Bi-global stability analysis in curvilinear coordinates

Abstract

A method is developed to solve biglobal stability functions in curvilinear systems which avoids reshaping of the airfoil or remapping the disturbance flow fields. As well, the biglobal stability functions for calculation in a curvilinear system are derived. The instability features of the flow over a NACA (National Advisory Committee for Aeronautics) 0025 airfoil at two different angles of attack, corresponding to a flow with a separation bubble and a fully separated flow, are investigated at a chord-based Reynolds number of 100 000. The most unstable mode was found to be related to the wake instability, with a dimensionless frequency close to one. For the flow with a separation bubble, there is an instability plateau in the dimensionless frequency ranging from 2 to 5.5. After the plateau and for an increasing dimensionless frequency, the growth rate of the most unstable mode decreases. For a fully separated flow, the plateau is narrower than that for the flow with a separation bubble. After the plateau, with an increased dimensionless frequency, the growth rate of the most unstable mode decreases and then increases once again. The growth rate of the upstream shear layer instability was found to be larger than that of the downstream shear layer instability.

Influence of upstream disturbances on the primary and secondary instabilities in a supersonic separated flow over a backward-facing step

“…Linear stability analysis is widely used to study the disturbance growth of a parallel flow in the linear regime with relatively low computational expenses compared with LES and DNS. 35,36 The spatial variant of LST was employed for the current investigation. According to this approach, the flow variables are decomposed into a steady partq and an unsteady perturbation q ′ , with the latter being represented by harmonic modes,…”

Prediction of Transition Locations in Regions of the Minor Axis of Hypersonic Elliptic Cones Using the BiGlobal-$e^N$ Method

“…As Li et al [1] pointed out, the boundary layer here changes significantly along both the wall-normal and circumferential directions, such that the conventional stability analysis that only takes wall-normal variation into consideration is not meaningful. It is necessary to use the global stability analysis, which takes both wall-normal and circumferential variation into consideration [2][3][4]. Consequently, if the e N method predicts the transitions herein, the N factors should also be obtained through global stability analysis.…”