On fluid–particle dynamics in fully developed cluster-induced turbulence

2015 ◽  
Vol 780 ◽  
pp. 578-635 ◽  
Author(s):  
Jesse Capecelatro ◽  
Olivier Desjardins ◽  
Rodney O. Fox
Keyword(s):  
Kinetic Energy ◽  
Volume Fraction ◽  
Finite Size ◽  
Fluid Phase ◽  
Particle Phase ◽  
Pressure Tensor ◽  
Production Term ◽  
Velocity Statistics ◽  
Gravity Driven ◽  
Momentum Coupling

At sufficient mass loading and in the presence of a mean body force (e.g. gravity), an initially random distribution of particles may organize into dense clusters as a result of momentum coupling with the carrier phase. In statistically stationary flows, fluctuations in particle concentration can generate and sustain fluid-phase turbulence, which we refer to as cluster-induced turbulence (CIT). This work aims to explore such flows in order to better understand the fundamental modelling aspects related to multiphase turbulence, including the mechanisms responsible for generating volume-fraction fluctuations, how energy is transferred between the phases, and how the cluster size distribution scales with various flow parameters. To this end, a complete description of the two-phase flow is presented in terms of the exact Reynolds-average (RA) equations, and the relevant unclosed terms that are retained in the context of homogeneous gravity-driven flows are investigated numerically. An Eulerian–Lagrangian computational strategy is used to simulate fully developed CIT for a range of Reynolds numbers, where the production of fluid-phase kinetic energy results entirely from momentum coupling with finite-size inertial particles. The adaptive filtering technique recently introduced in our previous work (Capecelatro et al., J. Fluid Mech., vol. 747, 2014, R2) is used to evaluate the Lagrangian data as Eulerian fields that are consistent with the terms appearing in the RA equations. Results from gravity-driven CIT show that momentum coupling between the two phases leads to significant differences from the behaviour observed in very dilute systems with one-way coupling. In particular, entrainment of the fluid phase by clusters results in an increased mean particle velocity that generates a drag production term for fluid-phase turbulent kinetic energy that is highly anisotropic. Moreover, owing to the compressibility of the particle phase, the uncorrelated components of the particle-phase velocity statistics are highly non-Gaussian, as opposed to systems with one-way coupling, where, in the homogeneous limit, all of the velocity statistics are nearly Gaussian. We also observe that the particle pressure tensor is highly anisotropic, and thus additional transport equations for the separate contributions to the pressure tensor (as opposed to a single transport equation for the granular temperature) are necessary in formulating a predictive multiphase turbulence model.

Effect of Domain Size on Fluid–Particle Statistics in Homogeneous, Gravity-Driven, Cluster-Induced Turbulence

2015 ◽  
Vol 138 (4) ◽  
Author(s):  
Jesse Capecelatro ◽  
Olivier Desjardins ◽  
Rodney O. Fox
Keyword(s):  
Volume Fraction ◽  
Finite Size ◽  
Domain Size ◽  
Spatial Filter ◽  
High Mass ◽  
Inertial Particles ◽  
Spatially Correlated ◽  
Gravity Driven ◽  
Adaptive Spatial Filter ◽  
Particle Statistics

Scaling of volume fraction and velocity fluctuations with domain size is investigated for high-mass-loading suspensions of finite-size inertial particles subject to gravity. Results from highly resolved Euler–Lagrange simulations are evaluated via an adaptive spatial filter with an averaging volume that varies with the local particle concentration. This filter enables the instantaneous particle velocity to be decomposed into a spatially correlated contribution used in defining the particle-phase turbulent kinetic energy (TKE), and a spatially uncorrelated contribution used in defining the granular temperature. The total granular energy is found to grow nearly linearly with the domain size, while the balance between the separate contributions remains approximately constant.

On multiphase turbulence models for collisional fluid–particle flows

2014 ◽  
Vol 742 ◽  
pp. 368-424 ◽  
Author(s):  
Rodney O. Fox
Keyword(s):  
Kinetic Energy ◽  
Hydrodynamic Model ◽  
Volume Fraction ◽  
Turbulence Models ◽  
Fluid Particle ◽  
Granular Temperature ◽  
Particle Phase ◽  
Phase Volume ◽  
Phase Volume Fraction ◽  
Particle Flows

AbstractStarting from a kinetic theory (KT) model for monodisperse granular flow, the exact Reynolds-averaged (RA) equations are derived for the particle phase in a collisional fluid–particle flow. The corresponding equations for a constant-density fluid phase are derived from a model that includes drag and buoyancy coupling with the particle phase. The fully coupled macroscale/hydrodynamic model, rigorously derived from a kinetic equation for the particles, is written in terms of the particle-phase volume fraction, the particle-phase velocity and the granular temperature (or total granular energy). As derived from the hydrodynamic model, the RA turbulence model solves for the RA particle-phase volume fraction, the phase-averaged (PA) particle-phase velocity, the PA granular temperature and the PA turbulent kinetic energy of the particle phase. Thus, unlike in most previous derivations of macroscale turbulence models for moderately dense granular flows, a clear distinction is made between the PA granular temperature $\Theta _\textit {p}$, which appears in the KT constitutive relations, and the particle-phase turbulent kinetic energy $k_\textit {p}$, which appears in the turbulent transport coefficients. The exact RA equations contain unclosed terms due to nonlinearities in the hydrodynamic model and we briefly discuss the available closures for these terms. Finally, we demonstrate by comparing model predictions with direct numerical simulation results that even for non-collisional fluid–particle flows it is necessary to provide separate models for $\Theta _\textit {p}$ and $k_\textit {p}$ in order to correctly account for the effect of the particle Stokes number and mass loading.

Investigating Multiphase Turbulence Statistics of Large-Scale Two-Way Coupled Gravity-Driven Flows

2014 ◽  
Author(s):  
Jesse Capecelatro ◽  
Olivier Desjardins ◽  
Rodney O. Fox
Keyword(s):  
Kinetic Energy ◽  
Kinetic Theory ◽  
Turbulent Kinetic Energy ◽  
Particle Velocity ◽  
Volume Fraction ◽  
Constitutive Relations ◽  
Granular Temperature ◽  
Particle Phase ◽  
Simulation Results ◽  
Filtering Approach

Starting from the kinetic theory (KT) model for monodisperse granular flow, the exact Reynolds-average (RA) equations were recently derived for the particle phase in a collisional gas-particle flow by Fox [1]. The turbulence model solves for the RA particle volume fraction, the phase-average (PA) particle velocity, the PA granular temperature, and the PA particle turbulent kinetic energy (TKE). A clear distinction is made between the PA granular temperature, which appears in the kinetic theory constitutive relations, and the particle-phase turbulent kinetic energy, which appears in the turbulent transport coefficients. Mesoscale direct numerical simulation (DNS) can be used to assess the validity of the closures proposed for the unclosed terms that arise due to nonlinearities in the hydrodynamic model. In order to extract meaningful statistics from simulation results, a separation of length scales must be established to distinguish between the PA particle TKE and the PA granular temperature. In this work, we introduce an adaptive spatial filter with an averaging volume that varies with the local particle-phase volume fraction. This filtering approach ensures sufficient particle sample sizes in order to obtain meaningful statistics while remaining small enough to avoid capturing variations in the mesoscopic particle field. Two-point spatial correlations are computed to assess the validity of the filter in extracting meaningful statistics. The filtering approach is applied to fully-developed cluster-induced turbulence (CIT), where the production of fluid-phase kinetic energy results entirely from momentum coupling with finite-size inertial particles. Simulation results show a strong correlation between the local volume fraction and granular temperature, with maximum values located just upstream of clusters (i.e., where maximum compressibility of the particle velocity field exists), and negligible particle agitation is observed within clusters.

Numerical study of collisional particle dynamics in cluster-induced turbulence

2014 ◽  
Vol 747 ◽  
Author(s):  
Jesse Capecelatro ◽  
Olivier Desjardins ◽  
Rodney O. Fox
Keyword(s):  
Velocity Field ◽  
Volume Fraction ◽  
Numerical Study ◽  
Computational Study ◽  
Finite Size ◽  
Fluid Phase ◽  
Spatial Filter ◽  
Particle Dynamics ◽  
Spatial Correlations ◽  
Phase Volume Fraction

AbstractWe present a computational study of cluster-induced turbulence (CIT), where the production of fluid-phase kinetic energy results entirely from momentum coupling with finite-size inertial particles. A separation of length scales must be established when evaluating the particle dynamics in order to distinguish between the continuous mesoscopic velocity field and the uncorrelated particle motion. To accomplish this, an adaptive spatial filter is employed on the Lagrangian data with an averaging volume that varies with the local particle-phase volume fraction. This filtering approach ensures sufficient particle sample sizes in order to obtain meaningful statistics while remaining small enough to avoid capturing variations in the mesoscopic particle field. Two-point spatial correlations are computed to assess the validity of the filter in extracting meaningful statistics. The method is used to investigate, for the first time, the properties of a statistically stationary gravity-driven particle-laden flow, where particle–particle and fluid–particle interactions control the multiphase dynamics. Results from fully developed CIT show a strong correlation between the local volume fraction and the granular temperature, with maximum values located at the upstream boundary of clusters (i.e. where maximum compressibility of the particle velocity field exists), while negligible particle agitation is observed within clusters.

scholarly journals Evolution of Shape and Volume Fraction of Superconducting Domains with Temperature and Anion Disorder in (TMTSF)2ClO4

Crystals ◽  
2021 ◽  
Vol 11 (1) ◽  
pp. 72
Author(s):  
Kaushal K. Kesharpu ◽  
Vladislav D. Kochev ◽  
Pavel D. Grigoriev
Keyword(s):  
Cooling Rate ◽  
Annealing Time ◽  
Volume Fraction ◽  
Density Wave ◽  
Spin Density Wave ◽  
Finite Size ◽  
Organic Superconductors ◽  
Organic Superconductor ◽  
Sample Length ◽  
Sample Shape

In highly anisotropic organic superconductor (TMTSF)2ClO4, superconducting (SC) phase coexists with metallic and spin-density wave phases in the form of domains. Using the Maxwell-Garnett approximation (MGA), we calculate the volume ratio and estimate the shape of these embedded SC domains from resistivity data at various temperature and anion disorder, controlled by the cooling rate or annealing time of (TMTSF)2ClO4 samples. We found that the variation of cooling rate and of annealing time affect differently the shape of SC domains. In all cases the SC domains have oblate shape, being the shortest along the interlayer z-axis. This contradicts the widely assumed filamentary superconductivity along the z-axis, used to explain the anisotropic superconductivity onset. We show that anisotropic resistivity drop at the SC onset can be described by the analytical MGA theory with anisotropic background resistance, while the anisotropic Tc can be explained by considering a finite size and flat shape of the samples. Due to a flat/needle sample shape, the probability of percolation via SC domains is the highest along the shortest sample dimension (z-axis), and the lowest along the sample length (x-axis). Our theory can be applied to other heterogeneous superconductors, where the size d of SC domains is much larger than the SC coherence length ξ, e.g., cuprates, iron-based or organic superconductors. It is also applicable when the spin/charge-density wave domains are embedded inside a metallic background, or vice versa.

scholarly journals Flow analysis of particulate suspension on an asymmetric peristaltic motion in a curved configuration with heat and mass transfer

2018 ◽  
Vol 19 (4) ◽  
pp. 401 ◽  
Author(s):  
Ahmed Zeeshan ◽  
Nouman Ijaz ◽  
Muhammad Mubashir Bhatti
Keyword(s):  
Volume Fraction ◽  
Biological Fluids ◽  
Particle Volume Fraction ◽  
Flow Analysis ◽  
Volumetric Flow Rate ◽  
Fluid Phase ◽  
Peristaltic Motion ◽  
Particle Volume ◽  
Two Phase ◽  
Peristaltic Pumping

This article addresses the influence of particulate-fluid suspension on asymmetric peristaltic motion through a curved configuration with mass and heat transfer. A motivation for the current study is that such kind of theory is helpful to examine the two-phase peristaltic motion between small muscles during the propagation of different biological fluids. Moreover, it is also essential in multiple applications of pumping fluid-solid mixtures by peristalsis, i.e., Chyme in small intestine and suspension of blood in arteriole. Long wavelength, as well as small Reynolds number, have been utilized to render the governing equations for particle and fluid phase. Exact solutions are presented for velocity (uf,p), temperature (θf,p) and concentration distributions (φf,p). All the parameters such as Prandtl number (Pr), particle volume fraction (C), suspension parameter (M1), curvature parameter (k), volumetric flow rate (Q), Schmidt number (Sc), phase difference (φ), Eckert number (Ec), and Soret number (Sr) discussed graphically for peristaltic pumping (Δp), pressure gradient (dp/dx), velocity (uf,p), temperature (θf,p) and concentration distributions (φf,p). The streamlines are also plotted with the aid of contour.

scholarly journals Discussion on improved method of turbulence model for supercritical water flow and heat transfer

2020 ◽  
Vol 24 (5 Part A) ◽  
pp. 2729-2741
Author(s):  
Zhenchuan Wang ◽  
Guoli Qi ◽  
Meijun Li
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Turbulence Model ◽  
Buoyancy Effect ◽  
Improved Method ◽  
Production Term ◽  
Flow And Heat Transfer ◽  
Effect Model

The turbulence model fails in supercritical fluid-flow and heat transfer simulation, owing to the drastic change of thermal properties. The inappropriate buoyancy effect model and the improper turbulent Prandtl number model are several of these factors lead to the original low-Reynolds number turbulence model unable to predict the wall temperature for vertically heated tubes under the deteriorate heat transfer conditions. This paper proposed a simplified improved method to modify the turbulence model, using the generalized gradient diffusion hypothesis approximation model for the production term of the turbulent kinetic energy due to the buoyancy effect, using a turbulence Prandtl number model for the turbulent thermal diffusivity instead of the constant number. A better agreement was accomplished by the improved turbulence model compared with the experimental data. The main reason for the over-predicted wall temperature by the original turbulence model is the misuse of the buoyancy effect model. In the improved model, the production term of the turbulent kinetic energy is much higher than the results calculated by the original turbulence model, especially in the boundary-layer. A more accurate model for the production term of the turbulent kinetic energy is the main direction of further modification for the low Reynolds number turbulence model.

Coherent Velocity Structures in the Mixed Layer: Characteristics, Energetics, and Turbulent Kinetic Energy Budget

2021 ◽  
Author(s):  
Ewa Jarosz ◽  
Hemantha W. Wijesekera ◽  
David W. Wang
Keyword(s):  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Mixed Layer ◽  
Vertical Velocity ◽  
Mixed Layer Depth ◽  
Vertical Transport ◽  
Rate Of Change ◽  
Production Term ◽  
Forcing Mechanisms ◽  
Surface Buoyancy

AbstractVelocity, hydrographic, and microstructure observations collected under moderate to high winds, large surface waves, and significant ocean-surface heat losses were utilized to examine coherent velocity structures (CVS) and turbulent kinetic energy (TKE) budget in the mixed layer on the outer shelf in the northern Gulf of Mexico in February 2017. The CVS exhibited larger downward velocities in downweling regions and weaker upward velocities in broader upwelling regions, elevated vertical velocity variance, vertical velocity maxima in the upper part of the mixed layer, and phasing of crosswind velocities relative to vertical velocities near the base of the mixed layer. Temporal scales ranged from 10 min to 40 min and estimated lateral scales ranged from 90 m to 430 m, which were 1.5 – 6 times larger than the mixed layer depth. Nondimensional parameters, Langmuir and Hoenikker numbers, indicated that plausible forcing mechanisms were surface-wave driven Langmuir vortex and destabilizing surface buoyancy flux. The rate of change of TKE, shear production, Stokes production, buoyancy production, vertical transport of TKE, and dissipation in the TKE budget were evaluated. The shear and Stokes productions, dissipation, and vertical transport of TKE were the dominant terms. The buoyancy production term was important at the sea surface, but it decreased rapidly in the interior. A large imbalance term was found under the unstable, high wind, and high-sea state conditions. The cause of this imbalance cannot be determined with certainty through analyses of the available observations; however, our speculation is that the pressure transport is significant under these conditions.

Interaction between a spatially growing turbulent boundary layer and embedded streamwise vortices

1996 ◽  
Vol 326 ◽  
pp. 151-179 ◽  
Author(s):  
Junhui Liu ◽  
Ugo Piomelli ◽  
Philippe R. Spalart
Keyword(s):  
Boundary Layer ◽  
Kinetic Energy ◽  
Turbulent Boundary Layer ◽  
Turbulent Kinetic Energy ◽  
Vortex Core ◽  
Eddy Viscosity ◽  
Shear Stresses ◽  
Streamwise Vortices ◽  
Mean Velocity ◽  
Production Term

The interaction between a zero-pressure-gradient turbulent boundary layer and a pair of strong, common-flow-down, streamwise vortices with a sizeable velocity deficit is studied by large-eddy simulation. The subgrid-scale stresses are modelled by a localized dynamic eddy-viscosity model. The results agree well with experimental data. The vortices drastically distort the boundary layer, and produce large spanwise variations of the skin friction. The Reynolds stresses are highly three-dimensional. High levels of kinetic energy are found both in the upwash region and in the vortex core. The two secondary shear stresses are significant in the vortex region, with magnitudes comparable to the primary one. Turbulent transport from the immediate upwash region is partly responsible for the high levels of turbulent kinetic energy in the vortex core; its effect on the primary stress 〈u′v′〉 is less significant. The mean velocity gradients play an important role in the generation of 〈u′v′〉 in all regions, while they are negligible in the generation of turbulent kinetic energy in the vortex core. The pressure-strain correlations are generally of opposite sign to the production terms except in the vortex core, where they have the same sign as the production term in the budget of 〈u′v′〉. The results highlight the limitations of the eddy-viscosity assumption (in a Reynolds-averaged context) for flows of this type, as well as the excessive diffusion predicted by typical turbulence models.

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