A numerical study of cavitating flows in high-pressure diesel injection nozzle holes using a two-fluid model

The flow of viscoelastic fluids may, under certain conditions, exhibit shear-banding characteristics that result from their susceptibility to unusual flow instabilities. In this work, we explore both the existing shear banding mechanisms in the literature, namely; constitutive instabilities and flow-induced inhomogeneities. Shear banding due to constitutive instabilities is modelled via either the Johnson–Segalman or the Giesekus constitutive models. Shear banding due to flow-induced inhomogeneities is modelled via the Rolie–Poly constitutive model. The Rolie–Poly constitutive equation is especially chosen because it expresses, precisely, the shear rheometry of polymer solutions for a large number of strain rates. For the Rolie–Poly approach, we use the two-fluid model wherein the stress dynamics are coupled with concentration equations. We follow a computational analysis approach via an efficient and versatile numerical algorithm. The numerical algorithm is based on the Finite Volume Method (FVM) and it is implemented in the open-source software package, OpenFOAM. The efficiency of our numerical algorithms is enhanced via two possible stabilization techniques, namely; the Log-Conformation Reformulation (LCR) and the Discrete Elastic Viscous Stress Splitting (DEVSS) methodologies. We demonstrate that our stabilized numerical algorithms accurately simulate these complex (shear banded) flows of complex (viscoelastic) fluids. Verification of the shear-banding results via both the Giesekus and Johnson-Segalman models show good agreement with existing literature using the DEVSS technique. A comparison of the Rolie–Poly two-fluid model results with existing literature for the concentration and velocity profiles is also in good agreement.

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A NUMERICAL STUDY OF TWO-PHASE FLOW USING A TWO-DIMENSIONAL TWO-FLUID MODEL

Numerical Heat Transfer Part A Applications ◽

10.1080/10407780490453891 ◽

2004 ◽

Vol 45 (10) ◽

pp. 1049-1066 ◽

Cited By ~ 6

Author(s):

Moon-Sun Chung ◽

Seung-Kyung Pak ◽

Keun-Shik Chang

Keyword(s):

Two Phase Flow ◽

Numerical Study ◽

Fluid Model ◽

Phase Flow ◽

Two Dimensional ◽

Two Phase ◽

Two Fluid Model ◽

Two Fluid

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Effect of liquid phase compressibility on modeling of gas-liquid two-phase flows using two-fluid model

Thermal Science ◽

10.2298/tsci171018148s ◽

2019 ◽

Vol 23 (5 Part B) ◽

pp. 3003-3013

Author(s):

Vahid Shokri ◽

Kazem Esmaeili

Keyword(s):

Liquid Phase ◽

Relative Velocity ◽

Numerical Study ◽

Fluid Model ◽

Shock Capturing ◽

Two Phase ◽

Solution Field ◽

Two Fluid Model ◽

Flow Variables ◽

Two Fluid

In this paper, a numerical study is performed in order to investigate the effect of the liquid phase compressibility two-fluid model. The two-fluid model is solved by using conservative shock capturing method. At the first, the two-fluid model is applied by assuming that the liquid phase is incompressible, then it is assumed that in three cases called water faucet case, large relative velocity shock pipe case, and Toumi?s shock pipe case, the liquid phase is compressible. Numerical results indicate that, if an intense pressure gradient is governed on the fluid-flow, single-pressure two-fluid model by assuming liquid phase incompressibility predicts the flow variables in the solution field more accurate than single-pressure two-fluid model by assuming liquid phase compressibility.

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NUMERICAL STUDY OF MAGNETIC PENETRATION DEPTH IN MgB2

International Journal of Modern Physics B ◽

10.1142/s0217979213620270 ◽

2013 ◽

Vol 27 (15) ◽

pp. 1362027

Author(s):

BO LI ◽

DE-HUA LIN

Keyword(s):

Penetration Depth ◽

Energy Gap ◽

Numerical Study ◽

Fluid Model ◽

Magnetic Penetration Depth ◽

Fitting Method ◽

Numerical Fitting ◽

Two Fluid Model ◽

Magnetic Penetration ◽

Two Fluid

The magnetic penetration depth formula in MgB 2 is more complex than that in BCS superconductors due to the existence of exotic two energy gap in MgB 2. A new simplified relationship between the penetration depth and temperature is presented, which is derived from the two-fluid model by means of numerical fitting method, and the physical meaning is relatively clear.

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Numerical study on the bubbly flow around a hydrofoil in pitching and heaving motions

Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science ◽

10.1243/095440603767764453 ◽

2003 ◽

Vol 217 (7) ◽

pp. 811-820 ◽

Cited By ~ 2

Author(s):

T Uchiyama

Keyword(s):

Horizontal Plane ◽

Numerical Study ◽

Fluid Model ◽

Bubbly Flow ◽

The Finite Element Method ◽

Flow Properties ◽

Volumetric Fraction ◽

Propulsive Performance ◽

Two Fluid Model ◽

Two Fluid

The air-water bubbly flow around a hydrofoil of NACA65-010, undergoing the heaving and pitching motions in the uniform flow on a horizontal plane, is simulated by an incompressible two-fluid model. The finite element method proposed in a prior paper is applied to solve the model. The Reynolds number defined by the volumetric velocity of the water is 10000 and the volumetric fraction of the air upstream of the hydrofoil, αg0, ranges from 0 to 0.06. The simulation reveals the effects of the αg0 value, the phase difference between the heaving and pitching motions, and the oscillating frequency. The propulsive performance is also discussed in relation to the time variation of the flow properties around the hydrofoil.

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Numerical Study of Two-Phase Flow in a Horizontal Pipeline Using an Unconditionally Hyperbolic Two-Fluid Model

Volume 7: Fluids Engineering ◽

10.1115/imece2018-87571 ◽

2018 ◽

Author(s):

Raphael V. N. de Freitas ◽

Carina N. Sondermann ◽

Rodrigo A. C. Patricio ◽

Aline B. Figueiredo ◽

Gustavo C. R. Bodstein ◽

...

Keyword(s):

Volume Fraction ◽

Numerical Study ◽

Fluid Model ◽

Momentum Conservation ◽

Design Stage ◽

Two Phase Flows ◽

Two Phase ◽

Efficient Manner ◽

Two Fluid Model ◽

Two Fluid

Numerical simulation is a very useful tool for the prediction of physical quantities in two-phase flows. One important application is the study of oil-gas flows in pipelines, which is necessary for the proper selection of the equipment connected to the line during the pipeline design stage and also during the pipeline operation stage. The understanding of the phenomena present in this type of flow is more crucial under the occurrence of undesired effects in the duct, such as hydrate formation, fluid leakage, PIG passage, and valve shutdown. An efficient manner to model two-phase flows in long pipelines regarding a compromise between numerical accuracy and cost is the use of a one-dimensional two-fluid model, discretized with an appropriate numerical method. A two-fluid model consists of a system of non-linear partial differential equations that represent the mass, momentum and energy conservation principles, written for each phase. Depending on the two-fluid model employed, the system of equations may lose hyperbolicity and render the initial-boundary-value problem illposed. This paper uses an unconditionally hyperbolic two-fluid model for solving two-phase flows in pipelines in order to guarantee that the solution presents physical consistency. The mathematical model here referred to as the 5E2P (five equations and two pressures) comprises two equations of continuity and two momentum conservation equations, one for each phase, and one equation for the transport of the volume fraction. A priori this model considers two distinct pressures, one for each phase, and correlates them through a pressure relaxation procedure. This paper presents simulation cases for stratified two-phase flows in horizontal pipelines solved with the 5E2P coupled with the flux corrected transport method. The objective is to evaluate the numerical model capacity to adequately describe the velocities, pressures and volume fraction distributions along the duct.

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Numerical study on the propulsive performance of a wiggling blade in bubbly flow

Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science ◽

10.1243/095440602321029427 ◽

2002 ◽

Vol 216 (12) ◽

pp. 1187-1196 ◽

Cited By ~ 6

Author(s):

T Uchiyama

Keyword(s):

Numerical Study ◽

Fluid Model ◽

Bubbly Flow ◽

The Finite Element Method ◽

Flow Properties ◽

Propulsive Performance ◽

Time Variations ◽

Two Fluid Model ◽

Straight Conduit ◽

Two Fluid

In order to search for an efficient propulsion mechanism in an air-water bubbly flow, the propulsive performance of a blade wiggling in the bubbly flow is analysed by a two-dimensional numerical method. The blade, whose geometry is similar to an NACA65–010 hydrofoil, is set in a straight conduit, in which the bubbly mixture flows. The wiggling motion is expressed by a progressive wave with reference to the swimming motions of fish. The bubbly flow is calculated by an incompressible two-fluid model in conjunction with the finite element method proposed by the author in an earlier paper. The calculations reveal the effects of a progressive waveform and volumetric fraction of air upstream of the blade on the propulsive performance of the blade. The time variations of the flow properties around the blade are also discussed in relation to the blade motion and propulsive performance.

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A Hyperbolicity Analysis of the 1991 OLGA’s Model for Isothermal Flow

Volume 7: Fluids Engineering ◽

10.1115/imece2018-87513 ◽

2018 ◽

Author(s):

Carina N. Sondermann ◽

Raphael V. N. de Freitas ◽

Rodrigo A. C. Patricio ◽

Aline B. Figueiredo ◽

Gustavo C. R. Bodstein ◽

...

Keyword(s):

Oil And Gas ◽

Numerical Study ◽

Fluid Model ◽

Oil And Gas Industry ◽

Isothermal Flow ◽

Offshore Platforms ◽

One Dimensional ◽

Drift Flux Model ◽

Two Fluid Model ◽

Two Fluid

Multiphase flows are encountered in many engineering problems. Particularly in the oil and gas industry, many applications involve the transportation of a mixture of oil and natural gas in long pipelines from offshore platforms to the continent. Numerical simulations of steady and unsteady flows in pipelines are usually based on one-dimensional models, such as the two-fluid model, the drift-flux model and the homogeneous equilibrium model. The 1991’s version of the well-known and widely-used commercial software OLGA describes a system of non-linear equations of the two-fluid-model type, with an extra equation for the presence of liquid droplets. It is well known that one-dimensional formulations may be physically inconsistent due to the loss of hyperbolicity. In these cases, the associated eigenvalues become complex numbers and the model loses physical meaning locally. This paper presents a numerical study of the 1991’s version of the software OLGA, for an isothermal flow of stratified pattern, in a horizontal pipeline. For each point of interest in the stratified-pattern flow map, the eigenvalues are numerically calculated in order to verify if the eigenvalues are real and also to assess their signs. The results indicate that the model is conditionally hyperbolic and loses hyperbolicity in a vast area of the stratified region under certain flow conditions. Even though the model is not unconditionally hyperbolic, some simulations here performed for typical offshore pipeline flows are shown to be in the hyperbolic region.

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