円柱背部における流れの剪断層内の速度変動に与える音響的撹乱の影響

抄録

It was found that there were two frequency groups of acoustic disturbances which gave much influence upon vortex-shedding from a circular cylinder in an air flow. One has a narrow frequency range centering on the natural vortex-shedding frequency f_n, the other has a relatively wide frequency range which corresponds with the frequency of the laminar-turbulent transition wave f_t in the separated boundary layer from the cylinder surface, i. e. , in the shear layer. In order to investigate the growth of the periodic velocity fluctuations, auto- and cross-correlation functions for the maximum velocity fluctuation (u)_<max> in the shear layer were analyzed with the aid of DISA hot-wire anemometers (model 55D01), a TEAC real-time digital correlator (model C-110) and so on. Fig 1 gives the block diagram used to obtain the cross-correlation function R_<12>(τ) defined by eq. (2). In our experiments, the datum probe in Fig. 1 was fixed at the position where two of the different frequencies of the periodic velocity fluctuations in f_n and f_t were observed simultaneously. We got the optimum delay time τ_0 from R_<12>(τ) to investigate the travelling of the periodic velocity fluctuations. The detail of the experimental apparatus is described in reference 1). Fig. 2-1 gives the auto-correlation coefficients R_<11>(τ)/(R_<11(0)>) for (u)_<max> in the natural shear layer (Re≒1800, U_∞≒3. 4 m/s, f_n≒85 Hz). In the laminar region of the shear layer close to the cylinder there was no periodicity in the velocity fluctuations. But, at x/d=1. 327, a sinusoidal velocity fluctuation by the transition wave was detected in the random velocity fluctuation, and it's amplitude grew downstream. The frequency of the transition wave was about 250 Hz. It was found from the cross-correlations (Fig. 3-1) that this wave propagated in the direction of the air flow with a velocity of about 0. 74U_∞ in the region 0. 8<x/d<2. 1. Further downstream, the correlation for the periodic turbulence originated from vortex-shedding was superior to that for the transition wave. On the other hand, the influence of acoustic disturbances upon the laminar region of the shear layer (Fig. 5). In this paper, two progressive sound fields with the frequency f_a=85 Hz (≒f_n) and 246 Hz (≒f_t) were superimposed upon the flow field. The intensity of the acoustic particle velocity in y-direction v_<fa>/U_∞ (U_∞≒3. 4 m/s) were about 0. 3% at the cylinder position in both sound fields. When the acoustic disturbance with f_a=246 Hz (≒f_t) was superimposed upon the flow field, even near the cylinder (at x/d=0. 449), the transition wave could be detected by auto-correlation measurements (Fig. 2-3), and propagated downstream in the region 0. 5<x/d<1. 8 by cross-correlation measurements (Fig. 3-3). This region was nearer to the cylinder than the natural one. Then, laminar-turbulent transition in the shear layer was promoted by the superimposition of this acoustic disturbance. But, the wave also had the velocity of about 0. 74U_∞, and this velocity was not influenced by the acoustic disturbance superimposed upon the flow field. When the acoustic disturbance with f_a=85 Hz (≒f_n) was superimposed, (u)_<max> in the shear layer behaved in an almost sinusoidal fluctuation in the vortex-shedding frequency throughout the whole shear layer (Fig. 2-2). The transition wave was not detected in the shear layer (Fig. 2-2). It is shown in Fig. 3-2 that throughout the laminar region of the shear layer, i. e. , x/d<(x/d)_t, optimum delay time τ_0/T was nearly 0. 5, where T was the period of vortex-shedding. In other words, velocity fluctuations in the vortex-shedding frequency between upper and lower shear layers are in adverse phase. Further downstream, in the region x/d>(x/d)_t, τ_0/T increased with increasing x/d, and in x/d>3. 5, vortices formed from the shear layer travel in the

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