# Overexpanded flow

#### sid_galt

A VERY low temperature (like 100 K) air flow at high velocities (400 m/s - mach number around 2, static pressure = 34440 Pa) is being discharged into the ambient atmosphere (300 K, static pressure 1E5 Pa) through a converging-diverging nozzle.

Flow separation will take place due to oblique shock waves. My question is how far can the flow separation go? Will it exceed even the throat?

If the same air is being exhausted at much lower speed (100m/s - mach number around 0.5, static pressure = 34440 Pa), what will happen. Will the air refuse to go out or will a gradual temperature gradient form after the flow becomes steady.

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#### FredGarvin

sid_galt said:
A VERY low temperature (like 100 K) air flow at high velocities (400 m/s - mach number around 2, static pressure = 34440 Pa) is being discharged into the ambient atmosphere (300 K, static pressure 1E5 Pa) through a converging-diverging nozzle.
How you're going to get low temperature flow at that velocity is a very good question, but let's keep going...

sid_galt said:
Flow separation will take place due to oblique shock waves. My question is how far can the flow separation go? Will it exceed even the throat?
Can you rephrase this? I think I am just misunderstanding what it is you are after here. Oblique shocks in overexpanded flow are what will give a rocket/jet engine the characteristic shock diamonds in the exhaust. I don't think this is what you are referring to though.

sid_galt said:
If the same air is being exhausted at much lower speed (100m/s - mach number around 0.5, static pressure = 34440 Pa), what will happen. Will the air refuse to go out or will a gradual temperature gradient form after the flow becomes steady.
Now it sounds like underexpaned flow. I think Clausius needs to tackle this one. I have no way to predict the flow.

Perhaps you might want to take a look at this applet:
http://www.engapplets.vt.edu/fluids/CDnozzle/cdinfo.html

http://www.aerospaceweb.org/question/propulsion/q0224.shtml

#### sid_galt

FredGarvin said:
How you're going to get low temperature flow at that velocity is a very good question, but let's keep going...
By cooling the air and using a fan to eject it out of a nozzle?

FredGarvin said:
Can you rephrase this? I think I am just misunderstanding what it is you are after here. Oblique shocks in overexpanded flow are what will give a rocket/jet engine the characteristic shock diamonds in the exhaust. I don't think this is what you are referring to though.
Well, since the mach number is greater than 1 and the flow has very low static pressure in comparision to the ambient pressure, wouldn't shock waves occur to compress the flow to increase its static pressure.

FredGarvin said:
Now it sounds like underexpaned flow. I think Clausius needs to tackle this one. I have no way to predict the flow.
Wouldn't underexpanded flow be when the flow static pressure is greater than the ambient pressure. Here the static pressure of the flow in both cases is less than the ambient static pressure.

#### Clausius2

Gold Member
You know, Fred. I have a lot of work to do around here. I have an exam on Tuesday.

sid_galt said:
A VERY low temperature (like 100 K) air flow at high velocities (400 m/s - mach number around 2, static pressure = 34440 Pa) is being discharged into the ambient atmosphere (300 K, static pressure 1E5 Pa) through a converging-diverging nozzle.
Ok. The flow is supersonic at the outlet, and the discharging pressure is less than ambient pressure. It would be oblique shocks at the outlet.

SidGalt said:
Flow separation will take place due to oblique shock waves. My question is how far can the flow separation go? Will it exceed even the throat?
This is not completely true. Inside the nozzle, there is a negative static pressure gradient, so there is not a trivial cause for separation. Anyway in a real flow, and specially for diverging angles larger than 7º, it is almost sure a boundary layer separation due to rugosity of walls. Also, the supersonic flow inside the diverging part is not too fair. Such microscopic rugosity will cause small shock waves and maybe a further separation. Once the flow has been exerted out the nozzle, it doesn't make sense to talk about separation.

Sidgalt said:
If the same air is being exhausted at much lower speed (100m/s - mach number around 0.5, static pressure = 34440 Pa), what will happen. Will the air refuse to go out or will a gradual temperature gradient form after the flow becomes steady.
This is impossible. If the flow is subsonic at the exhaust, the pressure must be equal to ambient pressure, because pressure waves are able to travel upstream and so the flow will feel the atmosphere which is standing downstream.

#### sid_galt

Clausius2 said:
This is not completely true. Inside the nozzle, there is a negative static pressure gradient, so there is not a trivial cause for separation. Anyway in a real flow, and specially for diverging angles larger than 7º, it is almost sure a boundary layer separation due to rugosity of walls. Also, the supersonic flow inside the diverging part is not too fair. Such microscopic rugosity will cause small shock waves and maybe a further separation. Once the flow has been exerted out the nozzle, it doesn't make sense to talk about separation.
You mean to say despite the extremely low static pressure, the flow separation will be caused by just the rugosity(viscosity?) of the walls?

Clausius2 said:
This is impossible. If the flow is subsonic at the exhaust, the pressure must be equal to ambient pressure, because pressure waves are able to travel upstream and so the flow will feel the atmosphere which is standing downstream.
Does that mean that supersonic flow is the ONLY way to discharge low pressure low temperature flow into the ambient atmosphere? Just confirming.

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#### Clausius2

Gold Member
sid_galt said:

You mean to say despite the extremely low static pressure, the flow separation will be caused by just the rugosity(viscosity?) of the walls?
Usually, boundary layer separation is due to two factors: i) A positive pressure gradient, which difusses positive vorticity through walls. This is not the case, because a diverging geometry in supersonic flow causes a decreasing in static pressure. ii) Geometry, if the nozzle is well machined and has little rugosity, the flow could be considered near ideality, but in a real nozzle, the flow would be supersonically turbulent due to the high Re involved and the proper wall rugosity. The interaction between walls and flow in supersonic speed is a not well know field as far as I am concerned. Further separation could be caused via microscopic rugosity and the continuous shocks and expansion fans in the interface between external and internal boundary layer flow. There is an interaction between external flow which is supersonic, and the proper boundary layer which is subsonic. I think that some perturbation caused by wall surface may be transmitted to external flow causing shocks / expansion fans. But I am not an expert in this stuff. Take a look at some advanced book of Gas Dynamics.

SidGalt said:
Does that mean that supersonic flow is the ONLY way to discharge low pressure low temperature flow into the ambient atmosphere? Just confirming.
If the jet is not confined, yes it is the only way. But do not include temperature in this issue. Temperature is not a mechanic boundary constraint. Any jet can be discharged into an atmosphere of different temperature. But none jet, except those supersonic, can modulate its discharge pressure to be different of the ambient one. Just one point: By ambient I am meaning an infinite atmosphere. It is not valid to consider as "ambient" a lenght of pipe of greater section or so. There must not be near any wall.

The reason of this is in the proper propagation phenomena of acoustic (pressure waves) which carry on the information about pressure flow. The flow in this range of Mach supersonic, has an hyperbolic behavior. This means that information is propagated via wave fronts with a finite speed of propagation. If the flow is supersonic at the outlet, any perturbation downstream will be convected before it can reach any zone of flow upstream. The supersonic jet "does not see" the ambient.

#### sid_galt

I understand. Thanks a lot for the help

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