Supercritical outflow from an orifice

flotus1 · August 6, 2019, 08:43

I have a rather fundamental fluid dynamics question.

Suppose we have an ideal gas flowing through a hole in a tank. (i.e. not a Laval nozzle). The pressure ratio between the tank and ambient is supercritical, so we get Ma=1 in the orifice.
Now I know what I learned in fluid dynamics about this kind of flow: in order to get Ma>1, we would need a special nozzle design, i.e. a Laval nozzle which increases the cross-section rather smoothly after Ma=1 was reached.
Now the question: for the hole in the tank, would it be possible to have a small region of Ma>1 behind the orifice? Or can we never get Ma>1 without a special nozzle? After all, even with a simple hole we get an increasing cross-section behind the orifice. The cross-section just increases more abruptly than in a Laval nozzle.

LuckyTran · August 6, 2019, 10:10

Some ideas...

1) When one considers real flows to be 3D, there is a Mach disk which extends slightly behind the jet exit into the dump

2) For poorly designed orifices, a separation bubble creates a constriction inside the mouthpiece, leading to a Laval nozzle-like situation.

agd · August 6, 2019, 10:14

In general downstream of the orifice the flow will seek to expand, which will lead to an acceleration locally. The size of this region my be small, but once the flow has passed through the minimum area it will seek to expand to the ambient pressure. The resulting jet will return to ambient conditions through a series of oblique shocks and expansions that depend on the actual pressure ratio. The shape of a de Laval nozzle allows us to reach a particular supersonic Mach number for a given pressure ratio, but it is not a requirement for the flow to reach supersonic Mach numbers, at least in a small local region.

flotus1 · August 6, 2019, 11:07

Thanks for the quick responses.
The reason I asked was because this is the result I got from a CFD solver. A small region behind the orifice with Ma>1. So a sanity check was needed.
I explained to myself that the flow separates at the orifice, creating its own nozzle-like shape that allows it to accelerate beyond Ma=1. Which seems to be in line with your explanations.

JBeilke · August 6, 2019, 13:00

It should be ok, if there is a small region with Ma > 1 in a 3d calculation. And in transient conditions you can get Ma > 1 even in a straight pipe.

Our knowledge about compressible flow is usually based on 1d and steady state!!

August 6, 2019, 08:43	Supercritical outflow from an orifice	#1
flotus1 Super Moderator Alex Join Date: Jun 2012 Location: Germany Posts: 3,399 Rep Power: 46	I have a rather fundamental fluid dynamics question. Suppose we have an ideal gas flowing through a hole in a tank. (i.e. not a Laval nozzle). The pressure ratio between the tank and ambient is supercritical, so we get Ma=1 in the orifice. Now I know what I learned in fluid dynamics about this kind of flow: in order to get Ma>1, we would need a special nozzle design, i.e. a Laval nozzle which increases the cross-section rather smoothly after Ma=1 was reached. Now the question: for the hole in the tank, would it be possible to have a small region of Ma>1 behind the orifice? Or can we never get Ma>1 without a special nozzle? After all, even with a simple hole we get an increasing cross-section behind the orifice. The cross-section just increases more abruptly than in a Laval nozzle.

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August 6, 2019, 10:10		#2
LuckyTran Senior Member Lucky Join Date: Apr 2011 Location: Orlando, FL USA Posts: 5,672 Rep Power: 65	Some ideas... 1) When one considers real flows to be 3D, there is a Mach disk which extends slightly behind the jet exit into the dump 2) For poorly designed orifices, a separation bubble creates a constriction inside the mouthpiece, leading to a Laval nozzle-like situation.

August 6, 2019, 10:14		#3
agd Senior Member Join Date: Jul 2009 Posts: 351 Rep Power: 18	In general downstream of the orifice the flow will seek to expand, which will lead to an acceleration locally. The size of this region my be small, but once the flow has passed through the minimum area it will seek to expand to the ambient pressure. The resulting jet will return to ambient conditions through a series of oblique shocks and expansions that depend on the actual pressure ratio. The shape of a de Laval nozzle allows us to reach a particular supersonic Mach number for a given pressure ratio, but it is not a requirement for the flow to reach supersonic Mach numbers, at least in a small local region.

August 6, 2019, 11:07		#4
flotus1 Super Moderator Alex Join Date: Jun 2012 Location: Germany Posts: 3,399 Rep Power: 46	Thanks for the quick responses. The reason I asked was because this is the result I got from a CFD solver. A small region behind the orifice with Ma>1. So a sanity check was needed. I explained to myself that the flow separates at the orifice, creating its own nozzle-like shape that allows it to accelerate beyond Ma=1. Which seems to be in line with your explanations.

August 6, 2019, 13:00		#5
JBeilke Senior Member Joern Beilke Join Date: Mar 2009 Location: Dresden Posts: 498 Rep Power: 20	It should be ok, if there is a small region with Ma > 1 in a 3d calculation. And in transient conditions you can get Ma > 1 even in a straight pipe. Our knowledge about compressible flow is usually based on 1d and steady state!!