SOME PROPERTIES OF C-FRAMES OF SUBSPACES

Abstract. In [13] frames of subspaces extended to continuous version namely c-frame of subspaces. In this article we consider to the relations between c-frames of subspaces and local c-frames. Also in this article we give some important relation about duality and parseval c-frames of subspaces. 1. Introduction an

A CFD-DEM Eulerian-Lagrangian solver for particle-laden viscoelastic flows (for oral presentation)

The ability to simulate the behavior of dense suspensions using computationally-efficient Eulerian-Lagrangian techniques requires accurate particulate-phase drag models that are valid for a wide range of material parameters. The present work aims at developing appropriate drag models for moderately-dense suspensions, in which the continuous phase also has viscoelastic characteristics. To this end, we parametrize the suspension properties through the Deborah number and the particle volume fraction, and compute the evolution in the drag coefficient of spheres translating through a viscoelastic fluid that is described by the Oldroyd-B model. To calculate the drag coefficient, we resort to 3D direct numerical simulations (DNS) of unconfined viscoelastic creeping flows (Re < 0.1) past random arrays of stationary spheres, over a wide range of Deborah numbers (De < 5), volume fractions (φ < 20%) and particle configurations. From these calculations we obtain a closure law F(De, φ) for the drag force in the viscoelastic fluid (with fixed retardation ratio = 0.5), which is on average within 4.7% of the DNS results. Subsequently, this closure law was incorporated into a CFD-DEM Eulerian-Lagrangian solver to handle particle-laden viscoelastic flow calculations, and two case studies were simulated to assess the accuracy and robustness of our numerical approach. These tests consisted of simulating the settling process in Newtonian and viscoelastic fluids within eccentric annular pipes and rectangular channels; configurations commonly employed in hydraulic fracturing operations. The numerical results obtained were found to be in good agreement with experimental data available for suspensions in Newtonian matrix fluids. For the case of viscoelastic fluids, the resulting particle distribution is presented for different elasticity numbers (i.e., El = De/Re) and particle volume fractions, and the results provide insight into the pronounced effects of viscoelastic matrix fluids in hydraulic fracturing operationsMIT-EXPL/TDI/0038/2019. 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 – Aprendizagem PROfunda na modelação de escoamentos com fluidos de matriz Viscoelástica Aditivados com partículas (POCI-01-0145-FEDER-016665). The authors would like to acknowledge the Minho University 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), 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) for providing HPC resources that have contributed to the research results reported within this work

CFD-DEM modeling of particle-laden viscoelastic flows in hydraulic fracturing operations

The ability to simulate the behavior of dense suspensions, using computationally-efficient Eulerian-Lagrangian techniques, requires accurate particulate-phase drag models that are valid for a wide range of process fluids and material parameters. The currently available closed-form drag models – which enable rapid calculation of the momentum exchange between the continuous and dispersed phases – are only valid for dilute suspensions with inelastic base fluids. The present work aims at developing appropriate drag models for moderately-dense suspensions (particle volume fractions < 20%), in which the continuous phase has viscoelastic characteristics. To this end, we parametrize the suspension properties through the Deborah number and the particle volume fraction, and compute the evolution in the drag coefficient of spheres translating through a viscoelastic fluid that is described by the Oldroyd-B model. To calculate the drag coefficient, we resort to three-dimensional direct numerical simulations (DNS) of unconfined viscoelastic creeping flows (Re < 0.1) past random arrays of stationary spheres, over a wide range of Deborah numbers (De < 5), volume fractions (φ < 20%) and particle configurations. From these calculations we obtain a closure law F(De, φ) for the drag force in a fluid described by the quasi-linear Oldroyd-B viscoelastic fluid model (with fixed retardation ratio β=0.5), which is, on average, within 4.7% of the DNS results. Subsequently, this closure law was incorporated into a CFD-DEM Eulerian-Lagrangian solver to handle particle-laden viscoelastic flow calculations, and two case studies were simulated to assess the accuracy and robustness of our numerical approach. These tests consisted of simulating the settling process in Newtonian and viscoelastic fluids within eccentric annular pipes and rectangular channels; configurations commonly employed in hydraulic fracturing operations. The numerical results obtained were found to be in good agreement with experimental data available for suspensions in Newtonian matrix fluids. For the case of viscoelastic fluids, the resulting particle distribution is presented for different elasticity numbers (i.e., El = De/Re) and particle volume fractions, and the results provide additional insights into the pronounced effects of viscoelastic matrix fluids in hydraulic fracturing operationsMIT-EXPL/TDI/0038/2019. y 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 – Aprendizagem PROfunda na modelação de escoamentos com fluidos de matriz Viscoelástica Aditivados com partículas (POCI-01-0145-FEDER-016665). The authors would like to acknowledge the Minho University 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), 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) for providing HPC resources that have contributed to the research results reported within this work

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

Attributes and VOs: Extending the UNICORE authorisation capabilities

Reliable authentication and authorisation are crucial for both service providers and their customers, where the former want to protect their resources from unauthorised access and fraudulent use while their customers want to be sure unauthorised access to their data is prevented. In Grid environments Virtual Organisations (VO) have been adopted as a means to organise and control access to resources and data based on roles that are assigned to users. Moreover, attribute based authorisation has emerged providing a decentralised approach with better scalability. Up to now UNICORE authentication and authorisation is based on X.509 certificates only. In this paper we will present two approaches to integrate both role or attribute based authorisation using VOMS and attribute based authorisation using Shibboleth into UNICORE

SOME PROPERTIES OF Lp,w(0 &lt; p ≤ 1)

Abstract. In this article we explain some properties of Lp,w when 0 &lt; p ≤ 1 and w is weight. These properties are general and we derive them from Lp spaces. 1. Introduction an

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