3. 2 Interaction of Shock Wave with Cylinder Array

Figure 9 shows the typical pattern of the pressure records in the far upstream (port # 1 ), just after the cylinders (#4) and in the far downstream (# 8). The cylinder arrangement is 4444-R (see Table 1 ) . The results in the absence of cylinders are also shown for comparison. The effects of the presence of the cylinder array are summarized by the features:

(1) pressure augmentation in the upstream region due to the shock wave reflected at the cylinder array,
(2) significant pressure oscillation just after the cylinder array,
(3) pressure attenuation in the transmitted shock wave and slight slowdown of its velocity. The wave diagram of the present flow is schematically shown in Fig. 10. For convenience of discussion, each state is numbered as indicated in the figure.

Fig.9.Pressure Records for Cylinder Arrangement 4444-R

Table 1. Cylinder Arrangement for Present Experiments(1)

Table 1. Cylinder Arrangement for Present Experiments(2)

Table 1. Cylinder Arrangement for Present Experiments(3)

Table 1. Cylinder Arrangement for Present Experiments(4)

Table 1. Cylinder Arrangement for Present Experiments(5)

Table 1. Cylinder Arrangement for Present Experiments(6)

Fig.10.Wave Diagram in Presence of Cylinder Array

Pressure Augmentation in the Upstream Region due to Reflected Shock Wave
The incident shock wave is partially reflected at the cylinder array. The reflected shock wave propagates upstream and the pressure augmentation occurs as seen in port # I of Fig. 9. The pressure rise due to the reflected shock wave seems slightly diffusive and the plateau portion after it becomes oscillatory in comparison with the incident shock wave, since the reflection does not occur in-stantaneously in the cylinder array. The schlieren picture in the upstream region of the cylinder array (Fig. 11 ) shows that the reflection does not occur as a single wave and that it consists of a couple of shock waves.

Fig.11.Schlieren Picture of Reflected Shock Wave

Pressure Oscillation in the Wake of Cylinders
In the present experiments, the flow behind the incident shock wave is subsonic and the wake behind the cylinders is expected to be similar to that in the incompressible flows. When the flow passes through the cylinder array, the starting vortices are generated and convected downstream. The starting vortices are expected to be located at the contact surface indicated in the wave diagram (Fig. 10), since they are convected at the flow velocity behind the transmitted shock wave, which is denoted by U5. Figure 12 shows the schlieren pictures of the starting vortices for the cylinder arrangement 0002-R. Comparison of the view in the direction of the cylinder axis (window A) and the spanwise view (window B) indicates that the wake flow behind the cylinders is almost two-dimensional. The Kármán vortex street follows the starting vortices in state # 6 of the wave diagram (Fig. l0). The view from window C (the spanwise view of the cylinders and their near wake) is shown in Fig. 13. The lines in parallel to the cylinder axis indicate the formation of the Kármán vortices. The propagation of the reflected shock wave is also seen in this figure. The Kármán vortices cause the cyclic oscillation of the pressure in the wake region of the cylinder array as observed in port # 4 of Fig. 9. In this case, the Strouhal number of the pressure oscillation and the Reynolds number referred to the cylinder diameter and the local flow velocity (U5) is 0.24 and 5 X 10⁴, respectively. The Strouhal number of 0.24 is close to 0.2 which is known as that for a cylinder in the freestream of the same Reynolds number range.

Fig.12.Schlieren Pictures of Starting Vortices

Fig.13.Schlieren Pictures of Karman Vortex Shedding

Pressure Attenuation in Transmitted Shock Wave
When the incident shock wave passes through the cylinder array, it is attenuated due to the drag force of the cylinders as seen in port # 8 of Fig. 9. The arrival of the transmitted shock wave is slightly delayed in comparison with the case in the absence of cylinders. The pressure oscillation is not so significant as that in port # 4, since the conveetion of the vortices is slower than the propagation of the transmitted shock wave and the starting vortices have not arrived at port # 8 by the end of the test duration (see Fig. l0). It should be noted that the pressure attenuation in the transmitted shock wave in the downstream region of the cylinder array is smaller than the pressure augmentation due to the reflected shock wave in the upstream region.
Figure 14 shows the schlieren pictures of the transmitted shock wave. The diamond-shaped cell pattern is observed behind the shock front. When the number of cylinders increases, the cell size becomes smaller and the number of cells increases. Such pattern is expected to be caused by the diffraction of the incident shock wave at the cylinders and the reflection of these diffraction waves at the test section wall. To reveal the precise mechanism of formation of such pattern, the viewing area of the schlieren picture should be much wider to cover both the near and far downstream regions.

Fig.14.Schlieren Pictures of Transmitted Shock Wave for Various Cylinder Arrangement

Three-dimensional Effects in Flow Field
In the present experiments, the three-dimensional effects on the flow are expected to be quite small. Figure 15 shows the schlieren pictures of the transmitted shock wave from window A (view in the direetion of cylinder axis) and window B (spanwise view). The cylinder arrangement is 4444-R. The complicated diamond-shaped cell pattern is observed only from window A. This means that the flow is almost uniform in the spanwise direction. The similar observation is obtained in Figs. 12 and 13.
The pressure records at ports # 2, 3 and ports # 6, 7 show that the pressure depends mainly on the streamwise location and that there is no significant pressure gradient on the transverse plane normal to the shock tube axis. Consequently, the one-dimensional model is appropriate to describe the flow in the present experiments.

Fig.15.Schlieren Pictures of Transmitted Shock Wave in Different Viewing Directions