Buckling of three-dimensional wavy collapsible tubes conveying viscous flows

This study investigates the buckling behaviors of wavy collapsible tubes conveying viscous flows using the immersed boundary-lattice Boltzmann method, with focus on the effect of several key parameters (including external pressure, bending rigidity, and wave number) on the deformation patterns and buckling behaviors. The results show that the higher circumferential modes occur when the bending stiffness decreases and/or the external pressure increases, as observed in straight tubes. The transition from mode-2 to mode-3 occurs earlier for the nw=1.5 case than the straight tube, even though the effective stiffness of the tube decreases when the wave number decreases with nw=0 corresponding to the straight tubes. This is due to the minimum fluid pressure at the lowest point of the wavy wall. The transition to mode-4 occurs earlier in the straight tube, highlighting the predominant effect of stiffness. Compared to the symmetric mode-2 in the straight tube, an asymmetric mode-2 is observed in the wavy tube (nw=1.5) due to the asymmetric flow structure and fluid–structure interactions. In addition, two distinct flow patterns are observed: the shell-based and the finger-shaped structures. Finally, a buckling analysis on the structure only shows that the critical buckling stress increases with the wave number, as demonstrated by a modification of the available analytical formulation for critical buckling.