Rayleigh Flow (Duct Flow with Heat Transfer and Negligible Friction)

Rayleigh Flow (Duct Flow with Heat Transfer and Negligible Friction)

Flow in a constant area duct with heat transfer and without friction is known as Rayleigh flow . Many compressible flow problems encountered in practice involve chemical reactions such as combustion, nuclear reactions, evaporation, and condensation as well as heat gain or heat loss through the duct wall Such problems are difficult to analyze Essential features of such complex flows can be captured by a simple analysis method where generation/absorption is modeled as heat transfer through the wall at the same rate

In certain engineering processes, heat is added either by external sources across the system boundary by heat exchangers or internally by chemical reactions in a combustion chamber. Such process are not truely adiabatic, they are called adiabatic processes.

Ø Applications

The combustion chambers inside turbojet engines usually have a constant area and the fuel mass addition is negligible. These properties make the Rayleigh flow model applicable for heat addition to the flow through combustion, assuming the heat addition does not result in dissociation of the air-fuel mixture. Producing a shock wave inside the combustion chamber of an engine due to thermal choking is very undesirable due to the decrease in mass flow rate and thrust. Therefore, the Rayleigh flow model is critical for an initial design of the duct geometry and combustion temperature for an engine.

The Rayleigh flow model is also used extensively with the Fanno flow model. These two models intersect at points on the enthalpy-entropy and Mach number-entropy diagrams, which is meaningful for many applications. However, the entropy values for each model are not equal at the sonic state. The change in entropy is 0 at M = 1 for each model, but the previous statement means the change in entropy from the same

arbitrary point to the sonic point is different for the Fanno and Rayleigh flow models.

Ø Combustion processes.

Ø Regenerator,

Ø Heat exchangers.

Ø Inter coolers.

The following are the assumptions that are made for analyzing the such flow problem.

Ø One dimensional steady flow.

Ø Flow takes place in constant area duct.

Ø The frictional effects are negligible compared to heat transfer effects..

Ø The gas is perfect.

Ø Body forces are negligible.

Ø There is no external shaft work.

Ø There is no obstruction in the flow.

Ø There is no mass addition or rejection during the flow.

Ø The composition of the gas doesn’t change appreciably during the flow.