[immortality]

hi
I have a doubt about how In incompressible solvers pressure can be varied.(like in simpleFoam)is temperature variable or consant while energy equation is not solved?
If density and temperature are constant Then according to ideal gas equation,pressure should be constant.
How can resolve this paradox?

[wyldckat]

Hi Ehsan,

A quick analogy is to think in incompressible flow as if it were forces applied to a solid object. The solid moves because there is a force applied to it; in incompressible fluid flow, the fluid moves because there is a pressure difference.

Best regards,
Bruno

[immortality]

thanks.your interpretation is correct Bruno.but in incompressible solvers energy equation is not solved at all.so temperature should be constant.in other hand its incompressible thus rho is constant too.so
p should be constant(in a gas flow with Mach<.3) but in incompressible tutorials variation of p can be see and also as you say an example p should be variable.
although its not related to my work but like to know more about it.

[wyldckat]

OK, for reference, this is the wiki page here at CFD-Online for this topic: http://www.cfd-online.com/Wiki/Incompressible_flow

If you look at the section "Governing Equations", only the continuity and momentum equations are calculated in simpleFoam. And more specifically, these are explained here: http://openfoamwiki.net/index.php/Th...hm_in_OpenFOAM

[immortality]

thanks.so equation of state is not used in incompressible.
but I have a doubt that energy equation is used or is a voluntary option?

A consequence of incompressible flow is that there is no equation of state for pressure, unlike in compressible flow. Since there is no separate equation for pressure, it must be obtained from the continuity and momentum equations. The main role of pressure is to satisfy the zero divergence condition of the velocity field. Note that pressure is only determined up to a constant.
If the viscosity is assumed to be constant, then the energy equation is decoupled from the continuity and momentum equations.

[wyldckat]

As you quoted:

If the viscosity is assumed to be constant, then the energy equation is decoupled from the continuity and momentum equations.

I believe that at least in simpleFoam, the energy equation is simply not calculated, since it's decoupled, therefore it's not needed for solving the fluid transport.

[cfdonline2mohsen]

Dear Ehsan

Ba Salam
I was reading the above discussion between you and Bruno.
In an incompressible Forced convection flow, the energy equation is decoupled from the momentum equation i.e. Temperature is a passive scalar. it means that it is dependent on velocity (the convection term in energy equation ) but its value does not have any effect on flow field (i.e. velocity). the incompressible solvers in OpenFOAM do not solve energy equation but you can simply add it to solve for T!
in contrast, in free (or natural) convection the momentum and energy equations are coupled together via Boussinesq approximation. in another word there is a term involving Temperature in momentum equation that couple the two equations together. If you look at the natural convection solvers, you will see energy equation for sure!
And the final point is that the equation of state is only valid for ideal (or perfect) gasses! in an incompressible flow there is an equation for temperature that involves 3 terms: temporal,convection and diffusion. it means that heat can be transferred via these 3 method so constant density dos not mean that Temperature is constant too!

These are the basic concepts of fluid mechanics and heat transfer and I recommend you to study them precisely otherwise using OpenFOAM without knowing this fundamental concepts will be like playing Xbox or PlayStation!

Good Luck