scholarly journals Exact solutions for steady granular flow in vertical chutes and pipes

2021 ◽  
Vol 930 ◽  
Author(s):  
T. Barker ◽  
C. Zhu ◽  
J. Sun
Keyword(s):  
Exact Solutions ◽  
Scaling Laws ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Finite Size ◽  
Shear Zones ◽  
Common Component ◽  
Dem Simulations ◽  
Simple Scaling ◽  
Fast Flow

Vertical chutes and pipes are a common component of many industrial apparatus used in the transport and processing of powders and grains. Here, a typical arrangement is considered first in which a hopper at the top feeds the chute and a converging outlet at the bottom controls the mass flux. Discrete element method (DEM) simulations reveal that steady uniform flow is only observed for intermediate flow rates, with jamming and unsteady waves dominating slow flows and non-uniform wall detachment in fast flow. Focusing on the steady uniform regimes, a progressive idealisation is carried out by matching with equivalent DEM simulations in periodic cells. These investigations justify a one-dimensional continuum modelling of the problem and provide key test data. Novel exact solutions are derived here for vertical flow using a linear version of the ‘ $\mu(I),\varPhi(I)$ -rheology’, for which the bulk friction $\mu$ and steady solid volume fraction $\varPhi$ depend on the inertial number I. Despite not capturing the full nonlinear complexities, the solutions match important aspects of the DEM flow fields and reveal simple scaling laws linking many quantities of interest. In particular, this study clearly demonstrates a linear relation between the chute width and the size of the shear zones at the walls. This finding contrasts with previous works on purely quasi-static flow, which instead predict a roughly constant shear zone width, a difference which implies that finite-size effects are minimal for the inertial flows studied here.

scholarly journals L-Box Form Filling of Thixotropic Cementitious Paste and Mortar

Materials ◽  
2020 ◽  
Vol 13 (7) ◽  
pp. 1760
Author(s):  
Mareike Thiedeitz ◽  
Nasime Habib ◽  
Thomas Kränkel ◽  
Christoph Gehlen
Keyword(s):  
Yield Stress ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Rheological Parameters ◽  
Empirical Equations ◽  
Dynamic Yield Stress ◽  
Shear Rates ◽  
Flow Length ◽  
Dynamic Yield ◽  
Fast Flow

Rheological properties of cementitious pastes and mortar affect the casting, placement, and setting properties of fresh concrete. Fundamental rheological knowledge thus helps in predicting concrete flowability and workability. Empirical equations correlate actual rheological parameters based on physical material characteristics to workability tests. Still, these equations generally only take the dynamic yield stress of the material into account. This is not sufficient for thixotropic cementitious pastes or mortars, which possess structural buildup at rest. Workability predictions regarding the flow of concrete are thus more complicated with thixotropic materials. During form-filling in L-shaped formworks, the flow velocity of concrete slows down, wherefore rheological parameters change with time. At initial fast flow, high shear rates without structural buildup can be assumed. Dynamic yield stress and a steady state viscosity thus are proper parameters for empirical equations describing concrete flowability. During low shear rates, partial structural buildup takes place. Viscosity and yield stress increase due to agglomeration and affect the flowability of concrete tremendously. Rheological parameters of various cementitious pastes and mortars varying in their solid volume fraction and flowability were investigated in a vane-in-cup rheometer. The workability of the same mixtures was investigated by measuring the flow length in an L-shaped formwork. The effect of yield stress, viscosity, and thixotropic structural buildup on flow length was investigated. Subsequently correlations and discrepancies between flowability parameters and workability equations were analyzed.

Ciliary Flow of Casson Nanofluid with the Influence of MHD having Carbon Nanotubes

2020 ◽  
Vol 16 ◽  
Author(s):  
Adel Alblawi ◽  
Saba Keyani ◽  
S. Nadeem ◽  
Alibek Issakhov ◽  
Ibrahim M. Alarifi
Keyword(s):  
Carbon Nanotubes ◽  
Velocity Profile ◽  
Pressure Gradient ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Pressure Rise ◽  
Shear Stresses ◽  
Left Wall ◽  
Coupled Equations ◽  
The Right

Objective: In this paper, we consider a model that describes the ciliary beating in the form of metachronal waves along with the effects of Magnetohydrodynamic fluid over a curved channel with slip effects. This work aims at evaluating the effect of Magnetohydrodynamic (MHD) on the steady two dimensional (2-D) mixed convection flow induced in carbon nanotubes. The work is done for both the single wall nanotube and multiple wall nanotube. The right wall and the left wall possess a metachronal wave that is travelling along the outer boundary of the channel. Methods: The wavelength is considered as very large for cilia induced MHD flow. The governing linear coupled equations are simplified by considering the approximations of long wavelength and small Reynolds number. Exact solutions are obtained for temperature and velocity profile. The analytical expressions for the pressure gradient and wall shear stresses are obtained. Term for pressure rise is obtained by applying Numerical integration method. Results: Numerical results of velocity profile are mentioned in a table form, for various values of solid volume fraction, curvature, Hartmann number [M] and Casson fluid parameter [ζ]. Final section of this paper is devoted to discussing the graphical results of temperature, pressure gradient, pressure rise, shear stresses and stream functions. Conclusion: Velocity profile near the right wall of the channel decreases when we add nanoparticles into our base fluid, whereas an opposite behaviour is depicted near the left wall due to ciliated tips whereas the temperature is an increasing function of B and ߛ and decreasing function of ߶.

scholarly journals Quantification of shear viscosity and wall slip velocity of highly concentrated suspensions with non-Newtonian matrices in pressure driven flows

2021 ◽  
Author(s):  
Patrick Wilms ◽  
Jan Wieringa ◽  
Theo Blijdenstein ◽  
Kees van Malssen ◽  
Reinhard Kohlus
Keyword(s):  
Shear Stress ◽  
Liquid Phase ◽  
Shear Rate ◽  
Shear Viscosity ◽  
Slip Velocity ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Wall Slip ◽  
Flow Index ◽  
Concentrated Suspensions

AbstractThe rheological characterization of concentrated suspensions is complicated by the heterogeneous nature of their flow. In this contribution, the shear viscosity and wall slip velocity are quantified for highly concentrated suspensions (solid volume fractions of 0.55–0.60, D4,3 ~ 5 µm). The shear viscosity was determined using a high-pressure capillary rheometer equipped with a 3D-printed die that has a grooved surface of the internal flow channel. The wall slip velocity was then calculated from the difference between the apparent shear rates through a rough and smooth die, at identical wall shear stress. The influence of liquid phase rheology on the wall slip velocity was investigated by using different thickeners, resulting in different degrees of shear rate dependency, i.e. the flow indices varied between 0.20 and 1.00. The wall slip velocity scaled with the flow index of the liquid phase at a solid volume fraction of 0.60 and showed increasingly large deviations with decreasing solid volume fraction. It is hypothesized that these deviations are related to shear-induced migration of solids and macromolecules due to the large shear stress and shear rate gradients.

Effects of uniform or non-uniform heating at bottom wall on MHD mixed convection in a porous cavity saturated by nanofluid

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Subramanian Muthukumar ◽  
Selvaraj Sureshkumar ◽  
Arthanari Malleswaran ◽  
Murugan Muthtamilselvan ◽  
Eswari Prem
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Transfer Rate ◽  
Hartmann Number ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Darcy Number ◽  
Bottom Wall ◽  
Uniform Heating ◽  
The Magnetic Field

Abstract A numerical investigation on the effects of uniform and non-uniform heating of bottom wall on mixed convective heat transfer in a square porous chamber filled with nanofluid in the appearance of magnetic field is carried out. Uniform or sinusoidal heat source is fixed at the bottom wall. The top wall moves in either positive or negative direction with a constant cold temperature. The vertical sidewalls are thermally insulated. The finite volume approach based on SIMPLE algorithm is followed for solving the governing equations. The different parameters connected with this study are Richardson number (0.01 ≤ Ri ≤ 100), Darcy number (10−4 ≤ Da ≤ 10−1), Hartmann number (0 ≤ Ha ≤ 70), and the solid volume fraction (0.00 ≤ χ ≤ 0.06). The results are presented graphically in the form of isotherms, streamlines, mid-plane velocities, and Nusselt numbers for the various combinations of the considered parameters. It is observed that the overall heat transfer rate is low at Ri = 100 in the positive direction of lid movement, whereas it is low at Ri = 1 in the negative direction. The average Nusselt number is lowered on growing Hartmann number for all considered moving directions of top wall with non-uniform heating. The low permeability, Da = 10−4 keeps the flow pattern same dominating the magnetic field, whereas magnetic field strongly affects the flow pattern dominating the high Darcy number Da = 10−1. The heat transfer rate increases on enhancing the solid volume fraction regardless of the magnetic field.

scholarly journals A sensitivity study on carbon nanotubes significance in Darcy–Forchheimer flow towards a rotating disk by response surface methodology

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Anum Shafiq ◽  
Tabassum Naz Sindhu ◽  
Qasem M. Al-Mdallal
Keyword(s):  
Heat Transfer ◽  
Carbon Nanotubes ◽  
Ethylene Glycol ◽  
Biot Number ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Rotating Disk ◽  
Sensitivity Study ◽  
Basic Fluid ◽  
Walled Cnts

AbstractThe current research explores incremental effect of thermal radiation on heat transfer improvement corresponds to Darcy–Forchheimer (DF) flow of carbon nanotubes along a stretched rotating surface using RSM. Casson carbon nanotubes’ constructed model in boundary layer flow is being investigated with implications of both single-walled CNTs and multi-walled CNTs. Water and Ethylene glycol are considered a basic fluid. The heat transfer rate is scrutinized via convective condition. Outcomes are observed and evaluated for both SWCNTs and MWCNTs. The Runge–Kutta Fehlberg technique of shooting is utilized to numerically solve transformed nonlinear ordinary differential system. The output parameters of interest are presumed to depend on governing input variables. In addition, sensitivity study is incorporated. It is noted that sensitivity of SFC via SWCNT-Water becomes higher by increasing values of permeability number. Additionaly, sensitivity of SFC via SWCNT-water towards the permeability number is higher than the solid volume fraction for medium and higher permeability levels. It is also noted that sensitivity of SFC (SWCNT-Ethylene-glycol) towards volume fraction is higher for increasing permeability as well as inertia coefficient. Additionally, the sensitivity of LNN towards the Solid volume fraction is higher than the radiation and Biot number for all levels of Biot number. The findings will provide initial direction for future device manufacturing.

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.

FEW-PARTICLE ANYON EXCITON: EXACT SOLUTIONS

2003 ◽  
Vol 02 (06) ◽  
pp. 461-468
Author(s):  
D. G. W. PARFITT ◽  
M. E. PORTNOI
Keyword(s):  
Exact Solutions ◽  
Finite Size ◽  
Spherical Geometry ◽  
Planar Geometry ◽  
Quantum Liquid ◽  
Dimensional Electron ◽  
Adequate Description ◽  
Exciton Model ◽  
Finite Size Effects ◽  
Dimensional Electron Gas

The anyon exciton model, which describes an exciton against the background of an incompressible quantum liquid, is generalized to the case of an arbitrary number of anyons. Some mathematical aspects of this quantum-mechanical few-particle problem are considered and several exact solutions are obtained. The four-particle case is also considered in the classical limit in both planar and spherical geometries. Such a classical approach gives an adequate description of an anyon exciton at large separation between the valence hole and the two-dimensional electron gas. It is shown that in this limit in a planar geometry the anyon exciton is always energetically more favorable than a charged anyon ion. This indicates that the appearance of fractionally-charged anyon ions reported in recent numerical calculations is an artefact apparently caused by finite-size effects in a spherical geometry.

Impact of viscosity variation on oblique flow of Cu–H2O nanofluid

2017 ◽  
Vol 232 (5) ◽  
pp. 622-631 ◽  
Author(s):  
R Tabassum ◽  
Rashid Mehmood ◽  
O Pourmehran ◽  
NS Akbar ◽  
M Gorji-Bandpy
Keyword(s):  
Heat Flux ◽  
Friction Coefficient ◽  
Skin Friction ◽  
Volume Fraction ◽  
Variable Viscosity ◽  
Solid Volume Fraction ◽  
Local Heat ◽  
Skin Friction Coefficient ◽  
Viscosity Parameter ◽  
Local Heat Flux

The dynamic properties of nanofluids have made them an area of intense research during the past few decades. In this article, flow of nonaligned stagnation point nanofluid is investigated. Copper–water based nanofluid in the presence of temperature-dependent viscosity is taken into account. The governing nonlinear coupled ordinary differential equations transformed by partial differential equations are solved numerically by using fourth-order Runge–Kutta–Fehlberg integration technique. Effects of variable viscosity parameter on velocity and temperature profiles of pure fluid and copper–water nanofluid are analyzed, discussed, and presented graphically. Streamlines, skin friction coefficients, and local heat flux of nanofluid under the impact of variable viscosity parameter, stretching ratio, and solid volume fraction of nanoparticles are also displayed and discussed. It is observed that an increase in solid volume fraction of nanoparticles enhances the magnitude of normal skin friction coefficient, tangential skin friction coefficient, and local heat flux. Viscosity parameter is found to have decreasing effect on normal and tangential skin friction coefficients whereas it has a positive influence on local heat flux.

scholarly journals Of isbræ and ice streams

2003 ◽  
Vol 36 ◽  
pp. 66-72 ◽  
Author(s):  
Martin Truffer ◽  
Keith A. Echelmeyer
Keyword(s):  
Ice Sheet ◽  
Shear Zones ◽  
West Antarctica ◽  
Ice Streams ◽  
Ice Flow ◽  
Bed Topography ◽  
Ice Stream ◽  
Fast Ice ◽  
Fast Flow ◽  
End Members

AbstractFast-flowing ice streams and outlet glaciers provide the major avenues for ice flow from past and present ice sheets. These ice streams move faster than the surrounding ice sheet by a factor of 100 or more. Several mechanisms for fast ice-stream flow have been identified, leading to a spectrum of different ice-stream types. In this paper we discuss the two end members of this spectrum, which we term the “ice-stream” type (represented by the Siple Coast ice streams in West Antarctica) and the “isbræ” type (represented by Jakobshavn Isbræ in Greenland). The typical ice stream is wide, relatively shallow (∼1000 m), has a low surface slope and driving stress (∼10 kPa), and ice-stream location is not strongly controlled by bed topography. Fast flow is possible because the ice stream has a slippery bed, possibly underlain by weak, actively deforming sediments. The marginal shear zones are narrow and support most of the driving stress, and the ice deforms almost exclusively by transverse shear. The margins seem to be inherently unstable; they migrate, and there are plausible mechanisms for such ice streams to shut down. The isbræ type of ice stream is characterized by very high driving stresses, often exceeding 200 kPa. They flow through deep bedrock channels that are significantly deeper than the surrounding ice, and have steep surface slopes. Ice deformation includes vertical as well as lateral shear, and basal motion need not contribute significantly to the overall motion. The marginal shear zone stend to be wide relative to the isbræ width, and the location of isbræ and its margins is strongly controlled by bedrock topography. They are stable features, and can only shut down if the high ice flux cannot be supplied from the adjacent ice sheet. Isbræs occur in Greenland and East Antarctica, and possibly parts of Pine Island and Thwaites Glaciers, West Antarctica. In this paper, we compare and contrast the two types of ice streams, addressing questions such as ice deformation, basal motion, subglacial hydrology, seasonality of ice flow, and stability of the ice streams.

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