scholarly journals Steady and unsteady fluidised granular flows down slopes

2017 ◽  
Vol 827 ◽  
pp. 67-120 ◽  
Author(s):  
D. E. Jessop ◽  
A. J. Hogg ◽  
M. A. Gilbertson ◽  
C. Schoof
Keyword(s):  
Gas Flow ◽  
Numerical Solutions ◽  
Volume Fraction ◽  
Granular Flows ◽  
Similarity Solutions ◽  
Two Phase ◽  
Basal Resistance ◽  
Front Position ◽  
Theoretical Predictions ◽  
Asymptotic Reduction

Fluidisation is the process by which the weight of a bed of particles is supported by a gas flow passing through it from below. When fluidised materials flow down an incline, the dynamics of the motion differs from their non-fluidised counterparts because the granular agitation is no longer required to support the weight of the flowing layer. Instead, the weight is borne by the imposed gas flow and this leads to a greatly increased flow mobility. In this paper, a framework is developed to model this two-phase motion by incorporating a kinetic theory description for the particulate stresses generated by the flow. In addition to calculating numerical solutions for fully developed flows, it is shown that for sufficiently thick flows there is often a local balance between the production and dissipation of the granular temperature. This phenomenon permits an asymptotic reduction of the full governing equations and the identification of a simple state in which the volume fraction of the flow is uniform. The results of the model are compared with new experimental measurements of the internal velocity profiles of steady granular flows down slopes. The distance covered with time by unsteady granular flows down slopes and along horizontal surfaces and their shapes are also measured and compared with theoretical predictions developed for flows that are thin relative to their streamwise extent. For the horizontal flows, it was found that resistance from the sidewalls was required in addition to basal resistance to capture accurately the unsteady evolution of the front position and the depth of the current and for situations in which sidewall drag dominates, similarity solutions are found for the experimentally measured motion.

scholarly journals Numerical study of radiative non-Darcy nanofluid flow over a stretching sheet with a convective Nield conditions and energy activation

2021 ◽  
Vol 10 (1) ◽  
pp. 159-176
Author(s):  
N. Vedavathi ◽  
Ghuram Dharmaiah ◽  
Kothuru Venkatadri ◽  
Shaik Abdul Gaffar
Keyword(s):  
Numerical Solutions ◽  
Volume Fraction ◽  
Numerical Study ◽  
Similarity Solutions ◽  
Physical Parameters ◽  
Stretching Surface ◽  
Two Phase ◽  
Relevant Variable ◽  
Flow And Heat Transfer ◽  
Metal Spinning

Abstract Numerous industrial processes such as continuous metal casting and polymer extrusion in metal spinning, include flow and heat transfer over a stretching surface. The theoretical investigation of magnetohydro-dynamic thermally radiative non-Darcy Nanofluid flows through a stretching surface is presented considering also the influences of thermal conductivity and Arrhenius activation energy. Buongiorno’s two-phase Nanofluid model is deployed in order to generate Thermophoresis and Brownian motion effects [1]. By similarity transformation technique, the transport equations and the respective boundary conditions are normalized and the relevant variable and concerned similarity solutions are presented to summarize the transpiration parameter. An appropriate Matlab software (Bvp4c) is used to obtain the numerical solutions. The graphical influence of various thermo physical parameters are inspected for momentum, energy and nanoparticle volume fraction distributions. Tables containing the Nusselt number, skin friction and Sherwood number are also presented and well argued. The present results are compared with the previous studies and are found to be well correlated and are in good agreement. The existing modelling approach in the presence of nanoparticles enhances the performance of thermal energy thermo-plastic devices.

scholarly journals A Method for Generating Approximate Similarity Solutions of Nonlinear Partial Differential Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Mazhar Iqbal ◽  
M. T. Mustafa ◽  
Azad A. Siddiqui
Keyword(s):  
Gas Flow ◽  
Numerical Solutions ◽  
Nonlinear Partial Differential Equations ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Similarity Solutions ◽  
Standard Application ◽  
Approximate Similarity ◽  
Initial Boundary Value ◽  
Unsteady Gas Flow

Standard application of similarity method to find solutions of PDEs mostly results in reduction to ODEs which are not easily integrable in terms of elementary or tabulated functions. Such situations usually demand solving reduced ODEs numerically. However, there are no systematic procedures available to utilize these numerical solutions of reduced ODE to obtain the solution of original PDE. A practical and tractable approach is proposed to deal with such situations and is applied to obtain approximate similarity solutions to different cases of an initial-boundary value problem of unsteady gas flow through a semi-infinite porous medium.

EQUILIBRIUM VELOCITY DISTRIBUTION FUNCTIONS FOR A KINETIC MODEL OF TWO-PHASE FLOWS

1995 ◽  
Vol 05 (02) ◽  
pp. 191-211 ◽  
Author(s):  
LIONEL SAINSAULIEU
Keyword(s):  
Velocity Distribution ◽  
Gas Flow ◽  
Stokes Equations ◽  
Volume Fraction ◽  
Velocity Distribution Function ◽  
Distribution Functions ◽  
Solid Particles ◽  
Navier Stokes ◽  
Two Phase ◽  
Entropy Balance

We consider a cloud of solid particles in a gas flow. The cloud is described by a probability density function which satisfies a kinetic equation. The gas flow is modeled by Navier-Stokes equations. The two phases exchange momentum and energy. We obtain the entropy balance of the gas flow and deduce some bounds for the volume fraction of the gas phase. Writing the entropy balance for the dispersed phase enables one to determine the particles equilibrium velocity distribution function when the gas flow is known.

Interaction of Shock and Expansion Wave With Solid Particles in Supersonic Flows

2002 ◽  
Author(s):  
Ali Dolatabadi ◽  
Javad Mostaghimi ◽  
Valerian Pershin
Keyword(s):  
Mach Number ◽  
Flow Regime ◽  
Drag Force ◽  
Gas Flow ◽  
Volume Fraction ◽  
Supersonic Flows ◽  
Operating Conditions ◽  
Solid Particles ◽  
Process Efficiency ◽  
Two Phase

Interaction of solid particles with shock and expansions in supersonic flows is analyzed. In this analysis, a dense cloud of solid particulates is modeled by using a fully Eulerian approach. The dispersed flow and the gas flow were considered in the Eulerian frame whereby most of the physical aspects of the gas-particle flow can be incorporated. In addition to the momentum and energy exchanges in the form of source terms appearing in the governing equations, the two phases were strongly coupled by considering the volume fraction of the particulate phase in the equations. The simulation performed for a High Velocity Oxy-Fuel (HVOF) process under typical operating conditions in which the powder loading is high and the two-phase flow is not dilute near the injection port. The simulations showed large variations in the flow regime in the region that most of the particles exist. Unlike the results corresponding to the Lagrangian approach, the flow becomes subsonic near the centerline and the drag force decreases significantly since the relative Mach number is small. The validation experiments showed that the variation of flow regime by changing the relative Mach number could significantly change the particle drag force, and consequently process efficiency.

Experimental Investigation on Air-Solid Two-Phase Mixture Discharge under AC Voltage

2011 ◽  
Vol 383-390 ◽  
pp. 4955-4961
Author(s):  
Wen Jun Yao ◽  
Zheng Hao He ◽  
He Ming Deng
Keyword(s):  
Gas Flow ◽  
Volume Fraction ◽  
Fundamental Problem ◽  
Solid Particles ◽  
Two Phase ◽  
The Common ◽  
Phase Mixture ◽  
Multi Phase ◽  
Inception Voltage ◽  
Statistical Rule

Multi-phase mixture (MPM) discharge has the common characteristics of randomness with air but more complex. How about the statistical rule of MPM discharge ? This is not only a fundamental problem for discharge research, but it has its own strong applied and practical characteristics. The air-solid two-phase mixtures(ASTPM) are employed to study and carry out some experiments for investigating the development and breakdown of MPM discharge under AC voltage. The results from experimental data show that the AC breakdown voltage and corona-inception voltage will drop when the solid particles are added to the discharge chamber with different permittivity and volume fraction. And there is no influence in gas flow and the corona current.

Transport of Cu–H2O nanofluid through a channel with wavy walls under velocity slip and connective boundary conditions

2016 ◽  
Vol 09 (02) ◽  
pp. 1650022 ◽  
Author(s):  
F. M. Abbasi ◽  
T. Hayat ◽  
A. Alsaedi
Keyword(s):  
Boundary Conditions ◽  
Pressure Gradient ◽  
Axial Velocity ◽  
Numerical Solutions ◽  
Volume Fraction ◽  
Pressure Rise ◽  
Velocity Slip ◽  
Fluid Temperature ◽  
Two Phase ◽  
Convective Boundary

Present study examines the mixed convective peristaltic transport of Cu–H2O nanofluid with velocity slip and convective boundary conditions. Analysis is performed using the two-phase model of the nanofluid. Viscous dissipation and heat generation/absorption effects are also taken into account. Problem is formulated using the long wavelength and low Reynolds number approach. Numerical solutions for the pressure rise per wavelength, pressure gradient, axial velocity, temperature and heat transfer rate at the boundary are obtained and studied through graphs. Results show that the area of peristaltic pumping decreases with an increase in the nanoparticles volume fraction. Increase in the velocity slip parameter shows an increase of the pressure gradient in the occluded part of the channel. Further, addition of copper nanoparticles reduces both the axial velocity and temperature of the base fluid. Temperature of the nanofluid also decreases sufficiently for an increase in the value of Biot number.

Numerical Simulation of Particle-Gas Flow Through a Fixed Pipe, Using One-Way and Two-Way Coupling Methods

2016 ◽  
Vol 33 (2) ◽  
pp. 205-212 ◽  
Author(s):  
Z. Namazian ◽  
A. F. Najafi ◽  
S. M. Mousavian
Keyword(s):  
Numerical Simulation ◽  
Gas Flow ◽  
Volume Fraction ◽  
Fluid Velocity ◽  
Particle Volume Fraction ◽  
Stokes Number ◽  
Continuous Phase ◽  
Turbulent Pipe Flow ◽  
Particle Volume ◽  
Two Phase

AbstractA numerical simulation of the particle-gas flow in a vertical turbulent pipe flow was conducted. The main objective of the present article is to investigate the effects of dispersed phase (particles) on continuous phase (gas). In so doing, two general forms of Eulerian-Lagrangian approaches namely, one-way (when the fluid flow is not affected by the presence of the particles) and two-way (when the particles exert a feedback force on the fluid) couplings were used to describe the equations of motion of the two-phase flow. Gas-phase velocities which are within the order of magnitude as that of particles, volume fraction, and particle Stokes number were calculated and the results were subsequently compared with the available experimental data. The simulated results show that when the particles are added, the fluid velocity is attenuated. With an increase in particle volume fraction, particle mass loading and Stokes number, velocity attenuation also increases. Moreover, the results indicate that an increase in particle Stokes number reduces the special limited particle volume fraction, according to which one-way coupling method yields plausible results. The results have also indicated that the significance of particle fluid interaction is not merely a function of volume fraction and particle Stokes number.

Gas-Solid Two-Phase Flow Simulation of Coaxial Powder Delivery Nozzle in Rapid Prototyping

2010 ◽  
Vol 29-32 ◽  
pp. 1663-1667 ◽  
Author(s):  
Zhi Jian Wang ◽  
Xiao Feng Shang
Keyword(s):  
Rapid Prototyping ◽  
Metal Powder ◽  
Gas Flow ◽  
Two Phase Flow ◽  
Volume Fraction ◽  
Flow Simulation ◽  
Phase Flow ◽  
Two Phase ◽  
Good Convergence ◽  
And Performance

Coaxial powder delivery nozzle plays an important role in metal part direct and rapid prototyping technology and the reasonable structure can ensure uniform and stable flow of metal powder. Gas-solid two-phase flow theory is considered to simulate outside flow field of carrying gas-type coaxial powder delivery nozzle. The physical and mathematical models are erected. FLUENT software is used to simulate the velocity distribution of gas and solid particle, the volume fraction distribution of particle and the focusing properties. The simulative results indicate that both the structure of coaxial powder delivery nozzle and inlet velocity affect the convergence of powder. When the metal powder is only driven by the carrying gas without the shield gas flow, the powder appears focusing and the focus is 8mm far from the nozzle exit, but the volume fraction at the focus is only 2.6 percent, which shows the convergence of powder is not good and the usage rate is not high. In the optimized structure the simulative results show that the powder flow is affected by the flow of shield gas. When the velocity of shield gas is 6m/s, the powder shows good convergence and the volume fraction of powder at the focus reaches 3.3 percent. The higher the velocity of shield gas is, the more uniformly the powder flows, but the volume fraction at the focus is slightly lower. It is obvious that the numerical simulation will benefit for coaxial nozzle designing and performance improving.

scholarly journals Gas holdup in a reciprocating plate bioreactor: Non-Newtonian - liquid phase

2002 ◽  
Vol 56 (5) ◽  
pp. 198-203 ◽  
Author(s):  
Olivera Naseva ◽  
Ivica Stamenkovic ◽  
Ivana Bankovic-Ilic ◽  
Miodrag Lazic ◽  
Vlada Veljkovic ◽  
...  
Keyword(s):  
Gas Flow ◽  
Volume Fraction ◽  
Methyl Cellulose ◽  
Gas Holdup ◽  
Degree Of Polymerization ◽  
Operating Conditions ◽  
Solid Particles ◽  
Flow Index ◽  
Two Phase ◽  
Vibration Rate

The gas holdup was studied in non-newtonian liquids in a gas-liquid and gas-liquid-solid reciprocating plate bioreactor. Aqueous solutions of carboxy methyl cellulose (CMC; Lucel, Lucane, Yugoslavia) of different degrees of polymerization (PP 200 and PP 1000) and concentration (0,5 and 1%), polypropylene spheres (diameter 8.3 mm; fraction of spheres: 3.8 and 6.6% by volume) and air were used as the liquid, solid and gas phase. The gas holdup was found to be dependent on the vibration rate, the superficial gas velocity, volume fraction of solid particles and Theological properties of the liquid ohase. Both in the gas-liquid and gas-liquid-solid systems studied, the gas holdup increased with increasing vibration rate and gas flow rate. The gas holdup was higher in three-phase systems than in two-phase ones under otter operating conditions being the same. Generally the gas holdup increased with increasing the volume fraction of solid particles, due to the dispersion action of the solid particles, and decreased with increasing non-Newtonian behaviour (decreasing flow index) i.e. with increasing degree of polymerization and solution concentration of CMC applied, as a result of gas bubble coalescence.

scholarly journals The Results of Numerical Simulation of Two-Phase Liquid-Gas Flow with Constant and Real Thermodynamics Properties of the Liquid in a Shock-Jet Nozzle

2019 ◽  
pp. 51-60
Author(s):  
A.D. Khlopov ◽  
M.S. Frantsuzov
Keyword(s):  
Liquid Phase ◽  
Thermophysical Properties ◽  
Gas Flow ◽  
Volume Fraction ◽  
Temperature Dependent ◽  
Two Phase ◽  
Dispersion Process ◽  
Commercial Software Package ◽  
Phase Liquid ◽  
Jet Nozzle

In this paper, the outflow of liquid in the coflowing airstream from a shock-jet nozzle is examined using a commercial software package with varying initial and boundary conditions. Gas-dynamic characteristics and distribution fields for pressure, velocity, temperature and volume fraction of the two-phase flow are obtained. The influence of thermophysical properties of the liquid on the process of jet dispersion is determined. The results of simulation of the liquid outflow from the shock-jet nozzle at constant and real (temperature dependent) thermophysical properties of the liquid phase are compared. The qualitative and quantitative influence of the input pressure in the nozzle on the jet dispersion process is determined. As a result of a series of calculations, the minimum required characteristics of temporal and spatial resolution for the correct solution of the problem are identified. It is established that the volume content of the liquid phase is higher with real thermophysical properties compared to the constant ones.

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