Aeroelastic phenomena in turbomachinery are one of the most challenging problems to model using computational fluid dynamics (CFD) due to their inherent nonlinear nature, the difficulties in simulating fluid–structure interactions and the considerable computational requirements. Nonetheless, accurate modelling of self-sustained flow-induced vibrations, known as flutter, has proved to be crucial in assessing stability boundaries and extending the operative life of turbomachinery. Flutter avoidance and control is becoming more relevant in compressors and fans due to a well-established trend towards lightweight and thinner designs that enhance aerodynamic efficiency. In this paper, an overview of computational techniques adopted over the years is first presented. The principal methods for flutter modelling are then reviewed; a classification is made to distinguish between classical methods, where the fluid flow does not interact with the structure, and coupled methods, where this interaction is modelled. The most used coupling algorithms along with their benefits and drawbacks are then described. Finally, an insight is presented on model order reduction techniques applied to structure and aerodynamic calculations in turbomachinery flutter simulations, with the aim of reducing computational cost and permitting treatment of complex phenomena in a reasonable time.

Transonic compressors are widely used today in propulsion and industrial applications thanks to their higher specific work compared to subsonic. In this work, the aerodynamic optimization of a two-dimensional Computational Fluid Dynamics (CFD) model of the transonic cascade ARL-SL19 is described. The validated computational model is used for a multi-objective optimization of the cascade at three different inlet Mach numbers using a genetic algorithm and an artificial neural network, with the aim of reducing total pressure loss and increasing maximum pressure ratio. Finally, the optimized shapes on the Pareto fronts are investigated, analyzing mechanisms responsible for loss reduction and enhanced compression. Profiles having the lowest losses have flatter camberlines and reduced acceleration of flow on the suction side, while geometries achieving the highest pressure ratio values have a more cambered shape with a concave suction side.

The accurate prediction of the aeroelastic behavior of turbomachinery for aircraft propulsion poses a difficult yet fundamental challenge, since modern aircraft engines tend to adopt increasingly slender blades to achieve a higher aerodynamic efficiency, incurring an increased aeroelastic interaction as a drawback. In the present work, we present a reduced order model for flutter prediction in axial compressors. The model exploits the aerodynamic influence coefficients technique with the adoption of a broadband frequency signal to compute the aerodynamic damping for multiple reduced frequencies using a single training simulation. The normalized aerodynamic work is computed for a single oscillation mode at three different vibration frequencies, comparing the outputs of aerodynamic input/output models trained with a chirp signal to those from single-frequency harmonic simulations. The results demonstrate the ability of the adopted model to accurately and efficiently reproduce the aerodynamic damping at multiple frequencies and arbitrary nodal diameters with a single simulation.

As aircraft engines are expected to achieve increasingly stricter goals in terms of efficiency and reliability, an accurate design of turbomachinery blades for aeronautic propulsion is fundamental. To fulfil this task, in the present work a multi-point and multi-objective optimization of a transonic compressor cascade is performed, in order to maximize pressure ratio and efficiency at three inlet Mach numbers. A commercial CFD code is employed to simulate the flow around the blades at steady conditions on a 2-d structured mesh and to compute the objective functions. A grid validation is performed by testing three different refinement levels against experimental data. A first iterative algorithm is used to identify and impose unique incidence conditions at the inflow, and a second algorithm to search for the maximum achievable pressure ratio while respecting the inlet conditions. An S-type transonic cascade, the NASA ARL-SL19, is used as baseline geometry: only the fore section of the camberline is parametrized using a Bezier curve, using four y-coordinates and one x-coordinate of the Bezier polygon as decision variables. The thickness distribution of the baseline profile is imposed to the generated camberlines to create new geometries. The continuity of the first derivative of the camberline between the parametrized fore section and the fixed rear section is enforced to preserve aerodynamic efficiency. Three optimizations are conducted, namely at inlet Mach numbers 1.2, 1.1 and 0.99, using a heuristic optimization algorithm, the NSGA-II. 20 profiles are evolved from a random pool for 10 generations at each condition, searching for the Pareto fronts of both objective functions. Eventually, an increase in pressure ratio is achieved, as well as a substantial improvement in efficiency at each operative point. The optimized profiles are compared to the baseline geometry, highlighting the dominant effect of the forepart of the chord in the generation of losses, as well as a strong negative correlation between the camber angle near the leading edge and the inflow angle in profiles achieving the highest efficiency. The leading edge of profiles on the Pareto front is progressively shifted downwards as the Mach number decreases, leading to more cambered shapes, while profiles with lowest losses retain the S-shape at Mach 1.2. The results show the ability of the employed optimization algorithm to consistently improve the performance parameters of a transonic cascade with a reduced number of simulations. The small and continuous camber bend with the inlet Mach number of optimized profiles suggest the opportunity of an active geometry control of profile shapes, as to achieve the best performance in a range of operative conditions.