Platform Centered Reduction: a Process Capturing the Essentials for Blade-Damper Coupled Optimization

The purpose of this paper is to develop an attractive tool for designers in the initial design phase of the damping of turbomachinery blades through dry friction underplatform dampers. The paper shows how, to this purpose, certain reasonable simplifications are introduced in the procedure and in the model, leaving the customary full high fidelity computations to the final design verification analysis. The key simplifications here considered are: the blade neck is modelled with Euler beam finite elements (FE) to speed up the updating of its dimensions during the optimisation process; the contact forces exerted by the dampers on the blade platform are represented by the resultant forces and moments applied to a reference point on the platform, associated to its displacements and rotations; the airfoil, which, due to its complex shape, is considered fixed during the coupled optimization of the damper, is obtained from a full 3D FE model after a component mode synthesis reduction. It is shown that the process captures the essentials of the nonlinear dynamics of the blade-damper problem without sacrificing in any way the accuracy of the results. This hybrid model is then employed in the process where the domains of optimal matching between the damper and the blade is searched for by exploring the influence of blade neck thickness (flexibility) and damper mass. Such a purposely simplified process allows a clear identification of relationships between relevant blade features and response with a focus on fatigue life.

Design Space Exploration of Rotor Blades Accounting for Vibratory Responses by Indirect Emulation

Turbomachines are an integral part of society, with global trends demanding more efficient designs while staying within structural limits. Fan blade designs must be designed for both steady and vibratory structural responses. Design space exploration (DSE) of turbomachinery blades allows improved designs to be found. DSE requires samples of vibratory responses. Traditionally, analysis to obtain these samples is too computationally expensive for thorough DSE. This work develops a simplified analysis method based on Reynolds-Average Navier-Stokes (RANS) CFD and Harmonic Mode Superposition (HMS) FEA. This reduces the computational cost and allows for enough samples to create surrogate models. This work also develops a surrogate method which indirectly emulates the vibratory responses to accurately handle the large spikes in vibratory stress found throughout the design space. It was found that combining these methods allows for accurate emulation of a fan blade design space while accounting for vibratory stress. The surrogates with improved accuracy allow better designs to be found while ensuring that those designs meet structural requirements.

Coupled Mode Flutter Analysis of Turbomachinery Blades Using an Adaptation of the P-k Method

Current trends in turbomachinery design significantly reduce the mass ratio of structure to air, making them prone to flutter by aerodynamic coupling between mode shapes, also called coupled-mode flutter. The p-k method, which solves an aeroelastic eigenvalue problem for frequency and damping respectively excitation of the aerodynamically coupled system, was adapted for turbomachinery application using aerodynamic responses computed in the frequency domain. A two-dimensional test case is validated against time-marching fluid-structure coupled simulations for subsonic and transonic conditions. A span of mass ratios is investigated showing that the adapted p-k method is able to predict the transition between aeroelastically stable and unstable cascades depending on the mass ratio. Finally, the p-k method is applied to a low mass ratio fan showing that the flutter-free operating range is significantly reduced when aerodynamic coupling effects are taken into account.

Optimizing Piezoelectric Material Location and Size for Multiple-Mode Vibration Reduction of Turbomachinery Blades

Modern turbomachinery blades have extremely low inherent damping, which can lead to high transient vibrations and failure through high-cycle fatigue. Smart materials enable vibration reduction while meeting strict blade requirements such as weight and aerodynamic efficiency. In particular, piezoelectric-based vibration reduction offers the potential to reduce vibration semi-actively while simultaneously harvesting sufficient energy to power the implementation. The placement and the size of the piezoelectric material is critical to the vibration reduction capabilities of the system. Furthermore, the implementation should target multiple vibration modes. This study develops a procedure to optimize electromechanical coupling across multiple vibration modes for a representative turbomachinery blade with surface-mounted piezoelectric patches. Experimental validation demonstrates good coupling across three targeted modes with a single piezoelectric patch. Placing the piezoelectric material in regions of high signed strain energy for all targeted modes enables vibration reduction across all of the targeted modes.