What y+ value shall we choose for laminar flow?
 

Hi,

May I ask what y+ value shall we choose for laminar flow? Is that the same as for turbulent flow? Could I still use the calculator given by this forum? (http://www.cfd-online.com/Tools/yplus.php)

Thank you very much.
lnk

I'm also wondering of this. Could anyone answer this question?

viscous-sub-layer
 

The y+ value is important for the turbulent-model. It defines the height of the viscous-sub-layer where a laminar flow near the wall in turbulent flows occurs. I'm not a specialist but i would say it doesn't matter how big the height of your first cell is because there isn't a turbulence model.

regards

hi the y+ is only important for turbulent flow because it used in turbulent flow.
boundary layer is three region in turbulent flow they are sub layer , buffer layer & log layer. velocity is linear in sub layer and it's logarithmic for log layer.
if y+ was below 5 then the first cell is in sub layer. velocity for first cell obtain linearly if y+ was larger than 30 the the first cell is in log layer . velocity for first cell obtain logarithmic. however boundary layer of laminar flow is one region and it's velocity is defined we do'nt need y+ for laminar flow

y+ is not typically mentioned in laminar flow but actually y+ can be defined for even laminar flows (actually it carries more physical meaning in laminar flows than turbulent ones).

That calculator uses skin friction correlations for turbulent flows and will not work for laminar flows. So it is best to avoid it. The grid requirements for laminar flows is not based on the need to achieve a particular Y+ value, but rather a sufficiently refined grid is needed to resolve all important flow features. Hence Y+ is not often not mentioned in laminar flows since you do not need to check for y+ < certain value in order to guarantee a specific wall approach is being used.

Consider the example of the plane channel flow. Then,

y+ = u_tau *y/ni = (u_tau *H/ni) * (y/H) = Re_tau* y'

being y' the non-dimensional position along the vertical direction. Assuming that y'=1 in the half-heigh of the channel, as in laminar flow one assumes Re_tau=O(1), you see that y+ will be very very small close to wall and will be O(1) in the half-height.

Thanks for your answer. But in order to resolve laminar boundary layer well, we still need a lowest wall cell width criteria, right? For example, what wall cell width would you choose for laminar pipe flow?

calculate first cell height based on boundary condition

Could you briefly give a short example of how? Thank you very much.

You can calculate the maximum displacement of the boundary layer from the Blasius solution and then you can figure out how many points you need in order to cover this (with a geometric distribution let's say) after you decide your initial ds. Usually, the initial ds should be small enough, let's say of order 10^-4.

Order of magnitude analysis will give you that y+ = 1 if you are at approximate 1/1000 of the overall boundary layer thickness.

I usually take 3 orders of magnitude less the boundary layer thickness and then take half that height if I want to be conservative.

El. K. suggested 10^-4 which should also work.

You just need to estimate the boundary layer thickness somehow (can always resort to Blasius solution).

Does that mean you are using even a smaller wall cell width than the 'Y+=1' wall cell width for laminar flow?

The modelling assumptions used with turbulence models usually require the first cell to be placed around a particular y+ location. For some it is deep within the laminar sublayer where the turbulent stresses are insignificant (y+ < 1) for others it is in the equilibrium layer (y+ ~ 30) where the assumption that turbulent energy production balances turbulent energy destruction and the transport terms are negligible.

Laminar flows have no turbulence models and hence have none of these constraints on y+ for the first cell. What is required for the first cell and every other cell in the grid is that the gradients in the flow are adequately resolved. This is a function of the discretisation scheme and how well the gradients need to be resolved at the cell location. For example, a fully developed flow in a pipe may require only 1 cell to be fully resolved with a higher order numerical scheme or tens of cells for a low order scheme.

A resolution criteria based on y+ is going to be rather limited in applicability compared to a normal one based on gradients of the solution variables.

y+ value
 

I don't think it matters for laminar flow. It is mainly important when running turbulent flow sims.

y+ value or first cell height for laminar flow
 

This may help

What is the reference for this??

DEVELOPED LAMINAR FLOW IN PIPE USING COMPUTATIONAL
FLUID DYNAMICS by M.sahu and et
http://citeseerx.ist.psu.edu/viewdoc...=rep1&type=pdf
http://www.fem.unicamp.br/~phoenics/...l%20fluent.pdf

Hello. Please did you mean pipe radius divide by 38 can be taken as the first cell height for any laminar flow in a pipe