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5 pages, 191 KiB

Open AccessEditorial

Introduction for the Special Issue: Statistical Fluid Dynamics

by Amine Ammar, Francisco Chinesta and Rudy Valette

Entropy 2022, 24(6), 782; https://doi.org/10.3390/e24060782 - 1 Jun 2022

Viewed by 1201

Abstract

Characterizing complex material consists in establishing the relationship between flow rheology during forming processes and the induced micro-structural state that affects directly the final mechanical properties of the formed parts [...] Full article

(This article belongs to the Special Issue Statistical Fluid Dynamics)

Research

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13 pages, 24892 KiB

Open AccessArticle

Numerical Study on the Coagulation and Breakage of Nanoparticles in the Two-Phase Flow around Cylinders

by Ruifang Shi, Jianzhong Lin and Hailin Yang

Entropy 2022, 24(4), 526; https://doi.org/10.3390/e24040526 - 8 Apr 2022

Cited by 3 | Viewed by 1305

Abstract

The Reynolds averaged N-S equation and dynamic equation for nanoparticles are numerically solved in the two-phase flow around cylinders, and the distributions of the concentration M₀ and geometric mean diameter d_g of particles are given. Some of the results are validated [...] Read more.

The Reynolds averaged N-S equation and dynamic equation for nanoparticles are numerically solved in the two-phase flow around cylinders, and the distributions of the concentration M₀ and geometric mean diameter d_g of particles are given. Some of the results are validated by comparing with previous results. The effects of particle coagulation and breakage and the initial particle concentration m₀₀ and size d₀ on the particle distribution are analyzed. The results show that for the flow around a single cylinder, M₀ is reduced along the flow direction. Placing a cylinder in a uniform flow will promote particle breakage. For the flow around multiple cylinders, the values of M₀ behind the cylinders oscillate along the spanwise direction, and the wake region in the flow direction is shorter than that for the flow around a single cylinder. For the initial monodisperse particles, the values of d_g increase along the flow direction and the effect of particle coagulation is larger than that of particle breakage. The values of d_g fluctuate along the spanwise direction; the closer to the cylinders, the more frequent the fluctuations of d_g values. For the initial polydisperse particles with d₀ = 98 nm and geometric standard deviation σ = 1.65, the variations of d_g values along the flow and spanwise directions show the same trend as for the initial monodisperse particles, although the differences are that the values of d_g are almost the same for the cases with and without considering particle breakage, while the distribution of d_g along the spanwise direction is flatter in the case with initial polydisperse particles. Full article

(This article belongs to the Special Issue Statistical Fluid Dynamics)

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12 pages, 679 KiB

Open AccessArticle

No Existence and Smoothness of Solution of the Navier-Stokes Equation

by Hua-Shu Dou

Entropy 2022, 24(3), 339; https://doi.org/10.3390/e24030339 - 26 Feb 2022

Cited by 3 | Viewed by 8744

Abstract

The Navier-Stokes equation can be written in a form of Poisson equation. For laminar flow in a channel (plane Poiseuille flow), the Navier-Stokes equation has a non-zero source term (∇²u(x, y, z) = F_x (x, y, [...] Read more.

The Navier-Stokes equation can be written in a form of Poisson equation. For laminar flow in a channel (plane Poiseuille flow), the Navier-Stokes equation has a non-zero source term (∇²u(x, y, z) = F_x (x, y, z, t) and a non-zero solution within the domain. For transitional flow, the velocity profile is distorted, and an inflection point or kink appears on the velocity profile, at a sufficiently high Reynolds number and large disturbance. In the vicinity of the inflection point or kink on the distorted velocity profile, we can always find a point where ∇²u(x, y, z) = 0. At this point, the Poisson equation is singular, due to the zero source term, and has no solution at this point due to singularity. It is concluded that there exists no smooth orphysically reasonable solutions of the Navier-Stokes equation for transitional flow and turbulence in the global domain due to singularity. Full article

(This article belongs to the Special Issue Statistical Fluid Dynamics)

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13 pages, 22163 KiB

Open AccessArticle

Analysis of Energy Dissipation of Interval-Pooled Stepped Spillways

by Xin Ma, Jianmin Zhang and Yaan Hu

Entropy 2022, 24(1), 85; https://doi.org/10.3390/e24010085 - 4 Jan 2022

Cited by 4 | Viewed by 2188

Abstract

The water flow characteristics over an interval-pooled stepped spillway are investigated by combining the renormalization group (RNG) k-ε turbulence model with the volume of fluid (VOF) interface capture technique in the present study. The results show that the energy dissipation performance of the [...] Read more.

The water flow characteristics over an interval-pooled stepped spillway are investigated by combining the renormalization group (RNG) k-ε turbulence model with the volume of fluid (VOF) interface capture technique in the present study. The results show that the energy dissipation performance of the interval-pooled stepped spillway was generally better than that of the pooled, stepped spillways and the traditional flat-panel stepped spillway. The omega vortex intensity identification method is introduced to evaluate the energy dissipation. Due to the formation of “pseudo-weir”, the energy dissipation did not increase with the growth of the pool’s height. In addition, the average vortex intensity can characterize the dissipation rate to some extent. Full article

(This article belongs to the Special Issue Statistical Fluid Dynamics)

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22 pages, 1829 KiB

Open AccessArticle

Numerical Prediction of Two-Phase Flow through a Tube Bundle Based on Reduced-Order Model and a Void Fraction Correlation

by Claire Dubot, Cyrille Allery, Vincent Melot, Claudine Béghein, Mourad Oulghelou and Clément Bonneau

Entropy 2021, 23(10), 1355; https://doi.org/10.3390/e23101355 - 16 Oct 2021

Viewed by 2158

Abstract

Predicting the void fraction of a two-phase flow outside of tubes is essential to evaluate the thermohydraulic behaviour in steam generators. Indeed, it determines two-phase mixture properties and affects two-phase mixture velocity, which enable evaluating the pressure drop of the system. The two-fluid [...] Read more.

Predicting the void fraction of a two-phase flow outside of tubes is essential to evaluate the thermohydraulic behaviour in steam generators. Indeed, it determines two-phase mixture properties and affects two-phase mixture velocity, which enable evaluating the pressure drop of the system. The two-fluid model for the numerical simulation of two-phase flows requires interaction laws between phases which are not known and/or reliable for a flow within a tube bundle. Therefore, the mixture model, for which it is easier to implement suitable correlations for tube bundles, is used. Indeed, by expressing the relative velocity as a function of slip, the void fraction model of Feenstra et al. and Hibiki et al. developed for upward cross-flow through horizontal tube bundles is introduced and compared. With the method suggested in this paper, the physical phenomena that occur in tube bundles are taken into consideration. Moreover, the tube bundle is modelled using a porous media approach where the Darcy–Forchheimer term is usually defined by correlations found in the literature. However, for some tube bundle geometries, these correlations are not available. The second goal of the paper is to quickly compute, in quasi-real-time, this term by a non-intrusive parametric reduced model based on Proper Orthogonal Decomposition. This method, named Bi-CITSGM (Bi-Calibrated Interpolation on the Tangent Subspace of the Grassmann Manifold), consists in interpolating the spatial and temporal bases by ITSGM (Interpolation on the Tangent Subspace of the Grassmann Manifold) in order to define the solution for a new parameter. The two developed methods are validated based on the experimental results obtained by Dowlati et al. for a two-phase cross-flow through a horizontal tube bundle. Full article

(This article belongs to the Special Issue Statistical Fluid Dynamics)

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15 pages, 681 KiB

Open AccessArticle

Study of Concentrated Short Fiber Suspensions in Flows, Using Topological Data Analysis

by Rabih Mezher, Jack Arayro, Nicolas Hascoet and Francisco Chinesta

Entropy 2021, 23(9), 1229; https://doi.org/10.3390/e23091229 - 18 Sep 2021

Cited by 2 | Viewed by 1525

Abstract

The present study addresses the discrete simulation of the flow of concentrated suspensions encountered in the forming processes involving reinforced polymers, and more particularly the statistical characterization and description of the effects of the intense fiber interaction, occurring during the development of the [...] Read more.

The present study addresses the discrete simulation of the flow of concentrated suspensions encountered in the forming processes involving reinforced polymers, and more particularly the statistical characterization and description of the effects of the intense fiber interaction, occurring during the development of the flow induced orientation, on the fibers’ geometrical center trajectory. The number of interactions as well as the interaction intensity will depend on the fiber volume fraction and the applied shear, which should affect the stochastic trajectory. Topological data analysis (TDA) will be applied on the geometrical center trajectories of the simulated fiber to prove that a characteristic pattern can be extracted depending on the flow conditions (concentration and shear rate). This work proves that TDA allows capturing and extracting from the so-called persistence image, a pattern that characterizes the dependence of the fiber trajectory on the flow kinematics and the suspension concentration. Such a pattern could be used for classification and modeling purposes, in rheology or during processing monitoring. Full article

(This article belongs to the Special Issue Statistical Fluid Dynamics)

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26 pages, 1990 KiB

Open AccessArticle

A Data-Driven Space-Time-Parameter Reduced-Order Model with Manifold Learning for Coupled Problems: Application to Deformable Capsules Flowing in Microchannels

by Toufik Boubehziz, Carlos Quesada-Granja, Claire Dupont, Pierre Villon, Florian De Vuyst and Anne-Virginie Salsac

Entropy 2021, 23(9), 1193; https://doi.org/10.3390/e23091193 - 9 Sep 2021

Cited by 1 | Viewed by 2305

Abstract

An innovative data-driven model-order reduction technique is proposed to model dilute micrometric or nanometric suspensions of microcapsules, i.e., microdrops protected in a thin hyperelastic membrane, which are used in Healthcare as innovative drug vehicles. We consider a microcapsule flowing in a similar-size microfluidic [...] Read more.

An innovative data-driven model-order reduction technique is proposed to model dilute micrometric or nanometric suspensions of microcapsules, i.e., microdrops protected in a thin hyperelastic membrane, which are used in Healthcare as innovative drug vehicles. We consider a microcapsule flowing in a similar-size microfluidic channel and vary systematically the governing parameter, namely the capillary number, ratio of the viscous to elastic forces, and the confinement ratio, ratio of the capsule to tube size. The resulting space-time-parameter problem is solved using two global POD reduced bases, determined in the offline stage for the space and parameter variables, respectively. A suitable low-order spatial reduced basis is then computed in the online stage for any new parameter instance. The time evolution of the capsule dynamics is achieved by identifying the nonlinear low-order manifold of the reduced variables; for that, a point cloud of reduced data is computed and a diffuse approximation method is used. Numerical comparisons between the full-order fluid-structure interaction model and the reduced-order one confirm both accuracy and stability of the reduction technique over the whole admissible parameter domain. We believe that such an approach can be applied to a broad range of coupled problems especially involving quasistatic models of structural mechanics. Full article

(This article belongs to the Special Issue Statistical Fluid Dynamics)

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16 pages, 4226 KiB

Open AccessArticle

Octree Optimized Micrometric Fibrous Microstructure Generation for Domain Reconstruction and Flow Simulation

by Nesrine Aissa, Louis Douteau, Emmanuelle Abisset-Chavanne, Hugues Digonnet, Patrice Laure and Luisa Silva

Entropy 2021, 23(9), 1156; https://doi.org/10.3390/e23091156 - 2 Sep 2021

Viewed by 1751

Abstract

Over recent decades, tremendous advances in the field of scalable numerical tools and mesh immersion techniques have been achieved to improve numerical efficiency while preserving a good quality of the obtained results. In this context, an octree-optimized microstructure generation and domain reconstruction with [...] Read more.

Over recent decades, tremendous advances in the field of scalable numerical tools and mesh immersion techniques have been achieved to improve numerical efficiency while preserving a good quality of the obtained results. In this context, an octree-optimized microstructure generation and domain reconstruction with adaptative meshing is presented and illustrated through a flow simulation example applied to permeability computation of micrometric fibrous materials. Thanks to the octree implementation, the numerous distance calculations in these processes are decreased, thus the computational complexity is reduced. Using the parallel environment of the ICI-tech library as a mesher and a solver, a large scale case study is performed. The study is applied to the computation of the full permeability tensor of a three-dimensional microstructure containing 10,000 fibers. The considered flow is a Stokes flow and it is solved with a stabilized finite element formulation and a monolithic approach. Full article

(This article belongs to the Special Issue Statistical Fluid Dynamics)

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20 pages, 28590 KiB

Open AccessArticle

Effect of Shear Flow on Nanoparticles Migration near Liquid Interfaces

by Ali Daher, Amine Ammar, Abbas Hijazi and Lazhar Benyahia

Entropy 2021, 23(9), 1143; https://doi.org/10.3390/e23091143 - 31 Aug 2021

Cited by 1 | Viewed by 1477

Abstract

The effect of shear flow on spherical nanoparticles (NPs) migration near a liquid–liquid interface is studied by numerical simulation. We have implemented a compact model through which we use the diffuse interface method for modeling the two fluids and the molecular dynamics method [...] Read more.

The effect of shear flow on spherical nanoparticles (NPs) migration near a liquid–liquid interface is studied by numerical simulation. We have implemented a compact model through which we use the diffuse interface method for modeling the two fluids and the molecular dynamics method for the simulation of the motion of NPs. Two different cases regarding the state of the two fluids when introducing the NPs are investigated. First, we introduce the NPs randomly into the medium of the two immiscible liquids that are already separated, and the interface is formed between them. For this case, it is shown that before applying any shear flow, 30% of NPs are driven to the interface under the effect of the drag force resulting from the composition gradient between the two fluids at the interface. However, this percentage is increased to reach 66% under the effect of shear defined by a Péclet number Pe = 0.316. In this study, different shear rates are investigated in addition to different shearing times, and we show that both factors have a crucial effect regarding the migration of the NPs toward the interfacial region. In particular, a small shear rate applied for a long time will have approximately the same effect as a greater shear rate applied for a shorter time. In the second studied case, we introduce the NPs into the mixture of two fluids that are already mixed and before phase separation so that the NPs are introduced into the homogenous medium of the two fluids. For this case, we show that in the absence of shear, almost all NPs migrate to the interface during phase separation, whereas shearing has a negative result, mainly because it affects the phase separation. Full article

(This article belongs to the Special Issue Statistical Fluid Dynamics)

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18 pages, 2126 KiB

Open AccessArticle

Viscosity and Rheological Properties of Graphene Nanopowders Nanofluids

by Abderrahim Bakak, Mohamed Lotfi, Rodolphe Heyd, Amine Ammar and Abdelaziz Koumina

Entropy 2021, 23(8), 979; https://doi.org/10.3390/e23080979 - 29 Jul 2021

Cited by 19 | Viewed by 2276

Abstract

The dynamic viscosity and rheological properties of two different non-aqueous graphene nano-plates-based nanofluids are experimentally investigated in this paper, focusing on the effects of solid volume fraction and shear rate. For each nanofluid, four solid volume fractions have been considered ranging from 0.1% [...] Read more.

The dynamic viscosity and rheological properties of two different non-aqueous graphene nano-plates-based nanofluids are experimentally investigated in this paper, focusing on the effects of solid volume fraction and shear rate. For each nanofluid, four solid volume fractions have been considered ranging from 0.1% to 1%. The rheological characterization of the suspensions was performed at 20

^{\circ}

C, with shear rates ranging from

10^{- 1} s^{- 1}

to

10^{3} s^{- 1}

, using a cone-plate rheometer. The Carreau–Yasuda model has been successfully applied to fit most of the rheological measurements. Although it is very common to observe an increase of the viscosity with the solid volume fraction, we still found here that the addition of nanoparticles produces lubrication effects in some cases. Such a result could be very helpful in the domain of heat extraction applications. The dependence of dynamic viscosity with graphene volume fraction was analyzed using the model of Vallejo et al. Full article

(This article belongs to the Special Issue Statistical Fluid Dynamics)

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