SPECTRA OF PRESSURE FLUCTUATIONS AT THE BOTTOM SEAL OF A MODEL RADIAL GATE

Jalal Attari

Power & Water Institute of Technology

P. O. Box 16765-1719, Tehran, Iran

E-mail: j_attari@yahoo.com

Abstract: Gates are widely used in hydraulic structures for regulating discharge and water level. An important in design of any type of gate is an effective seal to prevent leakage of water. It is known that elastic seals, especially of J-type, are susceptible to vibration at small gate openings. In the present study, a bar type bottom seal for a submerged radial gate is considered at very large gate openings from the standpoint of excitation of flow induced-vibration. Instead of a water channel, pressure fluctuations were measured on the bottom seal of a stationary model radial gate mounted in a wind tunnel. Power spectra of the pressure fluctuations showed some broad band peaks. Strouhal numbers were deduced using these frequencies and previously measured maximum shear layer velocities. Results show good agreement with the theoretical and experimental results of Martin et al. (1975) for a vertical gate with extended lip. Furthermore in the present experiments, results have been extended to a 3^rd mode of oscillation. Comparison of results shows a strong similarity of local flow processes between the gate with a protruding bottom seal and those with an extended lip despite their differing global geometry. This suggests that an instability-induced excitation with fluid-dynamic feed back is the governing mechanism.

Keywords: hydraulic structures, gates, seals, pressure fluctuations, shear layers, flow-induced vibrations

1    INTRODUCTION

Gates form an important part of many hydraulic projects as regulators of discharge or water level for storm barrier schemes, dams, barrages and conduits. On any type of gate, seals are designed to prevent leakage from the sides, bottom and sometimes top of the gate. It is well known that J-type seals can initiate flow-induced vibration of gates, particularly at small gate openings (e.g. Petrikat 1979). Pressure fluctuation measurements have shown that broad blocks of timber are not suitable for bottom seals because of the intermittent separation and reattachment of the shear layer to the seal. According to current practice bottom seals are of bar type and manufactured from natural rubber.  These are clamped to the upstream face or downstream side of the gates' skin plate. While such seals can be effective in eliminating leakage beneath a closed gate, some case studies have shown that application of those seals on radial gates could be associated with flow-induced vibration at very large gate-openings in the order of 3 meters (see Hardwick et al. 2000).

The cavity formed between the lip of a submerged radial gate and a protruding seal is somewhat similar to a vertical gate with a downwardly extended lip in the downstream plane of the gate. An inherently unstable shear layer formed beyond the point of separation from the skin plate impinges on the protruding surface. The fluid-dynamic feedback tends to organise the flow oscillations within the cavity and selectively amplify certain frequencies at the expense of others and thus to narrow the frequency band of pressure fluctuations (Naudascher & Rockwell 1994). If the dominant frequency of flow oscillation is close to a natural frequency of the gate and damping is low, this may lead to vibration of the gate.

The objective of the present study is to search for any dominant frequency range in the spectra of pressure fluctuations measured at the bottom seal of a model radial gate. Such information, presented in terms of Strouhal numbers, could be used by gate designers to avoid certain ranges of structural natural frequencies.

2    EXPERIMENTAL APPARATUS AND PROCEDURE

Experiments were carried out in a small open-circuit wind tunnel with a centrifugal fan located at the downstream end drawing air through the tunnel. The speed of the 3-phase fan motor could be varied by an A.C. controller to alter the flow velocity.The test section was rectangular of height 304 mm width 75 mm and length 470 mm (Fig.1.a). In the absence of the gate, the turbulence level of the wind tunnel was around 0.5% of the free stream velocity.

A 2mm thick aluminum plate representing a radial gate was mounted at the entrance of the test section (Fig.1.a). The lip of this stationary gate was at a height of 153.5 mm from the bed of the tunnel. In this experiment a 1:2.5 scale model of the bottom seal of the Torrumbarry weir gates (Hardwick et al. 2000) was built according to an early drawing which was later modified during construction. Reproducing the elastometric proprieties of the prototype rubber seal was not an objective of the present test and consequently two rigid, aluminum elements were attached to the lip to represent the bottom seal and its clamp (Fig.1b).

Fig.1    Schematic diagram for pressure measurements on the model bottom seal

A miniature piezoresistive pressure transducer was mounted flush with the vertical face of the seal and positioned on the centerline (Fig.1b). The operating range of this transducer was  0-13.8 kPa and its sensitivity was about 0.022 mV/Pa. Although the range of pressure fluctuations in this study was substantially lower than the full-scale range of the pressure transducer, its application was vital since it was the smallest sensitive transducer for use in wind tunnels. The nominal response frequency of the transducer is expected to be flat below 10kHz but the maximum frequency which can be spatially resolved is limited by the finite size ( 2mm in diameter) of sensing region of the transducer. The output signal of the transducer had to be amplified with a gain of 350 by a purposely-built differential amplifier.

During pressure measurements, the velocity profile was not measured simultaneously. Instead, a reliable calibration of the fan ar.p.m. made  previously with this flow configuration was used to  estimate the streamwise mean velocity. For such tests, the instantaneous velocity profile was measured by a single, normal hot wire anemometer (see Attari et al. 2000).

 The instantaneous pressure at the single location on the seal was measured for a range of flow velocities by altering the speed of the fan motor. The maximum shear layer velocities (U₀) were estimated to vary between 6.3to18m/s (i.e. maximum r.p.m. of the fan). The Reynolds number based on the lip thickness (d=6.5mm) was between 2730 and 7800.Within this range, the ratio of the pressure fluctuations to dynamic head was around 0.17.

3    SPECTRA OF PRESSURE FLUCTUATIONS

The time history of pressure measurements for each test (N=2¹⁷) was converted to the frequency domain using a Fast Fourier Transform programme incorporating a windowing technique with a frequency resolution of Df=4.9 Hz. The sampling rate of pressure measurements was 20 kHz with the same 6.5 seconds sampling duration as for the previous velocity measurements. A low pass filter was set at 10kHz before digitisation of the data to avoid aliasing.

This study focused on the spectra of pressure fluctuations rather than their magnitude. Figure 2 shows typical power spectra of pressure fluctuations on the seal for flow velocities between 9 to16.3 m/s where the signal to noise ratio was sufficiently high to illustrate dominant frequency ranges in the spectra.

In the high frequency range of the spectra (i.e. > 1kHz), sharp spikes were observed which are marked by (*) symbols in Fig. 2. Since these were also detected by the probe for zero flow, they were believed to arise from electronic noise in the measuring system. These noise spikes are exaggerated by the logarithmic scale of Fig. 2, but they were not strong enough in relation to the signal to prevent the detection of the dominant ranges of energy concentration which were clearly sensitive to the flow velocity. A representative peak within the relatively wide bands for each mode of oscillation was estimated from the spectra. These peak frequencies (i.e. f₁, f₂ and f₃) are marked by (  ) in Fig. 2.

It is useful to relate the peaks of pressure spectra to maximum shear layer velocity (U₀) in the form of a Strouhal number (S=fd/U₀) based on the model gate thickness (d=6.5mm) for comparison with other results. Fig. 3 illustrates the Strouhal numbers at peaks of pressure spectra plotted against Reynolds number ( ). The averages of these values for each mode shown by solid lines on the graph are compared with a simple kinematic model described below.

4    INVESTIGATION BY MARTIN ET AL.

Martin et al. (1975) measured fluctuating pressures on the bottom of a rigidly suspended model gate with two types of bottom geometry. In contrast with results for a flat-bottomed gate,  pronounced peaks were found in the power spectra for the gate with an extended lip. The average values of the Strouhal number, f_nd/U₀ for the two dominant peaks obtained from the experimental data were 0.33 and 0.84.

Fig.2    Spectra of pressure fluctuations at the bottom seal(↓)representative peaks,(*)electronic noise

In a theoretical analysis, Martin et al. (1975) initially examined the validity of a simple kinematic model for the case of an impinging shear layer under a gate. On this basis, the Strouhal number for the dominant frequency of excitation, f_{n ,}was given as:

                (1)

In the case of S_n = 0.5(n –¼), Martin et al. found that the values for the first two modes of excitation were 0.375 and 0.875 which were close to their experimental values.

In an extension of this work, Martin et al. (1975) employed linear inviscid stability theory for the shear layer impinging on the downstream extended lip of the stationary gate. According to this analysis, they calculated that the first-mode fluctuation should occur in a Strouhal number range 0.34<S<0.42 and the next possible mode 0.79<S<0.92. These predicted ranges were found to be in good agreement with the scatter of their experimental data points mentioned above.

5    CONCLUSION

In Table 1 the Strouhal numbers based on the present experimental results are compared with the calculated values from the simple kinematic model, S_n=0.5(n–¼). This relationship had been applied by Martin et al. for verification of their experimental results. A consideration  of  results indicates that the average Strouhal numbers in the present experiment agree well with the simple kinematic model and seems to validate both the value of ¼ and the negative sign in equation 1.

Fig. 3    Strouhal number at peaks of pressure spectra measured on the model seal

From a comparison of the experimental results of Martin et al. with the predicted theoretical values, (i.e.3^rd and 4^th columns of Table 1), Naudascher and Rockwell (1994) concluded that the "possible flow oscillations in impinging-systems are not necessarily harmonically related to each other". The present experimental results appear to have reinforced this conclusion by extension of the mode of oscillation for n=3 which was not available in Martin's experimental data.

  Table 1  Comparison of Strouhal number results

The scatter of experimental results in the present study (Fig.3) is found to be within the range of predicted values based on the linear stability theory employed by Martin et al. The results here with a bottom seal are in good agreement with the experimental results of Martin for a vertical gate with an extended lip. This close agreement suggests that the dominant flow process is a local phenomenon which is generated either with a protruding bottom seal or an extended lip.

Furthermore, the fact that similar results have been achieved for the present study conducted in a wind tunnel and Martin's experiment carried out in a water channel confirms that a free water surface plays no role in the fluid-dynamic feed back process. From the above remarks, it can be concluded that the Instability Induced Excitation (IIE) involving fluid-dynamic feed back is the governing mechanism of flow oscillation both in the present investigation and for gates with an extended lip.

Acknowledgements

The author would like to express his gratitude to Dr. J. D. Hardwick of the Civil Engineering Department, Imperial College, for his advice and valuable discussions throughout this project.

References

Attari, J., J.D. Hardwick, A. Heenan 2000. Hot wire anemometry in the near wake of a model radial gate. Proc. ASME 2000 fluids engineering summer meeting. Boston,USA.

Hardwick, J.D., J.Attari, J. Lewin 2000.Flow-induced vibration of Torrumbarry weir gates. Proc. 7^th International conference on flow-induced vibration. Lucerne ,Switzerland:219-224.

Naudascher, E.& D.Rockwell 1994. Flow-induced vibrations. IAHR Hydraulic Structures Design Manual 7, Balkema: p 139.

Martin, W.W., E. Naudascher, M.Padmanabhan1975. Fluid-dynamic excitation involving flow instability. ASCE Journal of Hydraulic Division, 101(HY6): 681-698.

Petrikat, K.1979. Seal vibration. Practical experiences with flow induced vibrations; Proc. IAHR-IUTAM Symp. Karlsruhe ,Germany: 476-497.