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Modeling Heavy-Gas Dispersion in Air with Two-Layer Shallow Water Equations

Scientific Research and Numerical Simulation (RS2N), 371 Chemin de Gaumin, 83640 Saint-Zacharie, France
Commissariat à l’Énergie Atomique et aux Energies Alternatives, Direction des Applications Militaires (CEA-DAM), CEA-Gramat, 46500 Gramat, France
Laboratory of Mechanics and Acoustics (LMA), Centrale Marseille, French National Centre for Scientific Research (CNRS), Aix-Marseille Univ, 4 Impasse Nikola Tesla, 13013 Marseille, France
Author to whom correspondence should be addressed.
Received: 6 November 2020 / Revised: 9 December 2020 / Accepted: 18 December 2020 / Published: 22 December 2020
(This article belongs to the Special Issue Recent Advances in Fluid Mechanics: Feature Papers)
Computation of gas dispersal in urban places or hilly grounds requires a large amount of computer time when addressed with conventional multidimensional models. Those are usually based on two-phase flow or Navier-Stokes equations. Different classes of simplified models exist. Among them, two-layer shallow water models are interesting to address large-scale dispersion. Indeed, compared to conventional multidimensional approaches, 2D simulations are carried out to mimic 3D effects. The computational gain in CPU time is consequently expected to be tremendous. However, such models involve at least three fundamental difficulties. The first one is related to the lack of hyperbolicity of most existing formulations, yielding serious consequences regarding wave propagation. The second is related to the non-conservative terms in the momentum equations. Those terms account for interactions between fluid layers. Recently, these two difficulties have been addressed in Chiapolino and Saurel (2018) and an unconditional hyperbolic model has been proposed along with a Harten-Lax-van Leer (HLL) type Riemann solver dealing with the non-conservative terms. In the same reference, numerical experiments showed robustness and accuracy of the formulation. In the present paper, a third difficulty is addressed. It consists of the determination of appropriate drag effect formulation. Such effects also account for interactions between fluid layers and become of particular importance when dealing with heavy-gas dispersion. With this aim, the model is compared to laboratory experiments in the context of heavy gas dispersal in quiescent air. It is shown that the model accurately reproduces experimental results thanks to an appropriate drag force correlation. This function expresses drag effects between the heavy and light gas layers. It is determined thanks to various experimental configurations of dam-break test problems. View Full-Text
Keywords: two-layer; shallow water; hyperbolic systems; drag effects; gas dispersal; experiments two-layer; shallow water; hyperbolic systems; drag effects; gas dispersal; experiments
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MDPI and ACS Style

Chiapolino, A.; Courtiaud, S.; Lapébie, E.; Saurel, R. Modeling Heavy-Gas Dispersion in Air with Two-Layer Shallow Water Equations. Fluids 2021, 6, 2.

AMA Style

Chiapolino A, Courtiaud S, Lapébie E, Saurel R. Modeling Heavy-Gas Dispersion in Air with Two-Layer Shallow Water Equations. Fluids. 2021; 6(1):2.

Chicago/Turabian Style

Chiapolino, Alexandre, Sébastien Courtiaud, Emmanuel Lapébie, and Richard Saurel. 2021. "Modeling Heavy-Gas Dispersion in Air with Two-Layer Shallow Water Equations" Fluids 6, no. 1: 2.

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