Long-span Gates Research Articles

721 下端放水を行うシェル形長径間ゲートの流体関連振動に関する研究 : 自励振動特性に及ぼす傾斜面の水平距離の影響

This paper presents effects of the horizontal length of the weir plate for flow-induced vibration of shell-type long-span gates with small underflow. Experimental results for flow-induced vibration of 5 model gates, which have different length of the weir plate, were shown first and the instability for each gate was described secondly. Furthermore the relationship between the instability and gate motion trajectory derived using experimental results for the hydrodynamic force acting on their inclined weir plate were discussed.

Model Development of Flow-Induced Vibrations of Shell-Type Long-Span Gates with Underflow. 2nd Report. Added Mass, Fluid Damping and Excitation Coefficients.

This paper presents added mass, fluid damping and excitation (negative damping) coefficients for flow-induced vibrations of a shell-type long span gate in which the upstream gate face consists of vertical and inclined skin plates.The equations of motion of the shell-type long-span gate include integral fluid terms which describing the fluid motion in the resorvoir. The fluid terms were calculated for a periodic gate vibration, to reduce to a superposition of the acceleration and velocity terms, thus deriving the added mass, the fluid damping and excitation coefficients in the form of a series summation. The major characteristics of these significant parameters were calculated and examined.Additionaly a fundamental mechanism of the self-excited vibration was described.

722 下端放水と越流を同時に行うシェル形長径間ゲートの流体関連振動に関する研究 : クレストに働く動水圧の計測と自励振動特性に関する検討(OS-4 振動・騒音制御の先端技術)

722 下端放水と越流を同時に行うシェル形長径間ゲートの流体関連振動に関する研究 : クレストに働く動水圧の計測と自励振動特性に関する検討(OS-4 振動・騒音制御の先端技術)

Model Development of Flow-Induced Vibrations of Shell-Type Long-Span Gates with Underflow. 1st Report. Derivation of Equation of Motion.

Shell-type long-span gates in which the upstream gate face consists of vertical and inclined skin plates (also referred to as weir plates) possess two degrees of freedom, one each in the streamwise (horizontal) and vertical directions, due to the gate's bending flexibility in these two directions. The streamwise and vertical directions can become closely which one another through hydrodynamic forces acting on the weir plates, resulting in sever eself-excited vibrations. Here, a two-dimensional model study of a shell-type long-span gate with small gate opening was performed to examine the validity of an asumption of a hydrodynamic pressure acting on the inclined weir plate. In addition, the hydrodynamic pressure acting on the upstream gate face and the exact equation of motion of the flow-induced vibration of shell-type long-span gates were described.

Flow-induced vibration of shell-type long-span gates

This study describes the fundamental dynamic characteristics of the flow-induced vibrations of shell-type long-span gates, in which the upstream gate face consists of vertical and inclined skin plates (also referred to as weir plates). Shell-type gates possess two degrees-of-freedom, one each in the streamwise (horizontal) and vertical directions, due to the gate bending flexibility in these two directions. The streamwise and vertical vibrations can become closely coupled with each other through hydrodynamic forces acting on the skin plates, resulting in severe self-excited vibrations. A two-dimensional model study of a shell-type long-span gate under small gate opening was performed to measure the vibration frequency, the excitation ratio † † The excitation ratio is defined as the logarithmic increment divided by 2π. The logarithmic increment is defined for an exponentially growing signal in the same manner as the classical logarithmic decrement for an exponentially decaying signal. The logarithmic increment is equal to minus the logarithmic decrement and the excitation ratio is equal to minus the damping factor. By defining the excitation ratio in this manner, it is always a positive number and one avoids the confusion concerning whether an increase in the magnitude of negative damping is referred to as an increase in negative damping or a decrease in negative damping. and the trajectories of gate motion. The measured trajectories of gate motion revealed that the coupling of the vertical and streamwise vibrations made the gate behave as a press-shut device; press-shut devices are known to undergo self-excited vibrations. In addition, fundamental dynamic characteristics, such as the ratios of horizontal to vertical frequencies, the ratios of in-water to in-air frequency, a reduced fluid-excitation coefficient, a reduced added mass, and the phase difference between vertical and horizontal vibratory motions, were determined. The experimental results for the horizontal in-water to in-air vibration frequency ratio and the reduced mass are carefully compared with the theoretical results for a slender long-span gate undergoing streamwise vibration. The trajectories of gate motion are carefully analysed by introducing theoretical results for the hydrodynamic pressure acting on the gate. Finally, the possibility of flow-induced vibration of shell-type long-span gates in practice is examined and criteria for dynamic stability are suggested.

Flow-induced vibration of long-span gates part I: Model development

This paper presents a theoretical analysis of the flow-induced flexural vibration of long-span gates at small openings. Such a gate is in most cases long enough to be subject to elastic vibration due to its bending flexibility in the streamwise direction. This vibration is accompanied by a variation of the flow rate from under the gate. If the skin-plate of the gate and the floor include an angle smaller than 90°, the gate acts as a “press-shut device”, and the variation of flow rate may cause severe self-excited gate vibrations. The streamwise gate vibration induces surface waves in the upstream channel and fluctuations of the hydraulic pressure due both to flow rate variations and the push-and-draw effect of the gate movement. The pressure induced by the flow-rate variation will supply energy to the vibrating gate, whereas the pressure induced by the push-and-draw effect will consume energy from the vibrating gate. If the energy supply due to the flow-rate variation exceeds the energy consumption due to the push-and-draw effect and to mechanical damping, the gate becomes self-excited. The calculation of the hydrodynamic pressure induced by an arbitrary gate motion is based on a potential theory developed by Rayleigh for dissipative-wave radiation problems. With the aid of this theory, the flow-fluctuation phenomenon is reduced to an initial-boundary value problem which can be solved by making use of mathematical techniques such as Fourier series, Fourier integrals and Laplace-transforms. The equation of gate motion is derived in the form of a second-order differential and integral homogeneous equation, the dimensionless variety of which yields the basic parameters determining the vibration characteristics. The dimensionless equation of motion includes an integral fluid term describing the effects of added mass, fluid damping and fluid excitation, as an acceleration and a velocity term. The major characteristics of gate vibration are discussed in terms of the solutions for the hydrodynamic pressures acting on the gate. Calculated data on fluid damping and fluid excitation, finally, reveal the tendency of long-span gates to undergo flow-induced vibrations.

Flow-Induced Vibration of Long-Span Gates due to Shed Vortices (Vibration Criteria, Level of Fluid Excitation and Added Mass).

Submerged long-span gates which dam wide rivers can undergo violent streamwise vibrations caused by vortex shedding beneath the gate. This study presents flow-induced vibration characteristics which were obtained in a model gate test. From the measured vibration frequencies and damping ratios in air and water, the level of fluid excitation and the added mass for small-amplitude gate vibrations are calculated and reduced to a dimensionless form. Thus, the vibration criteria are obtained. In addition, the average values of the maximum amplitudes of gate vibration were measured. The results of these experiments, taken as a whole, suggest that the flow-induced vibration characteristics of the long-span gates are well predicted by dimensionless parameters, such as the reduced gate opening and the reduced velocity.

Flow-induced vibration of shell-type long-span gates. 2nd report, A study for fundamental vibration characteristics of under-flow type.

This study examines the fundamental characteristics for a flow-induced vibration of shell-type long-span gates which have a gate front consisted of vertical and inclined weir plates. The shell-type gates possess two freedoms to vibrate in the streamwise and vertical directions due to their bending flexibility. Both streamwise and vertical vibrations couple well each other through hydrodynamical forces acting on the weir plates, thus resulting in a severe self-excited vibration. A two-dimensional model test for a shell-type long-span gate under small gate-openings was performed and a previous study reported the experimental results in detail. Here, the obtained results for the vibration frequency, the added mass of water and the dynamic press-shut gate trajectories are carefully studied. Moreover, the self-excited vibration mechanism is studied and the self-excited vibration possibility of Shell-type long-span gates under practical uses is examined. Finally a design criterion for dynamic stability is presented.

Flow-induced vibration of long-span gate. 4th Report. Vibration frequency ratio and fluid damping ratio.

This study presents the calculated results for flow-induced vibration frequency and fluid damping of a streamwise vibrating vertical long-span gate under a small gate-opening. The gate vibration characteristics are determined by the following three non-dimensional factors: basic Froude number composed of the gate-opening depth and the vibration frequency in air, mass ratio of water to gate, and water depth ratio of the gate opening depth and the reservoir depth. The calculated results are shown in figures from which vibration frequency ratio and fluid damping ratio can be easily found for given non-dimensional factors. When the basic Froude number takes a value larger than 10.0, the vibration frequency ratio with an error less than 7% takes a constant value given by a simple expression of the mass ratio.

Flow-induced vibration of shell-type long-span gates. 1st Report. Fundamental vibration characteristics of the under-flow type.

This study presents the fundamental characteristics for a flow-induced vibration of shell-type long-span gates which have a gate front consisting of vertical and inclined weir plates. The shell-type gates possess two freedoms to vibrate in the streamwise and vertical directions due to their bending flexibility. Both streamwise and vertical vibrations couple well with each other through hydrodynamical forces acting on the weir plates, thus resulting in a severe self-excited vibration. A two-dimensional model test for a shell-type long-span gate under small gate-openings was performed to measured the vibration frequency, the exciting ratio and the gate motion trajectories. From the obtained results, the fundamental characteristics, such as the vibration frequency ratios, a reduced fluid exciting coefficient, a reduced added mass, and a phase difference between the vertical and streamwise vibrations, were calculated. Furthermore, it was revealed from the measured gate motion trajectories that a press-shut device which causes a self-excited vibration is formed by a skillful dynamic mechanism of the coupled vibration.

Flow-Induced Vibration of Long-Span Gates : Verification of Added Mass and Fluid Damping

The added mass and the fluid damping coefficient were derived theoretically in a dimensionless form in a previous study. To verify the theoretical results of the added mass and the fluid damping coefficient, the experimental results of a model test are presented in this study. A planar vertical gate undergoes free damped vibrations in air and still water. The added mass and the fluid damping coefficient are calculated from the measured frequencies and damping ratios of the damped vibrations. Consequently, it is shown that there is good agreement between the theoretical and experimental results

Flow-induced vibration of long-span gates caused by shedding vortices. (1st report. vibration criteria, level of fluid excitation and added mass).

Submerged long span gates which dam a wide river undergo violent streamwise vibrations caused by vortex shedding beneath the gate. This study presents flow-induced vibration characteristics which were obtained in a model gate test. From the measured vibration frequencies and damping ratios in air and water, respectively, the level of fluid excitation and the added mass for small amplitude gate vibrations were calculated and reduced to a dimensionless form, and thus the vibration onset criteria were obtained. In addition to the average value of the maximum amplitude of gate vibration, was measured. The results of these experiments, taken as a whole, suggest that the flow-induced vibration characteristics of the long-span gates are well predicted by the dimensionless parameters, such as the reduced gate opening height and the reduced velocity.

Flow induced vidration of long span gates. (2nd report. Added mass and fluid damping).

To study the flow-induced small-amplitude vibration of long-span gates with small gate openings which are inclined toward the downstream side, this study presents an analytical method to derive the dimensionless parameters of the added mass and fluid damping coefficients induced by fluid motion. The equation of motion of long-span gates includes the integral fluid term which describes the effects of the added mass and fluid damping. In the calulation of the integral fluid term for a periodic gate vibration, it is reduced to a superposition of the acceleration and the velocity terms. Thus, the added mass and fluid damping coefficients are derived in the form of a series summation. They are calculated numerically and the major characteristics of added mass and fluid damping are revealed and discussed. Based on the calculated fluid damping effect on the gate vibration, the tendency of long-span gates to vibrate as a result of flow-induced vibrations is discussed.