Approximate analytical solution for the flow of a Phan-Thien-Tanner fluid through an axisymmetric hyperbolic contraction with slip boundary condition

An analytic approximation for the flow of a linear Phan-Thien-Tanner model fluid through an axisymmetric semi-hyperbolic contraction is presented. Such an approximation allows us to compute velocity and pressure response for the flow through axisymmetric contraction geometries; in particular, we have considered here the semi-hyperbolic contraction, which is a geometry where an almost constant extension-rate is reached at different radial positions. In addition, we present a semi-analytic solution capable of representing the exponential version of the selected viscoelastic model; this solution was compared to the results of commercial software, demonstrating the excellent approximation level of the semi-analytic model proposed. Alternatively, for both approaches (linear and exponential Phan-Thien-Tanner), the flow model equations are solved by considering the Navier boundary condition, which allows these models to represent flows with some degree of slip at the geometry wall.

Automated summary

An analytical approximation for the flow of a linear Phan-Thien-Tanner model fluid through an axisymmetric semi-hyperbolic contraction is presented in this study. The semi-analytical solution proposed can accurately represent the exponential version of the viscoelastic model. The flow model equations for both linear and exponential Phan-Thien-Tanner models are solved with the consideration of Navier boundary conditions to account for slip at the geometry wall.