Flow over periodic hills: Time resolved Tomo-PIV and 4D PTV evaluations

Abstract

Time-resolved tomographic particle image velocimetry measurements were performed in the ERCOFTAC test case Nr. 81 “Periodic hill” water tunnel at TU Munich within the frame work of the FP7 project AFDAR. The geometry scales with the hill height h = 50 mm, while the spacing between them was 9h, please see Fig. 1 for an overview of the facility. The channel has a total cross-section of 3.035 h×18 h. The tunnel is driven hydrostatically using a water reservoir fed by a pump. The water flow is homogenized by using honey combs and screens installed upstream of the test section. For the current experiment ten hills were arranged in a row and the measurements were performed at the seventh hill, where average periodic flow conditions are developed with respect to the up- and downstream hills. A detailed description of the setup can be found in Rapp and Manhart (2011). The Reynolds number, built with the averaged bulk velocity over the hill crest ub and the hill height h, was set to Re = 8000 and Re = 33,000 respectively. As previously shown by Cierpka et. al (Cierpka, 2013) using two-dimensional measurements, the region downstream of the hill shows large Reynolds stresses and is subject to strong three-dimensional flow features. Therefore time-resolved three-dimensional measurements were performed to further characterize the flow in these regions. The gained data was evaluated with two different approaches: First, Tomo-PIV processing (Scarano, 2013; Elsinga, 2006) was applied - yielding velocity vector volumes, which allow for convenient further processing of the data (being on a regular grid). Secondly, Lagrangian particle tracks were calculated from the particle images, using the novel 4D-PTV method “Shake the Box” (STB) (Schanz, 2013). The results of the STB algorithm are highly accurate, spatially dense and long Lagrangian tracks within the reconstructed measurement volume. Temporal fitting further enhances accuracy and allows for the determination of accelerations.