Highly spatially and temporally resolved measurements of the flow over periodic hills (measurements performed at TU Munich)
The flow over periodic hills is a common test case for the validation of numerical flow simulations (see ERCOFTAC test case Nr. 81). The numerical prediction is quite difficult, since flow separation and reattachment are not fixed in space and time due to the absence of sharp edges. Furthermore, the separated and fully three-dimensional flow from the previous hill impinges on the next hill and results in very complex flow features including turbulent splashing, Taylor-Görtler vortices and a very thin shear layer with developing Kelvin-Helmholtz instabilities (Rapp & Manhart, 2011). The complex dynamic of the flow can easily be seen in the instantaneous images in Fig. 1.
By combining the experimental capabilities of the partners of the consortium time-resolved planar and volumetric measurements were performed at two Reynolds numbers (8,000 and 33,000). Of special interest is the thin shear layer at the hill top. Using the advanced single-pixel ensemble-correlation method and particle tracking the steep gradient can be fully resolved as can be seen in Fig. 2. The much finer resolution compared to standard evaluation techniques was evaluated systematically (Kähler et al., 2012a,2012b) and an obvious improvement is observed looking at the small symbols. The vector spacing in each direction is 180 µm which corresponds to one Kolmogorov length scale Δxy ~ η for the lower Reynolds number and Δxy ~ 2.6η for Re = 33,000. The Reynolds stresses are of paramount importance for the validation of the turbulence models. A method to determine the Reynolds stresses from the correlation peak rather than using successive vector fields was recently developed by Scharnowski et. al (2012). The method has the advantage that it does not suffer from either underestimation due to velocity smoothing by outlier filters or overestimation due to strong outliers and thus provides reliably the Reynolds stresses with a grid spacing typical for DNS and finer than for LES within a field of view of 0.5 m length.
As it turned out that the region of the evolving shear layer from the hill top is highly populated with three-dimensional vortices with various orientations, only time-resolved tomographic PIV measurements are suitable to characterize these structures (Elsinga, 2006; Scarano, 2013). The high complexity of the flow, within a volume of 80x80x20 mm
3, located downstream of the hill-crest can be already seen in Fig. 3. As expected from the broad frequency spectra obtained by the 2D measurements, a manifold of differently sized vortical structures can be observed, including very small and randomly appearing ones as well as large structures that seem to be inclined with the mean flow at a defined angle.
These results display that the combined usage of planar high resolution PIV, time-resolved PIV and tomographic PIV is required to obtain an unambiguous description of the flow phenomena, as each technique has its specific strengths and weaknesses. This result is of paramount importance for industrial flow investigations or for the acquisition of data sets for the validation of numerical flow simulations, were the requirement regarding the accuracy are extremely high. In the future more detailed analysis of the whole data set will provide a much deeper inside to the flow and allows for a better validation of numerical methods which will greatly increase the impact and visibility of the AFDAR project to the scientific community.
Elsinga GE, Scarano F, Wieneke B, van Oudheusden BW (2006) Tomographic particle image velocimetry. Exp Fluids 41: 933-947
Kähler CJ, Scharnowski S, Cierpka C (2012a) On the resolution limit of digital particle image velocimetry. Exp Fluids 52:1629–1639
Kähler CJ, Scharnowski S, Cierpka C (2012b) On the uncertainty of digital PIV and PTV near walls. Exp Fluids 52:1641–1656
Rapp C, Manhart M (2011) Flow over periodic hills: an experimental study. Exp Fluids 51, 247–269.
Scarano F (2013) Tomographic PIV: principles and practice. Meas Sci Technol 24, 012001
Scharnowski S, Hain R, Kähler CJ (2012) Reynolds stress estimation up to single-pixel resolution using PIV-measurements. Exp Fluids 52, 985–1002.