中南大学学士学位论文 外文翻译 原文
Fig. 3. Measured values of the coe?cient
Fig. 4. Lift coefficient for different wind speeds
This figure shows that the effect of wind speed on the lift coefficient is limited for the majority of the angles of attack. This is also true for the other coefficients. The evolution of the coefficients as a function of the wind speed is in fact different for each angle of attack.
4. Galloping in wind tunnel
The sample is suspended by four vertical springs in the wind tunnel (Fig. 5). The four horizontal springs allow the horizontal oscillation of the system. All the springs have the same stiffness (14 N/m) but the vertical ones are prestressed in order to limit the static deformation due to the weight of the structure (2.99 kg). To prevent the wind from blowing on the springs and the part of the structure without ice, two vertical plates (not drawn in the figure) are placed just at the extremities of the ice sample. The convergent and the convergent and the divergent of the wind tunnel have been slightly modified to join these plates. Two circular (diameter 0.2 m) openings allow the movement of the sample but limit the maximum amplitude. The damping in the structure is very low, about 0.08% of critical damping for the vertical and horizontal movement and about 0.3% for the rotation (measured by logarithmic decrement). The ratio between vertical and torsional frequencies is a factor often used to avoid galloping, either by increasing the inertia or by increasing the torsional stiffness (addition of pendula on the overhead line). In this case, it is easier to change the torsional stiffness, simply by modifying the distance between the vertical springs.
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中南大学学士学位论文 外文翻译 原文
The frame anchoring points can be moved in the spring direction to keep the sample at the center of the plate openings when the wind blows (if no instabilities are considered). The vertical and horizontal displacements of the sample and its rotation are recorded by means of a CCD camera working at 50 Hz and with a resolution of 520 pixels. A row of LEDs is placed at the end of the tube to make the processing (in real time) of the signal by a PC easier.
Fig. 5. Diagram of the dynamic system in the wind tunnel
The angular position of the ice with regard to the horizontal is denoted by? (Fig. 1). The ice accretion angle(?0) is the angle ?when the structure is horizontal. Different ice accretion angles and frequency ratios have been tested, and for different wind speeds. First the vertical springs have been placed at 0.12 m from the center of the sample. For this configuration and without wind, the measured vertical (fv), rotational (f?) and the horizontal frequencies are0.845,0.865 and 0.995 Hz respectively. So the ratio between the vertical and the rotational frequencies is about 1, as for a real overhead line with bundle conductors. Different ice accretion angles have been tested: The classical upper quadrant windward (0° to 90°) and the following quadrant (-90° to-180°) in case of reverse wind [9]. The galloping amplitudes observed during our tests very often exceeded the limit of 0.2 m imposed by the openings in the vertical plates, even for the minimum wind speed allowed by the wind tunnel. Figs. 6—9 show the results for a case where the amplitude remains limited. The reduced wind speed is defined by the ratio U0/fd where U0 is the wind speed, f the galloping frequency and d he diameter of conductor.
For this ice accretion angle (?0=-30°), the instability is too high to obtain the limit cycle (actually, a more or less stabilized response) when the wind speed is below 9 m/s and above 12.5 m/s. For wind speeds between these two limits the following remarks can be made. The angular position variation remains constant (Fig. 8), but the maximal peak to peak rotational oscillation increases with the wind speed (from 36.1° to 52.8°). The vertical and horizontal oscillation amplitudes change with time (Figs. 6 and 7). The frequencies of the three movements are the same, 0.89 Hz, this is the galloping frequency (means a reduced wind speed of 335). The trajectory of one point of the sample in the x—y plane is called the galloping “ellipse”. Both the shape and the size of this ellipse are important for preventing the effect of galloping. This can be used by the designers of the towers as a passive countermeasure. For this ice accretion angle, the aspect of the galloping “ellipse” varies highly in relation with the wind speed, even if the wind variation is weak (Fig. 9).
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中南大学学士学位论文 外文翻译 原文
Fig. 6. Horizontal displacement, U0?9.7m/s,?0??30,fvf??0.98,U0/fd?335
?
Fig. 7. Vertical displacement, U0?9.7m/s,?0??30,fvf??0.98,U0/fd?335
?
Fig. 8. Angular position of the ice, U0?9.7m/s,?0??30,fv?
f??0.98,U0/fd?335
Fig. 9. Galloping ellipse for di?erent wind speeds, ?013
??30,fvf??0.98
?
中南大学学士学位论文 外文翻译 原文
In this case, the rotation has a reducing effect on the vertical amplitude, but is due to the changing slope of the galloping ellipse. In other cases it could be the opposite effect. In fact, the variation of the angle of attack is more important. And the phase shift between the variation of the angle of attack and the vertical movement could also influence the vertical amplitude.
Fig. 10 shows the results for an ice accretion angle of -165° (corresponding to a reverse wind). For this angle, the galloping had a behavior different from the previous angle. The amplitudes remained below the limit for all wind speeds below 20 m/s and the 3 movements were stable in amplitude. The galloping “ellipse” kept the same aspect for the different wind speeds. For 12 m/s the peak to peak rotational amplitude was about 13° and the galloping frequency was 0.86 Hz.
The system is strongly unstable for this frequency ratio (fvf??0.98) except between -20° and 0° where it is stable. But between -180° and -20° the system is so unstable that galloping begins for a wind speed below the minimum one allowed by the wind tunnel. So the critical wind speed cannot be measured. Sometimes the system is naturally unstable, sometimes a perturbation must be introduced, either a small rotation or a vertical displacement. For some ice accretion angles a special instability has been observed. It is a rotation in the horizontal plane around the center of the ice sample as the yaw movement for an airplane.
Den-Hartog galloping is characterized by a vertical movement and the absence of significant torsional movement. But for a frequency ratio around 1 it is possible to have an ice accretion angle for which the Den-Hartog criterion is respected and which is also sensitive to the flutter galloping. The Den-Hartog criterion applied to the aerodynamic curves of our ice shape shows two unstable areas (between -180° and 0°), one is located around !180° (classical for a realistic ice shape) and the other around -35°. So for a second time the system has been configured to have the maximum available detuning of the vertical and rotational frequencies. The vertical springs have been placed at 0.36 m from the center of the sample. For this configuration and without wind, the measured vertical, rotational and horizontal frequencies are, respectively, 0.85, 1.54 and 0.96 Hz(fvf??0.55).It allows also to verify the effect of detuning on the flutter galloping. Two areas of ice accretion angles corresponding to Den-Hartog instability were observed. Fig. 11 shows the galloping for an ice accretion angle of !180°. This is not the limit cycle (the amplitude became too high and the sample shocked the plates), but it is clear that the galloping ellipse was vertical and very thin. The rotational amplitude at the end of the recording was less than 3° peak to peak. The frequencies were different for each movement, 0.85 Hz for the vertical displacement, 1.27 for the horizontal displacement and 1.71 for the rotation.
Fig.10.Vertical displacement and galloping “elipse”, U0?12m/s,?0??165?,fvf??0.98,U0/fd?429
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中南大学学士学位论文 外文翻译 原文
Fig.11.Vertical displacement U0?8.5m/s,?0??180,fvf??0.55,U0/fd?308
?5. Conclusions
This experiment shows that the system used to simulate galloping on a suspended string model is appropriate. The observations made during these tests are in good agreement with the tendencies (effect of wind, detuning ratio, galloping ellipse, perturbation effect) noticed with the numerical simulations of a real overhead line. This is a splendid tool to validate the numerical model, both for instabilities and limit cycles in 3D. In the near future, tests will be performed to evaluate the wake effect in a bundle conductor on aerodynamic coefficients; This will cause a more appropriate modeling of bundle conductors by equivalent single conductors. Other tests will be performed to better define the influence of damping (in the three degrees of freedom) on galloping instabilities and amplitudes. Tests will be executed with different detuning ratios to cover single and bundle conductors. Unfortunately our wind tunnel is not convenient to evaluate the effect turbulence, which would also be of great interest.
Acknowledgements
The authors kindly acknowledge “la Communaute? Franc7aise de Belgique” for their financial support in this project. Les “cableries de Dour” gave us different conductor samples. Mike Tunstall from the National Grid has to be especially thanked for giving us some samples of artificial ice, close to natural icing.
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中南大学学士学位论文 外文翻译 原文
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