Extension of some numerical schemes to the analysis of gas and particle mixtures

García-Cascales, J.R.; Mulas-Pérez, J.; Paillère, H.

doi:10.1002/fld.1556

Cited by 9 publications

(10 citation statements)

References 27 publications

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“…The gravitational constant is g = 9.81 m s −2 . The last source term in the momentum equations represents the interfacial friction between phases [14] F dg = − 3 4…”

Section: The Model and Its Propertiesmentioning

confidence: 99%

“…We note that the initial solid density was chosen much higher than that of the gas phase. See for example the numerical tests in García-Cascales et al [14]. The solid phase corresponds to a compressible granular flow and the solid density is expected to vary weakly.…”

Section: Volume Fractionmentioning

confidence: 99%

“…More details on definitions for directional drilling of a wellbore are shown in Chenevert et al That is, the pipe is horizontal at the bottom and it becomes almost vertical near the surface. In this more realistic scenario and following [14], we consider an interfacial friction given by…”

Section: Accumulation Of Solids In Deviated Pipesmentioning

confidence: 99%

“…Interesting data is provided such as the Riemann invariants in the linearly degenerate characteristic fields and results related to the contact waves of the model without gravity are obtained. In García-Cascales et al [14] numerical schemes are constructed to obtain approximate solutions to a system derived from the Baer-Nunziato model assuming multiphase mixtures of gas and particles with a solid incompressible phase. This model includes drag force, interfacial convective heat transfer, and interfacial exchange of mass, momentum and energy due to phase changes and chemical reactions among others.…”

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confidence: 99%

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A positivity-preserving central-upwind scheme for isentropic two-phase flows through deviated pipes

Hernández-Dueñas¹,

Velasco-García²,

Hernández³

2019

ESAIM: M2AN

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Directional drilling in oil and gas extraction can encounter difficulties such as accumulation of solids in deviated pipes. Motivated by such phenomenon, we consider a model for isentropic twophase flows through deviated pipes. The system of partial differential equations is aimed at simulating the dynamics between a particle bed and a gas phase. The pipe can be either horizontal or vertically deviated where the effects of gravity are incorporated. Furthermore, the acceleration or deceleration due to friction between phases is investigated and spectral properties of the hyperbolic system of balance laws are described. The existence and characterization of steady states under appropriate conditions is analyzed. A new type of steady states arises when a balance between gas and solid phases results in a non-uniform solid particle bed and vanishing solid velocity. This state corresponds to an accumulation of sedimented solids. A central-upwind scheme that preserves the positivity of the gas and solid densities and volume fractions is presented. Including an application of the model to an analysis of accumulation of solids, a variety of numerical tests is presented to show the merits of the scheme.Mathematics Subject Classification. 35L65, 65M08, 76T25.

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“…The gravitational constant is g = 9.81 m s −2 . The last source term in the momentum equations represents the interfacial friction between phases [14] F dg = − 3 4…”

Section: The Model and Its Propertiesmentioning

confidence: 99%

Section: Volume Fractionmentioning

confidence: 99%

Section: Accumulation Of Solids In Deviated Pipesmentioning

confidence: 99%

mentioning

confidence: 99%

See 2 more Smart Citations

A positivity-preserving central-upwind scheme for isentropic two-phase flows through deviated pipes

Hernández-Dueñas¹,

Velasco-García²,

Hernández³

2019

ESAIM: M2AN

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“…The combustion process in gas–solid particle mixtures has raised the interest of many researchers in the last few decades. This is due to the major importance of the two‐phase flow problem in many different industrial fields, such as heat or power generation , propulsion , fire propagation , hazard explosions , prevention of detonations or, finally, the analysis and design of pyrotechnic and ballistic devices . In the particular case of internal ballistics, the use of computational methods has broadly extended in recent years.…”

Section: Introductionmentioning

confidence: 99%

An approach formulated in terms of conserved variables for the characterisation of propellant combustion in internal ballistics

Otón-Martínez¹,

Monreal-González

García-Cascales

et al. 2015

Numerical Methods in Fluids

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Summary A model formulated in terms of conserved variables is proposed for its use in the study of internal ballistic problems of pyrotechnical mixtures and propellants. It is a transient two‐phase flow model adapted from the non‐conservative Gough model. This conversion is mathematically attractive because of the wide range of numerical methods for this kind of systems that may be applied. We propose the use of the AUSM+, AUSM + up and Rusanov schemes as an efficient alternative for this type of two‐phase problem. A splitting technique is applied, which solves the system of equations in several steps. A second‐order approach based on Monotonic Upstream‐Centred Scheme for Conservation Laws (MUSCL) is also used. Some tests are used to validate the code, namely a shock wave test, a contact discontinuity problem and an internal ballistics problem. In this last case, one‐dimensional numerical results are compared with experimental data of 155‐mm gunshots. Copyright © 2015 John Wiley & Sons, Ltd.

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Remarks on the links between low‐order DG methods and some finite‐difference schemes for the Stokes problem

Minev

2008

Numerical Methods in Fluids

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SUMMARYIn this paper we demonstrate that some well-known finite-difference schemes can be interpreted within the framework of the local discontinuous Galerkin (LDG) methods using the low-order piecewise solenoidal discrete spaces introduced in (SIAM J. Numer. Anal. 1990; 27(6): 1466-1485). In particular, it appears that it is possible to derive the well-known MAC scheme using a first-order Nédélec approximation on rectangular cells. It has been recently interpreted within the framework of the Raviart-Thomas approximation by Kanschat (Int. J. Numer. Meth. Fluids 2007; published online). The two approximations are algebraically equivalent to the MAC scheme, however, they have to be applied on grids that are staggered on a distance h/2 in each direction. This paper also demonstrates that both discretizations allow for the construction of a divergence-free basis, which yields a linear system with a 'biharmonic' conditioning. Both this paper and Kanschat (Int. J. Numer. Meth. Fluids 2007; published online) demonstrate that the LDG framework can be used to generalize some popular finite-difference schemes to grids that are not parallel to the coordinate axes or that are unstructured.

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Extension of some numerical schemes to the analysis of gas and particle mixtures

Cited by 9 publications

References 27 publications

A positivity-preserving central-upwind scheme for isentropic two-phase flows through deviated pipes

A positivity-preserving central-upwind scheme for isentropic two-phase flows through deviated pipes

An approach formulated in terms of conserved variables for the characterisation of propellant combustion in internal ballistics

Remarks on the links between low‐order DG methods and some finite‐difference schemes for the Stokes problem

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