scholarly journals Particle-level simulations of flocculation in a fiber suspension flowing through a diffuser

2017 ◽  
Vol 21 (suppl. 3) ◽  
pp. 573-583 ◽  
Author(s):  
Jelena Andric ◽  
Stefan Lindstrom ◽  
Srdjan Sasic ◽  
Håkan Nilsson
Keyword(s):  
Short Range ◽  
Eddy Viscosity ◽  
Stokes Equations ◽  
Fiber Suspension ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Numerical Studies ◽  
Flow Interactions ◽  
Particle Level ◽  
Dilute Suspensions

We investigate flocculation in dilute suspensions of rigid, straight fibers in a decelerating flow field of a diffuser. We carry out numerical studies using a particle-level simulation technique that takes into account the fiber inertia and the non-creeping fiber-flow interactions. The fluid flow is governed by the Reynolds-averaged Navier-Stokes equations with the standard k-omega eddy-viscosity turbulence model. A one-way coupling between the fibers and the flow is considered with a stochastic model for the fiber dispersion due to turbulence. The fibers interact through short-range attractive forces that cause them to aggregate into flocs when fiber-fiber collisions occur. We show that ballistic deflection of fibers greatly increases the flocculation in the diffuser. The inlet fiber kinematics and the fiber inertia are the main parameters that affect fiber flocculation in the prediffuser region.

Numerical Investigation of Fiber Flocculation in the Air Flow of an Asymmetric Diffuser

2014 ◽  
Author(s):  
Jelena Andric ◽  
Stefan B. Lindström ◽  
Srdjan Sasic ◽  
Håkan Nilsson
Keyword(s):  
Fluid Flow ◽  
Short Range ◽  
Stokes Equations ◽  
Equations Of Motion ◽  
Navier Stokes ◽  
Forming Process ◽  
Navier Stokes Equations ◽  
Flow Fluctuations ◽  
Dry Forming ◽  
Particle Level

A particle-level rigid fiber model is used to study flocculation in an asymmetric planar diffuser with a turbulent Newtonian fluid flow, resembling one stage in dry-forming process of pulp mats. The fibers are modeled as chains of rigid cylindrical segments. The equations of motion incorporate hydrodynamic forces and torques from the interaction with the fluid, and the fiber inertia is taken into account. The flow is governed by the Reynolds-averaged Navier–Stokes equations with the standard k–ω turbulence model. A one-way coupling between the fibers and the flow is considered. A stochastic model is employed for the flow fluctuations to capture the fiber dispersion. The fibers are assumed to interact through short-range attractive forces, causing them to interlock as the fiber-fiber contacts occur during the flow. It is found that the formation of fiber flocs is driven by both the turbulence-induced dispersion and the gradient of the averaged flow field.

scholarly journals Error Analysis of a Subgrid Eddy Viscosity Multi-Scale Discretization of the Navier-Stokes Equations

SeMA Journal ◽  
2012 ◽  
Vol 60 (1) ◽  
pp. 51-74
Author(s):  
Christine Bernardi ◽  
Tomás Chacón Rebollo ◽  
Macarena Gómez Mármol
Keyword(s):  
Error Analysis ◽  
Eddy Viscosity ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Multi Scale

scholarly journals Gyrotactic swimmers in turbulence: shape effects and role of the large-scale flow

2018 ◽  
Vol 856 ◽  
Author(s):  
M. Borgnino ◽  
G. Boffetta ◽  
F. De Lillo ◽  
M. Cencini
Keyword(s):  
Large Scale ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Small Scale ◽  
Navier Stokes Equations ◽  
Preferential Sampling ◽  
Wide Range ◽  
Shape Effects ◽  
Dilute Suspensions ◽  
Large Scale Flow

We study the dynamics and the statistics of dilute suspensions of gyrotactic swimmers, a model for many aquatic motile microorganisms. By means of extensive numerical simulations of the Navier–Stokes equations at different Reynolds numbers, we investigate preferential sampling and small-scale clustering as a function of the swimming (stability and speed) and shape parameters, considering in particular the limits of spherical and rod-like particles. While spherical swimmers preferentially sample local downwelling flow, for elongated swimmers we observe a transition from downwelling to upwelling regions at sufficiently high swimming speed. The spatial distribution of both spherical and elongated swimmers is found to be fractal at small scales in a wide range of swimming parameters. The direct comparison between the different shapes shows that spherical swimmers are more clusterized at small stability and speed numbers, while for large values of the parameters elongated cells concentrate more. The relevance of our results for phytoplankton swimming in the ocean is briefly discussed.

Numerical Study of Wave Slamming on an Oscillating Flap

2014 ◽  
Author(s):  
Yanji Wei ◽  
Alan Henry ◽  
Olivier Kimmoun ◽  
Frederic Dias
Keyword(s):  
Stokes Equations ◽  
Numerical Study ◽  
Flow Characteristics ◽  
Ocean Waves ◽  
Navier Stokes ◽  
Time Step ◽  
Navier Stokes Equations ◽  
Numerical Studies ◽  
Wave Slamming ◽  
Volume Method

Bottom hinged Oscillating Wave Surge Converters (OWSCs) are efficient devices for extracting power from ocean waves. There is limited knowledge about wave slamming on such devices. This paper deals with numerical studies of wave slamming on an oscillating flap to investigate the mechanism of slamming events. In our model, the Navier–Stokes equations are discretized using the Finite Volume method with the Volume of Fluid (VOF) approach for interface capturing. Waves are generated by a flap-type wave maker in the numerical wave tank, and the dynamic mesh method is applied to model the motion of the oscillating flap. Basic mesh and time step refinement studies are performed. The flow characteristics in a slamming event are analysed based on numerical results. Various simulations with different flap densities, water depths and wave amplitudes are performed for a better understanding of the slamming.

Conical turbulent swirling vortex with variable eddy viscosity

1986 ◽  
Vol 403 (1825) ◽  
pp. 235-268 ◽  
Keyword(s):  
Eddy Viscosity ◽  
Stokes Equations ◽  
Variable Viscosity ◽  
Similarity Solutions ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Turbulent Vortex ◽  
The Core ◽  
Vortex Solutions ◽  
Variable Eddy Viscosity

In the one hundred years since Rankine suggested his well known two-dimensional vortex model with finite core, no one has ever found any exact vortex solutions of the Navier-Stokes equations that can satisfy a complete set of physical boundary conditions. In this paper a variable viscosity is introduced and the existence of conical turbulent vortex solutions of the Navier-Stokes equations is examined. It is found that for a class of deliberately chosen eddy viscosity function a steady turbulent vortex can, for the first time, satisfy both the regularity condition at the core and the adherence condition at the surface, except for a singularity at the origin inherent in all conical similarity solutions. In its asymptotic form, if the eddy viscosity only varies in a boundary layer near the surface or the core, outside the layer the solution given would approach one of the laminar solutions of Yih et al . ( Physics Fluids 25, 2147 (1982)) or that of Serrin ( Phil. Trans. R. Soc. Lond. A 271, 325 (1972)) respectively. These results reveal some remarkable relations between the behaviour, and even the existence, of a vortex and turbulence.

Modeling Of Turbulent Transport Equations

1996 ◽  
Author(s):  
Charles G. Speziale
Keyword(s):  
Turbulent Flows ◽  
Reynolds Stress ◽  
Time Scales ◽  
Eddy Viscosity ◽  
Ad Hoc ◽  
Stokes Equations ◽  
Transport Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Stress Models

The high-Reynolds-number turbulent flows of technological importance contain such a wide range of excited length and time scales that the application of direct or large-eddy simulations is all but impossible for the foreseeable future. Reynolds stress models remain the only viable means for the solution of these complex turbulent flows. It is widely believed that Reynolds stress models are completely ad hoc, having no formal connection with solutions of the full Navier-Stokes equations for turbulent flows. While this belief is largely warranted for the older eddy viscosity models of turbulence, it constitutes a far too pessimistic assessment of the current generation of Reynolds stress closures. It will be shown how secondorder closure models and two-equation models with an anisotropic eddy viscosity can be systematically derived from the Navier-Stokes equations when one overriding assumption is made: the turbulence is locally homogeneous and in equilibrium. A brief review of zero equation models and one equation models based on the Boussinesq eddy viscosity hypothesis will first be provided in order to gain a perspective on the earlier approaches to Reynolds stress modeling. It will, however, be argued that since turbulent flows contain length and time scales that change dramatically from one flow configuration to the next, two-equation models constitute the minimum level of closure that is physically acceptable. Typically, modeled transport equations are solved for the turbulent kinetic energy and dissipation rate from which the turbulent length and time scales are built up; this obviates the need to specify these scales in an ad hoc fashion. While two-equation models represent the minimum acceptable closure, second-order closure models constitute the most complex level of closure that is currently feasible from a computational standpoint. It will be shown how the former models follow from the latter in the equilibrium limit of homogeneous turbulence. However, the two-equation models that are formally consistent with second-order closures have an anisotropic eddy viscosity with strain-dependent coefficients - a feature that most of the commonly used models do not possess.

scholarly journals Coherent large-scale structures from the linearized Navier–Stokes equations

2019 ◽  
Vol 873 ◽  
pp. 89-109 ◽  
Author(s):  
Anagha Madhusudanan ◽  
Simon. J. Illingworth ◽  
Ivan Marusic
Keyword(s):  
Large Scale ◽  
Eddy Viscosity ◽  
Stokes Equations ◽  
Turbulent Channel Flow ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Large Scale Structures ◽  
Viscosity Profile ◽  
Wide Range ◽  
Scale Structures

The wall-normal extent of the large-scale structures modelled by the linearized Navier–Stokes equations subject to stochastic forcing is directly compared to direct numerical simulation (DNS) data. A turbulent channel flow at a friction Reynolds number of $Re_{\unicode[STIX]{x1D70F}}=2000$ is considered. We use the two-dimensional (2-D) linear coherence spectrum (LCS) to perform the comparison over a wide range of energy-carrying streamwise and spanwise length scales. The study of the 2-D LCS from DNS indicates the presence of large-scale structures that are coherent over large wall-normal distances and that are self-similar. We find that, with the addition of an eddy viscosity profile, these features of the large-scale structures are captured by the linearized equations, except in the region close to the wall. To further study this coherence, a coherence-based estimation technique, spectral linear stochastic estimation, is used to build linear estimators from the linearized Navier–Stokes equations. The estimator uses the instantaneous streamwise velocity field or the 2-D streamwise energy spectrum at one wall-normal location (obtained from DNS) to predict the same quantity at a different wall-normal location. We find that the addition of an eddy viscosity profile significantly improves the estimation.

scholarly journals SURPRISING BEHAVIOUR AND SINGULARITY IN THE SAINT VENANT APPROXIMATION FOR A FLUID

2018 ◽  
Author(s):  
Paolo Luchini
Keyword(s):  
Numerical Simulation ◽  
Eddy Viscosity ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Venant Equation ◽  
Change Of Perspective ◽  
The Subject ◽  
Substantial Change

A research line is reviewed which, over a few years, led to a substantial change of perspective about the simplified models that underlie the description of quasi-onedimensional streams, their instabilities, and their effects upon sandy beds. Even when the flow is assumed to be laminar, the Saint-Venant equation of quasi-onedimensional fluid flow can be formulated in more than one manner; it will be shown that only one of these choices is consistent with the complete three-dimensional Navier- Stokes equations. When the flow is turbulent, an added complication is the presence of a turbulence model, most often of the eddy-viscosity type; it will be shown that such a model can be in strong contrast with a direct numerical simulation of the same phenomenon, even to the point of producing results of opposite sign. In addition, the complete numerical simulation of flow past an undulated bottom exhibits a non-monotonic approach to its long-wave, quasi-onedimensional limit, with a surprising resonance that has no laminar counterpart and must become the subject of future investigations.

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