3. 3 Effects of Cylinder Arrangement

We evaluate the overall features of the interaction of the shock wave with the cylinder array by the pressure of the transmitted shock wave (denoted by P 5), the pressure behind the reflected shock wave (P7), and the Strouhal number (St) of the pressure oscillation in the wake (P6). By testing various cases listed in Table 1 , the effects of the cylinder arrangement on these values are clarified as follows:

Attenuation of Transmitted Shock Wave in Single Row or Single Column Arrangement
Figure 16 shows the effect of the number of cylinders on the pressure behind the transmitted shock wave (P5) for the single row arrangement and single column arrangement (for definition, see the category I and II in Table 1 ) . The initial pressure ratio (P4/P1) of the shock tube is varied from 4.0 to 7.0. In the case of the single row arrangement, the pressure behind the transmitted shock wave deereases with the increase in the number of cylinders. In the case of the single column arrangement, however, P5 is hardly affected by the number of cylinders. In the case of the single column arrangement, the effect of the distance between cylinders is investigated but it is negligibly small. Consequently, the attenuation of the transmitted shock wave mainly depends on the maximum blockage ratio of the cylinders in the channel.

Effects of Staggered Arrangement on Transmitted Shock Wave
Figure 18 shows the comparison between the regular arrangement and the staggered arrangement with respect to the pressure behind the transmitted shock wave in the case of one cylinder in a row (category IV in Table 1 ) . The comparison in the case of multi-cylinders in a row (categories III and V) is presented in Fig. 19. In both cases, the difference between the regular (in-a-line) arrangement and the staggered arrangement is quite small. In the pressure record at port # 4 (near wake region), however, the oscillation seems more significant for the staggered arrangement than for the regular arrangement as shown in Fig. 20.

(L)Fig.20.Effect of Staggered Cylinder Arrangement on Pressure Records
(R) Fig.21.Variation of Pressure behind Transmitted Shock Wave with Blockage Ratio

Effects of Cylinder Diameter on Transmitted Shock Wave
Figure 21 shows the variation of the pressure behind the transmitted shock wave with the blockage ratio for the single row arrangement. Note that the blockage ratio for one cylinder of 8 mm diameter is the same as that for two cylinders of 4 mm diameter. The curve for the 4 mm diameter cylinder almost coincides with that for the 8 mm diameter cylinder. The attenuation of the transmitted shock wave depends not on the cylinder diameter but on the blockage ratio.

Fig.22.Variation of Pressure behind Transmitted and Reflected Shock Wave
with the Total Number of Cylinders

Augmentation in Reflected Shock Wave and Attenuation in Transmitted Shock Wave
Figure 22 shows the variations of the pressure behind the transmitted wave (P5) and the pressure behind the reflected wave (P7) with the number of cylinders in the cases of the regular arrangement (category III), staggered arrangement (category V) and random arrangement (category VI) in Table 1 . The pressure augmentation due to the reflected shock wave in the upstream region of the cylinder array is much larger than the pressure attenuation of the transmitted shock wave. Both the pressure attenuation in the downstream and the pressure augmentation in the upstream seem to depend mainly on the number of cylinders, in other words, porosity (volume fraction of void).

Strouhal Number of Pressure Oscillation in Wake Region
Figure 23 shows the power spectrum of the pressure oscillation at port # 4 Iocated in the near wake of the cylinder array. The cylinder arrangement is O004-R and the initial pressure ratio of the shock tube is 5.0. A distinct peak is observed around 10 kHz. This peak is expected to represent the frequency of the Kármán vortex shedding. The variation of the Strouhal number with the number of cylinders or the number of rows is shown in Fig. 24. The Strouhal number St is defined by:

(L)Fig.23.Power Spectrum of Pressure Oscillation ib Wake of Cylinder Array
(R) Fig.24.Strouhal Number of Pressure Oscillation in Wake of Cylinder Array

cylinders or the number of rows is shown in Fig.24 The Strouhal number St is defined by:

......(1)