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12.2.2.7: Maximum Value of Oblique shock

The maximum values are summarized in the following Table .

\(M_x\) 1.1000 1.2000 1.3000 1.4000 1.5000 1.6000 1.7000 1.8000 1.9000 2.0000 2.2000 2.4000 2.6000 2.8000 3.0000 3.2000 3.4000 3.6000 3.8000 4.0000 5.0000 6.0000 7.0000 8.0000 9.0000 10.0000
\(M_y\) 0.97131 0.95049 0.93629 0.92683 0.92165 0.91941 0.91871 0.91997 0.92224 0.92478 0.93083 0.93747 0.94387 0.94925 0.95435 0.95897 0.96335 0.96630 0.96942 0.97214 0.98183 0.98714 0.99047 0.99337 0.99440 0.99559
\(\delta_{max}\) 1.5152 3.9442 6.6621 9.4272 12.1127 14.6515 17.0119 19.1833 21.1675 22.9735 26.1028 28.6814 30.8137 32.5875 34.0734 35.3275 36.3934 37.3059 38.0922 38.7739 41.1177 42.4398 43.2546 43.7908 44.1619 44.4290
\(\theta_{max}\) 76.2762 71.9555 69.3645 67.7023 66.5676 65.7972 65.3066 64.9668 64.7532 64.6465 64.6074 64.6934 64.8443 65.0399 65.2309 65.4144 65.5787 65.7593 65.9087 66.0464 66.5671 66.9020 67.1196 67.2503 67.3673 67.4419

It must be noted that the calculations are for the perfect gas model. In some cases, this assumption might not be sufficient and different analysis is needed. Henderson and Menikoff suggested a procedure to calculate the maximum deflection angle for arbitrary equation of state. When the mathematical quantity \(D\) becomes positive, for large deflection angle, there isn't a physical solution to an oblique shock. Since the flow "sees'' the obstacle, the only possible reaction is by a normal shock which occurs at some distance from the body. This shock is referred to as the detach shock. The detached shock's distance from the body is a complex analysis and should be left to graduate class and researchers in this area.

Contributors

  • Dr. Genick Bar-Meir. Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or later or Potto license.