2D Periodic Hill

Underlying Flow Regime 3-30

Cross-Comparison of Experiments

The 2D PIV results were checked with 1D LDA measurements. A satisfactory compliance was found as can be seen in the following figures (Re=10,600) [Rapp et al. (2009), Rapp (2009)].

Mean streamwise velocity component

<U>

Mean streamwise Reynolds stresses

<uu>

The PIV field data and the point by point LDA measurements show an excellent accordance. The mean velocity component in the x-direction and the streamwise Reynolds stress show only minor deviations that can be traced back to the measurement procedure. As the LDA data could only be acquired by measuring the particular points periodically and at different instants of time, the profiles turn out to be rougher than the PIV data.

Cross-Comparison of CFD Calculations

A cross-comparison of the results achieved by the different methods was carried out. For that purpose two different Reynolds numbers were considered. According to Table 1 two DNS predictions are available at Re = 2800. Case 4 was performed by LESOCC using a curvilinear grid and case 5 is based on MGLET using a Cartesian grid with about 3.5 times more grid points. At Re = 5600 case 7 is taken into account which denotes a wall-resolved LES prediction on the curvilinear grid. These results are compared with case 8 providing numerical data on an extremely fine Cartesian grid (231 million grid points) which is beyond all doubt a well-resolved DNS. The cross-comparison was also conducted for Re = 1400. However, since no new findings compared to the outcome presented in the following sections resulted, for the sake of brevity this Reynolds number is omitted here.

The figure below shows exemplarily the distribution of the averaged streamwise velocity $\langle U\rangle /U_{B}$ at four different vertical positions in the flow field, i.e. x / h = 0.5, 2, 4, and 6. The first position is located shortly after the separation line and crosses the strong shear layer; the second profile is at the beginning of the flat floor and hence within the main recirculation region. The third one is located near the end of the recirculation bubble and finally the last is positioned behind the main separation region in the reattached flow. At both Re the agreement observed between the results obtained by the different numerical methods is excellent. Only marginal deviations are found. For example, MGLET predicts slightly larger back-flow velocities at x / h = 4 for Re = 2800 compared with the data of LESOCC. This marginal deviation is still visible further downstream at x / h = 6 close to the lower wall. Besides that the profiles resulting from the two independent simulation techniques lie on top of each other at both Re.

Comparison of predictions by LESOCC and MGLET based on the streamwise velocity profiles at four different locations (x / h = 0.5, 2, 4, and 6) and two different Reynolds numbers, i.e. Re = 2800 (case 4 and 5) and 5600 (case 7 and 8, see Table 1)

More comparisons including wall shear stresses and pressure distributions can be found in Breuer et al. (2009).

Comparison of CFD Calculations with Experiments at Re = 10,595

The experimental data at Reynolds number 10,595 are compared with the highly resolved LES results by LESOCC [Breuer et al. (2009), Rapp et al. (2009)]. The following figures show averaged velocity profiles for <u>/u_b at four streamwise positions.

Mean streamwise velocity component

<U>

Mean streamwise velocity component

<V>

The agreement between the predicted and the measured mean streamwise velocity component in the x-direction is very good. Minor deviations can be found in the shear layer (slightly higher velocities in the experiment) and in the post-reattachment zone. The vertical velocity component <v>/u_b is about one order of magnitude smaller than the streamwise component and yet more sensitive. However, the measurements comply with the simulation results in a fully satisfactory manner. The largest deviations are found at x/h=2.

The measured and the predicted Reynolds shear stress show a close agreement at the different x/h-positions. The location of the experimental peak values and their distributions are in close accordance with the predictions. Solely at x/h=6 a slightly higher stress was found in the experimental data.