Nozzle Dynamics - Shockwaves
Supersonic flows have the possibility to create shock waves in the nozzle that can effect the properties of the flow across the shock wave boundary. Unlike normal nozzle assumptions, flow across a shock wave is not isentropic. This leads to a whole set of equations that describe the changes in flow conditions across a shock wave.
A unique property of shock waves is that they can reduce a supersonic flow to a subsonic flow across the discontinuity of the shock. This is in most cases undesirable, but can also be used as a design criteria. Since a shock is irreversible, it cannot be isentropic.
The Mach number changes across a shock wave (supersonic to subsonic) and is calculated through the following equations:
\[M{a_2}^2 = \frac{{(k - 1)M{a_1}^2 + 2}}{{2kM{a_1}^2 - (k - 1)}}\]
From this equation, for all specific heat ratios greater than one, the resultant Mach number on the other side of a supersonic shock wave must be subsonic. Shock waves in this regard can be dealt with as discontinuities within the flow and therefor have no width.
A unique property of shock waves is that they can reduce a supersonic flow to a subsonic flow across the discontinuity of the shock. This is in most cases undesirable, but can also be used as a design criteria. Since a shock is irreversible, it cannot be isentropic.
The Mach number changes across a shock wave (supersonic to subsonic) and is calculated through the following equations:
\[M{a_2}^2 = \frac{{(k - 1)M{a_1}^2 + 2}}{{2kM{a_1}^2 - (k - 1)}}\]
From this equation, for all specific heat ratios greater than one, the resultant Mach number on the other side of a supersonic shock wave must be subsonic. Shock waves in this regard can be dealt with as discontinuities within the flow and therefor have no width.
JL