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thegodfather April 15, 2012 14:40

Boundary layer separation
 
It is said that a boundary layer separates from the surface when the inertia of the fluid is not enough to counter the viscous and pressure forces...
But increasing the flow speed will increase the tendency of the boundary layer to separate...
Does that not mean that higher inertia in the fluid will make the boundary layer more susceptible to separation.. whereas from definition of separation it is clear that lower inertia should be responsible for flow separation..?

truffaldino April 16, 2012 04:02

Quote:

Originally Posted by thegodfather (Post 354762)
But increasing the flow speed will increase the tendency of the boundary layer to separate...

In general it will not. For instance, increase of reynolds number results in moving the separation point further downstream on airfoils.

thegodfather April 16, 2012 06:43

For example in the case of flow past a cylinder or a sphere, a low speed fluid stream will follow the curvature and will remain attached to it.. But increasing the speed will lead to separation... Isn't it a paradox??

truffaldino April 16, 2012 11:07

You are talking about very low reynolds number regime for highly curved objects where boundary layer approximation does not work: For cylnders and spheres the flow remains stationary only for reynolds number up to order 10^1-10^2, which means that the boundary layer size is of order of the object size, i.e. bl does not really exist. For higher reynolds numbers the flow past such objects becomes nonstationary, the vortex shedding occurs and bl theory does not really work too.

The bl layer theory works for high reynods numbers and mild adverse pressure gradients, e.g. for flows past airfoils in which case higher speed means later separation.

thegodfather April 16, 2012 12:03

Thanks for replying

I did not understand, what is the meaning of boundary layer size being of the order of the object size.. n how does low value of reynolds numbr imply the same..?

truffaldino April 16, 2012 12:33

Quote:

Originally Posted by thegodfather (Post 354925)
Thanks for replying

I did not understand, what is the meaning of boundary layer size being of the order of the object size.. n how does low value of reynolds numbr imply the same..?

The theory of boundary layer is an approximation where the fluid speed changes significantly only close to the surface and in the laminar flow case
ratio of the boundary layer thikness to the object size is of order 1/sqrt(Re).

In the case of spere or cylinder the flow is stationary up to Re of order 10^1-10^2. This means that bl size is about 1/3 to 1/10 of the object size, which is not really the boundary layer.

In the boundary layer theory the pressure does not change across the layer in direction normal to the surface, while it gradually changes along the direction parallel to the surface on the scale which is much greater than bl thikness. All this does not make sence when your bl thikness is 1/3 of the object curvature and Prandtl argumentation about decelleration of different parts of bl prior to separation simply does not work.

thegodfather April 17, 2012 02:56

Then, is there any other theory to predict flow separation for such cases...?
(i.e. other than Boundary layer approximation)

truffaldino April 17, 2012 04:16

Quote:

Originally Posted by thegodfather (Post 355060)
Then, is there any other theory to predict flow separation for such cases...?
(i.e. other than Boundary layer approximation)

I am not a specialist in this field, but what I have seen on this topic are only numerical simulation. BTW for very low speed regime numerical simulations are quite easy and reliable, since turbulence modelling is not involved.

LuckyTran April 17, 2012 07:21

Quote:

Originally Posted by thegodfather (Post 354762)
It is said that a boundary layer separates from the surface when the inertia of the fluid is not enough to counter the viscous and pressure forces...

Specifically, the viscous drag caused by a solid boundary. Fluid viscosity is a mechanism for momentum transport, hence it's alternate name momentum diffusivity.

Quote:

Originally Posted by thegodfather (Post 354854)
For example in the case of flow past a cylinder or a sphere, a low speed fluid stream will follow the curvature and will remain attached to it.. But increasing the speed will lead to separation... Isn't it a paradox??

For low speed fluid flows, viscosity is there to help force the fluid to follow the curvature (whereas the inertia of the flow does not!). The fluid wants to move tangentially along the surface of the cylinder, it definitely does not want to curve! Even in the inviscid case, there are many interactions needed to make the flow follow a solid boundary.

Quote:

Originally Posted by truffaldino (Post 354932)
The theory of boundary layer is an approximation where the fluid speed changes significantly only close to the surface and in the laminar flow case
ratio of the boundary layer thikness to the object size is of order 1/sqrt(Re).

In the case of spere or cylinder the flow is stationary up to Re of order 10^1-10^2. This means that bl size is about 1/3 to 1/10 of the object size, which is not really the boundary layer.

In the boundary layer theory the pressure does not change across the layer in direction normal to the surface, while it gradually changes along the direction parallel to the surface on the scale which is much greater than bl thikness. All this does not make sence when your bl thikness is 1/3 of the object curvature and Prandtl argumentation about decelleration of different parts of bl prior to separation simply does not work.

This discussion is referring to the formal Boundary Layer Theory by Prandtl. Boundary Layers in general do not have this restriction on their behaviour, and there is no limitation on boundary layer thickness.

For simple flows, there are engineering correlations for when and where a flow will separate and there are some models for how to treat the laminar to turbulent transition zone. The canonical example is the flat plate boundary layer. In general, transitional turbulence is a mess to deal with.

thegodfather April 17, 2012 08:54

Thanks truffaldino for clearing my doubt...
N thanks LuckyTran for deepening my understanding about the topic...
:)


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