Personnel: Prof. Ugo Piomelli, Ms. Junlin Yuan
Turbulent boundary layers subject to a favourable pressure gradient (FPG) induced by freestream acceleration are found in many engineering applications, including airfoils, turbine blades or curved ducts. If the acceleration is sufficiently large, the flow may revert to a laminar or quasi-laminar state and retransition back to turbulence once the cause of laminarization is removed. It is well known that roughness may occur in many of the applications in which FPGs are also important, and that it may significantly affect the characteristics of boundary layer flows and promote transition to turbulence. Therefore, a combined study of roughness and FPGs helps in the understanding of boundary layer flows in engineering applications.
The simulations are performed using a well-validated staggered code, with second-order differences for all terms, semi-implicit time advancement, and MPI parallelization. The unresolved SGS stresses are modeled using the Lagrangian Dynamic Eddy-Viscosity model. Virtual sandpaper (Figure 1), simulated by an immersed boundary method based on the volume-of-fluid (VOF) approach [1] with constant roughness height, covers the wall.
Figure 1: The Virtual Sandpaper
Results indicate that roughness plays a significant role in near-wall flow mixing, destabilizing the inner layer and reducing or eliminating relaminarization, by stimulating wall-normal velocity fluctuations close to the wall. Small-scale coherent structures are generated in the wake of the roughness elements. However the combined effect of roughness and favourable pressure gradient depends on the relative significance of the two (see Figure 2): the flow behaviour resembles a smooth-wall boundary layer in relaminarizing and retransitioning if the roughness height is small, although still in the transitionally rough regime; for high roughness height, the roughness effect prevents the flow from reorganizing under high freestream acceleration.
Future work includes studies on various roughness shapes, and quantification of bursts and streaks instability to further understand the opposite effects of roughness and pressure gradient.
Figure 2: Isosurfaces of the second invariant of the velocity gradient tensor, Q, coloured by U/U∞: high roughness (top), low roughness (middle), and smooth case (bottom).
[1] Scotti A, Direct numerical simulation of turbulent channel flows with boundary roughened with virtual sandpaper. Physics of Fluids,Vol.18, 2006
