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Secondary flow (also termed as stagnation flow, dead space, recirculation zone, and vortex) is rheological phenomenon occurring during flow of polymer melts through abrupt contraction channels as result of flow separation from solid boundary leading to accelerating flow regime with recirculating material in corners. Polymer melt captured in secondary flow slowly rotates in direction opposite to main flow direction and simultaneously moves in third direction through helical motion. This may first reduce flow stability and second increase residence time initiating highly undesirable thermal degradation of polymer melt. Since the first visual experimental observation performed by Tordella and preliminary theoretical prediction made by Langlois and Rivlin at the end of the 1950s, this phenomenon represents one of the most fundamental rheological problems ever with many practical and theoretical impacts discussed here. This comprehensive review written in historical perspective summarizes key factors (Newtonian viscosity, shear thinning, viscoelasticity, flow geometry, and extensional viscosity) influencing secondary entry flows for polymer melts and provides deep and critical discussion of the most important experimental and theoretical works on this topic (such as branched low-density polyethylene, LDPE, linear low-density polyethylene, LLDPE, high-density polyethylene, HDPE, polystyrene, PS, isotactic polypropylene, PP, polymethyl methacrylate, PMMA, polyamide, Nylon PA 66, or polybutadiene, BR). [ABSTRACT FROM AUTHOR]

Abstract: This paper investigates the behaviour of two non-mixing fluids flowing in a heated curved channel. In simulating this immiscible fluid flow, a multi-phase model based on VOF approach is developed for steady, turbulent, incompressible fluid flow through curved channel. The analysis examines the influence of centrifugal forces arising from channel curvature on the phase distribution and flow patterns, and their impact on the thermal characteristics. Unique flow features are identified through the interactions between the fluid phases and vortex structures of the immiscible flow in curved channels. The convective heat transfer in curved channel is appraised in relation to the behaviour of fluid components and curved channel flow parameters. Finally, the study presents a Second-Law irreversibility analysis whereby a thermal optimisation technique is developed for immiscible fluid flow through heated curved channels. [Copyright &y& Elsevier]

Abstract: In order to better understand the three-dimensional non-Newtonian flow in an 180° curved duct of square cross-section, simulations were carried out considering an incompressible viscoelastic fluid, which follows the non-linear FENE-CR model, having constant shear viscosity. A fully implicit finite-volume method was used for the solution of the governing equations. Numerical simulations were performed for different Reynolds and Weissenberg numbers, and by varying the model parameters, namely the retardation ratio (β) and the extensibility (L2 ). The aim was to analyse the development and distribution of velocity field in the cross-sections along the curved channel and as a consequence to understand the variation of maximum velocity with these parameters. The results reveal complex changes with increasing extensibility and decreasing retardation parameter, which are associated to transition from one to two pairs of vortices in the secondary flow. Comparison with the literature confirms and reveals that the absence of shear-thinning delays this transition. [Copyright &y& Elsevier]

Experimental data are presented for flow in compound channels with symmetrically narrowing floodplains. In such a geometry, the flow behavior presents similarities with the more complex flow in a meandering compound channel, yet without the curvature effects, because of mass transfers between the floodplains and the main channel, and secondary currents induced in the main channel. An estimation of the momentum transfer generated by the mass transfer is found significant compared to the frictional losses. It mainly depends on the geometrical parameters and is practically independent of the friction slope. Free-surface profile computations are performed with the exchange discharge model (EDM) to incorporate the effects of the momentum transfer in terms of an additional head loss. Agreement was found between measured and computed water surfaces, thus validating the EDM approach. [ABSTRACT FROM AUTHOR]