1. Mach Train and Pseudo-shock By: Ehsan Roohi
Advanced Propulsion
Mach Train and Pseudo-shock
By: Ehsan Roohi

2. Topic
Irregular Reflection
Shock Polar
Mach Train
Analytical Relations

3. MACH REFLECTION

7. Viscous Effects
The interaction with the boundary layer depends on whether the
boundary layer is laminar or turbulent, where the interaction of the incident shock wave with the boundary layer near the reflection point, R, of an RR is shown schematically
a Mach stem was always present and that the bottom of this wave was bifurcated

8. The reflection was said to be regular (RR) if the Mach stem and the lambda foot were confined to the boundary layer and irregular (IR) if either the Mach stem or the lambda foot extended into the main stream.
Two types of regular reflection were found, one that had a reflected compression wave and the other that had both reflected compression waves and expansion waves
There were two types of IR, one that had a Mach stem present in the main stream and the other that was characterized by a four wave configuration.

9. Shock Train
The interaction between a normal shock wave and a boundary layer along a wall surface in internal compressible flows causes a very complicated flow.
When the shock is strong enough to separate the boundary layer, the shock is bifurcated and one or more shocks appear downstream of the bifurcated shock.
A series of shocks thus formed, called shock train, is followed by an adverse pressure gradient region, if the duct is long enough

10. Shock Train
The term pseudo-shock is used to indicate the flow region from the head of the shock train to the end of the subsequent static pressure recovery region mentioned above.

11. By region of shock train, we represent the region where the series of shocks in line can be visible by optical observations.
Up to the present, the shock train defined above has been called in many ways by many researchers, such as multiple-branch shock [33], shock system [34], etc., as listed in Table 1

12. Curve 2 indicates that the pressure at the centreline rises and falls repeatedly as a result of the presence of the successive normal shocks in the shock train. It should be noted that curve 1 overlaps with curve 2 after the point j, and this point may be located near the end of shock train. Behind this point, the pressure still Increases.

18. Square Duct

20. the total entropy increase due to successive shocks would be negligible
compared with that due to a single normal shock.
He assumed that the essential dissipative phenomenon for the pseudo-shock does not reside in the shocks but in the turbulence generated in the dissipative region near the wall surface.
He made further assumption that in the limit the presence of the shocks may be disregarded entirely and that the main flow in the central core region is uniform and isentropic.
Crocco supposed that the non-uniform dissipative region may be approximately treated as an equivalent uniform region