Starred ratios on the Rayleigh line
For a perfect gas, P/P* = (1+γ) / (1 + γ M²) and T/T* = [M (1+γ) / (1 + γ M²)]². The stagnation-temperature ratio T0/T0* = 2(γ+1) M² (1 + (γ−1)M²/2) / (1 + γ M²)² reaches 1 at Mach 1: you cannot add more heat without choking the duct or changing the mass flow. At every starred station the ratios are 1, as they are on the Fanno line, but the path between stations is heat, not friction.
For friction without heat, use the Fanno flow calculator. Area change without heat or friction is isentropic flow. A normal shock can connect the subsonic and supersonic branches of a Rayleigh or Fanno line; that jump is on the normal-shock page.
Sources
- John and Keith, Gas Dynamics; Zucker and Biblarz, Fundamentals of Gas Dynamics.
- Anderson, Modern Compressible Flow.
Frequently asked questions
What does T0/T0* tell me?
How close the flow is to thermal choke. A value of 1 is Mach 1 on the same Rayleigh line; you cannot add more stagnation temperature without changing the inlet state or the mass flow.
Does heat addition always increase static temperature?
Not once you are past the point of maximum T on the subsonic branch. The table is the right place to look; T/T* has a peak near M = 1/√γ, not at M = 1.
Is this a burner model?
Only in the one-dimensional, constant-area, perfect-gas sense. A real combustor has area change, pressure loss, and a changing composition.