scholarly journals Stability analysis of rapid granular chute flows: formation of longitudinal vortices

2002 ◽  
Vol 467 ◽  
pp. 361-387 ◽  
Author(s):  
YOËL FORTERRE ◽  
OLIVIER POULIQUEN
Keyword(s):  
Stability Analysis ◽  
Kinetic Theory ◽  
Three Dimensional ◽  
Granular Flows ◽  
Granular Temperature ◽  
Instability Mechanism ◽  
Longitudinal Vortices ◽  
Spontaneous Formation ◽  
Wide Range ◽  
Inclined Planes

In a recent article (Forterre & Pouliquen 2001), we have reported a new instability observed in rapid granular flows down inclined planes that leads to the spontaneous formation of longitudinal vortices. From the experimental observations, we have proposed an instability mechanism based on the coupling between the flow and the granular temperature in rapid granular flows. In order to investigate the relevance of the proposed mechanism, we perform in the present paper a three-dimensional linear stability analysis of steady uniform flows down inclined planes using the kinetic theory of granular flows. We show that in a wide range of parameters, steady uniform flows are unstable under transverse perturbations. The structure of the unstable modes is in qualitative agreement with the experimental observations. This theoretical analysis shows that the kinetic theory is able to capture the formation of longitudinal vortices and validates the instability mechanism.

Kinetic-theory-based model of dense granular flows down inclined planes

2012 ◽  
Vol 24 (7) ◽  
pp. 073303 ◽  
Author(s):  
Cheng-Hsien Lee ◽  
Ching-Jer Huang
Keyword(s):  
Kinetic Theory ◽  
Granular Flows ◽  
Inclined Planes ◽  
Dense Granular Flows

scholarly journals Influence of granular temperature and grain rotation on the wall friction coefficient in confined shear granular flows

2021 ◽  
Vol 249 ◽  
pp. 03026
Author(s):  
Cheng-Chuan Lin ◽  
Riccardo Artoni ◽  
Fu-Ling Yang ◽  
Patrick Richard
Keyword(s):  
Friction Coefficient ◽  
Granular Matter ◽  
Scaling Law ◽  
Three Dimensional ◽  
Granular Flows ◽  
Force Sensor ◽  
Wall Friction ◽  
Granular Temperature ◽  
Research Perspective ◽  
Dense Granular Flows

A depth-weakening wall friction coefficient, µw, has been reported from three-dimensional numerical simulations of steady and transient dense granular flows. To understand the degradation mechanisms, a scaling law for µw/ f and χ has been proposed where f is the intrinsic particle-wall friction and χ is the ratio of slip velocity to square root of granular temperature (Artoni & Richard, Phys. Rev. Lett., vol. 115 (15), 2015, 158001). Independently, a friction degradation model has been derived which describes a monotonically diminishing friction depends on a ratio of grain angular and slip velocities, Ω (Yang & Huang, Granular Matter, vol. 18 (4), 2016, 77). In search of experimental evidence for how these two parameters degrade the µw, an annular shear cell experiment was performed to estimate the bulk granular temperature, angular and slip velocities at sidewall through image-processing. Meanwhile, µw was measured by a force sensor to confirm the weakening towards the creep zone. The measured µw/ f − χ and µw/ f − Ω were both well-fitted to the corresponding models showing that both granular temperature and angular velocity are significant mechanisms to degrade the µw which broadens the research perspective on modeling the boundary condition of dense granular flows.

Stability Analysis of Collisional Granular Flow on a Slope

2003 ◽  
Vol 17 (22n24) ◽  
pp. 4290-4294
Author(s):  
Namiko Mitarai ◽  
Hiizu Nakanishi
Keyword(s):  
Stability Analysis ◽  
Kinetic Theory ◽  
Numerical Simulations ◽  
Linear Stability ◽  
Granular Flow ◽  
Granular Flows ◽  
Uniform Flow ◽  
Density Region ◽  
Long Wavelength

We analyze the linear stability of a collisional granular flow on a slope under gravity using hydrodynamical equations based on kinetic theory of inelastic particles. It is shown that the steady, uniform flow is unstable against longitudinal long-wavelength perturbations in lower density region. The results are compared with the instabilities found in numerical simulations of granular flows.

Kinetic Theory for Granular Materials

2010 ◽  
pp. 102-127 ◽  
Author(s):  
Christine M. Hrenya
Keyword(s):  
Kinetic Theory ◽  
Granular Materials ◽  
Computational Efficiency ◽  
Driving Forces ◽  
Granular Flows ◽  
Recent Past ◽  
Systematic Assessment ◽  
Model Validity ◽  
Wide Range ◽  
Species Segregation

Kinetic-theory-based models of rapid, polydisperse, solids flows are essential for the prediction of a wide range of practical flows found in both nature and industry. In this work, existing models for granular flows are critically compared by considering the techniques used for their derivation and the expected implications of those techniques. The driving forces for species segregation, as predicted by kinetic theory models, are then reviewed. Although the rigor associated with the development of such models has improved considerably in the recent past, a systematic assessment of model validity and computational efficiency is still needed. Finally, a rigorous extension of such models to gas-solid flows is discussed.

A universal three-dimensional instability of the wakes of two-dimensional bluff bodies

2016 ◽  
Vol 792 ◽  
pp. 50-66 ◽  
Author(s):  
Anirudh Rao ◽  
Mark C. Thompson ◽  
Kerry Hourigan
Keyword(s):  
Reynolds Number ◽  
Stability Analysis ◽  
Steady Flow ◽  
Structural Stability ◽  
Rotation Rate ◽  
Three Dimensional ◽  
The Other ◽  
Two Dimensional ◽  
Other Hand ◽  
Wide Range

Linear stability analysis of a wide range of two-dimensional and axisymmetric bluff-body wakes shows that the first three-dimensional mode to became unstable is always mode E. From the studies presented in this paper, it is speculated to be the universal primary 3D instability, irrespective of the flow configuration. However, since it is a transition from a steady two-dimensional flow, whether this mode can be observed in practice does depend on the nature of the flow set-up. For example, the mode E transition of a circular cylinder wake occurs at a Reynolds number of $\mathit{Re}\simeq 96$, which is considerably higher than the steady to unsteady Hopf bifurcation at $\mathit{Re}\simeq 46$ leading to Bénard–von-Kármán shedding. On the other hand, if the absolute instability responsible for the latter transition is suppressed, by rotating the cylinder or moving it towards a wall, then mode E may become the first transition of the steady flow. A well-known example is flow over a backward-facing step, where this instability is the first global instability to be manifested on the otherwise two-dimensional steady flow. Many other examples are considered in this paper. Exploring this further, a structural stability analysis (Pralits et al.J. Fluid Mech., vol. 730, 2013, pp. 5–18) was conducted for the subset of flows past a rotating cylinder as the rotation rate was varied. For the non-rotating or slowly rotating case, this indicated that the growth rate of the instability mode was sensitive to forcing between the recirculation lobes, while for the rapidly rotating case, it confirmed sensitivity near the cylinder and towards the hyperbolic point. For the non-rotating case, the perturbation, adjoint and structural stability fields, together with the wavelength selection, show some similarities with those of a Crow instability of a counter-rotating vortex pair, at least within the recirculation zones. On the other hand, at much higher rotation rates, Pralits et al. (J. Fluid Mech., vol. 730, 2013, pp. 5–18) have suggested that hyperbolic instability may play a role. However, both instabilities lie on the same continuous solution branch in Reynolds number/rotation-rate parameter space. The results suggest that this particular flow transition at least, and probably others, may have a number of different physical mechanisms supporting their development.

scholarly journals Numerical realization of helical vortices: application to vortex instability

2019 ◽  
Vol 34 (1-2) ◽  
pp. 1-20
Author(s):  
Mattias Brynjell-Rahkola ◽  
Dan S. Henningson
Keyword(s):  
Stability Analysis ◽  
Vortex Core ◽  
Reference Frames ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Vortex System ◽  
Simple Method ◽  
Wide Range ◽  
Theoretical Predictions ◽  
Entire Flow

AbstractThe need to numerically represent a free vortex system arises frequently in fundamental and applied research. Many possible techniques for realizing this vortex system exist but most tend to prioritize accuracy either inside or outside of the vortex core, which therefore makes them unsuitable for a stability analysis considering the entire flow field. In this article, a simple method is presented that is shown to yield an accurate representation of the flow inside and outside of the vortex core. The method is readily implemented in any incompressible Navier–Stokes solver using primitive variables and Cartesian coordinates. It can potentially be used to model a wide range of vortices but is here applied to the case of two helices, which is of renewed interest due to its relevance for wind turbines and helicopters. Three-dimensional stability analysis is performed in both a rotating and a translating frame of reference, which yield eigenvalue spectra that feature both mutual inductance and elliptic instabilities. Comparison of these spectra with available theoretical predictions is used to validate the proposed baseflow model, and new insights into the elliptic instability of curved Batchelor vortices are presented. Furthermore, it is shown that the instabilities in the rotating and the translating reference frames have the same structure and growth rate, but different frequency. A relation between these frequencies is provided.

scholarly journals Self-diffusion scalings in dense granular flows

Soft Matter ◽  
2021 ◽  
Author(s):  
Riccardo Artoni ◽  
Michele Larcher ◽  
James T. Jenkins ◽  
Patrick Richard
Keyword(s):  
Shear Rate ◽  
Solid Fraction ◽  
Granular Flows ◽  
The Self ◽  
Granular Temperature ◽  
Restitution Coefficient ◽  
Self Diffusion ◽  
Diffusivity Tensor ◽  
Dense Granular Flows

The self-diffusivity tensor in homogeneously sheared dense granular flows is anisotropic. We show how its components depend on solid fraction, restitution coefficient, shear rate, and granular temperature.

Turbulent three-dimensional dielectric electrohydrodynamic convection between two plates

2012 ◽  
Vol 696 ◽  
pp. 228-262 ◽  
Author(s):  
A. Kourmatzis ◽  
J. S. Shrimpton
Keyword(s):  
Spatial Data ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Energy Budgets ◽  
Turbulent Regime ◽  
Scalar Flux ◽  
Wide Range ◽  
Scalar Variance

AbstractThe fundamental mechanisms responsible for the creation of electrohydrodynamically driven roll structures in free electroconvection between two plates are analysed with reference to traditional Rayleigh–Bénard convection (RBC). Previously available knowledge limited to two dimensions is extended to three-dimensions, and a wide range of electric Reynolds numbers is analysed, extending into a fully inherently three-dimensional turbulent regime. Results reveal that structures appearing in three-dimensional electrohydrodynamics (EHD) are similar to those observed for RBC, and while two-dimensional EHD results bear some similarities with the three-dimensional results there are distinct differences. Analysis of two-point correlations and integral length scales show that full three-dimensional electroconvection is more chaotic than in two dimensions and this is also noted by qualitatively observing the roll structures that arise for both low (${\mathit{Re}}_{E} = 1$) and high electric Reynolds numbers (up to ${\mathit{Re}}_{E} = 120$). Furthermore, calculations of mean profiles and second-order moments along with energy budgets and spectra have examined the validity of neglecting the fluctuating electric field ${ E}_{i}^{\ensuremath{\prime} } $ in the Reynolds-averaged EHD equations and provide insight into the generation and transport mechanisms of turbulent EHD. Spectral and spatial data clearly indicate how fluctuating energy is transferred from electrical to hydrodynamic forms, on moving through the domain away from the charging electrode. It is shown that ${ E}_{i}^{\ensuremath{\prime} } $ is not negligible close to the walls and terms acting as sources and sinks in the turbulent kinetic energy, turbulent scalar flux and turbulent scalar variance equations are examined. Profiles of hydrodynamic terms in the budgets resemble those in the literature for RBC; however there are terms specific to EHD that are significant, indicating that the transfer of energy in EHD is also attributed to further electrodynamic terms and a strong coupling exists between the charge flux and variance, due to the ionic drift term.

scholarly journals Application of Dendrimers for Treating Parasitic Diseases

Pharmaceutics ◽  
2021 ◽  
Vol 13 (3) ◽  
pp. 343
Author(s):  
Veronica Folliero ◽  
Carla Zannella ◽  
Annalisa Chianese ◽  
Debora Stelitano ◽  
Annalisa Ambrosino ◽  
...  
Keyword(s):  
Drug Delivery ◽  
Water Solubility ◽  
Parasitic Infection ◽  
Three Dimensional ◽  
Medical Knowledge ◽  
High Ratio ◽  
Molecular Volume ◽  
Parasitic Infections ◽  
Parasitic Diseases ◽  
Wide Range

Despite advances in medical knowledge, parasitic diseases remain a significant global health burden and their pharmacological treatment is often hampered by drug toxicity. Therefore, drug delivery systems may provide useful advantages when used in combination with conventional therapeutic compounds. Dendrimers are three-dimensional polymeric structures, characterized by a central core, branches and terminal functional groups. These nanostructures are known for their defined structure, great water solubility, biocompatibility and high encapsulation ability against a wide range of molecules. Furthermore, the high ratio between terminal groups and molecular volume render them a hopeful vector for drug delivery. These nanostructures offer several advantages compared to conventional drugs for the treatment of parasitic infection. Dendrimers deliver drugs to target sites with reduced dosage, solving side effects that occur with accepted marketed drugs. In recent years, extensive progress has been made towards the use of dendrimers for therapeutic, prophylactic and diagnostic purposes for the management of parasitic infections. The present review highlights the potential of several dendrimers in the management of parasitic diseases.

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