An Algorithm for Determining Volume Fractions in Two-Phase Liquid Flows by Measuring Sound Speed

2012 ◽  
Vol 134 (10) ◽  
Author(s):  
Anirban Chaudhuri ◽  
Curtis F. Osterhoudt ◽  
Dipen N. Sinha
Keyword(s):  
Seismic Waves ◽  
Volume Fraction ◽  
Quadratic Equation ◽  
Two Phase ◽  
Volume Fractions ◽  
Linear Rule ◽  
Calculated Volume ◽  
Instantaneous Temperature ◽  
The Individual ◽  
Liquid Flows

This paper presents a method of determining the volume fractions of two liquid components in a two-phase flow by measuring the speed of sound through the composite fluid and the instantaneous temperature. Two separate algorithms are developed, based on earlier modeling work by Urick (Urick, 1947, “A Sound Velocity Method for Determining the Compressibility of Finely Divided Substances,” J. Appl. Phys., 18(11), pp. 983–987) and Kuster and Toksöz (Kuster and Toksöz, 1974, “Velocity and Attenuation of Seismic Waves in Two-Phase Media: Part 1. Theoretical Formulations,” Geophysics, 39(5), pp. 587–606). The main difference between these two models is the representation of the composite density as a function of the individual densities; the former uses a linear rule-of-mixtures approach, while the latter uses a nonlinear fractional formulation. Both approaches lead to a quadratic equation, the root of which yields the volume fraction (φ) of one component, subject to the condition 0≤φ≤1. We present results of a study with mixtures of crude oil and process water, and a comparison of our results with a Coriolis meter. The liquid densities and sound speeds are calibrated at various temperatures for each fluid component, and the coefficients are used in the final algorithm. Numerical studies of sensitivity of the calculated volume fraction to temperature changes are also presented.

scholarly journals Determination of Volume Fractions in a Two-Phase Flows From Sound Speed Measurement

2012 ◽  
Author(s):  
Anirban Chaudhuri ◽  
Curtis F. Osterhoudt ◽  
Dipen N. Sinha
Keyword(s):  
Sound Speed ◽  
Volume Fraction ◽  
Quadratic Equation ◽  
Immiscible Fluids ◽  
Two Phase ◽  
Mean Values ◽  
Volume Fractions ◽  
Non Invasive ◽  
Instantaneous Temperature ◽  
The Difference

Accurate measurement of the composition of oil-water emulsions within the process environment is a challenging problem in the oil industry. Ultrasonic techniques are promising because they are non-invasive and can penetrate optically opaque mixtures. This paper presents a method of determining the volume fractions of two immiscible fluids in a homogenized two-phase flow by measuring the speed of sound through the composite fluid along with the instantaneous temperature. A linear chirp signal is transmitted through the fluid and de-chirp method is applied to calculate the sound speed in the medium. Two separate algorithms are developed by representing the composite density as (i) a linear combination of the two densities, and (ii) a non-linear fractional formulation. Both methods lead to a quadratic equation with temperature dependent coefficients, the root of which yields the volume fraction. The densities and sound speeds are calibrated at various temperatures for each fluid component, and the fitted polynomial is used in the final algorithm. We present results when the new algorithm is applied to mixtures of crude oil and process water from two different oil fields, and a comparison of our results with a Coriolis meter; the difference between mean values is less than 1%.

scholarly journals Simulation of the Effect of Oil Volume Fractions in an Oil-Water Flows Along a Circular Pipe: A Finite Element Approach

2018 ◽  
Vol 10 (5) ◽  
pp. 19
Author(s):  
Ferdusee Akter ◽  
Md. Bhuyan ◽  
Ujjwal Deb
Keyword(s):  
Finite Element ◽  
Volume Fraction ◽  
Fluid Velocity ◽  
Galerkin Approximation ◽  
Computational Domain ◽  
Two Phase Flows ◽  
Two Phase ◽  
Volume Fractions ◽  
Oil In Water ◽  
Element Approach

Two phase flows in pipelines are very common in industries for the oil transportations. The aim of our work is to observe the effect of oil volume fraction in the oil in water two phase flows. The study has been accomplished using a computational model which is based on a Finite Element Method (FEM) named Galerkin approximation. The velocity profiles and volume fractions are performed by numerical simulations and we have considered the COMSOL Multiphysics Software version 4.2a for our simulation. The computational domain is 8m in length and 0.05m in radius. The results show that the velocity of the mixture decreases as the oil volume fraction increases. It should be noted that if we gradually increase the volume fractions of oil, the fluid velocity also changes and the saturated level of the volume fraction is 22.3%.

On a Spring-Network Model and Effective Elastic Moduli of Granular Materials

1999 ◽  
Vol 66 (1) ◽  
pp. 172-180 ◽  
Author(s):  
K. Alzebdeh ◽  
M. Ostoja-Starzewaski
Keyword(s):  
Granular Materials ◽  
Disordered Systems ◽  
Granular Media ◽  
Elastic Moduli ◽  
Volume Fraction ◽  
Effective Medium ◽  
Solid State Physics ◽  
Two Phase ◽  
Effective Medium Theories ◽  
The Individual

Two challenges in mechanics of granular media are taken up in this paper: (i) development of adequate numerical discrete element models of topologically disordered granular assemblies, and (ii) calculation of macroscopic elastic moduli of such materials using effective medium theories. Consideration of the first one leads to an adaptation of a spring-network (Kirkwood) model of solid-state physics to disordered systems, which is developed in the context of planar Delaunay networks. The model employs two linear springs: a normal one along an edge connecting two neighboring vertices (grain centers) which accounts for normal interactions between the grains, as well as an angular one which accounts for angle changes between two edges incident onto the same vertex; edges remain straight and grain rotations do not appear. This model is then used to predict elastic moduli of two-phase granular materials—random mixtures of soft and stiff grains —for high coordination numbers. It is found here that an effective Poisson’s ratio, νeff, of such a mixture is a convex function of the volume fraction, so that νeff may become negative when the individual Poisson’s ratios of both phases are both positive. Additionally, the usefulness of three effective medium theories—perfect disks, symmetric ellipses, and asymmetric ellipses—is tested.

Phase-Separation of B2 Precipitates in an Fe-Ni-Al Alloy

2010 ◽  
Vol 638-642 ◽  
pp. 2274-2278 ◽  
Author(s):  
Yasuhiro Kuno ◽  
Yasuo Nakane ◽  
Takao Kozakai ◽  
Minoru Doi ◽  
Junji Yamanaka ◽  
...  
Keyword(s):  
Free Energy ◽  
Phase Separation ◽  
Volume Fraction ◽  
Heating Temperature ◽  
Phase System ◽  
Al Alloy ◽  
Two Phase ◽  
Chemical Free Energy ◽  
The Difference ◽  
The Individual

When Fe-10.3mol%Ni-14.3mol%Al alloy is heated at 1173 K for 8.64104 s, a number of B2 precipitates are dispersed in the A2 matrix. When the two-phase microstructure of A2+B2 is aged at 973 K, the phase-separation of B2 precipitate particles takes place to form a new A2 phase in each B2 particle. In the course of further ageing at 973 K, the new A2 phase grows but decreases in number, and finally only one A2 particle is left in the individual B2 particles. The appearance of new A2 phase in each B2 precipitate is due to the difference in the volume fraction of A2 phase that should exist in A2+B2 two-phase system depending on the heating temperature: i.e., the phase-separation of B2 precipitates starts with the aid of chemical free energy.

Microstructures and Mechanical Behavior of Two-Phase Niobium Silicide-Niobium Alloys

1988 ◽  
Vol 133 ◽  
Author(s):  
M. G. Mendiratta ◽  
D. M. Dimiduk
Keyword(s):  
Mechanical Behavior ◽  
Phase Transformations ◽  
Room Temperature ◽  
Volume Fraction ◽  
Two Phase ◽  
Niobium Alloys ◽  
Intermetallic Matrix ◽  
Two Phases ◽  
The Individual

ABSTRACTIn the Nb-Si system, it is possible to produce in-situ composites consisting of a brittle Nb5Si3 intermetallic matrix and ductile Nb particles. The two phases are thermochemically stable up to ∼ 1500∼C and are amenable to wide microstructural variations including morphology, volume fraction, and the size of the individual microconstituents. This paper presents microstructures and phase transformations in these composites as a function of composition and heat treatments and bend properties from room-temperature to 1400°C.

Experimental Study of Two-Phase Air/Water Flow in a Centrifugal Pump Working With a Closed or a Semi-Open Impeller

2018 ◽  
Author(s):  
Michael Mansour ◽  
Bernd Wunderlich ◽  
Dominique Thévenin
Keyword(s):  
Centrifugal Pump ◽  
Volume Fraction ◽  
Operating Conditions ◽  
Superior Performance ◽  
Flow Conditions ◽  
Two Phase ◽  
Volume Fractions ◽  
Acrylic Glass ◽  
Gas Volume Fraction ◽  
Gas Volume

The characteristics of a transparent centrifugal pump of radial type were investigated for different conditions when conveying two-phase (air/water) flows. A closed impeller and a geometrically similar semi-open impeller, both made out of acrylic glass, were employed for comparison purposes when increasing air loading. The performance of the pump was measured for either a constant gas volume fraction or a constant air flow rate at the pump inlet. Hysteresis effects were studied by considering three different experimental approaches to reach the desired operating conditions. A constant rotational speed of 650 rpm was set for all experiments. The whole system was made of transparent acrylic glass to allow high-quality flow visualization. A systematic experimental database was produced based on shadowgraphy imaging, so that the resulting two-phase regimes could be properly identified. The results show that for gas volume fractions between 1 and 3%, the deterioration of pump performance parameters is much lower in the semi-open impeller compared to that of the closed impeller. Nevertheless, in the gas volume fraction range between 4 and 6%, the trend is reversed; the semi-open impeller performance is reduced compared to the closed impeller, particularly in overload conditions. At even higher gas loading, the semi-open impeller shows again superior performance. Flow instabilities and pump surging were much stronger in the closed impeller. The main reason for that was the occurrence of alternating gas pockets on the blades of the closed impeller. Additionally, pump surging was observed only in a very limited range of flow conditions in the semi-open impeller. Comparing the different experimental procedures to set the desired flow conditions, no significant hysteresis effects could be observed in the closed impeller. However, in the semi-open impeller obvious hysteresis in the performance could be seen for gas volume fractions between 4 and 6%. All the obtained experimental results will be useful to check and validate computational models used for CFD in a comparison study.

Comparative Analysis of High Void Fraction Regimes Using an Averaging Euler-Euler Multi-Fluid Approach and a Generalized Two-Phase Flow (GENTOP) Concept

2014 ◽  
Author(s):  
Gustavo Montoya ◽  
Emilio Baglietto ◽  
Dirk Lucas ◽  
Eckhard Krepper ◽  
Thomas Hoehne
Keyword(s):  
Experimental Data ◽  
Void Fraction ◽  
Volume Fraction ◽  
Grid Size ◽  
Two Phase ◽  
Wide Range ◽  
Size Groups ◽  
Novel Concept ◽  
Liquid Flows ◽  
Gas Volume

Complex multiphase gas-liquid flows, including boiling, are usually encountered in safety related nuclear applications. For CFD purposes, modeling the transition from low to high void fraction regimes represents a non-trivial challenge due to the increasing complexity of its interface. For example, churn-turbulent and slug flows, which are typically encountered for these gas volume fraction ranges, are dominated by highly deformable bubbles. Multiphase CFD has been so far relying on an averaged Euler-Euler simulation approach to model a wide range of two-phase applications. While this methodology has shown to date demonstrated reasonable results (Montoya et al., 2013), it is evidently highly dependable on the accuracy and validity of the mechanistic models for interfacial forces, which are necessary to recover information lost during the averaging process. Unfortunately existing closures, which have been derived from experimental as well as DNS data, are hardly applicable to high void fraction highly-deformable gas structures. An alternative approach for representing the physics behind the high void fraction phenomena, is to consider a multi-scale method. Based on the structure of the gas-liquid interfaces, different gaseous morphologies should be described by different CFD approaches, such as interface tracking methods for larger than the grid size interfacial-scales, or the averaged Euler-Euler approach for smaller than grid size scales, such as bubbly or droplet flow. A novel concept for considering flow regimes where both, dispersed and continuous interfacial structures, could occur has been developed in the past (Hänsch et al., 2012), and has been further advanced and validated for pipe flows under high void fraction regimes (Montoya et al., 2014) and other relevant cases, such as the dam-break with an obstacle (Hänsch et al., 2013). Still, various short-comings have been shown in this approach associated mostly to the descriptive models utilized to obtain the continuous gas morphology from within the averaged Eulerian simulations. This paper presents improvements on both concepts as well as direct comparison between the two approaches, based on newly obtained experimental data. Both models are based on the bubble populations balance approach known as the inhomogeneous MUltiple SIze Group or MUSIG (Krepper et al., 2008) in order to define an adequate number of bubble size groups with its own velocity fields. The numerical calculations have been performed with the commercially available ANSYS CFX 14.5 software, and the results have been validated using experimental data from the MT-Loop and TOPFLOW facilities from the Helmholtz-Zentrum Dresden-Rossendorf in Germany (Prasser et al., 2007).

scholarly journals Numerical Study on an Interface Compression Method for the Volume of Fluid Approach

Fluids ◽  
2021 ◽  
Vol 6 (2) ◽  
pp. 80
Author(s):  
Yuria Okagaki ◽  
Taisuke Yonomoto ◽  
Masahiro Ishigaki ◽  
Yoshiyasu Hirose
Keyword(s):  
Linear Theory ◽  
Volume Fraction ◽  
Numerical Study ◽  
Volume Of Fluid ◽  
Interfacial Wave ◽  
Validation Process ◽  
Two Phase ◽  
Numerical Diffusion ◽  
Mesh Resolution ◽  
Water Reactors

Many thermohydraulic issues about the safety of light water reactors are related to complicated two-phase flow phenomena. In these phenomena, computational fluid dynamics (CFD) analysis using the volume of fluid (VOF) method causes numerical diffusion generated by the first-order upwind scheme used in the convection term of the volume fraction equation. Thus, in this study, we focused on an interface compression (IC) method for such a VOF approach; this technique prevents numerical diffusion issues and maintains boundedness and conservation with negative diffusion. First, on a sufficiently high mesh resolution and without the IC method, the validation process was considered by comparing the amplitude growth of the interfacial wave between a two-dimensional gas sheet and a quiescent liquid using the linear theory. The disturbance growth rates were consistent with the linear theory, and the validation process was considered appropriate. Then, this validation process confirmed the effects of the IC method on numerical diffusion, and we derived the optimum value of the IC coefficient, which is the parameter that controls the numerical diffusion.

scholarly journals An Intrinsic Material Tailoring Approach for Functionally Graded Axisymmetric Hollow Bodies Under Plane Elasticity

2021 ◽  
Author(s):  
Hassan Mohamed Abdelalim Abdalla ◽  
Daniele Casagrande
Keyword(s):  
Optimization Problem ◽  
Volume Fraction ◽  
Minimum Principle ◽  
Equivalent Stress ◽  
Micromechanical Model ◽  
Plane Elasticity ◽  
Functionally Graded ◽  
Pontryagin Minimum Principle ◽  
Volume Fractions ◽  
Material Tailoring

AbstractOne of the main requirements in the design of structures made of functionally graded materials is their best response when used in an actual environment. This optimum behaviour may be achieved by searching for the optimal variation of the mechanical and physical properties along which the material compositionally grades. In the works available in the literature, the solution of such an optimization problem usually is obtained by searching for the values of the so called heterogeneity factors (characterizing the expression of the property variations) such that an objective function is minimized. Results, however, do not necessarily guarantee realistic structures and may give rise to unfeasible volume fractions if mapped into a micromechanical model. This paper is motivated by the confidence that a more intrinsic optimization problem should a priori consist in the search for the constituents’ volume fractions rather than tuning parameters for prefixed classes of property variations. Obtaining a solution for such a class of problem requires tools borrowed from dynamic optimization theory. More precisely, herein the so-called Pontryagin Minimum Principle is used, which leads to unexpected results in terms of the derivative of constituents’ volume fractions, regardless of the involved micromechanical model. In particular, along this line of investigation, the optimization problem for axisymmetric bodies subject to internal pressure and for which plane elasticity holds is formulated and analytically solved. The material is assumed to be functionally graded in the radial direction and the goal is to find the gradation that minimizes the maximum equivalent stress. A numerical example on internally pressurized functionally graded cylinders is also performed. The corresponding solution is found to perform better than volume fraction profiles commonly employed in the literature.

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