Directed percolation in aerodynamics: resolving laminar separation bubble on airfoils

TL;DR

This study demonstrates that the onset of laminar separation bubbles on airfoils can be effectively modeled using directed percolation, revealing universal critical behavior and enabling precise transition point determination in fluid mechanics.

Contribution

First evidence that directed percolation models describe laminar separation bubbles on airfoils, linking phase transition theory with practical aerodynamics analysis.

Findings

Critical exponents are robust against parameter fluctuations.

Directed percolation accurately characterizes the transition point.

The model applies to both experimental and computational fluid dynamics data.

Abstract

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.