scholarly journals CALCULATION OF TWO-SPEED FLOW OF TWO-PHASE OPEN FLOW

2020 ◽  
Vol 6 (444) ◽  
pp. 203-212
Author(s):  
E. A. Nysanov ◽  
◽  
Zh. S. Kemelbekova ◽  
O. M. Ibragimov ◽  
A. E. Kozhabekova ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Free Surface ◽  
Longitudinal Velocity ◽  
Solid Particles ◽  
Empirical Formulas ◽  
Longitudinal Velocity Component ◽  
Two Phase ◽  
Method Of Calculation ◽  
Phase Velocities ◽  
Speed Flow

In this article the mathematical model of unsteady flow the two-phase open stream taking into account the redistribution of the particulate concentration, the depth of flow and water filtration on the bottom of the channel, and also created an efficient method of calculation. In this case, the two-speed flow is considered, i.e. the presence of the longitudinal and vertical components of the phase velocities is taken into account, and we also believe that the flow parameters along the flow do not change. Initial and boundary conditions are established based on theoretical and empirical formulas, which are widely used in practice. The flow in open channels is non-pressurized, occurs under the influence of gravity and is characterized by the fact that the flow has a free surface. At the initial moment of time, we consider the flow to be uniform in the longitudinal direction and all parameters are set by known theoretical and empirical formulas. At the bottom of the channel for longitudinal velocity component of the water use condition of adhesion, and for the longitudinal velocity component of solid phase condition for the shift and believe the known concentrations of solid particles, and vertical components of velocity the phases of the filtering conditions (for water), and hydraulic size (for solid particles). On the free surface, we consider that there are no solid particles, and for the longitudinal components of the phase velocities we neglect the force of air friction, and for the vertical components of the phase velocities we use the condition of non-uniformity of the free surface in time. On the basis of the developed mathematical model and the created method of calculation, the changes of the main parameters in the depth of the flow and in time are determined.

Mathematical Modeling of Impingement of an Air Jet in a Liquid Bath

2010 ◽  
Vol 1276 ◽  
Author(s):  
J. Solórzano-López ◽  
R. Zenit ◽  
M. A. Ramírez-Argáez
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Free Surface ◽  
Gas Flow ◽  
Two Phase ◽  
Arc Furnaces ◽  
Air Jet ◽  
Image Velocimetry ◽  
Oxygen Gas ◽  
The Mathematical Model

AbstractPhysical and mathematical modeling of jet-bath interactions in electric arc furnaces represent valuable tools to obtain a better fundamental understanding of oxygen gas injection into the furnace. In this work, a 3D mathematical model is developed based on the two phase approach called Volume of Fluid (VOF), which is able to predict free surface deformations and it is coded in the commercial fluid dynamics software FLUENTTM. Validation of the mathematical model is achieved by measurements on a transparent water physical model. Measurements of free surface depressions through a high velocity camera and velocity patterns are recorded through a Particle Image Velocimetry (PIV) Technique. Flow patterns and depression geometry are identified and characterized as function of process parameters like distance from nozzle to bath, gas flow rate and impingement angle of the gas jet into the bath. A reasonable agreement is found between simulated and experimental results.

Cluster-Based Modeling of Fluidized Catalytic Oxidation of n-Butane to Maleic Anhydride

2006 ◽  
Vol 4 (1) ◽  
Author(s):  
Hamid Reza Hakimelahi ◽  
Rahmat Sotudeh-Gharebagh ◽  
Navid Mostoufi
Keyword(s):  
Mathematical Model ◽  
Maleic Anhydride ◽  
Fluidized Bed ◽  
Flow Reactor ◽  
Plug Flow ◽  
Fluidized Bed Reactor ◽  
Solid Particles ◽  
Reactor Model ◽  
Two Phase ◽  
Cut Method

A mathematical model is proposed for the partial oxidation on n-butane to maleic anhydride (MAN) in a gas-solid fluidized bed reactor. The reactor consists of two regions, i.e., a lower dense region and an upper dilute region. The dynamic two-phase structure was used for modeling the lower dense bed hydrodynamics. The upper region hydrodynamics was modeled by a cluster based approach. This allows the porosity distribution to be calculated for plug flow reactor model assumed for the gas phase in this region. The basic assumption in the cluster based approach is that the solid particles move only as clusters and the amount of single particles in the upper region is negligible. The mathematical model was obtained from coupling the kinetic sub-model, obtained from the literature, with this hydrodynamics sub-model. Comparing the results of the model with the experimental data available in the literature showed close agreement. Two other methods (i.e., particle based approach and short-cut) were also tested in this work. However, it was found that the cluster based approach modeling is quite suitable for the fluidized bed reactor used in this study. The short-cut method seems reasonably applicable for the prediction of the overall conversion but does not provide any local information (such as concentration profiles, yield, etc.) within the fluidized bed reactor.

scholarly journals A two-phase mathematical model to describe the dissolution of corium crust by molten steel

2021 ◽  
Vol 375 ◽  
pp. 111062
Author(s):  
Shambhavi Nandan ◽  
Florian Fichot ◽  
Fabien Duval
Keyword(s):  
Mathematical Model ◽  
Molten Steel ◽  
Two Phase

A Ternary, Two-Phase, Mathematical Model of Oil Recovery With Surfactant Systems

1984 ◽  
Vol 24 (06) ◽  
pp. 606-616 ◽  
Author(s):  
Charles P. Thomas ◽  
Paul D. Fleming ◽  
William K. Winter
Keyword(s):  
Mathematical Model ◽  
Oil Recovery ◽  
Arbitrary Number ◽  
The Other ◽  
Phase System ◽  
Chemical Flooding ◽  
Two Phase ◽  
Oil Displacement ◽  
Surfactant Systems ◽  
And Diffusion

Abstract A mathematical model describing one-dimensional (1D), isothermal flow of a ternary, two-phase surfactant system in isotropic porous media is presented along with numerical solutions of special cases. These solutions exhibit oil recovery profiles similar to those observed in laboratory tests of oil displacement by surfactant systems in cores. The model includes the effects of surfactant transfer between aqueous and hydrocarbon phases and both reversible and irreversible surfactant adsorption by the porous medium. The effects of capillary pressure and diffusion are ignored, however. The model is based on relative permeability concepts and employs a family of relative permeability curves that incorporate the effects of surfactant concentration on interfacial tension (IFT), the viscosity of the phases, and the volumetric flow rate. A numerical procedure was developed that results in two finite difference equations that are accurate to second order in the timestep size and first order in the spacestep size and allows explicit calculation of phase saturations and surfactant concentrations as a function of space and time variables. Numerical dispersion (truncation error) present in the two equations tends to mimic the neglected present in the two equations tends to mimic the neglected effects of capillary pressure and diffusion. The effective diffusion constants associated with this effect are proportional to the spacestep size. proportional to the spacestep size. Introduction In a previous paper we presented a system of differential equations that can be used to model oil recovery by chemical flooding. The general system allows for an arbitrary number of components as well as an arbitrary number of phases in an isothermal system. For a binary, two-phase system, the equations reduced to those of the Buckley-Leverett theory under the usual assumptions of incompressibility and each phase containing only a single component, as well as in the more general case where both phases have significant concentrations of both components, but the phases are incompressible and the concentration in one phase is a very weak function of the pressure of the other phase at a given temperature. pressure of the other phase at a given temperature. For a ternary, two-phase system a set of three differential equations was obtained. These equations are applicable to chemical flooding with surfactant, polymer, etc. In this paper, we present a numerical solution to these equations paper, we present a numerical solution to these equations for I D flow in the absence of gravity. Our purpose is to develop a model that includes the physical phenomena influencing oil displacement by surfactant systems and bridges the gap between laboratory displacement tests and reservoir simulation. It also should be of value in defining experiments to elucidate the mechanisms involved in oil displacement by surfactant systems and ultimately reduce the number of experiments necessary to optimize a given surfactant system.

Experimental Determination of Statistical Properties of Two-Phase Turbulent Motion

1960 ◽  
Vol 82 (3) ◽  
pp. 609-621 ◽  
Author(s):  
S. L. Soo ◽  
H. K. Ihrig ◽  
A. F. El Kouh
Keyword(s):  
Gas Phase ◽  
Tracer Diffusion ◽  
Statistical Properties ◽  
Solid Particles ◽  
Turbulent Motion ◽  
Two Phase ◽  
Gaseous State ◽  
Diffusion Technique ◽  
And Diffusion

Experimental methods for the determination of certain statistical properties of turbulent conveyance and diffusion of solid particles in a gaseous state are presented. Methods include a tracer-diffusion technique for the determination of gas-phase turbulent motion and a photo-optical technique for the determination of motion of solid particles. Results are discussed and compared with previous analytical results.

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