Incompressible Solver - What does this mean?
 

Hello,

I am wondering what the effect of an incompressible solver is?

So I have a mass flow inlet and a pressure outlet. If I switch to an incompressible solver, the density of my ideal gas does no longer depend on pressure.

But what happens to my ideal gas formulation: p = rho *R *T

According to: https://www.sharcnet.ca/Software/Flu...ug/node332.htm my density is now calculated by an operating pressure.

1) So for each cell in my domain the navier-stokes equations are solved for velocity and pressure. But for calculating density, not the local pressure of the cell is used but the operating one in p = rho *R *T ?

2) But why can I avoid this way osciallations regarding my solution (for example air velocity).


Thank you for your explenations

Best regards
Moritz

Generally, we assume "incompressible" flow model when the characteristic velocity of the problem is much lower than the characteristic sound velocity. In other words dp/d rho -> Infinity, acustic waves propagate at infinite velocity.

These assumptions let the possibility that the density can vary in the momentum as function of temperature (for example introducing the Bousinnesq model for small temperature variation).

In Fluent you can set directly a constant value of the density or you can have the density depending only on T as described in your link.

Thank you for your answer.

2) But why can I avoid this way osciallations regarding my solution (for example air velocity).

In case of low Mach flow, the full NS system is stiff since very small perturbation in the density solution can be amplified in the pressure (dp/drho >> 1) and the pressure gradient in the momentum can produce oscillations also in the velocity field. For this reason the original system is modified by the assumption that the acoustic waves have infinite velocity and the density does not depend on the pressure.

But oscillations in the solution can be just due to the onset of numerical instability for a wrong setting of the time step value.

Fluent still solves the compressible N-S.

All you are doing is specifying the "incompressible ideal gas law" as the equation of state for density. A more extreme example is, you can even specify a constant density.



Yes the density is fixed at the operating pressure and depends only on temperature for this specific equation of state. It's not important that this looks like an ideal gas law. For example you can specify a polynomial function of temperature if you like.

What oscillations you are talking about?

From the math side, consider that not all incompressible solvers are actually equal.

Pressure based ones typically involve a Poisson equation for the pressure. In this case the continuity equation is actually forced to be elliptic.

Preconditioned density based solvers (of which artificial compressibility method is an example) instead retain the hyperbolic nature of the continuity equation but actually reduce the numerical speed of sound (instead of making it infinite) so that it is comparable to the flow velocity.

I don't know about compressible pressure based solvers.

Hi guys, seems that you are having a lot of fun here! Nothing more to add than Paolo's and Filippo's answers ;) Just to complete the last point, in compressbile pressure based solvers you have a very similar framework to the incompressible pressure based solver, but in the pressure-correction equation, you have an addtional hyperbolic term. Edit: the elliptic term scales as as 1/M^2 and becomes dominant for low mach flows. This feature is very appealing to adapt an existent incompressible solver and make it suitable also for compressible flows (mmmmh sooner or later I will do this jump also in my code)

I am not an expert in this topic - so what do you mean by this. Yes I have a low Mach flow.
a) But why are the NS "Stiff" vor low Mach flows?
b) can you maybe explain your statement with reference to the terms of the NS-equations?

I really want to understand this.

How can I understand this, that in an uncompressible case (what you are talking of?) the speed of sound in infinite?

Low Mach means that the sound waves travel at a velocity (a) much greater than the convective one (v). When a flow problem has different characteristic scales (lenght and time) you have a stiff problem.

Also, as a side problem, your pressure variations become tiny with respect to the background pressure value, which can give roundoff problems

What does this mean FM Denaro?

You once said

Where can I see this in the NS- equations?

Concerning Fluent http://www.afs.enea.it/project/neptu...th/node377.htm

but I strongly encourage you to study the general issue in good CFD texbooks

Stiff means a small perturbation in one parameter results in large change in another. Said another way, a "very small perturbation in the density solution can be amplified in the pressure." This is consistent with an incompressible substance where rho does not depend on density (drho/dp = 0) or flipped the other way (dp/drho is infinite). All these statements say the same thing. But dp/drho is related to the speed of sound...

So now that you realize you have infinitely fast acoustic waves propagating around...how do you suppose to solve for them?


I would like to mention with regards to the original post/question that regardless of which equation of state you select in Fluent, always you have still the same solver. If you had the pressure-based solver before, you still are using the pressure based solver. If you use the density-based solver, you stick with the density-based solver. If you are not using Fluent but building your own incompressible solver, then maybe we kill the mention of Fluent?