RD-V: 0400 Mok FSI Benchmark
Convergent channel with internal flexible plate is experiencing a parabolic profile inlet.

In this analysis, a fluid flow through a convergent channel with an internal flexible plate and the deflection of that plate are examined.
The geometric parameters of this problem are shown in Figure 1.
Fluid domain is modeled with /MAT/LAW6 for the main domain and /MAT/LAW11 for inlet and outlet boundaries, while the plate is modeled with /MAT/LAW2.
- Arbitrary Lagrangian Eulerian (ALE) formulation using the Displacement
Method for the ALE mesh formulation, in which the nodes at the fluid and
solid interfaces belong to both fluid and solid parts.
For the ALE formulation, three different interfaces are used to simulate the interface forces.
- Coupled Eulerian Lagrangian (CEL) formulation, where two separate meshes are created for each one of the fluid and solid domains and these domains can move independently, with a correction force applied between them.
The results of the analysis are compared with the results proposed by Mok (2001), based on two control points in the pressure surface of the plate.
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Model Files
Model Description
Units: kg, s, m, Pa, N
To model the fluid domain, /BRICK elements (/HEXA8N) are used and /MAT/LAW6 (HYDRO or HYD_VISC) is used. For the boundaries (inlet and outlet), /MAT/LAW11 (BOUND) is used. The elements at the interface between the fluid domain and the inlet and outlet must have the same nodes. An Ityp=2 formulation is used for both inlet and outlet.
To calculate the pressure in the fluid domain, a linear equation of state (/EOS/LINEAR) is used in /MAT/LAW6 and calibrated accordingly so that the fluid exhibits incompressible behavior.
To model the solid plate, /BRICK elements (/HEXA8N) are again used and assigned with an isotropic elastic-plastic Johnson-Cook material law (/MAT/LAW2).
The velocity inlet profile is inserted using the /IMPVEL load, with a different scale factor for each node, depending on its z coordinate. The velocity inlet is additionally a function of time. The equations describing the inlet are:
For the fast reproduction of different /IMPVEL loads for every node, two Altair Compose scripts are used and the 0000.rad is modified directly.
- ALE formulation
- Coincident Mesh (no interface established)
- Slip Interface - different velocity tangential to the interface are allowed (/INTER/TYPE1)
- Non-slip (tied) Interface – interface nodes have exactly the same normal and tangential velocity (/INTER/TYPE2)
- CEL formulation
- The solid mesh (Lagrangian) can move within the fluid mesh (Eulerian) (/INTER/TYPE18)
Due to its high accuracy and low runtime, the CEL model is further pushed with a multi-domain method to speed up the simulation. More precisely, the fluid and solid domains are solved with a different time step and connect in points defined by the higher time step. With this formulation, the CEL model is able to run in about an hour on a conventional laptop, achieving 10-times better performance than without this method.
Results

In Figure 2, the flow phenomena are simulated properly with the vertices located behind the plate. Additionally, despite the slow response caused by the deformation of the plate, the flow finally speeds up due to the convergent channel geometry and reaches a steady-state condition.


In Figure 4, the pressure is initially raised by the large resistance created by the neck the neck generated by the plate. This increase is responsible for the strong deformation of the plate in the first 10 seconds of the simulation. Then the systems reach a steady-state and the fluid pressure increases while the deformation of the plate reaches a constant value. In this contour, warm colors are used for positive pressure values and cool ones for negative pressure to clearly represent the phenomena.
The control points A (at the top of the pressure side of the plate) and B (at the middle of the pressure side of the plate) are used to investigate the simulation performance.


The different methods can lead to competing results, with the CEL method being the most accurate of all.

