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Direct Numerical Simulation of the Boundary Layers Transition and Interaction at the Entrance of a Plane Channel

Understanding the mechanisms involved in the turbulent transition in boundary layers is crucial for many engineering domains. The instabilities that develop in to those flows are highly non-linear and unsteady. They are mainly studied by analytical theories supplemented by direct numerical simulations (DNS) of the entire flow dynamics which must be sufficiently accurate to properly take into account all spatial and temporal characteristic scales and their non-linear interactions.

This project focuses on the turbulent transition of the boundary layers developing at the entrance of a plane channel. One of the motivations was to perform numerical experiments to explore transition scenarios, conducting parametric studies and time-evolution analysis of spatial structures. This requires high-order approximation methods such as the spectral ones that have been successfully used for fundamental studies on transitional and turbulent flows since the 70’s. To explore the spatially developing channel flow, very elongated geometries are mandatory. These configurations significantly differ in size from the ones commonly used for homogeneous turbulence and fully developed flows. This implies that the number of modes required here are significantly larger, typically more than one billion. Thus, this project addresses massively parallel computations on HPC platforms using ten thousands of cores.

The simulations have been performed on GCS HPC systems SuperMUC of LRZ and JUQUEEN of JSC thanks to the grant of a PRACE 4th call project (Partnership for Advanced Computing in Europe). The results obtained contribute to the analysis of the turbulent transition and the evolution towards a fully developed turbulent state as a function of the Reynolds number (based on the inlet bulk velocity and the distance between the walls). The flow is perturbed at the entrance section, leading to the growth of elongated structures close to the walls, known as streaks, which are subjected to the secondary instability that triggers transition. Optimal perturbations consist, as expected, in steady pairs of contra-rotating longitudinal vortices, but a 180° phase shift appears between the walls with decreasing Reynolds number. This is the consequence of the confinement, the staggered placement favouring a larger growth of the streaks. Moreover, it was observed that the sinuous nature of the secondary sinuous instability is dominant at large Reynolds number, whereas for small Reynolds number, a varicose one is selected.

Results of these studies have been published in a number of articles and conferences. New developments required by simulations on massively parallel platforms and their analysis have been communicated in various HPC meetings (details may be obtained by contacting the author of this article). The DNS data generated with this project can be used to improve engineering models for transitional and turbulent flows in many industrial applications.

Direct Numerical Simulation of the Boundary Layers Transition and Interaction at the Entrance of a Plane ChannelFlow at the entrance of the channel and spatially developing turbulence
Source: © Laboratoire de Mécanique des Fluides et d'Acoustique Université Claude Bernard Lyon, France

Direct Numerical Simulation of the Boundary Layers Transition and Interaction at the Entrance of a Plane ChannelVisualization of the varicose secondary instability of the boundary layer at the entrance of a plane channel (Reh=2500).
Source: © Laboratoire de Mécanique des Fluides et d'Acoustique Université Claude Bernard Lyon, France

Pr. Marc Buffat, Dr. Anne Cadiou, Dr. Lionel Le Penven
Laboratoire de Mécanique des Fluides et d'Acoustique
Université Claude Bernard Lyon 1
Bât. Omega, 43 Bd du 11 novembre 1918, 69622 Villeurbanne, France
e-mail: marc.buffat@univ-lyon1.fr

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