Eventos Anais de eventos
COBEM 2021
26th International Congress of Mechanical Engineering
MATRIX METHOD FOR A STABILITY ANALYSIS OF NON-NEWTONIAN FLUID FLOW
Submission Author:
Laison Junio da Silva Furlan , SP , Brazil
Co-Authors:
Laison Junio da Silva Furlan, Matheus Tozo de Araujo, Leandro Franco de Souza, Marcio Teixeira de Mendonca, Analice Costacurta Brandi
Presenter: Laison Junio da Silva Furlan
doi://10.26678/ABCM.COBEM2021.COB2021-1376
Abstract
The purpose of this paper is to describe how to solve stability analysis problem for a non-Newtonian fluid flow using the Chebyshev polynomials approximation for flutuation function and their respective derivatives. In spatial analysis, eigenvalues are obtained by solving an equations system for the alpha variable where the highest alpha power is 2nd power. This formulation allows us to obtain all the eigenvalues that are solutions of the stability problem. The domain used is known as Gauss-Lobatto collocation points. Using these collocation points, it is possible to obtain all the Chebyshev polynomials with a recurrence formula facilitating this process. The non-Newtonian constitutive equation used is the Oldroyd-B model. This model admits an analytical solution for the base flow for a channel fluid flow. Using the MATLAB/OCTAVE EIG function to obtain all the eigenvalues of the problem described above, it is obtained all the solutions of the problem for the dimensionless variables which is desired. Therefore, the stability analysis is done looking for the lowest imaginary value in all eigenvalues obtained by solving the eigenproblem. The verification of this solution method is based on results present in the literature, more specifically, the article published in 2019 with the title ``DNS and LST stability analysis of Oldroyd-B fluid in a flow between two parallel plates''. The verification is performed by comparing values for the amplification rate of disturbances for specified flows and some neutral stability curves. It is worth mentioning that solution obtained by matrix method, in general, are less accurate if we compare to local methods. Global methods of this type are easier to perform, but as we mentioned earlier, this type of solution presents a lower accuracy compared to local methods. The stability analysis problem is not different. Solving this problem for a Newtonian fluid flow, the accuracy is not much less than a local method, but when we are solving this problem for a non-Newtonian fluid flow, that accuracy is, in general, less.
Keywords
Linear Stability Analysis, Chebyshev Polynomials, Orr-Sommerfeld equation, Oldroyd-B model, Non-Newtonian fluid flow
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