Experimental Study of Separation from the Base of a Cone at Supersonic Speeds

Abstract

ranging from 1600 to 18,000. These results are plotted in Figs. 1 and 2 showing ar and a> vs the real frequency /i At each value of R the range of values of ft was chosen to include the whole region of amplification and also sections of the damping region near the neutral curve. In Fig. 1, the graphs of ar vs ft are monotonically increasing and the slope of these lines, representing the reciprocal of the group velocity, becomes slightly steeper as the Reynolds number increases. However, it is observed that at Reynolds number above 12,000, the slope d(y.r/dp, decreases with increasing ft at values of ft which correspond to points in the damping region beyond those of amplification. For amplification, a,must be negative and it is evident from Fig. 2 that, according to the present calculations, the critical Reynolds number is slightly less than 6000. The curves of a, = const are shown in Fig. 3. The important parameters of the neutral stability curve are given in Table 1. The critical Reynolds number, according to present calculations, is 5778 and the corresponding value of ar being 1.0219. The numerical calculations of Thomas give a neutral stability curve which is almost identical with the present results. Thomas found the critical Reynolds number to be 5780 with the corresponding a to be 1.026. Orszag's results of the critical Reynolds number and wave number a were 5772 and 1.0206, respectively. His numerical solution was based on expressing the differential equations in terms of Chebyshev polynomials. The frequency ft corresponding to the critical Reynolds number is found to be 0.269.