Three-dimensional Phan-Thien-Tanner viscoelastic flows around a sphere

This study investigates the steady and unsteady flow of a viscoelastic fluid around a sphere in three-dimensional space. Numerical simulations using the finite volume method incorporated a logarithmic mapping technique to overcome divergence issues at high elastic numbers. The fluid's behavior was characterized by the Phan-Thien-Tanner model, renowned for its accuracy and parametric simplicity. Key findings reveal that viscosity variations and stress relaxation times are pivotal in shaping the fluid's viscoelastic properties, surpassing the influence of other factors. Notably, the drag coefficient exhibited diverse behaviors—in some cases increasing, in others decreasing, and at times remaining constant—across different elasticity numbers. The study also explored the impact of fluid dilution, elasticity, and viscosity ratio on shear stress and drag coefficient variations, highlighting the profound role of elasticity in modulating the drag coefficient. A rise in velocity, elasticity number, viscosity ratio, and slip parameter was found to correspond with an increase in the drag coefficient, whereas an enhancement of the first model parameter reduced velocity, allowing viscous losses to dominate flow dynamics. The critical Reynolds number for Newtonian fluids was determined to be 300, with a noticeable decline as elasticity increased. The viscosity ratio demonstrated a strong influence on the critical Reynolds number, while the model parameters had minimal impact. Additionally, it was observed that as the vortex separation ratio increased, vortex length extended, and the separation angle decreased.