圆柱尾迹的时空结构英文文献和中文翻译(2)

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The present experimental investigation, which is based on a new and particularly welladapted anemometer, namely an ultrasound velocity profiler, brings a verification of this critical behavior of the wake near its threshold. Then, motivated by some of these measurements, we present some original visualizations of a varicose instability of the wake behind a very small aspect ratio cylinder.

Experimental arrangement and techniques

Our experimental facility consists of a water loop and is fully described by Le Gal et al(1996). The test section is 20 mm high and 128 mm wide. The water velocity can be varied between 0 and 1 m/s. It is measured by a home-made flow-meter and the back-ground turbulence intensity of the flow has been estimated by a hot-wire anemometer as about 0.5 %.To avoid the emergence of three-dimensionnal shedding, a small aspect ratio cylinder having a diameter d equal to 4 mm, is positionned on one of the horizontal walls of the channel. Its length is 1=20 mm (l/d=5) and it is in close contact with the other horizontal wall. As the cylinder touches the opposite wall and because no end-plates have been used to control the boundary conditions, horse-shoe vortices are created in the boundary layers of the walls of the water tunnel, around the ends of the cylinders. However, it is observed by visualisations and by ultrasound measurements that the alternate vortex shedding in the bulk flow is only slightly affected by the presence of these vortices. In the first part of this study, a classical hot-wire study of the temporal behavior of the wake is performed with a pobe placed seven diameter downstream the cylinder (x/d=7, y/d=O). The parameters of the Landau equation are calculated by a classical procedure based in particular on the impulse response of the wake. Then, its spatial shape is studied by ultrasound anemometry whose operation principle is ultrasound echography. An ultrasonic 4 MHz frequency pulse is emitted through the water flow by a piezoelectric probe having a diameter of 8 mm. The sound beam (roughly 5mm in diameter) propagates inside the flow and is reflected by 100 microns hydrogen bubbles which are generated by a electrolysis of water using a 0,1 mm platinium wire stretched across and at midheight of the channel, 100 mm upstream of the cylinder. When the piezoelectric transducer recieves the echoes back, the anemometer calculates the position of the reflecting bubbles by the time delay between the emitted and the recieved pulse, as well as the Doppler shift they generate because of their own velocity. More details about this technique can be found in Takeda et al (1993). When correctely seeded, the flow can be analysed by the measurements of instantaneous velocity profiles projected onto the direction of the sound beam. We performed to two sets of experiments. In the first, the ultrasound probe is placed in a groove machined in the middle plane of the side-wall of the channel. By this configuration, the transversal velocity profiles can be measured along lines crossing the main flow in the y direction. The transversal velocity profiles are recorded every 69.8 ms (or for some experiments, every 135.3 ms), in 128 spatial positions separated by 0.74 mm. 1024 instantaneous profiles are then recorded for several Reynolds numbers R. In the second set of experiments, the ultrasound probe is positionned inside the water flow, 80 mm downstream of the cylinder (x/d= 20) and 2 mm on its side (y/d= 0.5) in such a manner that longitudinal velocity profiles can be recorded.

Hot-wire determination of the temporal features of the wake

In the experimental conditions described in section 2, the critical Reynolds number Rc is determined by a careful hot-wire study of the wake. In particular, when studying the impulse response of the wake at different Reynolds numbers, the shedding frequency and the decay rate of the oscillations are obtained under the threshold. This study is then completed above the threshold, where the amplitude and the frequency of the saturated regimes are measured. The critical value (Rc=102±2) that we obtain agrees perfectly well with the previous study of Lee and Budwig (1990) concerning small aspect ratio cylinder wakes. The determination of the coefficient c2 leads to a value equal to -1 ± 0.1 which completes the study of Albarecte and Provansal (1995). Figure 1 shows the evolution of the frequency (a) and of the square of the amplitude (b) of the wake, measured on the axis, at 7 diameters downstream the cylinder. The change of slope of the frequency curve is reminiscent of the non linear feature of the wake oscillation and the ratio between the two slopes leads to the deternination of the ~ coefficient. Note also on Figure 1-b, that the prediction of the Landau equation - i.e. that the amplitude of the saturated oscillations above the threshold has to be proportionnal to the square root of the threshold distance- seems to be valid only for Reynolds numbers less than 160. Above this value, we note a saturation of the square of the amplitude that deviates from the linear prediction. Next section which presents a global description of the wake will give an explanation of this saturation.