Added mass and wave radiation damping for flow-induced rotational vibrations of skinplates of hydraulic gates

One observed vibration mode for Tainter gate skinplates involves the bending of the skinplate about a horizontal nodal line. This vibration mode can be approximated as a streamwise rotational vibration about the horizontal nodal line. Such a streamwise rotational vibration of a Tainter gate skinplate must push away water from the portion of the skinplate rotating into the reservoir and draw water toward the gate over that portion of the skinplate receding from the reservoir. The induced pressure is termed the push-and-draw pressure. In the present paper, this push-and-draw pressure is analyzed using the potential theory developed for dissipative wave radiation problems. In the initial analysis, the usual circular-arc skinplate is replaced by a vertical, flat, rigid weir plate so that theoretical calculations can be undertaken. The theoretical push-and-draw pressure is used in the derivation of the non-dimensional equation of motion of the flow-induced rotational vibrations. Non-dimensionalization of the equation of motion permits the identification of the dimensionless equivalent added mass and the wave radiation damping coefficients. Free vibration tests of a vertical, flat, rigid weir plate model, both in air and in water, were performed to measure the equivalent added mass and the wave radiation damping coefficients. Experimental results compared favorably with the theoretical predictions, thus validating the theoretical analysis of the equivalent added mass and wave radiation damping coefficients as a prediction tool for flow-induced vibrations. Subsequently, the equation of motion of an inclined circular-arc skinplate was developed by incorporating a pressure correction coefficient, which permits empirical adaptation of the results from the hydrodynamic pressure analysis of the vertical, flat, rigid weir plate. Results from in-water free vibration tests on a 1/31-scale skinplate model of the Folsom Dam Tainter gate are used to demonstrate the utility of the equivalent added mass coefficient.

Vibrational Relaxation of N2O (v2) by Atomic Oxygen Measured by Tunable Diode Laser Absorption Spectroscopy

Through the use of Transient Diode Laser Absorption Spectroscopy (TDLAS), the rate coefficient for the vibrational relaxation of N2O (ν2) by O(3P) at room temperature (32 ºC)) was determined to be (1.51 ± 0.11)x10-12 cm3molecule-1sec-1. A Q-switched, frequency quadrupled (266 nm) Nd:YAG laser pulse was used as the pump for this experiment. This pulse caused the photodissociation of O3 into O2 and O atoms.Excited oxygen (O(1D)) was collisionally quenched to ground state (O(3P)) by Ar and/or Xe. Photodissociation also caused a temperature jump within the system, exciting the ν2 state of N2O molecules. Population in the ν2 state was monitored through a TDLASobservation of a ν3 transition. Data were fit using a Visual Fortran 6.0 Global Fitting program. Analysis of room temperature data taken using only Ar to quench O atoms to the ground state gave the same rate coefficient as analysis of data taken using an Ar/Xe mixture, suggesting Ar alone is a sufficient bath gas. Experimentation was alsoperformed at -27 ºC and -82 ºC for a temperature dependence analysis. A linear regression analysis gave a rate coefficient dependence on temperature of ... for the rate coefficient of the vibrational relaxation of N2O (ν2) by atomic oxygen.