Dynamic stability boundaries for a sinusoidal shallow arch under pulse loads

Abstract

the position of shock Xs0 at zero turbulence level. The boundary-layer momentum thickness Reynolds number Re and boundary-layer displacement thickness <5* measured just before the shock are also shown in the figure. It is observed that an increase in Tu from 0.3 to 6% produces a shift in the shock position of 20%. Such a large change in the shock position cannot be explained solely in terms of the thickening of the boundary layer associated with the increase in freestream turbulence. First, the initial increase in d* followed by a decrease is not likely to produce such a large shift in the shock position in one direction. This is shown by the experiments performed by Delery3 on a similar model and at a constant freestream turbulence level. Second, Re does not increase continuously with the increase in Tu^, whereas the shock position shifts in only one direction with the increase in Tu^. Typically, Tu^ levels of 2.5 and 5.1% produce the same value of Re, whereas the shock positions for these two values of Re are not the same. It appears that the freestream turbulence has a direct effect on the shock interactions and, therefore, the shock position. Figure 3 shows the influence of Tu on the peak Mach number on the model Mpk. The influence of Tux on Mpk is larger at M pk ^1.3, a condition corresponding to significant shock-induced separation. This suggests that the freestream turbulence plays an important part in strong adverse pressure gradients where large regions of separation are present. The pressure distributions in the region of shock-induced separation for a constant value of Mpk = 1,44 and for various freestream turbulence levels Tu are shown in Fig. 4. The differences in Cp levels at the shock position are due to the differences in the freestream Mach numbers needed to achieve a constant value of Mpk. The shock position at this value of Mpk is typically 80% chord. Increase in Tux is shown to produce an increase in pressure recovery at the trailing edge of the motfel. Similar trends in Cp have been observed with the