Low Reynolds number flow
 

Hi!

I am modelling the flow of a highly viscous fluid where Re<< 1. In this case the acceleration term in the Navier Stokes equation is very small, meaning that the Navier Stokes equation

rho Du/Dt = - nabla p + nabla T

can be simplified to the Stokes equation

0 = - nabla p + nabla T

Is it possible to make this simplification in CFX? That is to neglect the accelaration term to speed up calculations?

I would be most thankfull for any help!

- Terje

rho - density u - velocity vector D(.)/Dt - substantial derivative p - pressure T - deviator of stress tensor

Re: Low Reynolds number flow
 

Dear Terje,

It is not possible (w/o source code modifications) to turn off the advection terms in ANSYS CFX..

ANSYS CFX uses a false transient approach to reach steady state solutions; therefore, the transient term is still present.. That means, you are only saving the assembling of the advection terms, which is not that great anyways.. The major expense is to assemble the viscous terms and the continuity (for pressure) equation.

What kind of problems are you having?

Opaque

Re: Low Reynolds number flow
 

Hi Opaque!

Thanks for the answer! I am modelling <a href = "http://en.wikipedia.org/wiki/Injection_molding">injection molding </a> of polymers in a transient simulation.

If I understand your answer correctly you are referring to the way a stationary solution is found by using a quasi transient approach. That is not exactly the case in my problem. I am running a transient simulation, but I do not want to include the acceleration terms in the momentum balance since they are very small.

My problem with the accelaration terms is that since they are not important in the physical description it would be best not to spend time calculating them. I am not sure on how much I will save though. It is also common to use this approach in commercial software (Moldflow) dedicated to injection molding, so I think there is something to save.

- Terje

Re: Low Reynolds number flow
 

Dear Terje,

I am sorry.. The reason some codes simplify the advection terms is to avoid the non-linearities it introduces on the velocity field. If by any chance the term becomes important (if the flow regime happens to be on the border line of the approximation) the user is out of luck. Sure, it will save some time but not enough to be worry about and distract you from the simulation at hand.

Best regards,

Opaque.