[CFD_10]

Hello,

I have some questions regarding following concepts:
The law of wall, where




which is described here: https://en.wikipedia.org/wiki/Law_of_the_wall



and the velocity profile of the boundary layer ,e.g: Blasius velocity profile, given here: https://en.wikipedia.org/wiki/Blasius_boundary_layer


1. What is the difference between these two concepts?
2. If the law of wall is universal ,then why not using this law for boundary layer?
3. Is the Blasius velocity profile a special case of the law of wall?


What is the difference/relation between these two velocity profiles?
Thanks

[veera]

especially blasious is not applicable for laminar flow
and law of the wall applicable to the turbulent one

[FMDenaro]

The velocity u+ stands for the statistically steady velocity in a fully developed confined turbulent field.
Blasius solution describes the spatial developing steady BL in a laminar flow.

[CFD_10]

Originally Posted by FMDenaro

The velocity u+ stands for the statistically steady velocity in a fully developed confined turbulent field.
Blasius solution describes the spatial developing steady BL in a laminar flow.

Could you please explain in more details?

[CFD_10]

Another question is:
In the law of wall, the boundary layer is devided to 3 sublayers: viscous sublayer, buffer sublayer, and the logarithmic sublayer.


But in the boundary layer theory I've never seen this terms.
Please give details (I cannot understand in two sentences, very detailed answers are very welcome!)

[FMDenaro]

Originally Posted by CFD_10

Another question is:
In the law of wall, the boundary layer is devided to 3 sublayers: viscous sublayer, buffer sublayer, and the logarithmic sublayer.


But in the boundary layer theory I've never seen this terms.
Please give details (I cannot understand in two sentences, very detailed answers are very welcome!)

Again, you are comparing the laminar theory to the turbulence theory. There are fundamental differences in the working model. That is a topic of basic fluid dynamics courses and can be found in any good textbook (one is Kundu).

[LuckyTran]

It would be more conducive if you tell us what you already do know about the law of the wall versus the Blasius solution.


As already mentioned, the law of the wall deals with turbulent boundary layers and Blasius laminar boundary layers.

Originally Posted by CFD_10

Another question is:
In the law of wall, the boundary layer is devided to 3 sublayers: viscous sublayer, buffer sublayer, and the logarithmic sublayer.

But in the boundary layer theory I've never seen this terms.
Please give details (I cannot understand in two sentences, very detailed answers are very welcome!)

You'll almost never see these come up if you study only laminar boundary layer theory. Turbulent boundary layers have these characteristic regimes and it takes really an entire course to explain it in detail. Again, tell us what you already know and we can fill in the holes. Otherwise, pick up a book on turbulence.


Turbulent boundary layers are divided into outer and inner layers and the inner layer is further sub-divided into the (linear/viscous/laminar) layer, buffer layer, and logarithm layer. They are divided because the turbulent characteristics in these regions are different. Each region has different solution forms. In laminar boundary layers there is no turbulence and that's why you never see these terms there and the Blasius equation describes the entire velocity profile.

[CFD_10]

Originally Posted by LuckyTran

It would be more conducive if you tell us what you already do know about the law of the wall versus the Blasius solution.


As already mentioned, the law of the wall deals with turbulent boundary layers and Blasius laminar boundary layers.




You'll almost never see these come up if you study only laminar boundary layer theory. Turbulent boundary layers have these characteristic regimes and it takes really an entire course to explain it in detail. Again, tell us what you already know and we can fill in the holes. Otherwise, pick up a book on turbulence.


Turbulent boundary layers are divided into outer and inner layers and the inner layer is further sub-divided into the (linear/viscous/laminar) layer, buffer layer, and logarithm layer. They are divided because the turbulent characteristics in these regions are different. Each region has different solution forms. In laminar boundary layers there is no turbulence and that's why you never see these terms there and the Blasius equation describes the entire velocity profile.

Thank you very much for the explanation.
I have read the book of white "Fluid mechanics" both topics can be found but I cannot find any comparison between the two.

[FMDenaro]

There is no comparison because the Blasius theory provides a solution for the Prandtl equations while the u+ velocity is the velocity for the statistically averaged NSE.

In a fully developed turbulence field you have the viscous sublayer, a very small region close to the wall (y+<5) where u+=y+ tends towards the laminar solution.

[CFD_10]

Originally Posted by FMDenaro

There is no comparison because the Blasius theory provides a solution for the Prandtl equations while the u+ velocity is the velocity for the statistically averaged NSE.

In a fully developed turbulence field you have the viscous sublayer, a very small region close to the wall (y+<5) where u+=y+ tends towards the laminar solution.

Thank you