Benchmarking FSI Capabilities

An important task in the development of ADINA is the appropriate verification and benchmarking of the code. This requires comparing ADINA solutions with analytical results, published computed or experimental data, making convergence studies, and so on.

The verification and benchmarking of a code for FSI solutions involving flexible structures and Navier-Stokes fluids is particularly difficult because relatively few results to compare with have been published.

We present here a typical benchmark problem and the solution. This problem has been published in reference [1]. Of course, the material data have been selected to be approximately actual physical data encountered in practice.

Figure 1  Problem solved

Figure 2  Incompatible meshes used (27-node 3D elements to model the rubber pipe and
8-node 3D flow-condition-based-interpolation elements to model the fluid)

The objective in this problem solution is to test whether mass conservation for the fluid is satisfied when, in the FSI solution, the fluid domain changes significantly as a result of the interaction with the structure. Here the incompressible fluid flows through a rubber pipe which expands as a result of the pressure in the fluid. The figure above describes the problem and gives the meshes used.

The deformations of the pipe as the fluid flow is increased are shown in the above movie. The largest stretch in the pipe is about 1.7 (meaning that the fibre of originally unit length is stretched to a length of 1.7).

The fluid is modeled using 3D 8-node FCBI elements. These CFD elements are based on a hybrid finite element/finite volume formulation to use interpolation functions dependent on the flow, to have stability, and satisfy for any mesh 'locally' mass and momentum conservation, see references [2] and [3].

The table below shows that mass conservation is well satisfied in the FSI solution.

t	Re	Flow rate (kg/s)
		z = 0 m	z = 0.5 m	z = 1 m
0.4	31.2	2.45199	2.45198	2.45198
1.0	121.1	9.51151	9.51151	9.51151
1.6	361.7	28.4088	28.4088	28.4088

Flow rates at three different sections along the axis. The Reynolds number is based on the average velocity at the inlet, z = 0 m and the channel diameter, D = 0.1 m.

Additional benchmark solutions can be found in reference [1] given below.

For more information on ADINA FSI, please refer to our page on CFD and Fluid-Structure Interaction. 

References

1. K. J. Bathe and G.A. Ledezma, Benchmark problems for incompressible fluid flows with structural interactions, Computers & Structures, 85, 628-644, 2007.
2. K. J. Bathe and H. Zhang, A Flow-Condition-Based Interpolation Finite Element Procedure for Incompressible Fluid Flows, Computers & Structures, 80, 1267-1277, 2002.
3. H. Kohno and K. J. Bathe, A Flow-Condition-Based Interpolation Finite Element Procedure for Triangular Grids, Int. J. Num. Meth. in Fluids, 49, 849-875, 2005.