Rayleigh flow

The heat addition causes a decrease in stagnation pressure, which is known as the Rayleigh effect and is critical in the design of combustion systems.

Solving the differential equation leads to the relation shown below, where T0* is the stagnation temperature at the throat location of the duct which is required for thermally choking the flow.

Figure 1 shows that heating will increase an upstream, subsonic Mach number until M = 1.0 and the flow chokes.

Differential equations can also be developed and solved to describe Rayleigh flow property ratios with respect to the values at the choking location.

For instance, the combustion chambers inside turbojet engines usually have a constant area and the fuel mass addition is negligible.

Therefore, the Rayleigh flow model is critical for an initial design of the duct geometry and combustion temperature for an engine.

These two models intersect at points on the enthalpy-entropy and Mach number-entropy diagrams, which is meaningful for many applications.

For Figure 3, these values are M = 3.0 and 0.4752, which can be found the normal shock tables listed in most compressible flow textbooks.

A given flow with a constant duct area can switch between the Rayleigh and Fanno models at these points.