IWNMNNF 2019 - FEUPiwnmnnf2019/ProcW2019_VF.pdf · IWNMNNF 2019 19th International Workshop on...

IWNMNNF 2019

19th International Workshop on Numerical Methods for

Non-Newtonian Flows

Organizers:Alexandre Afonso, Universidade do Porto

Manuel Alves, Universidade do PortoJoao Miguel Nobrega, Universidade do Minho

Fernando Tavares Pinho, Universidade do Porto

ISBN. 978-972-752-256-9

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Welcome Words

As in previous editions of the International Workshop on Numerical Methods for Non-Newtonian Flows,held somewhat regularly in North America and Europe since 1979, we wish to bring together leadingresearchers interested in discussing challenges, recent progress, future directions and emerging applica-tions in computational and mathematical non-Newtonian and multiphase flows of complex fluids.

This framework is expected to promote discussions on diverse numerical methods at various scalesfor complex fluids, such as polymer solutions and melts, surfactants, suspensions, granular material,multiphase mixtures or fluid/fluids interfaces, among others, as well as on work of experimental naturefocusing at exposing and understanding fluid mechanics and phenomena, within the workshop theme.The strong links between computation, analytical and experimental methods are emphasized in movingforward to robustly solve practical problems.

As in previous workshops, these include numerical methods for solutions of differential and integralconstitutive models from continuum descriptions of the flowing complex fluids to the phenomenologicaland statistical mechanical frameworks for describing them, and include also experiments of such fluidsin challenging flows.

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iv

Participant List

Hugo Abreu, IDMEC, Instituto Superior Técnico, Universidade de Lisboa, Lisboa, PortugalAlexandre Afonso, CEFT, Faculdade de Engenharia, Universidade do Porto, Porto, PortugalManuel Alves, CEFT, Faculdade de Engenharia, Universidade do Porto, Porto, PortugalHamidreza Anbarlooei, Institute of Mathematics, Federal University of Rio de Janeiro, BrazilManisha Chetry, ([email protected]) Institut de Calcul Intensif, Ecole Centrale de Nantes, FranceLuca Brandt, KTH Royal Institute of Technology, Stockholm, SwedenPamela Cook Ioannidis, University of Delaware, USAMichael Cromer,School of Mathematical Sciences, Rochester Institute of Technology, NY, USADaniel Cruz, Mechanical Engineering Program, Federal University of Rio de Janeiro, BrazilJan Helmig, CATS, RWTH Aachen University, Aechen, GermanyMarco Ellero, Basque Center for Applied Mathematics, BCAM, Bilbao, SpainAli Etrati, Mathematics Department, University of British Columbia, Vancouver, BC, CanadaJonathan Evans, Department of Mathematical Sciences, University of Bath, Bath, UKJulien Férec, Université de Bretagne-Sud, Lorient, FranceCélio Fernandes, i3N/Institute for Polymers and Composites, University of Minho, PortugalIan Frigaard, University of British Columbia, Vancouver, BC, CanadaMichael Graham, Department of Chemical and Biological Engineering, University of Wisconsin-Madison, USAMateus Carvalho Guimarães, IDMEC, Instituto Superior Técnico, Universidade de Lisboa, Lisboa, PortugalNaser Hamedi, Dep. of Eng. Sciences and Mathematics, Luleå University of Technology, Luleå, SwedenSimon Haward, Okinawa Institute of Science and Technology, Okinawa, JapanKiyosi Horiuti, IDMEC, Instituto Superior Técnico, Universidade de Lisboa, Lisboa, PortugalMartien Hulsen, Dept. Mech. Eng., Eindhoven University of Technology, Eindhoven, The NetherlandsSimon Ingelsten, Fraunhofer-Chalmers Centre, Chalmers Science Park, Gothenburg, SwedenAnke Lindner, PSL Research University, Université Paris Diderot, Paris, FranceJ. Esteban López-Aguilar, Dep. de Ing. Química, Universidad Nacional Autónoma de México, UNAM, MexicoStefano Lovato, Delft University of Technology, Delft, The NetherlandsFlávio Marchesini de Oliveira, Ghent University, BelgiumGilmar Mompean, Université de Lille, Polytech'Lille. UML,Villeneuve d'Ascq, FranceEkaterina Muravleva, Skolkovo Institute of Science and Technology, RussiaLarissa Muravleva, Lomonosov Moscow State University, RussiaMonica Naccache, Dept. Mech. Eng., Pontifícia Universidade Católica, PUC, Rio de Janeiro, BrazilAngela O. Nieckele, Dept. Mech. Eng., Pontifícia Universidade Católica, PUC, Rio de Janeiro, BrazilJoão Miguel Nóbrega, i3N/Institute for Polymers and Composites, University of Minho, PortugalMónica Oliveira, James Weir Fluids Laboratory, University of Strathclyde, Glasgow, UKOlivier Ozenda, Laboratoire Jean Kuntzmann, CNRS and University of Grenoble, France

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Saeed Parvar, CEFT, Faculdade de Engenharia, Universidade do Porto, Porto, PortugalAnselmo Pereira, PSL Research University, Mines Paris Tech, CEMEF, FranceTim Phillips, School of Mathematics, Cardiff University, Cardiff, UKFernando Pinho, CEFT, Faculdade de Engenharia, Universidade do Porto, Porto, PortugalRobert Poole, School of Engineering, University of Liverpool, Liverpool, UKFábio Ramos, Institute of Mathematics, Federal University of Rio de Janeiro, BrazilY. Sumitra Reddy, Indian Institute of Technology Madras, Chennai, IndiaCecília Mageski Santos, Mechanical Engineering Program, Federal University of Rio de Janeiro, BrazilPierre Saramito, Laboratoire Jean Kuntzmann, CNRS and University of Grenoble, FranceParisa Sarmadi, University of British Columbia, Vancouver, BC, CanadaCarlos Silva, Instituto Superior Técnico, Universidade de Lisboa, Lisboa, PortugalLuisa Silva, Institut de Calcul Intensif, Ecole Centrale de Nantes, FranceRadhakrishna Sureshkumar, Syracuse University, Syracuse, New York, USASeyed Mohammad Taghavi, Department of Chemical Engineering, Université Laval, Québec, CanadaRoger Tanner, School of Aerospace, Mechanical and Mechatronic Engineering, University of SydneyStefan Turek, TU-Dortmund University, Dortmund, GermanyStylianos Varchanis, Department of Chemical Engineering, University of Patras, GreeceLin Zhou, New York City College of Technology, CUNY, NY, USAKonstantinos Zografos, School of Engineering, University of Liverpool, Liverpool, UK

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Contents

Welcome Words iii

Participant List v

Session 1: Monday 17th [9h00 - 10h20] 1

Computations and experiments in non-colloidal suspension rheology(Roger I. Tanner) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

Critical layer structures and mechanisms in elastoinertial turbulence(Ashwin Shekar, Ryan M. McMullen, Sung-Ning Wang, Beverley J. McKeonand Michael D. Graham) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

The ”Tensor Diffusion” approach for simulating viscoelastic fluids without solvent(Stefan Turek and Patrick Westervoss) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

Cement curing process in the presence of a fluid loss zone(Sergio S. Ribeiro and Monica F. Naccache) . . . . . . . . . . . . . . . . . . . . . . . . 4


Stochastic mesoscale modeling for wormlike micellar and networked fluids(Lin Zhou and L. Pamela Cook) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

A dumbbell model with binary slip states in non-affine polymer-diluted turbulent flow(Kiyosi Horiuti) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

A Newton method for the log-conformation formulation of the Johnson-Segalman viscoelasticfluid(Pierre Saramito) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

Formation of static layers during displacement of Bingham fluids in eccentric annuli: three-dimensional simulations(Ali Etratiand Ian Frigaard) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

A generalized framework for viscoleastic flow hyper-reduction(Domenico Borzacchiello, Luisa Silva and Gaetano D’Avino) . . . . . . . . . . . . . . . 9


Beyond the maximum drag reduction asymptote(Anselmo Pereira, Gilmar Mompean and Roney L. Thompson) . . . . . . . . . . . . . . 11

A new tensorial model for non-colloidal suspensions: from microstructure anisotropy to normalstress differences and shear induced migration(Olivier Ozenda, Pierre Saramito and Guillaume Chambon) . . . . . . . . . . . . . . . . 12

Efficient viscoelastic flow computation using a Lagrangian-Eulerian method and GPU-acceleration(Simon Ingelsten, Andreas Mark, Roland Kadar and Fredrik Edelvik) . . . . . . . . . . . 13

Compressible and nonisothermal viscoelastic flow between eccentrically rotating cylinders(Alexander T Mackay and Timothy N Phillips) . . . . . . . . . . . . . . . . . . . . . . . 14

The accelerated proximal gradient method for yield-stress fluid flows with wall slip(Larisa Muravleva) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15


Effect of coupling 2D non-homogeneous flows and fiber orientation for Newtonian and power-law suspending fluids(Julien Ferec, Suresh G. Advani and Gilles Ausias) . . . . . . . . . . . . . . . . . . . . . 17

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Deep learning methods for viscoplastic flows modelling(Ekaterina Muravleva) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

A Phase Field approach for two-phase viscoelastic flows(Konstantinos Zografos, Alexandre M. Afonso, Robert J. Poole and Monica S. N. Oliveira) 19

Effects of wall slip on the stability of plane Poiseuille flow of Bingham fluids(Hossein Rahmani and Seyed M. Taghavi) . . . . . . . . . . . . . . . . . . . . . . . . . . 20

Effects of elasticity, inertia and viscosity ratio on the drag coefficient of a sphere translatingthrough a viscoelastic fluid(S.A. Faroughi, Celio Fernandes, Gareth H. McKinley and J. Miguel Nobrega) . . . . . 21

Session 5: Tuesday 18th [08h40 - 10h20] 23

Viscoelastic flow and instabilities around microfluidic cylinders(Simon J. Haward, Cameron Hopkins and Amy Q. Shen) . . . . . . . . . . . . . . . . . 23

Direct numerical simulations of turbulent planar jets of viscoelastic FENE-P fluids(Mateus C. Guimaraes, Nuno Pimentel, Fernando T. Pinho and Carlos B. da Silva) . . 24

Simulation of viscoelastic fluid flows using lattice Boltzmann method(Y.Sumithra Reddy, Sumesh P. Thampi and Abhijit P. Deshpande) . . . . . . . . . . . . 25

Progress with triple layer core-annular flows(Parisa Sarmadi, Otto Mierka, Stefan Turek, Sarah Hormozi and Ian Frigaard) . . . . . 26

Using the contravariant deformation tensor formulation in simulation of viscoelastic fluid flow(Martien A. Hulsen, Mick A. Carrozza, Markus Hutter and Patrick D. Anderson) . . . 27


Verification and Validation of CFD simulations of non-Newtonian laminar flows on canonicaltest cases(Stefano Lovato, Guilherme Vaz, Serge L. Toxopeus, Geert Keetels and Just Settels) . . 29

Influence of polymer additives on small scale dynamics of a turbulent/non-turbulent interfacein shearless flows(Hugo Abreu, Fernando T. Pinho and Carlos B. da Silva) . . . . . . . . . . . . . . . . . 30

New, faster and consistent FEM for viscoelastic flows(Stylianos Varchanis, Alexandros Syrakos, Yannis Dimakopoulos and John Tsamopoulos) 31

Unsteady, temperature-dependent, and non-Newtonian simulations in plastics processing(Stefanie Elgeti, Jan Helmig, and Philipp Knechtges) . . . . . . . . . . . . . . . . . . . . 32

A fully-resolved immersed boundary numerical method to simulate particle-laden viscoelasticflows(Celio Fernandes, S.A. Faroughi, Olga S. Carneiro, J. Miguel Nobrega and Gareth H.McKinley) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33


Shear-thickening of a non-colloidal suspension with a viscoelastic matrix(Adolfo Vazquez-Quesada, Pep Espanol, Roger I. Tanner and Marco Ellero) . . . . . . . 35

Direct numerical simulation of turbulent flows of power law fluids over rough walls(Hamidreza R. Anbarlooei, C.M.M. Santos, D.O.A. Cruz and F. Ramos) . . . . . . . . 37

Role of polymer physics and extensional rheology in the development of an elastic instabilityin cross-slot flow(Michael Cromer, Larry Villasmil, Henry Huang, Alberto Serrano, Alana Smith andCameron Grube) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

Die-swell singularity for PTT and Giesekus fluids(Jonathan D. Evans) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

Laminar and turbulent flows of an elastoviscoplastic fluid(Luca Brandt, Marco E. Rosti, Daulet Izabassarov, Sarah Hormozi and Outi Tammisola) 40


Non-linear Reynolds stress and conformation tensors models for viscoelastic turbulent flow(Angela .O. Nieckele, Roney L. Thompson and Gilmar Mompean) . . . . . . . . . . . . 41

Numerical predictions for contraction-flow of Boger fluids under various geometrical configu-rations(J.E. Lopez-Aguilar, H.R.Tamaddon-Jahromi and Michael F. Webster) . . . . . . . . . 42

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Study of polypropylene planar flow and extrudate swell: a comparison between 3D numericalsimulations and experiments(Dahang Tang, Flavio H. Marchesini, Dagmar R. D’hooge and Ludwig Cardon) . . . . . 43

Local similarity solution for a steady laminar planar jet of a viscoelastic FENE-P fluid(Saeed Parvar, Carlos B. da Silva and Fernando T. Pinho) . . . . . . . . . . . . . . . . 44

Optimised microfluidic designs for in situ characterisation of complex fluids and bio-particles(Konstantinos Zografos, Joana Fidalgo, Manuel A. Alves, Yanan Liu, Anke Lindner andMonica S. N. Oliveira) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

Session 9: Wednesday 19th [08h40 - 10h20] 47Secondary flows in serpentine microchannels with viscoelastic fluids

(Lucie Ducloue, Laura Casanellas, Simon J. Haward, Robert J. Poole, Manuel A. Alves,Sandra Lerouge, Amy Q. Shen and Anke Lindner) . . . . . . . . . . . . . . . . . . . . . 47

Water entry of yield-stress droplets(Anselmo Pereira, Rudy Valette and Elie Hachem) . . . . . . . . . . . . . . . . . . . . . 48

Modelling of flexible fibres in viscous fluid flow(Naser Hamedi and Lars G. Westerberg) . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

Direct numerical simulation of heat transfer reduction in viscoelastic turbulent channel flow(Radhakrishna Sureshkumar and Kyoungyoun Kim) . . . . . . . . . . . . . . . . . . . . 50

Viscoelastic fluid flow simulation using coupled solvers in OpenFOAM R©(F. Pimenta and Manuel A. Alves) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

Author Index 53

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Session 1: Monday 17th [9h00 -10h20]

Chairman: Ian Frigaard

Computations and experiments in non-colloidal suspension rheology 17th June9:00-9:20Session 1Roger I. Tanner1, �

1 School of Aerospace, Mechanical and Mechatronic Engineering, University of Sydney

Computations of the rheology of non-colloidal suspensions with Newtonian matrices have been surveyedseveral times [1-3]. It has become clear that friction between particles is very important. A schemeto deduce an average friction coefficient for suspensions is presented. The scheme uses data from fric-tionless computations and experimental viscosity data [4]. It appears that unless the friction coefficientvaries with sliding speed it is difficult to match computational and experimental results.Another survey [in preparation] using non-Newtonian matrix fluids found very few computations havebeen made, especially for concentrated suspensions. In the case of dilute and semi-dilute suspensionssome results are available [5]. In order to match experiments it may be necessary to refine the presentsingle-relaxation time Oldroyd-B models.While most of the literature discusses steady shear flows, there is a great need for the study of unsteadyflows and extensional flowsat present there is only one set of computations for uniaxial extension [6].Clearly there is scope for more computations in this area.

References[1] M. M. Denn and J. F. Morris, Rheology of non-Brownian suspensions, Annu. Rev. Chem. Biomol. Eng. 5,

203–228 (2014).

[2] M. M. Denn, J. F. Morris, and D. Bonn, Shear thickening in concentrated suspensions of smooth spheres in

Newtonian suspending fluids, Soft Matter 14, 170–184 (2018).

[3] R.I.Tanner. Aspects of non-colloidal suspension rheology. Phys. Fluids 30.art.101301 (2018).

[4] R.I Tanner, C. Ness, A. Mahmud, S-C Dai and J. Moon. A bootstrap mechanism for non-colloidal suspension

viscosity. Rheol Acta 57: 635–643 (2018).

[5] M. Yang,and E.S.G.Shaqfeh. Mechanism of shear thickening in suspensions of rigid spheres in Boger fluids.

Part II: Suspensions at finite concentration. J. Rheol. 62:1379–1396 (2018).

[6] O.Cheal, and C. Ness . Rheology of dense granular suspensions under extensional flow. J. Rheol. 62:501–512

(2018).

1

mailto:[email protected]

Critical layer structures and mechanisms in elastoinertial turbulence17th June9:20-9:40Session 1 Ashwin Shekar1, �, Ryan M. McMullen2, �, Sung-Ning Wang1, �, Beverley J. McKeon2, �

and Michael D. Graham1, �

1 Department of Chemical and Biological Engineering, University of Wisconsin-Madison, Madison WI53706,USA

2 Graduate Aerospace Laboratories, California Institute of Technology, Pasadena CA 91125, USA

Simulations of elastoinertial turbulence (EIT) of a polymer solution at low Reynolds number are shownto display localized polymer stretch fluctuations. These are very similar to structures arising fromlinear stability (Tollmien-Schlichting (TS) modes) and resolvent analysis: i.e., critical layer structureslocalized where the mean fluid velocity equals the wave speed. Computation of self-sustained nonlinearTS waves reveals that the critical layer exhibits stagnation points that generate sheets of large polymerstretch. These kinematics may be the genesis of similar structures in EIT.

2






The ”Tensor Diffusion” approach for simulating viscoelastic fluids withoutsolvent 17th June

9:40-10:00Session 1Stefan Turek1, � and Patrick Westervoss1, �

1 TU Dortmund, Institute for Applied Mathematics, Dortmund, Germany

In viscoelastic fluids, described by differential as well as by integral models, additional numerical chal-lenges besides the well-known HWNP problem arise in the case of negligible or even vanishing solventpart. In typical operator-splitting approaches which decouple the Navier-Stokes part from the evolutionequations for the viscoelastic stress as well as in fully monolithic methods (which seem to be preferablefor differential models particularly in direct stationary solvers), the case of no solvent requires numeri-cally special care, particularly w.r.t. the involved iterative solution methods.In this talk, we present the new ”Tensor Diffusion” approach which models the velocity - viscoelasticstress coupling via a tensor diffusion. We motivate this approach via several examples and present pre-liminary computational results for prototypical numerical test configurations based on the FEATFLOWsoftware.

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Cement curing process in the presence of a fluid loss zone17th June10:00-10:20

Session 1 Sergio S. Ribeiro1, � and Monica F. Naccache1, �

1 Department of Mechanical Engineering, Pontifıcia Universidade Catolica-RJ

In the cementing process of oil wells, cement or sometimes resin-based fluids are injected in the annulusto permanently isolate a zone. The fluid must withhold the formation pressures along the well lengththroughout the curing process. In addition, carbonate formations are known to be very heterogeneous[1] and susceptible to partial or total fluid exchanges with the well, called fluid or filtrate loss. Toevaluate this process, the annular flow of a slightly compressible and non-newtonian fluid is analyzedwhen submitted to a filtrate loss zone.Several authors [2-6] historically focused on understanding the pressure decay along the curing process.They proposed and reviewed 1-D models to describe this specific problem, specially due to the hugedifference between the characteristic lengths of each dimension. However, when analyzing the fluid lossproblem the radial and axial velocities must be considered, and both may vary with radius and length,i.e. vr = vr(r, z) and vz = vz(r, z).In this study, the cement mixture is considered a slightly compressible fluid composed by two chemicalspecies. Hence, the isothermal compressibility state equation can be combined with mass balance in(1) to correlate the changes of pressure p with the concentration of each specie C1 and C2.

∂p

∂t= c2

(ρ1∂C1

∂t+ ρ2

∂C2

∂t

)(1)

Despite the mixture density ρ may change, the flow can be considered incompressible, due to the lowMach number. Moreover, the simplified momentum equations are solved for r and z directions.The cement mixture is a non-Newtonian fluid. Its viscosity depends on the rate-of-strain tensor, andcan be modeled by the Herschel-Bulkley equation. Moreover, the cement viscosity also changes irre-versibly during the curing process, and this irreversible increase in viscosity is modeled as a combinationof two factors: (i) the bulk chemical reaction itself; (ii) and local changes in the mixture compositiondue to fluid loss. The numerical solution of the governing equations is obtained using the finite volumemethod. Pressure and velocity fields are obtained for different combinations of rheological parameters.

References[1] M. E. Chenevert and L. Jin. Society of Petroleum Engineers Annual Technical Conference and Exhibition,

Texas, USA, 1989.

[2] G. Daccord, L. De Rozieres, and B. Boussouira. First International Workshop on Hydration and Setting, 07

1991.

[3] S. Nishikawa and A. Wojtanowicz. Society of Petroleum Engineers Annual Technical Conference and Exhi-

bition, 2002.

[4] S. V. Patankar. Numerical heat transfer and fluid flow. New Jersey, 2nd edition, 1980.

[5] M. Prohaska, R. Fruhwirth, and M. J. Economides. Society of Petroleum Engineers Drilling and Completion,

10, 09 1995.

[6] M. Prohaska, D. O. Ogbe, and M. J. Economides. Society of Petroleum Engineers Western Regional Meeting,

1993.

[7] N. J. Tosca and V. P. Wright. Geological Society London Special Publications, pages SP435.1, 2015.

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Chairman: Mike Graham

Stochastic mesoscale modeling for wormlike micellar and networked fluids 17th June10:50-11:10Session 2Lin Zhou1, � and L. Pamela Cook2, �

1 New York City College of Technology, CUNY, NY, USA2 University of Delaware, USA

Complex fluids can be modeled and studied at the macroscopic or mesoscopic level. Mesoscale stochasticmodels have the advantage over macroscale models in that they capture the local properties of theembedded structural elements. Mesoscopic elements are often modeled as bead springs (Hookean ornon-Hookean) which in wormlike micellar mixtures or telechelic polymers self-assemble into long chainsor networks that dynamically break and reform. Long wormlike micelles in concentrated mixturesentangle and their motion is confined by nearby worms. This confinement can possibly be captured byallowing weak cross-chain attractions. These weaker cross-chain attractions exist in mucins and maybe a proxy for confinement modeling in wormlike-micellar mixtures. In this talk we discuss models andcomputational results for stochastic mesoscale breaking reforming systems and explore model parameterranges which lead to capturing particular properties of each of wormlike micelles, telechelic polymers,and mucins.

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A dumbbell model with binary slip states in non-affine polymer-dilutedturbulent flow17th June

11:10-11:30Session 2 Kiyosi Horiuti1, �

1 LAETA/IDMEC/Instituto Superior Tecnico, Universidade de Lisboa, Portugal

We develop a new dumbbell model in which commonly assumed constraint of affinity in the motion of thebead-spring configuration with the macroscopic fluid deformation is relaxed. Non-affinity is introducedby allowing slippage of the dumbbells as stretching of polymers progresses, which is represented by theslip parameter α. When the dumbbell is rotated from the affine (α = 0) direction to the completenon-affine (α = 1) direction, α is continuously adjusted from 0 to 1, so that altered orientation ismore precisely captured (Variable-α model). Assessment is conducted by dispersing the dumbbellsin homogeneous isotropic turbulence. Table shows the averaged values of the dissipation rate of thesolvent ε and the elastic energy production term Pe(= τijSji). Smaller ε and larger Pe imply largerdrag reduction (DR). In Variable-α model, DR larger than in the case in which α is fixed to 0 isobtained. This is due to elimination of emergence of the elasto-inertial turbulence (EIT) in the elongatedaffine dumbbells [1] by conversion of affine configuration to non-affine configuration. This conversion isrepeated alternately and quasi-periodically with lapse of temporal interval comparable to the relaxationtime. The largest elastic energy production is achieved in the highly stretched α = 1 dumbbells,whereas intermediate production is attained in α = 0 dumbbells with intermediate length. Affine andnon-affine dumbbells share the complementary roles in their elongation. DR obtained in Variable-αmodel, however, is smaller than in the case in which α is fixed to 1. This poor performance is obtainedbecause temporal variation in α encompasses the range α ≈ 0.5, at which the convective derivative isdegenerated into corotational and production of elastic energy is halted. To avoid encompassing thesingularity at α ≈ 0.5, in Binary-α model, α is confined to the binary values of either 0 or 1. Dummyvalue of α, α∗, is determined using Variable-α model, and then actual value of α is assigned to 0 when0 ≤ α∗ < 0.5, and to 1 when 0.5 ≤ α∗ ≤ 1. In Binary-α model, marked improvement in DR is achieved.The pdf of dumbbell length exhibits two peaks corresponding to α = 0 and 1. More dumbbells withα = 1 are created in Binary-α model than in Variable-α model, and as the dumbbells with α = 1 shrink,they are transformed into the dumbbells with α = 0. With stretching of the dumbbells with α = 0,they are transformed back into α = 1. It is shown that drastic enhancement of DR can be establishedby removal of singularity at α ≈ 0.5. References

Case Newtonian α = 0 (fixed) α = 1 (fixed) Variable-α Binary-αε 0.419 0.263 0.226 0.243 0.206Pe - 0.115 0.149 0.146 0.179

[1] P.C. Valente, C.B. Silva and F.T. Pinho, The effect of viscoelasticity on the turbulent kinetic energy cascade,

J. Fluid Mech. 760, 39–62 (2014).

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A Newton method for the log-conformation formulation of theJohnson-Segalman viscoelastic fluid 17th June

11:30-11:50Session 2Pierre Saramito1, �

1 LJK, CNRS and Grenoble univ., France

A modified log-conformation formulation of viscoelastic fluid flows is presented [1].This new formulation is non-singular for vanishing Weissenberg numbers and allows a direct steadynumerical resolution by a Newton method. Moreover, an exact computation of all the terms of thelinearized problem is provided. The use of an exact divergence-free finite element method for velocity-pressure approximation and a discontinuous Galerkin upwinding treatment for stresses leads to a robustdiscretization.A demonstration is provided by the computation of steady solutions at high Weissenberg numbers(denoted by We) for the difficult benchmark case of the lid driven cavity flow (see Fig. 1). Numericalresults are in good agreement, qualitatively with experiment measurements on real viscoelastic flows,and quantitatively with computations performed by others authors. The numerical algorithm is bothrobust and very efficient, as it requires a low mesh-invariant number of linear systems resolution toobtain solutions at high Weissenberg number. An adaptive mesh procedure is also presented: it allowsrepresenting accurately both boundary layers and the main and secondary vortices.

Figure 1: The driven cavity benchmark for We = 3:(left) adapted mesh and (right) stream functionisovalues.

References[1] P. Saramito, A damped Newton algorithm for computing viscoplastic fluid flows, J. Non-Newtonian Fluid

Mech., 238:6–15, 2016. https://www-ljk.imag.fr/membres/Pierre.Saramito/Sar-2016.pdf

7

[email protected]

https://www-ljk.imag.fr/membres/Pierre.Saramito/Sar-2016.pdf

Formation of static layers during displacement of Bingham fluids ineccentric annuli: three-dimensional simulations17th June

11:50-12:10Session 2 Ali Etrati1, � and Ian Frigaard1,2, �

1 Mathematics Department, University of British Columbia, Vancouver, BC, Canada2 Department of Mechanical Engineering, University of British Columbia, Vancouver, BC, Canada

We study displacement of a Bingham fluid using high-resolution three-dimensional numerical simu-lations. The Bingham fluid is displaced, upward, by a heavier Newtonian fluid in a narrow eccentricannulus to model mud displacement during primary cementing of an oil well. A volume of fluid approachis used to model the two fluids. The yield-stress is modelled using viscosity regularization method of[1].If the wall shear stress due to the imposed flow is not large enough, the mud remains unyielded at theannulus walls and static wall-layers form. Additionally, in case of high viscosity ratios the displacedfluid might be yielded in a thin layer next to the wall, with an unyielded plug near the interface. Thisleads to formation of mobile residual layer that are displaced very slowly. Formation of these layers arefirst studied in a two-dimensional geometry to benchmark the regularization method used here againstnumerical simulations of [2] where an Augmented Lagrangian method was used. Then the layer forma-tion and thickness is studied in the three-dimensional geometry, ie eccentric annuli. As the eccentricityis increased the narrow side becomes completely static and a mud channel forms.

References[1] M. Bercovier, M. Engleman, A finite-element method for incompressible non-Newtonian flows, Journal of

Computational Physics, 36, 313–326 (1980).

[2] M. Zare, I.A. Frigaard, Buoyancy effects on micro-annulus formation: Density stable displacement of New-

tonianBingham fluids. Journal of Non-Newtonian Fluid Mechanics, 280, 145–162 (2017).

8



A generalized framework for viscoleastic flow hyper-reduction 17th June12:10-12:30Session 2Domenico Borzacchiello1, �, Luisa Silva1, � and Gaetano D’Avino2, �

1 Institut de Calcul Intensif, Ecole Centrale de Nantes, France2 Universita degli Studi di Napoli Federico II (IT), Dipartimento di Ingegneria chimica, dei Materiali e della

Produzione Industriale, Napoli, Italy

Numerical simulation of viscoelastic flows is central to several engineering applications. For many ofthese, such as flow control, shape optimization, inverse analysis and numerical upscaling, among others,the demand of high computational power is associated to the need of evaluating multiple configurationsin the space of the physical parameters governing the flow dynamics. In recent years, parametric modelorder reduction (pMOR) has proved to be a reliable approach to tackle the numerical complexity ofmulti-parametric models [1,2,3]. The goal of pMOR is to discover the structure of a low dimensionalmanifold associated to the solution of the problem by leveraging the information obtained from trainingsimulations. Reduced complexity is achieved by reformulating the problem in the lower dimensionalspace of reduced variables, resulting in potentially impressive speed-ups. In this work we build uponthe numerical schemes presented in [4] and introduce a framework for model hyper-reduction, usingthe finite element solver proposed therein to train reduced order flow models for viscoelastic fluids.In particular, we address the problem of recovering sparse empirical quadrature schemes to efficientlyintegrate nonlinear terms with reduced complexity, while retaining the numerical stability of the originalhigh order scheme. We discuss the advantages and potential applications of the proposed approachedby showing results for several benchmark flows, with particular emphasis on the approximation of thestabilization terms resulting from the SUPG formulation of the constitutive equations.References[1] D. Borzacchiello et al. Non-intrusive sparse subspace learning for parametrized problems. Arch. Comput.

Methods Eng. (2017): 1–24.

[2] D. Borzacchiello et al. Reduced order modelling for efficient numerical optimisation of a hot-wall chemical

vapour deposition reactor. Int. J. Heat Fluid Fl. 27.7 (2017): 1602–1622.

[3] J.V. Aguado et al. A Simulation App based on reduced order modeling for manufacturing optimization of

composite outlet guide vanes. Adv. Mod. Simul. Eng. Sci. 4.1 (2017): 1.

[4] G. DAvino and M.A. Hulsen, Decoupled second-order transient schemes for the flow of viscoelastic fluids

without a viscous solvent contribution, J. NonNewton. Fluid. Mech., 165, (2010):1602–1612

9




10


Chairman: Martien Hulsen

Beyond the maximum drag reduction asymptote 17th June14:00-14:20Session 3Anselmo Pereira1, �, Gilmar Mompean2, � and Roney L. Thompson3, �

1 PSL Research University, MINES ParisTech, CEMEF, CNRS UMR 7635, CS 10207, rue Claude Daunesse,06904 Sophia-Antipolis Cedex, France

2 Universite de Lille, Polytech’Lille. Unite de Mecanique de Lille (UML - EA 7512), Cite Scientifique, F-59655Villeneuve d’Ascq, France

3 COPPE, Department of Mechanical Engineering, Universidade Federal do Rio de Janeiro, Centro deTecnologia, Ilha do Fundo, 21945-970, Rio de Janeiro, RJ, Brazil

The addition of a small amount of polymers of high molecular weight can lead to a considerable dragdecrease in turbulent flows. Initially, the drag reduction level is an increasing function of the polymerconcentration, but eventually it saturates, achieving what is known as the maximum drag reductionasymptote (MDR). Interestingly, recent experimental results conducted in pipes indicated that for anappropriate choice of parameters, polymers can reduce the drag beyond the suggested asymptotic limit,eliminating turbulence and giving way to laminar flow (Choueiri, Lopez, and Hof, Physical Review Let-ters, 2018). However, in the present work, we show through direct numerical simulations of viscoelasticplane Couette flows that, in the scenario in which the MDR is exceeded, the flow is not laminar. De-spite the low friction factor, a transient behavior is observed as a consequence of a very small rateof polymer energy injected into the flow. During this development stage, particular and very weakelliptical/hyperbolic turbulent structures are observed close to the wall. Later on, flow instabilities de-velop across the channel, triggering the viscoelastic turbulence. At this final stage, turbulence oscillatesbetween active and hibernating states and the mean drag reduction level is given by the MDR.

11




A new tensorial model for non-colloidal suspensions: from microstructureanisotropy to normal stress differences and shear induced migration17th June

14:20-14:40Session 3 Olivier Ozenda1, �, Pierre Saramito1, � and Guillaume Chambon2, �

1 Lab. J. Kuntzman, CNRS and univ. Grenoble, France2 IRSTEA Grenoble and univ. Grenoble, France

Non-colloidal suspensions in Newtonian fluids exhibit non-trivial behavior in several flowing conditions,such as normal stress differences and an anisotropic micro-structure during shear flow or a drop of theapparent viscosity just after a shear reversal.To predict these features, we introduce in [1] a new texture tensor that represents the local anisotropyof clusters of neighbouring particles. This tensor satisfies a rate-independent linear advection equationwhich is coupled to the bulk velocity. Hence suspensions are modelled like a visco-elastic fluid.As seen on the left plot, the apparent viscosity ηapp versus the deformation γ during a shear reversalsuddenly decreases at time t=0 then reaches smoothly a minimum and finally increases and goes backto its stationary value. Remark the excellent quantitative agreement between the observation from [3](in red) and the model prediction (in black).The plot in the middle represents, in polar coordinates, the probability g(θ) for a particle to have aneighboring particle in the θ ∈ [0, 2π] direction, which is called pair distribution function. The modelis able to predict the depletion angle θe, indicated by an arrow, where this probability is minimum.Observe also the global qualitative agreement between the observation (in red) from [4] and the modelprediction (in black). The right plot shows the reduced second normal stress difference α2 versus thereduced volumic fraction ψ. Our prediction (in black) agrees with the two experimental data sets,from [5] and [6] (in red and in green). This third comparison presented in [2] constitues a great leap insuspensions modelling as normal stress differences are responsible for shear induced migration.Finally, we integrate our new rheological model into a two velocities system in order to reproduce mi-gration phenomenon and predict jammed zones. When φ tends towards its maximal value, internalstresses diverge because of contact interactions and the flow is congested.

0

10

20

30

0 1 2 3 4

ηapp (Pa.s)

φ = 0.44

γ

experimentmodel

φ = 0.4

θe=27◦

0

0.3

0.6

0 0.5 1

α2 =−N2

ηapp|γ|

ψ = φ/φm

Dbouk et al.Couturier et al.

present

apparent viscosity after shear reversal pair distribution function second normal stress difference

References[1] O. Ozenda, P. Saramito, G. Chambon, A new rate-independent tensorial model for suspensions of non-

colloidal rigid particles in Newtonian fluids, JOR, 2018.

[2] O. Ozenda, P. Saramito, G. Chambon, Normal stress comparisons with a tensorial model for suspensions of

non-colloidal rigid particles, submitted, 2019.

[3] F. Blanc, F. Peters, E. Lemaire, Local transient rheological behavior of concentrated suspensions, JOR, 2011.

[4] T. Dbouk, L. Lobry, E. Lemaire, Microstructure in sheared non-Brownian concentrated, JFM, 2013.

[5] E. Couturier, F. Boyer, O. Pouliquen, E. Guazzelli, Normal stresses in concentrated non-Brownian suspen-

sions, JFM, 2011.

[6] E. Couturier, F. Boyer, O. Pouliquen, E. Guazzelli, Suspensions in a tilted trough: second normal stress

difference, JFM, 2011.

12


[email protected]


Efficient viscoelastic flow computation using a Lagrangian-Eulerian methodand GPU-acceleration 17th June

14:40-15:00Session 3Simon Ingelsten1,2, �, Andreas Mark1, �, Roland Kadar2, � and Fredrik Edelvik1, �

1 Fraunhofer-Chalmers Centre, Chalmers Science Park, Gothenburg SE-412 88, Sweden2 Division of Engineering Materials, Department of Industrial and Materials Science, Chalmers University of

Technology, Gothenburg SE-412 96, Sweden

Viscoelastic fluids are common in various industrial applications, including adhesive extrusion andapplication of sealant on automotive bodies, 3D-printing and polymer processing. Viscoelastic flowsare however complex and time consuming to simulate numerically. In turn, real viscoelastic materialstypically need to be modelled using multiple relaxation modes, which further increases the requiredCPU time. At the same time, calculation on graphical processing units (GPU) can provide significantspeedup of numerical simulations.In a recent publication [1] we presented a Lagrangian-Eulerian method to simulate viscoelastic fluidflow. The constitutive equation is solved in Lagrangian nodes and the fluid momentum and continuityequations are solved on an Eulerian grid using the finite volume method. Interior objects are treatedusing the mirroring immersed boundary method [2]. The coupling between the equations is establishedthrough robust interpolation using radial basis functions.In this work, we show that the method can be extended to calculate the viscoelastic stresses using theGPU. A major advantage is that the Lagrangian method used to solve the constitutive equation is mesh-free and trivially parallelizable. The method is therefore very suitable for GPU-acceleration. The largestgain in simulation speed is typically found for larger problems, since the bandwidth of transferring databetween the CPU and the GPU could be a limiting factor. The scaling of the computational performancewith respect to the size of the problem is therefore studied, aswell as the computational cost for thedifferent parts of the algorithm. For this, viscoelastic flows with both single and multiple relaxationmodes are simulated. A significant increase of the overall simulation speed is found, as the time forcalculating the stresses is heavily reduced.References[1] S. Ingelsten, A. Mark, F. Edelvik, A Lagrangian-Eulerian framework for simulation of transient viscoelastic

fluid flow, J. Non-Newton. Fluid Mech. 266 (2019) 20–32, doi:10.1016/j.jnnfm.2019.02.005.

[2] A. Mark, B.G.M. van Wachem, Derivation and validation of a novel implicit second-order accurate immersed

boundary method, J. Comput. Phys. 227 (2008) 6660–6680.

13





Compressible and nonisothermal viscoelastic flow between eccentricallyrotating cylinders17th June

15:00-15:20Session 3 Alexander T Mackay1, � and Timothy N Phillips1, �

1 School of Mathematics, Cardiff University, Cardiff, CF24 4AG, UK

Lubricants reduce wear and vibration in bearing systems by preventing contact between moving parts.The physical characteristics of lubricants are a crucial determining factor in the performance andlongevity of lubricated systems. Polymers are added to mineral oils to ensure that lubricants are ableto operate efficiently over a wide range of temperatures while preventing damage and wear. The flowbetween eccentrically rotating cylinders is of interest in the mathematical modelling of journal bearinglubrication since it is a benchmark problem that retains important elements of the engineering problem.The lubricant is modelled using the extended White-Metzner (EWM) and FENE-P-MP models. Thelatter is a variant of the FENE-P model that includes the capability of modelling compressibility andnon-isothermal flows. The model is derived using the generalized bracket framework which accounts forboth reversible and non-reversible dynamics and ensures that the derived models are consistent withthe laws of thermodynamics. The numerical scheme is based on a Taylor-Galerkin discretization in timeand a finite element method in space. Comparisons with results in the literature will be performed inthe case of incompressible flow to validate the numerical scheme. Computational predictions will bepresented that demonstrate that elasticity and compressibility both have a significant stabilising effecton the journal for the extended White-Metzner and FENE-P-MP models.

14



The accelerated proximal gradient method for yield-stress fluid flows withwall slip 17th June

15:20-15:40Session 3Larisa Muravleva1, �

1 Lomonosov Moscow State University, Russia

Viscoplastic or yield stress fluids are materials which behave like a solid below critical yield stress andflow like a viscous fluid for stresses higher than this threshold. The main difficulty in the numericalsimulation of viscoplastic fluid flow is related to the non-differentiable form of constitutive law andinability to evaluate the stresses in the rigid zones. There are two principal approaches to overcome thismathematical problem, the regularization approach, which consists in approximating the constitutiveequation by a smoother one, and augmented Lagrangian method (ALM), which is based variationalinequalities. The chief advantage of ALM over viscosity regularization is that the exact form of consti-tutive relation is used and the algorithm gives truly unyielded regions with exactly zero strain rate butits computing time is generally larger.Recently, Treskatis et al. [1], [2] suggested an accelerated version of the ALM - accelerated proximalgradient method, based on the fast iterative shrinkage-thresholding algorithm (FISTA) and provideuseful practical recommendations for efficient numerical simulations of yield-stress fluid flows with theno-slip condition at the wall. Many viscoplastic fluids slip at the wall with a yield slip. The fluid slipswhen the tangential stress exceeds a critical value called the yield slip, and otherwise, the fluid sticksat the wall.We exploit the analogy of structure between the slip law and the viscoplastic constitutive law and applyaccelerated proximal gradient method to both the viscoplastic model and the yield slip equation. Thetraditional ALM converges with rate O(1/

√k), an accelerated variant converges with the higher and

provably optimal bound O(1/k) convergence, where k is the iteration counter. This accelerated versionis obtained at a negligible extra computational cost. The proposed method is used to simulate the ax-isymmetric squeeze flow of Bingham, Casson, and Herschel-Bulkley fluids with the slip yield boundarycondition at the wall. The squeeze flow has shown three specific behaviors: stick, stick-slip transition,and slip. As a second example of the application of this algorithm, the Poiseuille flow of a Binghamfluid in ducts of various cross sections with slip yield boundary condition is considered. There existfive flow regimes: full slip, full stick, partial slip and stick at the wall, block translation, and stoppedmaterial.References[1] T. Treskatis, M. A. Moyers-Gonzalez, C. J. Price,An accelerated dual proximal gradient method for applica-

tions in viscoplasticity, J. Non-Newtonian Fluid Mech. 164 (2016) 544–550.

[2] T. Treskatis, A. Roustaei, I. Frigaard, A. Wachs, Practical guidelines for fast, efficient and robust simulations

of yield-stress flows without regularisation: A study of accelerated proximal gradient and augmented Lagrangian

methods, J. Non-Newtonian Fluid Mech. 164 (2018) 149–164.

15


16


Chairman: Marco Ellero

Effect of coupling 2D non-homogeneous flows and fiber orientation forNewtonian and power-law suspending fluids 17th June

16:10-16:30Session 4Julien Ferec1, �, Suresh G. Advani2, � and Gilles Ausias1, �

1 Universite de Bretagne-Sud, UMR CNRS 6027, IRDL, F-56100 Lorient, France2 Department of Mechanical Engineering, Center for Composite Materials, University of Delaware, 101

Academy Street, Newark, DE 19716, USA

A numerical study is presented for rigid fiber suspension flows through a parallel plate channel anda planar 4:1 contraction. In addition to examining a Newtonian suspending fluid, a non-Newtonianmatrix exhibiting a pseudo-plastic behavior and described by a power-law model is also investigated.Furthermore, instead of using orientation tensors for the macroscopic constitutive modeling, our ap-proach addresses the macroscopic scale by describing the fiber orientation state with the probabilitydistribution function. This enables us to eliminate the error introduced due to the closure approxima-tion which is inevitable when using orientation tensor description. Our numerical scheme solves theentire probability distribution function in both the spatial and configurational spaces. This allows usto correctly implement expressions for both the fiber extra stress, especially for the suspending matrixdisplaying a pseudo-plastic behaviour, and the fiber orientation state. Hence, these two constitutiverelations for suspensions are used to perform simulations in which flow and fiber orientation are fullycoupled. It is found that the coupling flattens the velocity profile for Newtonian and Non-Newtoniansuspending fluids but does not affect the fiber orientation distributions at the exit. However, in thecorner region where a vortex is observed, its magnitude increases with the coupling and this enhance-ment is more pronounced for the Newtonian suspending fluid. Newtonian viscosity model is replacedwith the Carreau model and results are compared to a bi-viscosity model. It gives qualitatively correctresults if no rapid fiber orientation change occurs along the streamlines.

17




Deep learning methods for viscoplastic flows modelling17th June16:30-16:50

Session 4 Ekaterina Muravleva1, �

1 Skolkovo Institute of Science and Technology, Russia

This talk will be devoted to possible application of machine learning/deep learning approaches to vis-coplastic flows modelling. The key idea is to create a surrogate model that is able to predict the solutiondirectly from the parameters by interpolating results from simulations for several known parameters.As a model example we consider the Mosolov problem. We have shown that such approach can beaccurate and efficient [1] for the approximation of the velocity. I will present possible extensions of thisidea to the approximation of yielded/unyielded regions, which is more complicated since the dependenceon the parameter (Bingham number) is non-smooth.References[1] E. Muravleva, I. Oseledets, and D. Koroteev. ”Application of machine learning to viscoplastic flow modeling.”

Physics of Fluids 30.10 (2018): 103102.

18


A Phase Field approach for two-phase viscoelastic flows 17th June16:50-17:10Session 4Konstantinos Zografos1,�, Alexandre M. Afonso2, �, Robert J. Poole1, � and Monica S. N.

Oliveira3, �

1 School of Engineering, University of Liverpool, Brownlow Street, Liverpool L69 3GH, UK2 CEFT, Dep. Eng. Mecanica, Faculdade da Engenharia da Universidade do Porto, 4200-465 Porto, Portugal

3 James Weir Fluids Laboratory, Department of Mechanical and Aerospace Engineering, University ofStrathclyde, G1 1XJ, Glasgow, UK

In this work, we present the performance of a two-phase solver based on a diffuse interface approachknown as Phase Field. The second phase is added to the in-house single-phase solver, which is originallybased on an implicit finite-volume method that is appropriate for viscoelastic fluids [1]. The numeri-cal investigation of the two-phase system is achieved by solving the conservation of mass, momentumand the stress-constitutive equation together with the convective Cahn-Hilliard equation [2], which isresponsible for the transport of each phase. In contrast to sharp interface approaches, the interfacebetween the two fluids for this method adopts a continuum approach which is responsible for smooth-ing the inherent discontinuities [3]. Therefore, studies that are related to morphological changes of theinterface, such as droplet breakup and coalescence, are more easily investigated. In order to evaluatethe efficiency of the numerical implementation several problems such as the Rayleigh-Taylor instability,the oscillation of an initially square droplet, the rising bubble and the deformation of a droplet undershear deformation, are investigated. For all these cases an overall good performance of the solver isobserved. Especially for the case of the Rayleigh-Taylor instability which presents the most complexinterfacial patterns among all the investigated cases, the numerical implementation manages to captureboth qualitatively (complex concentration patterns) and quantitatively (positions of the moving fronts)the behaviour of the interfacial instability.

References[1] P. J. Oliveira, F. T. Pinho and G. A. Pinto, 1998, Numerical simulation of non-linear elastic flows with a

general collocated finite-volume method, J Non-Newton Fluid Mech, 79:1–43

[2] D. Jacqmin, 1999, Calculation of Two-Phase NavierStokes Flows Using Phase-Field Modeling, J Comput

Phys, 155:96–127

[3] J. Kim, 2012, Phase-Field Models for Multi-Component Fluid Flows, Comput Method Appl M, 12:613–661

19





Effects of wall slip on the stability of plane Poiseuille flow of Bingham fluids17th June17:10-17:30

Session 4 Hossein Rahmani1, � and Seyed M. Taghavi1, �

1 Department of Chemical Engineering, Universite Laval, Quebec, QC G1V 0A6, Canada

Slip boundary conditions at solid walls are frequently observed in non-Newtonian fluid flows. The wallslip quality depends on several parameters mostly associated with the fluid and solid wall properties.In the present study, we investigate the effects of wall slip boundary conditions on the stability of planePoiseuille flows of Bingham fluids, with the focus being on asymmetric wall slip conditions. Developingthe motion equations considering a general asymmetric slip law boundary conditions, we are able toanalyze the fluid motion for three types of wall boundary conditions i.e. no-slip, symmetric slip andasymmetric slip. In our analysis, a number of significant dimensionless numbers appear, including theReynolds number, the Bingham number, and the wall slip numbers. We rely on numerical techniquesto solve the equations obtained from the linear stability approach to evaluate the role of slip boundaryconditions on the flow stability. We consider different values for the wall slip numbers to create bothsymmetric and asymmetric slip cases. Our results show that wall slip boundary conditions generallyhave stabilizing effects on the flow.

20



Effects of elasticity, inertia and viscosity ratio on the drag coefficient of asphere translating through a viscoelastic fluid 17th June

17:30-17:50Session 4S.A. Faroughi1, �, Celio Fernandes2, �, Gareth H. McKinley1, � and J. Miguel Nobrega2, �

1 Department of Mechanical Engineering, Massachusetts Institute of Technology, USA2 i3N/Institute for Polymers and Composites, University of Minho, Portugal

The ability to simulate the behavior of dilute suspensions, considering Eulerian-Lagrangian approaches,requires proper drag models, which should be valid for a wide range of process and material parameters.These drag models allow to calculate the momentum exchange between the continuous and dispersedphases. The currently available drag models are only valid for inelastic constitutive fluid models. Thiswork aims at contributing to the development of drag models appropriate for dilute suspensions, wherethe continuous phase presents viscoelastic characteristics. To this aim, we parametrize the effects offluid elasticity, namely, the relaxation and retardation times, as well as inertia on the drag coefficientof a sphere translating through a viscoelastic fluid, described by the Oldroyd-B model. To calculatethe drag coefficient we resort to three-dimensional direct numerical simulations of unconfined viscoelas-tic flows past a stationary sphere, at different Reynolds number, Re, over a wide range of Deborahnumbers (< 9), and the polymer viscosity ratios. For low Re (< 1), we identified a non-monotonictrend for the drag coefficient correction (the ratio between the calculated drag coefficient and the oneobtained for Stokes-flow). It initially decreases with the increase of De, for low De values (< 1), whichis followed by a significant growth, due to the large elastic stresses that are developed on both thesurface and wake of the sphere. These behaviors, observed in the inertia less flow regime, are amplifiedas the polymer viscosity ratio approaches unity. At higher Re (> 1), the drag coefficient correction isfound to be always bigger than unity, but smaller than the enhancement calculated in creeping flow limit.

Acknowledgments:

The authors would like to acknowledge the funding by FEDER funds through the COMPETE 2020 Programme

and National Funds through FCT - Portuguese Foundation for Science and Technology under the projects

UID/CTM/50025/2013 and POCI-01-0247-FEDER-017656.

21





22

Session 5: Tuesday 18th [08h40 -10h20]

Chairman: Robert Poole

Viscoelastic flow and instabilities around microfluidic cylinders 18th June8:40-9:00Session 5Simon J. Haward1, �, Cameron Hopkins1, � and Amy Q. Shen1, �

1 Okinawa Institute of Science and Technology, Onna-son, Okinawa 904-0495, Japan

Using a state-of-the-art glass 3D-printing technique called selective laser-induced etching (SLE) wehave realized the fabrication of extremely slender microfluidic cylinders (with radii r ∼ O(10 µm),which retain rigidity due to the high material modulus. The cylinders are confined in high aspect ratiomicrochannels (α = H/W = 5 where H and W are the channel height and width, respectively), andpresent a low blockage ratio (β = W/2r ∼ O(0.1)). The high value of α results in a good approximationto a uniform flow along the cylinder axial direction, while the low value of β allows the influence of theup- and downstream stagnation points to become pronounced. Quantitative full field flow velocimetryand birefringence imaging are used to investigate a wide range of viscoelastic flows through the devices,including of highly elastic polyethylene oxide solutions (both shear-thinning and non-shear-thinning),relatively inelastic but shear-thinning xanthan gum solutions, and both shear-banding and non-shearbanding wormlike micellar (WLM) solutions. With increasing Weissenberg number (Wi), the shear-banding WLM solution in particular displays a range of viscoelastic flow instabilities, beginning with asteady flow asymmetry and progressing to a complex spatiotemporally fluctuating state. By examiningthe contrasting responses of a range of rheologically distinct fluids, we develop an understanding of theparticular properties of the WLM solution that are responsible for producing these behaviors. As well asrigid post geometries, SLE allows the fabrication of flexible structures by simply detaching one end of thecylinder from the glass substrate. We will briefly discuss ongoing works using such flexible micropoststo examine fluid-structure interactions in unsteady flows at high Wi but negligible inertia. Modelingthe complex flows in these new geometries should provide an interesting challenge to computationalrheologists and our quantitative experimental data should provide a valuable benchmarking comparisonfor such future studies.

23




Direct numerical simulations of turbulent planar jets of viscoelasticFENE-P fluids18th June

9:00-9:20Session 5 Mateus C. Guimaraes1, �, Nuno Pimentel1, �, Fernando T. Pinho2, � and Carlos B. da Silva1, �

1 IDMEC, Instituto Superior Tecnico, Universidade de Lisboa, Lisboa, Portugal2CEFT, Faculdade de Engenharia, Universidade do Porto, Porto, Portugal

Spatial direct numerical simulations (DNS) of turbulent planar jets of dilute polymer solutions, describedby the finitely extensible non-linear elastic constitutive equation closed with the Peterlin approxima-tion (FENE-P), were carried out in order to understand this canonical flow and formulate a theory forthe far-field. The Reynolds number based on the inlet flow was fixed at Re = 3500 with L2 = 104,β = 0.8 and the Weissenberg number (Wi) was varied between 0 (Newtonian) and 2.2. These are thefirst massive DNS of viscoelastic jet flows, which relied on the algorithm proposed by [1] to tackle thecomplex numerical challenges posed by these heavy computations. The data cover the entire transi-tional region as well as the fully turbulent far-field up to 18 slot widths. The influence of Wi on theturbulent statistics is discussed, revealing considerable changes in comparison to the Newtonian flow.In particular, the maximum value of the mean rate of dissipation of turbulent kinetic energy by thesolvent is reduced by more than 80% for the maximum Wi flow, clearly showing the influence of thepolymers on the flow development. The jet spreading and decay rates, as well as the Reynolds stressand mean velocity profiles were also significantly affected. An order of magnitude analysis and theassumption of self-similar behavior of the mean flow successfully lead to a theoretical description ofmean flow characteristics, validated by the DNS data. This far-field theory showed the laws of variationof the jet width (δ) and centreline velocity (Uc) to be δ ∼ x and Uc ∼ x−1/2, with the maximum shear

polymer stress varying as σ[p]c ∼ x−3.

References[1] T. Vaithianathan, A. Robert, J. G. Brasseur, L. R. Collins; An improved algorithm for simulating three-

dimensional, viscoelastic turbulence. J. Non-Newtonian Fluid Mech., 140, 3–22 (2006).

24





Simulation of viscoelastic fluid flows using lattice Boltzmann method 18th June9:20-9:40Session 5Y.Sumithra Reddy1, �, Sumesh P. Thampi1, � and Abhijit P. Deshpande1, �

1 Indian Institute of Technology Madras, Chennai, India

Numerical simulations play a key role in examining the influence of rheological properties on the flowbehaviour of viscoelastic fluids. Such simulations are quite challenging due to the coupling betweenthe flow induced evolution of polymer molecule conformations and the resulting stresses that influencethe flow. For the past many decades, the flow behaviour of these fluids has been extensively studiedusing conventional numerical schemes. In the present work, lattice Boltzmann method coupled withOldroyd-B and FENE-P as rheological models is employed. The evolution equation of the conformationtensor is solved using method of lines while the mass and momentum conservation are ensured usinga lattice Boltzmann algorithm. Two dimensional numerical simulations are performed to analyze theshear flow driven by a moving plate and a channel flow driven by an external force for the two flu-ids. Periodic boundary conditions are imposed in the flow direction while no slip boundary conditionsfor the velocity field and no flux boundary conditions for the conformation tensor are imposed on thechannel walls. The important non-dimensional parameters which characterize the viscoelastic fluid floweffects are Weissenberg number (Wi), Reynolds number (Re), and viscosity ratio (β) [1]. In both shearflow and channel flow problems, the effect of elasticity is such that the velocity profiles overshoot theterminal velocity profile, oscillate around this profile before eventually tending to it with increasingtime [2]. This oscillating nature of velocity profile with time is related to the conformational changes ofthe polymer molecules in terms of both orientation and stretch [2]. In order to further understand theeffects of flow-conformation tensor coupling on the flow profiles, a complex geometry - a converging-diverging channel is considered. This geometry has contributions from both shear and extensional flowsand can be considered as prototypical to understand the viscoelastic fluid flow through porous media [3].

References[1] O.Malaspinas, N. fietier and M.Deville, Lattice Boltzmann method for the simulation of viscoelastic fluid

flows, J.non-Newtonian Fluid Mech., 165: 1637–1653, (2010).

[2] N.D.Waters and M.J.King, Unsteady flow of an elastico-viscous liquid, Rheologica Acta, Band 9, Heft 3

(1970).

[3] Michael Cromer and L.Pamela Cook, A study of pressure-driven flow of wormlike micellar solutions through

a converging/diverging channel, Journal of Rheology, 60, 953 (2016)

25




Progress with triple layer core-annular flows18th June9:40-10:00Session 5 Parisa Sarmadi1, �, Otto Mierka2, �, Stefan Turek2, �, Sarah Hormozi3, � and Ian Frigaard1, �

1 University of British Columbia, Vancouver, BC, Canada2 TU-Dortmund, Dortmund, Germany

3 Ohio University, Ohio,USA

In pipelining heavy oils, a major challenge is to reliably achieve high rates of pressure drop reductionin stable annular flow patterns. In [1] we introduced a novel methodology for efficient transport ofheavy oil via a triple-layer core-annular flow. The lubricating outer layer is separated from the coreby a shaped interface (a yield stress fluid). The lubricant reduced the pressure drop, the yield stresseliminates the interfacial instabilities and the shaped interface produces lift force to balance buoyancyof the core. In [2] we focused on how to sculpt the interface in very stable controlled way for a desirableinterface shape, i.e. how to establish the flow. Here we give an overview of progress so far and presentnew results on 3D triple layer computations and on the buoyant motion of the core to reach its equi-librium position. The 3D computations are performed using an extension of FEATFLOW [3] which isbenchmarked against axisymmetric computations from [2]. The corresponding module in FEATFLOWis based on a special variant of the Multilevel Pressure Schur Complement approach in combinationwith Newton-Krylow-Multigrid solvers [4]. The discretization is based on the Q2-P1 Stokes elementwhich together with adaptively aligned meshes to track dynamically the layer interfaces leads to highlyaccurate results. Moreover, to improve the efficiency, a parallel implementation has been utilized. Wediscuss pertinent features of the code and applications. We finish with consideration of how and wherethe 3D code is needed, where it gives new physical insights and where simplified models are preferredfor process design and control.

References[1] P. Sarmadi, S. Hormozi, I. Frigaard, Triple-layer configuration for stable high-speed lubricated pipeline trans-

port. Physical Review Fluids 2, 044302 (2017).

[2] P. Sarmadi, S. Hormozi, I. Frigaard, Flow development and interface sculpting in stable lubricated pipeline

transport. Journal of Non-Newtonian Fluid Mechanics 261 (2018) 60–80.

[3] S. Turek et al., www.featflow.de, TU Dortmund, Germany.

[4] S. Turek, O. Mierka, S. Hysing, D. Kuzmin, Numerical study of a high order 3D FEM-Level Set approach

for immiscible flow simulation, S. Repin, T. Tiihonen, T. Tuovinen, Computational Methods in Applied Sci-

ences, Vol. 27, 65–91, Numerical methods for differential equations, optimization, and technological problems,

Springer, ISBN 978-94-007-5287-0, 2013.

26






www.featflow.de

Using the contravariant deformation tensor formulation in simulation ofviscoelastic fluid flow 18th June

10:00-10:20Session 5Martien A. Hulsen1, �, Mick A. Carrozza1, �, Markus Hutter1, � and Patrick D. Anderson1, �

1 Department of Mechanical Engineering, Eindhoven University of Technology, Eindhoven, The Netherlands

Numerical simulations of viscoelastic fluid flow commonly employ conformation tensor based constitu-tive models. Standard stabilisation techniques known from convection dominated flows, such as SUPGin finite elements, are required but also insufficient to solve flows at high Weissenberg numbers on fixedgrids. The reason is a numerical imbalance of the convection and deformation terms in the conformationtensor equations [1]. The log-conformation representation (LCR) technique, introduced in [1], fixes theimbalance and has become a standard technique to obtain solutions for high Weissenberg numbers. Adisadvantage is that the LCR technique involves the spectral decomposition of the conformation tensor,which complicates the use of fully implicit time integration techniques or finding a steady state solutionusing Newton-Raphson iteration.Motivated by the introduction of thermal fluctuations, in [2] the conformation tensor models are rewrit-ten in terms of the so-called contravariant deformation tensor. However, it is also suggested that itcould help in solving the high Weissenberg problem similar to the LCR-technique. Since the resultingequations do not require a spectral decomposition, Newton-Raphson iteration would be easy to apply.A disadvantage is the inherent time-dependent formulation in terms of on-going rotations, even if theflow is steady.In this talk, we will show results of our finite element implementation of the contravariant deformationformulation for various conformation tensor models. We consider the standard benchmarks for the flowaround a confined cylinder and an initially perturbed shear flow. The stability for high Weissenbergnumbers turns out to be very good and comparable to the LCR technique.References[1] R. Fattal and R. Kupferman. Constitutive laws for the matrix-logarithm of the conformation tensor. Journal

of Non-Newtonian Fluid Mechanics, 123(2):281–285, 2004.

[2] M. Hutter, M.A. Hulsen, and P.D. Anderson. Fluctuating viscoelasticity. Journal of Non-Newtonian Fluid

Mechanics, 256:42–56, 2018.

27





28


Chairman: Pierre Saramito

Verification and Validation of CFD simulations of non-Newtonian laminarflows on canonical test cases 18th June

10:50-11:10Session 6Stefano Lovato1, �, Guilherme Vaz2, �, Serge L. Toxopeus2, �, Geert Keetels1, � and Just Settels2, �

1 Delft University of Technology, P.O. Box 5, 2600 AA Delft, The Netherlands2 MARIN, P.O. Box 28, 6700 AA Wageningen, The Netherlands

The finite-volume CFD code ReFRESCO [2,3] has been improved to account for the dynamic effects offluid mud on ships manoeuvrability. The Herschel-Bulkley model was chosen for this purpose as it isrecognized to be suitable in describing the shear-thinning (pseudoplastic) and viscoplastic behavioursof mud suspensions [4]. The constitutive equation was implemented together with the Papanastasiouregularisation to overcome numerical difficulties due to the discontinuity of the Herschel-Bulkley modelat zero rate of strain. Code Verification exercise was performed on plane laminar Poiseuille flow withHerschel-Bulkley fluids [6] to verify the correctness, accuracy and robustness of code. Grid refinementstudies showed that the order of accuracy tends to the expected second order, although the more thenon-Newtonian character, the worse the accuracy obtained on the same grid. Subsequently, SolutionVerification and Validation were performed on the isothermal steady laminar flow around a sphere. Sim-ulations were performed on a full 3D mesh at several combinations of Reynolds and Bingham number,flow index and regularisation parameter. Numerical uncertainties on the drag coefficient were estimatedby means of a widely used procedure for maritime CFD applications [7] based on Richardson extrapo-lation and least-square fits. In analogy with results of the Code Verification, it was found that the morethe fluid has non-Newtonian character, the larger the numerical uncertainties. Validation against bothnumerical and experimental results available in literature revealed acceptable agreement both in termsof drag coefficient and yield surface. In conclusion, all the studies suggested that the ReFRESCO isable to solve non-Newtonian laminar flows but further research is still needed to assess its applicabilityto non-Newtonian problems with multiphase systems and/or in turbulent regime.References[1] ASME - Standard for Verification and Validation in computational fluid dynamics and heat transfer.

[2] REFRESCO www.refresco.org

[3] G. Vaz, F. Jaouen, M. Hoekstra, Free-surface viscous flow computations. Validation of URANS code

FRESCO, in: Proceedings of OMAE2009, Honolulu, Hawaii, USA, June 2009.

[4] P. Coussot, J. M. Piau, On the behavior of fine mud suspensions, Rheologica Acta 33 (3) (1994) 175–184.

[5] S. Lovato, G. Vaz, S.L. Toxopeus, G. Keetels, J. Settels, Code verification exercise for 2D poiseuille flow with

non-Newtonian fluid, NuTTS 2018.

[6] L. Eca, M. Hoekstra, A procedure for the estimation of the numerical uncertainty of CFD calculations based

on grid refinement studies, Journal of Computational Physics 262 (2014) 104–130.

29






www.refresco.org

Influence of polymer additives on small scale dynamics of aturbulent/non-turbulent interface in shearless flows18th June

11:10-11:30Session 6 Hugo Abreu1, �, Fernando T. Pinho2, � and Carlos B. da Silva1, �

1 IDMEC, Instituto Superior Tecnico, Universidade de Lisboa, Lisboa, Portugal2CEFT, Faculdade de Engenharia, Universidade do Porto, Porto, Portugal

Many flows are characterised by the coexistence of turbulent (T) and irrotational (or non-turbulent -NT) flow regions e.g. wakes, where the two flow regions are separated by a very sharp interface layer:the turbulent/non-turbulent interface (TNTI) [1]. When very long chains of molecules (polymers) aredissolved into a Newtonian solvent the resulting medium exhibits complex viscoelastic properties thatsubstantially affect the flow, and present substantially less entrainment than Newtonian fluids [2].New direct numerical simulations (DNS) of turbulent fronts bounded by irrotational regions in vis-coelastic fluids are carried out in order to investigate the characteristics of the turbulent/non-turbulentinterface (TNTI) layer. The viscoelastic fluid analysed here consists of a Newtonian solvent carrying avery small fraction of long chained polymer molecules, which is described using the finitely extensiblenonlinear elastic constitutive equation closed with the Peterlin approximation (FENE-P), and the newsimulations attain the highest Reynolds numbers yet observed for this fluid, in simulations or experi-ments. The work focusses on the small scale aspects associated with the entrainment mechanism thatexists at the edges of wakes, jets, mixing layers and boundary layers. Specifically, we analyse the en-strophy and kinetic energy dynamics and their role in the turbulent entrainment mechanism in TNTIlayers from viscoelastic fluids. A detailed analysis of the energy transfer shows that at these scalesenergy is injected into the fluid flow through polymer relaxation.

References[1] da Silva C. B., Hunt J. C. R., Eames I. and Westerwell J., (2014), Interfacial layers between regions of

different turbulence intensity, Annual Review of Fluid Mechanics, vol. 46, pp. 567–590.

[2] G. Cocconi, G., De Angelis, E., Frohnapfel, B., Baevsky, M. and Liberzon, A., (2017), Small scale dynamics

of a shearless turbulent/non-turbulent interface in dilute polymer solutions, Physics of Fluids, vol. 29, pp.

75–102.

30




New, faster and consistent FEM for viscoelastic flows 18th June11:30-11:50Session 6Stylianos Varchanis1, �, Alexandros Syrakos1, �, Yannis Dimakopoulos1, � and John Tsamopoulos1, �

1 Laboratory of Fluid Mechanics & Rheology, Department of Chemical Engineering, University of Patras,Greece

In this study, we propose a new, fully consistent and highly stable finite element formulation for thesimulation of viscoelastic flows. In our method, we have implemented a combination of classical finite el-ement stabilization techniques (PSPG/DEVSS-TG/SUPG) with the log-conformation representation ofthe constitutive equation that has allowed us to obtain numerically stable solutions at high-Weissenbergnumbers using equal order interpolation schemes for all variables. The validity of the FEM frameworkthat we will present is verified by comparing the numerical results of our method to those in the literaturefor three benchmark tests: the 2-dimensional flows of a viscoelastic fluid in a square lid-driven cavityand past a cylinder in a channel, and the 3-dimensional flow in a cubic lid-driven cavity. We considerboth direct steady-state and transient calculations using the Oldroyd-B and linear PTT models. In allcases we can reach, and in certain cases surpass, the maximum Weissenberg number values attainableby mixed finite element methods, but at a considerably lower computational cost and programmingeffort. In addition, we have performed mesh convergence tests illustrating that the proposed method isconvergent and features almost 2nd order accuracy in space.

31





Unsteady, temperature-dependent, and non-Newtonian simulations inplastics processing18th June

11:50-12:10Session 6 Stefanie Elgeti1, �, Jan Helmig1, �, and Philipp Knechtges2, �

1 CATS, RWTH Aachen University, Aechen, Germany2 SC-HPC, German Aerospace Center (DLR)

Co-rotating twin-screw extruders are very important processing devices within the plastic-producingindustry. A single twin-screw extrusion process allows to carry out multiple operations at the sametime, such as: melting, compounding, blending, pressurization, shaping. Furthermore, the modularstructure of the extruder enables to design configurations that are tailored to specific processes. How-ever, it is exactly this freedom that makes the handling of twin-screw extruders so complex. As of today,industrial design of manufacturing machinery is still very much experience-based. A design engineerwill prepare, assess and modify the initial design until it can withhold the desired quality requirements.Numerical simulation is an important asset in this process.We present a boundary-conforming space-time finite element method to compute the flow inside co-rotating, self-wiping twin-screw extruders. The mesh update is carried out using the newly developedSnapping Reference Mesh Update Method (SRMUM). It allows to compute time-dependent flow so-lutions inside twin-screw extruders equipped with conveying screw elements without any need for re-meshing and projections of solutions – making it a very efficient method. With respect to materialmodeling, we present unsteady, temperature-dependent, shear-thinning cases in 3D [1]. Futhermore, wepresent a novel log-conformation formulation of Oldroyd-type viscoelastic models [2].

References[1] Jan Helmig, Marek Behr, Stefanie Elgeti, Boundary-Conforming Finite Element Methods for Twin-Screw

Extruders: Unsteady - Temperature-Dependent - Non-Newtonian Simulations, submitted to Computer & Fluids

[2] Philipp Knechtges, 2018, Simulation of Viscoelastic Free-Surface Flows, PhD Thesis, RWTH Aachen Uni-

versity, https://publications.rwth-aachen.de/record/748930/files/748930.pdf.

32




https://publications.rwth-aachen.de/record/748930/files/748930.pdf

A fully-resolved immersed boundary numerical method to simulateparticle-laden viscoelastic flows 18th June

12:10-12:30Session 6Celio Fernandes1, �, S.A. Faroughi2, �, Olga S. Carneiro1, �, J. Miguel Nobrega1, � and Gareth H.

McKinley2, �

1 i3N/Institute for Polymers and Composites, University of Minho, Portugal2 Department of Mechanical Engineering, Massachusetts Institute of Technology, USA

Fluid-particle transport systems present a significant practical relevance, in several engineering applica-tions, such as oil sands mining and polymer processing [1]. In several cases it is essential to consider thatthe fluid, in which the particles are dispersed, has underlying viscoelastic characteristics [2]. For thisaim, a novel numerical algorithm was implemented on an open-source finite-volume viscoelastic fluidflow solver coupled with an immersed boundary method, by extending the open-source computationalfluid dynamics library CFDEMcoupling [3]. The code is able to perform fully-resolved simulations,wherein all flow scales, associated with the particle motion, are resolved. Additionally, the formulationemployed exploits the log-conformation tensor approach [4], to avoid high Weissenberg number issues.The accuracy of the algorithm was evaluated by studying several benchmark flows, namely: (i) thesedimentation of a sphere in a bounded domain; (ii) rotation of a sphere in simple shear flow; (iii)the cross-stream migration of a neutrally buoyant sphere in a steady Poiseuille flow. In each case, acomparison of the results obtained with the newly developed code with data reported in the literature[5, 6] is performed, in order to assess the code accuracy and robustness. Finally, the capability of thecode to solve a physical challenging problem is illustrated by studying the interactions and flow-inducedalignment of three spheres in a wall-bounded shear flow [7]. The role of the fluid rheology and finitegap size on both the approach rate and pathways of the solid particles are described.References[1] G.K. Batchelor. Sedimentation in a dilute dispersion of spheres. Journal of Fluid Mechanics, 52:245–268,

1972.

[2] S. Padhy, E.S.G. Shaqfeh, G. Iaccarino, J.F. Morris, and N. Tonmukayakul. Simulations of a sphere sedi-

menting in a viscoelastic fluid with cross shear flow. Journal of Non-Newtonian Fluid Mechanics, 197:48–60,

2013.

[3] CFDEMcoupling. CFDEM project, 2011 https://www.cfdem.com/cfdemcoupling.

[4] F. Pimenta, M.A. Alves. Stabilization of an open-source finite volume solver for viscoelastic fluid flows.

Journal of Non-Newtonian Fluid Mechanics, 239:85–104, 2017.

[5] D. Rajagopalan, M.T. Arigo, and G.H. McKinley. The sedimentation of a sphere through an elastic fluid

Part 2. Transient motion. Journal of Non-Newtonian Fluid Mechanics, 65:17–46, 1996.

[6] F. Snijkers, G.D’Avino, P.L. Maffettone, F. Greco, M.A. Hulsen, and J. Vermant. Effect of viscoelasticity

on the rotation of a sphere in shear flow. Journal of Non-Newtonian Fluid Mechanics, 166:363–372, 2011.

[7] C. Fernandes, S.A. Faroughi, O.S. Carneiro, J. Miguel Nobrega and G.H. McKinley. Fully-resolved simula-

tions of particle-laden viscoelastic fluids using an immersed boundary method. Journal of Non-Newtonian Fluid

Mechanics, 266:80–94, 2019.

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https://www.cfdem.com/cfdemcoupling

34


Chairman: Pam Cook

Shear-thickening of a non-colloidal suspension with a viscoelastic matrix 18th June14:00-14:20Session 7Adolfo Vazquez-Quesada1, �, Pep Espanol2, �, Roger I. Tanner3, � and Marco Ellero4, �

1 Department of Theoretical Condensed Matter Physics, Universidad Autonoma Madrid, Spain2 Departamento de Fisica Fundamental, UNED, 28080 Madrid, Spain

3 School of Aerospace, Mechanical and Mechatronic Engineering, University of Sydney4 Basque Center for Applied Mathematics (BCAM), Alameda de Mazarredo 14, 48400 Bilbao, Spain

In this work we study the rheology of a non-colloidal suspension of rigid spherical particles interactingwith a viscoelastic matrix. Three-dimensional numerical simulations under shear flow are performedusing the smoothed particle hydrodynamics method [1,2,3] and compared with experimental data avail-able in the literature using different constant-viscosity elastic Boger fluids [4,5,6,7]. The rheologicalproperties of the Boger matrices are matched in simulation under viscometric flow conditions. Suspen-sion rheology under dilute to semi-concentrated conditions (i.e. up to solid volume fraction ϕ = 0.3) isexplored. It is found that at small Deborah numbers, relative suspension viscosities ηr exhibit a plateauat every concentration investigated. By increasing the Deborah number De shear-thickening is observedwhich is related to the extensional-thickening of the underlying viscoelastic matrix. Under dilute condi-tions (ϕ = 0.05) numerical results for ηr agree quantitatively with experimental data both in the De−and ϕ-dependencies. Even under dilute conditions, simulations of full many-particle systems with no apriori specification of their spatial distribution need to be considered to recover precisely experimentalvalues. By increasing the solid volume fraction towards ϕ = 0.3, despite the fact that the trend iswell captured, the agreement remains qualitative with discrepancies arising in the absolute values ofηr obtained from simulations and experiments but also with large deviations existing among differentexperiments. With regard to the specific mechanism of elastic thickening, the microstructural analysisshows that elastic thickening correlates well with the averaged viscoelastic dissipation function, requir-ing a scaling as ∼ Deα with α > 2 to take place. Locally, despite the fact that regions of large polymerstretching (and viscoelastic dissipation) can occur everywhere in the domain, flow regions uniquely re-sponsible of the elastic thickening are well correlated to areas with significant extensional component [8].

References[1] Vazquez-Quesada A., Ellero, M., 2016 Rheology and microstructure of non-colloidal suspensions under shear

studied with smoothed particle hydrodynamics. Journal of Non-Newtonian Fluid Mechanics 233, 37–47.

[2] Vazquez-Quesada A., Ellero M., Espanol P., 2009 Smoothed particle hydrodynamic model for viscoelastic

fluids with thermal fluctuations. Physical Review E 79 (5), 056707.

[3] Vazquez-Quesada A., Ellero, M. 2017 SPH modeling and simulation of spherical particles interacting in a

viscoelastic matrix. Physics of Fluids 29 (12), 121609.

[4] Zarraga Isidro E., Hill D. A., Leighton, D. T. 2001 Normal stresses and free surface deformation in concen-

trated suspensions of noncolloidal spheres in a viscoelastic fluid. Journal of Rheology 45 (5), 1065–1084.

[5] Scirocco R., Vermant J., Mewis, J. 2005 Shear thickening in filled boger fluids. Journal of Rheology 49 (2),

551–567.

35





[6] Pasquino R., Grizzuti N., Maffettone P.L., Greco F. 2008 Rheology of dilute and semidilute noncolloidal

hard sphere suspensions. Journal of Rheology 52 (6), 1369–1384.

[7] Dai S.-C., Qi F., Tanner R.I. 2014 Viscometric functions of concentrated non-colloidal suspensions of spheres

in a viscoelastic matrix. Journal of Rheology 58 (1), 183–198.

[8] Vazquez-Quesada, A. Espanol P., Tanner R.I., Ellero, M. 2019 Shear-thickening of a non-colloidal suspension

with a viscoelastic matrix, J. Fluid Mech., under review.

36

Direct numerical simulation of turbulent flows of power law fluids overrough walls 18th June

14:20-14:40Session 7Hamidreza R. Anbarlooei1, �, C.M.M. Santos2, �, D.O.A. Cruz2, � and F. Ramos1, �

1 Department of Applied Mathematics, Institute of Mathematics, Federal University of Rio de Janeiro, Brazil2 Mechanical Engineering Program, Federal University of Rio de Janeiro, Brazil

Recently and due to its practical importance, several studies are focused on the turbulent flow of non-Newtonian fluids, specifically viscoelastic fluids. Although direct numerical simulations have been usedas a major research tool in this field, lack of any theoretical framework (such as Kolmogorov K41) raisesserious concerns about validity of the simulations. In series of papers, current authors extended theKolmogorov K41 theory to purely viscous and viscoplastic fluids [1,2]. Such a development allows toobtain Kolmogorov microscales necessary in DNS simulations (for example the gird size). Combiningwith a phenomenological model, a new family of Blasius-type friction equations was developed fornon-Newtonian fluids. In this work, we present the extension of our previous works to the turbulentflow of non-Newtonian fluids over rough surfaces. Unexpectedly, our results show that at high enoughReynolds number the classically fully rough regimes (constant friction factor) ends and normal smoothbehaviour resumes (Figure 1). To our knowledge such a phenomenon has not been reported before.Same configuration has also been studied numerically (DNS of rough channel) for the Power-Law model(Figure 2). The simulations reveal important differences in turbulent structures in the rough cases.

1

10

1000 10000 100000 1e+06

f

Re

Fully Rough

Current Exp. (Smooth)Current Exp. (Type A)

f=64/ReBlasius Eq.

Nikuradse (R/k=126)Nikuradse(R/k=507)

Figure 1 Friction factor for the roughness type

A, compared with smooth pipe, Nikuradse and

Blasius equation.

0

5

10

15

20

25

1 10 100

∆U+

U+

Y+

Rough Channel n=0.75

Smooth Channel n=0.75

U+ = C y

+(1/(4n+3))

Dodge Metzner

Figure 2 Shift in velocity profile, due to

roughness effects in Power-law fluid (n=0.75).

References[1] H.R. Anbarlooei, D.O.A Cruz, F. Ramos and A.P. Silva Freire, 2015, Phenomenological Blasius-type Friction

Equation for Turbulent Power-law Fluid Flows, Physical Review E (92).

[2] H.R. Anbarlooei, D.O.A. Cruz, F. Ramos, C.M.M. Santos, A.P. SilvaFreire, On the Connection between

Kolmogorov Microscales and Friction in Pipe Flows of Viscoplastic Fluids, Physica D: Nonlinear Phenomena

(376–377).

37





Role of polymer physics and extensional rheology in the development of anelastic instability in cross-slot flow18th June

14:40-15:00Session 7 Michael Cromer1, �, Larry Villasmil2, �, Henry Huang3, �, Alberto Serrano3, �, Alana Smith4, � and

Cameron Grube5, �

1 School of Mathematical Sciences, Rochester Institute of Technology, NY, USA2 Manufacturing and Mechanical Engineering Technology, Rochester Institute of Technology, NY, USA

3 School of Physics and Astronomy, Rochester Institute of Technology, NY, USA4 School of Individualized Study, Rochester Institute of Technology, NY, USA

5 Department of Mechanical Engineering, Rochester Institute of Technology, NY, USA

In the last decade, there has been intense experimental investigations into the development of an asym-metric instability in the flow of complex fluids in a cross-slot. To date, numerical investigations into theelastic instability have focused on models for dilute polymer solutions. Near the hyperbolic stagnationpoint in the cross-slot, the polymer chains orient and stretch resulting in extensional thickening thatfeeds back on the flow, and may cause the symmetric flow to become asymmetric. The question weseek to address in this talk is how additional mesoscopic physics, for example entanglement, branchingand breaking/reforming, affect the onset of this instability, and whether we can use such informationto control flow behavior.The focus of this work revolves around stability analysis and numerical simulations of the cross-slotflow of various constitutive models, namely the Giesekus, Pom-Pom and VCM models. The modelsdescribe different materials, including concentrated linear polymers, branched polymers, and wormlikemicelles, respectively. Each model contains material parameters that describe the mesoscopic physicsand, when adjusted, control the shear and extensional rheological behaviors, e.g., shear thinning andextensional thinning/thickening. Using a combination of linear stability analysis and simulations, weshow that each model can predict the formation of an asymmetric elastic instability. More importantly,we show how the model parameters, hence the physics, affect the onset of the instability, and, specif-ically, how the instability can be completely eliminated within certain regimes. This combination oflinear analysis and nonlinear computations provides a strong predictive tool for understanding the roleof the polymer physics in complex flows, which provides the ability to design a material with physicalproperties specifically tailored to perform effectively and efficiently on a particular application.

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mailto:@rit.edu



mailto:@rit.edu

Die-swell singularity for PTT and Giesekus fluids 18th June15:00-15:20Session 7Jonathan D. Evans1, �

1 Department of Mathematical Sciences, University of Bath, Bath, UK

The behaviour of the stress singularity for Phan-Thien Tanner and Giesekus fluids is determined fordie-swell. In the presence of a Newtonian solvent viscosity, the solvent stress dominates the polymerstresses near the transition point from the solid (stick) surface inside the die to the free (slip) surfaceoutside the die. Consequently, the solvent stress is O

(r−(1−λ0)

), where r is the radial distance to the

transition point and λ0 is the Newtonian eigenvalue (dependent upon the angle of separation betweenthe solid and free surfaces). We show that the polymer stresses are O

(r−4(1−λ0)/(5+λ0)

)for PTT and

O(r−4(1−λ0)(3−λ0)/4

)for Giesekus. The polymer stresses require boundary layers at both the solid and

free surfaces.

39


Laminar and turbulent flows of an elastoviscoplastic fluid18th June15:20-15:40

Session 7 Luca Brandt1, �, Marco E. Rosti1, �, Daulet Izabassarov1, �, Sarah Hormozi2, � and OutiTammisola1, �

1 Linne FLOW Centre and SeRC, KTH Mechanics, Stockholm, Sweden2 Department of Mechanical Engineering, Ohio University, Athens, OH, USA

We present numerical simulations of laminar and turbulent channel flow of an elastoviscoplastic fluid.The non-Newtonian flow is simulated by solving the full incompressible Navier-Stokes equations coupledwith the evolution equation for the elastoviscoplastic stress tensor [1], following the model proposed bySaramito [2].We show that in the laminar flow regime the friction factor increases monotonically with the Binghamnumber (yield stress) and decreases with the viscosity ratio, while in the turbulent regime the frictionfactor is almost independent of the viscosity ratio and decreases with the Bingham number, until theflow eventually returns to a fully laminar condition for large enough yield stresses. The turbulent flowsimulations are performed at a fixed bulk Reynolds number equal to 2800.In the limit of negligible elasticity, three main regimes are found in the turbulent case, depending onthe Bingham number: for low values, the friction Reynolds number and the turbulent flow statisticsonly slightly differ from those of a Newtonian fluid; for intermediate values of the Bingham number,the fluctuations increase and the inertial equilibrium range is lost. Finally, for higher values the flowcompletely laminarizes. These different behaviours are associated with a progressive increase of thevolume where the fluid is not yielded, growing from the centreline towards the walls as the Binghamnumber increases [3].Increasing the polymer relaxation time (Weissenberg number), we observe that the drag reduces andthe flow laminarizes at low values of the Bingham number. At higher Bingham, the flow is first lami-nar, becomes again turbulent at higher Weissenberg numbers and then finally also laminarizes. At thehighest yield stress considered here, the flow remains always laminar.In the final contribution, we will also present ongoing work on the behavior of rigid particles suspendedin an elastoviscoplastic fluid.

References[1] D. Izbassarov, M. E. Rosti, M. Niazi Ardekani, M. Sarabian, S. Hormozi, L. Brandt and O. Tammisola, 2018,

Int. J. Numer Meth Fluids, 88, 521–543, 2018.

[2] Saramito, P. 2007 A new constitutive equation for elastoviscoplastic fluid flows. J. Non-Newtonian Fluid

Mech., 145 (1), 1–14.

[3] M. E. Rosti, D, Izbassarov, O. Tammisola, S. Hormozi and L. Brandt 2018, Turbulent channel flow of an

elastoviscoplastic fluid. J. Fluid Mech., 853, 488–514.

40







Chairman: Tim Phillips

Non-linear Reynolds stress and conformation tensors models forviscoelastic turbulent flow 18th June

16:10-16:30Session 8Angela .O. Nieckele1, �, Roney L. Thompson2, � and Gilmar Mompean3, �

1 Dept. Mech. Eng., Pontifıcia Universidade Catolica, PUC-Rio, Rio de Janeiro, RJ 22451-900, Brazil2 COPPE, Department of Mechanical Engineering, Universidade Federal do Rio de Janeiro, Centro de

Tecnologia, Ilha do Fundo, 21945-970, Rio de Janeiro, RJ, Brazil3 Universite de Lille, Polytech’Lille. Unite de Mecanique de Lille (UML - EA 7512), Cite Scientifique, F-59655

Villeneuve d’Ascq, France.

An efficient way to reduce drag of a turbulent flow is the addition of small quantities of polymers inNewtonian fluids. For these applications, the linear constitutive equation for the Newtonian fluid mustbe modified to take account the presence of the viscoelastic behavior of the diluted polymers. As aconsequence, the linear relation with the strain rate deformation tensor is no more adequate. Mostavailable models employ the Boussinesq hypothesis, however, as elasticity increases, the Boussinesqhypothesis decreases its capability to capture the Reynolds stress tensor. Therefore, in the presentwork, to represent the anisotropy of the Reynolds stresses for viscoelastic flows, nonlinear eddy viscositymodels are proposed. To this end, tensorial projections of a DNS database of the turbulent flow of aviscoelastic fluid are performed in order to find the corresponding coefficients of nonlinear Reynoldsstress tensor models, as well as of mean Conformation tensor models. In addition to the symmetric partof the mean velocity gradient, the proposed models make use of the non-persistence-of-straining tensorto compose the tensor basis employed to represent the quantity to be modeled. The non-persistence-of-straining tensor captures the rotational character of the flow being a measure of how the local fluidavoids being persistently stretched. Direct Numerical Simulation (DNS) data for plane channel flowsat friction Reynolds number (Reτ = 180, 395, 590, 1000), Weissenberg number Weτ = 50 and 115, andthe maximum molecular extensibility L2 (L = 30 and 100) are used to build and evaluate the models,which show good agreement with DNS results, both for the Reynolds stress and Conformation tensor.

41




Numerical predictions for contraction-flow of Boger fluids under variousgeometrical configurations18th June

16:30-16:50Session 8 J.E. Lopez-Aguilar1, �, H.R.Tamaddon-Jahromi2, � and Michael F. Webster2, �

1 Facultad de Qumica, Departamento de Ingeniera Qumica, Universidad Nacional Autnoma de Mxico(UNAM), Ciudad Universitaria, Coyoacn, Mexico

2 Institute of Non-Newtonian Fluid Mechanics, Swansea University, College of Engineering, Swansea, UK

This work presents a comparative modelling study against the experimental findings of Binding and Wal-ters [1], when observing abrupt planar and axisymmetric contraction flow of maltose-syrup+water/polyacrylamide-based Boger fluids (highly-elastic constant shear-viscosity). Here, planar 4:1 contraction geometry isstudied, in which experimental pressure-drop rise and flow-structure evolution are matched numerically.Their observations, with increasing flow-rate (shear-rate), revealed the progression of two distinct flowpatterns witnessing excess pressure-drop enhancement. In circular configuration, flow-structure, trackedthrough vortex growth and evolution, showed continual salient-corner vortex growth and lip/elastic-corner vortex formation; in contrast, the planar case exhibited bulb-flow kinematic structures. Inaddition, we tackle the problem of matching experiments reported by Boger [2], when observing abruptcircular contraction flow of two Boger fluids (of constant shear-viscosity), namely a PAA/corn-syrup(Fluid-1) and a PIB/PB solution (Fluid-2). Three geometries, with contraction ratios, 2:1, 4:1, and 8:1are cited. Here experimentally, with increasing flow-rate (shear-rate), revealed the progression of twodistinct flow patterns. The first test-fluid showed continual salient-corner vortex growth, whilst in con-trast, the second test-fluid exhibited combined lip/salient-corner vortices. Predictions with an advancedhybrid finite element/volume sub-cell algorithm, enhanced with the ABS-f and VGR corrections [3], areable to elucidate the rheological properties that dictate such alternative vortex-enhancement patterns.This is achieved by employing the novel swIM and swAM constitutive models [4-6], with their strongcontrol on elongational response.References[1] D.M. Binding, K. Walters, On the use of flow through a contraction to estimating the extensional viscosity

of mobile polymer solutions, J. Non-Newton. Fluid Mech. 30 (1988) 233–250.

[2] D.V. Boger, Viscoelastic flows through contractions, Ann. Rev. Fluid Mech. 19: 157-82 (1987).

[3] J.E. Lpez-Aguilar, M.F. Webster, H.R. Tamaddon-Jahromi, O. Manero, High-Weissenberg predictions for

micellar fluids in contraction-expansion flows, J. Non-Newton. Fluid Mech., 222 (2015) 190–208.

[4] J.E. Lpez-Aguilar, M.F. Webster, H.R. Tamaddon-Jahromi, K. Walters, Numerical vs experimental pressure

drops for Boger fluids in sharp-corner contraction flow, Phys. Fluids 28 (2016) 103104.

[5] J.E. Lpez-Aguilar, M.F. Webster, H.R. Tamaddon-Jahromi, O. Manero, D.M. Binding, K. Walters, On the

use of continuous spectrum and discrete-mode differential models to predict contraction-flow pressure drops for

Boger fluids, Phys. Fluids 29 (2017) 121613.

[6] H.R. Tamaddon-Jahromi, J.E. Lpez-Aguilar, M.F. Webster, On modelling viscoelastic flow through abrupt

circular 8:1 contractions matching experimental pressure-drops and vortex structures, J. Non-Newton. Fluid

Mech. 251 (2018) 28–42

42


[email protected]


Study of polypropylene planar flow and extrudate swell: a comparisonbetween 3D numerical simulations and experiments 18th June

16:50-17:10Session 8Dahang Tang1, �, Flavio H. Marchesini1, �, Dagmar R. D’hooge1, � and Ludwig Cardon1, �

1 Department of Materials, Textiles and Chemical Engineering, Ghent University, Belgium

In this work, the flow of neat polypropylene through a slit die is investigated by performing extrusionexperiments and 3D numerical simulations. The experiments are carried out at 200◦C to evaluate theflow behavior of polypropylene melt through the die. The rheological properties of the melt are obtainedwith the aid of both rotational and capillary rheometers. The 3D flow governing equations are solvednumerically using the finite element method and ANSYS Polyflow software. Two constitutive equa-tions are employed to describe the rheological behavior of polypropylene melts, namely (i) generalizedNewtonian constitutive model with the cross law viscosity function and (ii) multi-mode viscoelasticPhan-Thien-Tanner (PTT) constitutive model. Model validation is performed based on die pressureand real time experimental HD imaging for 3D die swell characterization. The evolution of the swellratios in both width and height directions is investigated downstream the die exit. It is demonstratedthat the PTT based swell ratio in the width direction increases in a much lower rate than the swell ratioin the height direction until equilibrium is achieved in both directions. Therefore, the distance from thedie exit in which the final extrudate shape is obtained strongly depends on the die width. The findingsare underpinned through a detailed analysis of the simulated 3D stress and velocity field distributions,as discussed elsewhere [1]. In addition, the effect of flow geometry on extrudate swell is investigatedthrough a comparison between 3D and the corresponding 2D simulations. The discrepancy between thetwo simulation patterns is attributed to 3D effects on the flow behavior.References[1] Dahang Tang, Flavio H. Marchesini, Dagmar R. D’hooge, and Ludwig Cardon, 2019, Journal of Non-

Newtonian Fluid Mechanics 266, 33–45.

43





Local similarity solution for a steady laminar planar jet of a viscoelasticFENE-P fluid18th June

17:10-17:30Session 8 Saeed Parvar1, �, Carlos B. da Silva2, � and Fernando T. Pinho1, �

1 CEFT, Faculdade de Engenharia, Universidade do Porto, Porto, Portugal2 IDMEC, Instituto Superior Tecnico, Universidade de Lisboa, Lisboa, Portugal

The flow characteristics of laminar planar jet flows are self-similar far from the jet inlet, at largeReynolds numbers (Re), and the corresponding solution can be obtained after simplification of the gov-erning equations based on an order of magnitude analysis inspired by Blasius solution for the boundarylayer flow over a flat plate. For viscoelastic fluids such type of solution requires also that the ratiobetween inertial and elastic forces is large [1]. Subsequently, Olagunju [2] showed that self-similarityis local and that for a FENE-P model fluid a Blasius type of solution requires that the Weissenberg

number (Wi) and Re are such that Wi = O(Re−1/2

). In this work we present the local similarity so-

lution for the steady laminar planar jet flow of FENE-P fluids, and compare it with two other similaritysolutions: (1) a simplified version based on the assumption that at low enough Wi the variations of thenormal stream-wise (C11) and transverse (C22) components of the conformation tensor are small andsymmetrical and (2) another solution based on Olagunju´s [2] simplification of the momentum equation,which is unable to properly describe the conformation tensor variations across the jet. Subsequently,we compare the similar solutions with the results of two different numerical simulations for the laminarplanar jet flow of FENE-P fluids, one obtained with the freely available RheoFoam code and anotherusing our in-house code for Direct Numerical Simulation of planar jet flows, as a validation of its correctimplementation of the FENE-P constitutive equation.

References[1] K.R. Rajagopal, A.S. Gupta, A.S. Wineman, 1980, On a boundary layer theory for non-Newtonian fluids,

Lett. Appl. Sci. Engng. 18, 875–883.

[2] D. O. Olagunju, 2006, Local similarity solutions for boundary layer flow of a FENE-P fluid, Appl. Maths.

and Comp. 173, 593602.

44




Optimised microfluidic designs for in situ characterisation of complex fluidsand bio-particles 18th June

17:30-17:50Session 8Konstantinos Zografos1,2,�, Joana Fidalgo1, �, Manuel A. Alves3, �, Yanan Liu4, �, Anke Lindner4,�

and Monica S. N. Oliveira1, �

1 James Weir Fluids Laboratory, Department of Mechanical and Aerospace Engineering, University ofStrathclyde, G1 1XJ, Glasgow, UK

2 School of Engineering, University of Liverpool, Brownlow Street, Liverpool L69 3GH, UK3 Departamento de Engenharia Quımica, Centro de Estudos de Fenomenos de Transporte, Faculdade de

Engenharia da Universidade do Porto, Rua Doutor Roberto Frias, 4200-465 Porto, Portugal4 Laboratoire Matiere et Systemes Complexes, CNRS UMR 75057-Universite Paris Diderot, 10 rue Alice

Domond et Leonie Duquet, 75205 Paris CEDEX, France

We have designed a number of single and multi-stream microfluidic configurations for studying complexfluids under controlled deformation (e.g. gradients of shear rate or homogeneous extension rate). Theability to reach high strain rates while maintaining inertia low allow us to explore regions in the Weis-senberg - Reynolds number parameter space typically unreachable at the macro-scale, making theseplatforms very interesting for studies that require high elasticity numbers. We will discuss applicationsin the analysis of single molecule, particle dynamics and in extensional rheology, in which we typicallywant to delay the onset of elastic instabilities to obtain the ideal flow field. We use DNA and actinfilaments as model systems and observe their dynamics in customised microfluidic flow geometries usingfluorescence labelling techniques and microscopic tracking methods.

45







46

Session 9: Wednesday 19th [08h40 -10h20]

Chairman: Luca Brandt

Secondary flows in serpentine microchannels with viscoelastic fluids 19th June8:40-9:00Session 9Lucie Ducloue1,�, Laura Casanellas1, �, Simon J. Haward2, �, Robert J. Poole3, �, Manuel A.

Alves4, �, Sandra Lerouge5, �, Amy Q. Shen2, � and Anke Lindner1,�

1 Laboratoire de Physique et Mecanique des Milieux Heterogenes, UMR 7636, CNRS, ESPCI Paris, PSLResearch University, Universite Paris Diderot, Sorbonne Universite, Paris, 75005, France

2 Okinawa Institute of Science and Technology, Onna-son, Okinawa 904-0495, Japan3 School of Engineering, University of Liverpool, Brownlow Street, Liverpool L69 3GH, UK

4 Departamento de Engenharia Quımica, Centro de Estudos de Fenomenos de Transporte, Faculdade deEngenharia da Universidade do Porto, Rua Doutor Roberto Frias, 4200-465 Porto, Portugal

5 Laboratoire Matiere et Systemes Complexes, CNRS UMR 75057-Universite Paris Diderot, 10 rue AliceDomond et Leonie Duquet, 75205 Paris CEDEX, France

Secondary flows often occur in channel flows, in which small velocity components perpendicular to thestreamwise main velocity arise, due to the complexity of the microchannel and/or driven by the flowitself, either from inertial or non-Newtonian effects. In this work, we present experimental results forinertialess secondary flows of viscoelastic fluids in curved microchannels of rectangular cross-sectionand constant, but alternating, curvature, usually known as “serpentine channels”. Previous numericalcalculations [1] for this geometry showed that for low to moderate Weissenberg number flows, a steadysecondary flow develops, in the form of two counter-rotating vortices in the plane of the channel cross-section. We present experimental evidence and characterize such steady secondary flows, using PIVmeasurements in the plane of the channel, and using confocal visualisations of dye-stream transportin the cross-section plane. The streamlines computed from the velocity measurements and the relativevelocity magnitude of the secondary flows agree qualitatively with the numerical results. The resultspresented are important to elucidate the mechanism responsible for the onset of purely elastic instabil-ities in serpentine flows of viscoelastic fluids.

References[1] Poole RJ, Lindner A, Alves MA (2013) Viscoelastic secondary flows in serpentine channels. Journal of

Non-Newtonian Fluid Mechanics 201:10–16

47









Water entry of yield-stress droplets19th June9:00-9:20Session 9 Anselmo Pereira1, �, Rudy Valette1, � and Elie Hachem1, �

1 PSL Research University, MINES ParisTech, CEMEF - Centre for material forming, France

We study through direct numerical simulations the water entry of yield-stress droplets. Following theimpact on water free surfaces, these Non-Newtonian fluids undergo at least three stages: a spreading one(1), related to the impact acceleration, driven by the viscous dissipation and during which the dropletreaches its maximum deformation; a droplet-water interaction stage (2) along which the viscoplasticmaterial tends to recover its initial morphology before being finally dominated by the yield-stress (3),which prevents further deformations. Different final shapes are observed as a function of the capillary,viscous and inertial effects. Their link with the fluid rheology is discussed in the light of scaling laws,kinematic and energy exchange analyses.

48




Modelling of flexible fibres in viscous fluid flow 19th June9:20-9:40Session 9Naser Hamedi1, � and Lars G. Westerberg1, �

1 Department of Engineering Sciences and Mathematics, Division of Fluid and Experimental Mechanics, LuleaUniversity of Technology, SE-971 87 Lulea, Sweden

The current study relates to the development of a multiphase model of flexible fibre suspensions. Anunderstanding of the rheology and dynamics of the deformation of such suspension is desirable in orderto be able to fully disclose the flow behaviour from very low to very high shear rates. We present anapproach for numerically simulating the dynamics of flexible fibres employing a particle-level method.This is performed by investigating the fibre dynamics against several orbit classes - i.e. rigid, springy,flexible and complex rotation of the fibres [1-3] enabling the model to have all degrees of freedom(translation, rotation, bending and twisting). The three-dimensional Navier-Stokes equations whichdescribes the fluid motion are employed while the fibrous phase of the fluid is modeled as chains of fibersegments interacting with the fluid through viscous- and drag forces. The simulations are performedusing OpenFOAM and the numerical outcomes are validated against experimental data. The purposeof the modelling framework applied in this work is to enable the numerical model to be extended to a4-way coupling model, capturing shear thinning, shear thickening and the yield stress properties of afibrous fluid suspension.References[1] Arlov, A., O. Forgacs, and S. Mason, Particle motions in sheared suspensions IV. General behaviour of wood

pulp fibres. Svensk Papperstidn, 1958. 61(3): p. 61–67.

[2] Forgacs, O. and S. Mason, Particle motions in sheared suspensions: X. Orbits of flexible threadlike particles.

Journal of Colloid Science, 1959. 14(5): p. 473–491.

[3] Forgacs, O., The hydrodynamic behaviour of papermaking fibres. Fundamentals of papermaking fibres, 1958.

447.

49



Direct numerical simulation of heat transfer reduction in viscoelasticturbulent channel flow19th June

9:40-10:00Session 9 Radhakrishna Sureshkumar1, � and Kyoungyoun Kim2, �

1 Syracuse University, Syracuse, New York, USA2 Hanbat National University, Daejeon, South Korea

The effects of polymer stress on the analogy between momentum and heat transfer are examined byusing direct numerical simulation (DNS) of viscoelastic turbulent channel flow using constant heat fluxboundary condition. The Reynolds number based on the friction velocity and channel half height is125, and the Prandtl number is 5. The polymer stress is modelled using the Finitely Extensible Nonlin-ear Elastic-Peterlin (FENE-P) constitutive model, and low (15%), intermediate (34%), and high dragreduction (DR) (52%) cases are examined. Colburn analogy is found to be inapplicable for viscoelasticturbulent flows, suggesting dissimilarity between the momentum and heat transfer at the macroscopiccoefficient level. The mean temperature profile also shows trends different from the mean velocity profilein drag-reduced flows. In contrast to the dissimilarity in the mean profiles, the turbulent Prandtl num-ber, Prt, predicted by the DNS is near unity. This implies that turbulent heat transfer is still analogousto turbulent momentum transfer in drag-reduced flows, as in Newtonian flow. An increase in DR isaccompanied by an increase in the correlation coefficient ρuθ between the instantaneous fluctuations inthe streamwise velocity, u, and temperature θ. The correlation coefficient between u and wall-normalvelocity fluctuations, v, ρ−uv exhibits a profile similar to that of ρ−vθ in drag-reduced and Newtonianflows. Finally, the budget analysis of the transport equations of turbulent heat flux shows a strongsimilarity between the turbulent momentum and heat transfer, which is consistent with the predictionsof Prt near unity.References[1] K. Kim and R. Sureshkumar, Effects of polymer stresses on analogy between momentum and heat transfer

in drag-reduced turbulent channel flow, Physics of Fluids 30, 035106 (2018); https://doi.org/10.1063/1.5018859

50



Viscoelastic fluid flow simulation using coupled solvers in OpenFOAM R© 19th June10:00-10:20Session 9F. Pimenta1, � and Manuel A. Alves1, �

1 Departmento de Engenharia Quımica, Faculdade de Engenharia, Universidade do Porto, Rua Dr. RobertoFrias, 4200-465 Porto, Portugal

We describe the implementation of coupled solvers in the opensource rheoTool library [1], which wasdeveloped in the framework of OpenFOAM R©. The methodology is used to simulate pressure-drivenand electrically-driven flows of viscoelastic fluids. The coupled systems of equations are solved using theefficient and scalable (parallel) PETSc library [2]. The performance of the coupled solvers is assessedin two test-cases: (i) induced-charge electroosmotic flow of a Newtonian fluid around a cylinder; (ii)electroosmotic flow of viscoelastic fluids in a microfluidic contraction/expansion device, using the Phan-Thien-Tanner (PTT) constitutive equation. The numerical results show the superior robustness andaccuracy of coupled solvers, allowing the use of larger time-steps without reducing the numerical stabilityand preserving higher accuracy compared with classical segregated methodologies. Additionally, thecapabilities of the rheoTool library are illustrated in several single and two-phase benchmark flows ofviscoelastic fluids.References[1] rheoTool https://github.com/fppimenta/rheoTool

[2] PETSc library https://www.mcs.anl.gov/petsc/

51



https://github.com/fppimenta/rheoTool

https://www.mcs.anl.gov/petsc/

52

Author Index

AAbreu

Hugo ([email protected]), 30Advani

Suresh ([email protected]), 17Afonso

Alexandre ([email protected]), 19Alves

Manuel ([email protected]), 45, 47, 51Anbarlooei

Hamidreza ([email protected]),37

AndersonPatrick ([email protected]), 27

AusiasGilles ([email protected]), 17

BBorzacchiello

Domenico ([email protected]),9

BrandtLuca ([email protected]), 40

CCardon

Ludwig ([email protected]), 43Carneiro

Olga ([email protected]), 33Carrozza

Mick ([email protected]), 27Casanellas

Laura ([email protected]),47

ChambonGuillaume ([email protected]),

12Cook

Pamela ([email protected]), 5Cromer

Michael ([email protected]), 38Cruz

Daniel ([email protected]), 37

DD’Avino

Gaetano ([email protected]), 9D’hooge

Dagmar ([email protected]), 43Deshpande

Abhijit ([email protected]), 25Dimakopoulos

Yannis ([email protected]), 31Ducloue

Lucie ([email protected]), 47

EEdelvik

Fredrik ([email protected]),13

ElgetiStefanie ([email protected]), 32

ElleroMarco ([email protected]), 35

EspanolPep ([email protected]), 35

EtratiAli ([email protected]), 8

EvansJonathan ([email protected]), 39

FFerec

Julien ([email protected]), 17Faroughi

S ([email protected]), 33S ([email protected]) Joao

Nobrega ([email protected]), 21Fernandes

Celio ([email protected]), 21, 33Fidalgo

Joana ([email protected]), 45Frigaard

Ian ([email protected]), 8, 26

GGraham

Michael ([email protected]), 2Grube

Cameron (@rit.edu), 38Guimaraes

53

Mateus([email protected]),24

HHachem

Elie ([email protected]), 48Hamedi

Naser ([email protected]), 49Haward

Simon ([email protected]), 23, 47Helmig

Jan ([email protected]), 32Hopkins

Cameron ([email protected]), 23Horiuti

Kiyosi ([email protected]), 6Hormozi

Sarah ([email protected]), 26, 40Huang

Henry (@rit.edu), 38Hulsen

Martien ([email protected]), 27Hutter

Markus ([email protected]), 27

IIngelsten

Simon ([email protected]),13

IzabassarovDaulet ([email protected]), 40

JJoao

Nobrega ([email protected]), 33

KKadar

Roland ([email protected] ), 13Keetels

Geert ([email protected]), 29Kim

Kyoungyoun ([email protected]), 50Knechtges

Philipp ([email protected]), 32

LLopez-Aguilar

Jose ([email protected] ), 42Lerouge

Sandra ([email protected]),47

LindnerAnke ([email protected]), 45, 47

LiuYanan ([email protected]), 45

Lovato

Stefano ([email protected]), 29

MMackay

Alexander ([email protected]), 14Marchesini

Flavio ([email protected]), 43Mark

Andreas ([email protected]),13

McKeonBeverley ([email protected]), 2

McKinleyGareth ([email protected]), 21, 33

McMullenRyan ([email protected]), 2

MierkaOtto ([email protected]

dortmund.de),26

MompeanGilmar

([email protected]),11, 41

MuravlevaEkaterina ([email protected]), 18Larisa ([email protected]), 15

NNaccache

Monica ([email protected]), 4Nieckele

Angela ([email protected]), 41

OOliveira

Monica ([email protected]),19, 45

OzendaOlivier (olivier.ozenda@univ-grenoble-

alpes.fr),12

PParvar

Saeed ([email protected]), 44Pereira

Anselmo (anselmo.soeiro [email protected]), 11,48

PhillipsTimothy ([email protected]), 14

PimentaFrancisco ([email protected]), 51

PimentelNuno ([email protected]), 24

PinhoFernando ([email protected]), 24, 30, 44

PooleRobert ([email protected]), 19, 47

54

RRahmani

Hossein ([email protected]),20

RamosFabio ([email protected]), 37

ReddyY-Sumithra ([email protected]),

25Ribeiro

Sergio ([email protected]), 4Rosti

Marco ([email protected]), 40

SSantos

Cecilia ([email protected]), 37Saramito

Pierre ([email protected]), 7,12

SarmadiParisa ([email protected]), 26

SerranoAlberto ([email protected]), 38

SettelsJust ([email protected]), 29

ShekarAshwin ([email protected]), 2

ShenAmy ([email protected]), 23, 47

SilvaCarlos ([email protected]), 24, 30, 44Luisa ([email protected]),

9Smith

Alana ([email protected]), 38Sureshkumar

Radhakrishna ([email protected]), 50Syrakos

Alexandros([email protected]), 31

TTaghavi

Seyed-Mohammad ([email protected]),20

Tamaddon-JahromiHamid ([email protected]), 42

TammisolaOuti ([email protected]), 40

Tang

Dahang ([email protected]), 43Tanner

Roger ([email protected]), 1, 35Thampi

Sumesh ([email protected]), 25Thompson

Roney([email protected]),11, 41

ToxopeusSerge ([email protected]), 29

TsamopoulosJohn ([email protected]), 31

TurekStefan ([email protected]

dortmund.de), 3,26

VValette

Rudy ([email protected]),48

VarchanisStylianos ([email protected]),

31Vaz

Guilherme ([email protected]), 29Vazquez-Quesada

Adolfo ([email protected]), 35Villasmil

Larry ([email protected]), 38

WWang

Sung-Ning ([email protected]), 2Webster

Michael ([email protected]), 42Westerberg

Lars ([email protected]), 49Westervoss

Patrick([email protected]),3

ZZhou

Lin ([email protected]), 5Zografos

Konstantinos ([email protected]), 19,45

55

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