Modelling detonation waves in condensed energetic materials: multiphase CJ conditions and multidimensional computations

Petitpas, Fabien; Saurel, Richard; Franquet, Erwin; Chinnayya, A.

doi:10.1007/s00193-009-0217-7

Cited by 67 publications

(60 citation statements)

References 18 publications

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“…Sound propagation is also very important as it determines critical (choked) flow conditions and associated mass flow rates. It has also fundamental importance on sonic conditions of detonation waves when the twophase mixture is exothermically reacting (Petitpas et al, 2009). Hyperbolicity is also related to the causality principle, meaning that initial and boundary conditions are responsible of time evolution of the solution.…”

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confidence: 99%

Modelling compressible dense and dilute two-phase flows

Saurel

Chinnayya

Carmouze³

2017

Physics of Fluids

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Many two-phase flow situations, from engineering science to astrophysics, deal with transition from dense (high concentration of the condensed phase) to dilute concentration (low concentration of the same phase), covering the entire range of volume fractions. Some models are now well accepted at the two limits, but none is able to cover accurately the entire range, in particular regarding waves propagation. In the present work an alternative to the Baer and Nunziato (1986) (BN for short) model, initially designed for dense flows, is built. The corresponding model is hyperbolic and thermodynamically consistent. Contrarily to the BN model that involves 6 wave speeds, the new formulation involves 4 waves only, in agreement with the Marble (1963) model based on pressureless Euler equations for the dispersed phase, a well-accepted model for low particle volume concentrations. In the new model, the presence of pressure in the momentum equation of the particles and consideration of volume fractions in the two phases render the model valid for large particle concentrations. A symmetric version of the new model is derived as well for liquids containing gas bubbles. This model version involves 4 wave speeds as well, but with different wave's speeds. Last, the two sub-models with 4 waves are combined in a unique formulation, valid for the full range of volume fractions. It involves the same 6 wave's speeds as the BN model, but at a given point of space 4 waves only emerge, depending on the local volume fractions. The non-linear pressure waves propagate only in the phase with dominant volume fraction. The new model is tested numerically on various test problems ranging from separated phases in a shock tube to shock -particle cloud interaction. Its predictions are compared to BN and Marble models as well as against experimental data.Key words: hyperbolic, two-phase, compressible, shocks Emails: Richard.Saurel@univ-amu.fr; Ashwin.Chinnayya@ensma.fr; Quentin.Carmouze@rs2n.eu 2 I. IntroductionIt is well accepted that hyperbolic models are mandatory to deal with phenomena involving wave propagation. This is the case for multiphase flow mixtures in many situations such as in particular shocks and detonations propagation in granular explosives and in fuel suspensions, as well as liquid-gas mixtures with bubbles, cavitation and flashing, as soon as motion is intense and governed by pressure gradients. This is thus the case of most unsteady two-phase flows situations. Wave propagation is important as it carries pressure, density and velocity disturbances. Sound propagation is also very important as it determines critical (choked) flow conditions and associated mass flow rates. It has also fundamental importance on sonic conditions of detonation waves when the twophase mixture is exothermically reacting (Petitpas et al., 2009). Hyperbolicity is also related to the causality principle, meaning that initial and boundary conditions are responsible of time evolution of the solution. When dealing with first-order partial different...

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confidence: 99%

Modelling compressible dense and dilute two-phase flows

Saurel

Chinnayya

Carmouze³

2017

Physics of Fluids

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“…This benchmark has been chosen due to its popularity among many authors as in [1,7,4,3], etc. We are dealing with a Riemann problem, where a tube of 1 meter length is divided into two chambers by an interface at x = 0.6m and initial conditions as outlined in Table 1.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…This stiff mechanical relaxation has been widely investigated in [3,4,1] and many more. The following paper treats a five equation reduced model, as also many contributions as [1,4,5,6,7,8,9,10] do. This system originates from Kapila et al [11], where they take the formal limit [12] of the Baer and Nunziato seven equation model when the relaxation parameters tend simultaneously to infinity, and thus permitting to assume a single pressure and velocity.…”

Section: Introductionmentioning

confidence: 99%

Hybrid Explicit Residual Distribution Scheme for Compressible Multiphase Flows

Bacigaluppi

Abgrall

Kaman

2017

J. Phys.: Conf. Ser.

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. With respect to other contributions in that area, we investigate a method that provides mesh convergence to the exact solutions, where the studied non-conservative system is associated to consistent jump relations. The adopted scheme consists of a coupled predictor-corrector scheme, which follows the concept of residual distributions in Ricchiuto and Abgrall (J. Comp. Physics 2010), with a classical Glimm's scheme (J. Sci. Stat. Comp. 1982) applied to the area where a shock is occurring. This numerical methodology can be easily extended to unstructured meshes. Test cases on a perfect gas for a two phase compressible flow on a Riemann problem have verified that the approximation converges to its exact solution. The results have been compared with the pure Glimm's scheme and the expected exact solution, finding a good overlap.

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“…The same equations are solved everywhere with a unique numerical scheme. Extension to extra physics is possible: capillary effects (Perigaud and Saurel, 2005), mass transfer , combustion and detonations (Petitpas et al, 2009b), elastic solid -fluid interfaces (Favrie et al, 2009), granular materials (Saurel et al, 2010). Dynamic interface creation.…”

Section: Review Of Existing Models and Methodsmentioning

confidence: 99%