Turbulent Length Scale
 

Hi, Could somebody tell me how you find out the turbulent length scale for the flow over a NACA0012 airfoil? Is there a source for finding out this information. I need it in order to define the inlet boundary condition, Eplison in my problem. k i can set from the turbulence intensity of the flow, but i'm just stuck in finding out Eplison. Any help would be great.

Regards James

Re: Turbulent Length Scale
 

(1). I am sure that this same question was asked and answered before, related to the inlet boundary condition using k-epsilon model. (2). So, as a first step, try to search through previous messages here. (3). Most commercial codes will give you several options to choose.

Re: Turbulent Length Scale
 

I am not sure about your software and your modeling about planes, but the turbulent scale you refer to is probably the largest scale that the Eddies can take - I guess.

Since your plane does not fly in turbulence, but only in a laminar flow, again, I guess that the turbulence is either in the wake of the wing or in the boundary layer on the surface of the wing. In the first case the turbulence will not be larger than -say the thickness of the wings, while in the second case the turbulence will have the size of the boundary layer. To find the size of the boundary layer you can use scaling arguments. The viscosity is in units of length times velocity. So the size of the boundary layer is of the order of the viscosity of the air (which I hope is given) divided by the velocity of the plane in the air.

I hope this helps.

Re: Turbulent Length Scale
 

Here is a rule of thumb we find quite handy in our company. Estimate the turbulent viscosity instead of the epsilon. This can be set to 10,100,1000 times the laminar viscosity for low, medium, high turbulence flow. If this airfoil is on an aircraft, I guess Mu_t=10*Mu is reasonable, 100* is reasonable for IGVs on a turbomachine, and 1000* perhaps for intermediate blade rows at off design conditions. Once you have a Mu_t, the epsilon can be computed from the definition.

One other fact to note is that if there is significant turbulence generation/dissipation within your solution domain, the inlet values rarely affect the solution. In the case of a free airfoil (i.e. not a cascade) though, the inlet values probably matter because this turbulence is simply convected by the field.

Re: Turbulent Length Scale
 

Hi,

Although my problem was related to an impinging jet, I thought that I might be of some help here. For an impinging jet I have used the following values at the inlet for k and epsilon:

kin=0.001U**2 and

epsin=0.1643*(kin**1.5/0.035*d)

where d is the jet diameter and U is the bulk fluid velocity.

As Cfd pointed out, if the turbulence intensity is fairly large for your problem, the inlet values will not be very important and are used only to initiate a turbulent solution.

All the best!!!

Re: Turbulent Length Scale
 

Hi Mahesh,

I'd like to ask you how you estimated this value for epsilon?

I believe the problem of specifying the lenght scale especially for the case of an impinging jet is often neglected in the literature. My own investigations suggests that the value seriously affects heat transfer results for this case. Different authours use different values, sometimes they diverge by a factor of 4 which may affect heat transfer in the stagnation zone by 100%!

Regards

Andreas Abdon

Re: Turbulent Length Scale
 

This note has less to do with the original question by James, more related to the comments by Andreas. I believe there is one other factor that may have been neglected in impinging flows. In codes which assume the "equilibrium KE model" at the walls, the Y₊ is obtained from the U_P (wall parallel component) and is zero at a stagnation or reattachment point. From Reynolds analogy, this results in zero heat transfer coefficient. I believe Fluent does this by default. In other codes (STAR-CD,for one) the Y₊ includes the effect of the cell K, and is non zero at the forward stagnation point (where K is convected in by the impinging flow), giving the correct physical result of maximum heat transfer coefficient there. (I'm keeping the presentation simple to focus on the essentials, the exact equations for both assumptions are available from the manuals or any good text)