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 gorka March 31, 2003 04:07

About low Re number turbulent flows

Hi,

As far as I know, a flow should be very turbulent (very high Reynolds number) to have the usual features explained by the turbulence theory: the energy cascade by means of vortex stretching, the energy spectrum with the inertial sub-range, production and dissipation equilibrium etc. Turbulence models used in the RANS approach are constructed accepting that the flow is very turbulent and thus the latter features would take place.

However, it is well known that these models have limitations even when the flow is very turbulent indeed. Therefore, can we expect the turbulence models to perform well in the calculation of low Reynolds number turbulent flows (i.e. when the mentioned features don't take place)?

Can we handle (fully) low Reynolds number turbulent flows with the so-called Low Reynolds number Turbulence Models? Or, are they suitable only to handle near wall effects in very turbulent flows?

Gorka

 Jonas Larsson March 31, 2003 04:59

Re: About low Re number turbulent flows

You can only expect low-Re turbulence models to handle near-wall effects in fully turbulent flows.

The term "low-Re" in these models does not refer to the global Re-number, it refers to the local Reynolds number close to the wall. Hence, a low-Re model can not predict transitional flows with the features you describe (non-equilibrium, no separation of scales, coherent structures, anisotropy, ...)

 Harry Fulmer March 31, 2003 05:25

Re: About low Re number turbulent flows

I was under the assumption that low-Re models generally have two aspects, near wall low Re effects and also a bulk flow modification. Actually I suppose I'm really talking about k-e models. I know the term f_mu is used to reduce the effective viscosity, f_mu being a smooth function related to the local turbulent Reynolds number. A model with no great finesse but one that at least attempts to reduce mu_t away from the wall when Re_t <50.

 Jonas Larsson March 31, 2003 08:47

Re: About low Re number turbulent flows

f_mu, together with the other damping functions and constants (f1, f2, Ceps1 and Ceps2), are used to enforce the correct behaviour in the boundary layer. Constants and functions in low-Re models are normally tuned based on channel and boundary layer data to correctly predict the boundary layer while reproducing the original "high-Re" model away from walls.

I have not seen any papers where low-Re models are tuned based on "global low-Re bulk flow effects". Have you got any references on this? (I have been out of the turbulence modeling business for 5 years so I might be wrong).

The f_mu function specifically is used to correct for the effect of molecular viscosity on the shear stress close to walls where the turbulent fluctutations are damped. Some models use f_mu functions based on Re_t (Jones Launder, Launder Sharma, ...) while others use f_mu functions based on y+ (Chien, Shih Mansour, ..)and some use a combination of both (Lam Bremhorst, Nagano Tagawa, ...). The goal when devising all of these models as far as I know have been to reproduce *boundary layer* properties correctly close to walls in fully turbulent flows. Sometimes you see transition-corrections to these models where they in addition are tuned to correctly predict the diffusion of turbulent energy into the boundary layer and thereby predict by-pass transition (boundary layer transition caused by the high level of free-stream turbulence).

 gorka April 1, 2003 05:28

Re: About low Re number turbulent flows

Thanks Jonas and Harry for your responses,

As Jonas, I don't know any turbulence model that would be tuned based on "global low-Re bulk flow effects".

Then, can we spect to obtain good results if we use a turbulence model in a global low-Re bulk flow? Would the results be better (more realistic) if the flow was more turbulent?

Regarding to LES, can we spect to obtain good results using the LES approach in these flows if actually no separation of turbulent scales takes place?? I suppose the separation of the scales is the main hypothesis of LES...!!

Gorka

 Harry Fulmer April 1, 2003 07:17

Re: About low Re number turbulent flows

Interesting! My experience was with the Launder Sharma model in what is now CFX (FLOW3D back then). My assumption (due to either my inexperience or over reliance on the user manual) was that f_mu was imposed in the bulk flow and that the other 3 modifications were wall specific.

Am I right in saying then that there is no turbulence model that even attempts to model low Re effects in the bulk flow!!?? Has any one investigated the validity of applying f_mu in the bulk flow?

 Jonas Larsson April 1, 2003 08:38

Re: About low Re number turbulent flows

For simplicity f_mu is most often applied in the whole flow domain. However, outside boundary layers it normally does not have any effect (it is equal to 1). The f_mu function in the Launder Sharma model has not been tuned for any low-Re bulk flow effects. However, since f_mu in the Launder Sharma model is only dependent on the turbulent Reynolds number and does not contain any explicit wall-distance it will have an effect also in the bulk region if you do get very low turbulent Reynolds numbers there. As far as I know the effect is un-tuned and un-known though. Also note that the turbulent Reynolds number (k^2/(molecular_kinematic_viscosity*epsilon)) used in the f_mu function is not at all the same as the global Reynolds number (velocity*length_scale/molecular_kinematic_viscosity).

 Harry Fulmer April 1, 2003 09:31

Re: About low Re number turbulent flows

>> Also note that the turbulent Reynolds number
:> (k^2/(molecular_kinematic_viscosity*epsilon)) used in
:> the f_mu function is not at all the same as the global
:> Reynolds number
:> (velocity*length_scale/molecular_kinematic_viscosity).

Not totally true I think! k/e is the length scale that is used in the eddy viscosity assumption, k is the velocity scale. The only difference then between Re_t and Re is the 'nature' of the velocity and length scales. The former uses turbulent quantities, the latter uses mean velocity and geometric quantities. What this means I don't know (apart from the fact that using f_mu in the bulk flow might not be so unrealistic after all?) :)

 Jonas Larsson April 1, 2003 09:47

Re: About low Re number turbulent flows

Of course both are Reynolds numbers. What I meant is that the turbulent Reynolds number is not at all representative of the bulk-flow global Reynolds number.

 Harry Fulmer April 1, 2003 10:12

Re: About low Re number turbulent flows

I wonder what the physical sense of these two Reynolds number is then.

If Re is the ratio of intertial forces to viscous forces then isn't Re_t the ratio of intertial eddy forces to viscous forces?

There inherent assumption in Re_t is that the flow is already turbulent.

Can't really find any physical use for Re_t. Anyone got any ideas??

 sylvain April 1, 2003 12:31

Re: About low Re number turbulent flows

Just some though :

turbulent length scale :

l_t ~ k*sqrt(k)/eps

turbulent velocity :

u_t ~ sqrt(k)

so turbulent Reynolds number :

Re_t = l_t*u_t / nu

For laminar flow Re_t = 0.

Turbulence Reynolds number has to deal with energy containing eddies (size l_t, velocity u_t).

One also may consider dissipative scale, characterized by the Kolmogorov length scale :

eta = (nu^3/eps)^(1/4)

to compare eta and l_t :

l_t/eta = Re_t^(3/4)

So Re_t characterized the separation between the energy containing eddies and the dissipative eddies.

When Re_t tends to zero, the dissipation occurs at the same scale than the production.

k-eps models are based on the hypothesis of spectral equilibrium. That's mean that all and only the energy tranfert throught the energy cascade is dissipated. This can only append when l_t and eta are clearly separated, so when Re_t is hight.

To "correct" k-eps model for low turbulent Reynolds number :

1) correct the c_eps_2 in the epsilon equation, since this constante drives the turbulence decay, which is modify for low turbulent Reynolds number (Mansour and Wray 1992 - Decay of isotropic turbulence at low Reynolds number - Phys. of Fluids, 6(2) pp 808-814)

2) Correct the production terms for k and eps. Since production occurs directly at the dissipative scale. This could be done using a third turbulent variable - see Lumley...

Sylvain

 Jonas Larsson April 1, 2003 16:19

Re: About low Re number turbulent flows

sylvain's interpretation is one way to look at it. Another interpretation that I can think of is this:

Re_t = k^2/(epsilon * nu)

nu_t = Cmu * k^2/epsilon

Hence

Re_t ~ nu_t / nu ~ turbulent "viscous" forces / molecular viscous forces

Where

nu = molecular kinematic viscosity

nu_t = turbulent kinematic viscosity

In words this means that the turbulent Reynolds number is propotional to the ratio between the turbulent viscosity and the molecular viscosity.

 Jonas Larsson April 1, 2003 16:25

Re: About low Re number turbulent flows

Very interesting, thanks sylvain! Do you know how successful these corrections for low turbulent Reynolds numbers flows are? For what kind of applications are they used?

I'd imagine that there are few low-Re_t cases where you have enough well-behaved (scale separation, isotropy etc.) turbulence to succefully use a k - epsilon model.

 gorka April 2, 2003 05:19

Re: About low Re number turbulent flows

I apologize if it seems selfish to take up again my previous questions ...

How can we handle global Low Re-number (turbulent) flows, if

1)Turbulence Models (RANS) are tuned for High Re-number flows.

2)LES supposes the scales of the turbulence to be separated, wich is not true in Low Re-number flows.

Is DNS the only reliable approach?

Thanks,

Gorka

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