One-Seventh power law in turbulent pipe flows
 

Hello Friends,

I am doing LES of fluid mixing in T junction flows. I read in CFX tutorial #11: Flow through a butterfly valve about the one seventh power law. I am interested in doing the same for my simulation. But is it correct to use it in turbulent pipe flows? The Reynolds number in the two T junction pipes in my simulation are 45650 and 3670 respectively. My question is:
1. Will the usage of this velocity profile in my inlets give a solution which is more realistic compared to the case of uniform velocity throughout the inlet cross section?
2. Is this one seventh power law suitable for a turbuelent inflow velocity profile?
3. You can see that the Reynolds number in one of my pipes is not very high (Re=3670). Is it ok to use the one seventh power law for this pipe inlet too?
I am attaching the picture of this one seventh power law that I found in CFX tutorial along with this post.
Thank you for your help and guidance in advance.

Regards,
Karthick

Specifying the velocity profile is the easy bit. You have not mentioned that for LES you also need to specify at an inlet the resolved turbulence, so you need eddy structures which have the correct energy and size scale. This is usually very difficult so ways around it are:
* Extend the inlet upstream so the flow can develop and naturally form the structures from a simple inlet condition.
* Do a simulation which generates the inlet conditions and then use these generated inlet conditions as the inlet condition for the real model.
* If appropriate, use periodic boundaries so the structures generated at the outlet are then fed back into the inlet.

In all of these approaches you will find generating the turbulence structures far harder than the velocity profile.

Turbulent inflow
 

Dear Glenn,

Thanks for the reply. Like you mentioned my motivation for this simulation is giving resolved turbulence at the inlet (Mainly at my hot pipe inlet as the Reynolds number is around 45000).

(i) I am planning to create a separate hot pipe geometry and do a steady state and LES only in this geometry (using a coarse mesh) and take the outlet velocity and temperature profile from the results and giving it as the inlet profile in my hot pipe inlet in T junction simulations. Since the Reynolds number in the cold pipe is 3600, I assume that a normal velocity profile would be enough as we did not observe any significant turbulence in the experiments.
(ii) Performing a steady state simulation for T junction geometry using the turbulent inlet profile generated from previous simulation.
(iii) Finally performing a LES using the steady state simulation result as the initial condition.

Please let me know if what I think is a right way to do it.

- Also, there is another related question on which I have only a partial understanding and wish to know more. When it is said that the inlet has a resolved turbulence, what are the variables in CFD Post that describe this? I always think that Vorticity is enough to describe it whenever I analyse this problem. But I would like to know more.

Thanks for your help in advance.

Regards,
Karthick

I doubt there is much to be gained in LES by starting with a steady state simulation initial condition. It is going to have to evolve so much to develop the turbulent structures that you might as well have not bothered and just start with a simple velocity=0 everywhere impulsive start.

When I say resolved turbulence I mean that if you look closely at the velocity vectors you will see eddy structures. These eddies are the resolved turbulence - the simulation is resolving the large scale turbulence structures. So if you calculated the vorticity of the flow then yes, you would seem them in the vorticity field, but you would also see them in the velocity, pressure and temperature fields as well.