Transition to turbulence of an incompressible flow past a multi-element airfoil: Mean-flow dynamics

Abstract

The present study explores the transition scenarios of an incompressible flow past an airfoil in a 30P30N configuration. Three low chordwise Reynolds numbers are considered: $R{e}_c=0.832\times 10^4$, $1.270\times 10^4$ and $1.830\times 10^4$, respectively. The angle of attack is fixed at 4.0 degrees. A series of well-resolved three-dimensional direct numerical simulations are implemented via a high-order spectral element method. The present work aims to examine the mean-flow behavior and address the fundamental instability mechanisms that govern the transition routes in three $R{e}_c$ cases. The focus is placed on a quantitative analysis through mean statistics, but also monitors the evolution of instantaneous coherent structures. In addition to the conventional aerodynamic parameters, i.e., drag and lift coefficients, and pressure and skin-friction coefficients, etc., the present study discusses low- and higher-order statistics systematically including both Reynolds stresses and budget analysis of turbulent kinetic energy (TKE). An analysis of the TKE budget reveals that, despite the differences in $R{e}_c$ considered, the overall characteristics of the budget remain qualitatively the same. In cases with a separation bubble, the Kelvin–Helmholtz instability mechanism acts as a local amplifier, driving the growth of the perturbations along the inflection point. Pairs of longitudinal counter-rotating vortices are pronounced near the main-element leading edge, bearing a qualitative similarity to the so-called Görtler vortices. Both the inviscid Rayleigh criterion and Görtler number indicate regions of strong centrifugal effect and imply a likelihood of centrifugal instability.