[Diger]

Having a static incompressible flow means that the density is constant everywhere in the domain. I do not see however where the density is determined from.
Having a long flowtube for example the pressure at the inlet is a bit higher than at the outlet in order for the flow to move. If the density would be determined from the ideal gas equation then also the density would be a bit higher at the entrance/inlet (though only slightly) than at the outlet except when the temperature compensates for that. I don't know if that is even the case?!
How is that implemented in ANSYS Fluent???

[deenriqu]

If I understand things correctly, you can have a pressure gradient which drives the flow, even in a unidensity fluid. In the case of a long pipe you have to set either the mass flow rate or the pressure gradient to drive the flow.

In the incompressible NSE the density is constant, but the pressure gradient is not. To conserve momentum, the fluid must move under a pressure gradient. The density would be constant through out the fluid in a single species domain.

This is a rough explanation, and Im sure someone can provide further details.

[Diger]

Yeah thanks but that was not the question.
I was asking how the density is calculated?

[deenriqu]

The species equation:

http://www.afs.enea.it/project/neptu...th/node128.htm

For a single species fluid, the mass fraction is 1.

I believe that the mixture-density would be calculated first, and then used in the incompressible equations.

[Diger]

In a (static) incompressible fluid the density cannot appear in the equations as a dependent variable. It is just a parameter. Thats what it should be, right???
The pressure is of course still calculated.
I pressume the density must be somehow calculated using an equation of state or predefined value, but where?

PS: Sorry, just found this: http://www.afs.enea.it/project/neptu...ug/node289.htm
So it uses the operating pressure...

[LuckyTran]

Incompressible flow does not mean that the density is a constant. They are not the same. A constant density substance (an incompressible substance) is an implicit equation of state (density is independent of pressure or temperature).

Incompressible flow means that the divergence of the velocity is zero. It doesn't have to be density that disappears, alternatively the pressure can disappear.

Of course, a constant density substance automatically satisfies the incompressible substance and incompressible flow property. In this case, the density is known so you need not need to solve for it.

A temperature dependent density can still result in an incompressible flow since density does not depend on pressure, i.e. the substance is not compressible. You apply a pressure and the mass density does not change!

Originally Posted by deenriqu

In the incompressible NSE the density is constant, but the pressure gradient is not. To conserve momentum, the fluid must move under a pressure gradient. The density would be constant through out the fluid in a single species domain.

That is not true. Density does not have to be constant in the incompressible NSE. The incompressible flow assumption is that the material derivative of the mass density is constant, which requires that either the substance itself is incompressible or that the the velocity field is divergence free. Hence incompressible flow generally refers to the divergence free velocity. Since density is a material property and provided through some sort of equation of state, there's no serious ambiguity.

[Diger]

Originally Posted by LuckyTran

Incompressible flow does not mean that the density is a constant. They are not the same. A constant density substance (an incompressible substance) is an implicit equation of state (density is independent of pressure or temperature).

Incompressible flow means that the divergence of the velocity is zero. It doesn't have to be density that disappears, alternatively the pressure can disappear.

Of course, a constant density substance automatically satisfies the incompressible substance and incompressible flow property. In this case, the density is known so you need not need to solve for it.

Yes you do not need to solve for it. However you still need to calculate it based on something and that was what I was refering to above within the link.

In particular:

A temperature dependent density can still result in an incompressible flow since density does not depend on pressure, i.e. the substance is not compressible. You apply a pressure and the mass density does not change!

Well after all the density is calculated with the equation of state, thus it is dependent on pressure and temperature even if I assume incompressibility and do not specifically solve for the density in the equations where I assume it to be constant.

When you solve an incompressible problem you will notice that (obviously) the pressure is a bit higher at the inlet (where u for example have a mass-flow-inlet) and the outlet where u specified a pressure-outlet with gauge pressure =0.
Now the density is calculated by the operating pressure and which temperature???
I would still assume that the equation of state is valid everywhere in the fluid domain, so
rho=p/(kB*T) = const.
at the outlet p=p_op and with some temperature you get a value for rho.
Now at the inlet the pressure is a bit higher but since the flow is incompressible the density should be the same as at the outlet.
According to the equation of state this would imply a slight change in the temperature in order for incompressiblity to hold...

That is not true. Density does not have to be constant in the incompressible NSE. The incompressible flow assumption is that the material derivative of the mass density is constant, which requires that either the substance itself is incompressible or that the the velocity field is divergence free. Hence incompressible flow generally refers to the divergence free velocity. Since density is a material property and provided through some sort of equation of state, there's no serious ambiguity.

You actually just said it:
incompressible => material derivative vanishes and thus in the static case (time independent) => grad rho =0 (or the velocity is always perpendicular to the density gradient) which implies rho=const everywhere. Nothing else I was saying!

[LuckyTran]

First, when you specify the material properties for your problem, what EOS of state are you selecting? Constant? Polynomial in T? Incompressible ideal gas? Ideal gas? Real gas? What is it?

Originally Posted by Diger

Well after all the density is calculated with the equation of state, thus it is dependent on pressure and temperature even if I assume incompressibility and do not specifically solve for the density in the equations where I assume it to be constant.

Unless you are explicitly assuming the density to be constant everywhere, which means that the density value is a user-supplied value, then you need to abandon the mindset that the density must be constant. There is no "solving for density" when density is a specified constant. Conversely, if you are using anything other than the constant density EOS, then you cannot assume in the equations that density is a constant. Density is whatever it needs to be to satisfy the governing equations.

Originally Posted by Diger

You actually just said it:
incompressible => material derivative vanishes and thus in the static case (time independent) => grad rho =0 (or the velocity is always perpendicular to the density gradient) which implies rho=const everywhere. Nothing else I was saying!

That's IF grad(rho)=0. If grad(rho) is not zero (such as an ideal gas) then you can still have incompressible flow, div(velocity)=0 without grad(rho) being 0.

When you define the problem, you define the equation of state. If you assume the density is constant (which is itself an equation of state), density is independent of pressure and temperature. Hence, the value of density is a user supplied value if you want to do a constant density simulation.

If you specify ideal gas law.... In Fluent you have a choice between ideal gas law and incompressible ideal gas law. In the incompressible ideal gas law, the density is calculated based on operating pressure and local cell temperature. Because a temperature dependent density is still incompressible while still allowing the density to change; incompressible does not mean that the density is constant!

If you choose regular ideal gas law, then density is dependent on local cell pressure and temperature.

Properties are calculated at the start of the iteration based on the current solution, i.e. using the initial pressure and temperature. Then the governing equations are solved for the dynamic variables of interest.

In the pressure based solver, you can use the coupled solver to simultaneously solve velocity and pressure (using continuity & momentum together) or you can use a segregated solver where you first solve the momentum equation and get an updated velocity using the assumed initial pressure. Then you go to continuity and correct the pressure using the most updated velocity. And back n' forth. What actually happens here depends on the pressure-velocity coupling scheme that you select, SIMPLE, SIMPLEC, SIMPLER, PISO, etc. Properties are pretty much untouched while you're solving for pressure and velocity. Only after you solve for velocity and pressure do then you address the other variables like temperature. Properties don't get updated until the next iteration.

In the density based solver, things get weird! Because you solve continuity, momentum, and energy equation together. Now you have a problem of figuring out which to solve for first: pressure, density, temperature? It turns out you use continuity, momentum, and energy to solve for the density, velocity, and temperature, then calculate pressure from the equation of state.

[Diger]

Before I go into the other stuff I (we?) should maybe clarify this first:
so when u start with div v = 0 for an incompressible flow then by continuity it follows

d/dt rho + div rho v = d/dt rho + rho div v + v grad rho = d/dt rho + v grad rho = 0
and if the flow is supposed to be time independent (thats how I interpret the "static" setting in Fluent "general")
then we just have
v*grad rho = 0
as in the other derivation.
So how do u see that rho does not have to be constant?
Do I not need a time dependent flow to talk about what you are talking?
That density along the pathline is constant but not everwhere?
Isn't that a time dependent thing?

Btw: I'm using ideal gas as EoS

[LuckyTran]

Originally Posted by Diger

v*grad rho = 0

Make sure you don't miss that it's actually v dot grad(rho) = 0 (the inner product) and not the scalar product vgrad(rho). grad(rho) is a vector field and v is a vector field.

Originally Posted by Diger

So how do u see that rho does not have to be constant?

grad(rho)=0 implying rho=constant is a sufficient but not a necessary condition for continuity to be satisfied, what you need is v dot grad(rho).

But it does give the result that you said, for time-independent flows density is constant along a pathline but not necessarily everywhere. That doesn't mean that the problem is now trivial to find the velocity field. These pathlines can be as complicated as needed to satisfy the flow boundary conditions.

What's important is that we haven't assumed anything about the equation of state (yet), we've only used the assumption/restriction that the flow does not explicitly depend on time.

[Diger]

Originally Posted by LuckyTran

Make sure you don't miss that it's actually v dot grad(rho) = 0 (the inner product) and not the scalar product vgrad(rho). grad(rho) is a vector field and v is a vector field.

True. Even in a stationary flow I could have a density gradient as long as it is not in the direction of flow (along pathlines) thus perpendicular to it.

What's important is that we haven't assumed anything about the equation of state (yet), we've only used the assumption/restriction that the flow does not explicitly depend on time.

What do you mean by that? What changes here when one assumes an EoS? Say ideal gas.