Liquid Film Model
Liquid Film: Theoretical Foundations
Overview
Professor, what is a liquid film model?
It's a model that calculates the flow, evaporation, and splashing of a thin liquid film formed on a wall surface. It predicts the behavior of liquid films flowing on walls, such as rainwater on an automobile windshield, icing on aircraft wings, fuel films on engine interior walls, and paint coatings.
Is it different from solving for a wall film using the VOF method?
Since the film thickness is extremely thin, ranging from tens of micrometers to a few millimeters, directly resolving it with the VOF method would require an impractically fine mesh. The liquid film model describes the film using 2D shell equations on the wall surface, allowing for efficient computation independent of the 3D mesh.
Governing Equations
Please explain the equations for the liquid film.
The equation describing the mass conservation of the liquid film (change in film thickness) is as follows.
$h$ is the liquid film thickness, $\bar{\mathbf{u}}_f$ is the film-thickness-averaged liquid film velocity, and $\nabla_s$ is the gradient operator along the wall surface. The source terms on the right-hand side represent mass changes due to droplet impingement, evaporation, and splashing, respectively.
How is the liquid film velocity determined?
We use the thin-film approximation (lubrication theory). The velocity profile inside the film becomes a parabolic distribution due to the no-slip condition at the wall and the balance of shear forces (shear stress $\tau_g$ from the airflow) at the film surface. Averaging over the film thickness gives:
The first term is the driving force due to the pressure gradient and the tangential component of gravity, and the second term is the driving force due to airflow shear. The energy equation for the liquid film is also solved similarly using the thin-film approximation to calculate the evaporation rate.
Droplet-Wall Interaction
How is the behavior of a droplet impacting a wall surface modeled?
The impact regime is determined by the Weber number and wall temperature.
| Regime | Condition | Behavior |
|---|---|---|
| Stick | $We < We_{cr,low}$ | Adheres to the wall |
| Rebound | High-temperature wall | Reflects elastically |
| Spread | Moderate $We$ | Spreads and forms a liquid film |
| Splash | $We > We_{cr,high}$ | Splashes and generates secondary droplets |
The Stanton-Rutland model and the Bai-Gosman model are representative and are implemented in Fluent and STAR-CCM+.
The Complexity Born from Thinness—Governing Equations at the µm Scale
A wall film is an extremely thin liquid layer with a thickness of 1–1000 µm, appearing in diverse locations from aircraft icing and engine wall cooling to the gastric mucus layer. The Thin Film Approximation assumes a parabolic velocity profile in the thickness direction, reducing the three-dimensional Navier-Stokes equations to two-dimensional thin-film equations. Marangoni convection (flow driven by surface tension differences due to temperature or concentration gradients) occurring on the film surface directly affects coating uniformity in painting processes and film non-uniformity in heat exchangers, making it a phenomenon of high practical importance.
Computational Methods for Liquid Film
Details of Numerical Methods
Please explain the numerical solution method for the liquid film model.
The liquid film is solved on the wall surface mesh. Independently of the 3D CFD mesh, the transport equations for film thickness, velocity, and temperature are solved using the 2D connectivity information of the wall boundary faces.
The coupling between the gas-phase CFD ↔ liquid film model is performed via the following information exchange.
| Gas Phase → Liquid Film | Liquid Film → Gas Phase |
|---|---|
| Wall shear stress $\tau_g$ | Mass source due to evaporation |
| Temperature & concentration near the wall | Heat source due to evaporation |
| DPM droplet wall impingement | Splashed droplets from the film |
| Wall pressure distribution | Roughness effect of the film surface |
So DPM droplets impact the wall and become a film, and then they can break up and become droplets again.
Implementation by Tool
| Tool | Liquid Film Model Name | Main Features |
|---|---|---|
| Ansys Fluent | Eulerian Wall Film | Liquid film flow, evaporation, splash, DPM coupling |
| STAR-CCM+ | Thin Film Model | Liquid film flow, heat transfer, evaporation, splashing |
| OpenFOAM | regionFaModel | Finite Area Method, basic liquid film flow |
| Ansys CFX | Wall Film (limited) | Basic liquid film tracking |
So Fluent and STAR-CCM+ are well-developed in this area.
Since the demand for liquid film models is high in the automotive and aerospace industries, these two tools have the most mature implementations. OpenFOAM's regionFaModel is based on the Finite Area Method and is suitable for research-oriented customization.
Thin-Film Numerical Solution—Unified Treatment of Wall Curvature and Gravity
In CFD implementation of wall films, the shell element approach is effective for liquid film flow on complex-shaped walls. The integral method, integrating in the wall-normal direction, derives transport equations for film thickness h and average velocity. ANSYS Fluent's wall film model treats gravity, pressure gradient, shear stress, evaporation, and condensation uniformly as source terms and is widely used for predicting engine wall oil film behavior. However, for thick films (h > ~1 mm) or turbulent films, the thin-film approximation may break down, necessitating a switch to 3D VOF.
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