Velocity profile out of a duct

MarcelloAsciolla · April 13, 2018, 06:04

Good morning,
I do not know if this is the right section, but I am looking for material (books, notes, papers, ...) on the development of velocity profile out of a duct. Let's consider a fluid inside the duct with a velocity profile and a generic value V on the axis of the duct and out of the duct the fluid is at rest.
I imagine that there is a distance from the outlet where the fluid has a flat velocity profile equal to 0.
How can I calculate this distance? Are there any matemathical models?

LuckyTran · April 20, 2018, 18:25

A laminar or turbulent jet?

This is the classical mixing layer problem. Tennekes and Lumley's "A First Course in Turbulence" devotes a good part of chapter 4 to this topic.

For the axissymmetric laminar jet, Landau produced an analytical solution.

Another important distinction is whether the exit of the pipe is flush mounted onto a wall or not because the jet entrains the surrounding fluid. If there is a wall blocking the entrainment, the solution becomes harder.

MarcelloAsciolla · April 21, 2018, 13:22

For the moment I need a simple evaluation of the order of magnitude, so maybe the solution for an axissymmetric laminar jet could be good enough. I do not know if I have to expect a big difference if there is turbulence, I will check this too.
Thank you very much! I will read the chapter 4 of that book.

April 13, 2018, 06:04	Velocity profile out of a duct	#1
MarcelloAsciolla Member Marcello Asciolla Join Date: Apr 2018 Location: Italy Posts: 43 Rep Power: 8	Good morning, I do not know if this is the right section, but I am looking for material (books, notes, papers, ...) on the development of velocity profile out of a duct. Let's consider a fluid inside the duct with a velocity profile and a generic value V on the axis of the duct and out of the duct the fluid is at rest. I imagine that there is a distance from the outlet where the fluid has a flat velocity profile equal to 0. How can I calculate this distance? Are there any matemathical models?

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April 20, 2018, 18:25		#2
LuckyTran Senior Member Lucky Join Date: Apr 2011 Location: Orlando, FL USA Posts: 5,761 Rep Power: 66	A laminar or turbulent jet? This is the classical mixing layer problem. Tennekes and Lumley's "A First Course in Turbulence" devotes a good part of chapter 4 to this topic. For the axissymmetric laminar jet, Landau produced an analytical solution. Another important distinction is whether the exit of the pipe is flush mounted onto a wall or not because the jet entrains the surrounding fluid. If there is a wall blocking the entrainment, the solution becomes harder.

April 21, 2018, 13:22		#3
MarcelloAsciolla Member Marcello Asciolla Join Date: Apr 2018 Location: Italy Posts: 43 Rep Power: 8	For the moment I need a simple evaluation of the order of magnitude, so maybe the solution for an axissymmetric laminar jet could be good enough. I do not know if I have to expect a big difference if there is turbulence, I will check this too. Thank you very much! I will read the chapter 4 of that book.