An examination of the upstream and downstream instabilities that occur for highly confined and bounded viscoelastic flows around a cylinder is presented. An elasticity number-Mach number (El-Ma) phase space is used to demonstrate that the onset of downstream instabilities at Ma = 1; these instabilities are instigated by the disturbance of the base flow by traveling elastic waves. After the onset of the downstream instability, an upstream instability eventually occurs for Macrit ~ 10; however, this number is affected by both channel geometry and fluid properties. The upstream instability is instigated by perturbations of the flow field caused by the downstream instability and does not occur until a critical perturbation size at a given velocity is exceeded. The effects of these flow regimes on flow resistance are characterized by examining excess pressure drop; a significant increase in flow resistance is observed at the onset of the upstream instability.
- Boger fluid
- Viscoelastic fluid