Transient particle dynamics and statistical force and stress metrics for design validation.
Challenges
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:
- High structural stresses and material fatigue
- Cargo instability or loss of vehicle control
- Damage to internal components and increased maintenance costs
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.
Engineering Solutions
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.
- Analytical methods form the foundation of sloshing studies, using linear wave theory and simplified assumptions to predict natural frequencies and resonance conditions in partially filled tanks. Though limited to simple geometries, they offer valuable first insights into instability modes [1].
- Experimental methods allow direct observation of liquid motion and pressure loads through scaled models and advanced measurement techniques such as high-speed imaging and pressure sensors. Their main challenges are cost and scalability to real operational conditions [2].
- Numerical methods provide a practical way to evaluate transient free-surface behavior under real accelerations and tank geometries. Eulerian VOF captures interface topology but is sensitive to mesh topology during large deformations. SPH, as implemented in Ansys FreeFlow [3], avoids mesh distortion entirely and is especially robust for violent sloshing, wave breaking, and impact loads.
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:
- Maximum acceleration of 0.3g (2.94 m/s2) during 2 s
- Constant velocity during 2 s
- Critical deceleration of 0.7g (6.9 m/s2, severe sloshing) during 0.86 s
Material properties. Default material properties were used for both phases. The liquid was assigned a density of 1000 kg/m³ and a dynamic viscosity of 0.001 Pa·s. For the tank walls, the following values were applied: density 7800 kg/m³, Young’s modulus 1×10¹¹ Pa, and Poisson’s ratio 0.3. The SPH element size was 0.01 m. Based on the tank's volume, the mass of the liquid is 391.13 kg to fill it up to the desired level.
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.
- No baffles. Flow behavior during the acceleration and deceleration phases.
- Design with baffles. Flow behavior during the acceleration and deceleration phases.
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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Suggested blogs
- [1] Book: Liquid Sloshing Dynamics: Theory and Applications (DOI)
- [2] Paper: Role of transverse baffle design on transient three-dimensional liquid slosh in a a partly-filled circular tank (DOI)
- [3] Ansys FreeFlow: Smoothed-Particle Hydrodynamics (SPH) Simulation Software (Link)
- Getting started with Ansys FreeFlow: Modeling a Stirred Tank (Link)