Delay transition to turbulence by mimicking lotus leaves – DETAIL

The lotus leaf is known for its self-cleaning properties that are due to its high water repellence, also called superhydrophobicity (SH). This interesting property is due to the nanostructure of its surface, which is composed by a hierarchical structure of microepidermis covered in hairlike nanowaxes, that traps the air underneath it, reducing the surface of contact with the water droplets, and thus the wetting of the surface. Superhydrophobicity has important implications in drag reduction for fluid transport: recent studies have shown that, in channel flows, a superhydrophobic surface can reduce the drag of 50% in both laminar or turbulent regimes. However, nothing is still known about the effect of such surfaces on a flow in the transitional regime. This might be a very promising research topic since, in general, the transition from laminar to turbulent flow induces a strong increase in skin friction, along with a strong increase of the drag. Thus, in the transitional regime, the competition between the drag decrease due to the surface micro structure, and the drag increase due to transition to turbulence might provide surprising results. In particular, the following points need to be investigated in detail: i) how is drag reduction affected by the transition from a laminar to turbulent regime in this kind of flows? ii) are SH surfaces able to delay transition to turbulence? iii) is it possible to optimize the shape and location of the micro roughnesses on the surface in order to optimally delay transition?
Up to now, very few studies have been performed on transition to turbulence of a laminar flow over SH surfaces, focusing only on the very first phase of transition, namely, linear instability. For a channel flow, it has been proved by a local instability analysis that, when imposing a simple slip condition, the onset of two-dimensional Tollmien-Schlichting waves is considerably postponed, allowing the flow to stay laminar up to larger Reynolds numbers, and further decreasing the drag. However, shear flows very often experience subcritical transition to turbulence, due to the transient growth of non-modal disturbances, bypassing the asymptotic growth of Tollmien-Schlichting waves. How SH surfaces influence the growth of these disturbances, in both linear and non-linear conditions, and how drag reduction is affected remain completely open questions. Preliminary studies performed using a simple slip condition have provided conflicting results: on the one hand, slip boundary conditions have a very weak influence on the linear maximum transient energy growth of perturbations at subcritical Reynolds numbers, but on the other hand they can induce a strong delay of subcritical transition to turbulence provided that the disturbance amplitude is sufficiently large. However, these works assumed a constant homogeneous flow, hypothesis which is not generally valid for a heterogeneous SH surface as the ones encountered in nature.
The present project aims at simulating fluid flows in channels with bio-inspired microstructured surfaces taking into account the complex alternance of air/water and solid/water interfaces, in order to unravel its transient instability and subcritical transition to turbulence. Linear and non-linear optimizations of initial perturbations, as well as Direct Numerical Simulations using the Immersed boundary technique will be used to clarify in detail how the drag reduction is affected by the transition from a laminar to turbulent regime, and wether these microstructured surfaces are able to delay transition to turbulence. The overall goal of the project is to optimize the shape and location of the surface microroughnesses to optimally delay transition and thus further reduce drag.