# Turbulent boundary layer development in channel flow

I'm currently working on my Bachelor's thesis about the numerical simulation of a turbulent air flow through a rectangular channel. As part of that I'd like to compare my results to empirical correlations for the boundary layer thickness as a function of distance from the inlet for such a flow. However, I can only find correlations for a flat plate (Schlichting, White, Anderson). Does somebody know such correlations? Thanks! This is the essential part of the geometry:

I study the development of the boundary layer from the tip of the plate downstream.

Simon

• What CFD package are you using? What turbulent solvers does it offer? What are the assumptions made in each? – Solar Mike Oct 2 '20 at 16:34
• I use ANSYS Fluent with the k-omega SST model. My BCs are one velocity-inlet and two pressure-outlets where one is the main outlet and the other the outlet of the boundary layer suction before the plate on which the boundary layer develops. – Simon Henn Oct 3 '20 at 17:43
• @SimonHenn I'm confused. Why are you having two outlets? what do you mean by boundary layer suction? and are you simulating a 2D channel or a flow over flat plate? – Algo Oct 3 '20 at 21:21
• The difference between a flat plate and a rectangular channel doesn't become important until the boundary layer gets so thick that it interacts with the boundary layer on the opposite wall. Once that happens, one doesn't usually call it a "boundary layer" any more, but a "pipe flow". If you want to examine the region before (i.e. upstream of where) that happens, the flat plate correlations will be fine. If you want to examine the region where the interaction is starting to happen, it might help to drop "boundary layer" from your search terms, and search instead for "entrance flow". – Daniel Hatton Oct 3 '20 at 21:41
• I have edited the question to make it more clear what I'm trying to do. The thing is that from the beginning of the development of the lower boundary layer on the plate the upper boundary layer is fully developed because it hasn't been removed by a suction. So i'd imagine it will influence the lower boundary layer. What do you think? – Simon Henn Oct 4 '20 at 10:59

There is a validation case for turbulent flow in a two-dimensional channel at NASA's Langley Research Center Turbulence Modeling Resource website. You will also find results for many turbulence models used to simulate the case such as Wilcox's standard 2006 $$k-\omega$$ model and Spalart-Allmaras one-equation model.