Abstract
Experimental and numerical investigations of the modal behavior of a prototype Kaplan turbine runner in air have been conducted in this paper. The widely used roving accelerometer method was used in the experimental modal analysis. A systematic approach from a single blade model to the whole runner has been used in the simulation to get a thorough understanding. The experimental results show that all the detected modes concentrate their displacements on the impacted blade. The numerical results show that the modes of the single blade form different mode families of the runner, and each mode family corresponds to a narrow frequency band. Harmonic response analysis shows that, at the response peak point, the single blade excitation can only get mode shapes with concentrations on the exciting blade due to the superposition of the close modes in each mode family, which explains the experimental results well, while the mode superposition can be avoided by the order excitation method. With the reduction of the connection stiffness between the blades and hub/control system, the frequencies of most modes change from insensitive to more and more sensitive to the connection stiffness change, which results in a sensitive area and an insensitive area. Through comparison with the experimental results, it is indicated that the natural frequencies of the runner can probably be predicted by merging the runner into a whole body.
Highlights
Nowadays, hydropower contributes a lot to world electricity generation [1]
Among all types of renewable sources, hydropower is the only one with a wide range of power regulation with fast responses (20–100% max. power, less than 1 minute) to offset the unstableness of the electricity grid caused by some other renewable sources, such as solar and wind energy. erefore, hydraulic turbines operate at extreme off-design conditions and experience transient events much more times one day than before, which leads to even larger forces [2]
Kaplan turbines are one type of widely used hydraulic turbines, which can be seen mostly in low water head and large capacity hydropower plants [3], and the blades of Kaplan turbine runners can rotate to make the runner operate under high efficiencies for a wide range of operation. e rotation of the blades is controlled by a complex control system located inside the runner body. e typical structure of Kaplan turbines is shown in Figure 1. e excitation forces of Kaplan turbine runners can be both static and dynamic pressure loads [4, 5]. e static pressure load is positively correlated with the flow rate passing through the runner, and the dynamic pressure load mostly comes from the rotor-stator interaction (RSI) [6, 7]
Summary
Hydropower contributes a lot to world electricity generation [1]. To meet the daily increasing demand for electricity, the power intensity in hydraulic turbines is promoted for both new construction and the updating of power plants, which makes the fluid pressures and velocities higher, resulting in higher hydraulic excitation forces. Erefore, hydraulic turbines operate at extreme off-design conditions and experience transient events much more times one day than before, which leads to even larger forces [2] Such higher forces can produce higher vibration levels in the runners, which can cause fatigue damage and shorten their lifetime. Ere are some studies about the fluid-structure coupling vibration with only blade models of Kaplan turbine runners, but the influence of the hub/control system was not considered [17]. E complex connections between the blades and the runner body, as well as the complicated connections inside the control system, bring many difficulties to numerically study the modal behavior of Kaplan turbine runners. The modal behavior of the same prototype Kaplan turbine in [15] has been studied experimentally and numerically after the reparation of the damaged blade. The roving accelerometer method was used and the peak-hold method was used to capture the mode shapes and natural frequencies. e influence of the connection stiffnesses on the modal behavior of the whole runner has been investigated numerically, and through comparison with the experimental results, the connection stiffness level is talked about. is paper is organized as follows: first, the theoretical background, experimental procedures, and numerical settings are introduced, experimental and numerical results are presented, and experimental and numerical results are compared and discussed
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