EPTT 2022

13th Spring School on Transition and Turbulence

Linear stability analysis of the boundary layer flow past gaps in bypass transition conditions

Submission Author: Victor Barcelos Victorino , SP
Co-Authors: Victor Barcelos Victorino, Marcello Augusto Faraco de Medeiros, Marlon Sproesser Mathias
Presenter: Victor Barcelos Victorino

doi://10.26678/ABCM.EPTT2022.EPT22-0045

 

Abstract

Boundary layer turbulence transition provokes a significant impact on aircraft performance. It is crucial to understand the phenomena to build models that accurately predict the transition location. The boundary layer transition is related to its stability. Additionally, several surface imperfections occur in a real aircraft’s boundary layer, among them the presence of gaps. Recent studies demonstrated that, depending on the gap geometry and flow conditions, the physics of the boundary layer’s transition deviates from its usual form. Therefore, the main objective of the present work was to investigate the impact of gaps with aspect ratio L/D = 5 and 10 on the boundary layer stability. We chose as parametric space the threshold for the transition dominated by Tollmien-Schlichting waves and another bypass mechanism, according to the literature. We developed a numerical study via two-dimensional direct numerical simulation as a precursor stage to get the steady solution (base flow) of the compressible Navier-Stokes Equations. Next, we analyzed the flow stability to two- and three-dimensional disturbances, assuming periodicity in the spanwise axis for the latter. We conducted the linear stability analysis through an in-house algorithm that uses an Arnoldi-based time-stepping method. The study revealed unstable oscillation modes for 2D (Rossiter) and 3D (centrifugal) analysis. The stability limits of centrifugal modes were lesser than the Rossiter’s in the flow conditions covered. The runs immediately preceding the bypass transition presented a weakly unstable Rossiter mode, whereas runs that occurred bypass, according to Crouch, Kosorygin and Sutanto (2020), presented strong oscillations attributed to the Rossiter mode. The frequency agreed within 4% of relative error compared to the literature. The numerical results supported the conjecture that the centrifugal instability causes 3D flow over the gap and the Rossiter mode triggers the transition.

Keywords

Boundary Layer, Gap, stability, transition, Rossiter modes, Centrifugal modes

 

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