Sloshing Analysis and Control of Tuned Liquid Dampers With Paddles: Hydrodynamic Interactions

Accurately estimating the damping and added mass produced by damping devices is critical for achieving efficient vibration control with tuned liquid dampers (TLDs). To satisfy the design damping requirements, multiple paddles are usually arranged inside the TLD. However, the interference effects caused by closely spaced paddles may significantly alter the TLD's hydrodynamic characteristics. This paper establishes a linearized equivalent mechanical model (EMM) and a third‐order nonlinear multimodal model (NMM) for a TLD with 3 × 3 paddles. Both models incorporate analytical expressions for the damping ratio and added mass of the paddles. The key unknown parameters—the drag coefficient C d and the inertia coefficient C m —are determined by minimizing the error between the predicted responses of the EMM and the computational fluid dynamics (CFD) simulation responses. To characterize the degree of hydrodynamic interference between the transverse paddles, the paddle blockage ratio is introduced. Then, hydrodynamic coefficient models for C d and C m are established by investigating their variation laws with the liquid depth ratio, Keulegan–Carpenter number, and paddle blockage ratio. Results show that the sloshing response and the frequency shift predicted by the NMM generally agree with the CFD results and existing experimental data. Due to the neglect of interference effect and amplitude dependence, the existing constant hydrodynamic coefficient models for 3 × 3 paddle configuration have limited applicability. A case study of a supertall building also shows that the proposed hydrodynamic coefficient models can provide beneficial design guidance for the wind‐induced vibration control of TLD.