A Mathematical Model of the Solid Flow Behavior in a Real Dimension Blast Furnace: Effects of the Solid Volume Fraction on the Velocity Profile

2013 ◽  
pp. n/a-n/a ◽  
Author(s):  
Reza Safavi Nick ◽  
Anders Tilliander ◽  
Lage T. I. Jonsson ◽  
Pär G. Jönsson
Keyword(s):  
Mathematical Model ◽  
Blast Furnace ◽  
Velocity Profile ◽  
Volume Fraction ◽  
Flow Behavior ◽  
Solid Volume Fraction ◽  
Solid Flow ◽  
Real Dimension

scholarly journals Mathematical Model of Solid Flow Behavior in a Real Dimension Blast Furnace

2013 ◽  
Vol 53 (6) ◽  
pp. 979-987 ◽  
Author(s):  
Reza Safavi Nick ◽  
Anders Tilliander ◽  
Tord Lage Ingemar Jonsson ◽  
Pär Göran Jönsson
Keyword(s):  
Mathematical Model ◽  
Blast Furnace ◽  
Flow Behavior ◽  
Solid Flow ◽  
Real Dimension

2D CFD Simulation of Hydrodynamics of the Dense Zone of a 65t/h High-Low Bed CFB

2012 ◽  
Vol 614-615 ◽  
pp. 596-599
Author(s):  
Qing Wang ◽  
Jian Bo Xiao ◽  
Hong Peng Liu
Keyword(s):  
Size Distribution ◽  
Cfd Simulation ◽  
Volume Fraction ◽  
Flow Behavior ◽  
Solid Volume Fraction ◽  
Multiphase Model ◽  
Interphase Interaction ◽  
Solid Flow ◽  
Drag Model ◽  
Dense Zone

Gas-solid flow behavior of the bottom zone of a 65t/h High-low bed CFB was simulated using the commercial computational fluid dynamics (CFD) software package Fluent. The Eulerian-Eulerian model (EEM) based on the kinetic theory of granular flow (KTGF) was adopted. This approach treated each phase as continuous separately. The link between the gas and solid phases was through drag model and turbulence model. While the turbulence was simulated by the standard k-ε and mixture multiphase model, the Gidaspow drag model was used to model the interphase interaction. Four phases were set to achieve size distribution in the EEM. Gas and solid flow profiles are obtained for solid velocity, solid volume fraction, pressure, and size distribution. The results show that EEM can predict preferably the internal circulation process of the dense zone high-low bed CFB.

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 ߶.

Numerical treatment for Casson liquid flow in a microchannel due to porous medium: A hybrid nanoparticles aspects

2021 ◽  
pp. 095440622110089
Author(s):  
Gombi Rachappa Manohar ◽  
Puttaswamy Venkatesh ◽  
Bijjanal Jayanna Gireesha ◽  
Gosikere Kenchappa Ramesh
Keyword(s):  
Porous Medium ◽  
Volume Fraction ◽  
Flow Behavior ◽  
Solid Volume Fraction ◽  
Velocity Slip ◽  
Casson Fluid ◽  
Hybrid Nanoparticles ◽  
Hybrid Nanofluid ◽  
Current Investigation ◽  
Numerical Treatment

In the current investigation a mathematical model is simplified to explore the numerical treatment for the thermal and flow behavior in a magneto hydrodynamics Casson fluid through a micro channel by taking [Formula: see text] nanoparticles. The combined effects of temperature jump, porous medium and velocity slip are incorporated. Using the dimensionless variables one can obtain the governing differential equations thereafter resolved numerically using RKF45 method. The velocity, temperature, skin friction and Nusselt number coefficient are addressed for different pertaining parameter. The upshots of the current investigation are visualized through graphically elucidation. Out comes shows that larger values of solid volume fraction decreases both velocity and temperature field. Furthermore drag coefficient is increases for increase in magnetic parameter, also hybrid nanofluid gives more impact than nanofluid.

Thixotropy of Semisolid Metals

1999 ◽  
Vol 578 ◽  
Author(s):  
Andreas N. Alexandrou ◽  
Gilmer R. Burgos ◽  
Vladimir M. Entov
Keyword(s):  
Volume Fraction ◽  
Fluid Model ◽  
Flow Behavior ◽  
Solid Volume Fraction ◽  
Computer Code ◽  
Rheological Parameters ◽  
Structural Parameter ◽  
Order Kinetic ◽  
Thixotropic Behavior ◽  
Dependent Flow

AbstractUnderstanding the time-dependent flow behavior of metal alloys in semisolid state is essential for the further development of the process. In the present investigation, the thixotropic behavior of semisolid slurries is modeled using conservation equations and the Herschel-Bulkley fluid model. The rheological parameters are assumed to be functions of the solid volume fraction, and of a structural parameter that changes with processing history. The evolution of the structural parameter is described by a first order kinetic differential equation that relates the rate of build-up and break-down of the solid skeleton. The model is implemented into a computer code to predict die filling.

Stochastic Lagrangian model for hydrodynamic acceleration of inertial particles in gas–solid suspensions

2016 ◽  
Vol 788 ◽  
pp. 695-729 ◽  
Author(s):  
Sudheer Tenneti ◽  
Mohammad Mehrabadi ◽  
Shankar Subramaniam
Keyword(s):  
Particle Acceleration ◽  
Particle Velocity ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Density Ratio ◽  
Granular Temperature ◽  
Solid Flow ◽  
Acceleration Model ◽  
The Mean ◽  
Solid Suspensions

The acceleration of an inertial particle in a gas–solid flow arises from the particle’s interaction with the gas and from interparticle interactions such as collisions. Analytical treatments to derive a particle acceleration model are difficult outside the Stokes flow regime, but for moderate Reynolds numbers (based on the mean slip velocity between gas and particles) particle-resolved direct numerical simulation (PR-DNS) is a viable tool for model development. In this study, PR-DNS of freely-evolving gas–solid suspensions are performed using the particle-resolved uncontaminated-fluid reconcilable immersed-boundary method (PUReIBM) that has been extensively validated in previous studies. Analysis of the particle velocity variance (granular temperature) equation in statistically homogeneous gas–solid flow shows that a straightforward extension of a class of mean particle acceleration models (drag laws) to their corresponding instantaneous versions, by replacing the mean particle velocity with the instantaneous particle velocity, predicts a granular temperature that decays to zero, which is at variance with the steady particle granular temperature that is obtained from PR-DNS. Fluctuations in particle velocity and particle acceleration (and their correlation) are important because the particle acceleration–velocity covariance governs the evolution of the particle velocity variance (characterized by the particle granular temperature), which plays an important role in the prediction of the core annular structure in riser flows. The acceleration–velocity covariance arising from hydrodynamic forces can be decomposed into source and dissipation terms that appear in the granular temperature evolution equation, and these have already been quantified in the Stokes flow regime using a combination of kinetic theory closure and multipole expansion simulations. From PR-DNS data we show that the fluctuations in the particle acceleration that are aligned with fluctuations in the particle velocity give rise to a source term in the granular temperature evolution equation. This approach is used to quantify the hydrodynamic source and dissipation terms of granular temperature from PR-DNS results for freely-evolving gas–solid suspensions that are performed over a wide range of solid volume fraction ($0.1\leqslant {\it\phi}\leqslant 0.4$), Reynolds number based on the slip velocity between the solid and the fluid phase ($10\leqslant \mathit{Re}_{m}\leqslant 100$) and solid-to-fluid density ratio ($100\leqslant {\it\rho}_{p}/{\it\rho}_{f}\leqslant 2000$). The straightforward extension of drag law models does not give rise to any source in the granular temperature due to hydrodynamic effects. This motivates the development of better Lagrangian particle acceleration models that can be used in Lagrangian–Eulerian formulations of gas–solid flow. It is found that a Langevin equation for the increment in the particle velocity reproduces PR-DNS results for the stationary particle velocity autocorrelation in freely-evolving suspensions. Based on the data obtained from the simulations, the functional dependence of the Langevin model coefficients on solid volume fraction, Reynolds number and solid-to-fluid density ratio is obtained. This new Lagrangian particle acceleration model reproduces the correct steady granular temperature and can also be adapted to gas–solid flow computations using Eulerian moment equations.

Three-Dimensional Simulation of Gas-Solid Flow in the Biomass Circulating Fluidized Bed Gasifier’s Riser

2011 ◽  
Vol 383-390 ◽  
pp. 6537-6542
Author(s):  
Wen Yi Chen ◽  
Xin Liu ◽  
Xiao Xu Fan ◽  
Lei Zhe Chu ◽  
Yi Mei Yang ◽  
...  
Keyword(s):  
Pressure Drop ◽  
Fluidized Bed ◽  
Circulating Fluidized Bed ◽  
Volume Fraction ◽  
Mutual Influence ◽  
Solid Volume Fraction ◽  
Three Dimensional ◽  
Momentum Exchange ◽  
Solid Flow ◽  
Radial Profiles

Using the Gidaspow model as the momentum exchange coefficient to take a full-loop simulation of miniature circulating fluidized bed gasifier (CFBG) in the lab, and taking mutual influence of different parts in consideration, it focus on the gas-solid flow structure in the riser in this paper. The heterogeneous behavior in the CFBG riser and the radial profiles of solid volume fraction under different solid inventories in simulation are showed in this paper as a replenishment of certain data which are hard to measure in experiments. The results showed it can’t form an obvious core-annulus flow because of the riser’s high height-diameter ratio and the big refeed line diameter. There are clusters growing and dissipation in a short time. A turning point of pressure drop may be seem as a separation of dense area and dilute area.The three-dimensional (3D) simulation revealed the solid flux and the pressure drop agree with the experimental data.

Hydrodynamics Simulation of Gas-Solid Flow Field in Conveying Vessel

2011 ◽  
Vol 236-238 ◽  
pp. 1528-1531
Author(s):  
Yue Cui ◽  
Hong Gao ◽  
Jin Sheng Sun ◽  
Xu Chen
Keyword(s):  
Flow Field ◽  
Uniform Distribution ◽  
Volume Fraction ◽  
Dead Zone ◽  
Solid Volume Fraction ◽  
Three Dimensional ◽  
Gas Velocity ◽  
Dimensional Model ◽  
Three Dimensional Model ◽  
Solid Flow

Flow field of gas and particles in a conveying vessel is investigated by use of a three-dimensional model combined Eulerian approach. Because of the nozzles’ arrangement in this study, the flow patterns of spouts and bubbles can be seen in the gas-solid flow field, which lead to a non-uniform distribution of gas velocity. Solid volume fraction is high near the bottom and low at the top part. The porosity rises with gas speed increasing, as well as time. An improvement is examined to remove the dead zone at the bottom, which results in particles remaining.

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