Re-visiting the theoretical investigation of the near wake for turbulent wake flows at zero-pressure gradient

Kurzfassung

This report re-visits a theoretical investigation for the symmetric wake of a flat plate turbulent boundary layer at zero pressure gradient. The focus is on the near wake, which is the region, where the remnant of the universal mean velocity profile of the inner 15% of the boundary layer still can be observed. The remnant of the universal wall-law, i.e., the universal log-law, is eaten up, as the flow evolves downstream. The streamwise extent of this region is around 7 to 10 boundary layer thicknesses. Alber (1980) gives an analytical formula for the streamwise development of the centerline velocity and an analytical description of the mean velocity profiles. He derives a similarity solution for the mean velocity profile for the inner 15% of the wake, the region typically occupied by the log-law of the flat plate, in the form of an asymptotic expansion. The similarity transformation involves an inner-layer length scale g, which is the perturbation parameter of the asymptotic expansion. The theory by Alber (1980) has several crucial points, which require special care from a mathematical of point. One of the crucial elements is the order of magnitude analysis based on the inner wake characteristic length scale g. This is studied in more depth in this work. Moreover, the experimental data by Ramaprian & Patel (1982) are re-visited to compare with the theoretical results by Alber. The motivation for this study is to validate and to improve turbulence models based on the RANS approach for the flow phenomenon of wake flow at adverse pressure gradient. Modern transport aircraft employ high-lift systems to provide the necessary lift for low-speed operations during take-off and landing. One critical flow feature of high-lift configurations are confluent flows of the wake of an upstream located element and the boundary layer on downstream located elements, subjected to a strong adverse pressure gradient. For some settings of the flap, the lift stall at high incidence angles can be caused by flow reversal of the wake of the main element above the flap. This is called off-surface flow reversal. The work presented in this report is part of the joint project “Turbulent Wake Flow at Adverse Pressure Gradient” between the Center for Computer Applications in AeroSpace Science and Engineering (C2A2S2E) at the DLR Institute of Aerodynamics and Flow Technology (DLR AS), the Institute of Fluid Mechanics (ISM) at Technische Universität Braunschweig, and the research lab headed by Prof. M. Strelets from Peter the Great St. Petersburg Polytechnic University (SPbPTU). This project of the author together with Prof. R. Radespiel and Dr. P. Scholz from ISM and with Prof. M. Strelets from SPbPTU was funded by DFG and the Russian Foundation for Basic Research (RFBR) under Grant No. RA 595/26-1, KN 888/3-1 and No. 17-58-12002.