[Ryan.]

Hello people!

does anyone know a reliable empirical approach for estimating the boundary layer thickness in turbulent channel flows similar to that of the flat plates? I cannot afford RANS simulations in this particular application and I need to know the boundary layer thickness based on the Reynolds number and the channel height.

Regards,
Ryan

[LuckyTran]

Maybe you can explain why the information on wikipedia is not what you need: Boundary layer thickness

[Ryan.]

Originally Posted by LuckyTran

Maybe you can explain why the information on wikipedia is not what you need: Boundary layer thickness

I should have been more specific. I need to estimate the boundary layer thickness in a square channel. As the development of the boundary layer is affected by the adjacent walls, the rate of growth of the boundary layer is not the same as in a flat plate. So I was wondering if there are any estimation methods for the boundary layer thickness in square channel flows considering the influence of the adjacent walls.

[LuckyTran]

Square channels aren't that much different than circular pipes.

Away from corners, the rate of boundary layer growth is nominally the same as the flat plate. Only in the corners where the boundary layers of adjacent walls have merged does it deviate and even then the growth is accelerated by only roughly 20% if one continues to use distance to the nearest wall as a metric.

If you need more predictive capability than this please specify. I would recommend doing the numerical simulation (but even that might not get you better than 10% accuracy).

[gnwt4a]

What do u mean by "boundary layer"? There is no irrotational
outer flow in internal turbulent flows.

suitable bcs near the corner of a turbulent duct flow do not exist.
there, the flow has its own unique dynamics and the standard scalings
of flat wall-layers do not apply.

only thing u can do is apply the standard models using some
contrived composite length scale, and hope that the rest of your

calculation is not contaminated. such estimates always understate

the strength of the secondary velocities and near-corner wall stresses.

these velocities and stresses depend on nonlinear instabilities

unique to the near-corner flow.
--

[FMDenaro]

The question should be better detailed. Is the inflow in the square channel supposed to be uniform as in the BL theory over a flat plate? If so, you can immagine a first size of laminar development of the BL (far from the corners) before turbulence is developed. That depends on the local Re number.

I am not sure that you can find in literature exactly this flow problem, I remember several papers about rectangular duct but the inflow is different.

[Ryan.]

Originally Posted by FMDenaro

The question should be better detailed. Is the inflow in the square channel supposed to be uniform as in the BL theory over a flat plate? If so, you can immagine a first size of laminar development of the BL (far from the corners) before turbulence is developed. That depends on the local Re number.

I am not sure that you can find in literature exactly this flow problem, I remember several papers about rectangular duct but the inflow is different.

That's exactly right, the inflow is uniform and the channel is long enough to develop a turbulent boundary layer (based on Re_x) but not quite long so that the flow becomes fully turbulent. Could you please tell me a bit more about what you mean by imagining the size of the laminar development first?

[FMDenaro]

Originally Posted by Ryan.

That's exactly right, the inflow is uniform and the channel is long enough to develop a turbulent boundary layer (based on Re_x) but not quite long so that the flow becomes fully turbulent. Could you please tell me a bit more about what you mean by imagining the size of the laminar development first?

Well, the lenght is one of the parameters, if the velocity inflow is sufficiently high you can have a fully development. On a flat plate, the transitional region appears at Re_x>O(10^5)