[Techies]

Hi guys,
I'm begginer to understand FVM, What is the different between the fluid element and fluid particle; rate and net rate ?
Thanks

[LuckyTran]

It's called net rate of flow because stuff can flow in and out of a fluid element at the same time in different places. But the overall amount determines whether the phi in the fluid element increases or decreases.

I'm not a fan of this word equation. Fluid element and particle are usually synonymous, they mean the same thing. It's better to just read the math symbols in this case. If you need help understanding the meaning of each term in the equation ask. Otherwise, don't get stuck on trying to grasp this poor presentation. I can't even see the equation but the fluid particle in this context refers to the material volume.

[FMDenaro]

Originally Posted by Techies

Hi guys,
I'm begginer to understand FVM, What is the different between the fluid element and fluid particle; rate and net rate ?
Thanks

The textbook you're reading?

[Techies]

Originally Posted by FMDenaro

The textbook you're reading?

A Introduction to CFD, H K Versteeg and W Malalasekera

[Techies]

Originally Posted by LuckyTran

It's called net rate of flow because stuff can flow in and out of a fluid element at the same time in different places. But the overall amount determines whether the phi in the fluid element increases or decreases.

I'm not a fan of this word equation. Fluid element and particle are usually synonymous, they mean the same thing. It's better to just read the math symbols in this case. If you need help understanding the meaning of each term in the equation ask. Otherwise, don't get stuck on trying to grasp this poor presentation. I can't even see the equation but the fluid particle in this context refers to the material volume.

Thanks for your reply. I have other questions that is why do we divide momentum equation into 3 equations but not with continuity and energy ?
For pressure-velocity coupling, why have we 4 equations (1 continuity and 3 momentum) and 4 unknows (1 p, 3 velocity) instead of 6 equations and 6 unknows (3 pressure xyz and 3 velocity uvw)?
Thanks.

[LuckyTran]

Originally Posted by Techies

Thanks for your reply. I have other questions that is why do we divide momentum equation into 3 equations but not with continuity and energy ?
For pressure-velocity coupling, why have we 4 equations (1 continuity and 3 momentum) and 4 unknows (1 p, 3 velocity) instead of 6 equations and 6 unknows (3 pressure xyz and 3 velocity uvw)?
Thanks.

It depends who you ask. The momentum equation is considered 1 vector equation or 3 equations in the x,y,z components. It depends only on whether you are talking about the full 3D velocity vector or the directional components of the velocity vector. Why? Some people just don't like to juggle with vectors and like to work in their x,y,z components.

Continuity is a scalar equation, so always it is 1 equation. Energy equation is also a scalar equation in temperature (or internal energy or enthalpy). There isn't a x,y,z component for a scalar. Pressure is also a scalar (1 variable).

So for p-v coupling, you will have either 2 equations (continuity & momentum) in 2 unknowns (pressure and your velocity vector) or 4 equations (continuity + 3 momentum equations) in 4 unknowns (pressure, & 3 velocity components). You never have 6, there is no such thing as pressure in x,y,z direction.

[Techies]

Originally Posted by LuckyTran

It depends who you ask. The momentum equation is considered 1 vector equation or 3 equations in the x,y,z components. It depends only on whether you are talking about the full 3D velocity vector or the directional components of the velocity vector. Why? Some people just don't like to juggle with vectors and like to work in their x,y,z components.

Continuity is a scalar equation, so always it is 1 equation. Energy equation is also a scalar equation in temperature (or internal energy or enthalpy). There isn't a x,y,z component for a scalar. Pressure is also a scalar (1 variable).

So for p-v coupling, you will have either 2 equations (continuity & momentum) in 2 unknowns (pressure and your velocity vector) or 4 equations (continuity + 3 momentum equations) in 4 unknowns (pressure, & 3 velocity components). You never have 6, there is no such thing as pressure in x,y,z direction.

I gett it, thanks for helping.

[FMDenaro]

Originally Posted by Techies

A Introduction to CFD, H K Versteeg and W Malalasekera

Unfortunately, that textbook starts the presentation in a misleading way. They present first the differential equations while I suggest to start from the physical law expressed by the Reynolds theorem. The link between the lagrangian and eulerian representation is in the Eq.(2.40) you should consider as the starting equation for the FVM. Conservation principle, concept of flux and flow rates require the integral formulation.

Have a look also to the textbook of Ferziger, Peric, Street.