# Obtaining the correct flat plate turbulent boundary layer thickness in a CFD simulation

I used a commercial CFD software to simulate incompressible turbulent flow of air over a flat plate. I setup a 2D domain 1.5m long in the x direction and .2m in the y direction. The boundary conditions are as follows:

Left side (x=0): is a velocity inlet
u = 100m/s
$\nabla p\cdot n = 0$

Right side (x=1.5) is a pressure outlet
$p = 0$ Pa
$\nabla u\cdot n = 0$

Bottom Side (y=0) is a wall boundary
u=0m/s
$\nabla p\cdot n = 0$

Top Side (y=0.2) is a symmetry boundary

For turbulence, I enabled a $k-\omega$SST model and prescribed turbulent intensity of 5% and a viscosity ratio $\frac{\mu_t}{\mu}=10$ at the inlet. My program automatically sets conditions at all other boundaries automatically.

My mesh consists of 300 quadrilateral elements in the x-direction and 100 quadrilateral elements in the y-direction. To ensure that the mesh is sufficiently refined to capture the boundary layer, I biased the mesh so that the elements connected to the wall boundary are 4000 times smaller than the elements connected to the symmetry boundary (i.e. the elements connected to the wall boundary are approximately $4*10^{-6}$m )

With a time step of 0.01s, I ran my simulation up to 30s to ensure a steady state was achieved. In the end, I was surprised to find that my boundary layer thicknesses $\delta$ were smaller than the well-known 1/7 power law, given by:

$$\frac{\delta}{x} = \frac{0.16}{(Re_x)^{\frac{1}{7}}}$$

where $\frac{u x}{\nu}$, where $x$ is the horizontal distance from the beginning of the plate, and $\nu$ is the kinematic viscosity.

I thought that I should be able to achieve a close match to this 1/7 power law with my simulation independently of how I choose the turbulent conditions at the inlet. But my boundary layer ended up being almost 30% smaller than the 1/7th power law all across the plate and I'm not entirely sure why. Is there a minimum turbulent viscosity ratio and turbulent intensity required to achieve 1/7th power law?

• Shouldn't the boundary layer thickness depend on the near-wall treatment method you picked for the simulation? – Algo Oct 4 '16 at 17:49
• @Algo: Of course. But in this case, there is no special wall function at work. I'm more curious if under the current boundary conditions, should I expect to achieve a boundary layer thickness akin to the 1/7th power law without a wall function. Does the 1/7th power law assume certain inlet conditions on k and omega to achieve it? – Paul Oct 4 '16 at 17:53