2D Periodic Hill

Underlying Flow Regime 3-30

Test Case Study

Brief Description of the Study Test Case

The measures of the geometry introduced by Mellen et al. (2000) relate to the hill height h. The hill constricts the channel height of 3.035h by about one third whereas the inter hill distance is 9h. The contour of the 3.857h long two dimensional hill is described by the following six polynomials. $x\;\epsilon \;\left[0;\;0.3214h\right];\quad y(x)=\min(1;1+0\cdot x+2.420\cdot 10^{-4}\cdot x^{2}-7.588\cdot 10^{-5}\cdot x^{3});$ $x\;\epsilon \;\left[0.3215h;\;0.5h\right];\quad y(x)=0.8955+3.484\cdot 10^{-2}\cdot x-3.629\cdot 10^{-3}\cdot x^{2}+6.749\cdot 10^{-5}\cdot x^{3};$ $x\;\epsilon \;\left[0.5h;\;0.7143h\right];\quad y(x)=0.9213+2.931\cdot 10^{-2}\cdot x-3.234\cdot 10^{-3}\cdot x^{2}+5.809\cdot 10^{-5}\cdot x^{3};$ $x\;\epsilon \;\left[0.7144h;\;1.071h\right];\quad y(x)=1.445-4.927\cdot 10^{-2}\cdot x+6.950\cdot 10^{-4}\cdot x^{2}-7.394\cdot 10^{-6}\cdot x^{3};$ $x\;\epsilon \;\left[1.071h;\;1.429h\right];\quad y(x)=0.6401+3.123\cdot 10^{-2}\cdot x-1.988\cdot 10^{-3}\cdot x^{2}+2.242\cdot 10^{-5}\cdot x^{3};$ $x\;\epsilon \;\left[1.429h;\;1.929h\right];\quad y(x)=\max(0;2.0139-7.180\cdot 10^{-2}\cdot x+5.875\cdot 10^{-4}\cdot x^{2}+9.553\cdot 10^{-7}\cdot x^{3});$

At x/h=0 the hill height is maximal whereas the boundary is flat in the range between x/h=1.929 and x/h=7.071. Between x/h=7.071 and x/h=9 the contour follows the above equations in axis-symmetry. Besides the geometry, the following figure shows streamlines at a Reynolds number, that is based on the hill height h and the bulk velocity above the crest, of 5,600 [Rapp 2009)].

$Re={\frac {u_{b}h}{\nu }}$