Free-Surface CFD — Sloshing, Waves & Liquid Interfaces

What Makes a Free Surface Special?

A free surface is a moving interface between a liquid and a gas whose shape forms part of the solution. Tank sloshing, wave impact, filling and draining, spill behaviour and partially filled piping all depend on that evolving interface. Unlike a fixed wall boundary, the interface can translate, deform, break, merge and trap gas. Its motion changes the liquid mass distribution and can generate highly transient pressure loads. For structural assessment the important result is often not the visually striking surface shape but the resulting pressure-time history, wetted area, fluid centre of mass or impact impulse at a structural boundary.

Interface-Capturing Formulation

Volume-of-fluid methods are widely used for engineering free-surface CFD because they conserve liquid volume and can accommodate large interface motion. A phase-fraction transport equation identifies liquid, gas and mixed interface cells. The interface-reconstruction or compression scheme controls how sharply the front is represented. Too much numerical diffusion smears the surface and damps waves; excessive compression can create unphysical wrinkling or spurious currents. The interface method, mesh and time step must therefore be treated as a coupled numerical choice. Verification should include liquid-volume conservation and sensitivity of the engineering load to interface sharpening parameters.

Gravity, Froude Number & Scaling

Gravity is central to most free-surface flows because it provides the restoring force for waves and sloshing. Froude number compares inertia with gravitational effects and is often the governing similarity parameter for scale-model testing of free-surface behaviour.

Froude number:

Fr = V / √(gL)

where:
V = characteristic velocity
g = gravitational acceleration
L = characteristic length

For gravity-dominated free-surface similarity, matching Fr is often more important than matching Reynolds number exactly.

Sloshing Frequencies & Structural Coupling

Partially filled vessels possess natural sloshing modes whose frequencies depend on geometry, fill level and gravity. If base motion, vehicle manoeuvre or structural vibration excites those modes, the liquid can amplify interface motion and wall loads. The liquid also changes the effective inertia and damping of the structure. A rigid-wall CFD model can be adequate when structural deformation is small relative to liquid motion, but flexible tanks or lightweight structures may require one-way or two-way fluid–structure coupling. At minimum, compare the dominant slosh frequencies with the imposed motion spectrum and the structural modes that could interact with them.

Wave Impact & Local Pressure Peaks

Wave impact and slamming produce local pressure peaks that can be much shorter than the global sloshing period. Their prediction is highly sensitive to interface resolution, trapped gas, wall geometry and time step. A single-cell pressure maximum is rarely a defensible structural load. Instead, examine pressure over physically meaningful areas, impulse, duration, spatial coherence and convergence with mesh refinement. Trapped gas can cushion an impact or create a secondary compression pulse; treating the gas as incompressible can therefore distort the peak. Structural assessment should use a load representation that preserves the physically relevant impulse and spatial footprint rather than simply mapping the largest instantaneous cell value.

Filling, Draining & Venting

Filling and draining problems couple the free surface to inlet momentum, venting and pressure equalisation. If the gas phase cannot vent as assumed, pocket compression can dominate the pressure history. Conversely, an overly simple pressure outlet can remove a physically important gas restriction. The analyst should model the actual vent path or justify an equivalent boundary condition. For rapid filling, jet impingement and entrained gas can control local loads; for draining, vortex formation and air ingestion can change flow rate. Mass balance of both liquid and gas, where gas compression matters, should be monitored throughout the event.

Mesh & Time-Step Strategy

The mesh should resolve the smallest interface feature that materially affects load, not every visually interesting ripple. Refine near expected impact zones, narrow gaps, vents and moving contact regions. Temporal resolution should capture both global wave motion and short-duration local impacts. Courant-based controls can be useful for interface advection, but final adequacy must be demonstrated on pressure, force or interface position. A free-surface calculation can look stable while under-predicting a peak because the time step is too coarse. Perform temporal refinement on integrated wall force or impulse in addition to local pressure.

Validation & Measurement Compatibility

Free-surface validation benefits from combining interface measurements and load measurements. High-speed imaging or wave probes can validate interface timing and amplitude, while pressure transducers validate local wall loading. Tank force measurements can provide global resultant checks. Synchronisation matters because a correct peak magnitude at the wrong phase may indicate the wrong wave dynamics. Sensor size and sampling frequency should also be reflected in CFD post-processing: a physical pressure transducer averages over a finite diaphragm and may not reproduce an infinitesimal numerical peak. Filter and spatially average the CFD data consistently before judging correlation.

Engineering Verification

• Check liquid-volume conservation and gas mass where compression matters.
• Demonstrate sensitivity to interface resolution and time step for the structural load metric.
• Compare slosh frequencies and phase with analytical or test expectations.
• Assess pressure peaks using area, duration and impulse rather than isolated cell maxima.
• Confirm vents, outlets and trapped-gas assumptions reproduce the physical system.
• Map loads using a representation consistent with structural spatial and temporal resolution.

Initial Conditions & Artificial Transients

Free-surface calculations are especially sensitive to how the initial liquid level, velocity field and pressure field are established. Starting from an inconsistent hydrostatic state can generate an artificial pressure pulse or wave that persists for several natural periods and contaminates the event of interest. Initialise pressure consistently with gravity and phase distribution, and where practical allow the model to settle before applying the prescribed motion or inflow. For manoeuvre or launch cases, ramping the excitation may be appropriate only if the real event is also gradual; otherwise the ramp can suppress a genuine transient. Separate numerical start-up behaviour from the physical response by monitoring total liquid momentum, wall force and free-surface energy before the analysis window used for design.

Key Takeaways

• Free-surface CFD solves the interface motion as part of the flow problem
• Sloshing and wave impact require different temporal and spatial resolution checks
• Froude similarity is often central to gravity-dominated scale testing
• Local cell pressure peaks should not be used as structural loads without area, duration and convergence checks
• Venting and trapped gas can materially change the pressure history