FSI Model: ANSYS R System Coupling

value compared to the CFD analyses and it was decided that there was no need to further simplify the structural model.

• Co-Simulation Sequence: where the working sequence of numerical solvers is defined.

Data Transfer

As mentioned in Section 4.4, when straightforward one-way coupling (without using the System Cou- pling) is used, for non-matching meshes at the fluid-solid interface Mechanical nodal values are cal- culated by linear interpolation from the surrounding CFD nodes, and such process of mapping is not conservative [34, 68]. If interpolation process cannot find a face to map to, then the closest point is chosen. When using theSystem Coupling, the Data Transfer is a critical part of the FSI analysis. Each data transfer incorporates the following algorithmic components [69]:

• Data Pre-Processing: first component used in the data transfer process and can involve the gen- eration of supplemental data on mesh locations that are needed by the mapping and interpolation algorithms;

• Mapping: the second component used in the data transfer process that involves the match- ing/pairing of a source and a target location (mesh) to generate weights. For a two-way FSI problem, a fluid node must be mapped to a shell element to receive displacements, and similarly the shell element must be mapped to a fluid element to receive stress or displacement;

• Interpolation: third component used in the data transfer process and involves the (re)use of the generated weights to project source data onto target locations.

For one-way and two-way FSI problems usingSystem Coupling there are two different methods of mapping generally applied [34, 69]. If a conservative quantity such as the mass and momentum is trans- ferred, a method called General Grid Interfaceis applied by generating weights that conserves locally the transferred quantity. If all nodes are mapped correctly, the method is also globally conservative.

On the other side, for transferring non-conservative quantities such as displacements, temperatures and stresses, another method called Smart Bucket Algorithmis used. Complete description of these algorithms is available in ANSYS^R System Coupling User’s Guide [69].

4.5.1 One-Way versus Two-Way Coupling

As previously mentioned in the beginning of this section, a non-qualitative small sub-study was con- ducted to assess the computational effort on the different techniques of FSI that can be used in ANSYS^R Workbench. Also, with this sub-study, another issue to be clarified was the solution and procedure of solving FSI problems for thin structures (such as the endplates and vertical supports parts of the rear wings). For that, a1×1msimple flat plate geometry was generated and succeeding FSI analyses were done to simulate plate deformation when exposed to wind flow (Figure 4.6). The meshing strategy used was similar to Subsection 4.3.2, but for inflation option with30layers and1.2growth rate.

First, with respect to the FSI analysis of thin structures, the geometry of the plate was done using a surface-body without thickness (it is a numerical parameter to be defined inMechanical). The outcome

Figure 4.6: Test case geometry used to assess the computational effort for different FSI coupling tech- niques and the solution process to solve FSI analyses for thin structures.

was not expected as limitations in the software were found, even after discussion with ANSYS^R Tech- nical Support staff. When meshing, the inflation generation was neglected, even though instructions where given to generate it, and no errors were given after generation (Figure 4.7(a)). Second, additional boundary conditions (wall-shadow) inFluent were automatically defined when assigning wall condition to the plate surface (top face), that represented the opposite face of the plate. This meant that for one- way FSI analysis (and for both possibilities of performing it), doubled conditions existed at the fluid-solid interface, one for the top and the other for the opposite side of the plate, not to mention the bad mesh quality involved unable to correctly solve the boundary layer generated. Two-way FSI analyses using System Couplingcould not be performed has data transfers did not distinguish the pressure distribution from both sides of the plate and only one side of them could be attributed to the fluid-solid interface.

Concern to ensure meshing quality for the rear wings endplates and vertical supports is essential, which means that another approach needed to be used when designing thin structures. In order to solve it, the plate geometry was created assuming a certain thickness (in this case0.01m), which resulted in a hol- low plate (single surface-body made of6faces). This solved the mentioned problems and in particular, the mesh generation of the inflation was not affected (Figure 4.7(b)). FSI analyses were then performed for this case to evaluate the computational effort of the different strategies that can be used.

(a) Section view mesh for thin plate (1 surface-body made of1face)

(b) Section view mesh for hollow plate (1 surface-body made of6faces).

Figure 4.7: Plate section view of Inflation mesh option for the thin and hollow plate.

CFD and CSM solutions were performed considering steady-state and static conditions, respec- tively, which means that for the System Coupling model a single time-step was used, with5 coupling iterations/steps performed for both one-way and two-way FSI analyses. Approximated values for the

computational time required are presented in Table 4.10.

Table 4.10: Approximate values of the computational time when performing FSI analyses using different available coupling techniques in ANSYS^R Workbench for the plate exposed to wind flow test case.

Fluid-structure interaction technique Computational time One-way FSI with straightforward technique 8min One-way FSI usingSystem Coupling 40min Two-way FSI usingSystem Coupling 1h30min

The use of System Coupling to solve FSI problems and specially for two-way analysis proved to be computationally expensive when compared to the straightforward technique of importing directly the pressure distribution to the Mechanical component (one-way coupling). Even for one-way coupling, the System Coupling module proved to be 5 times slower, and for this specific version of ANSYS^R (14.5) it was advised not to use it for one-way analyses by the ANSYS^R Technical Support staff. The reason is related to the process thatSystem Couplinguses. For each coupling iteration, the process of mapping/interpolation is done (which takes more time than the direct approach without using theSystem Coupling), than the CFD solution is computed and used to calculate the structural response. For two- way analyses, also in the same coupling iteration the incremental displacement, or nodal displacements, are applied to the mesh of the CFD solution and the process of mapping/interpolation occurs again to compute the CFD solution. This is done for the number of coupling iterations the user defines. It is not feasible to use more than one coupling iteration when using the System Couplingfor one-way FSI approach, and even so, the solution process is slower than without using theSystem Coupling. This is why the ANSYS^R Technical Support staff recommended not to use it for one-way coupling.

Taking into attention the computational resources and in particular the duration of performing FSI analyses to better fit the objectives proposed for this thesis, the straightforward technique of one-way coupling was used to perform all the structural parametric and optimisation solutions. Furthermore, in particular for rear wings, the deformations usually are small, which fits the FSI one-way coupling approach [34].