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Old   April 8, 2017, 04:40
Default Shock in CD nozzle?
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Hello everyone,

I am new to gas dynamics, so I am now confused by the system that I am trying to simulate, which is schematically shown in the picture below. It is a cold spraying system. A convergent-divergent nozzle (CD-nozzle) is mounted to a heating chamber. A main Nitrogen flow enters the heating chamber and is heated by the heating element in the chamber. The mass flow rate of main nitrogen flow (m0) is measured somewhere upstream of the system. At the entrance of the chamber, the temperature (T0) and pressure (p0) are also measured. Not far from the nozzle entrance, the temperature (T1) was measured again with a second thermal couple. Here comes also a small pipe connected to a powder feeder (PF) to inject powder into the nozzle. The pressure in the PF (p1) and mass flow rate into PF (m1) are also monitored.

Picture1.png

Firstly, I am trying to simulate the flow through the CD-nozzle with only the main Nitrogen flow. I have a nozzle with a throat diameter of 2.7 mm and a exit diameter of 8.5 mm, which resulted in a area ratio of Aexit/Athroat = 9.9108. I tried to get a rough estimation of the flow through the nozzle using the isentropic gas flow equations. I typed the area ratio into the calculator on the sites below and I get a pressure ratio, pexit/pentrance, of 0.007405.

http://www.dept.aoe.vt.edu/~devenpor/aoe3114/calc.html
https://www.grc.nasa.gov/www/BGH/isentrop.html

Because my system can only reach a pressure (reading of p0) as high as 40 bar. That means my pexit can be at most 0.2962 bar. Because it is much lower than the ambient pressure, so I can only get shock inside the nozzle at all the operating conditions of my system.

I am very confused that why the nozzle is designed in this way. Therefore, I think there must be something wrong with my estimation. But I could not find out what it is. Can anyone help me with that?

Thanks a lot in advance!
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Old   April 8, 2017, 08:42
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CD nozzle can experience shocks (oblique) in the divergent part depending on the area schedule and ratio.
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Old   April 8, 2017, 10:36
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Thanks for your reply, turbo.

The system is designed to accelerate injected particles to highest possible velocity. If shocks will always be present in the nozzle due to the pressure limitation and nozzle design, it is not efficient for this purpose. I have also seen one paper about CFD simulation of this nozzle. It claimed that shocks are outside the nozzle with a nozzle inlet pressure of 14 bar.

Therefore, I am afraid that there is something wrong with my estimation about the nozzle exit pressure using the area ratio and isentropic flow caculator. Could you tell me if I am wrong in the estimation and where I have done it wrong?
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Old   April 8, 2017, 12:12
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If you want to get supersonic all the way to the exit without shocks, you need to find the right p-static-exit for a given p-total-inlet by trial-and-error. Above all, you should be choked at the throat beforehand, otherwise you will return to subsonic. This is the so-called rocket science.
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Old   April 8, 2017, 12:50
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Quote:
Originally Posted by turbo View Post
If you want to get supersonic all the way to the exit without shocks, you need to find the right p-static-exit for a given p-total-inlet by trial-and-error. Above all, you should be choked at the throat beforehand, otherwise you will return to subsonic. This is the so-called rocket science.
Let's say I can not make any change to this specific system. Because the area ratio of the nozzle, Aexit/Athroat, is 9.9108 and the ambient pressure is 1 atm, there will alaways be shocks inside the nozzle, even if I get a inlet pressure of 40 bar (I think the velocity of the gas flow at the inlet will not be very high, so the dynamic pressure can be neglected in comparison to static pressure). Is that right?
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Old   April 9, 2017, 07:26
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Post your CFD Mach contours at your target mass flow.
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Old   April 9, 2017, 16:18
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mach number sym1.png

Above is the Mach number contour. I used a 5 slice of the nozzle and the cylindric outer space to run a 2D simulation. The mass flow rate is 2.9282e-4 kg s^-1 for this 5 slice, which corresponds to a volume flow of 1100 standard liter per minute for the whole 360 nozzle.
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Old   April 10, 2017, 11:13
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Your nozzle looks not too bad because you have a gradual supersonic flow in the divergent section. Problem is you have a shock at discharge leading to subsonic again afterwards. If you carefully reduce p-static-exit in CFD, you will be able to be supersonic without shocks. However, the very p-static-exit cannot be realized in the current hardware, as you described.
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