Dam break against a flexible wall: flexibleDamBreak
Prepared by Amirhossein Taran and Philip Cardiff
Tutorial Aims
- Demonstrates how to perform a multi-phase fluid-solid interaction simulation
- Demonstrates the use of a large strain solid model within an FSI case
- Compares the
solids4foamprediction against published benchmark solutions
Case Overview
This case extends the traditional OpenFOAM damBreak tutorial to include a flexible dam. This benchmark has been examined several times in the literature, including by Walhorn et al. [1], Meduri et al. [2], and Ryzhakov et al. [3]. The initial configuration of this example is shown in Figure 1, where a column of water of width \(L\) and height \(2L\) is initially at rest behind a membrane on the left side of a tank of width \(4L\). At time \(t = 0\), the membrane is removed, and the column of water collapses. During the collapse, the water impacts a flexible obstacle (the "dam") standing at a distance \(2L\) from the left wall, causing it to deflect elastically. For benchmarking, the horizontal displacement of the top-left (upstream) corner of the dam is tracked over time. Table 1 provides the material properties and geometry data for reference. The solid component employs a neo-Hookean large strain constitutive law. The total Lagrangian solid model (nonLinearGeometryTotalLagrangianTotalDisplacement) is used as the solid solver, and the volume-of-fluid incompressible multiphase fluid model (interFluid) is used as the fluid solver.
Figure 1: Problem geometry and initial conditions
Table 1: Problem Physical Parameters
| Parameter | Value |
|---|---|
| Solid Young's modulus (\(E\)) | 1 MPa |
| Solid density \((\rho_s)\) | 2500 kg m\(^{-3}\) |
| Solid Poisson's ratio \((\nu)\) | 0 |
| Water viscosity \((\mu)\) | 0.001 Pa s |
| Water density \((\rho)\) | 1000 kg m\(^{-3}\) |
| Air viscosity \((\mu)\) | 1.48e-05 Pa s |
| Air density \((\rho)\) | 1 kg m\(^{-3}\) |
| Gravity \((g)\) | 9.81 m s\(^{-2}\) |
| Water column width (\(L\)) | 0.146 m |
| Dam height (\(H\)) | 0.080 m |
| Dam thickness (\(W\)) | 0.012 m |
The tank is \(4L\) wide, the water column is \(L \times 2L\), and the dam stands at a distance \(2L\) from the left wall, as shown in Figure 1.
Results
Upon starting the solution, the water column collapses due to gravity and will hit the flexible dam. Video 1 shows the time evolution of the volume-of-fluid field in the fluid domain and the displacement field in the solid domain. The solids4foam predictions for the deflection of the top-left corner of the dam are compared with numerical solutions from the literature in Figure 2.
The impact, the peak deflection and the subsequent decay are captured well. From about \(t = 0.6\) s, once the water has run up the right wall and the reflected wave returns to the dam, the predicted response lags the reference solutions. Note that the two reference solutions also differ noticeably from one another over this later period. The fluid mesh used here is the coarse mesh inherited from the standard damBreak tutorial, and refining it is the main lever for improving the late-time agreement; a full mesh and time-step independence study should be performed before drawing quantitative conclusions.
Figure 2: Displacement over time for the top-left corner of the flexible obstacle (the "dam")
Video 1: Evolution of the volume-of-fluid field in the fluid domain and the displacement field in the solid domain
Running the Case
The tutorial case is located at solids4foam/tutorials/fluidSolidInteraction/flexibleDamBreak. The case can be run using the included Allrun script, i.e. > ./Allrun. The Allrun script first executes blockMesh for both the solid and fluid domains (> blockMesh -region solid and > blockMesh -region fluid), then initialises the water volume fraction with > setFields -region fluid, and finally runs the case with > solids4Foam. To remove the generated results and return the case to its initial state, use > ./Allclean.
The displacement history of the tracked point is recorded by the solidPointDisplacement functionObject, configured in system/controlDict, which writes to postProcessing/0/solidPointDisplacement_displacement.dat. If gnuplot is installed, Allrun uses this data to produce displacement.pdf, comparing the solids4foam prediction with the reference solutions.