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-   -   Question about conjugate heat transfer mesh for laminar model (http://www.cfd-online.com/Forums/main/117250-question-about-conjugate-heat-transfer-mesh-laminar-model.html)

Anna Tian May 5, 2013 11:59

Question about conjugate heat transfer mesh for laminar model
 
Hi,

Setting Y+<1 is essential to more accurately predict the conjugate heat transfer behavior. But if the laminar model is used, then there won't be a Y+ value any more. I'm wondering how large is the wall cell width at the conjugate heat transfer interface shall I set up for laminar flow?

agd May 5, 2013 19:05

Why is there no y+? The y+ parameter is still defined for laminar flow.

Anna Tian May 6, 2013 12:34

Quote:

Originally Posted by agd (Post 425427)
Why is there no y+? The y+ parameter is still defined for laminar flow.

Yes. It's defined. But it doesn't make any sense any more. Right? You can check with the link below.


http://www.cfd-online.com/Forums/mai...inar-flow.html


How would you decide the first cell width for laminar flow for conjugate heat transfer simulation?

agd May 6, 2013 13:03

What does y+ really represent? Whether turbulence is present or not, y+ is a way of defining a grid resolution sufficient to capture an important gradient at the wall. The best approach to your problem is to run a case, refine your grid and repeat. Continue to do so your heat transfer reaches a limiting value.

Anna Tian May 6, 2013 13:19

Quote:

Originally Posted by agd (Post 425617)
What does y+ really represent? Whether turbulence is present or not, y+ is a way of defining a grid resolution sufficient to capture an important gradient at the wall. The best approach to your problem is to run a case, refine your grid and repeat. Continue to do so your heat transfer reaches a limiting value.

Grid independence study is always good way to know how fine the grids need to be. But before the grid independence study, we need a way to estimate a starting point for the grid independence study. Right? My question is how to estimate how large the wall cell width need to be at the very beginning.

agd May 6, 2013 14:22

If you know your Re and fluid velocity, assume a parabolic velocity profile. You can estimate how thick the BL is (or if it's fully developed internal flow then you can use the radius of your pipe/duct). Then simply decide how many points you need to reproduce this gradient. If you have any idea of how much heat flux to expect, then you can use that to estimate the thermal gradient and base your grid spacing off that. But the process is similar - you estimate the distance of the overall change (i.e. the boundary layer thickness) and the shape of the change (parabolic for laminar flow) and the pick a spacing to give a good representation (10 points, 20 points across the BL, etc.)

Anna Tian May 7, 2013 05:22

Quote:

Originally Posted by agd (Post 425636)
If you know your Re and fluid velocity, assume a parabolic velocity profile. You can estimate how thick the BL is (or if it's fully developed internal flow then you can use the radius of your pipe/duct). Then simply decide how many points you need to reproduce this gradient. If you have any idea of how much heat flux to expect, then you can use that to estimate the thermal gradient and base your grid spacing off that. But the process is similar - you estimate the distance of the overall change (i.e. the boundary layer thickness) and the shape of the change (parabolic for laminar flow) and the pick a spacing to give a good representation (10 points, 20 points across the BL, etc.)

We can estimate the velocity boundary layer by Blasius theory

http://en.wikipedia.org/wiki/Blasius_boundary_layer

.

But how do we estimate the thermal boundary layer thickness (if heat flux is already known)? Is there any theory or estimation method about that?

agd May 7, 2013 08:51

Look for information on the Pohlhausen method.

Anna Tian May 7, 2013 09:40

Quote:

Originally Posted by agd (Post 425833)
Look for information on the Pohlhausen method.

I look at it. It seems that it is not for thermal boundary layer.

triple_r May 7, 2013 10:13

Use the Prandtl number to calculate the thermal boundary layer thickness:

(viscous boundary-layer thickness) / (thermal boundary-layer thickness) = f(Pr)

If I remember correctly, f(Pr) = Pr^0.3 is a good start for most materials. If the pipe that you are looking at is very long and straight, then depending on the boundary conditions, you can find the gradient of temperature at wall analytically (for constant heat flux and constant temperature this value is known, for others, it is a value in between these two). So, you just need to have a first layer thickness that is fine enough to capture that gradient.

Coming back to y+, yes, we don't use y+ in laminar flow, but y+ is just a Reynolds number defined by a very special velocity (shear-stress-based velocity), so y+ at the thickness of first layer just is a measure of hoe steep the velocity profile is near the wall. If you have a large y+ (no matter if it is laminar or turbulent) the first layer is too thick. So, in my opinion, you can still use the y+~1 criterion, but it might be over-kill for laminar flow.

Anna Tian May 7, 2013 11:33

Quote:

Originally Posted by triple_r (Post 425857)
Use the Prandtl number to calculate the thermal boundary layer thickness:

(viscous boundary-layer thickness) / (thermal boundary-layer thickness) = f(Pr)

If I remember correctly, f(Pr) = Pr^0.3 is a good start for most materials. If the pipe that you are looking at is very long and straight, then depending on the boundary conditions, you can find the gradient of temperature at wall analytically (for constant heat flux and constant temperature this value is known, for others, it is a value in between these two). So, you just need to have a first layer thickness that is fine enough to capture that gradient.

Coming back to y+, yes, we don't use y+ in laminar flow, but y+ is just a Reynolds number defined by a very special velocity (shear-stress-based velocity), so y+ at the thickness of first layer just is a measure of hoe steep the velocity profile is near the wall. If you have a large y+ (no matter if it is laminar or turbulent) the first layer is too thick. So, in my opinion, you can still use the y+~1 criterion, but it might be over-kill for laminar flow.


Thank you very much!

By the way, how to estimate the turbulent thermal boundary layer before the simulation? Or we just try to make y+<1?

The estimation

(viscous boundary-layer thickness) / (thermal boundary-layer thickness) = f(Pr) with f(Pr) = Pr^0.3

is really nice. Can you tell me what is the name of this theory? Where could I find it?

triple_r May 7, 2013 12:13

Unfortunately, I can't remember what the name of the correlation is, but the fact that the ratio of boundary layers is equal to Prandtl number is because of the definition of that number.

Pr = nu / alpha

nu is kinematic viscosity, but it also is a measure of how fast viscous information travels in the fluid. Take a look at the solution for a plate in a semi-infinite liquid. When you start moving the plate at time zero, and look at how the edge of boundary layer grows as a function of time, you'll see its growth speed is a function of nu.

The same applies for thermal diffusivity (and mass diffusivity or any other measure of diffusivity for that matter). If you look at a semi-infinite domain, and introduce a change in a quantity that can diffuse (like internal energy or temperature) and look at the edge of influenced area over time, you'll find out that the speed that this area is growing is a function of the diffusivity of that quantity (for temperature, it is alpha).

Now, edge of a boundary layer, is just the loci of fluid particles that have felt the presence of a wall (in other words, they have received the information that a wall exists). So to compare the thickness of thermal and viscous boundary layer, is to compare the speed at which the thermal and viscous information travel in a liquid. And we saw that these speeds are functions of their corresponding diffusivities (or Prandtl number).

Sorry for my loooong answer. I hope it points you in the right direction.


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