3D Navier-Stokes fan blade computations

5.3.1 Unsteady Navier-Stokes response to harmonic motion. Pre­scribed harmonic motion Navier-Stokes simulations have been performed for a 3D wide chord fan. This fan is made up with 22 swept blades. The maxi­mum radius of the fan is about 0.9 m. A Navier-Stokes grid of moderate size has been built in order to run Spalart steady and unsteady computations. It is made up with 6 blocks, and its total number of nodes is 397044. The first grid layer thickness at the wall is about 5.e-06 m. A view of the grid and of its multi-block topology is given in the next figure.

A steady computation is initially per­formed for an upstream absolute Mach number of 0.5. The rotating speed of the compressor for this computation is 4066.4 RPM. 4000 iterations were run using the Spalart-Allmaras model at a CFL value of 5. The computation time was about 12 hours on a single Itanium2 900MHz pro­cessor. Here is shown the quadratic resid­ual convergence history of the conserva­tive variables for one block. Figure 6 Convergence history

The outlet boundary condition prescribes the value of the output pressure on the hub. For this computation, the mass fbw of the compressor is about 458 kg/s. A shock occurs near the tip, either on the suction side or on the pressure side. The maximum Mach number is about 1.5. Figure 7 shows the Mach contours on the suction and pressure sides.

Dynamic Navier-Stokes fluid – structure coupling. Navier-Stokes dy­namic fliid-structure coupling computa­tions have been performed for an ad­vanced wide-chord swept blade fan. The linear structural model was made of 10 modes. The numerical coupled scheme as described in a previous section has been used. The computation was performed on a 6 block grid gathering 372036 nodes. 320 physical iterations have been per­formed for a total simulated time of about 0.1 s. 100 dual time steps have been run at each physical time step, leading to a total computation CPU time of about 150 hours onItanium2. We present in Figs. 10 and 11 the time history of the generalized coordi­nates and that of the mechanical energy of the blade, for specific operating point and initial conditions.

The blade is clearly aeroelastically stable, which can be more precisely char­acterized through the processing of the generalized coordinates time histories, in order to extract frequencies and damping for this operating point.

4. Conclusion

A Navier-Stokes numerical tool has been developed for the computation of unsteady turbomachinery applications. An Arbitrary Lagrangian Eulerian formulation has been developed, and the dual time stepping acceleration tech­nique has been implemented in the 3D code. The basic scheme has also been modified in order to allow moving meshes computations. Static and dynamic fhid-structure coupling schemes have also been developed in the case of a modal structural model. Some results of the validation processes of the 2.5D

and 3D aeroelastic Navier-Stokes codes have been presented. An example of a dynamically coupled 3D Navier-Stokes Arid-structure computation has been given. We intend to go on with 3D developments in order to be able to per­form fully 3D Navier-Stokes unsteady turbomachinery computations for more complex configurations.

References

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