管路中の管群から発生する変動圧力

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The heat exchangers with tube banks have been widely used for steam power plants and other purposes. In such heat exchangers, violent acoustical oscillations have often been experienced and they have yielded extraordinarily heavy noises and such intensive vibrations that the duct wall breaks sometimes. It has been revealed by many authors that those phenomena resulted from fluctuating pressure due to periodic generation of Karman vortices from the tube bank. In this study, the model tube banks of an in-line arrangement or a staggered one, such as shown in Fig. 2 and Table 1, were used and the fluctuating pressure occurring in the tube banks was elaborately measured and the associated phenomena were observed. The notations to express the tube arrangements were defined as follows. For example, S8-4(-10) shows the staggered arrangement, P_L=L/D=8, P_T=T/D=4 (and that the number of rows of tubes in the flow direction is 10), or P4-2(-5) does in-line arrangement, P_L=4, P_T=2 (and the number of rows of tubes in the flow direction is 5). The used apparatus, measuring devices and instrumentation were such as shown in Fig. 1 to Fig. 5. Since the working section was the duct with the rectangular section which had one side shorter than the other, it was able to be regarded as a two-dimensional field. As the representive value of fluctuating pressure in the tube bank, the measured one on the upper wall at the section immediately upstream form the tube bank was taken. Fig. 6 is typical example of the overall level of fluctuating pressure, L_0, shedding frequency of Karman vortices, f_k and intensity of the component of f_k, L_k plotted against mean flow velocity in the duct, U_0. In this example, L_0 took two extreme values at f_k=375Hz and f_k=705Hz. These values were nearly equal to the natural acoustic frequencies of the duct, f_b(1/2)=355Hz for 1/2 wave mode and f_b(1)=710Hz for 1 wave mode. These and following facts proved acoustical resonance. Such extremities were observed in the relations of L_0 or L_k over U_0 for all arrangements of 2<P_L<10 and 2<P_T<4. While, Fig. 9 shows the same relations in the case of P2-4. In this case, though the fluctuating pressure component of f_k could be clearly identified, no resonant state was observed, that is no extreme point was found on its L_0-U_0 or L_k-U_0 relation. Therefore, it was clear that, even if Karman vortices may generate from tubes, resonance does not always occur but needs the condition that the tube arrangement must be confined with in a certain range. In each case, f_k was accurately proportional to U_0 and , then, the Strouhal number became a certain constant depending only on the pattern of tube arrangement, regardless of the total number of tubes. The Strouhal numbers gained in this study are shown in Table 3. From these results, it was deduced that a slight variation of tube arrangement gave a considerable change to the value of the Strouhal number. It seems that the relation of St with P_L and P_T is not very simple but quite complicated and perhaps discontinuous. Fig. 7 shows the distribution of L_0 along Y-axis at the duct section immediately upstream of tube bank in the case of S8-4 with U_0/U_r as parameter. Where, U_r is the flow velocity at resonance. Fig. 8(b) is an example of the distribution of equal L_0 lines over X-Y plane at resonance. As evidently shown in both the figures, on the resonant state, an obvious standing wave was found in within in the tube bank or its close vicinity. In Fig. 10, the resonance level of 1/2 wave mode standing wave, L_b(1/2) is plotted against the total number of tubes, N, for different types of tube arrangement. It followed from these results, that, as the number of tubes increased, resonance became stronger. Further, by comparing the level of 1/2 wave mode for S4-4-10 with that of 1 wave mode for the same arrangement which is shown in Fig. 10, it is known that the resonance of a higher mode is stronger than that of a lower
社団法人日本音響学会の論文
1971-08-10

管路中の管群から発生する変動圧力

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