PSI - Issue 24

Pierluigi Fanelli et al. / Procedia Structural Integrity 24 (2019) 939–948 Author name / Structural Integrity Procedia 00 (2019) 000–000

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influence the fluid motion field. FSI problems have a key-role in several engineering applications; nonetheless, a comprehensive study of these prob lems is a treat due to their strong non-linearity and multidisciplinarity. The main fields of interest of Fluid Structure Interaction regards marine (Ma et al. (2017)), aeronautical and aerospace (Seddon and Moatamedi (2006), Patel et al. (2014), Groth et al. (2019)), biomedical (Gerbeau et al. (2005), Kanyanta et al. (2007), Friedman et al. (2010), Lee et al. (2012)) and energy engineering (Singh et al. (2012), Campbell and Paterson (2011), Korobenko et al. (2013), Yoon et al. (2009), Falcucci et al. (2011)). Moreover, a wide range of laboratory tests allows a deep analysis of FSI sys tems in the above-mentioned engineering fields (Steen and V (1987), Todd (1951), Gad-el Hak (1987), Ringsberg et al. (2017), Faltinsen and Timokha (2010)). During these tests, data acquisition requires the use of direct measurements suited sensors and of non-invasive techniques, such as image analysis techniques (PIV and PIBV) (Thielicke and Stamhuis (2014), Facci et al. (2015)). Nevertheless, in great part of FSI problems an analytical solution for the model equations cannot be reached, whereas laboratory experiments are limited in scope; thus, numerical simulations are required for the investigation of the fun damental physics related to the complex interaction between fluids and solids. The numerical procedures for FSI problems solution may be broadly classified into two approaches: the monolithic approach and the partitioned approach (Hou et al. (2012a)). In monolithic approach, the fluid and structure dynamics are treated in a single mathematical framework, with the aim of forming a single system of equations for the whole problem, which is simultaneously solved through a unified algorithm. In the solution procedure interfacial conditions are implicit. This kind of approach can potentially allows the reach of a better accuracy, but it may require more resources and expertise in development like a specialized code. On the other hand, a partitioned approach deals with fluid and structure as two di ff erent computational fields, which solutions are obtained separately with their respective mesh discretization and numerical algorithm. The interface con ditions are applied with the aim of communicating explicitly informations between the fluid and structure solutions. A motivation for this later approach is to integrate available disciplinary (i.e., fluid and structural) algorithms and to save code development time by exploiting advantages of the legacy codes or numerical validated algorithms, used for complex fluid or structural problems solution. As a consequence, an e ff ective partitioned method can solve a FSI problem with complex fluid and structural physics. A Partitioned approach, referring to with the structural solution, can be based on numerical methods. In past years, the Finite Element Method (FEM) has been the most popular method for solid body stress analysis applications. Otherwise, the Finite Volume Method (FVM) has been established as a very e ff ective way for fluid flow problems solution. It is known that solid body mechanics and fluid mechanics share the same governing equations, and di ff er in constitutive relations only, has meant that, in the last years, many attempts in applying FEM to thermofluidody namic analyses and FVM to structural analyses have been taken place. Although they are inherently similar, these two methods have both advantages and disadvantages, which make them better suited for di ff erent classes of problems. Nevertheless, the situation is not as clear-cut. In fact, it is not known in advance whether the block solution of the FEM gives an advantage over the FVM segregated solver even for a simple linear elastic problem. This is a question of the trade-o ff between the high expense of the direct solver for a large matrix and the cheaper iterative solvers with the necessary iteration over the explicit cross-component coupling. Although the FV discretization may be thought to be less suited than the FEM in linear elasticity, the first mentioned method is inherently good in treating complicated, coupled and non-linear di ff erential equations, typical of fluid flows. By analogy, as the more complex mathematical model becomes (e.g. in the case of FSI problems), the the more interesting is FVM as an alternative to the FEM (Jasak and Weller (2000)). In addition, in the partitioned approach, still in relation to structural solution, it is possible to consider other analyses to obtain structural displacement and strain fields (Heil et al. (2008), Hou et al. (2012b)). The partitioned approach is the numerical procedure used to build the here-described FSI solver in OpenFOAM, an opensource software developed for Linux distributions and released under a GPL license with the C ++ source code. It has allowed the application of two di ff erent methods for fluid and solid solutions. It has to be considered that in Open FOAM environment several FSI solvers, such as icoFsiElasticNonLinULSolidFoam that belongs to SolidMechanics folder and based on the Finite Volume Method (FVM) for both fluid and structural solutions, can be found. Since satisfactory results have not been obtained in previous works, it has been chosen to build the original here-described code that, in relation to the structural solution, replaces the FVM with a theoretical approach based on modal super-