EPTT 2022

13th Spring School on Transition and Turbulence

Shooting and Matrix Method Applied to the Analysis of Stability of Viscoelastic Jet Flows

Submission Author: Rafael de Lima Sterza , SP
Co-Authors: Rafael de Lima Sterza, Leandro Franco de Souza, Marcio Teixeira de Mendonca, Analice Brandi
Presenter: Rafael de Lima Sterza

doi://10.26678/ABCM.EPTT2022.EPT22-0018

 

Abstract

In the present work, linear stability theory is used to investigate the hydrodynamic stability of viscoelastic jet flows, particularly two-dimensional, planar, incompressible, submerged jets discharging from a nozzle into a medium of the same fluid as the jet. The constitutive stress relations will be those of the Oldroyd-B model. The instabilities found in jet flows are of the Kelvin-Helmholtz type, through two unstable modes: sinuous and varicose. This work aims to provide additional information on viscoelastic jet stability compared with the Newtonian jet results. This will be accomplished by comparing the two instability modes spatial growth rates and unstable frequency ranges. In addition, a comparison will be made between two ways of obtaining the stability analysis results, the Shooting method, through the numerical solution of the Orr-Sommerfeld equation, and solving an eigenvalue system through the matrix stability analysis. It was observed that the different approaches present similar results, that the matrix method corrects some spurious results obtained by the Shooting method, and that the non-Newtonian effect strongly influences the results for low Reynolds numbers.

Keywords

Jet flow, Oldroyd-B fluid, Linear stability theory, Orr-Sommerfeld equation, matrix method

 

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