Solving U-RANS k-ω SST Equations and Post-Processing Motion Independent Fluid Forces in a Tube Bundle

Abstract

The computation of the dynamic response of a structure subjected to a fluid flow requires the knowledge of the fluid forces acting on the structure. At least three classes of these forces can be distinguished: - fluid-elastic forces due to the coupling between fluid flow and structure displacement; - random forces due to the turbulent nature of the flow. In cases of two-phase fluid configurations, such as those occurring in steam generators of nuclear power plants, forces due to the two-phase nature of the fluid are also assumed to be part of this type of excitations; - fluid forces due to coherent structures in the flow, such as Von Karman vortex-streets downstream of a single tube in cross-flow. In this paper we focus on the numerical study of this last class of excitations. We propose here a method to compute the dimensionless spectrum of those forces as a function of a scaled parameter called “reduced frequency” [1]. We perform CFD (Computational Fluid Dynamics) calculations with the EDF (Electricite´ De France) CFD software Code_Saturne® [2], using a U-RANS (Unsteady-Reynolds Averaged Navier Stokes) approach, and a k-ω SST (Shear Stress Transport) model. Tube wall fluid stresses are derived and post-processed into spectra. This numerical methodology allows one to distinguish the drag from the lift component in overall fluid force. The paper includes three parts: - In the first part, the numerical method of our study is presented: the k-ω SST model developed to solve U-RANS equations [2] is described. We then detail the post-processing used to compute the dimensionless spectrum starting from fluid stresses at tube walls. - In the second part, k-ω SST model’s implementation is validated on the case of a single rigid tube in an upwards cross-flow of water. CFD results are compared to experimental measurements [3]. - Eventually the study of a 2D rigid tube bundle subjected to a two-phase cross-flow modeled by an equivalent single phase flow is presented. A sensitivity analysis is carried out to study the influence of bundle’s bulk and the Reynolds number. Wall pressures are post-processed to derive the dimensionless spectrum associated with fluid forces due to coherent structures.