Modeling of tuned liquid dampers with paddles: Hydrodynamic effects and estimation

Abstract

The hydrodynamic coefficients of internal damping devices, including drag coefficient C_d and inertia coefficient C_m, are crucial parameters affecting the damping and frequency design of the tuned liquid damper (TLD). However, studies on their variation laws are few. This paper presents an approach for estimating paddle hydrodynamic coefficients under harmonic excitation. An equivalent mechanical model (EMM) of the TLD, incorporating C_d and C_m of the paddles, is developed using potential flow theory. The computational fluid dynamics (CFD) method is employed to obtain the TLD’s steady-state response. The discrepancy between the EMM and CFD model responses is then utilized as the objective function and optimized using an improved Archimedes algorithm to determine C_d and C_m. On the basis of the above, a comprehensive parameter analysis is conducted for the TLD with paddles, and the effects of paddle dimension, water depth, and harmonic excitation amplitude on C_d and C_m are examined. Two new dimensionless parameters are introduced based on the Keulegan–Carpenter (KC) number to obtain the empirical formulas for C_d and C_m with superior fitting accuracy. The findings demonstrate that the wave height and base shear force predicted by the EMM generally agree with the CFD results. Compared with the previous constant C_m (C_m = 1), the proposed nonlinear empirical formula for C_m exhibits better accuracy in predicting paddle force and natural sloshing frequency shift generated by the paddles.