Newbie: why don't I hear anyone refer to Re in FEM and FD methods?
 

Hello all:

I'm a bit of a newbie to advanced fluid dynamics. I'm a chemist and I often use code for 1- and 2-D advection/diffusion, based on finite element/difference/volume methods to deal with things like contaminant transport.

This is probably a very silly question, but I'd really appreciate a push in the right direction...

Since I started using finite element/difference/volume, I have heard anyone refer to the Reynolds number. I know I have to obey the CFL when using explicit schemes. But as far as going from laminar to turbulent flow, it seems like I don't need to worry about anything. In other words, is it true that I can use the exact same numerical schemes to model laminar and turbulent flow?

If this is not true, can anyone suggest a book that might help me figure out how to deal with turbulent flow within finite element/difference/volume schemes? I would like to start modeling higher Re flows.

Thanks a lot.

hello
 

Well, Re should be discussed in FD,FV or FE schemes is not a clause or pivotal point. Re is used to judge type of flow or one can say it is used as a SI unit to discuss and convey type of flow or physics of flow in research community.

As far as different methods are concerned they can extract velocity from Re, that is all. But yes in experimental fluid dynamics it has got big significance as compared to computational fluid dynamics. Nevertherless, do not worry why Re is not discussed in computational methods. Rather think Re should be discussed only while pre-processing ( to understand flow boundary and expected result) and post-processing to interpret the results from nemerical schemes.
I hope , this would give you a direction to think on this matter.
All the best.

regards,
CFDkid

Your assessment that no-one has referred to the Reynolds number (i.e., dealt with the turbulence issue) is incorrect. Turbulence modeling has been one of the most intensely active (and difficult) research fields in fluid dynamics for decades. There are volumes upon volumes of information on this.

As for the question on whether the same equation can be used for laminar and turbulent flows, the answer is "yes, so long as the numerics resolve the length and time scales associated with the Reynolds number". The Navier Stokes equations are a statement of conservation of mass and momentum (in the continuum regime), and the diffusion term essentially accounts for the proper Reynolds number effect. However, in discrete form, for this diffusion term to balance convection (and pressure) we would need ever increasingly smaller grid (and timestep) sizes. At present, this is computationally unfeasible except for very small physical domain sizes and very simple problems. The term "Direct Numerical Simulation" or DNS is used to imply direct accounting of all the Navier Stokes terms in a turbulent flow regime. Since DNS of complicated and large domains is not possible, one must resort to turbulence modeling, which is effectively a method to handle the complexities associated with convective non-linearity. Generally, this latter is formulated in terms of a "turbulent diffusion" term, and various models with various degrees of complexity exist to model the diffusivity "constant" (which is really not a constant as in the case of laminar diffusion of Newtonian fluids).

This is a very brief description; I hope it helps clear out your confusion.

adrin

Thanks guys.

Without touching the context of accounting turbulence which has already been said adrin, back to the context of the stability of the solution (was referred to CFL), in some numerical schemes used by the cell Peclet number, which includes the cell Reynolds number (Pe = Re * Pr), for example in hybrid numerical scheme for switching between UD and CD. Thus, indirectly, higher Reynolds numbers can create problems for the stability of some numerical schemes.

PS: We must distinguish the Reynolds number for the domain which includes the characteristic size of the domain that points to the nature of the flow in a domain (laminar, turbulent or transitional) and cell Reynolds number which includes the cell size.

I am wondering how one solves the Peclet no., or Prandtl no Pr, which involves the viscous and thermal diffusion rate. Wikipedia says for air, it's 0.7-0.8. So can I use it to get the Peclet no. in my CFD code, for switching between UD and CD?

Thanks

You have a look http://www.cham.co.uk/phoenics/d_pol...scheme.htm#3.3 Hybrid-Differencing Scheme as example