Numerical Investigation of Viscoelastic Fluid Flow into a Hyperbolic Wavy Hele–Shaw Cell

This study numerically investigates the flow characteristics of a viscoelastic fluid in a two-dimensional Hele–Shaw cell with hyperbolic expansions and contractions. The fluid's rheology is described using the Phan–Thien–Tanner constitutive model, with the governing equations solved using the finite-volume method in OpenFOAM. Within the explored range of Weissenberg numbers (0.5 ≤ Wi ≤ 4), increasing the Weissenberg number leads to higher velocity magnitude, reduced principal stress difference, and more pronounced elastic effects, resulting in a stable, symmetric flow. No vortex formation or instabilities are observed along the geometry. Furthermore, the analysis comprehensively examines velocity fields, principal stress differences, stress ratios, flow types, and apparent viscosities.