Directed percolation in aerodynamics: resolving laminar separation bubble on airfoils

In nature, phase transitions prevail amongst inherently different systems, while frequently showing a universal behavior at their critical point. As a fundamental phenomenon of fluid mechanics, recent studies suggested laminar-turbulent transition belonging to the universality class of directed percolation. Beyond, no indication was yet found that directed percolation is encountered in technical relevant fluid mechanics. Here, we present first evidence that the onset of a laminar separation bubble on an airfoil can be well characterized employing the directed percolation model on high fidelity particle image velocimetry data. In an extensive analysis, we show that the obtained critical exponents are robust against parameter fluctuations, namely threshold of turbulence intensity that distinguishes between ambient flow and laminar separation bubble. Our findings indicate a comprehensive significance of percolation models in fluid mechanics beyond fundamental flow phenomena, in particular, it enables the precise determination of the transition point of the laminar separation bubble. This opens a broad variety of new fields of application, ranging from experimental airfoil aerodynamics to computational fluid dynamics.

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