I am modelling transitional fluid flow over a flat plate, and investigating the effects of free stream velocity on boundary layer thickness. From what we have been told, increasing free stream velocity should decrease boundary layer thickness. The critical distance should also move towards the front of the plate with increasing free stream velocity, which holds true for all free stream velocities tested.

In my Excel model, the assumption for boundary layer thickness holds true for the laminar region. However, past the critical distance, when flow is turbulent this does not hold true.

I have modelled a flat plate 2m long by 0.2m wide. Free stream velocities used are 0.7 m/s, 1.05 m/s, and 1.4 m/s. Using water, with density = 1000 kg/m^3 and Dynamic Viscosity = 0.001 kg m^-1 s^-1.

Using the Blausius equation and the 1/7th Power Law the same boundary layer thickness is found at the critical distance, indicating the modelling is done correctly.

I just cannot understand why the boundary layer thickness is not lower in the turbulent region for greater free stream velocities. Any help in understanding would be very much appreicated!

Below I have included an image of the graph obtained.


Varying Free Stream Velocities


I think you are not presenting the fully developed boundary layer.

Because the transition to a turbulent flow occurs sooner for higher velocities you see up to 2 meters a greater boundary layer for double the speed. If you calculated further down - e.g for X>5 -then the boundary layer thickness would have stopped (somewhat) developing and in that case the higher velocities should exhibit thinner boundary layers.


This might explain.

Turbulent boundary layer consists of three main layers formed in the direction normal to the wall: Viscous Sub-layer, Buffer Layer, Turbulent Region.

enter image description here

Friction velocity is calculated using the wall shear stress and fluid density

  • U* = friction velocity = sqrt (wall shear stress/density) , m/s

Non-dimensional distance and velocity are defined as :

  • Y+ = normal distance × U*/kinematic viscosity

  • U+ = local velocity / friction velocity

  1. Non-dimensional velocity is plotted with non-dimensional distance

  2. Three main layers of turbulent region are formed as shown below

Viscous Sub-layer

  • Viscous stress is dominant

  • The plot shows a linear variation : U+ =Y+

  • Requires very fine mesh to capture very steep gradient close to the wall

Buffer Layer

  • Both viscous and turbulent stress exist

  • U+ = f(Y+)

  • Requires very fine mesh to capture very steep gradient near the wall

Turbulent Region

  • Turbulent stress is dominant

  • U+ = 1/k ln (Y+)+ B

  • Requires coarse mesh to capture less gradient away from the wall

enter image description here



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