This work presents new analytical and semi-analytical solutions for the pure Couette and Poiseuille–Couette flows, described by the recently proposed (Ferrás et al., A Generalised Phan-Thien–Tanner Model, JNNFM 2019) viscoelastic model, known as the generalised Phan-Thien–Tanner constitutive equation. This generalised version considers the Mittag–Leffler function instead of the classical linear or exponential functions of the trace of the stress tensor, and provides one or two new fitting constants in order to achieve additional fitting flexibility. The analytical solutions derived in this work allow a better understanding of the model, and therefore contribute to improve the modelling of complex materials, and will provide an interesting challenge to computational rheologists, to benchmarking and to code verification.
This work presents analytical and numerical studies for pure Couette and combined Poiseuille-Couette flows under slip. The fluid behaviour is described by the recently proposed viscoelastic model, known as the generalised simplified Phan-Thien-Tanner constitutive equation, that considers the Mittag-Leffler function instead of the classical linear and exponential functions of the trace of the stress tensor, and provides one or two new fitting constants in order to achieve additional fitting flexibility. The solutions derived in this work allow a better understanding of the model and its influence on the slippery behaviour of some complex fluids, contributing in this way to improve the modeling of complex fluids. K E Y W O R D S Couette flow, generalised simplified PTT, Mittag-Leffler, Poiseuille-Couette flow, PTT model, wall slip
Numerical simulations of fluid flows can produce a huge amount of data and inadvertently important flow structures can be ignored, if a thorough analysis is not performed. The identification of these flow structures, mainly in transient situations, is a complex task, since such structures change in time and can move along the domain. With the decomposition of the entire data set into smaller sets, important structures present in the main flow and structures with periodic behaviour, like vortices, can be identified. Therefore, through the analysis of the frequency of each of these components and using a smaller number of components, we show that the Proper Orthogonal Decomposition can be used not only to reduce the amount of significant data, but also to obtain a better and global understanding of the flow (through the analysis of specific modes). In this work, the von Kármán vortex street is decomposed into a generator base and analysed through the Proper Orthogonal Decomposition for the 2D flow around a cylinder and the 2D flow around two cylinders with different radii. We consider a Newtonian fluid and two non-Newtonian power-law fluids, with n=0.7 and n=1.3. Grouping specific modes, a reconstruction is made, allowing the identification of complex structures that otherwise would be impossible to identify using simple post-processing of the fluid flow.
The inherent design freedom promoted by the employment of thermoplastic profiles is one of the major reasons for their attractiveness. Theoretically, thermoplastic profiles can be produced with any cross section suited for a specific application. The design of the corresponding extrusion dies usually employ a methodology based on experimental trial-and-error approaches, being highly dependent on the experience of the designer and highly demanding in terms of resources. These difficulties are obviously more evident when the plastic profile has a complex geometry. This research team is involved since the mid-nineties on the development of computational tools to aid the design of thermoplastic profile extrusion dies. Initially, the numerical code employed was based on structured meshes that limited its use to simple geometries. In this work, a numerical modelling code developed to work with unstructured meshes is described and employed in a case study involving the design of a extrusion die for the production of complex cross section profile. The results obtained show that the developed code can be a useful tool to aid the design of complex profile extrusion dies.
This work presents new semi-analytical solutions for the combined fully-developed electro-osmotic (EO) pressure-driven flow in microchannels of viscoelastic fluids, described by the generalised Phan-Thien-Tanner model (gPTT) recently proposed by Ferrás et al. [Journal of Non-Newtonian Fluid Mechanics, 269: 88-99, 2019]. This generalised version of the PTT model presents a new function for the trace of the stress tensor -the Mittag-Leffler function -where one or two new fitting constants are considered in order to obtain additional fitting flexibility. The semi-analytical solution is obtained under sufficiently weak electric potentials that allows the Debye-Hückel approximation for the electrokinetic fields and for thin electric double layers.Based on the solution, the effects of the various relevant dimensionless numbers are assessed and discussed, such as the influence of εW i 2 , of the parameters α and β of the gPTT model, and also of κ, the dimensionless Debye-Hückel parameter. We conclude that the new model characteristics enhance the effects of both εW i 2 and κ on the velocity distribution across the microchannels. The effects of a high zeta potential are also studied numerically.
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