Charles W. Knisely

STROUHAL NUMBERS OF RECTANGULAR CYLINDERS AT INCIDENCE: A REVIEW AND NEW DATA

Experimentally determined Strouhal numbers for a family of rectangular cylinders with side ratios (B/D) ranging from 0·04 to 1·0 and with angles of attack from 0° to 90° are presented. Tests were conducted both in a water channel with Reynolds numbers between 7·2 × 102 and 3·1 × 104 and in a wind tunnel with Reynolds numbers between 8·8 × 103 and 8·1 × 104, based on the projected cross stream dimension and the mean velocity. In addition, the mean drag as well as the mean and fluctuating lift were measured as functions of the angle of attack in the wind tunnel tests for B/D =0·25, 0·5 and 1. The Strouhal number of all except the thinnest plate showed qualitatively similar behavior with changing angle of attack. The general tendency is for a rapid rise in the Strouhal number to occur at relatively small angles of attack. This rapid rise is associated with reattachment of the separated shear layer. The angle of attack where reattachment and, hence, the rapid rise in Strouhal number occurs is dependent on the B/D ratio. After the sudden rise, the Strouhal number levels off with a further increase in angle of attack. As the angle of attack approaches 90°, there is a sudden decline in the value of the Strouhal number, again associated with shear layer-comer interaction (i.e. detachment). For the thinnest plate, the Strouhal number was found to be essentially independent of the angle of attack over a wide range of angles. Measured force coefficients show a strong dependence on the angle of attack, suggesting that for 0·5 ≤ B/D ≤ 2·0 there is an optimum incidence that makes most efficient use of the load-bearing capacity of the structure. The present data agree well with available results from previously published papers which are reviewed.

Flow-Induced Vibration of Shell-Type Long-Span Gates

Abstract 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 † 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.

Theoretical Model of Lubrication Mechanism in the Thrust Slide-Bearing of Scroll Compressors

This study presents a theoretical model of the remarkably good lubrication characteristics of the thrust slide-bearings found in scroll compressors experimentally by Ishii et al. (2007). It has been suggested that the thrust plate undergoes elastic deformation due to axial loading. As a result of this deformation, a fluid wedge is believed to form at the periphery of the thrust plate. The fluid wedge angle between the sliding surfaces was calculated with a finite element method analysis and then used in the average Reynolds equation from Patir and Cheng (1978, 1979) to analyze the fluid lubrication on rough sliding surfaces. The plastic and elastic contacts between the orbiting and fixed thrust plates were analyzed using the solid contact theory from Greenwood and Williamson (1966). The derived theoretical model permitted the calculation of the oil film pressure, the solid contact force, the fluid frictional force, and the solid shearing drag force. These results were used, in turn, to determine the resultant friction coefficient at the thrust slide-bearing. Finally, it is shown that the predicted theoretical results agree well with the experimental lubrication test results of Ishii et al. (2007). The proposed theoretical development appears to model accurately the essential mechanism for the remarkably good mixed fluid-and-solid lubrication in a thrust slide-bearing.

Critical Reynolds Number in Constant-Acceleration Pipe Flow From an Initial Steady Laminar State

The transition to turbulence in a constant-acceleration pipe flow from an initial laminar state was investigated in a custom-made apparatus permitting visual access to the water flow in the pipe. The apparatus allowed both laser Doppler velocimetry measurements and flow visualization using a tracer. The experiment was carried out by accelerating the flow from a steady laminar state to a steady turbulent state. The relation between the critical Reynolds number for transition to turbulence and the acceleration was found to be similar to that in a constant-acceleration pipe flow started from rest. In addition, with increased acceleration, the turbulent transition was found to be delayed to higher Reynolds numbers using flow visualization with simultaneous laser Doppler velocimetry measurements.

Experimental Study of the Lubrication Mechanism for Thrust Slide Bearings in Scroll Compressors

This study focuses on the effect that a pressure difference across the orbiting thrust plate of a thrust-slide bearing has on the improved lubrication of the bearing in scroll compressor applications. A thrust slide bearing model submerged in a refrigerant oil, VG-56, was operated under pressurized conditions using R-22 as the pressurizing gas, where the pressure difference across the friction surface of the thrust bearing was adjusted from 0 to 1.0 MPa and the friction force and friction coefficient at the thrust slide bearing were measured over a range of orbital speeds. As a result, significant improvement in lubrication at the thrust slide bearing due to the pressure difference was identified. Furthermore, careful observation of the wear state of the thrust slide bearing revealed the formation of a fluid wedge between the sliding surfaces due to axial loadings. This fluid wedge appears responsible for the observed improvement in lubrication. In addition, the wedge formation was quantitatively investigated using finite element method (FEM) analysis of the elastic deformation of the thrust plate. The FEM analysis was subsequently validated through strain measurement on the thrust plate.

Effect of Initial Constant Acceleration on the Transition to Turbulence in Transient Circular Pipe Flow

Experimental investigation is carried out on the transition to turbulence in a transient circular pipe flow. The flow is accelerated from rest at a constant acceleration until its cross-sectional mean velocity reaches a constant value. Accordingly, the history of the flow thus generated consists of the initial stage of constant acceleration and the following stage of constant cross-sectional mean velocity. The final Reynolds number based on the constant cross-sectional mean velocity and the pipe diameter is chosen to be much greater than the transition Reynolds number of a steady pipe flow of about 3000. The transition to turbulence is judged from the output signal of the axial velocity component and its root-mean-square value measured with a hot-wire anemometer. A turbulent slug appears after the cross-sectional mean velocity of the flow reaches the predetermined constant value under every experimental condition. Turbulence production therefore is suppressed, while the flow is accelerated. The time lag for the appearance of the turbulent slug after the cross-sectional mean velocity of the flow reaches the constant value decreases with an increase in the constant acceleration value. An empirical equation is proposed for estimating the time lag. The propagation velocity of the leading edge of the turbulent slug is independent of the constant acceleration value under the present experimental conditions.

Field Measurement of Dynamic Instability of a 50-Ton Tainter-Gate

The 2-degrees-of-freedom coupled-mode self-excited vibration of Tainter gate has been demonstrated in hydraulic model studies of 2D and 3D gate models. The concurrent development of a theoretical model has permitted the prediction that some full-scale Tainter-gates could be potentially susceptible to this coupled-mode self-excited vibration. However, there are many people who regard with suspicion the prediction that a massive Tainter-gate might actually undergo this type of vibrations. In response to these skeptics, this paper presents the test results from an actual operational 50-ton Tainter-gate to determine its propensity for large-amplitude self-excited vibration. Further, the previously developed theoretical analysis was applied to the tested gate to uncover an essential dynamic instability for this installation, as well as to provide a framework for the design of a retrofit and an optimized maintenance plan.Copyright

Hydrodynamic Pressure Load on Folsom Dam Tainter-Gate at Onset of Failure Due to Flow-Induced Vibrations

An analysis of a Folsom dam Tainter-gate which failed during operation in 1995 is presented. First, an empirical evaluation of the excessive push-and-draw hydrodynamic pressure induced by streamwise rotational vibration of the inclined circular-arc skinplate over the curved dam crest with a vertical step down at the upstream side is developed. This development is based on a theoretical analysis for a simplified flow field model. The simplified model consisted of a vertical flat rigid weir plate undergoing streamwise rotational vibration and a horizontal flat bed surface with a vertical step down at the gate position. Secondly, the resultant hydrodynamic load on the skinplate is determined. Thirdly, the dynamic instability of the Tainter-gate is theoretically examined and the major characteristics of this instability are presented. Finally, an FEM analysis of the structure reveals that the small vibration amplitude of at most 11.9mm at the spanwise center and bottom end of the skinplate induced the excessive hydrodynamic pressure load of about 1.6 times the static load, thus causing incipient failure of 4 bolts connecting a diagonal member to the main struts.Copyright

Field Vibration Tests and Dynamic Stability Analysis of a Full-Scaled Tainter-Gate

This study presents results from in-air and in-water field vibration tests of a 29-ton full-scaled Tainter-gate installed on a river in Japan. These tests were conducted to confirm the validity of our theoretical analyses especially for a large value of Froude number. First, with the gate raised, an in-air experimental modal analyses, using an impact hammer and accelerometers, was conducted to determine the natural frequencies and the damping ratios for two modes of gate vibration. These two modes corresponded to the rigid body vibration of the whole gate around the trunnion pin and the streamwise rotational vibration of the skinplate. Subsequently, with the gate again lowered and exposed to flowing water, the gate vibration characteristics were carefully measured. Only weak, unsynchronized vibrations were recorded and the gate was found to be dynamically stable. A theoretical analysis developed to predict the hydrodynamic pressure, the vibration frequency ratios and the dynamic stability were applied to the full-scaled gate. The theoretical analysis correctly predicted both the measured frequency ratios and the gate’s dynamic stability.Copyright

Vibration Tests With a 1/13-Scaled 3-D Model of the Folsom Dam Tainter-Gate and Its Prediction by Theory

This study presents 3-D model gate vibration test results demonstrating violent spontaneous vibrations and validating the basic assumptions made in previously published theoretical analyses. First, the design of a 1/13-scaled 3-D model of Folsom dam Tainter-gate is presented, in which the streamwise natural bending vibration mode of the skinplate, measured in the field vibration tests on the remaining Folsom gate, is shown to be correctly replicated with the aid of FEM simulations. Secondly, in-air and in-water vibration test results with the 1/13-scaled 3-D model are presented, reproducing the intense coupled-mode self-excited vibrations. Thirdly, test results are plotted on a theoretically calculated stability criterion diagram to confirm the validity of the theoretical analysis. Finally, the intense dynamic instability of the Folsom gate, which could have caused its failure, is presented.Copyright