Fluid–Structure Interaction Using a Modal Approach

Abstract

A new method for fluid‐structure interaction (FSI) predictions is here introduced, based on a reduced-order model (ROM) for the structure, described by its mode shapes and natural frequencies. A linear structure is assumed as well as Rayleigh damping. A two-way coupling between the fluid and the structure is ensured by a loosely coupling staggered approach: the aerodynamic loads computed by the flow solver are used to determine the deformations from the modal equations, which are sent back to the flow solver. The method is first applied to a clamped beam oscillating under the effect of von Karman vortices. The results are compared to a full-order model. Then a flutter application is considered on the AGARD wing 445.6. Finally, the modal approach is applied to the aeroelastic behavior of an axial compressor stage. The influence of passing rotor blade wakes on the downstream stator blades is investigated.

A Review of Computational Methods and Reduced Order Models for Flutter Prediction in Turbomachinery

“…Another parameter is the accuracy in assessing fluid-structure equilibrium at each physical timestep in time-marching simulations. In the works by Sayma [34], Sadeghi [31], Debrabandere [35], Zheng [36] and Li [37], the eigenmodes were computed using constant or Rayleigh structural damping model, and the domain was reduced to one or two passages to contain the computational effort, with a limitation on the explorable IBPA range as a payoff. Coupled simulations showed that the normal 'in-vacuum' eigenmodes can be significantly different from the aeroelastic mode, especially at low mass ratios, leading to inaccurate results when assumed modes and the energy method are employed, as evidenced in Figure 7.…”

“…Furthermore, a nonlinear fluid-structure interaction can lead to the oscillation of blades around a displaced position, with two different harmonics and a pattern of alternated chocked and unchocked flows in neighbouring passages, as evidenced by Sadeghi [31]. Fluid-structure coupling also permits the simulation of a forced response [35]; the influence of the passing rotor on stator blades is captured, and the Fourier transformation of induced vibrations showed that they are more related to the natural stator frequencies than to the rotor passing frequency. Various works adopted multiple mode superposition in coupled simulations, but some evidence suggested that the influence of modes next to the first is often negligible.…”

Aerodynamic Damping Prediction for Turbomachinery Based on Fluid-Structure Interaction with Modal Excitation

“…Generally, the numerical damping is so small that it can be neglected, and the total damping with the Rayleigh damping constants of α = 0, β = 0 are considered to be mainly due to aerodynamics. Figure 17 shows the aerodynamic damping values which are calculated according to Equation (14) with in accordance with the Rayleigh damping constants α = 0, β = 6 × 10 −6 and α = 0, β = 0 for the first bending modal excitation, respectively. As shown in Figure 17, these results basically conform to the predictions.…”

“…Zheng and Yang [13] proposed a time-domain coupled fluid-structure method and applied it to the flutter analysis of Rotor 67. Debrabandere et al [14] and Zhang et al [15] adopted a two-way fluid-structure coupled method for aeroelastic analysis of a transonic axial compressor. The results showed that the blade vibration frequency deviated from the natural frequency due to the coupled influence.…”

A modal approach for coupled fluid structure computations of wing flutter

“…16 Hall and coworkers [17][18][19] proposed several ROM for CFD based on the Proper Orthogonal Decomposition approach. Debrabandere et al 20 introduced the modal method to compute the wing vibration in coupled fluid structure computations. Thus, the computing time of the flow can be reduced using the ROM for CFD, and the computing time of the wing vibration can be reduced using the modal method.…”