A numerical technique for the solution of the structural dynamics equations of motion is presented. The structural dynamics mass and momentum conservation equations are solved using a control volume technique which is secondorder accurate in space along with a dual time-step scheme that is second order accurate in time. The momentum conservation equation is written in terms of the Piola-Kirchoff stresses and the displacement velocity components. The stress tensor is related to the Lagrangian strain and displacement tensors using the St. Venant-Kirchoff constitutive relationship. Source terms are included to account for surface pressure and body forces. Verification of the structural dynamics solution procedure is presented for a two-dimensional vibrating cantilever beam. In addition, the structural dynamics solution procedure has been implemented into a general purpose two dimensional conjugate heat transfer solution procedure that uses a similar dual time-step control volume technique to solve the fluid mass, energy, and Navier-Stokes equations as well as the structural energy heat conduction equation. The resulting overall solution procedure allows for solutions to fluid/structure, fluid/thermal, or fluid/thermal/structure interaction problems. Verification of the multidisciplinary procedure is performed using a cylinder with a flexible solid protruding downstream that mimics a cylinder-flag configuration. The approach is a proof of concept for compressible flow with continuum based solids. The methods are currently being extended to 3D flow fields and solids.

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A high fidelity, fully coupled numerical technique for the simulation of airfoil and turbomachinery aeroelasticity configurations is presented. The unsteady structural and fluid dynamics equations are discretized by a control volume technique which is second order accurate in space along with a dual time-step scheme that is second order accurate in time. The momentum conservation equation for the solid is written in terms of the Piola-Kirchoff stresses and the displacement velocity components. The stress tensor is related to the Lagrangian strain and displacement tensors using the St. Venant-Kirchoff constitutive relationship. Source terms at the surface of the solid are included to account for surface pressure and body forces. Previous fluid-structure interaction studies of Turek’s cylinder flag and the AGARD 445.6 airfoil have provided confidence needed to accurately perform fluid structure interaction simulations in turbomachinery. In this study, a 1½ stage axial transonic turbine is simulated and results are validated with experimental data. Simulation results indicate that the inclusion of airfoil vibration leads to improved agreement with experimental unsteady surface pressures compared to simulations with fixed airfoils.

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