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We investigate the effects of fluid elasticity on the flow forces and the wake structure when a rigid cylinder is placed in a viscoelastic flow and is forced to oscillate sinusoidally in the transverse direction. We consider a two-dimensional, uniform, incompressible flow of viscoelastic fluid at$$Re=100$$, and use the FENE-P model to represent the viscoelastic fluid. We study how the flow forces and the wake patterns change as the amplitude of oscillations,$$A^*$$, the frequency of oscillations (inversely proportional to a reduced velocity,$$U^*$$), the Weissenberg number,$$Wi$$, the square of maximum polymer extensibility,$$L^2$$, and the viscosity ratio,$$\beta$$, change individually. We calculate the lift coefficient in phase with cylinder velocity to determine the range of different system parameters where self-excited oscillations might occur if the cylinder is allowed to oscillate freely. We also study the effect of fluid elasticity on the added mass coefficient as these parameters change. The maximum elastic stress of the fluid occurs in between the vortices that are observed in the wake. We observe a new mode of shedding in the wake of the cylinder: in addition to the primary vortices that are also observed in the Newtonian flows, secondary vortices that are caused entirely by the viscoelasticity of the fluid are observed in between the primary vortices. We also show that, for a constant$$Wi$$, the strength of the polymeric stresses increases with increasing reduced velocity or with decreasing amplitude of oscillations.
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This content will become publicly available on March 25, 2026
Pulsatile flow in a thin-walled viscoelastic tube
Low-inertia pulsatile flows in highly distensible viscoelastic vessels exist in many biological and engineering systems. However, many existing works focus on inertial pulsatile flows in vessels with small deformations. As such, here we study the dynamics of a viscoelastic tube at large deformation conveying low-Reynolds-number oscillatory flow using a fully coupled fluid–structure interaction computational model. We focus on a detailed study of the effect of wall (solid) viscosity and oscillation frequency on tube deformation, flow rate, phase shift and hysteresis, as well as the underlying flow physics. We find that the general behaviour is dominated by an elastic flow surge during inflation and a squeezing effect during deflation. When increasing the oscillation frequency, the maximum inlet flow rate increases and tube distention decreases, whereas increasing solid viscosity causes both to decrease. As the oscillation frequency approaches either$$0$$(quasi-steady inflation cycle) or$$\infty$$(steady flow), the behaviours of tubes with different solid viscosities converge. Our results suggest that deformation and flow rate are most affected in the intermediate range of solid viscosity and oscillation frequency. Phase shifts of deformation and flow rate with respect to the imposed pressure are analysed. We predict that the phase shifts vary throughout the oscillation; while the deformation always lags the imposed pressure, the flow rate may either lead or lag depending on the parameter values. As such, the flow rate shows hysteresis behaviour that traces either a clockwise or counterclockwise curve, or a mix of both, in the pressure–flow rate space. This directional change in hysteresis is fully characterised here in the appropriate parameter space. Furthermore, the hysteresis direction is shown to be predicted by the signs of the flow rate phase shifts at the crest and trough of the oscillation. A distinct change in the tube dynamics is also observed at high solid viscosity which leads to global or ‘whole-tube’ motion that is absent in purely elastic tubes.
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- Award ID(s):
- 1922839
- PAR ID:
- 10582480
- Publisher / Repository:
- Cambridge University Press
- Date Published:
- Journal Name:
- Journal of Fluid Mechanics
- Volume:
- 1007
- ISSN:
- 0022-1120
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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