Study on Prediction Model of Transverse Fluidelastic Instability for Normal Triangular Tube Bundle Based on Quasi-steady Theory

Lead-bismuth eutectic (LBE) fast reactor tube bundles are highly susceptible to transverse fluidelastic instability (FEI) under local cross-flow, which is induced when the fluid excitation energy exceeds the system’s damping dissipation. Full two-way fluid-structure interaction calculations incur exorbitant computational costs, while traditional theoretical models highly depend on experimental parameters and are mostly based on conventional water media, failing to fully consider the special physical properties of heavy liquid metals. To address these limitations, this paper proposes an efficient hybrid prediction model combining computational fluid dynamics (CFD) and a modified quasi-steady theory. Firstly, the semi-rigid method was introduced in the theoretical modeling. To account for the tremendous fluid inertia caused by the high density of LBE and the convective time lag within the tube bundles, a fluid added mass correction term and a time delay factor were strictly introduced into the traditional vibration governing equations. Secondly, the high-resolution SST-SAS turbulence model combined with truncated half-tube boundaries was employed to finely simulate the three-dimensional transient flow field of the normal triangular tube bundle. Based on accurately capturing the non-linear vortex shedding characteristics, the initial time-averaged lift and drag coefficients of the central tube were extracted with high fidelity, and their local spatial derivatives were obtained through fitting. Finally, the extracted fluid force parameters were substituted into the modified governing equations, and the analytical solution of the system’s critical instability boundaries under two degrees of freedom was achieved by separating the real and imaginary parts of the purely imaginary characteristic equation. The results indicate that the instability boundaries predicted by this hybrid model are in high agreement with classical experimental trends. The enormous fluid inertia of LBE makes the system highly prone to falling into the high-risk region of extremely low mass-damping parameters (MDP<10). Within this damping-controlled region, the large inertia exacerbates the convective time lag effect, significantly raising the instability flow velocity threshold. In the mechanistic analysis, adopting a time delay coefficient of \mu =2.0 can more accurately characterize the long-term memory effect of fluid dynamics, thereby achieving the best prediction accuracy in the medium-to-high damping region. In engineering applications, given that LBE fast reactors mostly operate under extremely low damping conditions, it is recommended to adopt \mu =1.0 based on conservative design principles to deduce the safety lower bound. This method effectively overcomes the limitations of high computational costs in bidirectional coupling and the reliance on experiments in traditional models, providing theoretical support for the vibration resistance assessment of lead-bismuth fast reactor tube bundles.