MadSci Network: Engineering
Query:

Re: Mach diamonds or shock diamonds

Date: Thu Aug 26 01:37:40 1999
Posted By: Troy Goodson, Staff, Spacecraft Navigation, Jet Propulsion Laboratory
Area of science: Engineering
ID: 934919579.Eg
Message:

Dave,

I have to admit that your question sent me back to my books. At first, I did a little search of the web re: "mach diamonds" I did find a web page with a nice picture: http://www.gas-turbines.com/hobby/nt5.htm. A search for Mach diamonds on Google's image locator found additional images.

This reminded me of a diagrams my professors drew in propulsion class, but it didn't strike up any chords about speed of the aircraft (its Mach number).

I found the diagram in a section titled "Rocket Exhaust Nozzles" in "Mechanics and Thermodynamics of Propulsion" by P. G. Hill & C. R. Petersen, Addison-Wesley Publishing Company.

And I quote, for underexpanded nozzles, where the outside (ambient) pressure is less than the pressure of the exhaust gases: "the pressure adjustment ocurs beyond the exit plane as a series of expansion waves whose initial influence propagates at the Mach angle alpha. ... The expansion waves reflect from the jet boundary as compression waves which may actually converge to form a shock. The pattern of alternate expansion and compression is repeated downstream and the associated temperature pattern may, becuase of varying gas incandescence, render the pressure pattern visible." (about the mach angle: sqrt(M*M - 1)*tan(alpha) = 1 where sqrt is the square-root, M is the Mach number, tan is the tangent function, and alpha is the Mach angle.)

The situation is different for an overexpanded nozzle. In this case, the angle of the shock wave is not the Mach angle.

There is a very very very nice, interactive description at http://www.allstar.fiu.edu/aero/rocket3.htm

As you may have guessed, I can't speak as an expert on the thermodynamics of rocket exhaust. However, I can tell you that the shear number of these shock waves is not going to reveal the Mach number of the exhaust. The number of these waves is going to be determined by dissipation effects.

As far as calling them Mach diamonds or Shock diamonds, I think that's a personal preference.

If you find more information that confirms or denys what I've written, I'd really like to hear about it.

Troy http://surf.to/tdg/


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