### Tech Briefs

Adaptive Meshing in FSI

There are numerous applications where fluid flows are fully coupled to the response of structures. While many such problems can now already be solved quite effectively using the ADINA arbitrary-Lagrangian-Eulerian formulation, in some analyses, when the structure undergoes very large deformations, the fluid mesh gets highly distorted. In fact, the mesh may become so distorted that the solution cannot be continued, unless the mesh is repaired or iteratively adapted.

ADINA offers a unique general solution capability to solve complex CFD and FSI problems with all structural capabilities available in the program. The problems may contain incompressible (including slightly compressible) flows or highly compressible (including low-speed compressible) flows. In FSI, the structural deformations can be complex and highly affected by the fluid flow. Vice versa, the fluid flow can be highly affected by the structural deformations (see our web page ADINA for Fluid-structure Interaction).

To further increase the generality of the FSI solution capability, and the accuracy in solutions, ADINA 8.6 offers the capability to adapt and repair CFD meshes so that appropriate mesh grading is used, and very large deformations of a structure can be accommodated. The ADINA techniques operate on CFD solution gradients and involve adapting (that is, refining and coarsening) the mesh in the various regions of flow for adequate element sizes throughout the fluid region.

The ADINA capability operates on general free-form meshing and hence accommodates meshes from many pre-processors, and in particular also meshes prepared for Nastran (see our News ADINA Pre- and Post-processing Options and Using NASTRAN Models for 3D CFD and FSI Analyses).

As an illustration, we present the solution of the problem described below. The above movie (obtained with EnSight) shows the flow response.

**Figure 1** FSI problem of steady-state flow through blades

To obtain an accurate solution, a fairly fine CFD mesh needs to be used near the blades, but away from the blades a coarser mesh can be employed. The number of CFD elements generated in the initial mesh is 34,041 tetrahedral elements, and this number is increased in 6 mesh adaptations to 547,741 elements in the final mesh. The blades are modeled with 196 MITC4 large deformation shell elements.

To solve this problem, symmetry conditions could be used to reduce the size of the model, but in this solution the complete geometry was employed. Figure 2 shows the starting (coarse) mesh and Figure 3 shows the fine mesh reached adaptively. Figure 4 gives the velocity field and pressure on a longitudinal cutting plane and Figure 5 shows the velocity field on a vertical cross-section 1.5 cm from the inlet, all solutions as calculated with the final mesh. We notice that the secondary flow is well captured, which could not have been obtained with the coarse mesh.

**Figure 2** CFD mesh used for analysis of flow around blades: starting mesh

**Figure 3** CFD mesh used for analysis of flow around blades: final mesh with

transverse and longitudinal cuts through the mesh

**Figure 4** Results using final mesh: velocity field and pressure

on a
longitudinal cutting plane

**Figure 5** Results using final mesh: velocity field on a vertical

cross-section 1.5 cm from the inlet

This new ADINA solution capability makes it possible to solve even more complex CFD and FSI problems, and in particular free-form meshes of complex 3D geometries from various mesh generators can be used. The possibility of using Nastran input is also an important feature.

*Keywords:*

CFD, FSI, Fluid-structure interaction, large deformations, adaptive mesh,
strongly coupled FSI, Arbitrary Lagrangian-Eulerian formulation, ALE