Analytical and Numerical Studies of Seismic Fluid-Structure Interaction in Liquid-Filled Vessels

Published September 2, 2020

Graduate Students: Ching-Ching Yu and Faizan Ul Haq Mir

Principal Investigator: Andrew S. Whittaker

Project Completion Date: 12-31-21

Seismic design, qualification, and risk assessment of liquid-filled advanced nuclear reactors will rely on verified and validated numerical models for seismic fluid-structure interaction (FSI) analysis. Report MCEER-20-0003 verifies FSI numerical models for a cylindrical tank and submerged components using analytical solutions. The verified models of the tank are validated by comparing analysis results with test data generated in earthquake-simulator tests for a base-supported cylindrical tank.


Base-supported cylindrical tank filled with water.

Base-supported cylindrical tank filled with water

A liquid metal reactor includes a vessel, and internal components submerged in a liquid metal coolant. Earthquake shaking of this liquid (fluid)-filled reactor induces fluid-structure interaction (FSI) between the vessel, the submerged components, and the contained coolant. Seismic design, qualification, and risk assessment of the reactor must consider response due to FSI, the actual geometries and support conditions, and three-directional seismic inputs of a site-specific intensity, none of which can be accommodated using analytical solutions. Physical testing of reactor vessels and internal components for seismic qualification is also not feasible because of the large scales involved. These limitations on analytical solutions and physical testing leave numerical simulations as the only plausible pathway for seismic design and qualification of fluid-filled reactors. However, reliable numerical models for FSI analysis that are both verified and validated are not available at the time of this writing.


Numerical models can be verified by comparing predictions with analytical solutions and then validated using data from physical testing. Report MCEER-20-0003 performs 1) verification and validation studies on numerical models for rigid and flexible, cylindrical vessels (tanks), supported at either the base or the top (head); and 2) a verification study on numerical models for flexible, submerged internal components. Two solvers capable of predicting nonlinear fluid responses are used to perform seismic FSI analysis in LS-DYNA: Arbitrary-Lagrangian-Eulerian and Incompressible Computational Fluid Dynamics. Analytical solutions, both extracted from prior studies and developed in this report, are used for the verification. The prior analytical solutions are corrected as needed. The validation study uses test data generated from earthquake-simulator experiments for a base-supported cylindrical tank (see the above photo) performed at the University at Buffalo.

In general, the ALE models of tanks are verified and validated for calculating fluid pressures on the tank wall and reactions (shear force and moment) at the support, and the ICFD models are also verified and validated for calculating these responses, if wave action (i.e., the convective mode) is not significant. The ALE and ICFD models are not verified and validated for calculating wave heights. The ALE and ICFD models of submerged components are verified for calculating lateral frequencies.



The project herein was funded in part by the Advanced Research Projects Agency-Energy (ARPA-E), U.S. Department of Energy, under Award Number DE-AR0000978, and in part by TerraPower, Bellevue, WA and the U.S. Department of Energy under CRADA 14CR04.