[Ulixes]

Hi everyone, I am another student that has trouble to understand how to mesh the boundary layer.

Basically I am simulating a laminar flow in a pipe (Re ~100) in a 2D geometry. What I have understood so far from my researches on the web is that the boundary layers merge in the centre of the duct once the flow fully developped. On the other hand I have seen that it is possible to define a parameter y+ to characterize the BL thickness. I have also found a formula given the BL thickness correspinding to a velocity equal to 99% the free-stream velocity.

I am quite confused about all this informations. If the boundary layers merge in the center of the duct so there is no need to specifically mesh them since they account for the whole domain.

Could someone provide me informations about how to simply mesh the BL in this simple problem ?

Sorry for the bad english.

[FMDenaro]

Originally Posted by Ulixes

Hi everyone, I am another student that has trouble to understand how to mesh the boundary layer.

Basically I am simulating a laminar flow in a pipe (Re ~100) in a 2D geometry. What I have understood so far from my researches on the web is that the boundary layers merge in the centre of the duct once the flow fully developped. On the other hand I have seen that it is possible to define a parameter y+ to characterize the BL thickness. I have also found a formula given the BL thickness correspinding to a velocity equal to 99% the free-stream velocity.

I am quite confused about all this informations. If the boundary layers merge in the center of the duct so there is no need to specifically mesh them since they account for the whole domain.

Could someone provide me informations about how to simply mesh the BL in this simple problem ?

Sorry for the bad english.

Do not worry about y+ for yor case...It is relevant for high Re number flows where you have turbulence. At Re=100 the flow is laminar and you can easily generate a grid to work at cell Re number of O(1).

[Ulixes]

Ok but how should I define the boundary layer ? Can I assume a constant thickness along the wall ? In this case how to evaluate the thickness and the number of layers I have to compute ?

[FMDenaro]

for laminar flow you can consider the channel equivalent to two flat plates where the BL evolves spatially. Hence, you can use the Blasius solution for delta(x)/L. You have all you need, just be sure to work with a small cell Re number.

[Ulixes]

I do not undestand the reason of why a space evolving boundary layer has to be considered. Since the boundary layers will merge at the center of the pipe, the mesh will be uniform after the entrance length or did I miss something ?

My duct has a diameter of 50 µm, the inlet velocity is a flat profile of 1,667 m/s and viscosity and density are the ones of water (0,001 Pa*s ; 1 000 kg/m^3).

By computing the Basius equation with the global Re I get a BL larger than the diameter of the pipe...

[FMDenaro]

Originally Posted by Ulixes

I do not undestand the reason of why a space evolving boundary layer has to be considered. Since the boundary layers will merge at the center of the pipe, the mesh will be uniform after the entrance length or did I miss something ?

But do you want to simulate the evolving BL in the channel starting from uniform condition at inflow or you just wanto to check your code using the Poiseulle solution and setting the parabolic profile at inflow? At Re=100, the mesh can be uniform everywhere, it is just sufficient to have a small Re_h.

[Ulixes]

Actually I am using a VOF model to simulate the motion of a liquid droplet in a microcanal. Basically I just want to set a boundary layer to get a correct flow fluid near the walls.

Maybe the evolution of the BL along the tube is not so important to me ; what I want is to catch fluid field properties near the wall with suitable accuracy.

I have read that for meshing the BL with constant thickness along the walls, usually the 1st grid point is set so that y+ = 1. So in my case that would correspond to the first grid point at y = 2.24 µm. However I am using a uniform quadrilateral mesh of maximum length 1 µm ; in this case meshing the BL makes no sense. Or did I miss something ?

By the way, thank you for your first answers.

[FMDenaro]

In your case, it makes no sense using y+ as evaluation..you have laminar condition everywhere while the y+ is a non-dimensional length used for high Re number turbulent flow.
Use the delta(x) Blasius estimation to define the BL frontier, than you have an analytical solution for the velocity field. This is for a spatially evolving BL. When delta(x*)=h/2 (h is height of the channel) you have that x* is the position where the two BL merge and you can use the classical parobolic velocity profile of the Poiseulle solution.

[Ulixes]

Basically the attached picture is the result I would like to obtain (excepted that in my case the unstructured part of the mesh will be finer). Here the boundary layer mesh does not evolve in space.

Is there no simple solution to calculate the characteristics of this boudary layer meshing ? Because if I undestand well, Blasius' equation give which still depends of the position with respect to the inlet.

Furthermore I do not understand why knowing x* would be helpful ?

Sorry I really have troubles with this issue.

[FMDenaro]

this is an elbow, you cannot use here the BL theory... just use a grid size such that Re_h=O(1) everywhere, in 2D I think you can realize easily that with O(10^5) grid points.