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.

Modeling of Wall Friction for Multispecies Solid-Gas Flows

1986 ◽  
Vol 108 (4) ◽  
pp. 486-488 ◽  
Author(s):  
E. D. Doss ◽  
M. G. Srinivasan
Keyword(s):  
Shear Stress ◽  
Flow Model ◽  
Flow Characteristics ◽  
Wall Friction ◽  
Gas Flows ◽  
Two Phase ◽  
One Dimensional ◽  
Friction Models ◽  
Wall Interaction ◽  
The One

The empirical expressions for the equivalent friction factor to simulate the effect of particle-wall interaction with a single solid species have been extended to model the wall shear stress for multispecies solid-gas flows. Expressions representing the equivalent shear stress for solid-gas flows obtained from these wall friction models are included in the one-dimensional two-phase flow model and it can be used to study the effect of particle-wall interaction on the flow characteristics.

scholarly journals The development of biofilm architecture

2016 ◽  
Vol 472 (2188) ◽  
pp. 20150798 ◽  
Author(s):  
A. C. Fowler ◽  
T. M. Kyrke-Smith ◽  
H. F. Winstanley
Keyword(s):  
Bacterial Biofilm ◽  
Governing Equations ◽  
Biofilm Growth ◽  
One Dimensional ◽  
Direct Numerical Solution ◽  
The Common ◽  
Common Observation ◽  
The Stability ◽  
The One ◽  
A Free Boundary Problem

We extend the one-dimensional polymer solution theory of bacterial biofilm growth described by Winstanley et al . (2011 Proc. R. Soc. A 467 , 1449–1467 ( doi:10.1098/rspa.2010.0327 )) to deal with the problem of the growth of a patch of biofilm in more than one lateral dimension. The extension is non-trivial, as it requires consideration of the rheology of the polymer phase. We use a novel asymptotic technique to reduce the model to a free-boundary problem governed by the equations of Stokes flow with non-standard boundary conditions. We then consider the stability of laterally uniform biofilm growth, and show that the model predicts spatial instability; this is confirmed by a direct numerical solution of the governing equations. The instability results in cusp formation at the biofilm surface and provides an explanation for the common observation of patterned biofilm architectures.

scholarly journals Study of Unsteady Flow in a Heat Exchanger by the Method of Characteristics

1992 ◽  
Vol 114 (4) ◽  
pp. 459-463 ◽  
Author(s):  
Yuan Mao Huang
Keyword(s):  
Heat Exchanger ◽  
Unsteady Flow ◽  
Transfer Rate ◽  
Method Of Characteristics ◽  
Governing Equations ◽  
One Dimensional ◽  
The Method Of Characteristics ◽  
Improvement Factor ◽  
The One ◽  
Good Agreement

The one-dimensional, unsteady flow in an air-to-air heat exchanger is studied. The governing equations are derived and the method of characteristics with the uniform interval scheme is used in the analysis. The effect of the fin improvement factor on the air temperature in the heat exchanger and the heat transfer rate of the heat exchanger, and air properties in the heat exchanger are analyzed. The numerical results are compared and show good agreement with the available data.

Miscible rectilinear displacements with gravity override. Part 1. Homogeneous porous medium

2000 ◽  
Vol 420 ◽  
pp. 225-257 ◽  
Author(s):  
MICHAEL RUITH ◽  
ECKART MEIBURG
Keyword(s):  
Flow Characteristics ◽  
Point Of View ◽  
Governing Equations ◽  
Vorticity Field ◽  
Miscible Displacements ◽  
Homogeneous Porous Medium ◽  
Combined Action ◽  
Parameter Ranges ◽  
Impermeable Boundary ◽  
Upper Boundary

Rectilinear homogeneous miscible displacements with gravity override are analysed by means of direct numerical simulations on the basis of the vorticity–streamfunction formulation of the governing equations. The vorticity-based point of view offers the advantage of clearly attributing the dominant flow characteristics to the effects of viscosity contrast, density difference, impermeable boundary conditions, or interactions among the above. Basic considerations regarding the vorticity field show that in an integral sense the coupling between viscosity and gravity vorticity is predominantly one way in nature, in that the gravity vorticity can amplify the viscous vorticity, but not vice versa. In particular, the vorticity point of view provides an explanation for the formation of the gravity tongue in terms of a focusing mechanism, which results from the combined action of the unfavourable viscosity gradient and the potential flow field generated by the interaction of the gravitational vorticity with the horizontal boundaries. This potential velocity field locally enhances the uniform global displacement velocity near the upper boundary, and thereby amplifies the viscous fingering instability along this section of the interface. In some parameter ranges, the gravity tongue exhibits interesting interactions with the viscous fingers next to it, such as pinching and partial merging. The influence of the Péclet number, the viscosity and density contrasts, and the aspect ratio on the dynamic evolution of the displacement is investigated quantitatively.

Modeling Shrouded Stator Cavity Flows in Axial-Flow Compressors

1999 ◽  
Vol 122 (1) ◽  
pp. 55-61 ◽  
Author(s):  
S. R. Wellborn ◽  
I. Tolchinsky ◽  
T. H. Okiishi
Keyword(s):  
Flow Analysis ◽  
Flow Characteristics ◽  
Axial Flow ◽  
Analysis Tool ◽  
Cavity Flows ◽  
Dimensional Model ◽  
Primary Flow ◽  
One Dimensional ◽  
Stage Matching ◽  
The One

Experiments and computational analyses were completed to understand the nature of shrouded stator cavity flows. From this understanding, a one-dimensional model of the flow through shrouded stator cavities was developed. This model estimates the leakage mass flow, temperature rise, and angular momentum increase through the cavity, given geometry parameters and the flow conditions at the interface between the cavity and primary flow path. This cavity model consists of two components, one that estimates the flow characteristics through the labyrinth seals and the other that predicts the transfer of momentum due to windage. A description of the one-dimensional model is given. The incorporation and use of the one-dimensional model in a multistage compressor primary flow analysis tool is described. The combination of this model and the primary flow solver was used to reliably simulate the significant impact on performance of the increase of hub seal leakage in a twelve-stage axial-flow compressor. Observed higher temperatures of the hub region fluid, different stage matching, and lower overall efficiencies and core flow than expected could be correctly linked to increased hub seal clearance with this new technique. The importance of including these leakage flows in compressor simulations is shown. [S0889-504X(00)00501-8]

THE FINITE-DIFFERENCE METHOD OF ONE-DIMENSIONAL NONLINEAR SYSTEMS ANALYSIS

Fractals ◽  
2000 ◽  
Vol 08 (01) ◽  
pp. 49-65 ◽  
Author(s):  
A. YU. SHAHVERDIAN
Keyword(s):  
Time Series ◽  
Systems Analysis ◽  
Computational Study ◽  
Brain Activity ◽  
Logistic Map ◽  
Cantor Sets ◽  
Point Of View ◽  
One Dimensional ◽  
Time Flow ◽  
The One

The paper introduces one-dimensional analogy of Poincare "section" method. It reduces the one-dimensional nonlinear system orbit's study to consideration of some special conjugate orbit's "asymptotical" intersections with a thin arithmetical space of zero Lebesgue measure. The application of this approach to analysis of the logistic map orbits, earthquake time-series, and the sequences of fractional parts, is considered. Through computational study of these time-series, the existence of some Cantor sets, to which the conjugate orbits are attracted, is established. A fractal dynamical system, describing these different systems from a unified point of view, is introduced. The inner differential Cantorian structure of brain activity and time flow is discussed.

A Parametric Study of Surge and Flow Instabilities in Gas Pipeline Compression Systems: The Effect of Pipe Parameters on Surge Margins

2002 ◽  
Author(s):  
K. Albayrak ◽  
D. Burtaskiray ◽  
O. C. Eralp ◽  
K. M. Akyuzly
Keyword(s):  
Parametric Study ◽  
Gas Flow ◽  
Coupling Effect ◽  
Flow Characteristics ◽  
Working Fluid ◽  
Geometrical Parameters ◽  
Pipe Length ◽  
Compression System ◽  
One Dimensional ◽  
Numerical Experimentation

There is a need to understand the effect of coupling of the flow characteristics of a compressor with that of the pipeline and how this coupling effect the stability of the flow in a compression system. This study addresses such a need by carrying out a numerical simulation of the flow in the whole compression system including the compressor, the pipeline, and the other associated flow elements. A nonlinear, one-dimensional mathematical model is adopted for the present study. In this model, the gas flow inside the pipeline is assumed one-dimensional, viscous, and compressible. A parametric study is carried out using the proposed model, with air as the working fluid, to predict the surge margins for a subscale compression system and to study the effect of pipe length and diameter on these margins. Furthermore, the effect of these geometrical parameters on the amplitude and frequency of the flow oscillations are also established by numerical experimentation.

Phenomenological Approach to Flow and Volume Change in Soils and Other Media

1995 ◽  
Vol 48 (10) ◽  
pp. 650-658 ◽  
Author(s):  
J. R. Philip
Keyword(s):  
Volume Change ◽  
Colloidal Particles ◽  
Three Dimensional ◽  
Phenomenological Approach ◽  
Solid Particles ◽  
Soil Physics ◽  
One Dimensional ◽  
Component Systems ◽  
Poisson Boltzmann Equation ◽  
The One

We review the phenomenological approach, on the macroscopic or Darcy scale, to flow and volume change in clays and other swelling media. The formulation represents the generalization to media subject to volume change of the well-established phenomenological approach to flow in non-swelling media primarily established in the context of soil physics. The one-dimensional generalization to swelling media is straightforward, and may be usefully applied to practical one-dimensional systems, including three-component systems with solid particles, water, and air. On the other hand, the further generalizations to two- and three-dimensional systems have not yet been developed fully convincingly. Difficult questions include the mode of stress transmission and the tensorial stress-strain relations in multidimensional and multi-component systems. One means of gaining insight into these questions for media of high colloid content (such as clays) is through relevant solutions of the Poisson-Boltzmann equation governing electrical double-layer interactions in dense arrays of colloidal particles. These solutions give pertinent information on both the macroscopic and the microscopic scales. We present a progress report on work along these lines.

scholarly journals Analytical studies of suspension acoustics

2019 ◽  
Vol 14 (1) ◽  
pp. 27-35
Author(s):  
M.N. Galimzyanov ◽  
V.Sh. Shagapov
Keyword(s):  
Sound Velocity ◽  
Speed Of Sound ◽  
Carrier Phase ◽  
Original System ◽  
Solid Particles ◽  
Dispersed Phase ◽  
Low Frequencies ◽  
One Dimensional ◽  
Perturbation Frequency ◽  
The One

The one-dimensional unsteady flow of the suspension is considered taking into account the standard assumptions for this problems: the mixture is monodisperse, there is no crushing and sticking of particles, viscosity and thermal conductivity are essential only in the process of interfacial interaction. The mixture supposed perfect. The particles are taken absolutely solid and spherical, and the liquid is linearly compressible. The frictional force acting on a single spherical particle is taken into account. The solution to the original system is sought in the form of a traveling wave. On the basis of one-dimensional unsteady equations of fluid flow with solid particles dispersion relations are written out and formulas for phase velocities are derived. Formulas for the attenuation coefficient of the perturbation frequency are got. It has been established that at low frequencies, depending on the magnitude of <i>ρ&#771;<sup>0</sup><sub>p0</sub>=ρ<sup>0</sup><sub>p0</sub>/ρ<sup>0</sup><sub>&#8467;0</sub></i> the equilibrium speed can be higher or lower than the speed of sound in the carrier phase. If the dispersed phase is heavier than the carrier phase (<i>ρ&#771;<sup>0</sup><sub>p0</sub>>1</i>), then the equilibrium velocity exceeds the speed of sound. This is due to the fact that at low frequencies, when velocity equilibrium is realized, the compressibility of the mixture occurs only owing to the carrier phase, and the mixture becomes heavier (inertial) because of the content of the dispersed phase at (<i>ρ&#771;<sup>0</sup><sub>p0</sub>>1</i>). When (<i>ρ&#771;<sup>0</sup><sub>p0</sub><1</i>), the mixture in contrast is lighter than the carrier phase, and the equilibrium velocity becomes higher than the speed of sound. At high frequencies the sound velocity does not depend on <i>ρ&#771;<sup>0</sup><sub>p0</sub></i> and is equal to the sound velocity for the carrier phase.

Numerical Solutions of the Equations for One-Dimensional Multi-Phase Flow in Porous Media

1966 ◽  
Vol 6 (01) ◽  
pp. 62-72 ◽  
Author(s):  
Byron S. Gottfried ◽  
W.H. Guilinger ◽  
R.W. Snyder
Keyword(s):  
Porous Media ◽  
Numerical Methods ◽  
Numerical Solutions ◽  
Flow In Porous Media ◽  
Phase Flow ◽  
Two Phase ◽  
One Dimensional ◽  
Three Phase ◽  
Three Phase Flow ◽  
The One

Abstract Two numerical methods are presented for solving the equations for one-dimensional, multiphase flow in porous media. The case of variable physical properties is included in the formulation, although gravity and capillarity are ignored. Both methods are analyzed mathematically, resulting in upper and lower bounds for the ratio of time step to mesh spacing. The methods are applied to two- and three-phase waterflooding problems in laboratory-size cores, and resulting saturation and pressure distributions and production histories are presented graphically. Results of the two-phase flow problem are in agreement with the predictions of the Buckley-Leverett theory. Several three-phase flow problems are presented which consider variations in the water injection rate and changes in the initial oil- and water-saturation distributions. The results are different physically from the two-phase case; however, it is shown that the Buckley-Leverett theory can accurately predict fluid interface velocities and displacing-fluid frontal saturations for three-phase flow, providing the correct assumptions are made. The above solutions are used as a basis for evaluating the numerical methods with respect to machine time requirements and allowable time step for a fixed mesh spacing. Introduction Considerable progress has been made in recent years in obtaining numerical solutions of the equations for two-phase flow in porous media. Douglas, Blair and Wagner2 and McEwen11 present different methods for solving the one-dimensional case for incompressible fluids with capillarity (the former using finite differences, the latter with an approach based upon characteristics). Fayers and Sheldon4 and Hovanesian and Fayers8 have extended these studies to include the effects of gravity. West, Garvin and Sheldon,14 in a pioneer paper, treat linear and radial systems with both capillarity and gravity and they also include the effects of compressibility. Douglas, Peaceman and Rachford3 consider two-dimensional, two-phase, incompressible flow with gravity and capillarity and Blair and Peaceman1 have extended this method to allow for compressible fluids. No one, however, has examined the case of three-phase flow, even for the relatively simple case of one-dimensional flow of incompressible fluids in the absence of gravity and capillarity. In obtaining a numerical technique for simulating forward in situ combustion laboratory experiments, Gottfried5 has developed a method for solving the one-dimensional, compressible flow equations with any number of flowing phases. Gravity and capillarity are not included in the formulation. The method has been used successfully, however, for two- and three-phase problems in a variable-temperature field with sources and sinks. This paper examines the algorithm of Gottfried more critically. Two numerical methods are presented for solving the one-dimensional, multi-phase flow equations with variable physical properties. Both methods are analyzed mathematically, and are used to simulate two- and three-phase waterflooding problems. The numerical solutions are then taken as a basis for comparing the utility of the methods. Problem Statement Consider a one-dimensional system in which capillarity, gravity and molecular diffusion are negligible. If n immiscible phases are present, n 2, the equation describing the flow of the ith phase is:12Equation 1 where all terms can vary with x and t.

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