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The water-added-mass to a hydro turbine-shaft-line can significantly affect its modal behavior including the vibration modes and their natural frequencies. So it is of great significance to consider the effect of added water mass on the modal behavior of a hydro turbine to assure the safe and efficient operation of the hydro turbine-shaft-line system. In this investigation, the effect of water-added-mass on the shaft-line of one large prototype hydroelectric generator unit has been investigated in detail via the finite element tool. First, a CAD model of the shaft-line was created based on actual dimensions. Then a finite element model of the entire shaft-line was generated with high-quality hexahedral and tetrahedral cells. A first round of finite element simulation of the shaft-line in the air was performed without considering the effect of surrounding water, but the results were not realistic. On this basis, a finite element-based water-structure coupling simulation was carried out to analyze the effect of water-added-mass on the modal behavior of the shaft-line of the large hydroelectric generator unit. The result is more realistic to reality than that in the air. The results of this study show that when the water surrounding the turbine runner is added to the hydro-turbine shaft-line, it increases the overall mass of the shaft-line system, thereby reducing the natural frequencies of the system. The decrease in natural frequencies can cause the shaft-line to approach its critical speed during operation, vibrate at higher amplitudes than usual, and even lead to potential damage to the shaft-line system. According to the results calculated with the finite element water-structure coupling method, the countermeasures to improve the evaluation of the water-added-mass effect on the structural modal behavior of the shaft-line for the hydroelectric generator units have been provided. The conclusion can also apply to other hydraulic turbine and pump units.

Unlike uniform motion, when an object moves underwater with variable speed, it experiences additional resistance from the water, commonly referred to as added mass force. At present, several methods exist to solve this force, including theoretical, experimental, and simulation approaches. This paper addresses the challenge of determining the added mass force for irregularly shaped small objects undergoing variable speed motion underwater, proposing a method to obtain the added mass force through numerical simulation. It employs regression analysis and parameter separation analysis to solve the added mass force, added mass, viscous drag coefficient, and pressure drag coefficient. The results indicate that an added mass force exists during both the acceleration and deceleration of the object, with little difference between them. Under the same velocity conditions, significant differences exist in pressure drag forces, while differences in viscous drag forces are not significant. This suggests that the primary source of added mass force is pressure drag, with viscous drag having little effect on it. During acceleration, the surrounding fluid accelerates with the object, increasing the pressure drag with a high-pressure area concentrating at the object’s front, forming an added mass force that is directed backward. By contrast, during deceleration, the fluid at the object’s front tends to detach, and the fluid at the rear rushes forward, leading to a smaller high-pressure area at the front and a larger one at the rear, reducing the pressure drag and forming an added mass force that is directed forward. By comparing the added mass of a standard ellipsoid obtained from numerical simulation with theoretical values, the regression analysis method is proven to be highly accurate and entirely applicable for solving the added mass of underwater vehicles.

In this article, the effects of the changes in the mass of the floating wind turbine (as a multi-body system) on its nonlinear vertical vibrations are investigated. The fluctuations of the hydrodynamic added mass of the floating platform and the mass of the vibration absorbers, which added to the structure to mitigate the lateral vibrations, change the mass and consequently the dynamics of the vertical vibrations. In this regard, first, the governing equations of the vertical vibrations of the floating wind turbine are derived. The FAST code is used to validate the proposed model of the dynamics of the vertical vibrations through numerical simulations. Then, derived equations are solved approximately by the perturbation method. According to the approximate solutions, the fluctuations of the added mass of the floating platform and the masses of the vibration absorbers increase the frequency and amplitude of the vertical vibrations, which increases the fatigue loads on the tower of the wind turbine as well as moorings of the floating platform.

We present a non-iterative algorithm, FloatStepper, for coupling the motion of a rigid body and an incompressible fluid in computational fluid dynamics (CFD) simulations. The purpose of the algorithm is to remove the so-called added mass instability problem, which may arise when a light, floating body interacts with a heavy fluid. The idea underlying the presented coupling method is to precede every computational time step by a series of prescribed probe body motions in which the fluid response is determined, thus revealing the decomposition of the net force and torque into two components: (i) an added mass contribution proportional to the instantaneous body acceleration and (ii) all other forces and torques. The algorithm is implemented and released as an open-source extension module to the widely used CFD toolbox, OpenFOAM, as an alternative to the existing body motion solvers. The accuracy of the algorithm is investigated with several single-phase and two-phase flow benchmark cases. The benchmarks demonstrate excellent stability properties, allowing simulations even with massless bodies. They also highlight aspects of the implementation, such as the mesh motion method, where it can be improved to further enhance the flexibility and predictive capabilities of the code.

Purpose The gaps between runner and nearby structures play an important role in the dynamic response of runner, especially for pump-turbines. This paper aims to evaluate the gap influence on the added mass and dynamic stress of pump-turbine runner and provide an improved method to predict the resonance of runner. Design/methodology/approach Acoustic-structural coupling method was used to evaluate the added mass factors of a reduced scale pump-turbine with different axial and radial gap size between runner and nearby rigid walls. Improved one-way fluid-structural interaction (FSI) simulation was used to calculate the dynamic stress of the runner, which takes into account fluid added mass effect. The time-dependent hydraulic forces on the runner surfaces that were obtained from unsteady CFD simulation were transferred to the runner structure as a boundary condition, by using mesh-matching algorithm at the FSI surfaces. Findings The results show that the added mass factors increase as the gap size decreases. The axial gaps have greater influence on the added mass factors for the in-phase (IP) modes than the counter-phase (CP) and crown-dominant (CD) modes, while the CP and CD modes are very sensitive to the radial gaps. The largest added mass factor is observed in (2 + 4)ND-CP mode (resonance mode). The results reveal that the transient structural dynamic stress analysis, with the consideration of gaps and fluid added mass, can accurately predict the resonance phenomenon. Resonance curve of the pump-turbine has been obtained which agrees well with the test result. The gap fluid has great influence on the resonance condition, while for non-resonance operating points, the effect of gaps on the dynamic stress amplitude is quite small. Originality/value This paper provides an accurate method to analyze the dynamic response during runner design stage for safety assessment. The resonance curve prediction has more significance than previous methods which predict the resonance of runner by modal or harmonic analysis.

Heave plate is one of the most commonly used plates for controlling the movement of floating structures that are used for offshore deep water operations. Heave plates, in fact, move in both directions simultaneously. Therefore, the primary goal of this work is to examine the coupling motion’s effects on hydrodynamic coefficients caused by the heave and pitch motion of a heave plate. Numerical simulations are used to first simulate coupling motion in phase, and then out of phase which varies from 0 ∘ to 90 ∘ . The effects of added mass and moment, as well as pitching and heaving damping are investigated. Based on the results of the coupling oscillation of the heaving plate at different Keulegan–Carpenter (KC), the results indicate that added mass and pitching damping have more influence than added moment and heave damping coefficient.

The dynamic interaction between water and cylindrical structures can significantly affect the dynamic responses and properties of offshore structures. Among the key factors, the free-surface boundary condition plays a crucial role in determining the hydrodynamic forces on cylinders, leading to frequency-dependent added mass and damping effects. Although the dynamic responses of the cylinder can be readily obtained using frequency-domain methods, their computational efficiency is much lower than that of the time-domain methods, and they are not well suited for nonlinear structure analysis. To address this, this study proposes a time-domain substructure method for simulating water–cylinder interaction considering the boundary condition of free surface waves, where the frequency-dependent added mass and added damping are equivalently represented by a spring-dashpot-mass model in time domain. The results indicated that the calculation efficiency of the proposed method has improved by approximately two orders of magnitude compared with the frequency-domain finite element method. Moreover, the water–cylinder interaction can markedly influence the seismic responses with small mass ratios, whereas its effect on wave-induced responses becomes negligible when the wave period exceeds 5 s. The effects of the free-surface boundary condition on the wave responses of the cylinder can be generally negligible, except when the wave period approaches the natural vibration period of the cylinder. In addition, its influence on seismic responses can be ignored when the damping ratio of the cylinder exceeds 0.02.

The hydrodynamic characteristics are crucial for accurately analysing floating offshore wind systems. In this paper, the added mass and damping coefficients of a semisubmersible floater are examined around the natural periods of the surge, heave, and pitch motion, using computational fluid dynamics (CFD). The OpenFOAM CFD setup is validated against experimental measurements from the free decay tests, and the same setup is used to determine the hydrodynamic coefficients of the platform subjected to forced motions with different amplitudes and periods. The added mass and quadratic damping coefficients obtained from forced oscillations are consistent with the free decay results. Moreover, the added mass coefficients obtained by CFD is significantly higher than the estimations of the potential flow theory: around 10% larger for surge and 22% larger for heave. The damping is almost independent of the frequency while it varies with the motion amplitude. The deviations in the CFD results from the potential flow theory are due to the viscous effects. Besides, viscous damping is dependent on the drag coefficient specified in the Morison’s equation.

In this study, a method of measuring the added mass for an object oscillating in a viscous fluid using nonlinear self-excited oscillations was developed. The added mass produces an additional inertial effect on the vibrating object. In previous methods, the added mass is obtained experimentally from the response frequency and amplitude at the peak in the frequency response curve under a harmonically forced excitation. However, such methods cannot be utilized in highly viscous environments because the peak becomes ambiguous as a result of damping. Moreover, in very high-viscosity environments, the resonance peak ceases to exist in the frequency response curves. To solve this problem, self-excited oscillations were induced in the system using linear velocity feedback. Because linear velocity feedback can be used to eliminate the viscous damping effect when the linear feedback gain is set near the Hopf bifurcation point related to self-excited oscillations, the object becomes self-excited at a frequency equal to the natural frequency of the object oscillating in a vacuum, i.e., the undamped natural frequency. What distinguishes the proposed method from the abovementioned previous methods is that the value of the response is not needed; however, a reduction in the oscillation amplitude is required to obtain accurate measurement results. In the proposed method, to avoid an increase in the response amplitude under the applied linear velocity feedback, nonlinear feedback is also applied to produce a limit cycle similar to that produced in a van der Pol oscillator. A prototype of the measurement system was constructed based on the proposed method. A comparison of the experimentally and theoretically obtained added mass values confirmed the validity of the proposed method for added mass sensing.

Kim, D.; Shim, J.-S.; Min, Y.; Min, I.K., and Lim, H.S., 2021. Estimation of added mass and radiation damping of large ocean observation buoy using numerical analysis. In: Lee, J.L.; Suh, K.-S.; Lee, B.; Shin, S., and Lee, J. (eds.), Crisis and Integrated Management for Coastal and Marine Safety. Journal of Coastal Research, Special Issue No. 114, pp. 221–225. Coconut Creek (Florida), ISSN 0749-0208. A vane is to be installed to control the yawing behavior of a large ocean observation buoy (LOOB). The role of the vane is to control the yaw motion of the one-point mooring LOOB against current and waves. The lengths of the vanes were 0.8, 1.6, and 2.0 m, and the added mass tensor (6 × 6) and radiation damping tensor (6 × 6) at that time were estimated using computational fluid dynamics. In addition, the added mass tensor and radiation damping tensor according to the wave frequency domain are presented. Estimating the added mass and radiation damping of LOOB is important because it presents the hydrodynamic relationship between the structure and fluid. As a result of the analysis, the added mass was almost unchanged in other components except m66. On the other hand, m66 was proportional to the length of vane. When the length of the vane is 0.8 m, the maximum added mass is 1.28 × 104 kg (wave frequency 3.7 rad/s), and when the lengths are 1.6 and 2.0 m, it increases to 2.79 × 104 and 3.58 × 104 kg, respectively. This means that the length of the vane affects the resistance to rotational motion. In the case of radiation damping, the results were that the length of the vane and the radiation damping (component c66) were proportional. However, there is no significant difference depending on the length of the vane in the other components (c11 to c55). Radiation damping (c66) increased to 1.12 × 104, 3.56 × 104 and 4.46 × 104 kg, according to the length of the vane. In conclusion, it can be seen that the longer the vane, the better the yaw control effect. However, as the length of the vane increases, the geometric asymmetry of the LOOB increases. In addition, it can be cause fatal damage to small boats berthing the LOOB. Therefore, it is necessary to optimally design it by considering the advantages and disadvantages according to the length of the vane.