1. S. Varchanis, Syrakos

PEGAFEM-V: A new petrov-galerkin finite element method for free surface viscoelastic flows Journal Article

In: Journal of Non-Newtonian Fluid Mechanics, 284 , pp. 104365, 2020.

Abstract | Links | BibTeX | Tags: finite element method, free surface, petrov-galerkin, Viscoelastic flows

@article{Varchanis2020c,

title = {PEGAFEM-V: A new petrov-galerkin finite element method for free surface viscoelastic flows},

author = {Varchanis, S., Syrakos, A., Dimakopoulos, Y., Tsamopoulos, J.},

doi = {10.1016/j.jnnfm.2020.104365},

year = {2020},

date = {2020-08-07},

journal = {Journal of Non-Newtonian Fluid Mechanics},

volume = {284},

pages = {104365},

abstract = {The recently proposed finite element (FE) formulation for viscoelastic flows that allows the use of equal order linear interpolants for all variables and simultaneously does not suffer from the high Weissenberg number problem, is extended to free surface flows. The coupling of this Petrov-Galerkin stabilized FE formulation with the quasi-elliptic mesh generator allows us to obtain stable numerical solutions in highly deformed meshes and for very high values of the Weissenberg number (Wi). We present benchmark solutions in three free surface flows: the axisymmetric filament stretching, the elastocapillary-driven formation of bead-on-a-string, and the 2-dimensional, planar extrudate swell flow. In all cases, we attain converged solutions for values of Wi that have never been reached before by FE. The accuracy and robustness of the proposed numerical scheme are illustrated by achieving mesh and time step convergence under extreme mesh deformation conditions such as the bead-on-a-string (BOAS) formation during filament stretching. The formulation is enriched further with a discontinuity capturing scheme that enhances the quality of the solution around singularities dramatically. Finally, our simulations reveal for the first time the existence of lip-vortices in the steady planar extrudate-swell flow of Oldroyd-B fluids, which converge with mesh refinement.},

keywords = {finite element method, free surface, petrov-galerkin, Viscoelastic flows},

pubstate = {published},

tppubtype = {article}

}

The recently proposed finite element (FE) formulation for viscoelastic flows that allows the use of equal order linear interpolants for all variables and simultaneously does not suffer from the high Weissenberg number problem, is extended to free surface flows. The coupling of this Petrov-Galerkin stabilized FE formulation with the quasi-elliptic mesh generator allows us to obtain stable numerical solutions in highly deformed meshes and for very high values of the Weissenberg number (Wi). We present benchmark solutions in three free surface flows: the axisymmetric filament stretching, the elastocapillary-driven formation of bead-on-a-string, and the 2-dimensional, planar extrudate swell flow. In all cases, we attain converged solutions for values of Wi that have never been reached before by FE. The accuracy and robustness of the proposed numerical scheme are illustrated by achieving mesh and time step convergence under extreme mesh deformation conditions such as the bead-on-a-string (BOAS) formation during filament stretching. The formulation is enriched further with a discontinuity capturing scheme that enhances the quality of the solution around singularities dramatically. Finally, our simulations reveal for the first time the existence of lip-vortices in the steady planar extrudate-swell flow of Oldroyd-B fluids, which converge with mesh refinement.2. Fraggedakis, D; Pavlidis, M; Dimakopoulos, Y; Tsamopoulos, J

On the velocity discontinuity at a critical volume of a bubble rising in a viscoelastic fluid Journal Article

In: Journal of Fluid Mechanics, 789 , pp. 310-346, 2016, ISSN: 00221120, (cited By 31).

Abstract | Links | BibTeX | Tags: bubbles, drops, free surface, interfacial flows, non-Newtonian flows

@article{Fraggedakis2016310,

title = {On the velocity discontinuity at a critical volume of a bubble rising in a viscoelastic fluid},

author = {D Fraggedakis and M Pavlidis and Y Dimakopoulos and J Tsamopoulos},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-84954500253&doi=10.1017%2fjfm.2015.740&partnerID=40&md5=c2b49680bd59b9b7015498cf1615ca98},

doi = {10.1017/jfm.2015.740},

issn = {00221120},

year = {2016},

date = {2016-01-01},

journal = {Journal of Fluid Mechanics},

volume = {789},

pages = {310-346},

abstract = {We examine the abrupt increase in the rise velocity of an isolated bubble in a viscoelastic fluid occurring at a critical value of its volume, under creeping flow conditions. This 'velocity discontinuity', in most experiments involving shear-thinning fluids, has been somehow associated with the change of the shape of the bubble to an inverted teardrop with a tip at its pole and/or the formation of the 'negative wake' structure behind it. The interconnection of these phenomena is not fully understood yet, making the mechanism of the 'velocity jump' unclear. By means of steady-state analysis, we study the impact of the increase of bubble volume on its steady rise velocity and, with the aid of pseudo arclength continuation, we are able to predict the stationary solutions, even lying in the discontinuous area in the diagrams of velocity versus bubble volume. The critical area of missing experimental results is attributed to a hysteresis loop. The use of a boundary-fitted finite element mesh and the open-boundary condition are essential for, respectively, the correct prediction of the sharply deformed bubble shapes caused by the large extensional stresses at the rear pole of the bubble and the accurate application of boundary conditions far from the bubble. The change of shape of the rear pole into a tip favours the formation of an intense shear layer, which facilitates the bubble translation. At a critical volume, the shear strain developed at the front region of the bubble sharply decreases the shear viscosity. This change results in a decrease of the resistance to fluid displacement, allowing the developed shear stresses to act more effectively on bubble motion. These coupled effects are the reason for the abrupt increase of the rise velocity. The flow field for stationary solutions after the velocity jump changes drastically and intense recirculation downstream of the bubble is developed. Our predictions are in quantitative agreement with published experimental results by Pilz & Brenn (J. Non-Newtonian Fluid Mech., vol. 145, 2007, pp. 124-138) on the velocity jump in fluids with well-characterized rheology. Additionally, we predict shapes of larger bubbles when both inertia and elasticity are present and obtain qualitative agreement with experiments by Astarita & Apuzzo. © 2016 Cambridge University Press.},

note = {cited By 31},

keywords = {bubbles, drops, free surface, interfacial flows, non-Newtonian flows},

pubstate = {published},

tppubtype = {article}

}

We examine the abrupt increase in the rise velocity of an isolated bubble in a viscoelastic fluid occurring at a critical value of its volume, under creeping flow conditions. This 'velocity discontinuity', in most experiments involving shear-thinning fluids, has been somehow associated with the change of the shape of the bubble to an inverted teardrop with a tip at its pole and/or the formation of the 'negative wake' structure behind it. The interconnection of these phenomena is not fully understood yet, making the mechanism of the 'velocity jump' unclear. By means of steady-state analysis, we study the impact of the increase of bubble volume on its steady rise velocity and, with the aid of pseudo arclength continuation, we are able to predict the stationary solutions, even lying in the discontinuous area in the diagrams of velocity versus bubble volume. The critical area of missing experimental results is attributed to a hysteresis loop. The use of a boundary-fitted finite element mesh and the open-boundary condition are essential for, respectively, the correct prediction of the sharply deformed bubble shapes caused by the large extensional stresses at the rear pole of the bubble and the accurate application of boundary conditions far from the bubble. The change of shape of the rear pole into a tip favours the formation of an intense shear layer, which facilitates the bubble translation. At a critical volume, the shear strain developed at the front region of the bubble sharply decreases the shear viscosity. This change results in a decrease of the resistance to fluid displacement, allowing the developed shear stresses to act more effectively on bubble motion. These coupled effects are the reason for the abrupt increase of the rise velocity. The flow field for stationary solutions after the velocity jump changes drastically and intense recirculation downstream of the bubble is developed. Our predictions are in quantitative agreement with published experimental results by Pilz & Brenn (J. Non-Newtonian Fluid Mech., vol. 145, 2007, pp. 124-138) on the velocity jump in fluids with well-characterized rheology. Additionally, we predict shapes of larger bubbles when both inertia and elasticity are present and obtain qualitative agreement with experiments by Astarita & Apuzzo. © 2016 Cambridge University Press.3. Chatzidai, N; Dimakopoulos, Y; Tsamopoulos, J

Viscous effects on the oscillations of two equal and deformable bubbles under a step change in pressure Journal Article

In: Journal of Fluid Mechanics, 673 , pp. 513-547, 2011, ISSN: 00221120, (cited By 7).

Abstract | Links | BibTeX | Tags: bubble, free surface, interfacial flows

@article{Chatzidai2011513,

title = {Viscous effects on the oscillations of two equal and deformable bubbles under a step change in pressure},

author = {N Chatzidai and Y Dimakopoulos and J Tsamopoulos},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-79956033066&doi=10.1017%2fS0022112010006361&partnerID=40&md5=bc005bf9ad09f9970c34a29bb1f2459a},

doi = {10.1017/S0022112010006361},

issn = {00221120},

year = {2011},

date = {2011-01-01},

journal = {Journal of Fluid Mechanics},

volume = {673},

pages = {513-547},

abstract = {According to linear theory and assuming the liquids to be inviscid and the bubbles to remain spherical, bubbles set in oscillation attract or repel each other with a force that is proportional to the product of their amplitude of volume pulsations and inversely proportional to the square of their distance apart. This force is attractive, if the forcing frequency lies outside the range of eigenfrequencies for volume oscillation of the two bubbles. Here we study the nonlinear interaction of two deformable bubbles set in oscillation in water by a step change in the ambient pressure, by solving the Navier-Stokes equations numerically. As in typical experiments, the bubble radii are in the range 1-1000 m. We find that the smaller bubbles (~5 m) deform only slightly, especially when they are close to each other initially. Increasing the bubble size decreases the capillary force and increases bubble acceleration towards each other, leading to oblate or spherical cap or even globally deformed shapes. These deformations may develop primarily in the rear side of the bubbles because of a combination of their translation and harmonic or subharmonic resonance between the breathing mode and the surface harmonics. Bubble deformation is also promoted when they are further apart or when the disturbance amplitude decreases. The attractive force depends on the Ohnesorge number and the ambient pressure to capillary forces ratio, linearly on the radius of each bubble and inversely on the square of their separation. Additional damping either because of liquid compressibility or heat transfer in the bubble is also examined. Copyright © Cambridge University Press 2011.},

note = {cited By 7},

keywords = {bubble, free surface, interfacial flows},

pubstate = {published},

tppubtype = {article}

}

According to linear theory and assuming the liquids to be inviscid and the bubbles to remain spherical, bubbles set in oscillation attract or repel each other with a force that is proportional to the product of their amplitude of volume pulsations and inversely proportional to the square of their distance apart. This force is attractive, if the forcing frequency lies outside the range of eigenfrequencies for volume oscillation of the two bubbles. Here we study the nonlinear interaction of two deformable bubbles set in oscillation in water by a step change in the ambient pressure, by solving the Navier-Stokes equations numerically. As in typical experiments, the bubble radii are in the range 1-1000 m. We find that the smaller bubbles (~5 m) deform only slightly, especially when they are close to each other initially. Increasing the bubble size decreases the capillary force and increases bubble acceleration towards each other, leading to oblate or spherical cap or even globally deformed shapes. These deformations may develop primarily in the rear side of the bubbles because of a combination of their translation and harmonic or subharmonic resonance between the breathing mode and the surface harmonics. Bubble deformation is also promoted when they are further apart or when the disturbance amplitude decreases. The attractive force depends on the Ohnesorge number and the ambient pressure to capillary forces ratio, linearly on the radius of each bubble and inversely on the square of their separation. Additional damping either because of liquid compressibility or heat transfer in the bubble is also examined. Copyright © Cambridge University Press 2011.