A fluid structure interaction framework for digital twins in turbomachinery

Fluid Structure Interaction (FSI) is a class of multiphysics problems that couple the analysis of fluid dynamics of flows around solid objects and the structural dynamics of the same solid that interacts with the flow around it. By solving an FSI problem, is possible to obtain information about both the fluid and solid phases, as a function of their complex interactions, exchanges of forces, changes in shape, induced dynamics. This class of problem can be recognized in a large number of phenomena in nature, and also in the human technologies. Recently, following the constant effort to push forward the performances of the existing energy conversion technologies, FSI has been applied to several classes of rotating fluid machines: wind turbines, tidal turbines, air turbines, fans can all be observed from the FSI perspective when the designer is interested into the optimization and improvement of a device that, for different reasons (extremely large rotor radius, flexible blades, passive adaptive appendices or blades, thin structures) is expressing a non negligible interaction between the structure and the fluid flow. So far, the FSI problem for complex geometries and flows such the ones characterizing internal and external flows in turbomachinery, was solved numerically using computational FSI models and algorithms, that are designed to couple the approximate solution of the Navier-Stokes (NS) equations with the elastodynamics equations. At the same time, the growing interest in Cyber-Physical Systems (CPS) and Digital Twin (DT) technologies from the turbomachinery producers is explained by the numerous benefits that would occur adopting those technologies: prediction capabilities, design, testing and monitoring, in a real time digital environment would cut by a significative amount costs and time consumption at multiple stages of the products lifetime. The attempt to build a DT (or in general, a CPS) able to describe some of the FSI phenomena in turbomachinery represents a challenging task, yet extremely interesting and promising. Among the several technical obstacles that a DT (or a CPS in general) would face when demanded to describe the FSI of a rotating fluid machinery there's the evident mismatch of the time scales of the time consuming FSI numerical simulations, and the real time functioning required by the DT to process the input signals and to give an adequate output with the least possible delay. This obstacle can be possibly overcome by decoupling the slow but high fidelity simulations and the data usage from the DT: to achieve this, a database that collects FSI data can be built for a specific set of problems, and a Machine Learning (ML) algorithm might be used to build a Reduced Order Model (ROM) that would constitute the virtual core of the DT. A DT built on top of a ROM should be able to obtain results comparable to the ones from a canonical numerical simulation in a fraction of the time required by the simulation (orders of magnitudes). The shortcoming of this approach, aside of the complexity of the entire system, and the technical difficulties to build a suitable database and a reliable ROM, would obviously be the lack of generalization: such ROM (and DT) would be appplicable only to the specific subset of conditions that built the original database, possibly accepting only minor deviations. In spite of this shortcoming, from a manifacturer perspective this issue would be minor: the lack of generalization can still be compensated for by the production in series of the device, and the technology could still fit the scale economy. In an attempt to follow the research path that would eventually lead to a DT with FSI capabilities in turbomachinery, in this dissertation is introduced the first fundamental block of this roadmap, on top of which the subsequent components will be built: FEMpar, a in-house developed software for FSI analysis using Finite Elements Method (FEM), is presented together with a description of the numerical models implemented to solve the NS equations, the nonlinear structural dynamics equations and the moving mesh problem. Along with the presentation of the software tool and its main components, several applications of FEMpar to CFD-FSI analysis in turbomachinery are showcased as well, to highlight the potential and relevance of FSI analysis in those devices. The proposed cases were selected to highlight different features and benefits to adopt FSI at the design and testing stage of a rotating fluid machinery: the flow around fans with large diameters, extreme aspect ratio, or made with flexible materials is simulated to observe the interaction of thin structures immersed in an unsteady flow; the possible adoption of low stiffness materials to design passive adaptive blade, and the design of specific constraints that would allow the passive morphing of the blades up to the desired configurations, are explored for a reversible axial fan and a Wells turbine (both devices characterized by quick and impulsive changes in the flow direction).