A numerical stabilization framework for viscoelastic fluid flow using the finite volume method on general unstructured meshes

A robust finite volume method for viscoelastic flow analysis on general unstructured meshes is developed. It is built upon a general-purpose stabilization framework for high Weissenberg number flows. The numerical framework provides full combinatorial flexibility between different kinds of rheological models on the one hand, and effective stabilization methods on the other hand. A special emphasis is put on the velocity-stress-coupling on co-located computational grids. Using special face interpolation techniques, a semi-implicit stress interpolation correction is proposed to correct the cell-face interpolation of the stress in the divergence operator of the momentum balance. Investigating the entry-flow problem of the 4:1 contraction benchmark, we demonstrate that the numerical methods are robust over a wide range of Weissenberg numbers and significantly alleviate the high Weissenberg number problem. The accuracy of the results is evaluated in a detailed mesh convergence study

The finite-volume method in computational rheology

The finite volume method (FVM) is widely used in traditional computational fluid dynamics (CFD), and many commercial CFD codes are based on this technique which is typically less demanding in computational resources than finite element methods (FEM). However, for historical reasons, a large number of Computational Rheology codes are based on FEM. There is no clear reason why the FVM should not be as successful as finite element based techniques in Computational Rheology and its applications, such as polymer processing or, more recently, microfluidic systems using complex fluids. This chapter describes the major advances on this topic since its inception in the early 1990’s, and is organized as follows. In the next section, a review of the major contributions to computational rheology using finite volume techniques is carried out, followed by a detailed explanation of the methodology developed by the authors. This section includes recent developments and methodologies related to the description of the viscoelastic constitutive equations used to alleviate the high-Weissenberg number problem, such as the log-conformation formulation and the recent kernel-conformation technique. At the end, results of numerical calculations are presented for the well-known benchmark flow in a 4:1 planar contraction to ascertain the quality of the predictions by this method

An adaptive solver for viscoelastic incompressible two-phase problems applied to the study of the splashing of slightly viscoelastic droplets

We propose an adaptive numerical solver for the study of viscoelastic 2D two-phase flows using the volume-of-fluid method. The scheme uses the robust log conformation tensor technique of Fattal & Kupferman (2004,2005} combined with the time-split scheme proposed by Hao & Pan (2007}. The use of this time-split scheme has been proven to increase the stability of the numerical computation of two-phase flows. We show that the adaptive computational technique can be used to simulate viscoelastic flows efficiently. The solver is coded using the open-source libraries provided by the \basilisk \cite{Basilisk} platform. In particular, the method is implemented for Oldroyd-B type viscoelastic fluids and related models (FENE-P and FENE-CR). The numerical scheme is then used to study the splashing of weakly viscoelastic drops. The solvers and tests of this work are freely available on the Basilisk web sit

High Weissenberg number simulations with incompressible Smoothed Particle Hydrodynamics and the log-conformation formulation

Viscoelastic flows occur widely, and numerical simulations of them are important for a range of industrial applications. Simulations of viscoelastic flows are more challenging than their Newtonian counterparts due to the presence of exponential gradients in polymeric stress fields, which can lead to catastrophic instabilities if not carefully handled. A key development to overcome this issue is the log-conformation formulation, which has been applied to a range of numerical methods, but not previously applied to Smoothed Particle Hydrodynamics (SPH). Here we present a 2D incompressible SPH algorithm for viscoelastic flows which, for the first time, incorporates a log-conformation formulation with an elasto-viscous stress splitting (EVSS) technique. The resulting scheme enables simulations of flows at high Weissenberg numbers (accurate up to Wi=85 for Poiseuille flow). The method is robust, and able to handle both internal and free-surface flows, and a range of linear and non-linear constitutive models. Several test cases are considerd included flow past a periodic array of cylinders and jet buckling. This presents a significant step change in capabilties compared to previous SPH algorithms for viscoelastic flows, and has the potential to simulate a wide range of new and challenging applications.Comment: submitted to JNNFM Sept. 2020, revised March 202

An unstructured geometrical un-split VOF method for viscoelastic two-phase flows

We present an unstructured geometrical Volume-of-Fluid (VOF) method for handling two-phase flows with a viscoelastic liquid phase. The viscoelastic behavior is modeled via generic rate-type constitutive equations. A one-field formulation is employed, which results from conditional volume averaging of the local instantaneous bulk equations and interface jump conditions. The method builds on the 'plicRDF-isoAdvector' geometrical VOF solver that is extended and combined with the modular framework 'DeboRheo' for viscoelastic CFD. A piecewise-linear geometrical interface reconstruction technique on general unstructured meshes is employed for discretizing the viscoelastic stresses across the fluid interface in a numerically consistent and highly accurate way. Because of the numerical challenges posed by the high Weissenberg number problem, we employ an appropriate stabilization approach to the constitutive equation of the viscoelastic phase to increase the robustness of the method at higher fluid elasticity. DeboRheo facilitates a flexible combination of different rheological models with appropriate stabilization methods to address the high Weissenberg number problem. We discuss the theoretical formulation and implementation of the proposed method and demonstrate its effectiveness using numerical examples of viscoelastic flows. The results highlight the method's ability to accurately capture the behavior of viscoelastic fluids in various applications. The proposed method holds promise for furthering our understanding and predictive capabilities of viscoelastic flows in various industrial and natural processes.Comment: 30 pages, 18 figure

Numerical Simulation of Viscoelastic Flow in Micro/Nanochannels

Micro/Nanofluidic devices often involve use of biological fluids or polymeric solutions that cannot be simply treated as Newtonian fluids. The numerical simulation for the complex fluids at micro/nanoscale presents a significant computational challenge, and the inclusion of electrokinetic body force further increases the complexity. Specifically, the well-known High Weissenberg Number Problem (HWNP) has become a challenge for the numerical simulation of viscoelastic fluid. This dissertation is aimed to develop a numerical tool to simulate the behavior of viscoelastic fluid in the micro/nanochannel. The most popular log-conformation reformulation to solve the HWNP is presented and implemented in a finite volume scheme. The implemented solver is validated by applying to several classical viscoelastic fluid benchmark problems, ranging from 2D to 3D, stationary to transient problems. Then, flow behavior of viscoelastic fluid in a three-dimensional curvy channel is investigated. A Finitely Extensible Nonlinear Elastic with Peterlin closure (FENE-P) constitutive model is utilized to describe the viscoelastic fluid. The characterization of viscoelastic instability and elastic turbulence at a relatively high Weissenberg number is identified from the fluctuation of velocity field, streamlines, secondary flow patterns, and the intensity of secondary flow. The mechanism of this phenomenon is analyzed from the interaction between the flow and polymer molecules. Parametric study shows that the level of elastic turbulence decreases with viscosity ratio and becomes stronger with the extensibility parameter. The implemented solver is further applied to investigate the electroosmotic flow (EOF) of viscoelastic fluid with a linear Phan-Thien and Tanner (LPTT) model in nanoslit and nanochannel with reservoirs. Under the condition in which the Electrical Double Layer (EDL) thickness is comparable to the characteristic length of the nanochannel and the surface charge density is relatively high, the effects of viscoelasticity on EOF, ionic current, and ion transport are investigated. Obvious enhancement of velocity, flow rate and ionic current is observed for viscoelastic fluid compared to the Newtonian fluid. The EDL thickness and the presence of microscale reservoirs also have significant influence on the EOF of viscoelastic fluid

A Lagrangian-Eulerian simulation method for viscoelastic flows applied to adhesive joining

Viscoelastic flows are important for many industrial processes, such as adhesive joining, polymer extrusion and additive manufacturing. Numerical simulations enable virtual evaluation and product realization, which can support the design phase and reduce the amount of costly physical testing. However, such applications are challenging to simulate. Thus, efficient, robust and user-friendly simulation methods are needed. In this thesis, a Lagrangian--Eulerian simulation framework for viscoelastic flow is presented. The constitutive equation is solved at Lagrangian nodes, convected by the flow, while the momentum and continuity equations are discretized with the finite volume method. The volume of fluid method is used to model free-surface flow, with an injection model for extrusion along arbitrary nozzle paths. The solver combines an automatic and adaptive octree background grid with implicit immersed boundary conditions. In contrast to boundary-conformed mesh techniques, the framework handles arbitrary geometry and moving objects efficiently. Furthermore, novel coupling methods between the Lagrangian and Eulerian solutions as well as unique treatment of the Lagrangian stresses at the fluid-fluid interface are developed. Consequently, the resulting method can simulate the complex flows associated with the intended applications, without the need for advanced stabilization techniques. The framework is validated for a variety of flows, including relevant benchmarks as well as industrial adhesive joining applications. The latter includes robot-carried adhesive extrusion onto a car fender as well as a hemming application. The results agree with the available experimental data. As such, the research presented in this thesis can contribute to enable virtual process development for joining applications

Lid-driven cavity flow of viscoelastic liquids

The lid-driven cavity flow is a well-known benchmark problem for the validation of new numerical methods and techniques. In experimental and numerical studies with viscoelastic fluids in such lid-driven flows, purely-elastic instabilities have been shown to appear even at very low Reynolds numbers. A finite-volume viscoelastic code, using the log-conformation formulation, is used in this work to probe the effect of viscoelasticity on the appearance of such instabilities in two-dimensional lid-driven cavities for a wide range of aspect ratios (0.125 < height/length < 4.0), at different Deborah numbers under creeping-flow conditions and to understand the effects of regularization of the lid velocity. The effect of the viscoelasticity on the steady-state results and on the critical conditions for the onset of the elastic instabilities are described and compared to experimental results

Further developments on theoretical and computational rheology

Tese financiada pela FCT - Fundação para a Ciência e a Tecnologia, Ciência.Inovação2010, POPH, União Europeia FEDERTese de doutoramento. Engenharia Química e Biológica. Faculdade de Engenharia. Universidade do Porto. 201

The relationship between viscoelasticity and elasticity

Soft materials that are subjected to large deformations exhibit an extremely rich phenomenology, with properties lying in between those of simple fluids and those of elastic solids. In the continuum description of these systems, one typically follows either the route of solid mechanics (Lagrangian description) or the route of fluid mechanics (Eulerian description). The purpose of this review is to highlight the relationship between the theories of viscoelasticity and of elasticity, and to leverage this connection in contemporary soft matter problems. We review the principles governing models for viscoelastic liquids, for example solutions of flexible polymers. Such materials are characterized by a relaxation time λ, over which stresses relax. We recall the kinematics and elastic response of large deformations, and show which polymer models do (and which do not) correspond to a nonlinear elastic solid in the limit λ → ∞. With this insight, we split the work done by elastic stresses into reversible and dissipative parts, and establish the general form of the conservation law for the total energy. The elastic correspondence can offer an insightful tool for a broad class of problems; as an illustration, we show how the presence or absence of an elastic limit determines the fate of an elastic thread during capillary instability