| Full text | |
| Author(s): |
Furlan, Laison Junio da Silva
;
de Mendonca, Marcio Teixeira
;
de Araujo, Matheus Tozo
;
de Souza, Leandro Franco
Total Authors: 4
|
| Document type: | Journal article |
| Source: | Journal of Non-Newtonian Fluid Mechanics; v. 307, p. 8-pg., 2022-07-21. |
| Abstract | |
This work presents a practical methodology to verify the validity of Squire's theorem for viscoelastic fluid flow stability analysis. Squire's theorem presents a relationship between two-dimensional and three-dimensional disturbances. The theorem shows that the critical Reynolds number for two-dimensional disturbances is smaller than any value for which unstable three-dimensional disturbances exist. This conclusion simplifies the stability analysis for fluid flows which satisfies this theorem by becoming sufficient for the stability analysis to look only for the two-dimensional disturbances to find the most dangerous condition. In the present investigation, the validity of Squire's theorem is accessed for viscoelastic fluid flows considering the Upper-Convected Maxwell, Oldroyd-B, Giesekus, LPTT and FENE-type models. The mass, momentum, and viscoelastic constitutive equations are manipulated to arrive at the equivalent two-dimensional equations required for Squire's Theorem validity. It was verified that Squire's theorem is valid for the Upper-Convected Maxwell and the Oldroyd-B isotropic models as already known in the literature, showing that the proposed methodology is consistent with previous results. However, for the Giesekus, the LPTT and the FENE-type anisotropic models, the analysis shows that Squire's theorem is not valid, indicating the relation between the isotropic behavior of the fluids and the validity of Squire's theorem. (AU) | |
| FAPESP's process: | 13/07375-0 - CeMEAI - Center for Mathematical Sciences Applied to Industry |
| Grantee: | Francisco Louzada Neto |
| Support Opportunities: | Research Grants - Research, Innovation and Dissemination Centers - RIDC |