When a half-full tank is transported, the liquid inside moves freely and impacts the walls. In tanker vehicles, ship fuel tanks, spacecraft propellant tanks and LNG carriers this is a structural and dynamic design criterion.
Fill level governs
A full tank does not slosh — there is no free surface to move. Nor does an empty one. The worst case lies somewhere between, usually near half full.
This gives a counter-intuitive operational rule: transporting a tank either full or empty is safer than transporting it half full.
Natural frequency and resonance
The free surface has natural sloshing frequencies that depend on the tank geometry and the liquid depth. If the vehicle's or ship's motion frequency approaches one of them, the amplitude grows rapidly and the wall pressure multiplies.
The classical remedy is to put baffles inside the tank. A baffle breaks up the free motion of the liquid, shifts the natural frequency and dissipates energy. The baffle pattern and open-area ratio are directly an analysis question: too closed and you add weight and filling problems, too open and the damping is insufficient.
Modelling
The problem is by definition free surface and transient. Points to watch:
- Interface resolution and Courant number. Keep it below one in the interface region, or the surface blurs numerically.
- Impact pressure is very short-lived. To capture the peak, the time step is set by the impact duration, not by the structural response.
- Tank motion is a boundary condition. Either the tank itself is moved or an equivalent acceleration field is applied. Both fall under moving boundary logic.
- Do not neglect the gas phase. In a closed tank the trapped air cushion markedly softens the impact pressure; a single-phase model overpredicts the peak.
References
- Hirt, C. W. & Nichols, B. D. (1981). Volume of fluid (VOF) method for the dynamics of free boundaries. Journal of Computational Physics, 39(1), 201–225. DOI: 10.1016/0021-9991(81)90145-5
- Ferziger, J. H., Perić, M. & Street, R. L. (2020). Computational Methods for Fluid Dynamics, 4th ed. Springer. DOI: 10.1007/978-3-319-99693-6