Numerical investigations of two-phase finger-like instabilities

Chiapolino, Alexandre; Saurel, Richard

doi:10.1016/j.compfluid.2020.104585

Cited by 10 publications

(15 citation statements)

References 34 publications

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“…RSIR-type solvers seem flexible for many applications where most of the physics is governed by two extreme waves and an intermediate one as they can be simplified at different levels when complex systems of equations are addressed. Two-phase flow models are for instance part of those applications as seen in Carmouze et al (2019) [8] and Chiapolino and Saurel (2020) [14].…”

Section: Discussionmentioning

confidence: 99%

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Investigation of Riemann Solver with Internal Reconstruction (RSIR) for the Euler Equations

Chiapolino¹

2021

CICP

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The Riemann solver with internal reconstruction (RSIR) of Carmouze et al. ( 2019) is investigated, revisited and improved for the Euler equations. In this reference, the RSIR approach has been developed to address the numerical resolution of the non-equilibrium two-phase flow model of Saurel et al. (2017). The main idea is to reconstruct two intermediate states from the knowledge of a simple and robust intercell state such as HLL, regardless of the number of waves present in the Riemann problem. Such reconstruction improves significantly the accuracy of the HLL solution, preserves robustness and maintains stationary discontinuities. Consequently, when dealing with complex flow models, such as the aforementioned one, RSIR-type solvers are quite easy to derive compared to HLLC-type ones that may require a tedious analysis of the governing equations across the different waves. In the present contribution, the RSIR solver of Carmouze et al. ( 2019) is investigated, revisited and improved with the help of thermodynamic considerations, making a simple, accurate, robust and positive Riemann solver. It is also demonstrated that the RSIR solver is strictly equivalent to the HLLC solver of of Toro et al. (1994) for the Euler equations when the Rankine-Hugoniot relations are used. In that sense, the RSIR approach recovers the HLLC solver in some limit as well as the HLL one in another limit and can be simplified at different levels when complex systems of equations are addressed. For the sake of clarity and simplicity, the derivations are performed in the context of the one-dimensional Euler equations. Comparisons and validations against the conventional HLLC solver and exact solutions are presented.

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Section: Discussionmentioning

confidence: 99%

“…Thanks to the RSIR approach, stationary interfaces are maintained and numerical dissipation is reduced while circumventing the difficulties related to the construction of a HLLC-type solver. Chiapolino and Saurel (2020) [14] provide illustrative results of the RSIR solver in this two-phase flow context.…”

Section: Introductionmentioning

confidence: 99%

Investigation of Riemann Solver with Internal Reconstruction (RSIR) for the Euler Equations

Chiapolino¹

2021

CICP

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“…For the gas phase, the volume-averaged governing equations, (2.1)–(2.3), constructed in the Eulerian frame are based on a five-equation transport model, i.e. a simplified form of the Baer–Nunziato model (Baer & Nunziato 1986), which has been modified to account for compressible multiphase flows ranging from dilute to dense gas– particle flows (Carmouze et al 2020; Chiapolino & Saurel 2020): …”

Section: Methodsmentioning

confidence: 99%

Shock-induced interfacial instabilities of granular media

Xue

Zeng

et al. 2021

J. Fluid Mech.

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This paper investigates the shock-induced instability of the interfaces between gases and dense granular media with finite length via the coarse-grained compressible computational fluid dynamics–discrete parcel method. Despite generating a typical spike-bubble structure reminiscent of the Richtmyer–Meshkov instability (RMI), the shock-driven granular instability (SDGI) is governed by fundamentally different mechanisms. Unlike the RMI arising from baroclinic vorticity deposition on the interface, the SDGI is closely associated with the interfacial and bulk granular dynamics, which evolve with the transient coupling between particles and gases. Consequently, the SDGI follows a growth law distinctly different from that of the RMI, namely a semilinear slow regime followed by an exponentially expedited regime and a quadratic asymptotic regime. We further establish the instability criteria of the SDGI for granular media with infinite and finite lengths, which do not exist in the RMI. A scaling growth law of the SDGI for dense granular media with finite length is derived by normalizing the time with the rarefaction propagation time, which successfully collapses the data from cases with varying shock strength, particle column length and particle volume fraction and ought to hold for granular media with varying particle parameters. The effect of the initial perturbation magnitude can be properly considered in the scaling growth law by incorporating it into the length normalization.

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“…The generally accepted approach to design a two-phase flow model is based on the assumption that a mixture is a system of two interacting single phase continua, see, for example, [40]. The most widely used PDE system is the Baer-Nunziato model [2], various modifications of which have been applied by many authors to study different types of flows, including flows with phase transitions and chemical reactions, see, for example recent papers [11,27,73] and references therein.…”

Section: Introductionmentioning

confidence: 99%

Exact and Numerical Solutions of the Riemann Problem for a Conservative Model of Compressible Two-Phase Flows

2022

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In this work we study the solution of the Riemann problem for the barotropic version of the conservative symmetric hyperbolic and thermodynamically compatible (SHTC) two-phase flow model introduced in Romenski et al. (J Sci Comput 42(1):68, 2009, Quart Appl Math 65(2):259–279, 2007). All characteristic fields are carefully studied and explicit expressions are derived for the Riemann invariants and the Rankine–Hugoniot conditions. Due to the presence of multiple characteristics in the system under consideration, non-standard wave phenomena can occur. Therefore we briefly review admissibility conditions for discontinuities and then discuss possible wave interactions. In particular we will show that overlapping rarefaction waves are possible and moreover we may have shocks that lie inside a rarefaction wave. In contrast to nonconservative two phase flow models, such as the Baer–Nunziato system, we can use the advantage of the conservative form of the model under consideration. Furthermore, we show the relation between the considered conservative SHTC system and the corresponding barotropic version of the nonconservative Baer–Nunziato model. Additionally, we derive the reduced four equation Kapila system for the case of instantaneous relaxation, which is the common limit system of both, the conservative SHTC model and the non-conservative Baer–Nunziato model. Finally, we compare exact solutions of the Riemann problem with numerical results obtained for the conservative two-phase flow model under consideration, for the non-conservative Baer–Nunziato system and for the Kapila limit. The examples underline the previous analysis of the different wave phenomena, as well as differences and similarities of the three systems.

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Numerical investigations of two-phase finger-like instabilities

Cited by 10 publications

References 34 publications

Investigation of Riemann Solver with Internal Reconstruction (RSIR) for the Euler Equations

Investigation of Riemann Solver with Internal Reconstruction (RSIR) for the Euler Equations

Shock-induced interfacial instabilities of granular media

Exact and Numerical Solutions of the Riemann Problem for a Conservative Model of Compressible Two-Phase Flows

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