Numerical simulation of fluid-structure interaction for elastic cylinders in axial flow

Abstract

When elastic cylinders are subjected to an axial flow, they will vibrate due to the loading imposed on the structure by the flow. This vibration is called axial-flow-induced vibration. In general, the amplitude of axial-flow-induced vibration is very small, about 10⁻³ ~ 10⁻² diameter of the cylinder, compared to that of cross-flow-induced vibration. Nevertheless, this so weak vibration can wear the fuel rods in nuclear industry and make the cladding so thin that the radioactive material may be released. Thus it is necessary in engineering to study this vibration. In this project, the numerical simulation is carried out to study the fluid-structure interaction for elastic cylinders subjected to axial flow. The fluid and structure solvers are coupled together by an explicit partitioned scheme. The CFD solver is FLUENT 12.0, in which the ALE N-S equations are numerical solved by finite volume method (FVM). The cylinders are regarded as Euler-Bernoulli beams and the dynamic equation is numerically solved by finite element method (FEM). The structure solver is integrated into the fluid solver by user-defined functions (UDF), which is provided by the fluid solver. The LES model is adopted to model the turbulence for the flow simulation. The fluid solver calculates the loading for the structure solver, while the latter calculates the displacements of the cylinders, which are utilized to update the mesh of fluid domain by the fluid solver. Firstly the dynamics of a single cylinder, which is subjected to axial flow and is limited to vibrate only in one plane, is studied. When the flow is laminar, the vibration of the cylinder is always damped by the flow for current dimensionless flow velocities and the damping increases with increasing the dimensionless flow velocity. For turbulent flow, when the dimensionless flow velocity is lower, the strong vibration of the cylinder is damped into weak vibration. However, the vibration becomes instable and the cylinder is eventually buckled if the dimensionless flow velocity is large enough. Secondly, the dynamics of a cylinder, however, which can be free to vibrate in any transverse directions in axial turbulent flow, is studied. The dynamics of the cylinder is similar to that when it is constrained to vibrate in one direction. However, the flutter instability is captured as well as the buckling instability. It is more appropriate to explain the simultaneous occurrence of the buckling and flutter instabilities by the nonlinear theory, in which the solution due to the flutter can be a bifurcation based on a buckling solution. The dynamics of two simple clusters consisting of respectively two and four cylinders is also studied. These structures are similar to the fuel assembly in pressurized water reactor (PWR). The cylinders are free to vibrate in any directions. At small dimensionless flow velocity, the damping of the flow on strong vibration is also captured. When the dimensionless flow velocity becomes large enough, the buckling instability can be captured. The flutter instability is not captured, due to the extreme distortion of the mesh of the fluid domain at higher dimensionless flow velocity. The current results are qualitatively consistent with the available experiments and theoretical analyses, and they could capture the features of fluid-structure interaction in detail. The numerical methods applied in this project can be used to predict the vibrations of the rods in nuclear industry, which should be helpful for the design of pressurized water reactor.