Total pressure bc source code description

karamiag · March 17, 2020, 11:18

Hello everybody,
does anyone know why in the source code description of total pressure boundary condition, gamma is equal 1 for compressible transonic cases and it is greater than 1 for supersonic cases?
AFAIK gamma=Cp/Cv and it is a property of the considered gas not depending on the sub/supersonic flow condition.
Thank you all.

peterhess · March 18, 2020, 10:05

See 1.101:

https://k.kakaocdn.net/dn/cjKN6m/btq...&knm=tfile.pdf

Regards

Peter

karamiag · March 18, 2020, 11:16

Thank you Peter,
what I find in the pdf file your link points to is in the attached image. It is the description of the bc. I am sorry but I am not able to find were it is explained why gamma changes for different flow conditions. The total pressure expression I know is

$\frac{p_0}{p} =\left( 1 + \frac{\gamma -1}{2} Mach^2 \right)^{\frac{\gamma}{\gamma - 1}}$

How to obtain the formulas in the attached image from this one?
Thank you again!

karamiag · March 26, 2020, 10:22

Ok these are my answers to my questions. I hope they are not wrong!

Quote:

why in the source code description of total pressure boundary condition, gamma is equal 1 for compressible transonic cases and it is greater than 1 for supersonic cases?

I think that it is only an implementation trick, i.e. when in the p file, in correspondence of gamma there is 1, openfoam knows that the user chosen the transonic case (the flow in correspondence of the patch for which the total pressure bc is imposed is transonic). If the user put a number greater than 1 means openfoam knows that the user chosen the supersonic case (the flow in correspondence of the patch for which the total pressure bc is imposed is supersonic) and uses that number as the value of Cp/Cv.

Quote:

How to obtain the formulas in the attached image from this one?

The McLaurin series expansion of the function $\left(1+x\right)^{\alpha}$ is

$\left(1+x\right)^{\alpha}= 1 +ax+ \frac{\alpha\left(\alpha-1\right)}{2}x^2+\frac{\alpha\left(\alpha-1\right)\left(\alpha-2\right)}{6}x^3 +...+ \binom{\alpha}{n} x^n + o\left(x^n\right)$

so, considering the total pressure expression

$p_0=p \left(1+ \frac{\gamma - 1}{2} M^2\right)^{\frac{\gamma}{\gamma-1}}$
and expanding it, one obtains

$p_0=p\left(1+\frac{\gamma}{2}M^2+\frac{\gamma}{8}M^4+ \frac{\gamma\left(2-\gamma\right)}{48}M^6+...\right)$

from which

$p_0-p=\frac{1}{2} \rho V^2 \left(1+\frac{M^2}{4}+\frac{2-\gamma}{24}M^4 +...\right)$

and, considering M<<1

$p_0-p=\frac{1}{2} \rho V^2$

Hoping this could help, I ask you to correct me if I am wrong.
Thank you!

March 17, 2020, 11:18	Total pressure bc source code description	#1
karamiag Member Giovanni Caramia Join Date: Mar 2009 Location: Bari, ITALY Posts: 58 Rep Power: 17	Hello everybody, does anyone know why in the source code description of total pressure boundary condition, gamma is equal 1 for compressible transonic cases and it is greater than 1 for supersonic cases? AFAIK gamma=Cp/Cv and it is a property of the considered gas not depending on the sub/supersonic flow condition. Thank you all.

Similar Threads
Thread	Thread Starter	Forum	Replies	Last Post
[Other] Tabulated thermophysicalProperties library	chriss85	OpenFOAM Community Contributions	62	October 2, 2022 03:50
[swak4Foam] swak4foam for OpenFOAM 4.0	mnikku	OpenFOAM Community Contributions	80	May 17, 2022 08:06
question regarding LES of pipe flow - pimpleFoam	Dan1788	OpenFOAM Running, Solving & CFD	37	December 26, 2017 14:42
centOS 5.6 : paraFoam not working	yossi	OpenFOAM Installation	2	October 9, 2013 01:41
[swak4Foam] funkySetFields compilation error	tayo	OpenFOAM Community Contributions	39	December 3, 2012 05:18

March 18, 2020, 10:05		#2
peterhess Senior Member Peter Hess Join Date: Apr 2011 Location: Austria Posts: 250 Rep Power: 17	See 1.101: https://k.kakaocdn.net/dn/cjKN6m/btq...&knm=tfile.pdf Regards Peter