulations were performed: one for the tank without baffles and another with a set of baffles shown below.
The total force on the tank walls and baffles was obtained as the square root of the sum of squares of the three Cartesian components (Fx, Fy, Fz). In the configuration without baffles, sharp force peaks appear during the acceleration and deceleration phases, as the liquid is free to move along the entire tank length. The addition of baffles leads to a significant reduction in these forces, and alternative designs can be evaluated to achieve the desired stress levels. The animations were generated in Ansys FreeFlow and show the acceleration and deceleration for each configuration.
A similar trend is observed in the total stress plot. Here, the total stress is calculated as the square root of the sum of squares of the SPH normal and tangential components (Sn, St). As expected, the force peaks produce high stress levels in the tank without baffles, exceeding the yield strength of some steels commonly used in liquid transport tanks. The results also clearly demonstrate how the inclusion of baffles helps maintain stresses within acceptable limits.
Hardware. All simulations were performed using a single NVIDIA RTX A6000 GPU. The processing time was approximately between 53-70 minutes. The computational time increases as the SPH particle size is reduced.
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