Numerical Investigation of Added Mass and Hydrodynamic Damping on a Blunt Trailing Edge Hydrofoil

Abstract

Added mass and hydrodynamic damping play significant roles in fluid-structure interaction (FSI) in hydraulic turbines. Added mass can reduce natural frequencies, while hydrodynamic damping could result in a higher amplitude decay speed of the vibration. In order to quantify the added mass and hydrodynamic damping of a three-dimensional (3D) NACA 0009 hydrofoil with a blunt trailing edge, a two-way FSI simulation method was employed. The effects of grid scale, time-step, turbulence model, exciting force, and numerical damping on the calculation accuracy of the two-way FSI numerical simulation were analyzed in great detail through comparison with the previously published experimental data. Hydraulic force was obtained by using a transitional shear stress transport model at the flow region of the Reynolds number ReL = 0.2 × 106–2 × 106. The vortex shedding frequency, the natural frequency of the first-order bending mode in water, and the hydrodynamic damping ratio obtained from the numerical simulations agree well with the experimental data, with maximum deviations in 6.12%, 4.53%, and 8.82%, respectively. As the flow velocity increases, the natural frequency may not significantly change, while the added mass coefficient gradually increases, considering the effect of added stiffness. Above the first-order bending mode lock-in region, the results indicate that the first-order bending mode hydrodynamic damping ratio increases linearly with velocity. The present numerical achievements offer a higher level of accuracy for predicting the added mass and hydrodynamic damping characteristics of a hydrofoil.

Numerical Investigation of the Turbulent Wake-Boundary Interaction in a Translational Cascade of Airfoils and Flat Plate

“…The viscous sublayer flow can be directly solved by the SST k-ω turbulence model, The SST k-ω model combined with turbulent shear stress transmission and is quite accurate in the prediction of flow separation near the wall under an inverse pressure gradient [33], however, this model has some defects in the prediction of the transition phenomenon [34]. Based on an empirical formula, the γ-Re θt transition SST model proposed by Langtry et al [35] is more accurate in the prediction of the location of the transition point.…”

Numerical Investigation of the Trailing Edge Shape on the Added Damping of a Kaplan Turbine Runner

“…Generally, the two-way FSI method is more theoretical integrity, but the calculation cost is usually very high. Zeng et al used the two-way FSI method to investigate the influence of trailing edge shape on the added damping of the NACA 0009 hydrofoil, and the results fitted the experimental results very well [25,26]. In their investigations, they also investigated the influence of turbulence models on the results, including the k − ϵ, k − ω SST, and transition SST models, and they found that the transition SST model can accurately capture the velocity and pressure distributions in the boundary layer, thus accurate damping compared with experimental results.…”

“…e simulated hydrofoil is the 3D NACA 0009 hydrofoil used in [24][25][26], and in their research, the influence of the trailing edge shape on the added damping was studied. Blunt trailing edge hydrofoil is presented by Figure 1 with a chord length L � 100 mm, the width of the span is w � 150 mm, and the trailing edge thickness is h � 3.22 mm.…”

Understanding the Influence of Wake Cavitation on the Dynamic Response of Hydraulic Profiles under Lock-In Conditions

“…The study of fluid-structure interaction (FSI) phenomena requires considering the flow behavior at the wake of hydrofoils and the structure dynamic response. In this sense, Zeng et al [24] studied the dynamic response of the first bending mode of a blunt trailing-edge hydrofoil in a fluid stream through two-way FSI simulations. They concluded that this approach is suitable for the prediction of the vibration amplitude with a maximum deviation of around 8.82% for the hydrodynamic damping.…”

“…In summary, most of the literature related to the study of hydrofoils under vortex shedding flows deals with: (i) the prediction of the vortex shedding frequency for free-wake cavitation conditions [12,15,16,[29][30][31][32], (ii) the influence of the wake cavitation on the vortex shedding dynamic behavior [4,[20][21][22][23], and (iii) the prediction of the vibration amplitudes of hydrofoil under lock-off and lock-in conditions when no wake cavitation occurs [17,[24][25][26][27][28]. However, solely Ausoni et al [6] experimentally studied the interaction between wake cavitation and the dynamic response of a hydrofoil under a lock-in condition.…”