[Vi raj]

Hi all,
I am interested in understanding the direct usage of dimensionless variables in CFD solvers. When I started looking at research papers, many papers have non-dimensional variables (eg, velocity, temperature) which are obtained by using reference values of those. But I am little confused about choosing the reference values.
Any explanation will be appreciated. Also, if someone can provide an example for doing dimensional conversion back and forth, it will be helpful. Thanks in advance.

[FMDenaro]

Originally Posted by Vi raj

Hi all,
I am interested in understanding the direct usage of dimensionless variables in CFD solvers. When I started looking at research papers, many papers have non-dimensional variables (eg, velocity, temperature) which are obtained by using reference values of those. But I am little confused about choosing the reference values.
Any explanation will be appreciated. Also, if someone can provide an example for doing dimensional conversion back and forth, it will be helpful. Thanks in advance.

This is a fundamental topic of a fluid dynamics course, I suggest you to read the relevant textbooks, for example Kundu.
The reference variables are chosen based on the specific problems, the key is not only in getting non-dimensional variables but having that the terms in the equations are O(1) so that the non-dimensional numbers are the correct indication of their magnitude compared to other terms.

[Vi raj]

Thank you for your suggestions, great. Another quick question, the dimensional equation of state, P=rho R T, P-pressure; R-gas constant; T-Temperature; rho-density.
But, when the variables are non-dimensionalized in CFD,
P* = P / Pref
rho* = rho / rhoref
T* = T / Tref
How will the gas constant be scaled and E.o.S becomes?

[FMDenaro]

Originally Posted by Vi raj

Thank you for your suggestions, great. Another quick question, the dimensional equation of state, P=rho R T, P-pressure; R-gas constant; T-Temperature; rho-density.
But, when the variables are non-dimensionalized in CFD,
P* = P / Pref
rho* = rho / rhoref
T* = T / Tref
How will the gas constant be scaled and E.o.S becomes?

Pref=R*rho_ref*Tref

[Vi raj]

Thanks for your quick reply. Then, P* = rho* x T*, which is not dimensional E.o.S? sorry if I'm wrong.

[LuckyTran]

rho* is non-dimensional, T* is non-dimensional, so P*=rho*xT* is non-dimensional.

[namdosan1409]

Originally Posted by LuckyTran

rho* is non-dimensional, T* is non-dimensional, so P*=rho*xT* is non-dimensional.

n order to make a non-dimensional variable we have to divide the dimensional term by the reference value. car games