Behavior of heat addition in a compressible flow

[MysticDream]

TL;DR

trying to understand Rayleigh flow limitations

Rayleigh flow refers to frictionless, non-adiabatic flow through a constant area duct where the effect of heat addition or rejection is considered.

Consider the case of air traveling through a heat exchanger: The air travels through the duct and picks up heat from the surface of the heat exchanger which is at a higher temperature. The flow will increase in velocity and temperature and lower in pressure as heat is added until it reaches around Mach .85 at which point the velocity continues to increase but the pressure AND temperature decrease as it approaches Mach 1. It is said at this point, no more heat can be added to the flow and it's "thermally choked".

My question is, how is it possible that when reaching Mach 1 with the temperature still lower than the surface of the heat exchanger can no more heat be transferred to the fluid? What prevents this from happening? You'd still have a fluid at a lower temperature touching a solid surface at a higher temperature which in all other cases results in heat transfer.

 

[Philip Koeck]

TL;DR Summary: trying to understand Rayleigh flow limitations

Rayleigh flow refers to frictionless, non-adiabatic flow through a constant area duct where the effect of heat addition or rejection is considered.

Consider the case of air traveling through a heat exchanger: The air travels through the duct and picks up heat from the surface of the heat exchanger which is at a higher temperature. The flow will increase in velocity and temperature and lower in pressure as heat is added until it reaches around Mach .85 ....

Why would pressure decrease?

 

[Lnewqban]

My question is, how is it possible that when reaching Mach 1 with the temperature still lower than the surface of the heat exchanger can no more heat be transferred to the fluid? What prevents this from happening? You'd still have a fluid at a lower temperature touching a solid surface at a higher temperature which in all other cases results in heat transfer.

Energy outside the tube is available, but the molecules forming the fluid that is moving inside the tube are spinning and vibrating at a maximum limit; therefore, are unable to absorb any more energy.

You can study practical examples in jet engines by researching “Enthalpy-Entropy Diagram for an Axial Compressor Stage”.

 

[boneh3ad]

Energy can still be added but the flow will have to move to a new Rayleigh curve at lower total mass flow rate.

 

[MysticDream]

Why would pressure decrease?

Bernoulli's principle. As velocity increases, pressure decreases. In a Rayleigh flow, as heat is added, velocity increases.

 

[MysticDream]

Energy can still be added but the flow will have to move to a new Rayleigh curve at lower total mass flow rate.

Ok, I think I understand. The temperature would increase but pressure would have to increase because the flow velocity is choked at Mach 1. That changes the downstream condition and overall mass flow rate. So when it is described that no more heat can be added to a Rayleigh flow, they mean it can't be added at that flow rate on that Rayleigh curve. Correct me if I'm wrong.

 

[MysticDream]

Energy outside the tube is available, but the molecules forming the fluid that is moving inside the tube are spinning and vibrating at a maximum limit; therefore, are unable to absorb any more energy.

You can study practical examples in jet engines by researching “Enthalpy-Entropy Diagram for an Axial Compressor Stage”.

Are you sure about this? See the post below yours.

 

[Philip Koeck]

Bernoulli's principle. As velocity increases, pressure decreases. In a Rayleigh flow, as heat is added, velocity increases.

But temperature also increases (leading to higher pressure and/or larger volume), so how do we know that in sum pressure decreases?
It's not completely obvious to me.

Another way of seeing it: The velocity increases because the gas expands due to an increase in temperature (at constant pressure??). So why should pressure decrease?
Isn't the Bernoulli effect usually derived for constant temperature?

 

[MysticDream]

But temperature also increases (leading to higher pressure and/or larger volume), so how do we know that in sum pressure decreases?
It's not completely obvious to me.

Another way of seeing it: The velocity increases because the gas expands due to an increase in temperature (at constant pressure??). So why should pressure decrease?
Isn't the Bernoulli effect usually derived for constant temperature?

Because the heat energy is converted to kinetic energy and the velocity increases. Rayleigh flow refers to a flow through a constant area duct. So if the temperature increases but expansion is constrained by the constant area duct, then velocity must increase. The formulas for Rayleigh flow clearly show that the pressure decreases as heat is absorbed. Now if the cross sectional area of the duct increased, then certainly the pressure would also, as long as the flow is subsonic and the back pressure is subcritical.

 

[Philip Koeck]

Because the heat energy is converted to kinetic energy and the velocity increases. Rayleigh flow refers to a flow through a constant area duct. So if the temperature increases but expansion is constrained by the constant area duct, then velocity must increase. The formulas for Rayleigh flow clearly show that the pressure decreases as heat is absorbed. Now if the cross sectional area of the duct increased, then certainly the pressure would also, as long as the flow is subsonic and the back pressure is subcritical.

Makes sense now. I guess a lot of the heat goes to increased velocity and only a part actually increases the temperature.
Thanks for the answers.