scholarly journals Modeling of multiphase flow at solid particles hydropelling

2019 ◽  
pp. 67-71
Author(s):  
A.Yu. Dreus ◽  
A.V. Haminich ◽  
N.V. Koval ◽  
S.V. Dziuba
Keyword(s):  
Multiphase Flow ◽  
Gas Flow ◽  
Solid Phase ◽  
Flow Simulation ◽  
Solid Particles ◽  
Hydraulic Lift ◽  
Algebraic Equations ◽  
Flow Parameters ◽  
Three Phase ◽  
Nonlinear Algebraic Equations

Purpose. Development of methods for calculating the parameters of the solid particles lifting from the bottom of reservoirs based on the three-phase (gas-liquid-solid particles) flow simulation in an air-lift pipe. Methodology. Mathematical modeling of multiphase flows based on hydraulic ratios. In doing so, heights of up to 10 m (short airlift) are considered with corresponding physical assumptions. Findings. A methodological support has been developed for calculating rational parameters of modes of transporting solid particles with a short airlift. The solution of the problem of the solid particles hydraulic lift by a short airlift is reduced to solving a system of nonlinear algebraic equations. Parametric calculations were carried out and the dependences of the gas flow rate required to ensure a given airlift performance were determined, and the influence of the geometric characteristics of the pipelines on the flow of the solid phase was estimated. Originality. The proposed method allows one to determine the parameters of the solid particles hydraulic lift in a short airlift by solving a system of nonlinear algebraic equations, without using the apparatus of mathematical physics methods. Practical value. It consists in the development of a method for calculating and determining rational parameters of pulp transportation processes in short airlifts. These methods make it possible to determine the dependence of the air flow on the solid particles flow and substantiate the corresponding geometric and flow parameters of the hydraulic lift system. Key words: short airlift, multiphase flow, solid particles hydraulic lift, technological calculatio.

Predictable Model for Characteristics of One-Dimensional Solid-Gas-Liquid Three-Phase Mixtures Flow Along a Vertical Pipeline With an Abrupt Enlargement in Diameter

1999 ◽  
Vol 121 (2) ◽  
pp. 330-342 ◽  
Author(s):  
Natsuo Hatta ◽  
Masaaki Omodaka ◽  
Fumitaka Nakajima ◽  
Takahiro Takatsu ◽  
Hitoshi Fujimoto ◽  
...  
Keyword(s):  
Gas Flow ◽  
Sudden Change ◽  
Flow Characteristics ◽  
Point Of View ◽  
Solid Particles ◽  
Governing Equations ◽  
One Dimensional ◽  
Three Phase ◽  
Experimental Values ◽  
The One

This paper treats the numerical analysis of the rising process of a solid-gas-liquid three-phase mixture along a vertical pipeline with an abrupt enlargement in diameter. The system of governing equations used is based upon the one-dimensional multifluid model and the transitions of gas flow pattern are taken into account in the system of governing equations. For the case of a sudden enlargement in diameter in a coaxial pipeline, the procedure of the numerical calculation to obtain the flow characteristics in the pipeline section after a sudden change in diameter has been established here. Furthermore, in order to confirm the validity of the present theoretical model by the comparison between the calculated and experimental values, the experiments have been made using four kinds of lifting pipes, including the straight one. Thereby, it has been found that the numerical model proposed here gives good fit to the prediction of the flow rates of lifted water and solid particles against that of air supplied for the case of a sudden change in diameter. In addition, the flowing process for each phase has been investigated from a photographic point of view. As a result, we found that the moving process of the solid particles depends strongly upon the volumetric flux of gas-phase as well as the submergence ratio.

scholarly journals Axial dispersion of the liquid phase on a three-phase Karr reciprocating plate column

2004 ◽  
Vol 69 (7) ◽  
pp. 581-599 ◽  
Author(s):  
Ljubisa Nikolic ◽  
Vesna Nikolic ◽  
Vlada Veljkovic ◽  
Miodrag Lazic ◽  
Dejan Skala
Keyword(s):  
Liquid Phase ◽  
Gas Flow ◽  
Dispersion Coefficient ◽  
Solid Phase ◽  
Axial Dispersion ◽  
Two Phase ◽  
Three Phase ◽  
Phase Liquid ◽  
Similar Equation ◽  
Plate Column

The influence of the gas flow rate and vibration intensity in the presence of the solid phase (polypropylene spheres) on axial mixing of the liquid phase in a three phase (gas-liquid-solid) Karr reciprocating plate column (RPC) was investigated. Assuming that the dispersionmodel of liquid flow could be used for the real situation inside the column, the dispersion coefficient of the liquid phase was determined as a function of different operating parameters. For a two-phase liquid-solid RPC the following correlation was derived: DL = 1.26(Af)1.42 UL 0.51 ?S 0.23 and a similar equation could be applied with ? 30 % confidence for the calculation of axial dispersion in the case of a three-phase RPC: DL = 1.39(Af)0.47 UL0.42UG0.03 ?S -0.26.

A three-phase nonequilibrium model for catalytic distillation

2009 ◽  
Vol 63 (2) ◽  
Author(s):  
Marcel Kotora ◽  
Zuzana Švandová ◽  
Jozef Markoš
Keyword(s):  
Effective Diffusivity ◽  
Solid Catalyst ◽  
Algebraic Equations ◽  
Catalytic Distillation ◽  
Nonequilibrium Model ◽  
Three Phase ◽  
Nonlinear Algebraic Equations ◽  
Steady State Simulation ◽  
Heat Transfers ◽  
Fortran Programming Language

AbstractNonequilibrium model for steady state simulation of catalytic distillation is presented. Mathematical model takes into account both mass and heat transfers across the gas liquid interface and through the liquid-solid (catalyst) interface. Equations describing the mentioned phenomena are based on the effective diffusivity approach. The resulting system of nonlinear algebraic equations was implemented in the FORTRAN programming language and solved by the BUNLSI (Ferraris & Tronconi, 1986) solver. The described model was verified using the experimental data obtained from a continuous distillation column equipped with catalytic packing. As an experimental model system, synthesis of propyl propionate from propan-1-ol and propionic acid was chosen. Comparison of experimental and simulation data is presented, and appropriateness of the developed model for other types of catalytic distillation processes is discussed.

Computations of Particle-Laden Turbulent Jet Flows Based on Eulerian Model

2013 ◽  
Vol 136 (1) ◽  
Author(s):  
Pandaba Patro ◽  
Sukanta K. Dash
Keyword(s):  
Gas Flow ◽  
Fine Particles ◽  
Solid Phase ◽  
Fluid Model ◽  
Particle Diameter ◽  
Velocity Profiles ◽  
Solid Particles ◽  
Jet Flows ◽  
Particle Sizes ◽  
Turbulent Characteristics

Numerical simulations using an Eulerian two-fluid model were performed for spatially developing, two-dimensional, axisymmetric jets issued from a 30-mm-diameter circular nozzle. The nozzle was simulated separately for various flow conditions to get fully developed velocity profiles at its exit. The effect of interparticle collisions in the nozzle gives rise to solids pressure and viscosity, which are modeled using kinetic theory of granular flows (KTGF). The particle sizes are in the range of 30 μm to 2 mm, and the particle loading is varied from 1 to 5. The fully developed velocity profiles are expressed by power law, U=Uc(1-(r/R))N. The exponent, N, is found to be 0.14 for gas phase, irrespective of particle sizes and particulate loadings. However, the solid-phase velocity varies significantly with the particle diameter. For particle sizes up to 200 μm, the exponent is 0.12. The center line velocity (Uc) of the solid phase decreases and, hence, the slip velocity increases as the particle size increases. For 1 mm and 2 mm size particles, the exponent is found to be 0.08 and 0.05, respectively. The developed velocity profiles of both the phases are used as the inlet velocities for the jet simulation. The modulations on the flow structures and turbulent characteristics of gas flow due to the solid particles with different particle sizes and loadings are investigated. The jet spreading and the decay of the centerline mean velocity are computed for all particle sizes and loadings considered under the present study. Additions of solid particles to the gas flow significantly modulate the gas turbulence in the nozzle as well as the jet flows. Fine particles suppress the turbulence, whereas coarse particles enhance it.

Use of Different Numerical Solution Approaches for a Three-Phase Slurry Catalytic Reactor Model

2003 ◽  
Vol 1 (1) ◽  
Author(s):  
Mardonny Nazareno Barreira ◽  
Eduardo Coselli Vasco de Toledo ◽  
Rubens Maciel Filho ◽  
Maria das Graças Enrique
Keyword(s):  
Steady State ◽  
Steady State Solution ◽  
Distributed Parameter ◽  
Algebraic Equations ◽  
Orthogonal Collocation ◽  
Reactor Model ◽  
Three Phase ◽  
Steady State Model ◽  
Nonlinear Algebraic Equations ◽  
Volume Method

In this paper two different numerical approaches are used to find out the steady-state solution for multiphase chemical reactors. Such systems are distributed parameter systems and the steady-state formulation problem leads to a system of nonlinear algebraic equations. The problem is to solve the equations in a robust way so that reliable predictions can be made. Bearing this in mind in this work two methods are implement and their performances compared, to know the Orthogonal Collocation Method e the Finite Volume Method. The results show that in spite of good qualitative agreement in the predictions the latter approaches in more suitable to have a direct solution of the steady-state model of the reactor.

The influence of the Stokes and Archimedes forces on the stability of a two-phase flow

2003 ◽  
Vol 3 ◽  
pp. 266-270
Author(s):  
B.H. Khudjuyerov ◽  
I.A. Chuliev
Keyword(s):  
Spectral Method ◽  
Stability Region ◽  
Gas Flow ◽  
Two Phase Flow ◽  
Solid Phase ◽  
Stability Characteristic ◽  
Phase Flow ◽  
Two Phase ◽  
The Stability

The problem of the stability of a two-phase flow is considered. The solution of the stability equations is performed by the spectral method using polynomials of Chebyshev. A decrease in the stability region gas flow with the addition of particles of the solid phase. The analysis influence on the stability characteristic of Stokes and Archimedes forces.

Modeling of pressure losses on friction in three-layer laminar flows

2003 ◽  
Vol 3 ◽  
pp. 208-219
Author(s):  
A.M. Ilyasov
Keyword(s):  
Pressure Loss ◽  
Gas Flow ◽  
Mutual Influence ◽  
Fluid Model ◽  
Immiscible Liquid ◽  
Laminar Flows ◽  
Pressure Losses ◽  
Flow Parameters ◽  
Interphase Boundaries ◽  
Closing Relations

In this paper we propose a model for determining the pressure loss due to friction in each phase in a three-layer laminar steady flow of immiscible liquid and gas flow in a flat channel. This model generalizes an analogous problem for a two-layer laminar flow, proposed earlier. The relations obtained in the final form for the pressure loss due to friction in liquids can be used as closing relations for the three-fluid model. These equations take into account the influence of interphase boundaries and are an alternative to the approach used in foreign literature. In this approach, the wall and interphase voltages are approximated by the formulas for a single-phase flow and do not take into account the mutual influence of liquids on the loss of pressure on friction in phases. The distribution of flow parameters in these two models is compared.

scholarly journals Enhanced discrete phase model for multiphase flow simulation of blood flow with high shear stress

2021 ◽  
Vol 104 (1) ◽  
pp. 003685042110080
Author(s):  
Zheqin Yu ◽  
Jianping Tan ◽  
Shuai Wang
Keyword(s):  
Blood Flow ◽  
Shear Stress ◽  
Multiphase Flow ◽  
Experimental Verification ◽  
Flow Simulation ◽  
Turbulence Models ◽  
Phase Model ◽  
Force Model ◽  
Discrete Phase Model ◽  
Discrete Phase

Shear stress is often present in the blood flow within blood-contacting devices, which is the leading cause of hemolysis. However, the simulation method for blood flow with shear stress is still not perfect, especially the multiphase flow model and experimental verification. In this regard, this study proposes an enhanced discrete phase model for multiphase flow simulation of blood flow with shear stress. This simulation is based on the discrete phase model (DPM). According to the multiphase flow characteristics of blood, a virtual mass force model and a pressure gradient influence model are added to the calculation of cell particle motion. In the experimental verification, nozzle models were designed to simulate the flow with shear stress, varying the degree of shear stress through different nozzle sizes. The microscopic flow was measured by the Particle Image Velocimetry (PIV) experimental method. The comparison of the turbulence models and the verification of the simulation accuracy were carried out based on the experimental results. The result demonstrates that the simulation effect of the SST k- ω model is better than other standard turbulence models. Accuracy analysis proves that the simulation results are accurate and can capture the movement of cell-level particles in the flow with shear stress. The results of the research are conducive to obtaining accurate and comprehensive analysis results in the equipment development phase.

scholarly journals Frequency–Amplitude Relationship of a Nonlinear Symmetric Panel Absorber Mounted on a Flexible Wall

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1188
Author(s):  
Yiu-Yin Lee
Keyword(s):  
Elliptic Integral ◽  
Algebraic Equations ◽  
Cavity Depth ◽  
Nonlinear Algebraic Equations ◽  
Flexible Panel ◽  
Flexible Wall ◽  
Elliptic Integral Method ◽  
Flexible Panels ◽  
Relationship Of ◽  
Panel Absorber

This study addresses the frequency–amplitude relationship of a nonlinear symmetric panel absorber mounted on a flexible wall. In many structural–acoustic works, only one flexible panel is considered in their models with symmetric configuration. There are very limited research investigations that focus on two flexible panels coupled with a cavity, particularly for nonlinear structural–acoustic problems. In practice, panel absorbers with symmetric configurations are common and usually mounted on a flexible wall. Thus, it should not be assumed that the wall is rigid. This study is the first work employing the weighted residual elliptic integral method for solving this problem, which involves the nonlinear multi-mode governing equations of two flexible panels coupled with a cavity. The reason for adopting the proposed solution method is that fewer nonlinear algebraic equations are generated. The results obtained from the proposed method and finite element method agree reasonably well with each other. The effects of some parameters such as vibration amplitude, cavity depth and thickness ratio, etc. are also investigated.

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