Elasto-thinning dynamics of viscoelastic flow past a square cylinder at extreme Weissenberg numbers

We investigate viscoelastic flow past a square cylinder using the Phan-Thien–Tanner model to disentangle the competing effects of elasticity and shear-thinning. Simulations cover Weissenberg numbers ranging from 0.1 to 10 000, at a fixed Reynolds number of 10 and a solvent viscosity ratio of 0.6. The results are compared with the Newtonian, Oldroyd-B and Carreau–Yasuda models to isolate the influence of each rheological mechanism on drag, vortex shedding and wake structure. For Weissenberg numbers less than 50, elastic stresses dominate; drag increases by up to 30 %, vortex shedding is delayed as the critical Reynolds number increases by approximately 18 %, and the wake contracts sharply, with recirculation lengths reduced by up to 85 %. In the intermediate regime, where Weissenberg numbers range from 50 to 500, elasticity generates distinctive features, including asymmetric upstream vortices, triangular vortex cores and persistent upstream vortices, with their lifetimes increasing with the retardation ratio. For Weissenberg numbers greater than 500, shear-thinning becomes dominant, restoring behaviour similar to that of Newtonian fluids. Vortex lengths recover, drag decreases steadily, the critical Reynolds number drops and the shedding frequency increases by 15%–40 %, depending on fluid extensibility. These results reveal that the interaction between elasticity and shear-thinning controls wake dynamics through a complex balance.