Numerical Modelling of Fluid Structure Interaction for Nuclear Thermal Hydraulics

Abstract

The fluid flow in tube bundle heat exchangers is of importance to the power generating sector, with the goal of optimizing heat transfer while reducing friction and vibrations. In nuclear power reactors, lower tubes encounter mixed flow directions, including chaotic jet impingement from entering baffle jets. Due to interaction between fluid and structure system, and under certain flow conditions, vortex-induced vibration (𝑉𝐼𝑉) phenomenon occurs. In this research numerical simulations were conducted using 𝑅𝐴𝑁𝑆-based models, followed by Large Eddy Simulations (𝐿𝐸𝑆) to investigate this phenomenon. The behavior of the coupled flow-structure interaction system was analyzed over a wide range of the reduced velocities (𝑈𝑟) including the lock-in range (i.e., where body motion and flow unsteadiness are synchronized resulting in high vibration amplitude). The simulation results were evaluated in terms of drag coefficient, lift coefficient, Strouhal number, displacement, vorticity, flow streamlines, pressure and velocity contours. This research's findings are intended to improve the design of pressure vessels that are susceptible to flow-induced vibrations by minimizing the effects of baffle jetting. First simulations of flow around single cylinders were performed to investigate VIV of isolated freely vibrating cylinders. The results show good agreement with the reported data in literature. The study was then extended to systematically explore the accuracy of computational fluid dynamics (𝐶𝐹𝐷) simulations for VIV, focusing on the influence of dimensional modeling, turbulence approaches, and geometric parameters. By comparing two-dimensional (2𝐷) and three-dimensional (3𝐷) simulations using the Shear Stress Transport (𝑆𝑆𝑇) turbulence model, this analysis highlights the computational advantages of 2D modeling while identifying its limitations in capturing critical transition dynamics such as boundary layer detachment and super upper-branch behaviors. A comprehensive evaluation of Reynolds-averaged Navier-Stokes (𝑅𝐴𝑁𝑆) turbulence models—including 𝑘 − 𝜀, Spalart-Allmaras (𝑆 − 𝐴), and 𝑆𝑆𝑇 𝑘 − 𝜔—against large eddy simulation (𝐿𝐸𝑆) underscores the superior capability of LES in resolving unsteady and chaotic flow structures, while 𝑆𝑆𝑇 𝑘 − 𝜔 provides a balance between accuracy and computational efficiency, but still underestimates upper-branch characteristics. The study also examines the impact of cylinder diameter on oscillation characteristics, revealing that larger cylinders have extended lower-branch range before entering unsynchronized-branch, whereas smaller cylinders experience dampened oscillations due to dual-frequency interactions. Results are detailed through key performance metrics, including drag coefficient (𝐶𝑑), lift coefficient (𝐶𝑙), Strouhal number (𝑆𝑡), vibrational amplitudes (𝐴𝑦/𝐷,𝐴𝑥/𝐷), frequency analysis, and vortex shedding patterns. The study is then extended to investigate VIV in tandem cylinders, modeling basic configurations relevant to reactor fuel rods. It examines how cylinder spacing ratios (𝑆𝑥/𝐷 = 2,3,5,9) and (Ur = 2 to 14) influence vibrational and vortex dynamics. The results highlight distinct behaviors between upstream and downstream cylinders in tandem configurations. At closer spacings, the upstream cylinder shows pronounced vibrations due to strong wake interference, while the downstream cylinder experiences amplified responses influenced by the disturbed flow. As the spacing increases, interference effects diminish, leading to upstream cylinder responses resembling those of a single isolated cylinder. However, downstream vibrations remain significant, reflecting ongoing wake interactions. The study also reveals that vortex shedding patterns transition from irregular and chaotic at closer spacing to more stable and periodic at greater distances. This evolution is shaped by the interaction between flow velocity and the spacing between cylinders. Lift forces acting on the cylinders are strongly influenced by these interactions, with the downstream cylinder generally experiencing larger fluctuations. Moreover, further investigation was performed to suppress the vibrational amplitude through nonlinear energy sink (𝑁𝐸𝑆) system under a variety of 𝑈𝑟. Over 3,000 scenarios were examined to assess the impact of 𝑁𝐸𝑆 properties—mass ratio (𝛽 = 0.01 − 0.5), spring ratio (𝛾 = 0.01−2.0), and damping ratio (𝜉 = 0.01− 2.0)—on the vibrational response. Vibrational contour maps were developed from the CFD data at various ranges of 𝑈𝑟,𝛽,𝛾,𝑎𝑛𝑑 𝜉. Finding indicates that the process of tuning the 𝑁𝐸𝑆 parameters (𝛽,𝛾,𝑎𝑛𝑑 𝜉) can either diminish vibrational amplitudes (𝐴𝑦/𝐷) or, if not carefully optimized, it can amplify them. With optimal 𝑁𝐸𝑆 parameter tuning, an amplitude reduction of 94% is possible. Furthermore, Sobol sensitivity analysis was performed, and it indicated that while 𝐴𝑦/𝐷 highly depends on 𝑈𝑟, proper tuning of the 𝛽 in combination with 𝛾 can be critical, especially in regimes where parameter interactions become significant. While global optimization is challenging, it is recommended that the optimized 𝑁𝐸𝑆 parameters for a lock-in region differ from those for the lower-branch vibration region. These findings significantly advance nuclear thermal hydraulics by improving the prediction and control of VIV for reactor safety and efficiency. The turbulence model evaluation highlights the necessity of LES for accurate VIV prediction in the lock-in region. Tandem cylinder simulations emphasize the heightened vulnerability of downstream cylinders due to wake interference, underscoring the need for refined design strategies. Lastly, the NES-based suppression study demonstrates its potential as a passive control method to mitigate VIV, enhancing the longevity and reliability of critical reactor components. This CFD study improves our understanding of FSI responses in nuclear reactors, which affects fuel assembly thermal-hydraulic performance and mechanical stability in operating conditions.

Date of Award	5 May 2025
Original language	American English
Supervisor	Imran Afgan (Supervisor)