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How do oblique shockwaves differ from 2D to 3D problems? More specifically, how are the conditions after the shock calculated for a shockwave formed on a cone (e.g. the inlet cone on a ramjet)?

I am familiar with the process/calculations of the after-shock conditions of obliques shockwaves at a ramp, namely for the deflection angle:

Deflection angle calculation

where theta is the deflection angle, beta is the angle between the shockwave and the normal, M is Mach number and gamma is the ratio of specific heats.

Firstly, is there a difference in the conditions when the ramp is revolved into a cone? Secondly, if they are different, what are these differences, specifically in the calculation of the deflection angle and velocity after the shock?


EDIT: Looking at the link suggested and a few textbooks, I found Modern Compressible Flow: with Historical Perspective by John D. Anderson explained conical flow very clearly. To summarise, the ODE to solve is the following:

Taylor-Maccoll

Finding the solution of the flow involves being given either the cone angle and surface Mach number, or the shock angle and the surface Mach number, and then numerically integrating the ODE above.

As for the other conditions after the shock, the shock wave relations for immediately after the shock still hold. Similarly, after the solution to the Taylor-Maccoll equation has been found, the usual isentropic relations for density, pressure, temperature etc. can be used.

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To reiterate my edit and close the question:

Looking at the link suggested and a few textbooks, I found Modern Compressible Flow: with Historical Perspective by John D. Anderson explained conical flow very clearly. To summarise, the ODE to solve is the following:

Taylor-Maccoll

Finding the solution of the flow involves being given either the cone angle and surface Mach number, or the shock angle and the surface Mach number, and then numerically integrating the ODE above.

As for the other conditions after the shock, the shock wave relations for immediately after the shock still hold. Similarly, after the solution to the Taylor-Maccoll equation has been found, the usual isentropic relations for density, pressure, temperature etc. can be used.


EDIT: The comment I was referring to regarding a link was deleted so I'll link the website here: https://www.grc.nasa.gov/WWW/K-12/airplane/coneflow.html

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