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Shock diamonds are formed when the exhaust (or any other flow) exits a nozzle supersonically and at a pressure different than that of the ambient atmosphere, i.e., the nozzle is either underexpanded or overexpanded. Because the flow is supersonic, the adjustment to the atmospheric pressure is through waves; these are initially either oblique shocks or Prandtl-Meyer fans. As the waves reflect from the edges of the jet, they change polarity, i.e., an expansion fan reflects as a compression wave and a compression shock reflects as an expansion fan. Thus, both types will ultimately be present. In the above sketch, the nozzle is taken to be overexpanded so that the initial wave system is comprised of oblique shock waves. The initial oblique shock is marked as 1 in the diagram. The reflected expansion fan is marked with a 3 in the diagram.
Each type of wave will intersect its counterpart originating at the other side of the jet or nozzle exit at the plane or line of symmetry. Because of the symmetry, the intersection can be modeled as a reflection from a rigid wall. It is well known that shock waves may reflect from rigid walls either as a regular reflection or a Mach reflection. The case of a Mach reflection is depicted in the above sketch. The Mach stem is marked with a 2 in the diagram. In the case of an axisymmetric jet, the Mach stem is a Mach disk which is recognized as the shock diamonds seen in the exhaust of many high speed aircraft.
Because of repeated reflections and re-reflections, several Mach stems will appear until the disturbances are damped out by viscous effects. The second Mach stem is marked with a 5 in the above sketch.
The situation for an underexpanded nozzle is essentially the same. The main difference is that the initial wave system is a Prandtl-Meyer expansion fan similar to that marked by a 3 in the above sketch. As pointed out above, the expansion wave converts into a compression wave upon reflection from the contact surface, i.e., the edge of the jet. The Mach lines then converge to form a compression shock which may then undergo a Mach reflection similiar to that in the case of the overexpanded nozzle. An example of a compression shock resulting from this convergence is denoted by the number 4 in the above sketch.
The sketch at the above right is mine. Please contact me if you have any comments or suggestions. ( I know, I know, ..... there is no slipstream at the triple point. I didn't want to clutter the picture.) Click on the image to see a larger ( 14 Kb ) version.
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