# Study of flow separation (and reattachment) dynamics

## Context and motivation

The boundary layer is the layer flowing on a solid surface in contact with a fluid. As a result, in the case of a wing or a turbomachinery blade, its behavior determines the performance and efficiency of a plane or a gas turbine. Under certain conditions, the boundary layer can separate and reattach, leading to a loss of efficiency of the system considered. In aerodynamics for example, in addition to increasing the drag of wings, thus inducing higher fuel consumption, this generates an abrupt drop of the lift, a dangerous phenomenon called the aerodynamic stall. In 1904, Prandtl defined flow conditions that generate boundary-layer separation in two-dimensional (2D) steady flows. For unsteady or three-dimensional (3D) flows, however, this criterion is not valid. Although several approaches have contributed to new advances and ideas since the pioneering work of Prandtl, they have often proved to be incomplete or inapplicable, and have revealed that the definition of a clear and practical criterion for the detection of separation is challenging. This probably explains that we had to wait exactly one century after the criterion derived by Prandtl to find a complete theory of separation thanks to the works of Haller (2004), Surana et al. (2006) and Surana et al. (2008).

This very recent theory is remarkable because it detects separation, but probably more importantly, it predicts that while the separation surface can move and deform over time inside the flow, it originates from a fixed line on the boundary. Therefore, these results can be applied not only to the laminar regime, but also to fluctuating flows, including turbulence, which represents a new and invaluable advance. The time-independent location of the separation on the wall is determined from time-averaged on-wall measurements of shear stress and pressure. The wall pressure is relatively easy to obtain, but the shear-stress is still challenging to measure accurately. As a consequence, separation criteria have been validated mainly with computational flow models (Surana et al., 2007, 2008). Regarding experimental approaches, only one case has been reported in the literature. Weldon et al. (2008) studied a rotating cylinder whose axis can be oscillated close to a wall, thus manipulating an unsteady separation. Under different forcing conditions, observations showed that the separation was fixed on the surface, the location and orientation of

which were accurately predicted by the theory. However, this unique example concerns a slow viscous flow (Reynolds Number, Re < 1), and numerical simulations were used to provide missing information that cannot be obtained from experiments.

## Objectives

The research program proposes to deepen fundamental knowledge of separation phenomena and to explore emerging theories that provide innovative prediction criteria of separation.

## Methodology

- Build an experimental water set-up generating a developed, laminar or turbulent jet impinging on a flat plane designed to generate separation and attachment surfaces;
- use the state of the art, time-resolved tomographic PIV technique to acquire 3D unsteady velocity fields, and the polarographic technique to measure the time-resolved components of the wall shear stress;
- to analyze and extract the separation and attachment surfaces over time by computing the finite-time Lyapunov exponent, a recently developed Lagrangian method adapted to identify flow structures [Shadden et al., 2005];
- and provide more recent and extended data to complete existing databases dedicated to numerical validation of computational codes and to explain the physic of turbulent flow;
- to confront theoretical predictions with flow measurements that are more practically relevant to the industry and to propose experimental methodologies to predict separation only from on-wall measurements to allow the new approaches to be applied to engineering problems.

## Originality and importance of the research

The prediction of separation phenomena is crucial in the air, land and marine transport and in the field of energy production. The fact that the needed information can be deduced from simple on-wall measurements greatly facilitates the implementation of the technique to engineering problems such as those found in the aerospace industry. This research proposal will deepen fundamental knowledge of separation phenomena and will simultaneously propose experimental methodologies to gather and analyze pertinent information to increase the level of computational validation.

## References

Philippe Miron et Jérôme Vétel

Towards the detection of moving separation in unsteady flows

Journal of Fluid Mechanics, Volume 779, September 2015, p.819-841, 2015 Cambridge University Press

DOI:http://dx.doi.org/10.1017/jfm.2015.461

Philippe Miron, Jérôme Vétel et André Garon

On the flow separation in the wake of a fixed and a rotating cylinder

Chaos: An Interdisciplinary Journal of Nonlinear Science, 25, 087402 (2015)

DOI:http://dx.doi.org/10.1063/1.4921212