Experimental Study on Tollmien-Schlichting Waves over Forward- Facing Steps

Abstract

Current manufacturing techniques in the aviation industry result in a number of two-dimensional surface irregularities (e.g. panel joints, seals, seams) which can lead to an increase in skin friction due to premature boundary layer transition. Panel joints are commonly modeled in the form of two-dimensional steps. Prior studies have shown that Backward-Facing Steps (BFS) promote transition earlier than Forward-Facing Steps (FFS). Therefore, in the design of laminar flow components, FFS are preferred over BFS. However, the understanding of which mechanisms are responsible for the larger growth experienced by Tollmien-Schlichting (TS) waves in the presence of FFS remains unknown. Prior experimental works focused on parametric studies on transition location with limited measurements close to the step. In addition, studies using Direct Numerical Simulations (DNS) assume two-dimensional flow and consequently do not capture transition location. All of this makes comparison between existing experimental and numerical data rather cumbersome, hindering the problem understanding.

In light of this, the present study aims to close-examine the TS waves at the step to identify which are the relevant mechanisms that modify their growth and move transition upstream. To do so, this work presents an experimental and numerical investigation jointly conducted by TU Delft and the German Aerospace Center (DLR) on Tollmien-Schlichting (TS) waves interaction with a Forward-Facing Step (FFS). Experiments are conducted at the TU Delft low-turbulence anechoic wind tunnel (A-tunnel) on an unswept flat plate model. Single-frequency disturbances are introduced using controlled acoustic excitation. The temporal response of the flow in the vicinity of the step is measured using Hot-Wire Anemometry (HWA). In addition, the global effect of the step on laminar-turbulent transition is captured using Infrared Thermography (IR). Two-dimensional (2D) Direct Numerical Simulations (DNS) performed at DLR provide detailed information at the step. Experimental and numerical comparison is performed in subcritical step conditions. At larger step heights only experimental data is provided.

Experimental and DNS results in clean and subcritical step conditions present very good agreement. Both methods predict large distortion of the TS wave downstream of the step, where DNS results present different growth trends between streamwise and wall-normal components of the fundamental mode. Furthermore, while upstream of the step the TS waves exhibit exponential growth, downstream of it they present a complex growth behavior followed by regions where the perturbation energy production term changes sign along the streamwise direction. Finally, regions of highly negative and positive production seem to correlate with the tilting of TS waves in and against the mean shear direction, respectively. These findings point towards the presence of different growth mechanisms triggered by the step which could modify the level of amplification of disturbances far downstream.