3D instability in the viscoelastic flow around a confined cylinder

Increasing elasticity in a viscoelastic fluid, turns the 2D symmetric flow normal to the axis of a cylinder confined between two planes parallel to its axis into a 3D flow around the rear stagnation point with periodic velocity fluctuations along the axis of the cylinder [1,2] . We investigate this elastic instability by means of 3D linear stability analysis. We solve the 3D problem at steady state with our stabilized finite element method [3] and then, we linearize it. We solve the resulting eigenvalue problem using the SLEPc toolkit [4] . We capture the 3D periodic instability, in agreement with experimental results about the critical conditions and the wavelength in the third direction [1,2] . We investigate the effect of the material properties and the geometry on the onset of the instability. The instability becomes more pronounced when the solvent contribution is smaller and when the flow is more confined by the two plates. Additionally, we perform full 3D transient simulations to gain insight into the dynamic evolution of the instability. We observe similar critical flow conditions in comparison with linear stability analysis, verifying once more that the latter is capable of accurately predicting the instability.

[1] G. McKinley, R. Armstrong, R. Brown, Phil. Trans., Phys. Sci. Eng. 344, 1671 (1993).

[2] J. A. Byars, PhD dissertation thesis (1996).

[3] S. Varchanis, A. Syrakos, Y. Dimakopoulos, J. Tsamopoulos, JNNFM. 267 (2019).

[4] V. Hernandez, J. Roman, V. Vidal, ACM Tran. Math. Softw. 31, 3 (2005).