Where [x.sup.n], [y.sup.n], [x.sup.n+1], and are the positions of x and y at n and n+1 time step respectively, [[beta].sup.n-1], [[beta].sup.n] and [[beta].sup.n+1] are orthogonal coefficients at [beta] at n-1, n, and n+1 time step, [[theta].sup.n] and [[theta].sup.n+1] are
wave angle at n and n+1 time step, and i, i + 1, i - 1 and j, j + 1, j - 1 are distance position on grid x and y at distance step, [Delta]x, [Delta]y, [Delta]t, [Delta]s are the grid spaces of x, y, t and s, and [xi] and [eta] are the elevation factor toward x and y grid.
Schlieren pictures of incident and reflected shock wave angles at flight Mach number 7.72 in perfect gas mode (air in the driver) (Figure 11(a)), emanating from the 14.5[degrees] deflection ramp and reflection at the cowl of 14-X B model, are compared with the correspondent CFD simulation (Figure 11(b)).
Schlieren pictures of the incident and reflected shock wave angles for the flight Mach number 7.1 in real gas mode (helium in the driver) are shown in Figure 13(a).
The temperature ratio (t) and pressure ratio increases when the wave angle increases.
Table 1: Downstream Mach no for various wave angle at [M.sub.1]=3 S.No Deflection Weak shock Downstream Strong Downstream angle deg solution Mach No.
Models of partially perforated and plain wall structures were installed 5 m from the wave generator and the angle of position ([beta]) was changed from 10 to 40 degrees in order to give the effect of the incident wave angle variation.
In order to investigate the wave energy dissipation when the incident wave direction is parallel to the front wall, the relative wave heights along the wall (PV_NS and PVPS) were plotted in Figure 6 when the incident wave angle is 0 degree.
Figure 12 shows the relative wave height distribution in y-direction under the wave conditions of M2 and R2 when the incident wave angle is zero and the relative chamber width is 0.042 which is similar to Figure 9 but the relative chamber width is small.
Both Figure 13 and Figure 14 indicate that the PV_PS and PV_VS reduce the wave energy more than the PW and PV_NS do and there still is a little frequency dependency according to the incident wave angle.
In the case of smaller incident wave angle (10 degrees), the relative wave heights along the wall when the relative chamber width ([C.sub.W.sup.*]) is 0.202 are smaller by 30% than the results with the relative chamber width of 0.101.
Equation (10) describes the kinematical aspect of wave transformation (
wave angle [theta]), while (9) describes the dynamical aspect (wave height H).
