Temperature drop ideal gas choked flow.

LJA_Koers · June 30, 2023, 07:05

Hi all,

I'm trying to make a transient simulation of the choked flow of methane in a piping system. I want the flow to become choked when the outlet pressure is reduced to atmospheric pressure (1atm). With a heat capacity ratio of 1.32, the critical pressure ratio of methane becomes 0.542. Hence the inlet pressure is set to 1 atm / 0.542 = 1.845 atm. And the speed of sound of methane at atmospheric pressure is 453.6 m/s.

To see if the flow is indeed choked at these conditions. I ran a steady state simulation and used the ideal-gas equation of state and an inlet and backflow temperature of 26.85C (isothermal throttling). Running the pressure based solver.

The result in the velocity contour shows a maximum velocity magnitude of 484 m/s, exceeding the critical velocity. To find the cause of this, I plotted the density and subsequently temperature plots to find that the temperature in the jet exiting the orifice drops to -26C. A 53C drop in temperature!

This setup is supposed to simulate the throttling of an ideal gas and thus be isothermal, yet the result is not.

Does anyone know what causes this?
And in addition, are there any other tips for modeling throttling/choked flow?

Thanks in advance.

CFDKareem · June 30, 2023, 10:59

I would try and set the density behavior of the gas more explicitly, i.e. don't use the ideal gas model. You should be able to find the density information for methane and use the polynomial or piecewise polynomial for the density. I don't think the ideal gas formulation will capture the temperature correctly.

LuckyTran · June 30, 2023, 19:48

These results look right.

Gas expansion is not isothermal, the temperature should drop, except over very long distances for enough heat transfer to take place so that the gas returns to its original temperature. This is approximately what you have at the exit. If you want an isothermal gas, don't use an ideal gas.

The heat capacity ratio for an isothermal gas is 1. Clearly, 1.32 is not 1.

LJA_Koers · July 3, 2023, 06:04

Hi LuckyTran,

You're right. I should have read up more on the matter. The wiki on choked flow just mentions the static pressure and density drop.

I am however still unable to get the choked flow behavior, i.e the limited massflow,when I reduce the outlet pressure. I'm getting shock diamonds and Mach-numbers greater than 1.

LuckyTran · July 4, 2023, 03:30

You will find Mach numbers greater than 1 because the critical pressure ratio in the wiki is for 1D flow and doesn't account for 3D effects. Real flows choke well before this pressure ratio. However, you should be able to find a Mach=1 disc near the throat.

Plot the Mach number contour and make an isosurface of M=1 or just make an isosurface of the sonic velocity.

Btw you can push more mass flow through a nozzle by increasing the upstream pressure. Choked only means that the downstream pressure becomes decoupled. If you change your upstream BC to 2 atm for example, you'll get more flow. This is a super duper important to understand because the choked pressure ratio for 3D bodies is more like 0.9 (not 0.5). In other words, you can lower your inlet pressure to about 0.7 atm and still find Mach discs and this is very real.

In summary, it is choked. You just need to convince yourself.

June 30, 2023, 10:59		#2
CFDKareem Senior Member Kareem Join Date: Nov 2022 Location: New York Posts: 125 Rep Power: 4	I would try and set the density behavior of the gas more explicitly, i.e. don't use the ideal gas model. You should be able to find the density information for methane and use the polynomial or piecewise polynomial for the density. I don't think the ideal gas formulation will capture the temperature correctly. __________________ Please like the answer if it helped! Video Tutorials and Tips: https://www.youtube.com/@cfdkareem/featured

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June 30, 2023, 19:48		#3
LuckyTran Senior Member Lucky Join Date: Apr 2011 Location: Orlando, FL USA Posts: 5,754 Rep Power: 66	These results look right. Gas expansion is not isothermal, the temperature should drop, except over very long distances for enough heat transfer to take place so that the gas returns to its original temperature. This is approximately what you have at the exit. If you want an isothermal gas, don't use an ideal gas. The heat capacity ratio for an isothermal gas is 1. Clearly, 1.32 is not 1.

July 3, 2023, 06:04		#4
LJA_Koers New Member Laurens Join Date: Sep 2018 Location: the Netherlands Posts: 20 Rep Power: 8	Hi LuckyTran, You're right. I should have read up more on the matter. The wiki on choked flow just mentions the static pressure and density drop. I am however still unable to get the choked flow behavior, i.e the limited massflow,when I reduce the outlet pressure. I'm getting shock diamonds and Mach-numbers greater than 1.

July 4, 2023, 03:30		#5
LuckyTran Senior Member Lucky Join Date: Apr 2011 Location: Orlando, FL USA Posts: 5,754 Rep Power: 66	You will find Mach numbers greater than 1 because the critical pressure ratio in the wiki is for 1D flow and doesn't account for 3D effects. Real flows choke well before this pressure ratio. However, you should be able to find a Mach=1 disc near the throat. Plot the Mach number contour and make an isosurface of M=1 or just make an isosurface of the sonic velocity. Btw you can push more mass flow through a nozzle by increasing the upstream pressure. Choked only means that the downstream pressure becomes decoupled. If you change your upstream BC to 2 atm for example, you'll get more flow. This is a super duper important to understand because the choked pressure ratio for 3D bodies is more like 0.9 (not 0.5). In other words, you can lower your inlet pressure to about 0.7 atm and still find Mach discs and this is very real. In summary, it is choked. You just need to convince yourself.