Computing Fluid Structure Interaction Coupling Time Spectral Method (TSM) and Harmonic Balance Method (HBM)

Abstract

This paper deals with fluid-structure interactions (FSI), involving a blade profile, submitted to different sources of excitations, as if it were included in a real engine. Two forces of excitation will be considered on the NACA 64A010 airfoil, described in : an external force, due to a forced rotation motion of the blade, and an aerodynamic force, induced by fluid flow around the structure. By using the Harmonic Balance Method, the airfoil’s motion equation becomes an algebraic problem. Then, this system is solved for each frequency of a chosen range. Therefore, the fluid effect on the translation motion of the profile is studied. To compute the time periodic aerodynamic field, the Time Spectral Method, implemented in the Onera’s elsA solver, is used for a fast and efficient resolution. This method relies on a time-integration scheme that turns the resolution of the turbulent Navier-Stokes problem into the resolution of several coupled steady state problems computed at different instants of the time period of the movement. The Theodorsen approach with several hypothesis exposed in allows an analytic estimation of the unsteady lift effort. The two approaches are compared for an imposed motion. In order to predict the dynamic behavior of the system, a fully coupled numerical methodology is developed. For each frequency and at each iteration, TSM supplies the flow field which is used by HBM as a nonlinear excitation on the structure to computate a periodic response and conversely, HBM supplies the new deformed mesh used by TSM to compute the flow field. This strategy has the advantage that all computations take place in the spectral domain, allowing thus to find the steady-state behavior of the fluid and the structure without computing any transient state. The analysis provides the Frequency Forced Response. Some frequencies in the range corresponding to a contribution change between structure and fluid damping are precisely highlighted.

Development of a Fully-Coupled Harmonic Balance Method and a Refined Energy Method for the Computation of Flutter-Induced Limit Cycle Oscillations of Bladed Disks with Nonlinear Friction Contacts

“…(d) Assuming symmetric behavior within the blade row, the computational domains can be reduced to a reference sector (only one blade or one passage) with appropriate cyclic symmetry boundary conditions. First attempts to co-simulate cascade flutter in the time or frequency domain are limited to linear [31][32][33][34] or single-degree-of-freedom nonlinear [35,36] structural models. As described above, the current approach to design against flutter relies on linear vibration theory.…”