Sig WindE/Validation Cases

The aim of this page is to hold validation cases for ABL (Atmospheric Boundary Layer) flows that are of interest to anybody starting to model in OF. The page will hold links to databases and articles describing experiments, and also instructions on how to make meshes and set boundary conditions that give fair results, hopefully the end result will be complete cases. The simulations I perform, and refer to mainly in this text are RANS with k-epsilon turbulence closure models, using simpleFoam.

---

(0) Maintaining a logarithmic inlet profile over a 2D domain

The wall function boundary condition implemented in OF is the Nikuradse's grain of sand roughness. It produces an anomaly in the k profile in the first cell above the ground which propagates upwards and down-flow. This is discussed extensively in the literature, and alternative wall functions have been suggested such as Richards and Hoexy 1993 (RH). There has lately been a very good documentation of testing this anomaly by Martinez in his Ms.C. thesis [1].

Attached File:HomogenousTerrain.tar.gz is a case ("_BL2Dtemplate") and two python scripts using the pyFoam library to run different z0 values. To reproduce these graphs (p. 24 [2]) use "runZ0.py _BL2Dtemplate BL2Dvalidation_ 1 0.001 0.005 0.01 0.03 0.05 0.1"

(1) Flow over Isolated 2D Hill

Experiments by Khurshudyan et al.[3]

This is a wind tunnel experiment with a 2D hill of several aspect ratios, named also RUSHIL experiment. The latest comparison to it was published by Kasmi and Mason 2010 [4]

Creating the STL surface

The shape of the 2D hill is an analytical function described in [5] as:

$x = \frac{1}{2} \xi \left[ 1+\frac{a^2}{\xi^2+m^2(a^2- \xi^2)} \right]$ for $|x| \leq a$

$z = \frac{1}{2} m \sqrt{a^2-\xi^2} \cdot \left[ 1- \frac{a^2}{\xi^2+m^2(a^2- \xi^2)} \right]$

where $m = \frac{h}{a}+\sqrt{\frac{h}{a}+1}$ and h is the height of the hill ($h = 0.117 [m]$) and a is the length of the hill. $\xi$ is a parameter that changes from 0 to a. The aspect ratio of the hill is 3, 5 and 8.

The experimental setting was:

logarithmic inlet profile with $z_0=0.157 \cdot 10^-3 [m]$, $u_{*} = 0.178 \left[ \frac{m}{s}\right]$ which gives for instance $U_\infty = 3.9 \left[ \frac{m}{s} \right]$ at $z = 1 [m]$

1 The Profile was created with the desired discretization in a spreadsheet program. Column x (1st column) was the width of the hill (arbitrary width), 2nd column is x and the third z. Finally the 3 columns where exported as a csv file File:RUSHIL 8.csv (This should be according to the .xyz format).

Next, paraview is used to transform the csv into a STL surface, as explained in this thread, an reiterated here:

2 The profile is uploaded in paraview.

3 Open the csv in paraview using the csv reader, choose 1 column for each coordinate.

4 Use the "TableToPoints' filter to obtain an array of points. The columns choice here is important so that the result will be a right hand side coordinate system. For the file above the order is y - x - z

5 Use the delaunay tool to "map" a suface from the point (The Delaunay 2D filter)

6 Save the data, you 'll be able to save it as an stl

Creating the mesh

---