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Physical Instabilities in FSI

It is well known that some problems involving fluid-structure interactions exhibit physical instabilities. Hence, it is important to study the behavior of systems using only numerical techniques that can accurately resolve such instabilities. More importantly, solution methods should not introduce numerical instabilities that could be confused with the actual physical phenomena.

In this Brief, we present two examples. The first example involves fluid-structure interactions in a lid-driven cavity with a flexible bottom. The second example shows how ADINA FSI can be used in fluid-structure interaction problems involving physical instabilities (e.g., flutter).

Figure 1 shows the schematic of the first example. An open cavity is confined with rigid vertical walls and a flexible plate at the bottom and is driven by a harmonic horizontal velocity applied at its top (see Ref. [1]). The details of the model are depicted in the figure. For a similar problem, see Ref. [2] and the observations in Ref. [1].



Figure 1 Schematic of the lid-driven cavity problem

While the time-varying response is required, the problem is initially solved for the steady-state response corresponding to the maximum velocity loading (Figure 1). The objective of this part of the study was to obtain a good mesh using the adaptive meshing capability of ADINA CFD.

The adaptively reached mesh is then used for the transient dynamic solution. The response of the system is also analyzed using a uniform grid of 120 X 120, 4-node FCBI elements. Results of the transient analysis using the adaptively reached mesh and the uniform 4-node element mesh are compared in Figures 2 and 3. In all analyses the flexible plate at the bottom was modeled using 2-node isoparametric plane strain beam elements.




Figure 2 Time history of the vertical displacement at the mid-point of the flexible plate


         (a) Results using adaptively reached mesh               b) Results using uniform mesh


Figure 3 Pressures at time 68 using the adaptively reached mesh and the uniform mesh


The first movie below shows the particle trace plot when the problem is solved using the adaptively reached mesh. The next movie shows the velocity vector field in the fluid using the same mesh. It is interesting to note that while the flexible bottom oscillates up and down during the solution, the mean displacement is downward (see Figure 2).







The above problem, for the parameters given in Figure 1, does not exhibit a physical instability and as can be seen in Figure 2 even after running the simulation for a long duration, the solution does not show any instability.

The second example involves the model of a wing flutter problem. The 3D CFD mesh used and its close-up around the airfoil are shown in Figure 4. The fluid inlet velocity is 12 m/s. The outlet is set to be traction free and the rest of the fluid boundaries are modeled as wall boundary conditions.




Figure 4 CFD mesh of the flutter problem

The fluid is modeled as an incompressible Navier-Stokes fluid with the k-ω turbulence model and is discretized using the FCBI-C fluid elements. The wing is modeled using 4-node shell elements. As a simplification, only a portion of the wing is represented and the flexibility and mass of the rest of the wing are modeled by introducing lateral and torsional springs and a lumped mass. A small perturbation load is applied to the wing in the z-direction.

The movie at the top of the page shows the oscillation and Figure 5 depicts the time history of pitching and plunging of the airfoil. As seen, the wing starts oscillating and the oscillation amplitude grows with time; which is a fundamental characteristic of the flutter phenomenon.




Figure 5 Plots of displacement and rotation of the wing

The movies below show contour plots of nodal pressures and velocity magnitudes in the fluid.



The above examples show some of the analysis capabilities of ADINA for FSI. An overview of the features with many case studies and publications is given at ADINA FSI.


Keywords:
Fluid-structure interaction, FSI, transient analysis, FCBI, FCBI-C, adaptive meshing, flutter, physical instability, aeroelasticity


References

  1. K.J. Bathe, H. Zhang, "A mesh adaptivity procedure for CFD and fluid-structure interactions", Computers and Structures, 87:604-617, 2009.

  2. U. Küttler, W. Wall, "Fixed-point fluid-structure interaction solvers with dynamic relaxation", Comput Mech, 43:61-72, 2008.

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