Fluid-Structure Interactions in a Tube Bundle Subject to Cross-Flow. Part A: Porous Medium Approach

The objective of this paper is to develop a Eulerian porous medium formulation to model the fluid-structure interactions of a tube bundle in a two-phase cross-flow. This is the first part of a two-part paper. Part A. deals with the model developed to account for the fluid-structure interactions. In Part B. (see Ref. 1) the current model will be extended to two-phase flows. Using volume averaging, we develop transport equations for the conservation of mass and momentum. In these equations the effects of the tubes on the flow are lumped into the porosity model. This porous variant of the Navier–Stokes equations greatly simplifies the computational model. First, the volume averaging process filters many details of the flow such as the geometry of the tubes and small-scale vortices. The resulting macroscopic model presents smoother variations so that coarser meshes may be used. Second, the fluid mesh and the tubes are independent. Therefore, fixed meshes may be used to simulate unsteady problems. The averaging process is described and the resulting equations for momentum and mass conservation are developed. The averaged equations are solved by a finite element method. Simulations are performed using an implicit and fully coupled formulation. The same high order time integration schemes are used for both the fluid and the structure equations. The code is verified by the method of manufactured solutions. The ability of the porous medium model to represent the two-way coupling is assessed by comparing its predictions to DNS predictions of laminar cross-flow interactions with a tube bundle. The proposed methodology is then applied to sample problems of practical interest.