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FSI Simulation of Airfoil Using AcuSolve and RADIOSS

One of the rich features of AcuSolve lies in its ability to simulate Fluid Structure Interaction (FSI) problems. AcuSolve simulates these problems using two different technologies:

  1. Practical FSI (P-FSI)
  2. Direct Coupled FSI (DC-FSI)

In P-FSI simulations, AcuSolve and the structural code are run separately. The eigen solution obtained from a modal/frequency analysis is used as input to AcuSolve. The eigen vectors of the solid model are projected onto the CFD mesh and used as boundary conditions to displace the fluid mesh. The mass, stiffness and damping arrays are also transferred from the structural model to the flexible body in the CFD model, completing the inputs necessary to compute the structural deformation. P-FSI is preferred for simulations which have a linear structural response (linear material properties and small mesh deformations). For applications involving a nonlinear structural response, AcuSolve is coupled at run time to a structural solver using the DC-FSI approach. The codes are run in tandem and exchange forces and displacements at each time step. This technique captures all non-linearities in the structural model and can exploit the full capabilities of the structural solver. The DC-FSI technology within AcuSolve performs all projection and interpolation between the structural and CFD meshes without the use of any middleware.

To demonstrate the P-FSI technology, a simulation is performed to study the influence of water flowing across a steel airfoil with an emphasis on hydrodynamic damping effects. The modal data for the simulation is obtained from RADIOSS (mode shapes computer courtesy of Altair) in OP2 format. The CAD model with boundary conditions is shown in Figure 1.

Computational domain with boundary conditions
Figure 1: Computational domain with boundary conditions

The airfoil is considered as a flexible no-slip wall and is fully fixed (clamped) at both side walls. The four sides of the model are treated as slip walls. The inlet has a constant velocity of 20 m/s.

An unstructured mesh is generated on the CAD model in AcuConsole. Boundary layer mesh is created around the airfoil to achieve reasonable y+ values and the adjacent region is refined to accurately resolve the flow gradients. The top and front views of the mesh along with zoomed view around the airfoil are shown in Figures 2(a), 2(b) and 2(c).

Top view
Figure 2(a): Top view

Front view
Figure 2(b): Front view

Zoomed view of mesh around airfoil
Figure 2 (c): Zoomed view of mesh around airfoil

The airfoil is deformed initially by displacing the first natural mode shape with a maximum deflection of 0.1 mm. The modal force was ramped over the first 40 time steps to avoid an impulsive load on the structure.

A time history output point is placed on the airfoil at the spanwise center position and ¾ of the chord length in the flow direction. The time history output point on the airfoil is shown in Figure 3. The structural displacement of the monitor point in the vertical direction is plotted in Figure 4.

Location of monitor point on airfoil
Figure 3: Location of monitor point on airfoil

Vertical displacement at monitor point
Figure 4: Vertical displacement at monitor point

The damping ratio is determined by evaluating the logarithmic decrement of the displacement time history. Damping ratio is given as

Damping Ratio

where, δ is the logarithmic decrement

Log Decrement

x0 is greatest of two amplitudes
xn is n periods away

Using the above formula, the value of damping ratio is calculated as 0.24.

This application demonstrates AcuSolve’s capability of handling hydrodynamic damping problems. The added mass of the surrounding water makes this a challenging FSI application from a numerical stability standpoint. However, AcuSolve’s P-FSI approach in conjunction with Multi-Iterative Coupling (MIC) algorithm provides stability and accuracy for this type of problem.