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January 23, 2021, 09:16 
Incompressibility of the flow

#1 
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Shabi
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A flow is incompressible if the density of the flow is constant within a fluid parcel and also the whole flow.
How do these fluid parcels are distributed in the domain? In other words, do we have the same number of the parcels in the area with different velocities? E.g., if there is an object and flow pasts it, do we have the same number of parcels in an specific area(volume) everywhere in the domain? Last edited by Shabi; January 23, 2021 at 12:49. 

January 23, 2021, 11:29 

#2 
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Reasoning in 3D requires using streamsurfaces, not streamlines, so let's focus on 2D.
Streamlines are defined as lines parallel to the local velocity field, so there can be no mass flow trough them. If two streamlines get closer (thus there are more in a cell), then the velocity in between them is higher to keep the same mass flow rate with a smaller passage area. I have no idea of what you mean by parcels. Could you define them? What does it mean that the flow is made plenty of fluid parcels? How? How do you end up with a different number of fluid parcels in each cell? 

January 23, 2021, 11:34 

#3 
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Vinícius Alves
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Hi, I am new to CFD, but what I know is that streamlines doesn't show about the density of the fluid, Its more like about the velocity, the direction of the flow.
*I ask someone with more experience to help too, so we can both learn 1)No, not that, it means that the flow is redirecting to that direction 2) The cell is what we call finite volume, what the solvers do its the calculation of the characteristics of that fluid in that volume, based on the boundaries of that volume. So, to have an equal volume on the cells, your flow must be incompressible. 3) If you have density variation you have a compressible flow. 

January 23, 2021, 12:36 

#4  
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Shabi
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Quote:
If the flow is made up plenty of small tiny fluid particles, do we have the same number of them in the whole domain? we have the definition of the fluid parcels also here: https://en.wikipedia.org/wiki/Incomp...ow%20velocity. I edited my question, as i used some terms in my questions which could make confusion 

January 23, 2021, 14:04 

#5 
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andy
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Since you are learning I shall point out there is an issue with this terminology. For example, many combustion codes will assume the flow is incompressible and yet predict strong density variations. So what is the assumption made by incompressible CFD codes if not constant density?


January 23, 2021, 14:51 

#6  
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Filippo Maria Denaro
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Quote:
Fluid parcels is strictly related the the assumption of the continuum: https://en.wikipedia.org/wiki/Continuum_mechanics You assume the density of the fluid rho(x,t) to be the result of the averaging over a very small but finite volume, centered in x. Assuming that the density is constant means you assume that wherever you put this small volume, the average will provide the same value for the density. 

January 23, 2021, 16:21 

#7 
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The flow is incompressible when the density does not depend on the velocity/pressure field. There can be incompressible flow with changing density, e.g., nonisothermal flow.


January 23, 2021, 18:14 

#8 
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Filippo Maria Denaro
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Maybe there is an issue to be clarified.
Any real material is somehow compressible (that is changes its own volume under normal stress) even if apparently rigid. The real nature of a fluid such a gas is to be compressible, this is our normal experience. Liquids are much less compressible but at some level they are, too. Speaking about "incompressibility" of a flow refers to a model, that is an approximation of the reality. Thus, the same fluid can be studied with a compressible or incompressible flow model. Have a look here https://www.researchgate.net/post/Wh...ressiblefluid 

January 23, 2021, 18:37 

#9  
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Shabi
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January 24, 2021, 07:36 

#10  
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Filippo Maria Denaro
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Quote:
A position x means everywhere in the flow 

January 25, 2021, 02:11 

#11 
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Lucky
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Density need not be constant everywhere for a flow to be incompressible. You can show that if density is a function of temperature (but not pressure), the flow is always still incompressible. And since temperature can be a spatial function of x,y,z; it is sufficient to show that density need not be a constant function of x,y,z for a flow to remain incompressible.
And this is partially also why combustion codes can have strong density variations and still use incompressible flow assumptions. The pressure does not change much across a flame surface (and if it did, we call those detonations). 

January 25, 2021, 04:52 

#12  
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Filippo Maria Denaro
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Quote:
Consider a pipe filled with water (single phase) being at the rest. This case is still compatible to produce a nonvanishing gradient of the density rho since drho/dt +v .Grad rho =  rho div v is satisfied for a zero velocity field. 

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