closed pipe decompression

Ardalan · February 23, 2016, 09:07

Consider a pipe filled with compressed air (1.5 atm). Both ends of the pipe are closed. At the time=0 right end is opened and is exposed to atmospheric pressure. consider the flow to be one dimensional and the governing equations to be Euler equations.
1- What are the appropriate boundary conditions at both ends (opened and closed)?
2- Is there a reference solution for this problem in the literature?
3- is it possible that the pressure inside the pipe falls below the atmosphere?

FMDenaro · February 23, 2016, 09:25

I think you can get many details from the classical Riemann problem in a textbook of gasdynamic. Your problem will generate three characteristic waves

Ardalan · February 23, 2016, 09:46

Existing Riemann solutions in the gasdynamics textbooks are only about shock tube problems with both ends closed. A diaphragm somewhere inside the pipe ruptures and the flow begins. I can simulate this flow perfectly. But I get in trouble with the one end opened pipes (as mentioned above)

FMDenaro · February 23, 2016, 11:03

Quote:

Originally Posted by Ardalan

Existing Riemann solutions in the gasdynamics textbooks are only abou

?????

Ardalan · February 23, 2016, 12:31

Quote:

Originally Posted by FMDenaro

?????

Sorry, I didn't noticed that my comment has been sent incompletely. I corrected it.

FMDenaro · February 23, 2016, 12:53

Quote:

Originally Posted by Ardalan

Existing Riemann solutions in the gasdynamics textbooks are only about shock tube problems with both ends closed. A diaphragm somewhere inside the pipe ruptures and the flow begins. I can simulate this flow perfectly. But I get in trouble with the one end opened pipes (as mentioned above)

Actually, the classical solution in a shock tube is for an infinite lenght of the tube, not for a closed one ...
As you want a 1D approximation the exit from the pipe in the ambient that would generate oblique waves is not considered and I think you can afford the model as a unique 1D model with 2 Riemann problems. Of course, after waves touch each other in the pipe you must consider reflection.

Ardalan · February 23, 2016, 17:28

Thanks for your response.
But I didn't get any answer to my questions:
1- What are the appropriate boundary conditions at both ends (opened and closed)?
2- Is there a reference solution for this problem in the literature?
3- is it possible that the pressure inside the pipe falls below the atmosphere?

Ardalan · February 28, 2016, 03:04

Any help is greatly appreciated

February 23, 2016, 09:07	closed pipe decompression	#1
Ardalan Member Ardalan Join Date: Feb 2010 Location: Baku Posts: 50 Rep Power: 16	Consider a pipe filled with compressed air (1.5 atm). Both ends of the pipe are closed. At the time=0 right end is opened and is exposed to atmospheric pressure. consider the flow to be one dimensional and the governing equations to be Euler equations. 1- What are the appropriate boundary conditions at both ends (opened and closed)? 2- Is there a reference solution for this problem in the literature? 3- is it possible that the pressure inside the pipe falls below the atmosphere?

February 23, 2016, 09:46		#3
Ardalan Member Ardalan Join Date: Feb 2010 Location: Baku Posts: 50 Rep Power: 16	Existing Riemann solutions in the gasdynamics textbooks are only about shock tube problems with both ends closed. A diaphragm somewhere inside the pipe ruptures and the flow begins. I can simulate this flow perfectly. But I get in trouble with the one end opened pipes (as mentioned above) Last edited by Ardalan; February 23, 2016 at 12:23.

February 28, 2016, 03:04		#8
Ardalan Member Ardalan Join Date: Feb 2010 Location: Baku Posts: 50 Rep Power: 16	Any help is greatly appreciated Last edited by Ardalan; February 29, 2016 at 12:56.

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February 23, 2016, 09:25		#2
FMDenaro Senior Member Filippo Maria Denaro Join Date: Jul 2010 Posts: 6,768 Rep Power: 71	I think you can get many details from the classical Riemann problem in a textbook of gasdynamic. Your problem will generate three characteristic waves

February 23, 2016, 17:28		#7
Ardalan Member Ardalan Join Date: Feb 2010 Location: Baku Posts: 50 Rep Power: 16	Thanks for your response. But I didn't get any answer to my questions: 1- What are the appropriate boundary conditions at both ends (opened and closed)? 2- Is there a reference solution for this problem in the literature? 3- is it possible that the pressure inside the pipe falls below the atmosphere?