A hybrid Lagrangian–Eulerian flow solver applied to elastically mounted cylinders in tandem arrangement

Abstract

The fluid–structure interaction of cylinders in tandem arrangement is used as validation basis of a multi-domain Lagrangian–Eulerian hybrid flow solver. The solver is built on a Lagrangian approximation of the entire flow-field using particles, in which grid based Eulerian flow solutions are overlaid, one for every solid body. The Eulerian grids are body fitted but of limited width and may overlap in cases of close proximity of the bodies. The Eulerian and Lagrangian solutions are strongly (implicitly) interconnected in two ways: The Lagrangian solution provides the conditions over the outer boundaries of the Eulerian grids, while the Eulerian solutions update the flow properties of the particles that are within their own domains. Also, implicit is the coupling of the solver with the structural dynamics in case the cylinders are elastically supported. The Lagrangian solver is based on the density–dilatation–vorticity–pressure formulation and makes use of the Particle Mesh method to obtain the flow velocity field while the Eulerian one on the density–velocity–pressure formulation. The hybrid solver is first validated in the case of an isolated rigid cylinder at Re=100. Then the case of a single elastically mounted cylinder at Re=200 is considered, followed by the case of two cylinders in tandem arrangement that are either rigid or elastically mounted. Good agreement with results produced with spectral element and immersed boundary methods is found indicating the capabilities of the hybrid predictions. Also the flexibility of the method in handling complex multi-body fluid–structure interaction problems is demonstrated by allowing grid-overlapping.