A mixture-energy-consistent six-equation two-phase numerical model for fluids with interfaces, cavitation and evaporation waves

Pelanti, Marica; Shyue, Keh‐Ming

doi:10.1016/j.jcp.2013.12.003

Cited by 141 publications

(170 citation statements)

References 52 publications

(156 reference statements)

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“…Such difficulties were, for example, reported by Pelanti and Shyue [115] where the six-equation two-phase model was studied. Therein, these difficulties are attributed to the stiffness of the source terms.…”

Section: B(u)w(u)mentioning

confidence: 82%

“…A more sophisticated extension, the HLLC (HLLContact) scheme, was proposed by Toro et al [139] in 1994. Today, the HLL and HLLC schemes are widely used in a number of different fields, such as multiphase flow modeling [149,137,136,115,28,27,92], relativistic flows and magnetohydrodynamics [67,88,98,97,69,59], shallow water equations [2] and radiative transfer [9]. For more references we refer to the book by Toro [138].…”

Section: Goals and Thesis Outlinementioning

confidence: 99%

“…This can be done by combining elements of wave propagation form and the HLLC scheme, as is done for instance by Pelanti and Shyue [115]. We skip technical details and give a final result.…”

Section: Lts-hll(c) Schemes For Systems Of Conservation Lawsmentioning

confidence: 99%

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Large Time Step Roe scheme for a common 1D two-fluid model

Prebeg

Flåtten

Müller

2017

Applied Mathematical Modelling

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Large Time Step (LTS) finite volume methods are presented, analyzed and applied to one-dimensional hyperbolic conservation laws.The HLL (Harten-Lax-van Leer) and HLLC (HLL-Contact) schemes are extended to LTS-HLL(C) schemes. The LTS-HLL-type schemes for scalar conservation laws are defined in the numerical viscosity, flux-difference splitting and wave propagation form, and TVD conditions on wave velocity estimates are determined. It is shown that the LTS-HLL-type schemes contain some already existing LTS methods such as the LTS-Roe and LTS-Lax-Friedrichs, and that they allow us to deduce LTS extensions of other methods, such as the Rusanov and Engquist-Osher schemes. The LTS-HLL(C) schemes for systems of conservation laws are developed by standard field-by-field decomposition. Numerical results suggest that the computational efficiency of LTS methods depends on the type of problem under consideration. In certain cases LTS methods for nonlinear systems of equations yield increased accuracy, efficiency and convergence rate compared to standard methods.Entropy stability of LTS-HLL-type schemes is analyzed. We use modified equation analysis to gain insight into numerical diffusion in LTS-HLLtype schemes and to conjecture about entropy stability of LTS methods. Theoretical results obtained through the modified equation analysis are in agreement with numerical results for both scalar conservation laws and the Euler equations.Positivity preservation in LTS methods is investigated. We show that the positivity preserving conditions for LTS methods are stronger than for standard methods. We describe different ways positivity can be lost in LTS-HLL-type schemes for the Euler equations, and we propose a simple way to increase the robustness of the LTS-HLL-type schemes by adding numerical diffusion. Numerical investigations show that LTS-HLL-type schemes successfully handle test cases for positivity preservation, and where the positivity is lost we can improve the robustness by adding numerical diffusion.In addition, we applied the LTS-Roe scheme to a two-fluid model and focused on the treatment of the boundary conditions and the source terms. It is shown that stability and accuracy of the solution can be greatly improved by appropriate treatment of boundary conditions and source terms.i

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Section: B(u)w(u)mentioning

confidence: 82%

Section: Goals and Thesis Outlinementioning

confidence: 99%

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Large Time Step Roe scheme for a common 1D two-fluid model

Prebeg

Flåtten

Müller

2017

Applied Mathematical Modelling

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“…In order to investigate thermal effects in LH 2 cryogenic cavitating flows, one-dimensional cavitation tube problems are proposed. Such rarefaction tube problems involving cavitation are one of the most used case to study the behaviour of phase transition models and to test and develop numerical schemes (Saurel & Metayer 2001, Barberon & Helluy 2005, Saurel et al 2008, Zein et al 2010, Causon & Mingham 2013, Spina et al 2014, Pelanti & Shyue 2014. This paper is organized as follows.…”

Section: Introductionmentioning

confidence: 99%

Numerical simulation of unsteady cavitation in liquid hydrogen flows

Goncalves

Zeidan

2017

IJESMS

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An unsteady cavitation model in liquid hydrogen flow is studied in the context of compressible, two-phase, one-fluid inviscid solver. This is accomplished by applying three conservation laws for mixture mass, mixture momentum and total energy along with gas volume fraction transport equation, with thermodynamic effects. Various mass transfers between phases are utilized to study the process under consideration. A numerical procedure is presented for the simulation of cavitation due to rarefaction and shock waves. Attention is focused on cavitation in which the simulated fluid is liquid hydrogen in cryogenic conditions. Numerical results are in close agreement with theoretical solutions for several test cases. The current numerical results show that liquid hydrogen flow can be accurately modeled using an accurate inviscid approach to describe the features of thermodynamic effects on cavitation.Keywords: Two-phase flow; heat and mass transfer; liquid and hydrogen, cavitation; homogeneous model; splitting techniques, inviscid simulation. Reference · · · Biographical notes: Eric Goncalvès is a Professor in the Aeronautical EngineeringSchool ISAE-ENSMA, Poitiers, France. Currently, he is the head of the Department Fluid Mechanics and Aerodynamics. His research interests are related to the modelling and the simulation of flows for which the density is variable such as compressible flow, two-phase flow and cavitation. Recent work include shock wave boundary layer interaction, thermal effects in cavitation and investigation of three-dimensional effects on cavitation pocket. Dia Zeidan is currently a Tenure-track Assistant Professor in the School of Basic Sciences and Humanities at the German Jordanian University, Amman, Jordan. His expertise is in the mathematical modelling and numerical simulations of multiphase fluid flow problems. Recent work also includes hyperbolicity and conservativity resolution related to two-phase flows equations in the context of the Riemann problem and simulations of such flows over a wide range of non-equilibrium behaviours.

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“…Note the algorithms and software developed are more widely applicable and could be adapted to study related experiments. For instance, cavitation could perhaps be directly modeled by extending these methods using a six-equation two-phase numerical model instead of Euler equations [75,87].…”

mentioning

confidence: 99%

Computational and In Vitro Studies of Blast-Induced Blood-Brain Barrier Disruption

Razo

Morofuji

Meabon

et al. 2016

SIAM J. Sci. Comput.

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Abstract. There is growing concern that blast-exposed individuals are at risk of developing neurological disorders later in life. Therefore, it is important to understand the dynamic properties of blast forces on brain cells, including the endothelial cells that maintain the blood-brain barrier (BBB), which regulates the passage of nutrients into the brain and protects it from toxins in the blood. To better understand the effect of shock waves on the BBB we have investigated an in vitro model in which BBB endothelial cells are grown in transwell vessels and exposed in a shock tube, confirming that BBB integrity is directly related to shock wave intensity. It is difficult to directly measure the forces acting on these cells in the transwell container during the experiments, and so a computational tool has been developed and presented in this paper.Two-dimensional axisymmetric Euler equations with the Tammann equation of state were used to model the transwell materials, and a high-resolution finite volume method based on Riemann solvers and the Clawpack software was used to solve these equations in a mixed Eulerian/Lagrangian frame. Results indicated that the geometry of the transwell plays a significant role in the observed pressure time series in these experiments. We also found that pressures can fall below vapor pressure due to the interaction of reflecting and diffracting shock waves, suggesting that cavitation bubbles could be a damage mechanism. Computations that include a simulated hydrophone inserted in the transwell suggest that the instrument itself could significantly alter blast wave properties. These findings illustrate the need for further computational modeling studies aimed at understanding possible blastinduced BBB damage.

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A mixture-energy-consistent six-equation two-phase numerical model for fluids with interfaces, cavitation and evaporation waves

Cited by 141 publications

References 52 publications

Large Time Step Roe scheme for a common 1D two-fluid model

Large Time Step Roe scheme for a common 1D two-fluid model

Numerical simulation of unsteady cavitation in liquid hydrogen flows

Computational and In Vitro Studies of Blast-Induced Blood-Brain Barrier Disruption

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