Numerical investigation of the influence of realistic surface irregularities on the expected laminar-turbulent transition location

Kurzfassung

Growing environmental concerns has led to the search for methods to reduce specific fuel consumption in commercial aircraft. An avenue of research has been the reduction of total drag by maintaining laminar flow over the aircraft wing. One of the major challenges in achieving laminar wings is the presence of surface irregularities which could potentially amplify instabilities leading to transition. This thesis aims to study the influence of surface irregularities in the form of forward- and backward-facing steps on the growth of primary instabilities called Tollmien-Schlichting (TS) waves. In particular, the effect of introducing a rounded corner on the step is evaluated. The two-dimensional, laminar, steady, compressible base flow at Ma∞ = 0.5 over a flat plate with the surface irregularity without an imposed pressure gradient was computed. All lengths were nondimensionalized using the boundary layer displacement thickness of the clean case at the streamwise position where the step would be located. The step was incorporated at a non-dimensional distance of about 550 from the leading edge of the flat plate and three non-dimensional step heights of H = 0.8,1.2 and 1.6 for the forward-facing step (FFS) and one backward-facing step (BFS) height of H = 1.2 were considered. The corner radius, implemented as a 45◦ arc of a circle tangent to the upper surface of the step, was varied from 0 (rectangular) to that which corresponds to the entire step being built up by the circular arc. The evolution of TS waves in the base flow was then computed and the eN methodology was used to quantify the growth of instabilities. The study revealed that the presence of the step caused a local distortion of the base flow and amplified incoming TS waves. From the investigated FFS configurations, it was concluded that the incorporation of the corner radius had an impact on the N-factor only for step heights over a certain value, with no effects observed for the height of H = 0.8. In the cases where the radius played a role (H = 1.2, 1.6), generally, with increasing corner radius, a downstream shift of the transition location compared to the corresponding rectangular configuration was observed. This could be attributed to the alleviation of adverse pressure gradients and the reduction in size and eventual disappearance of the laminar separation bubble on top of the step, resulting from increasing the corner radius. Furthermore, it was observed that, for the two largest heights, increasing the radius beyond a critical value produced no significant changes in terms of N-factor. The results for the BFS of height H = 1.2 revealed no significant influence of the corner radius on the transition location compared to the rectangular configuration.