Grétar Tryggvason - Academia.edu (original) (raw)

Papers by Grétar Tryggvason

Biophysical Journal, 1999

The effect of a nonuniform solute concentration on the osmotic transport of water through the bou... more The effect of a nonuniform solute concentration on the osmotic transport of water through the boundaries of a simple model cell is investigated. A system of two ordinary differential equations is derived for the motion of a single cell in the limit of a fast solute diffusion, and an analytic solution is obtained for one special case. A two-dimensional finite element model has been developed to simulate the more general case (finite diffusion rates, solute gradient induced by a solidification front). It is shown that the cell moves to regions of lower solute concentration due to the uneven flux of water through the cell boundaries. This mechanism has apparently not been discussed previously. The magnitude of this effect is small for red blood cells, the case in which all of the relevant parameters are known. We show, however, that it increases with cell size and membrane permeability, so this effect could be important for larger cells. The finite element model presented should also have other applications in the study of the response of cells to an osmotic stress and for the interaction of cells and solidification fronts. Such investigations are of major relevance for the optimization of cryopreservation processes.

International Journal of Multiphase Flow, Oct 1, 2017

The effect of an insoluble surfactant on the structure of turbulent bubbly upflow in a vertical c... more The effect of an insoluble surfactant on the structure of turbulent bubbly upflow in a vertical channel is examined by direct numerical simulations (DNS). For nearly spherical bubbles the presence of a surfactant reduces the lateral lift on the bubbles and changes the structure of the flow in major ways. Clean bubbles are driven to the walls by the lift force and the void fraction distribution has a well defined peak near the walls, resulting in significant reduction in flow rate. Bubbles with strong enough surfactants do not experience significant lateral lift and remain in the bulk flow. Indeed, when surfactant is present the addition of bubbles to a turbulent flow has relatively little effect on the flow, once the pressure gradient is adjusted to account for the reduced weight of the mixture.

International Journal of Multiphase Flow, Oct 1, 2016

Data generated by direct numerical simulations (DNS) of bubbly up-flow in a periodic vertical cha... more Data generated by direct numerical simulations (DNS) of bubbly up-flow in a periodic vertical channel is used to generate closure relationships for a simplified two-fluid model for the average flow. Nearly spherical bubbles, initially placed in a fully developed parabolic flow, are driven relatively quickly to the walls, where they increase drag and slowly reduce the flow rate. Once the flow rate has been decreased enough, some of the bubbles move back into the channel interior and the void fraction there approaches the value needed to balance the weight of the mixture and the imposed pressure gradient. A database is generated by averaging the DNS results over planes parallel to the walls, and a Model Averaging Neural Network (MANN) is used to find the relationships between unknown closure terms in a simple model equations for the average flow and the resolved variables. The closure relations are then tested, by following the evolution of different initial conditions, and it is found that the model predictions are in reasonably good agreement with DNS results.

Bulletin of the American Physical Society, Nov 24, 2020

Bulletin of the American Physical Society, Nov 25, 2019

Bulletin of the American Physical Society, Nov 24, 2015

Submitted for the DFD15 Meeting of The American Physical Society DNS and Modeling of Turbulent Ga... more Submitted for the DFD15 Meeting of The American Physical Society DNS and Modeling of Turbulent Gas-Liquid Channel Flows 1 GRE-TAR TRYGGVASON, MING MA, JIACAI LU, Univ of Notre Dame-DNS studies of gas-liquid flows in vertical turbulent channels are presented. Results from a simulation of a pressure driven turbulent channel flow with a friction Reynolds number of 500 where a large number of bubbles of different sizes are injected at time zero, shows that small bubbles quickly migrate to the wall, but the flow takes much longer to adjust to the new bubble distribution. The evolution of turbulent statistic and the void fraction distribution is examined, including area concentration and the components of the area tensor. Another series of simulations of bubbles injected into turbulent channel flow, where the bubbles are allowed to coalesce and break apart, is also presented. For high enough surface tension all the bubbles coalesce into one large slug, but as the surface tension is reduced, large enough bubbles break up and the flow eventually reaches an approximate equilibrium where coalescence is matched by breakups. The resulting state generally contains bubbles with a distribution of sizes. The various quantities characterizing the flow are followed over time and their dependency of the flow parameters examined. Preliminary attempts to model the flow using a set of averaged equations, using closure relations derived from the DNS data are discussed.

Social Science Research Network, 2022

Nucleation and Atmospheric Aerosols, 2020

Journal of Computational Physics, Apr 1, 2021

International Journal of Heat and Mass Transfer, Aug 1, 2019

Fully resolved simulations are used to study a few aspects of fused filament fabrication. The sim... more Fully resolved simulations are used to study a few aspects of fused filament fabrication. The simulations are done using a finite-volume/front tracking method where the governing conservation equations are solved for the air and polymer flow in a rectangular cuboid using a fixed structured grid and the interface is tracked using connected marker particles. The nozzle is modeled as a moving source for mass and heat. The viscosity of the polymer depends on the shear rate and the temperature, and once the polymer cools down and the viscosity is high enough, it is effectively solid. The effects of the control parameters are examined for the construction of three objects: an inverted cone, a ''bridge", and a rectangle formed by parallel filaments. The results show that the shape of the objects depends sensitively on the control parameters. We find that an inverted cone, built with partially overlapping filaments, requires the polymer to quickly become very viscous for a stable shape, that parallel filaments need to be spaced closely for the formation of a large contact area and we show how the sagging of a freely suspended filament depends on the injection temperature.

Rapid Prototyping Journal, Sep 28, 2018

Purpose-This paper continues the development of a comprehensive methodology for fully resolved nu... more Purpose-This paper continues the development of a comprehensive methodology for fully resolved numerical simulations of fusion deposition modeling. Design/methodology/approach-A front-tracking/finite volume method introduced in Part I to simulate the heat transfer and fluid dynamics of the deposition of a polymer filament on a fixed bed is extended by adding an improved model for the injection nozzle, including the shrinkage of the polymer as it cools down, and accounting for stresses in the solid. Findings-The accuracy and convergence properties of the new method are tested by grid refinement and the method is shown to produce convergent solutions for the shape of the filament, the temperature distribution, the shrinkage and the solid stresses. Research limitations/implications-The method presented in the paper focuses on modeling the fluid flow, the cooling and solidification, as well as volume changes and residual stresses, using a relatively simple viscoelastic constitutive model. More complex material models, depending, for example, on the evolution of the configuration tensor, are not included. Practical implications-The ability to carry out fully resolved numerical simulations of the fusion deposition process is expected to be critical for the validation of mathematical models for the material behavior, to help explore new deposition strategies, and to provide the "ground truth" for the development of reduced order models. Originality/value-The paper completes the development of the first numerical method for fully resolved simulation of fusion filament modeling.

Computer Methods in Applied Mechanics and Engineering, Apr 1, 2019

Highlights • A front-tracking/finite volume method is introduced to model Fused Filament Fabricat... more Highlights • A front-tracking/finite volume method is introduced to model Fused Filament Fabrication. • Fluid flow, heat transfer, viscoelasticity and moving boundary are included. • A fully resolved simulation is presented with accuracy and convergence validations. • Effects of including viscoelastic stresses are presented and discussed.

APS Division of Fluid Dynamics Meeting Abstracts, Nov 1, 2019

Bulletin of the American Physical Society, Nov 19, 2018

ASME Press eBooks, 2018

Recent progress in direct numerical simulations (DNS) of gas-liquid flows is discussed. We start ... more Recent progress in direct numerical simulations (DNS) of gas-liquid flows is discussed. We start by reviewing briefly DNS of cavitating and non-cavitating flows and then address two advanced topics: How to use results for bubbly flows to help generate improved models for the large-scale or average flow, and simulations of flows undergoing massive topology changes. For the first topic we have started to experiment with the use of machine learning methods to extract complex correlations from the DNS data and for the second we are exploring how to diagnose the flow and describe its structure.

International Journal of Heat and Fluid Flow, Dec 1, 2015

The effects of bubbles and inclination angle on the flow and heat transfer in a channel are exami... more The effects of bubbles and inclination angle on the flow and heat transfer in a channel are examined by direct numerical simulations (DNS), where every continuum length and time scale are resolved using a front-tracking/finite volume method. Earlier simulations of bubbles in turbulent flows in vertical channels have shown that the presence of the bubbles increases the Nusselt number, compared to flow without bubbles. Here the flow and the enhancement of the heat transfer is described as a function of the angle of inclination of a channel where a constant heat flux is applied at the walls. The bubbles are nearly spherical and the void fraction is 3%. The results show that the temperature difference between the wall where the bubbles are concentrated and the fluid near to that wall is lower when the channel is inclined 30°and 60°than for vertical and horizontal channels, indicating that the heat transfer is more efficient in these cases.

Physical review fluids, Aug 30, 2018

Multifluid flows in a vertical channel are examined by direct numerical simulations, for situatio... more Multifluid flows in a vertical channel are examined by direct numerical simulations, for situations where the topology of the interface separating the different fluids changes. Several bubbles are initially placed in a turbulent channel flow at a sufficiently high void fraction so that the bubbles collide and the liquid film between them becomes very thin. This film is ruptured at a predetermined thickness and the bubbles are allowed to coalesce. For the cases with high surface tension the bubbles continue to coalesce, eventually forming one large bubble. At low surface tension, on the other hand, the large bubbles break up again, sometimes undergoing repeated coalescence and breakup. The evolution of various integral quantities, such as the average flow rate, wall-shear, and interface area are monitored and compared for different governing parameters. Averages of the flow field and the phase distribution over planes parallel to the walls are also examined, and the microstructure, at statistically steady state, is examined using low order probability functions.

APS Division of Fluid Dynamics Meeting Abstracts, Nov 1, 2019

Abstract The breakup of a periodic jet is examined computationally, using a front-tracking/finite... more Abstract The breakup of a periodic jet is examined computationally, using a front-tracking/finite-volume method, where the interface is represented by connected marker points moving with the fluid, while the governing equations are solved on a fixed grid. Tracking the interface allows control of whether topology changes take place or not. The Reynolds and Capillary numbers are kept relatively low ( R e = 150 and C a = 2 ) so most of the flow is well resolved. The effect of topology changes is examined by following the jet until it has mostly disintegrated, for different “coalescence criterion,” based on the thickness of thin films and threads. The evolution of both two-dimensional and fully three-dimensional flows is examined. It is found that although there is a significant difference between the evolution when no breakup takes place and when it does, once breakup takes place the evolution is relatively insensitive to exactly how it is triggered for a range of coalescence criterion, and any differences are mostly confined to the smallest scales.

APS Division of Fluid Dynamics Meeting Abstracts, 2020

Biophysical Journal, 1999

The effect of a nonuniform solute concentration on the osmotic transport of water through the bou... more The effect of a nonuniform solute concentration on the osmotic transport of water through the boundaries of a simple model cell is investigated. A system of two ordinary differential equations is derived for the motion of a single cell in the limit of a fast solute diffusion, and an analytic solution is obtained for one special case. A two-dimensional finite element model has been developed to simulate the more general case (finite diffusion rates, solute gradient induced by a solidification front). It is shown that the cell moves to regions of lower solute concentration due to the uneven flux of water through the cell boundaries. This mechanism has apparently not been discussed previously. The magnitude of this effect is small for red blood cells, the case in which all of the relevant parameters are known. We show, however, that it increases with cell size and membrane permeability, so this effect could be important for larger cells. The finite element model presented should also have other applications in the study of the response of cells to an osmotic stress and for the interaction of cells and solidification fronts. Such investigations are of major relevance for the optimization of cryopreservation processes.

International Journal of Multiphase Flow, Oct 1, 2017

The effect of an insoluble surfactant on the structure of turbulent bubbly upflow in a vertical c... more The effect of an insoluble surfactant on the structure of turbulent bubbly upflow in a vertical channel is examined by direct numerical simulations (DNS). For nearly spherical bubbles the presence of a surfactant reduces the lateral lift on the bubbles and changes the structure of the flow in major ways. Clean bubbles are driven to the walls by the lift force and the void fraction distribution has a well defined peak near the walls, resulting in significant reduction in flow rate. Bubbles with strong enough surfactants do not experience significant lateral lift and remain in the bulk flow. Indeed, when surfactant is present the addition of bubbles to a turbulent flow has relatively little effect on the flow, once the pressure gradient is adjusted to account for the reduced weight of the mixture.

International Journal of Multiphase Flow, Oct 1, 2016

Data generated by direct numerical simulations (DNS) of bubbly up-flow in a periodic vertical cha... more Data generated by direct numerical simulations (DNS) of bubbly up-flow in a periodic vertical channel is used to generate closure relationships for a simplified two-fluid model for the average flow. Nearly spherical bubbles, initially placed in a fully developed parabolic flow, are driven relatively quickly to the walls, where they increase drag and slowly reduce the flow rate. Once the flow rate has been decreased enough, some of the bubbles move back into the channel interior and the void fraction there approaches the value needed to balance the weight of the mixture and the imposed pressure gradient. A database is generated by averaging the DNS results over planes parallel to the walls, and a Model Averaging Neural Network (MANN) is used to find the relationships between unknown closure terms in a simple model equations for the average flow and the resolved variables. The closure relations are then tested, by following the evolution of different initial conditions, and it is found that the model predictions are in reasonably good agreement with DNS results.

Bulletin of the American Physical Society, Nov 24, 2020

Bulletin of the American Physical Society, Nov 25, 2019

Bulletin of the American Physical Society, Nov 24, 2015

Submitted for the DFD15 Meeting of The American Physical Society DNS and Modeling of Turbulent Ga... more Submitted for the DFD15 Meeting of The American Physical Society DNS and Modeling of Turbulent Gas-Liquid Channel Flows 1 GRE-TAR TRYGGVASON, MING MA, JIACAI LU, Univ of Notre Dame-DNS studies of gas-liquid flows in vertical turbulent channels are presented. Results from a simulation of a pressure driven turbulent channel flow with a friction Reynolds number of 500 where a large number of bubbles of different sizes are injected at time zero, shows that small bubbles quickly migrate to the wall, but the flow takes much longer to adjust to the new bubble distribution. The evolution of turbulent statistic and the void fraction distribution is examined, including area concentration and the components of the area tensor. Another series of simulations of bubbles injected into turbulent channel flow, where the bubbles are allowed to coalesce and break apart, is also presented. For high enough surface tension all the bubbles coalesce into one large slug, but as the surface tension is reduced, large enough bubbles break up and the flow eventually reaches an approximate equilibrium where coalescence is matched by breakups. The resulting state generally contains bubbles with a distribution of sizes. The various quantities characterizing the flow are followed over time and their dependency of the flow parameters examined. Preliminary attempts to model the flow using a set of averaged equations, using closure relations derived from the DNS data are discussed.

Social Science Research Network, 2022

Nucleation and Atmospheric Aerosols, 2020

Journal of Computational Physics, Apr 1, 2021

International Journal of Heat and Mass Transfer, Aug 1, 2019

Fully resolved simulations are used to study a few aspects of fused filament fabrication. The sim... more Fully resolved simulations are used to study a few aspects of fused filament fabrication. The simulations are done using a finite-volume/front tracking method where the governing conservation equations are solved for the air and polymer flow in a rectangular cuboid using a fixed structured grid and the interface is tracked using connected marker particles. The nozzle is modeled as a moving source for mass and heat. The viscosity of the polymer depends on the shear rate and the temperature, and once the polymer cools down and the viscosity is high enough, it is effectively solid. The effects of the control parameters are examined for the construction of three objects: an inverted cone, a ''bridge", and a rectangle formed by parallel filaments. The results show that the shape of the objects depends sensitively on the control parameters. We find that an inverted cone, built with partially overlapping filaments, requires the polymer to quickly become very viscous for a stable shape, that parallel filaments need to be spaced closely for the formation of a large contact area and we show how the sagging of a freely suspended filament depends on the injection temperature.

Rapid Prototyping Journal, Sep 28, 2018

Purpose-This paper continues the development of a comprehensive methodology for fully resolved nu... more Purpose-This paper continues the development of a comprehensive methodology for fully resolved numerical simulations of fusion deposition modeling. Design/methodology/approach-A front-tracking/finite volume method introduced in Part I to simulate the heat transfer and fluid dynamics of the deposition of a polymer filament on a fixed bed is extended by adding an improved model for the injection nozzle, including the shrinkage of the polymer as it cools down, and accounting for stresses in the solid. Findings-The accuracy and convergence properties of the new method are tested by grid refinement and the method is shown to produce convergent solutions for the shape of the filament, the temperature distribution, the shrinkage and the solid stresses. Research limitations/implications-The method presented in the paper focuses on modeling the fluid flow, the cooling and solidification, as well as volume changes and residual stresses, using a relatively simple viscoelastic constitutive model. More complex material models, depending, for example, on the evolution of the configuration tensor, are not included. Practical implications-The ability to carry out fully resolved numerical simulations of the fusion deposition process is expected to be critical for the validation of mathematical models for the material behavior, to help explore new deposition strategies, and to provide the "ground truth" for the development of reduced order models. Originality/value-The paper completes the development of the first numerical method for fully resolved simulation of fusion filament modeling.

Computer Methods in Applied Mechanics and Engineering, Apr 1, 2019

Highlights • A front-tracking/finite volume method is introduced to model Fused Filament Fabricat... more Highlights • A front-tracking/finite volume method is introduced to model Fused Filament Fabrication. • Fluid flow, heat transfer, viscoelasticity and moving boundary are included. • A fully resolved simulation is presented with accuracy and convergence validations. • Effects of including viscoelastic stresses are presented and discussed.

APS Division of Fluid Dynamics Meeting Abstracts, Nov 1, 2019

Bulletin of the American Physical Society, Nov 19, 2018

ASME Press eBooks, 2018

Recent progress in direct numerical simulations (DNS) of gas-liquid flows is discussed. We start ... more Recent progress in direct numerical simulations (DNS) of gas-liquid flows is discussed. We start by reviewing briefly DNS of cavitating and non-cavitating flows and then address two advanced topics: How to use results for bubbly flows to help generate improved models for the large-scale or average flow, and simulations of flows undergoing massive topology changes. For the first topic we have started to experiment with the use of machine learning methods to extract complex correlations from the DNS data and for the second we are exploring how to diagnose the flow and describe its structure.

International Journal of Heat and Fluid Flow, Dec 1, 2015

The effects of bubbles and inclination angle on the flow and heat transfer in a channel are exami... more The effects of bubbles and inclination angle on the flow and heat transfer in a channel are examined by direct numerical simulations (DNS), where every continuum length and time scale are resolved using a front-tracking/finite volume method. Earlier simulations of bubbles in turbulent flows in vertical channels have shown that the presence of the bubbles increases the Nusselt number, compared to flow without bubbles. Here the flow and the enhancement of the heat transfer is described as a function of the angle of inclination of a channel where a constant heat flux is applied at the walls. The bubbles are nearly spherical and the void fraction is 3%. The results show that the temperature difference between the wall where the bubbles are concentrated and the fluid near to that wall is lower when the channel is inclined 30°and 60°than for vertical and horizontal channels, indicating that the heat transfer is more efficient in these cases.

Physical review fluids, Aug 30, 2018

Multifluid flows in a vertical channel are examined by direct numerical simulations, for situatio... more Multifluid flows in a vertical channel are examined by direct numerical simulations, for situations where the topology of the interface separating the different fluids changes. Several bubbles are initially placed in a turbulent channel flow at a sufficiently high void fraction so that the bubbles collide and the liquid film between them becomes very thin. This film is ruptured at a predetermined thickness and the bubbles are allowed to coalesce. For the cases with high surface tension the bubbles continue to coalesce, eventually forming one large bubble. At low surface tension, on the other hand, the large bubbles break up again, sometimes undergoing repeated coalescence and breakup. The evolution of various integral quantities, such as the average flow rate, wall-shear, and interface area are monitored and compared for different governing parameters. Averages of the flow field and the phase distribution over planes parallel to the walls are also examined, and the microstructure, at statistically steady state, is examined using low order probability functions.

APS Division of Fluid Dynamics Meeting Abstracts, Nov 1, 2019

Abstract The breakup of a periodic jet is examined computationally, using a front-tracking/finite... more Abstract The breakup of a periodic jet is examined computationally, using a front-tracking/finite-volume method, where the interface is represented by connected marker points moving with the fluid, while the governing equations are solved on a fixed grid. Tracking the interface allows control of whether topology changes take place or not. The Reynolds and Capillary numbers are kept relatively low ( R e = 150 and C a = 2 ) so most of the flow is well resolved. The effect of topology changes is examined by following the jet until it has mostly disintegrated, for different “coalescence criterion,” based on the thickness of thin films and threads. The evolution of both two-dimensional and fully three-dimensional flows is examined. It is found that although there is a significant difference between the evolution when no breakup takes place and when it does, once breakup takes place the evolution is relatively insensitive to exactly how it is triggered for a range of coalescence criterion, and any differences are mostly confined to the smallest scales.

APS Division of Fluid Dynamics Meeting Abstracts, 2020