Compressible or imcompressible?

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Discussion Overview

The discussion revolves around the use of the Navier-Stokes equations in computational fluid dynamics (CFD) simulations involving two-phase flow of water and air. Participants explore the conditions under which air can be treated as incompressible and the implications for modeling in Fluent.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions whether air can be considered incompressible in the context of their simulation, noting that the Navier-Stokes equations are typically applied to incompressible fluids.
  • Another participant asserts that air is not an incompressible fluid but suggests that if the pressure is low enough, it might be reasonable to make that assumption, albeit with some error introduced.
  • A participant references the Mach number and suggests that for air to be treated as incompressible, the flow velocity should be low, with a recommendation of using Mach number less than 0.3 for better accuracy.
  • There is a clarification that while nothing is truly incompressible, fluids like water are often treated as such due to their low compressibility under typical conditions.
  • Another participant emphasizes the importance of understanding the limitations of the incompressibility assumption, especially in mixtures like water and air, which may be more compressible than water alone.

Areas of Agreement / Disagreement

Participants generally agree that air is compressible and that the assumption of incompressibility can introduce errors. However, there is no consensus on the specific conditions under which air might be treated as incompressible in the context of the simulation.

Contextual Notes

Participants discuss the relevance of the Mach number and flow velocity in determining the validity of the incompressibility assumption, but the exact thresholds and implications remain unresolved.

vivavee
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Hello,

I'm doing the simulation by using the CFD Fluent.
The reactor is 10 cm diameter and 1 m height.

There is the water inlet (15mm) tangentially to the wall at the bottom end to produce the upward vortex flow.
and the air-bubble injection axially at the middle of bottom end.

The water inlet flowrate is maximum 900 L/hr
and the air inlet flowrate is about 40 L/hr

Fluent is the computational fluid dynamic package which base on the Navier-stoke equation.

with my simulation it will be two phases :water-air
My question is, Navier-stoke equation is used only for imcompressible liquid.
Is Air imcompressible?
If not, is there the assumption to explain that I can use two phases in Fluent?

all comments are welcome :)
Thank you very much,
 
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Air is not an incompressible fluid. If you can make the argument that your pressure is relatively low, then you can go on that assumption, but you would be introducing some error.

I am not really sure about the last part of your question when you ask
If not, is there the assumption to explain that I can use two phases in Fluent?
Are you wondering if you will have two phase flow?
 
Thank you very much FredGavin,

my last part question is because,
I searched in the internet and I got to know about the Mach number.
There is a case that Air is incompressible.
but I don't understand very well about Mach number.

Still, I want to say Air is incompressible in order to simulate in Fluent with two phases.
But is there any assumption to say that air is incompressible ? (so it can be used with Navier stoke's equation)

as you said, we can make argument that the pressure is relatively low.
How low? :)

Thank you very much again,
 
In referencing the Mach number (M), you will need to know the velocity (v) of the air and the speed of sound at your given conditions (sea level altitude?). Incompressible flow does not occur in nature, but for "slow" enough flows, incompressiblity can be assumed. For basic calculations, you can assume incompressible flow for v < 100 m/s, but using M<0.3 is a much better solution
 
to be clear nothing is incompressible. fluids like water and fuel are not easily compressed and gases like air are very compressible. But you should be aware of the limitations of this assumption even when using "incompressible" fluids, or in your case a mixture which will be much more compressible than water itself.
 
Even though fluids like water are strictly compressible, if one looks at the real compressibility of water, the incompressible assumption is a very valid one. Water loses only about 1.5% of it's volume at 6000 psi (or there abouts). For 90% of common engineering problems, incompressibility is a good assumption.

This is the kind of rationale you need to present to back up your modeling technique.
 

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