Exploratory project 2019 - deep learning for particle-laden viscoelastic flow modelling

[extract] Objetives: explore the possibility of using Deep Learning (DL) techniques to evaluate the drag coefficient of small non-Brownian particles translating and settling in nonlinear viscoelastic fluids. The long-term objective is the development of a 3D numerical code for particle-laden viscoelastic flows (PLVF), which will contribute to understanding many advanced manufacturing and industrial operations, specifically the hydraulic fracturing process

Effects of elasticity, inertia and viscosity ratio on the drag coefficient of a sphere translating through a viscoelastic fluid

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 dispersed phases. The currently available drag models are only valid for inelastic constitutive fluid models. This work aims at contributing to the development of drag models appropriate for dilute suspensions, where the continuous phase presents viscoelastic characteristics. To this aim, we parametrize the effects of fluid elasticity, namely, the relaxation and retardation times, as well as inertia on the drag coefficient of a sphere translating through a viscoelastic fluid, described by the Oldroyd-B model. To calculate the 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 Deborah numbers (< 9), and the polymer viscosity ratios. For low Re (< 1), we identified a non-monotonic trend for the drag coefficient correction (the ratio between the calculated drag coefficient and the one obtained for Stokes-flow). It initially decreases with the increase of De, for low De values (< 1), which is followed by a significant growth, due to the large elastic stresses that are developed on both the surface and wake of the sphere. These behaviors, observed in the inertia less flow regime, are amplified as the polymer viscosity ratio approaches unity. At higher Re (> 1), the drag coefficient correction is found to be always bigger than unity, but smaller than the enhancement calculated in creeping flow limit.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

A fully-resolved immersed boundary numerical method to simulate particle-laden viscoelastic flows

Fluid-particle transport systems present a significant practical relevance, in several engineering applications, such as oil sands mining and polymer processing. In several cases it is essential to consider that the fluid, in which the particles are dispersed, has underlying viscoelastic characteristics. For this aim, a novel numerical algorithm was implemented on an open-source finite-volume viscoelastic fluid flow solver coupled with an immersed boundary method, by extending the open-source computational fluid dynamics library CFDEMcoupling. The code is able to perform fully-resolved simulations, wherein all flow scales, associated with the particle motion, are resolved. Additionally, the formulation employed exploits the log-conformation tensor approach, to avoid high Weissenberg number issues. The accuracy of the algorithm was evaluated by studying several benchmark flows, namely: (i) the sedimentation 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, a comparison of the results obtained with the newly developed code with data reported in the literature is performed, in order to assess the code accuracy and robustness. Finally, the capability of the code to solve a physical challenging problem is illustrated by studying the interactions and flowinduced alignment of three spheres in a wall-bounded shear flow. The role of the fluid rheology and finite gap size on both the approach rate and pathways of the solid particles are described [1].This work is funded by FEDER funds through the COMPETE 2020 Programme and National Funds through FCT - Portuguese Foundation for Science and Technology under the project UID/CTM/50025/2013. The authors would like to acknowledge the Minho University cluster under the project Search-ON2: Revitalization of HPC infrastructure of UMinho (NORTE-07-0162-FEDER-000086), co-funded by the North Portugal Regional Operational Programme (ON.2-0 Novo Norte), under the National Strategic Reference Framework (NSRF), through the European Regional Development Fund (ERDF)

Development of a two-way coupled fully resolved immersed boundary method numerical code for particle laden viscoelastic flows

Understanding the behaviour of multiphase flows of solid in viscoelastic fluids is essential in several industrial applications, such as oil sands mining and polymer processing. For this aim, a novel numerical algorithm was implemented on an open-source finite-volume fluid flow solver coupled with an immersed boundary method, to allow the use of viscoelastic constitutive equations on the fluid (continuous) phase. To avoid numerical issues related to high Weissenberg number flows the log-conformation tensor approach can be employed on the newly developed algorithm. The accuracy of the algorithm was evaluated by studying several benchmark flows, namely: (i) the sedimentation of a sphere in a bounded domain surrounded by either Newtonian or viscoelastic fluids; (ii) rotation of a sphere in a homogeneous shear viscoelastic fluid flow; (iii) the cross-stream migration of a neutrally buoyant sphere in a steady Poiseuille flow, considering both Newtonian and viscoelastic suspending fluids. All the results obtained, on the referred case studies, allowed either to replicate the ones available on the published literature, or to describe additional effects promoted by the assumption of viscoelastic behaviour on the continuous phase. To illustrate the potential of the developed code, a newly case study of the shear-induced solid particle alignment in wall-bounded Newtonian and viscoelastic fluids was studied. The role of the fluid rheology and finite gap size on both the approach rate and pathways of the solid particles are described.This work is funded by FEDER funds through the COMPETE 2020 Programme and National Funds through FCT - Portuguese Foundation for Science and Technology under the project UID/CTM/50025/2013. The authors would like to acknowledge the Minho University cluster under the project Search-ON2: Revitalization of HPC infrastructure of UMinho (NORTE-07-0162-FEDER-000086), co-funded by the North Portugal Regional Operational Programme (ON.2-0 Novo Norte), under the National Strategic Reference Framework (NSRF), through the European Regional Development Fund (ERDF)

Digital-Twin approach to predict the drag coefficient of random arrays of spheres suspended in Giesekus viscoelastic fluids

Apresentação efetuada na 17th International Conference of Computational Methods in Sciences and Engineering (ICCMSE 2021), Greece, 2021The 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 UIDB/05256/2020 and UIDP/05256/2020 and MIT-EXPL/TDI/0038/2019 – APROVA - Deep learning for particle-laden viscoelastic flow modelling (POCI-01-0145-FEDER-016665)

Multi-scale modeling of hydraulic fracturing operations

Apresentação efetuada no 17th International Conference of Computational Methods in Sciences and Engineering (ICCMSE 2021), em Crete, Greece, 202

Finite volume simulations of particle‑laden viscoelastic fuid fows: application to hydraulic fracture processes

Accurately resolving the coupled momentum transfer between the liquid and solid phases of complex fluids is a fundamental problem in multiphase transport processes, such as hydraulic fracture operations. Specifically we need to characterize the dependence of the normalized average fluid–particle force ⟨F⟩ on the volume fraction of the dispersed solid phase and on the rheology of the complex fluid matrix, parameterized through the Weissenberg number Wi measuring the relative magnitude of elastic to viscous stresses in the fluid. Here we use direct numerical simulations (DNS) to study the creeping flow (Re≪1) of viscoelastic fluids through static random arrays of monodisperse spherical particles using a finite volume Navier–Stokes/Cauchy momentum solver. The numerical study consists of N=150 different systems, in which the normalized average fluid–particle force ⟨F⟩ is obtained as a function of the volume fraction ϕ (0<ϕ≤0.2) of the dispersed solid phase and the Weissenberg number Wi (0≤Wi≤4). From these predictions a closure law ⟨F(ϕ,Wi)⟩ for the drag force is derived for the quasi-linear Oldroyd-B viscoelastic fluid model (with fixed retardation ratio β=0.5) which is, on average, within 5.7% of the DNS results. In addition, a flow solver able to couple Eulerian and Lagrangian phases (in which the particulate phase is modeled by the discrete particle method (DPM)) is developed, which incorporates the viscoelastic nature of the continuum phase and the closed-form drag law. Two case studies were simulated using this solver, to assess the accuracy and robustness of the newly developed approach for handling particle-laden viscoelastic flow configurations with O(105−106) rigid spheres that are representative of hydraulic fracture operations. Three-dimensional settling processes in a Newtonian fluid and in a quasi-linear Oldroyd-B viscoelastic fluid are both investigated using a rectangular channel and an annular pipe domain. Good agreement is obtained for the particle distribution measured in a Newtonian fluid, when comparing numerical results with experimental data. For the cases in which the continuous fluid phase is viscoelastic we compute the evolution in the velocity fields and predicted particle distributions are presented at different elasticity numbers 0≤El≤30 (where El=Wi/Re) and for different suspension particle volume fractions.This work is funded by FEDER funds through the COMPETE 2020 Programme and National Funds through FCT (Portuguese Foundation for Science and Technology) under the projects UID-B/05256/2020, UID-P/05256/2020 and MIT-EXPL/TDI/0038/2019 - APROVA - Deep learning for particle-laden viscoelastic flow modelling (POCI-01-0145-FEDER-016665) under MIT Portugal program. The authors would like to acknowledge the University of Minho cluster under the project NORTE-07-0162-FEDER-000086 (URL: http://search6.di.uminho.pt), the Minho Advanced Computing Center (MACC) (URL: https:// macc.fccn.pt) under the project CPCA_A2_6052_2020, the Texas Advanced Computing Center (TACC) at The University of Texas at Austin (URL: http://www.tacc.utexas.edu), the Gompute HPC Cloud Platform (URL: https://www.gompute.com), and PRACE - Partnership for Advanced Computing in Europe under the project icei-prace-2020-0009, for providing HPC resources that have contributed to the research results reported within this paper

A closure model for the drag coefficient of a sphere translating in a viscoelastic fluid

In many large-scale industrial applications dealing with particle-laden viscoelastic fluids, the ensemble-averaged behavior of the mixture is of most interest. The first step to parametrize this behavior is to develop an accurate expression to rapidly evaluate the drag coefficient over a broad range of kinematic parameters. The drag coefficient of a spherical particle translating in a viscoelastic matrix is strongly affected by the viscoelasticity of the fluid. In this study, we aim to parametrize the effects of fluid elasticity, especially the relaxation and retardation times, as well as inertia on the drag coefficient of a sphere translating in a viscoelastic fluid described by the Oldroyd-B model. To this end, we employed three-dimensional direct numerical simulations of viscoelastic flow past a stationary sphere. The accuracy of the numerical formulation is thoroughly tested against a number of benchmark problems consisting of steady flow past a sphere in a bounded circular or square domain filled with either a Newtonian or viscoelastic fluid. Initially, the numerical computations for the drag coefficient over a wide range of geometric and flow parameters are validated by comparison with existing data and drag correction models from the literature. The drag coefficient correction is then evaluated for unconfined flow past a sphere at different Reynolds number, Re, over a wide range of Deborah number, De 1), the drag is enhanced due to the large elastic stresses that develop on both the surface and wake of the sphere. These canonical behaviors, observed in the inertia-less flow regime (Re ≤ 1) are amplified as the polymer viscosity ratio approaches unity. At higher Reynolds numbers (Re > 1), the drag coefficient correction arising from viscoelasticity is found to be always bigger than unity, but smPOFC - Programa Operacional Temático Factores de Competitividade (UID/CTM/50025/2019

Fully-resolved simulations of particle-laden viscoelastic fluids using an immersed boundary method

This study reports the development of a direct simulation code for solid spheres moving through viscoelastic fluids with a range of different Theological behaviors. The numerical algorithm was implemented on an open source finite-volume solver coupled with an immersed boundary method, and is able to perform fully-resolved simulations, wherein all flow scales associated with the particle motion are resolved. The formulation employed exploits the log-conformation tensor to avoid high Weissenberg number issues when calculating the polymeric extra stress. A number of benchmark flows were simulated using this method, to assess the accuracy of the newly developed solver. First, the sedimentation of a sphere in a bounded domain surrounded by either Newtonian or viscoelastic fluid was computed, and the numerical results were verified by comparison with experimental and computational data from the literature. Additionally, the spatial and temporal accuracies of the algorithm were evaluated, and different transient and advection discretization schemes were investigated. Second, the rotation of a sphere in a homogeneous shear flow was studied, and again the numerical results obtained were compared to those from the literature. Good agreement is obtained for the variation in the particle rotation rate as a function of Weissenberg number, using both the newly implemented algorithm and an alternative fixed-mesh approach. Finally, the cross-stream migration of a neutrally buoyant sphere in a steady Poiseuille flow, consisting of either a Newtonian or viscoelastic suspending fluid was investigated. For the Newtonian fluid good agreement was obtained for the particle equilibrium position when compared to the well known Segre-Silberberg effect, and for the viscoelastic fluid the effect of the retardation ratio on the final particle equilibrium position was studied. Additionally, the newly-developed solver capabilities were tested to study the shear-induced particle alignment in wall-bounded Newtonian and viscoelastic fluids. The rThis work is funded by FEDER funds through the COMPETE 2020 Programme and National Funds through FCT - Portuguese Foundation for Science and Technology under the project UID/CTM/50025/2013 as well as by the MIT Portugal Program (MPP). The authors would like to acknowledge the Minho University cluster under the project Search-ON2: Revitalization of HPC infrastructure of UMinho (NORTE-07-0162-FEDER-000086), co-funded by the North Portugal Regional Operational Programme (ON.2-0 Novo Norte), under the National Strategic Reference Framework (NSRF), through the European Regional Development Fund (ERDF). Additionally, the authors would like to acknowledge the Texas Advanced Computing Center (TACC) at The University of Texas at Austin for providing HPC resources that have contributed to the research results reported within this paper. http://www.tacc.utexas.edu Finally, the authors thank Bruno Santos from FSD blueCAPE Lda for insightful comments regarding the usage of the TACC resources