Modeling the Shock Wave

When you go faster than the speed of sound you make a shock wave where the air is compressed. As the ideal gas law indicates, when you compress air it gets hotter. This is the basic idea we use for modeling the shockwave and the temperatures it produces.

There is a nice Java applet showing shock angle as a function of mach and the shape of the wedge going through the air. You can also see the formulas for shock angle and temperature. There is also a web page with more information on shock angles and it has a fortran program to calculate it. Another web page has another fortran program. And on the applet the "Oblique Shock Relations" will also tell you shock angle. These 2 different applets and 2 different programs all seem to get about the same result. Also, these match examples

In this simulator we currently assume that the specific heat of air is constant at 1.4. Looking at the properties of air the specific heat ratio does not seem to change much from 1.4. Not sure how much error this introduces though.

In this simulator we use an ideal gas model. It turns out that at high Reynolds numbers, the shock layer can be treated as inviscid (meaning there is no friction). Also, the "caloric perfect gas assumption" is not too bad, but at high temperatures some of the heat goes into chemical reactions in air and so the caloric perfect gas assumption overpredicts the temperature.

So as I understand it, the the way the simulator works it is reporting temperatures that are higher that in the real world. So if our SSTT design can handle the temperatures indicated by the simulator then it can handle the real world. Also, it seems that we can keep under most of the chemically reactive temperatures with the SSTT approach anyway.

A few other papers to look at:

The simulator massNoseAngle is the angle for an equivalent wedge. They say that a "relatively simple hypersonic flow analysis technique is an approximate method based on equating the body of interest with a two-dimensional wedge for modeling cones". So if the user really has some shape other than a wedge they should apply this relatively simple technique to generate an input angle for this simulator. :-).

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