Cylinder-lamina system fluid–structure interaction problem solved with an original OpenFOAM code☆
Introduction
Fluid–structure interaction (FSI) problems can be defined as the interaction between a deformable structure and a surrounding fluid. The main fields of interest of Fluid Structure Interaction regards marine [1], [2], [3], aeronautical and aerospace [4], [5], biomedical [6], [7] and energy engineering [8], [9]. The resolution of the problem involves not only the calculation of the velocity and pressure fields in a fluid but also stresses and deformations in a solid material moving within the fluid. In these cases, a purely structural or purely fluid-dynamic analysis may be insufficient or not accurate enough. Both phenomena must be considered simultaneously. The structural displacements and deformations change the fluid motion field, which will load the structure differently in the next moment. Thus, solving this challenging multi-physics phenomenon requires numerical analyses. In that regard, an improvement of the already published partitioned solver, ModsFsiFoam [10], has been reached, to study more complex cases.
ModsFsiFoam is a solver developed using a partitioned approach. As such, it makes it possible to solve the two physical fields exploiting for each one its own time, geometry and solving equations discretisation, and different numerical schemes [11]. Although a monolithic approach is more accurate [12], a partitioned approach is more versatile. In fact, through the latter approach, it is possible to consider different methods of obtaining the required fields. In the specific case of ModsFsiFoam, this strategy has allowed the use of two different numerical methods to solve the fluid-dynamic problem and the structural problem. Whereas the Navier–Stokes equations have been discretised through the Finite Volume Method (FVM), which is by far the most widely used method for fluid-dynamics and gas-dynamics problems, the modal superposition method has been used to research in a computationally less onerous way the structural displacements field, algorithm which provides a certain solution from the structural mechanics’ theory.
Moreover, in the partitioned approach two resolution schemes should be developed: the weakly coupled scheme or the strongly coupled scheme. The first scheme provides only one solution of either field, sequentially [13]. Its implementation is easier; on the other hand, it is subject to instability. In the strong coupling, the convergence of the variables at the interface is required. Thus, in every time step, it is necessary to solve both the solid and the fluid domain equations several times, to reach a predetermined divergence value.
Implemented in OpenFOAM, a development environment consisting of libraries and applications for Linux distributions, written in the C++ language, ModsFsiFoam has already been applied with satisfactory results to a case of weak coupling found in literature, in which airflow is introduced in axial direction [14]. A good correspondence between experimental values and numerical results of the sinusoidal trend around an equilibrium position of the free end of an inverted flag, modeled as a flexible lamina, clamped to the wall of a wind tunnel, has been shown.
ModsFsiFoam workflow and its solver code have been presented in detail, step by step, in the previous work [10].
In this paper, a further solver improvement in terms of coupling nature is presented. In fact, in the present work ModsFsiFoam solver outputs are compared with a system the results of which are known for both fluid-dynamics and structural fields, in terms of characteristic time-dependent quantities and corresponding plots [15], [16], [17], [18]. The FSI system is made of a flow able, in the laminar regime, to deform the elastic compressible polypropylene structure.
Section snippets
Solid-dynamics theoretical background
The characteristics of a system influence its response to given perturbations. To determine the response of such a system to these perturbations, i.e. for the differential equations of motion resolution, it is of fundamental importance whether the system is linear or non-linear. In particular, in a linear system, the response is directly proportional to the forces; if this is not the case, the system is non-linear. In a linear system, the solution research can be simplified by exploiting the
Hron-Turek benchmark application
To evaluate the effectiveness of the solver, ModsFsiFoam has been applied on a typical fluid–structure interaction case. The configuration consists of a laminar incompressible channel flow around a solid structure with an elastic part which results in self-induced oscillations. In particular, the domain is based on a 2D version of the benchmark above-mentioned. The circle center is located in a position of 0.2 m from the left wall and 0.2 m from the lower wall. Its radius is 0.05 m. The elastic
Conclusions
In this paper, a further ModsFsiFoam solver improvement in terms of its coupling nature is presented. This upgrade has made it suitable for application to more complex cases, in particular strong couplings where the interaction influence is greater for both solid and fluid domains.
In this work, solver outputs are compared with an axially loaded cylinder-lamina system the numerical results of which are known for both fluid-dynamics and structural fields, in terms of characteristic time-dependent
Declaration of Competing Interest
The authors report no declarations of interest.
Acknowledgment
This work has been supported by the Italian Ministry of Education, University and Research under PRIN grant no. 20154EHYW9“Combined numerical and experimental methodology for fluid structure interaction in free surface flows under impulsive loading”, with Prof. C. Biscarini as principal investigator.
Chiara Stefanini is a Ph.D. student in “Engineering for Energy and Environment”, Tuscia University, under the supervision of Prof. Pierluigi Fanelli. Her research is centered on the study of fluid–structure interaction (FSI) problems for deformable bodies. She earned the Master's Degree in Mechanical Engineering with a thesis focused on the development of new C++ codes, for OpenFOAM open-source software, aimed at solving FSI problems.
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Chiara Stefanini is a Ph.D. student in “Engineering for Energy and Environment”, Tuscia University, under the supervision of Prof. Pierluigi Fanelli. Her research is centered on the study of fluid–structure interaction (FSI) problems for deformable bodies. She earned the Master's Degree in Mechanical Engineering with a thesis focused on the development of new C++ codes, for OpenFOAM open-source software, aimed at solving FSI problems.
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The code (and data) in this article has been certified as Reproducible by Code Ocean: (https://codeocean.com/). More information on the Reproducibility Badge Initiative is available at https://www.elsevier.com/physical-sciences-and-engineering/computer-science/journals.