Incompressible Ideal Gas law Vs Ideal gas Law
 

Hello

I am using Energy Equation in FLuent as the flow is in high temperature medium. For density, "incompressible Ideal gas law" seems to be a good option(as it takes into account change in density with temperature). However, the known pressure (@the inlets) is 2 Bar and there is pressure variation (inlets and outlets) in the domain (the incompressible ideal gas law assumes that there is very little pressure variation), hence, as there is a pressure variation in the domain the other option "ideal gas law" (compressible) can be used. but then the Mach number (@the inlets) is well below 0.3 as the velocity is very low so again "Incompressible ideal gas law" seems to be a better option. So, What do you think, for density of the fluid (nitrogen gas) Incompressible Ideal gas law or Ideal gas law (compressible) would be appropriate in this case?
Your guidance will be highly appreciated.
Thanks

Dear Mohsin,

First of all, check the worst condition that whether using Ideal gas law is acceptable or not. (according to deviation of compressibility factor Z from unity)
Then, note that "incompressible Ideal gas law" is just a simplification for "ideal gas law" when dependence of density to pressure is negligible. For this case it's better to use "ideal gas law" which is applicable in wide range; i.e., if the variation of pressure would be negligible, it reduces to "incompressible Ideal gas law".
restriction of mach No is just a rule of thumb which expresses possibility of compressibility due to fluid motion but it's not a general rule for setting gas state law; e.g., if you had N2 in enclosed domain with Z=1 and rigid boundaries, didn't you use ideal gas law? Did you concern about Ma! ?

Bests,

Thank you very much for your kidn reply.

The temperature in the domain is about 700 K and the Pressure is about 2 bar at the inlet for Nitrogen gas. Hence, the flow can be considered as an ideal gas as Z is approximately 1. velocity is about 5 m/s so Mach number is very less. Aparently, it seems that Ideal gas assumption would give accurate results. However, the pressure at the outlet Pguage=-6666Pa. which means that pressure variation is there (from 2 bar to -6666pa) so if there is such a large pressure variation is it fine to use "incompressible ideal gas law" rather than "ideal gas law" for compressible fluids.

Thanks

Dear Mohsin,

Ok, Z=1 and you can use ideal gas law without any doubt. Note that here, you are discussing about gauge pressure; i.e, variation of pressure with respect to operating pressure and it seems that you have chosen 2 Bar as op. pressure, so your variation is between 0 to -6666pa. As a rule, you cannot use "incompressible ideal gas law" where pressure variation is high, but now the question is that whether this variation (0 to -6666) is high or not; obviously, it depends on many parameters and also flow parameters; indeed, density would affect by this variation and use in momentum equation directly which can affect other parameters in this manner. In other words, ideal gas law gives more accurate results because of Z=1 and accuracy of "incompressible ideal gas law" depends on how much density contour of this law is similar to ideal gas law.

Bests,

Thank you Amir,

1. if my operating pressure is 2 bar (200Kpa) and the lowest pressure in the domain is -6666 Pa, could you kindly tell me how the variation is from "0 to -6666pa"? Wouldnt it be from 200Kpa to -6666pa?

2. You mean to say, i should first simulate for "incompressible ideal gas law" condition and check for Density contours. After this, I should simulate again for "ideal gas law condition" and check for Density contours, if the variation is not too much then i can safely use incompressible ideal gas law? Right?

Thank you again

As I understood from your posts:
Max static pressure=200 kPa
min gauge pressure=-6666 Pa
op. pressure= 200 kPa
So, Max. gauge pressure=0 Pa ; min gauge pressure=-6666 Pa
-6666< gauge pressure < 0
but it seems that Max gauge pressure=200 kPa not static one, oops; anyway, I meant that consider range of gauge pressure according to your op pressure.
I said that ideal gas law is more reliable in this case but if you insist on using incompressible ideal gas law; yes, you're right.

Bests,

Amir, Thank you so much.

Thanks Amir. Excellent Explanation. In my case gaseous fluid is a pressure(around 20 MPa). For trial I am using Air as fluid. I was calculating the air density at high pressure and entering the value and keeping it constant. But I realize as the temperature drops, so will the density change occur.